Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files
xet
Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 39, 91, 99, 71 ]
80
[ "91-39=52", "99-71=28", "52+28=80" ]
Current State: 80:[39, 91, 99, 71], Operations: [] Exploring Operation: 91-39=52, Resulting Numbers: [99, 71, 52] Generated Node #2: [99, 71, 52] from Operation: 91-39=52 Current State: 80:[99, 71, 52], Operations: ['91-39=52'] Exploring Operation: 99-71=28, Resulting Numbers: [52, 28] Generated Node #3: [52, 28] from Operation: 99-71=28 Current State: 80:[52, 28], Operations: ['91-39=52', '99-71=28'] Exploring Operation: 52+28=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[39, 91, 99, 71], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [39, 71, 8] Generated Node #0,0: 80:[39, 71, 8] Operation: 99-91=8 Exploring Operation: 99-71=28, Resulting Numbers: [39, 91, 28] Generated Node #0,1: 80:[39, 91, 28] Operation: 99-71=28 Exploring Operation: 91-71=20, Resulting Numbers: [39, 99, 20] Generated Node #0,2: 80:[39, 99, 20] Operation: 91-71=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[39, 71, 8], Operations: ['99-91=8'] Exploring Operation: 39+8=47, Resulting Numbers: [71, 47] Generated Node #0,0,0: 80:[71, 47] Operation: 39+8=47 Exploring Operation: 71+8=79, Resulting Numbers: [39, 79] Generated Node #0,0,1: 80:[39, 79] Operation: 71+8=79 Exploring Operation: 71-39=32, Resulting Numbers: [8, 32] Generated Node #0,0,2: 80:[8, 32] Operation: 71-39=32 Moving to Node #0,0,1 Current State: 80:[39, 79], Operations: ['99-91=8', '71+8=79'] Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 39+79=118, Resulting Numbers: [118] 118,80 unequal: No Solution Exploring Operation: 39*79=3081, Resulting Numbers: [3081] 3081,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[8, 32], Operations: ['99-91=8', '71-39=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[71, 47], Operations: ['99-91=8', '39+8=47'] Exploring Operation: 71*47=3337, Resulting Numbers: [3337] 3337,80 unequal: No Solution Exploring Operation: 71-47=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 71+47=118, Resulting Numbers: [118] 118,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[39, 91, 28], Operations: ['99-71=28'] Exploring Operation: 39-28=11, Resulting Numbers: [91, 11] Generated Node #0,1,0: 80:[91, 11] Operation: 39-28=11 Exploring Operation: 91-28=63, Resulting Numbers: [39, 63] Generated Node #0,1,1: 80:[39, 63] Operation: 91-28=63 Exploring Operation: 91-39=52, Resulting Numbers: [28, 52] Generated Node #0,1,2: 80:[28, 52] Operation: 91-39=52 Moving to Node #0,1,0 Current State: 80:[91, 11], Operations: ['99-71=28', '39-28=11'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[39, 91, 99, 71], Operations: [] Exploring Operation: 99-71=28, Resulting Numbers: [39, 91, 28] Generated Node #0,1: 80:[39, 91, 28] Operation: 99-71=28 Moving to Node #0,1 Current State: 80:[39, 91, 28], Operations: ['99-71=28'] Exploring Operation: 39-28=11, Resulting Numbers: [91, 11] Generated Node #0,1,0: 80:[91, 11] Operation: 39-28=11 Moving to Node #0,1,0 Current State: 80:[91, 11], Operations: ['99-71=28', '39-28=11'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 73, 85, 69, 83 ]
77
[ "85-83=2", "73*2=146", "146-69=77" ]
Current State: 77:[73, 85, 69, 83], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [73, 69, 2] Generated Node #2: [73, 69, 2] from Operation: 85-83=2 Current State: 77:[73, 69, 2], Operations: ['85-83=2'] Exploring Operation: 73*2=146, Resulting Numbers: [69, 146] Generated Node #3: [69, 146] from Operation: 73*2=146 Current State: 77:[69, 146], Operations: ['85-83=2', '73*2=146'] Exploring Operation: 146-69=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[73, 85, 69, 83], Operations: [] Exploring Operation: 85-69=16, Resulting Numbers: [73, 83, 16] Generated Node #0,0: 77:[73, 83, 16] Operation: 85-69=16 Exploring Operation: 83-69=14, Resulting Numbers: [73, 85, 14] Generated Node #0,1: 77:[73, 85, 14] Operation: 83-69=14 Exploring Operation: 85-73=12, Resulting Numbers: [69, 83, 12] Generated Node #0,2: 77:[69, 83, 12] Operation: 85-73=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[73, 83, 16], Operations: ['85-69=16'] Exploring Operation: 83-16=67, Resulting Numbers: [73, 67] Generated Node #0,0,0: 77:[73, 67] Operation: 83-16=67 Exploring Operation: 83-73=10, Resulting Numbers: [16, 10] Generated Node #0,0,1: 77:[16, 10] Operation: 83-73=10 Exploring Operation: 73+16=89, Resulting Numbers: [83, 89] Generated Node #0,0,2: 77:[83, 89] Operation: 73+16=89 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[16, 10], Operations: ['85-69=16', '83-73=10'] Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,77 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[73, 67], Operations: ['85-69=16', '83-16=67'] Exploring Operation: 73*67=4891, Resulting Numbers: [4891] 4891,77 unequal: No Solution Exploring Operation: 73-67=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 73+67=140, Resulting Numbers: [140] 140,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[83, 89], Operations: ['85-69=16', '73+16=89'] Exploring Operation: 83*89=7387, Resulting Numbers: [7387] 7387,77 unequal: No Solution Exploring Operation: 83+89=172, Resulting Numbers: [172] 172,77 unequal: No Solution Exploring Operation: 89-83=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[73, 85, 14], Operations: ['83-69=14'] Exploring Operation: 85-14=71, Resulting Numbers: [73, 71] Generated Node #0,1,0: 77:[73, 71] Operation: 85-14=71 Exploring Operation: 85-73=12, Resulting Numbers: [14, 12] Generated Node #0,1,1: 77:[14, 12] Operation: 85-73=12 Exploring Operation: 73+14=87, Resulting Numbers: [85, 87] Generated Node #0,1,2: 77:[85, 87] Operation: 73+14=87 Moving to Node #0,1,1 Current State: 77:[14, 12], Operations: ['83-69=14', '85-73=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,77 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[73, 71], Operations: ['83-69=14', '85-14=71'] Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,77 unequal: No Solution Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,77 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[85, 87], Operations: ['83-69=14', '73+14=87'] Exploring Operation: 87-85=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 85+87=172, Resulting Numbers: [172] 172,77 unequal: No Solution Exploring Operation: 85*87=7395, Resulting Numbers: [7395] 7395,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[69, 83, 12], Operations: ['85-73=12'] Exploring Operation: 83-69=14, Resulting Numbers: [12, 14] Generated Node #0,2,0: 77:[12, 14] Operation: 83-69=14 Exploring Operation: 83-12=71, Resulting Numbers: [69, 71] Generated Node #0,2,1: 77:[69, 71] Operation: 83-12=71 Exploring Operation: 69+12=81, Resulting Numbers: [83, 81] Generated Node #0,2,2: 77:[83, 81] Operation: 69+12=81 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[12, 14], Operations: ['85-73=12', '83-69=14'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 12*14=168, Resulting Numbers: [168] 168,77 unequal: No Solution Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[83, 81], Operations: ['85-73=12', '69+12=81'] Exploring Operation: 83+81=164, Resulting Numbers: [164] 164,77 unequal: No Solution Exploring Operation: 83*81=6723, Resulting Numbers: [6723] 6723,77 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[69, 71], Operations: ['85-73=12', '83-12=71'] Exploring Operation: 69+71=140, Resulting Numbers: [140] 140,77 unequal: No Solution Exploring Operation: 69*71=4899, Resulting Numbers: [4899] 4899,77 unequal: No Solution Exploring Operation: 71-69=2, Resulting Numbers: [2] 2,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 75, 75, 16, 66 ]
69
[ "75-66=9", "16*9=144", "144-75=69" ]
Current State: 69:[75, 75, 16, 66], Operations: [] Exploring Operation: 75-66=9, Resulting Numbers: [16, 9] Generated Node #2: [16, 9] from Operation: 75-66=9 Current State: 69:[16, 9], Operations: ['75-66=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,69 equal: Goal Reached Exploring Operation: 144-75=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[75, 75, 16, 66], Operations: [] Exploring Operation: 75-75=0, Resulting Numbers: [16, 66, 0] Generated Node #0,0: 69:[16, 66, 0] Operation: 75-75=0 Exploring Operation: 75-16=59, Resulting Numbers: [75, 66, 59] Generated Node #0,1: 69:[75, 66, 59] Operation: 75-16=59 Exploring Operation: 75/75=1, Resulting Numbers: [16, 66, 1] Generated Node #0,2: 69:[16, 66, 1] Operation: 75/75=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[16, 66, 1], Operations: ['75/75=1'] Exploring Operation: 66+1=67, Resulting Numbers: [16, 67] Generated Node #0,2,0: 69:[16, 67] Operation: 66+1=67 Exploring Operation: 16+1=17, Resulting Numbers: [66, 17] Generated Node #0,2,1: 69:[66, 17] Operation: 16+1=17 Exploring Operation: 16*1=16, Resulting Numbers: [66, 16] Generated Node #0,2,2: 69:[66, 16] Operation: 16*1=16 Moving to Node #0,2,0 Current State: 69:[16, 67], Operations: ['75/75=1', '66+1=67'] Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,69 unequal: No Solution Exploring Operation: 16+67=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 16*67=1072, Resulting Numbers: [1072] 1072,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[66, 17], Operations: ['75/75=1', '16+1=17'] Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,69 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[66, 16], Operations: ['75/75=1', '16*1=16'] Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[16, 66, 0], Operations: ['75-75=0'] Exploring Operation: 16+0=16, Resulting Numbers: [66, 16] Generated Node #0,0,0: 69:[66, 16] Operation: 16+0=16 Exploring Operation: 16-0=16, Resulting Numbers: [66, 16] Generated Node #0,0,1: 69:[66, 16] Operation: 16-0=16 Exploring Operation: 16*0=0, Resulting Numbers: [66, 0] Generated Node #0,0,2: 69:[66, 0] Operation: 16*0=0 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[66, 0], Operations: ['75-75=0', '16*0=0'] Exploring Operation: 66-0=66, Resulting Numbers: [66] 66,69 unequal: No Solution Exploring Operation: 66*0=0, Resulting Numbers: [0] 0,69 unequal: No Solution Exploring Operation: 66+0=66, Resulting Numbers: [66] 66,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[66, 16], Operations: ['75-75=0', '16+0=16'] Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,69 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[66, 16], Operations: ['75-75=0', '16-0=16'] Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,69 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[75, 66, 59], Operations: ['75-16=59'] Exploring Operation: 75-59=16, Resulting Numbers: [66, 16] Generated Node #0,1,0: 69:[66, 16] Operation: 75-59=16 Exploring Operation: 75-66=9, Resulting Numbers: [59, 9] Generated Node #0,1,1: 69:[59, 9] Operation: 75-66=9 Exploring Operation: 66-59=7, Resulting Numbers: [75, 7] Generated Node #0,1,2: 69:[75, 7] Operation: 66-59=7 Moving to Node #0,1,0 Current State: 69:[66, 16], Operations: ['75-16=59', '75-59=16'] Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,69 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[75, 7], Operations: ['75-16=59', '66-59=7'] Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[59, 9], Operations: ['75-16=59', '75-66=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 59*9=531, Resulting Numbers: [531] 531,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 72, 34, 35, 70 ]
76
[ "72-34=38", "70/35=2", "38*2=76" ]
Current State: 76:[72, 34, 35, 70], Operations: [] Exploring Operation: 72-34=38, Resulting Numbers: [35, 70, 38] Generated Node #2: [35, 70, 38] from Operation: 72-34=38 Current State: 76:[35, 70, 38], Operations: ['72-34=38'] Exploring Operation: 70/35=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 70/35=2 Current State: 76:[38, 2], Operations: ['72-34=38', '70/35=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[72, 34, 35, 70], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [72, 34, 2] Generated Node #0,0: 76:[72, 34, 2] Operation: 70/35=2 Exploring Operation: 70-34=36, Resulting Numbers: [72, 35, 36] Generated Node #0,1: 76:[72, 35, 36] Operation: 70-34=36 Exploring Operation: 72-35=37, Resulting Numbers: [34, 70, 37] Generated Node #0,2: 76:[34, 70, 37] Operation: 72-35=37 Exploring Operation: 72-34=38, Resulting Numbers: [35, 70, 38] Generated Node #0,3: 76:[35, 70, 38] Operation: 72-34=38 Exploring Operation: 72-70=2, Resulting Numbers: [34, 35, 2] Generated Node #0,4: 76:[34, 35, 2] Operation: 72-70=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 76:[34, 35, 2], Operations: ['72-70=2'] Exploring Operation: 34+35=69, Resulting Numbers: [2, 69] Generated Node #0,4,0: 76:[2, 69] Operation: 34+35=69 Exploring Operation: 34/2=17, Resulting Numbers: [35, 17] Generated Node #0,4,1: 76:[35, 17] Operation: 34/2=17 Exploring Operation: 35-34=1, Resulting Numbers: [2, 1] Generated Node #0,4,2: 76:[2, 1] Operation: 35-34=1 Exploring Operation: 34+2=36, Resulting Numbers: [35, 36] Generated Node #0,4,3: 76:[35, 36] Operation: 34+2=36 Exploring Operation: 35+2=37, Resulting Numbers: [34, 37] Generated Node #0,4,4: 76:[34, 37] Operation: 35+2=37 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 76:[2, 1], Operations: ['72-70=2', '35-34=1'] Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 76:[35, 17], Operations: ['72-70=2', '34/2=17'] Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,76 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,76 unequal: No Solution Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 76:[35, 36], Operations: ['72-70=2', '34+2=36'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,76 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 76:[34, 37], Operations: ['72-70=2', '35+2=37'] Exploring Operation: 34*37=1258, Resulting Numbers: [1258] 1258,76 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 34+37=71, Resulting Numbers: [71] 71,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 76:[2, 69], Operations: ['72-70=2', '34+35=69'] Exploring Operation: 2*69=138, Resulting Numbers: [138] 138,76 unequal: No Solution Exploring Operation: 2+69=71, Resulting Numbers: [71] 71,76 unequal: No Solution Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[72, 34, 2], Operations: ['70/35=2'] Exploring Operation: 72-34=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 72-34=38 Exploring Operation: 34/2=17, Resulting Numbers: [72, 17] Generated Node #0,0,1: 76:[72, 17] Operation: 34/2=17 Exploring Operation: 72+2=74, Resulting Numbers: [34, 74] Generated Node #0,0,2: 76:[34, 74] Operation: 72+2=74 Exploring Operation: 34+2=36, Resulting Numbers: [72, 36] Generated Node #0,0,3: 76:[72, 36] Operation: 34+2=36 Exploring Operation: 72/2=36, Resulting Numbers: [34, 36] Generated Node #0,0,4: 76:[34, 36] Operation: 72/2=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['70/35=2', '72-34=38'] Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,76 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,76 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[72, 34, 35, 70], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [72, 34, 2] Generated Node #0,0: 76:[72, 34, 2] Operation: 70/35=2 Moving to Node #0,0 Current State: 76:[72, 34, 2], Operations: ['70/35=2'] Exploring Operation: 72-34=38, Resulting Numbers: [2, 38] Generated Node #0,0,0: 76:[2, 38] Operation: 72-34=38 Moving to Node #0,0,0 Current State: 76:[2, 38], Operations: ['70/35=2', '72-34=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 14, 67, 53, 41 ]
41
[ "67-14=53", "53+41=94", "94-53=41" ]
Current State: 41:[14, 67, 53, 41], Operations: [] Exploring Operation: 67-14=53, Resulting Numbers: [53, 41, 53] Generated Node #2: [53, 41, 53] from Operation: 67-14=53 Current State: 41:[53, 41, 53], Operations: ['67-14=53'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,41 equal: Goal Reached Exploring Operation: 94-53=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[14, 67, 53, 41], Operations: [] Exploring Operation: 67-14=53, Resulting Numbers: [53, 41, 53] Generated Node #0,0: 41:[53, 41, 53] Operation: 67-14=53 Exploring Operation: 14+67=81, Resulting Numbers: [53, 41, 81] Generated Node #0,1: 41:[53, 41, 81] Operation: 14+67=81 Exploring Operation: 14+53=67, Resulting Numbers: [67, 41, 67] Generated Node #0,2: 41:[67, 41, 67] Operation: 14+53=67 Exploring Operation: 53-14=39, Resulting Numbers: [67, 41, 39] Generated Node #0,3: 41:[67, 41, 39] Operation: 53-14=39 Moving to Node #0,0 Current State: 41:[53, 41, 53], Operations: ['67-14=53'] Exploring Operation: 53-41=12, Resulting Numbers: [53, 12] Generated Node #0,0,0: 41:[53, 12] Operation: 53-41=12 Exploring Operation: 53-41=12, Resulting Numbers: [53, 12] Generated Node #0,0,1: 41:[53, 12] Operation: 53-41=12 Exploring Operation: 53-53=0, Resulting Numbers: [41, 0] Generated Node #0,0,2: 41:[41, 0] Operation: 53-53=0 Exploring Operation: 53/53=1, Resulting Numbers: [41, 1] Generated Node #0,0,3: 41:[41, 1] Operation: 53/53=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 41:[41, 1], Operations: ['67-14=53', '53/53=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[14, 67, 53, 41], Operations: [] Exploring Operation: 67-14=53, Resulting Numbers: [53, 41, 53] Generated Node #0,0: 41:[53, 41, 53] Operation: 67-14=53 Moving to Node #0,0 Current State: 41:[53, 41, 53], Operations: ['67-14=53'] Exploring Operation: 53/53=1, Resulting Numbers: [41, 1] Generated Node #0,0,3: 41:[41, 1] Operation: 53/53=1 Moving to Node #0,0,3 Current State: 41:[41, 1], Operations: ['67-14=53', '53/53=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 70, 52, 57, 50 ]
11
[ "70-52=18", "57-50=7", "18-7=11" ]
Current State: 11:[70, 52, 57, 50], Operations: [] Exploring Operation: 70-52=18, Resulting Numbers: [57, 50, 18] Generated Node #2: [57, 50, 18] from Operation: 70-52=18 Current State: 11:[57, 50, 18], Operations: ['70-52=18'] Exploring Operation: 57-50=7, Resulting Numbers: [18, 7] Generated Node #3: [18, 7] from Operation: 57-50=7 Current State: 11:[18, 7], Operations: ['70-52=18', '57-50=7'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[70, 52, 57, 50], Operations: [] Exploring Operation: 70-52=18, Resulting Numbers: [57, 50, 18] Generated Node #0,0: 11:[57, 50, 18] Operation: 70-52=18 Exploring Operation: 70-57=13, Resulting Numbers: [52, 50, 13] Generated Node #0,1: 11:[52, 50, 13] Operation: 70-57=13 Moving to Node #0,1 Current State: 11:[52, 50, 13], Operations: ['70-57=13'] Exploring Operation: 52/13=4, Resulting Numbers: [50, 4] Generated Node #0,1,0: 11:[50, 4] Operation: 52/13=4 Exploring Operation: 52-50=2, Resulting Numbers: [13, 2] Generated Node #0,1,1: 11:[13, 2] Operation: 52-50=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[13, 2], Operations: ['70-57=13', '52-50=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[70, 52, 57, 50], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [52, 50, 13] Generated Node #0,1: 11:[52, 50, 13] Operation: 70-57=13 Moving to Node #0,1 Current State: 11:[52, 50, 13], Operations: ['70-57=13'] Exploring Operation: 52-50=2, Resulting Numbers: [13, 2] Generated Node #0,1,1: 11:[13, 2] Operation: 52-50=2 Moving to Node #0,1,1 Current State: 11:[13, 2], Operations: ['70-57=13', '52-50=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 72, 39, 60, 23 ]
44
[ "72*23=1656", "60+1656=1716", "1716/39=44" ]
Current State: 44:[72, 39, 60, 23], Operations: [] Exploring Operation: 72*23=1656, Resulting Numbers: [39, 60, 1656] Generated Node #2: [39, 60, 1656] from Operation: 72*23=1656 Current State: 44:[39, 60, 1656], Operations: ['72*23=1656'] Exploring Operation: 60+1656=1716, Resulting Numbers: [39, 1716] Generated Node #3: [39, 1716] from Operation: 60+1656=1716 Current State: 44:[39, 1716], Operations: ['72*23=1656', '60+1656=1716'] Exploring Operation: 1716/39=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[72, 39, 60, 23], Operations: [] Exploring Operation: 60-39=21, Resulting Numbers: [72, 23, 21] Generated Node #0,0: 44:[72, 23, 21] Operation: 60-39=21 Exploring Operation: 72-23=49, Resulting Numbers: [39, 60, 49] Generated Node #0,1: 44:[39, 60, 49] Operation: 72-23=49 Exploring Operation: 72-60=12, Resulting Numbers: [39, 23, 12] Generated Node #0,2: 44:[39, 23, 12] Operation: 72-60=12 Exploring Operation: 72-39=33, Resulting Numbers: [60, 23, 33] Generated Node #0,3: 44:[60, 23, 33] Operation: 72-39=33 Moving to Node #0,2 Current State: 44:[39, 23, 12], Operations: ['72-60=12'] Exploring Operation: 39+12=51, Resulting Numbers: [23, 51] Generated Node #0,2,0: 44:[23, 51] Operation: 39+12=51 Exploring Operation: 23-12=11, Resulting Numbers: [39, 11] Generated Node #0,2,1: 44:[39, 11] Operation: 23-12=11 Exploring Operation: 39-12=27, Resulting Numbers: [23, 27] Generated Node #0,2,2: 44:[23, 27] Operation: 39-12=27 Exploring Operation: 39-23=16, Resulting Numbers: [12, 16] Generated Node #0,2,3: 44:[12, 16] Operation: 39-23=16 Moving to Node #0,1 Current State: 44:[39, 60, 49], Operations: ['72-23=49'] Exploring Operation: 60-49=11, Resulting Numbers: [39, 11] Generated Node #0,1,0: 44:[39, 11] Operation: 60-49=11 Exploring Operation: 49-39=10, Resulting Numbers: [60, 10] Generated Node #0,1,1: 44:[60, 10] Operation: 49-39=10 Exploring Operation: 39+60=99, Resulting Numbers: [49, 99] Generated Node #0,1,2: 44:[49, 99] Operation: 39+60=99 Exploring Operation: 60-39=21, Resulting Numbers: [49, 21] Generated Node #0,1,3: 44:[49, 21] Operation: 60-39=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[39, 11], Operations: ['72-23=49', '60-49=11'] Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,44 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,44 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 #0,1,3 Current State: 44:[49, 21], Operations: ['72-23=49', '60-39=21'] Exploring Operation: 49*21=1029, Resulting Numbers: [1029] 1029,44 unequal: No Solution Exploring Operation: 49+21=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,44 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 #0,1,1 Current State: 44:[60, 10], Operations: ['72-23=49', '49-39=10'] Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 60*10=600, Resulting Numbers: [600] 600,44 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 #0,1,2 Current State: 44:[49, 99], Operations: ['72-23=49', '39+60=99'] Exploring Operation: 49+99=148, Resulting Numbers: [148] 148,44 unequal: No Solution Exploring Operation: 49*99=4851, Resulting Numbers: [4851] 4851,44 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,44 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: 44:[60, 23, 33], Operations: ['72-39=33'] Exploring Operation: 33-23=10, Resulting Numbers: [60, 10] Generated Node #0,3,0: 44:[60, 10] Operation: 33-23=10 Exploring Operation: 60-23=37, Resulting Numbers: [33, 37] Generated Node #0,3,1: 44:[33, 37] Operation: 60-23=37 Exploring Operation: 60-33=27, Resulting Numbers: [23, 27] Generated Node #0,3,2: 44:[23, 27] Operation: 60-33=27 Exploring Operation: 23+33=56, Resulting Numbers: [60, 56] Generated Node #0,3,3: 44:[60, 56] Operation: 23+33=56 Moving to Node #0,0 Current State: 44:[72, 23, 21], Operations: ['60-39=21'] Exploring Operation: 23-21=2, Resulting Numbers: [72, 2] Generated Node #0,0,0: 44:[72, 2] Operation: 23-21=2 Exploring Operation: 72-23=49, Resulting Numbers: [21, 49] Generated Node #0,0,1: 44:[21, 49] Operation: 72-23=49 Exploring Operation: 72-21=51, Resulting Numbers: [23, 51] Generated Node #0,0,2: 44:[23, 51] Operation: 72-21=51 Exploring Operation: 23+21=44, Resulting Numbers: [72, 44] Generated Node #0,0,3: 44:[72, 44] Operation: 23+21=44 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[21, 49], Operations: ['60-39=21', '72-23=49'] Exploring Operation: 21*49=1029, Resulting Numbers: [1029] 1029,44 unequal: No Solution Exploring Operation: 21+49=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,44 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 #0,0,2 Current State: 44:[23, 51], Operations: ['60-39=21', '72-21=51'] Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,44 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,44 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 #0,0,0 Current State: 44:[72, 2], Operations: ['60-39=21', '23-21=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,44 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,44 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 #0,0,3 Current State: 44:[72, 44], Operations: ['60-39=21', '23+21=44'] Exploring Operation: 72+44=116, Resulting Numbers: [116] 116,44 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 72*44=3168, Resulting Numbers: [3168] 3168,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 44:[39, 11], Operations: ['72-60=12', '23-12=11'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,44 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[12, 16], Operations: ['72-60=12', '39-23=16'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,44 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[23, 27], Operations: ['72-60=12', '39-12=27'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[23, 27], Operations: ['72-39=33', '60-33=27'] Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,44 unequal: No Solution Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[23, 51], Operations: ['72-60=12', '39+12=51'] Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,44 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[60, 10], Operations: ['72-39=33', '33-23=10'] Exploring Operation: 60*10=600, Resulting Numbers: [600] 600,44 unequal: No Solution Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[33, 37], Operations: ['72-39=33', '60-23=37'] Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,44 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[60, 56], Operations: ['72-39=33', '23+33=56'] Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,44 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,44 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 3, 12, 52, 52 ]
65
[ "12/3=4", "52/4=13", "52+13=65" ]
Current State: 65:[3, 12, 52, 52], Operations: [] Exploring Operation: 12/3=4, Resulting Numbers: [52, 52, 4] Generated Node #2: [52, 52, 4] from Operation: 12/3=4 Current State: 65:[52, 52, 4], Operations: ['12/3=4'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,65 equal: Goal Reached Exploring Operation: 52+13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[3, 12, 52, 52], Operations: [] Exploring Operation: 12+52=64, Resulting Numbers: [3, 52, 64] Generated Node #0,0: 65:[3, 52, 64] Operation: 12+52=64 Exploring Operation: 3+52=55, Resulting Numbers: [12, 52, 55] Generated Node #0,1: 65:[12, 52, 55] Operation: 3+52=55 Exploring Operation: 52/52=1, Resulting Numbers: [3, 12, 1] Generated Node #0,2: 65:[3, 12, 1] Operation: 52/52=1 Exploring Operation: 52-52=0, Resulting Numbers: [3, 12, 0] Generated Node #0,3: 65:[3, 12, 0] Operation: 52-52=0 Exploring Operation: 12+52=64, Resulting Numbers: [3, 52, 64] Generated Node #0,4: 65:[3, 52, 64] Operation: 12+52=64 Moving to Node #0,2 Current State: 65:[3, 12, 1], Operations: ['52/52=1'] Exploring Operation: 12*1=12, Resulting Numbers: [3, 12] Generated Node #0,2,0: 65:[3, 12] Operation: 12*1=12 Exploring Operation: 3/1=3, Resulting Numbers: [12, 3] Generated Node #0,2,1: 65:[12, 3] Operation: 3/1=3 Exploring Operation: 12+1=13, Resulting Numbers: [3, 13] Generated Node #0,2,2: 65:[3, 13] Operation: 12+1=13 Exploring Operation: 3+1=4, Resulting Numbers: [12, 4] Generated Node #0,2,3: 65:[12, 4] Operation: 3+1=4 Exploring Operation: 3*1=3, Resulting Numbers: [12, 3] Generated Node #0,2,4: 65:[12, 3] Operation: 3*1=3 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[3, 13], Operations: ['52/52=1', '12+1=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,65 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,65 unequal: No Solution No 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: 65:[12, 4], Operations: ['52/52=1', '3+1=4'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,65 unequal: No Solution No 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: 65:[3, 12], Operations: ['52/52=1', '12*1=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,65 unequal: No Solution No 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: 65:[12, 3], Operations: ['52/52=1', '3/1=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,65 unequal: No Solution No 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: 65:[12, 3], Operations: ['52/52=1', '3*1=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 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: 65:[3, 12, 0], Operations: ['52-52=0'] Exploring Operation: 3+0=3, Resulting Numbers: [12, 3] Generated Node #0,3,0: 65:[12, 3] Operation: 3+0=3 Exploring Operation: 3-0=3, Resulting Numbers: [12, 3] Generated Node #0,3,1: 65:[12, 3] Operation: 3-0=3 Exploring Operation: 12/3=4, Resulting Numbers: [0, 4] Generated Node #0,3,2: 65:[0, 4] Operation: 12/3=4 Exploring Operation: 12+0=12, Resulting Numbers: [3, 12] Generated Node #0,3,3: 65:[3, 12] Operation: 12+0=12 Exploring Operation: 12-0=12, Resulting Numbers: [3, 12] Generated Node #0,3,4: 65:[3, 12] Operation: 12-0=12 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 65:[12, 3], Operations: ['52-52=0', '3+0=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,65 unequal: No Solution No 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: 65:[12, 3], Operations: ['52-52=0', '3-0=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,65 unequal: No Solution No 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: 65:[3, 12], Operations: ['52-52=0', '12+0=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution No 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: 65:[3, 12], Operations: ['52-52=0', '12-0=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,65 unequal: No Solution No 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: 65:[0, 4], Operations: ['52-52=0', '12/3=4'] Exploring Operation: 0+4=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 0*4=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,65 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: 65:[3, 52, 64], Operations: ['12+52=64'] Exploring Operation: 64-3=61, Resulting Numbers: [52, 61] Generated Node #0,0,0: 65:[52, 61] Operation: 64-3=61 Exploring Operation: 3+64=67, Resulting Numbers: [52, 67] Generated Node #0,0,1: 65:[52, 67] Operation: 3+64=67 Exploring Operation: 64-52=12, Resulting Numbers: [3, 12] Generated Node #0,0,2: 65:[3, 12] Operation: 64-52=12 Exploring Operation: 3+52=55, Resulting Numbers: [64, 55] Generated Node #0,0,3: 65:[64, 55] Operation: 3+52=55 Exploring Operation: 52-3=49, Resulting Numbers: [64, 49] Generated Node #0,0,4: 65:[64, 49] Operation: 52-3=49 Moving to Node #0,4 Current State: 65:[3, 52, 64], Operations: ['12+52=64'] Exploring Operation: 64-52=12, Resulting Numbers: [3, 12] Generated Node #0,4,0: 65:[3, 12] Operation: 64-52=12 Exploring Operation: 3+64=67, Resulting Numbers: [52, 67] Generated Node #0,4,1: 65:[52, 67] Operation: 3+64=67 Exploring Operation: 3+52=55, Resulting Numbers: [64, 55] Generated Node #0,4,2: 65:[64, 55] Operation: 3+52=55 Exploring Operation: 64-3=61, Resulting Numbers: [52, 61] Generated Node #0,4,3: 65:[52, 61] Operation: 64-3=61 Exploring Operation: 52-3=49, Resulting Numbers: [64, 49] Generated Node #0,4,4: 65:[64, 49] Operation: 52-3=49 Moving to Node #0,1 Current State: 65:[12, 52, 55], Operations: ['3+52=55'] Exploring Operation: 12+52=64, Resulting Numbers: [55, 64] Generated Node #0,1,0: 65:[55, 64] Operation: 12+52=64 Exploring Operation: 52-12=40, Resulting Numbers: [55, 40] Generated Node #0,1,1: 65:[55, 40] Operation: 52-12=40 Exploring Operation: 55-12=43, Resulting Numbers: [52, 43] Generated Node #0,1,2: 65:[52, 43] Operation: 55-12=43 Exploring Operation: 55-52=3, Resulting Numbers: [12, 3] Generated Node #0,1,3: 65:[12, 3] Operation: 55-52=3 Exploring Operation: 12+55=67, Resulting Numbers: [52, 67] Generated Node #0,1,4: 65:[52, 67] Operation: 12+55=67 Moving to Node #0,0,2 Current State: 65:[3, 12], Operations: ['12+52=64', '64-52=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Moving to Node #0,4,0 Current State: 65:[3, 12], Operations: ['12+52=64', '64-52=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,1,3 Current State: 65:[12, 3], Operations: ['3+52=55', '55-52=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,4,2 Current State: 65:[64, 55], Operations: ['12+52=64', '3+52=55'] Exploring Operation: 64+55=119, Resulting Numbers: [119] 119,65 unequal: No Solution Exploring Operation: 64*55=3520, Resulting Numbers: [3520] 3520,65 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[55, 64], Operations: ['3+52=55', '12+52=64'] Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,65 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,65 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[64, 55], Operations: ['12+52=64', '3+52=55'] Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 64*55=3520, Resulting Numbers: [3520] 3520,65 unequal: No Solution Exploring Operation: 64+55=119, Resulting Numbers: [119] 119,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[52, 67], Operations: ['12+52=64', '3+64=67'] Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,65 unequal: No Solution Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,65 unequal: No Solution Moving to Node #0,1,4 Current State: 65:[52, 67], Operations: ['3+52=55', '12+55=67'] Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,65 unequal: No Solution Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,65 unequal: No Solution Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,4,1 Current State: 65:[52, 67], Operations: ['12+52=64', '3+64=67'] Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,65 unequal: No Solution Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,65 unequal: No Solution Moving to Node #0,4,4 Current State: 65:[64, 49], Operations: ['12+52=64', '52-3=49'] Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,65 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,65 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,0,4 Current State: 65:[64, 49], Operations: ['12+52=64', '52-3=49'] Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,65 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[52, 61], Operations: ['12+52=64', '64-3=61'] Exploring Operation: 52+61=113, Resulting Numbers: [113] 113,65 unequal: No Solution Exploring Operation: 52*61=3172, Resulting Numbers: [3172] 3172,65 unequal: No Solution Exploring Operation: 61-52=9, Resulting Numbers: [9] 9,65 unequal: No Solution Moving to Node #0,4,3 Current State: 65:[52, 61], Operations: ['12+52=64', '64-3=61'] Exploring Operation: 61-52=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 52+61=113, Resulting Numbers: [113] 113,65 unequal: No Solution Exploring Operation: 52*61=3172, Resulting Numbers: [3172] 3172,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[55, 40], Operations: ['3+52=55', '52-12=40'] Exploring Operation: 55*40=2200, Resulting Numbers: [2200] 2200,65 unequal: No Solution Exploring Operation: 55+40=95, Resulting Numbers: [95] 95,65 unequal: No Solution Exploring Operation: 55-40=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[52, 43], Operations: ['3+52=55', '55-12=43'] Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,65 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,65 unequal: No Solution Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,65 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 70, 83, 51, 23 ]
79
[ "70+83=153", "51+23=74", "153-74=79" ]
Current State: 79:[70, 83, 51, 23], Operations: [] Exploring Operation: 70+83=153, Resulting Numbers: [51, 23, 153] Generated Node #2: [51, 23, 153] from Operation: 70+83=153 Current State: 79:[51, 23, 153], Operations: ['70+83=153'] Exploring Operation: 51+23=74, Resulting Numbers: [153, 74] Generated Node #3: [153, 74] from Operation: 51+23=74 Current State: 79:[153, 74], Operations: ['70+83=153', '51+23=74'] Exploring Operation: 153-74=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[70, 83, 51, 23], Operations: [] Exploring Operation: 51+23=74, Resulting Numbers: [70, 83, 74] Generated Node #0,0: 79:[70, 83, 74] Operation: 51+23=74 Exploring Operation: 83+23=106, Resulting Numbers: [70, 51, 106] Generated Node #0,1: 79:[70, 51, 106] Operation: 83+23=106 Exploring Operation: 70-23=47, Resulting Numbers: [83, 51, 47] Generated Node #0,2: 79:[83, 51, 47] Operation: 70-23=47 Exploring Operation: 70+23=93, Resulting Numbers: [83, 51, 93] Generated Node #0,3: 79:[83, 51, 93] Operation: 70+23=93 Exploring Operation: 83-23=60, Resulting Numbers: [70, 51, 60] Generated Node #0,4: 79:[70, 51, 60] Operation: 83-23=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[70, 83, 74], Operations: ['51+23=74'] Exploring Operation: 83-70=13, Resulting Numbers: [74, 13] Generated Node #0,0,0: 79:[74, 13] Operation: 83-70=13 Exploring Operation: 83-74=9, Resulting Numbers: [70, 9] Generated Node #0,0,1: 79:[70, 9] Operation: 83-74=9 Exploring Operation: 70+83=153, Resulting Numbers: [74, 153] Generated Node #0,0,2: 79:[74, 153] Operation: 70+83=153 Exploring Operation: 74-70=4, Resulting Numbers: [83, 4] Generated Node #0,0,3: 79:[83, 4] Operation: 74-70=4 Exploring Operation: 70+74=144, Resulting Numbers: [83, 144] Generated Node #0,0,4: 79:[83, 144] Operation: 70+74=144 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 79:[83, 144], Operations: ['51+23=74', '70+74=144'] Exploring Operation: 83*144=11952, Resulting Numbers: [11952] 11952,79 unequal: No Solution Exploring Operation: 144-83=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 83+144=227, Resulting Numbers: [227] 227,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[74, 13], Operations: ['51+23=74', '83-70=13'] Exploring Operation: 74*13=962, Resulting Numbers: [962] 962,79 unequal: No Solution Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 74+13=87, Resulting Numbers: [87] 87,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[70, 9], Operations: ['51+23=74', '83-74=9'] Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[70, 83, 51, 23], Operations: [] Exploring Operation: 51+23=74, Resulting Numbers: [70, 83, 74] Generated Node #0,0: 79:[70, 83, 74] Operation: 51+23=74 Moving to Node #0,0 Current State: 79:[70, 83, 74], Operations: ['51+23=74'] Exploring Operation: 83-74=9, Resulting Numbers: [70, 9] Generated Node #0,0,1: 79:[70, 9] Operation: 83-74=9 Moving to Node #0,0,1 Current State: 79:[70, 9], Operations: ['51+23=74', '83-74=9'] Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 31, 34, 4, 3 ]
17
[ "31+34=65", "3+65=68", "68/4=17" ]
Current State: 17:[31, 34, 4, 3], Operations: [] Exploring Operation: 31+34=65, Resulting Numbers: [4, 3, 65] Generated Node #2: [4, 3, 65] from Operation: 31+34=65 Current State: 17:[4, 3, 65], Operations: ['31+34=65'] Exploring Operation: 3+65=68, Resulting Numbers: [4, 68] Generated Node #3: [4, 68] from Operation: 3+65=68 Current State: 17:[4, 68], Operations: ['31+34=65', '3+65=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[31, 34, 4, 3], Operations: [] Exploring Operation: 31-4=27, Resulting Numbers: [34, 3, 27] Generated Node #0,0: 17:[34, 3, 27] Operation: 31-4=27 Exploring Operation: 34-31=3, Resulting Numbers: [4, 3, 3] Generated Node #0,1: 17:[4, 3, 3] Operation: 34-31=3 Exploring Operation: 31-3=28, Resulting Numbers: [34, 4, 28] Generated Node #0,2: 17:[34, 4, 28] Operation: 31-3=28 Exploring Operation: 4*3=12, Resulting Numbers: [31, 34, 12] Generated Node #0,3: 17:[31, 34, 12] Operation: 4*3=12 Start Sub Search at level 1: Moving to Node #0,3 Current State: 17:[31, 34, 12], Operations: ['4*3=12'] Exploring Operation: 31+12=43, Resulting Numbers: [34, 43] Generated Node #0,3,0: 17:[34, 43] Operation: 31+12=43 Exploring Operation: 34-31=3, Resulting Numbers: [12, 3] Generated Node #0,3,1: 17:[12, 3] Operation: 34-31=3 Exploring Operation: 31-12=19, Resulting Numbers: [34, 19] Generated Node #0,3,2: 17:[34, 19] Operation: 31-12=19 Exploring Operation: 34-12=22, Resulting Numbers: [31, 22] Generated Node #0,3,3: 17:[31, 22] Operation: 34-12=22 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 17:[12, 3], Operations: ['4*3=12', '34-31=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 17:[34, 19], Operations: ['4*3=12', '31-12=19'] Exploring Operation: 34+19=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 34*19=646, Resulting Numbers: [646] 646,17 unequal: No Solution Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 17:[31, 22], Operations: ['4*3=12', '34-12=22'] Exploring Operation: 31+22=53, Resulting Numbers: [53] 53,17 unequal: No Solution Exploring Operation: 31*22=682, Resulting Numbers: [682] 682,17 unequal: No Solution Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 17:[34, 43], Operations: ['4*3=12', '31+12=43'] Exploring Operation: 43-34=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 34*43=1462, Resulting Numbers: [1462] 1462,17 unequal: No Solution Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,17 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: 17:[34, 3, 27], Operations: ['31-4=27'] Exploring Operation: 27-3=24, Resulting Numbers: [34, 24] Generated Node #0,0,0: 17:[34, 24] Operation: 27-3=24 Exploring Operation: 34-3=31, Resulting Numbers: [27, 31] Generated Node #0,0,1: 17:[27, 31] Operation: 34-3=31 Exploring Operation: 34-27=7, Resulting Numbers: [3, 7] Generated Node #0,0,2: 17:[3, 7] Operation: 34-27=7 Exploring Operation: 27/3=9, Resulting Numbers: [34, 9] Generated Node #0,0,3: 17:[34, 9] Operation: 27/3=9 Moving to Node #0,0,0 Current State: 17:[34, 24], Operations: ['31-4=27', '27-3=24'] Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,17 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[3, 7], Operations: ['31-4=27', '34-27=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[27, 31], Operations: ['31-4=27', '34-3=31'] Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,17 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,17 unequal: No Solution Moving to Node #0,0,3 Current State: 17:[34, 9], Operations: ['31-4=27', '27/3=9'] Exploring Operation: 34*9=306, Resulting Numbers: [306] 306,17 unequal: No Solution Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,17 unequal: No Solution No 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: 17:[4, 3, 3], Operations: ['34-31=3'] Exploring Operation: 4*3=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 17:[3, 12] Operation: 4*3=12 Exploring Operation: 4+3=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 17:[3, 7] Operation: 4+3=7 Exploring Operation: 4*3=12, Resulting Numbers: [3, 12] Generated Node #0,1,2: 17:[3, 12] Operation: 4*3=12 Exploring Operation: 3*3=9, Resulting Numbers: [4, 9] Generated Node #0,1,3: 17:[4, 9] Operation: 3*3=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[3, 12], Operations: ['34-31=3', '4*3=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 17:[3, 12], Operations: ['34-31=3', '4*3=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 17:[4, 9], Operations: ['34-31=3', '3*3=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,17 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[3, 7], Operations: ['34-31=3', '4+3=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,17 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: 17:[34, 4, 28], Operations: ['31-3=28'] Exploring Operation: 34-4=30, Resulting Numbers: [28, 30] Generated Node #0,2,0: 17:[28, 30] Operation: 34-4=30 Exploring Operation: 34-28=6, Resulting Numbers: [4, 6] Generated Node #0,2,1: 17:[4, 6] Operation: 34-28=6 Exploring Operation: 28/4=7, Resulting Numbers: [34, 7] Generated Node #0,2,2: 17:[34, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [34, 24] Generated Node #0,2,3: 17:[34, 24] Operation: 28-4=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[28, 30], Operations: ['31-3=28', '34-4=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,17 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 17:[4, 6], Operations: ['31-3=28', '34-28=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 17:[34, 24], Operations: ['31-3=28', '28-4=24'] Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,17 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[34, 7], Operations: ['31-3=28', '28/4=7'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,17 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,17 unequal: No Solution Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,17 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
[ 84, 78, 24, 60 ]
63
[ "78-60=18", "84*18=1512", "1512/24=63" ]
Current State: 63:[84, 78, 24, 60], Operations: [] Exploring Operation: 78-60=18, Resulting Numbers: [84, 24, 18] Generated Node #2: [84, 24, 18] from Operation: 78-60=18 Current State: 63:[84, 24, 18], Operations: ['78-60=18'] Exploring Operation: 84*18=1512, Resulting Numbers: [24, 1512] Generated Node #3: [24, 1512] from Operation: 84*18=1512 Current State: 63:[24, 1512], Operations: ['78-60=18', '84*18=1512'] Exploring Operation: 1512/24=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[84, 78, 24, 60], Operations: [] Exploring Operation: 84-24=60, Resulting Numbers: [78, 60, 60] Generated Node #0,0: 63:[78, 60, 60] Operation: 84-24=60 Exploring Operation: 84-78=6, Resulting Numbers: [24, 60, 6] Generated Node #0,1: 63:[24, 60, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[24, 60, 6], Operations: ['84-78=6'] Exploring Operation: 24/6=4, Resulting Numbers: [60, 4] Generated Node #0,1,0: 63:[60, 4] Operation: 24/6=4 Exploring Operation: 60/6=10, Resulting Numbers: [24, 10] Generated Node #0,1,1: 63:[24, 10] Operation: 60/6=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[60, 4], Operations: ['84-78=6', '24/6=4'] Exploring Operation: 60+4=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[24, 10], Operations: ['84-78=6', '60/6=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[78, 60, 60], Operations: ['84-24=60'] Exploring Operation: 78-60=18, Resulting Numbers: [60, 18] Generated Node #0,0,0: 63:[60, 18] Operation: 78-60=18 Exploring Operation: 78-60=18, Resulting Numbers: [60, 18] Generated Node #0,0,1: 63:[60, 18] Operation: 78-60=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[60, 18], Operations: ['84-24=60', '78-60=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[60, 18], Operations: ['84-24=60', '78-60=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 95, 97, 80, 46 ]
12
[ "97-95=2", "46*2=92", "92-80=12" ]
Current State: 12:[95, 97, 80, 46], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [80, 46, 2] Generated Node #2: [80, 46, 2] from Operation: 97-95=2 Current State: 12:[80, 46, 2], Operations: ['97-95=2'] Exploring Operation: 46*2=92, Resulting Numbers: [80, 92] Generated Node #3: [80, 92] from Operation: 46*2=92 Current State: 12:[80, 92], Operations: ['97-95=2', '46*2=92'] Exploring Operation: 92-80=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[95, 97, 80, 46], Operations: [] Exploring Operation: 95-80=15, Resulting Numbers: [97, 46, 15] Generated Node #0,0: 12:[97, 46, 15] Operation: 95-80=15 Exploring Operation: 97-95=2, Resulting Numbers: [80, 46, 2] Generated Node #0,1: 12:[80, 46, 2] Operation: 97-95=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[80, 46, 2], Operations: ['97-95=2'] Exploring Operation: 80-46=34, Resulting Numbers: [2, 34] Generated Node #0,1,0: 12:[2, 34] Operation: 80-46=34 Exploring Operation: 80/2=40, Resulting Numbers: [46, 40] Generated Node #0,1,1: 12:[46, 40] Operation: 80/2=40 Moving to Node #0,1,0 Current State: 12:[2, 34], Operations: ['97-95=2', '80-46=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,12 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[46, 40], Operations: ['97-95=2', '80/2=40'] Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 46+40=86, Resulting Numbers: [86] 86,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[97, 46, 15], Operations: ['95-80=15'] Exploring Operation: 97-46=51, Resulting Numbers: [15, 51] Generated Node #0,0,0: 12:[15, 51] Operation: 97-46=51 Exploring Operation: 97-15=82, Resulting Numbers: [46, 82] Generated Node #0,0,1: 12:[46, 82] Operation: 97-15=82 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[15, 51], Operations: ['95-80=15', '97-46=51'] Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,12 unequal: No Solution Exploring Operation: 15+51=66, Resulting Numbers: [66] 66,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[46, 82], Operations: ['95-80=15', '97-15=82'] Exploring Operation: 46+82=128, Resulting Numbers: [128] 128,12 unequal: No Solution Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 18, 19, 71, 2 ]
87
[ "71-18=53", "2*53=106", "106-19=87" ]
Current State: 87:[18, 19, 71, 2], Operations: [] Exploring Operation: 71-18=53, Resulting Numbers: [19, 2, 53] Generated Node #2: [19, 2, 53] from Operation: 71-18=53 Current State: 87:[19, 2, 53], Operations: ['71-18=53'] Exploring Operation: 2*53=106, Resulting Numbers: [19, 106] Generated Node #3: [19, 106] from Operation: 2*53=106 Current State: 87:[19, 106], Operations: ['71-18=53', '2*53=106'] Exploring Operation: 106-19=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[18, 19, 71, 2], Operations: [] Exploring Operation: 19-18=1, Resulting Numbers: [71, 2, 1] Generated Node #0,0: 87:[71, 2, 1] Operation: 19-18=1 Exploring Operation: 18+19=37, Resulting Numbers: [71, 2, 37] Generated Node #0,1: 87:[71, 2, 37] Operation: 18+19=37 Exploring Operation: 18+71=89, Resulting Numbers: [19, 2, 89] Generated Node #0,2: 87:[19, 2, 89] Operation: 18+71=89 Exploring Operation: 19+71=90, Resulting Numbers: [18, 2, 90] Generated Node #0,3: 87:[18, 2, 90] Operation: 19+71=90 Moving to Node #0,2 Current State: 87:[19, 2, 89], Operations: ['18+71=89'] Exploring Operation: 19*2=38, Resulting Numbers: [89, 38] Generated Node #0,2,0: 87:[89, 38] Operation: 19*2=38 Exploring Operation: 19-2=17, Resulting Numbers: [89, 17] Generated Node #0,2,1: 87:[89, 17] Operation: 19-2=17 Exploring Operation: 19+2=21, Resulting Numbers: [89, 21] Generated Node #0,2,2: 87:[89, 21] Operation: 19+2=21 Exploring Operation: 89-2=87, Resulting Numbers: [19, 87] Generated Node #0,2,3: 87:[19, 87] Operation: 89-2=87 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[89, 21], Operations: ['18+71=89', '19+2=21'] Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 89*21=1869, Resulting Numbers: [1869] 1869,87 unequal: No Solution Exploring Operation: 89+21=110, Resulting Numbers: [110] 110,87 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:[19, 87], Operations: ['18+71=89', '89-2=87'] Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 19+87=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 19*87=1653, Resulting Numbers: [1653] 1653,87 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:[89, 38], Operations: ['18+71=89', '19*2=38'] Exploring Operation: 89*38=3382, Resulting Numbers: [3382] 3382,87 unequal: No Solution Exploring Operation: 89-38=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 89+38=127, Resulting Numbers: [127] 127,87 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:[89, 17], Operations: ['18+71=89', '19-2=17'] Exploring Operation: 89*17=1513, Resulting Numbers: [1513] 1513,87 unequal: No Solution Exploring Operation: 89+17=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,87 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: 87:[18, 2, 90], Operations: ['19+71=90'] Exploring Operation: 18/2=9, Resulting Numbers: [90, 9] Generated Node #0,3,0: 87:[90, 9] Operation: 18/2=9 Exploring Operation: 18+2=20, Resulting Numbers: [90, 20] Generated Node #0,3,1: 87:[90, 20] Operation: 18+2=20 Exploring Operation: 18*2=36, Resulting Numbers: [90, 36] Generated Node #0,3,2: 87:[90, 36] Operation: 18*2=36 Exploring Operation: 90/18=5, Resulting Numbers: [2, 5] Generated Node #0,3,3: 87:[2, 5] Operation: 90/18=5 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 87:[2, 5], Operations: ['19+71=90', '90/18=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,87 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 #0,3,0 Current State: 87:[90, 9], Operations: ['19+71=90', '18/2=9'] Exploring Operation: 90+9=99, Resulting Numbers: [99] 99,87 unequal: No Solution Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 90*9=810, Resulting Numbers: [810] 810,87 unequal: No Solution Exploring Operation: 90-9=81, Resulting Numbers: [81] 81,87 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 #0,3,2 Current State: 87:[90, 36], Operations: ['19+71=90', '18*2=36'] Exploring Operation: 90+36=126, Resulting Numbers: [126] 126,87 unequal: No Solution Exploring Operation: 90*36=3240, Resulting Numbers: [3240] 3240,87 unequal: No Solution Exploring Operation: 90-36=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 #0,3,1 Current State: 87:[90, 20], Operations: ['19+71=90', '18+2=20'] Exploring Operation: 90*20=1800, Resulting Numbers: [1800] 1800,87 unequal: No Solution Exploring Operation: 90+20=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,87 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: 87:[71, 2, 1], Operations: ['19-18=1'] Exploring Operation: 71+1=72, Resulting Numbers: [2, 72] Generated Node #0,0,0: 87:[2, 72] Operation: 71+1=72 Exploring Operation: 71*1=71, Resulting Numbers: [2, 71] Generated Node #0,0,1: 87:[2, 71] Operation: 71*1=71 Exploring Operation: 71+2=73, Resulting Numbers: [1, 73] Generated Node #0,0,2: 87:[1, 73] Operation: 71+2=73 Exploring Operation: 2+1=3, Resulting Numbers: [71, 3] Generated Node #0,0,3: 87:[71, 3] Operation: 2+1=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[2, 72], Operations: ['19-18=1', '71+1=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,87 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:[1, 73], Operations: ['19-18=1', '71+2=73'] Exploring Operation: 1*73=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 1+73=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,87 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:[71, 3], Operations: ['19-18=1', '2+1=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 71*3=213, Resulting Numbers: [213] 213,87 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,87 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:[2, 71], Operations: ['19-18=1', '71*1=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,87 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,87 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: 87:[71, 2, 37], Operations: ['18+19=37'] Exploring Operation: 71+2=73, Resulting Numbers: [37, 73] Generated Node #0,1,0: 87:[37, 73] Operation: 71+2=73 Exploring Operation: 71-37=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 87:[2, 34] Operation: 71-37=34 Exploring Operation: 71+37=108, Resulting Numbers: [2, 108] Generated Node #0,1,2: 87:[2, 108] Operation: 71+37=108 Exploring Operation: 37-2=35, Resulting Numbers: [71, 35] Generated Node #0,1,3: 87:[71, 35] Operation: 37-2=35 Moving to Node #0,1,1 Current State: 87:[2, 34], Operations: ['18+19=37', '71-37=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[2, 108], Operations: ['18+19=37', '71+37=108'] Exploring Operation: 2*108=216, Resulting Numbers: [216] 216,87 unequal: No Solution Exploring Operation: 108-2=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 2+108=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 108/2=54, Resulting Numbers: [54] 54,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[37, 73], Operations: ['18+19=37', '71+2=73'] Exploring Operation: 37+73=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 37*73=2701, Resulting Numbers: [2701] 2701,87 unequal: No Solution Exploring Operation: 73-37=36, Resulting Numbers: [36] 36,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[71, 35], Operations: ['18+19=37', '37-2=35'] Exploring Operation: 71*35=2485, Resulting Numbers: [2485] 2485,87 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 71+35=106, Resulting Numbers: [106] 106,87 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 95, 9, 30, 92 ]
24
[ "95-9=86", "92-30=62", "86-62=24" ]
Current State: 24:[95, 9, 30, 92], Operations: [] Exploring Operation: 95-9=86, Resulting Numbers: [30, 92, 86] Generated Node #2: [30, 92, 86] from Operation: 95-9=86 Current State: 24:[30, 92, 86], Operations: ['95-9=86'] Exploring Operation: 92-30=62, Resulting Numbers: [86, 62] Generated Node #3: [86, 62] from Operation: 92-30=62 Current State: 24:[86, 62], Operations: ['95-9=86', '92-30=62'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[95, 9, 30, 92], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [9, 30, 3] Generated Node #0,0: 24:[9, 30, 3] Operation: 95-92=3 Exploring Operation: 95-30=65, Resulting Numbers: [9, 92, 65] Generated Node #0,1: 24:[9, 92, 65] Operation: 95-30=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[9, 30, 3], Operations: ['95-92=3'] Exploring Operation: 30/3=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 24:[9, 10] Operation: 30/3=10 Exploring Operation: 30-9=21, Resulting Numbers: [3, 21] Generated Node #0,0,1: 24:[3, 21] Operation: 30-9=21 Moving to Node #0,0,0 Current State: 24:[9, 10], Operations: ['95-92=3', '30/3=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[3, 21], Operations: ['95-92=3', '30-9=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[95, 9, 30, 92], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [9, 30, 3] Generated Node #0,0: 24:[9, 30, 3] Operation: 95-92=3 Moving to Node #0,0 Current State: 24:[9, 30, 3], Operations: ['95-92=3'] Exploring Operation: 30-9=21, Resulting Numbers: [3, 21] Generated Node #0,0,1: 24:[3, 21] Operation: 30-9=21 Moving to Node #0,0,1 Current State: 24:[3, 21], Operations: ['95-92=3', '30-9=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 38, 52, 97, 94 ]
62
[ "97-94=3", "38*3=114", "114-52=62" ]
Current State: 62:[38, 52, 97, 94], Operations: [] Exploring Operation: 97-94=3, Resulting Numbers: [38, 52, 3] Generated Node #2: [38, 52, 3] from Operation: 97-94=3 Current State: 62:[38, 52, 3], Operations: ['97-94=3'] Exploring Operation: 38*3=114, Resulting Numbers: [52, 114] Generated Node #3: [52, 114] from Operation: 38*3=114 Current State: 62:[52, 114], Operations: ['97-94=3', '38*3=114'] Exploring Operation: 114-52=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[38, 52, 97, 94], Operations: [] Exploring Operation: 94-38=56, Resulting Numbers: [52, 97, 56] Generated Node #0,0: 62:[52, 97, 56] Operation: 94-38=56 Exploring Operation: 97-94=3, Resulting Numbers: [38, 52, 3] Generated Node #0,1: 62:[38, 52, 3] Operation: 97-94=3 Exploring Operation: 97-38=59, Resulting Numbers: [52, 94, 59] Generated Node #0,2: 62:[52, 94, 59] Operation: 97-38=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[38, 52, 3], Operations: ['97-94=3'] Exploring Operation: 52+3=55, Resulting Numbers: [38, 55] Generated Node #0,1,0: 62:[38, 55] Operation: 52+3=55 Exploring Operation: 38-3=35, Resulting Numbers: [52, 35] Generated Node #0,1,1: 62:[52, 35] Operation: 38-3=35 Exploring Operation: 52-38=14, Resulting Numbers: [3, 14] Generated Node #0,1,2: 62:[3, 14] Operation: 52-38=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[3, 14], Operations: ['97-94=3', '52-38=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,62 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 #0,1,0 Current State: 62:[38, 55], Operations: ['97-94=3', '52+3=55'] Exploring Operation: 38+55=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 38*55=2090, Resulting Numbers: [2090] 2090,62 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,62 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:[52, 35], Operations: ['97-94=3', '38-3=35'] Exploring Operation: 52*35=1820, Resulting Numbers: [1820] 1820,62 unequal: No Solution Exploring Operation: 52+35=87, Resulting Numbers: [87] 87,62 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[52, 94, 59], Operations: ['97-38=59'] Exploring Operation: 94-59=35, Resulting Numbers: [52, 35] Generated Node #0,2,0: 62:[52, 35] Operation: 94-59=35 Exploring Operation: 94-52=42, Resulting Numbers: [59, 42] Generated Node #0,2,1: 62:[59, 42] Operation: 94-52=42 Exploring Operation: 59-52=7, Resulting Numbers: [94, 7] Generated Node #0,2,2: 62:[94, 7] Operation: 59-52=7 Moving to Node #0,2,0 Current State: 62:[52, 35], Operations: ['97-38=59', '94-59=35'] Exploring Operation: 52*35=1820, Resulting Numbers: [1820] 1820,62 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 52+35=87, Resulting Numbers: [87] 87,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[59, 42], Operations: ['97-38=59', '94-52=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[94, 7], Operations: ['97-38=59', '59-52=7'] Exploring Operation: 94+7=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,62 unequal: No Solution Exploring Operation: 94*7=658, Resulting Numbers: [658] 658,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[52, 97, 56], Operations: ['94-38=56'] Exploring Operation: 97-56=41, Resulting Numbers: [52, 41] Generated Node #0,0,0: 62:[52, 41] Operation: 97-56=41 Exploring Operation: 56-52=4, Resulting Numbers: [97, 4] Generated Node #0,0,1: 62:[97, 4] Operation: 56-52=4 Exploring Operation: 97-52=45, Resulting Numbers: [56, 45] Generated Node #0,0,2: 62:[56, 45] Operation: 97-52=45 Moving to Node #0,0,0 Current State: 62:[52, 41], Operations: ['94-38=56', '97-56=41'] Exploring Operation: 52*41=2132, Resulting Numbers: [2132] 2132,62 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[56, 45], Operations: ['94-38=56', '97-52=45'] Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 56+45=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 56*45=2520, Resulting Numbers: [2520] 2520,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[97, 4], Operations: ['94-38=56', '56-52=4'] Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,62 unequal: No Solution Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,62 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
[ 85, 25, 21, 54 ]
82
[ "21+54=75", "75/25=3", "85-3=82" ]
Current State: 82:[85, 25, 21, 54], Operations: [] Exploring Operation: 21+54=75, Resulting Numbers: [85, 25, 75] Generated Node #2: [85, 25, 75] from Operation: 21+54=75 Current State: 82:[85, 25, 75], Operations: ['21+54=75'] Exploring Operation: 75/25=3, Resulting Numbers: [85, 3] Generated Node #3: [85, 3] from Operation: 75/25=3 Current State: 82:[85, 3], Operations: ['21+54=75', '75/25=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[85, 25, 21, 54], Operations: [] Exploring Operation: 25-21=4, Resulting Numbers: [85, 54, 4] Generated Node #0,0: 82:[85, 54, 4] Operation: 25-21=4 Moving to Node #0,0 Current State: 82:[85, 54, 4], Operations: ['25-21=4'] Exploring Operation: 85-54=31, Resulting Numbers: [4, 31] Generated Node #0,0,0: 82:[4, 31] Operation: 85-54=31 Moving to Node #0,0,0 Current State: 82:[4, 31], Operations: ['25-21=4', '85-54=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,82 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 11, 81, 49, 18 ]
88
[ "18-11=7", "49/7=7", "81+7=88" ]
Current State: 88:[11, 81, 49, 18], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [81, 49, 7] Generated Node #2: [81, 49, 7] from Operation: 18-11=7 Current State: 88:[81, 49, 7], Operations: ['18-11=7'] Exploring Operation: 49/7=7, Resulting Numbers: [81, 7] Generated Node #3: [81, 7] from Operation: 49/7=7 Current State: 88:[81, 7], Operations: ['18-11=7', '49/7=7'] Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[11, 81, 49, 18], Operations: [] Exploring Operation: 11+81=92, Resulting Numbers: [49, 18, 92] Generated Node #0,0: 88:[49, 18, 92] Operation: 11+81=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[49, 18, 92], Operations: ['11+81=92'] Exploring Operation: 92-49=43, Resulting Numbers: [18, 43] Generated Node #0,0,0: 88:[18, 43] Operation: 92-49=43 Moving to Node #0,0,0 Current State: 88:[18, 43], Operations: ['11+81=92', '92-49=43'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 32, 98, 33, 91 ]
58
[ "98-32=66", "33+91=124", "124-66=58" ]
Current State: 58:[32, 98, 33, 91], Operations: [] Exploring Operation: 98-32=66, Resulting Numbers: [33, 91, 66] Generated Node #2: [33, 91, 66] from Operation: 98-32=66 Current State: 58:[33, 91, 66], Operations: ['98-32=66'] Exploring Operation: 33+91=124, Resulting Numbers: [66, 124] Generated Node #3: [66, 124] from Operation: 33+91=124 Current State: 58:[66, 124], Operations: ['98-32=66', '33+91=124'] Exploring Operation: 124-66=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[32, 98, 33, 91], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [32, 91, 65] Generated Node #0,0: 58:[32, 91, 65] Operation: 98-33=65 Exploring Operation: 98-91=7, Resulting Numbers: [32, 33, 7] Generated Node #0,1: 58:[32, 33, 7] Operation: 98-91=7 Exploring Operation: 91-32=59, Resulting Numbers: [98, 33, 59] Generated Node #0,2: 58:[98, 33, 59] Operation: 91-32=59 Exploring Operation: 91-33=58, Resulting Numbers: [32, 98, 58] Generated Node #0,3: 58:[32, 98, 58] Operation: 91-33=58 Exploring Operation: 98-32=66, Resulting Numbers: [33, 91, 66] Generated Node #0,4: 58:[33, 91, 66] Operation: 98-32=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[32, 33, 7], Operations: ['98-91=7'] Exploring Operation: 32-7=25, Resulting Numbers: [33, 25] Generated Node #0,1,0: 58:[33, 25] Operation: 32-7=25 Exploring Operation: 33-7=26, Resulting Numbers: [32, 26] Generated Node #0,1,1: 58:[32, 26] Operation: 33-7=26 Exploring Operation: 33-32=1, Resulting Numbers: [7, 1] Generated Node #0,1,2: 58:[7, 1] Operation: 33-32=1 Exploring Operation: 32+7=39, Resulting Numbers: [33, 39] Generated Node #0,1,3: 58:[33, 39] Operation: 32+7=39 Exploring Operation: 32+33=65, Resulting Numbers: [7, 65] Generated Node #0,1,4: 58:[7, 65] Operation: 32+33=65 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[32, 26], Operations: ['98-91=7', '33-7=26'] Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[32, 98, 33, 91], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [32, 33, 7] Generated Node #0,1: 58:[32, 33, 7] Operation: 98-91=7 Moving to Node #0,1 Current State: 58:[32, 33, 7], Operations: ['98-91=7'] Exploring Operation: 33-7=26, Resulting Numbers: [32, 26] Generated Node #0,1,1: 58:[32, 26] Operation: 33-7=26 Moving to Node #0,1,1 Current State: 58:[32, 26], Operations: ['98-91=7', '33-7=26'] Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 21, 61, 10, 33 ]
37
[ "61-21=40", "40/10=4", "33+4=37" ]
Current State: 37:[21, 61, 10, 33], Operations: [] Exploring Operation: 61-21=40, Resulting Numbers: [10, 33, 40] Generated Node #2: [10, 33, 40] from Operation: 61-21=40 Current State: 37:[10, 33, 40], Operations: ['61-21=40'] Exploring Operation: 40/10=4, Resulting Numbers: [33, 4] Generated Node #3: [33, 4] from Operation: 40/10=4 Current State: 37:[33, 4], Operations: ['61-21=40', '40/10=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[21, 61, 10, 33], Operations: [] Exploring Operation: 61-10=51, Resulting Numbers: [21, 33, 51] Generated Node #0,0: 37:[21, 33, 51] Operation: 61-10=51 Exploring Operation: 61-33=28, Resulting Numbers: [21, 10, 28] Generated Node #0,1: 37:[21, 10, 28] Operation: 61-33=28 Exploring Operation: 21+10=31, Resulting Numbers: [61, 33, 31] Generated Node #0,2: 37:[61, 33, 31] Operation: 21+10=31 Exploring Operation: 10+33=43, Resulting Numbers: [21, 61, 43] Generated Node #0,3: 37:[21, 61, 43] Operation: 10+33=43 Exploring Operation: 61-21=40, Resulting Numbers: [10, 33, 40] Generated Node #0,4: 37:[10, 33, 40] Operation: 61-21=40 Moving to Node #0,0 Current State: 37:[21, 33, 51], Operations: ['61-10=51'] Exploring Operation: 33-21=12, Resulting Numbers: [51, 12] Generated Node #0,0,0: 37:[51, 12] Operation: 33-21=12 Exploring Operation: 51-33=18, Resulting Numbers: [21, 18] Generated Node #0,0,1: 37:[21, 18] Operation: 51-33=18 Exploring Operation: 21+33=54, Resulting Numbers: [51, 54] Generated Node #0,0,2: 37:[51, 54] Operation: 21+33=54 Exploring Operation: 51-21=30, Resulting Numbers: [33, 30] Generated Node #0,0,3: 37:[33, 30] Operation: 51-21=30 Exploring Operation: 21+51=72, Resulting Numbers: [33, 72] Generated Node #0,0,4: 37:[33, 72] Operation: 21+51=72 Moving to Node #0,4 Current State: 37:[10, 33, 40], Operations: ['61-21=40'] Exploring Operation: 33-10=23, Resulting Numbers: [40, 23] Generated Node #0,4,0: 37:[40, 23] Operation: 33-10=23 Exploring Operation: 40/10=4, Resulting Numbers: [33, 4] Generated Node #0,4,1: 37:[33, 4] Operation: 40/10=4 Exploring Operation: 10+33=43, Resulting Numbers: [40, 43] Generated Node #0,4,2: 37:[40, 43] Operation: 10+33=43 Exploring Operation: 10+40=50, Resulting Numbers: [33, 50] Generated Node #0,4,3: 37:[33, 50] Operation: 10+40=50 Exploring Operation: 40-10=30, Resulting Numbers: [33, 30] Generated Node #0,4,4: 37:[33, 30] Operation: 40-10=30 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 37:[40, 43], Operations: ['61-21=40', '10+33=43'] Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,37 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 37:[33, 30], Operations: ['61-21=40', '40-10=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,37 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,37 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 37:[40, 23], Operations: ['61-21=40', '33-10=23'] Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,37 unequal: No Solution Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 37:[33, 50], Operations: ['61-21=40', '10+40=50'] Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 33*50=1650, Resulting Numbers: [1650] 1650,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 37:[33, 4], Operations: ['61-21=40', '40/10=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[21, 61, 10, 33], Operations: [] Exploring Operation: 61-21=40, Resulting Numbers: [10, 33, 40] Generated Node #0,4: 37:[10, 33, 40] Operation: 61-21=40 Moving to Node #0,4 Current State: 37:[10, 33, 40], Operations: ['61-21=40'] Exploring Operation: 40/10=4, Resulting Numbers: [33, 4] Generated Node #0,4,1: 37:[33, 4] Operation: 40/10=4 Moving to Node #0,4,1 Current State: 37:[33, 4], Operations: ['61-21=40', '40/10=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_5
mult_heuristic
[ 57, 60, 20, 76 ]
53
[ "60-57=3", "76-20=56", "56-3=53" ]
Current State: 53:[57, 60, 20, 76], Operations: [] Exploring Operation: 60-57=3, Resulting Numbers: [20, 76, 3] Generated Node #2: [20, 76, 3] from Operation: 60-57=3 Current State: 53:[20, 76, 3], Operations: ['60-57=3'] Exploring Operation: 76-20=56, Resulting Numbers: [3, 56] Generated Node #3: [3, 56] from Operation: 76-20=56 Current State: 53:[3, 56], Operations: ['60-57=3', '76-20=56'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[57, 60, 20, 76], Operations: [] Exploring Operation: 76-20=56, Resulting Numbers: [57, 60, 56] Generated Node #0,0: 53:[57, 60, 56] Operation: 76-20=56 Exploring Operation: 60-20=40, Resulting Numbers: [57, 76, 40] Generated Node #0,1: 53:[57, 76, 40] Operation: 60-20=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[57, 60, 56], Operations: ['76-20=56'] Exploring Operation: 60-56=4, Resulting Numbers: [57, 4] Generated Node #0,0,0: 53:[57, 4] Operation: 60-56=4 Exploring Operation: 60-57=3, Resulting Numbers: [56, 3] Generated Node #0,0,1: 53:[56, 3] Operation: 60-57=3 Moving to Node #0,0,0 Current State: 53:[57, 4], Operations: ['76-20=56', '60-56=4'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[57, 60, 20, 76], Operations: [] Exploring Operation: 76-20=56, Resulting Numbers: [57, 60, 56] Generated Node #0,0: 53:[57, 60, 56] Operation: 76-20=56 Moving to Node #0,0 Current State: 53:[57, 60, 56], Operations: ['76-20=56'] Exploring Operation: 60-56=4, Resulting Numbers: [57, 4] Generated Node #0,0,0: 53:[57, 4] Operation: 60-56=4 Moving to Node #0,0,0 Current State: 53:[57, 4], Operations: ['76-20=56', '60-56=4'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 51, 59, 49, 40 ]
61
[ "51*49=2499", "2499-59=2440", "2440/40=61" ]
Current State: 61:[51, 59, 49, 40], Operations: [] Exploring Operation: 51*49=2499, Resulting Numbers: [59, 40, 2499] Generated Node #2: [59, 40, 2499] from Operation: 51*49=2499 Current State: 61:[59, 40, 2499], Operations: ['51*49=2499'] Exploring Operation: 2499-59=2440, Resulting Numbers: [40, 2440] Generated Node #3: [40, 2440] from Operation: 2499-59=2440 Current State: 61:[40, 2440], Operations: ['51*49=2499', '2499-59=2440'] Exploring Operation: 2440/40=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[51, 59, 49, 40], Operations: [] Exploring Operation: 51+40=91, Resulting Numbers: [59, 49, 91] Generated Node #0,0: 61:[59, 49, 91] Operation: 51+40=91 Exploring Operation: 49+40=89, Resulting Numbers: [51, 59, 89] Generated Node #0,1: 61:[51, 59, 89] Operation: 49+40=89 Exploring Operation: 59+40=99, Resulting Numbers: [51, 49, 99] Generated Node #0,2: 61:[51, 49, 99] Operation: 59+40=99 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[51, 59, 89], Operations: ['49+40=89'] Exploring Operation: 89-59=30, Resulting Numbers: [51, 30] Generated Node #0,1,0: 61:[51, 30] Operation: 89-59=30 Exploring Operation: 51+59=110, Resulting Numbers: [89, 110] Generated Node #0,1,1: 61:[89, 110] Operation: 51+59=110 Exploring Operation: 89-51=38, Resulting Numbers: [59, 38] Generated Node #0,1,2: 61:[59, 38] Operation: 89-51=38 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[59, 38], Operations: ['49+40=89', '89-51=38'] Exploring Operation: 59*38=2242, Resulting Numbers: [2242] 2242,61 unequal: No Solution Exploring Operation: 59+38=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[51, 30], Operations: ['49+40=89', '89-59=30'] Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,61 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[89, 110], Operations: ['49+40=89', '51+59=110'] Exploring Operation: 110-89=21, Resulting Numbers: [21] 21,61 unequal: No Solution Exploring Operation: 89*110=9790, Resulting Numbers: [9790] 9790,61 unequal: No Solution Exploring Operation: 89+110=199, Resulting Numbers: [199] 199,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[59, 49, 91], Operations: ['51+40=91'] Exploring Operation: 59+49=108, Resulting Numbers: [91, 108] Generated Node #0,0,0: 61:[91, 108] Operation: 59+49=108 Exploring Operation: 91-59=32, Resulting Numbers: [49, 32] Generated Node #0,0,1: 61:[49, 32] Operation: 91-59=32 Exploring Operation: 91-49=42, Resulting Numbers: [59, 42] Generated Node #0,0,2: 61:[59, 42] Operation: 91-49=42 Moving to Node #0,0,2 Current State: 61:[59, 42], Operations: ['51+40=91', '91-49=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,61 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[49, 32], Operations: ['51+40=91', '91-59=32'] Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,61 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[91, 108], Operations: ['51+40=91', '59+49=108'] Exploring Operation: 108-91=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 91+108=199, Resulting Numbers: [199] 199,61 unequal: No Solution Exploring Operation: 91*108=9828, Resulting Numbers: [9828] 9828,61 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 #0,2 Current State: 61:[51, 49, 99], Operations: ['59+40=99'] Exploring Operation: 99-49=50, Resulting Numbers: [51, 50] Generated Node #0,2,0: 61:[51, 50] Operation: 99-49=50 Exploring Operation: 99-51=48, Resulting Numbers: [49, 48] Generated Node #0,2,1: 61:[49, 48] Operation: 99-51=48 Exploring Operation: 51+49=100, Resulting Numbers: [99, 100] Generated Node #0,2,2: 61:[99, 100] Operation: 51+49=100 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[51, 50], Operations: ['59+40=99', '99-49=50'] Exploring Operation: 51+50=101, Resulting Numbers: [101] 101,61 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 51*50=2550, Resulting Numbers: [2550] 2550,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[49, 48], Operations: ['59+40=99', '99-51=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,61 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[99, 100], Operations: ['59+40=99', '51+49=100'] Exploring Operation: 100-99=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 99*100=9900, Resulting Numbers: [9900] 9900,61 unequal: No Solution Exploring Operation: 99+100=199, Resulting Numbers: [199] 199,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 9, 49, 60, 28 ]
90
[ "9+49=58", "60-28=32", "58+32=90" ]
Current State: 90:[9, 49, 60, 28], Operations: [] Exploring Operation: 9+49=58, Resulting Numbers: [60, 28, 58] Generated Node #2: [60, 28, 58] from Operation: 9+49=58 Current State: 90:[60, 28, 58], Operations: ['9+49=58'] Exploring Operation: 60-28=32, Resulting Numbers: [58, 32] Generated Node #3: [58, 32] from Operation: 60-28=32 Current State: 90:[58, 32], Operations: ['9+49=58', '60-28=32'] Exploring Operation: 58+32=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[9, 49, 60, 28], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [9, 49, 32] Generated Node #0,0: 90:[9, 49, 32] Operation: 60-28=32 Exploring Operation: 60+28=88, Resulting Numbers: [9, 49, 88] Generated Node #0,1: 90:[9, 49, 88] Operation: 60+28=88 Exploring Operation: 60-49=11, Resulting Numbers: [9, 28, 11] Generated Node #0,2: 90:[9, 28, 11] Operation: 60-49=11 Moving to Node #0,2 Current State: 90:[9, 28, 11], Operations: ['60-49=11'] Exploring Operation: 11-9=2, Resulting Numbers: [28, 2] Generated Node #0,2,0: 90:[28, 2] Operation: 11-9=2 Exploring Operation: 28-9=19, Resulting Numbers: [11, 19] Generated Node #0,2,1: 90:[11, 19] Operation: 28-9=19 Exploring Operation: 28-11=17, Resulting Numbers: [9, 17] Generated Node #0,2,2: 90:[9, 17] Operation: 28-11=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[9, 17], Operations: ['60-49=11', '28-11=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[28, 2], Operations: ['60-49=11', '11-9=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[11, 19], Operations: ['60-49=11', '28-9=19'] Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,90 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,90 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: 90:[9, 49, 32], Operations: ['60-28=32'] Exploring Operation: 49-9=40, Resulting Numbers: [32, 40] Generated Node #0,0,0: 90:[32, 40] Operation: 49-9=40 Exploring Operation: 49-32=17, Resulting Numbers: [9, 17] Generated Node #0,0,1: 90:[9, 17] Operation: 49-32=17 Exploring Operation: 9+32=41, Resulting Numbers: [49, 41] Generated Node #0,0,2: 90:[49, 41] Operation: 9+32=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[9, 17], Operations: ['60-28=32', '49-32=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,90 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[32, 40], Operations: ['60-28=32', '49-9=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[49, 41], Operations: ['60-28=32', '9+32=41'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[9, 49, 60, 28], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [9, 49, 32] Generated Node #0,0: 90:[9, 49, 32] Operation: 60-28=32 Moving to Node #0,0 Current State: 90:[9, 49, 32], Operations: ['60-28=32'] Exploring Operation: 9+32=41, Resulting Numbers: [49, 41] Generated Node #0,0,2: 90:[49, 41] Operation: 9+32=41 Moving to Node #0,0,2 Current State: 90:[49, 41], Operations: ['60-28=32', '9+32=41'] Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_3
mult_heuristic
[ 51, 73, 28, 22 ]
28
[ "73-51=22", "28+22=50", "50-22=28" ]
Current State: 28:[51, 73, 28, 22], Operations: [] Exploring Operation: 73-51=22, Resulting Numbers: [28, 22, 22] Generated Node #2: [28, 22, 22] from Operation: 73-51=22 Current State: 28:[28, 22, 22], Operations: ['73-51=22'] Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,28 equal: Goal Reached Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[51, 73, 28, 22], Operations: [] Exploring Operation: 73-22=51, Resulting Numbers: [51, 28, 51] Generated Node #0,0: 28:[51, 28, 51] Operation: 73-22=51 Exploring Operation: 73-51=22, Resulting Numbers: [28, 22, 22] Generated Node #0,1: 28:[28, 22, 22] Operation: 73-51=22 Exploring Operation: 73-28=45, Resulting Numbers: [51, 22, 45] Generated Node #0,2: 28:[51, 22, 45] Operation: 73-28=45 Exploring Operation: 51-22=29, Resulting Numbers: [73, 28, 29] Generated Node #0,3: 28:[73, 28, 29] Operation: 51-22=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[28, 22, 22], Operations: ['73-51=22'] Exploring Operation: 22/22=1, Resulting Numbers: [28, 1] Generated Node #0,1,0: 28:[28, 1] Operation: 22/22=1 Exploring Operation: 22-22=0, Resulting Numbers: [28, 0] Generated Node #0,1,1: 28:[28, 0] Operation: 22-22=0 Exploring Operation: 28-22=6, Resulting Numbers: [22, 6] Generated Node #0,1,2: 28:[22, 6] Operation: 28-22=6 Exploring Operation: 28-22=6, Resulting Numbers: [22, 6] Generated Node #0,1,3: 28:[22, 6] Operation: 28-22=6 Moving to Node #0,1,0 Current State: 28:[28, 1], Operations: ['73-51=22', '22/22=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[51, 73, 28, 22], Operations: [] Exploring Operation: 73-51=22, Resulting Numbers: [28, 22, 22] Generated Node #0,1: 28:[28, 22, 22] Operation: 73-51=22 Moving to Node #0,1 Current State: 28:[28, 22, 22], Operations: ['73-51=22'] Exploring Operation: 22/22=1, Resulting Numbers: [28, 1] Generated Node #0,1,0: 28:[28, 1] Operation: 22/22=1 Moving to Node #0,1,0 Current State: 28:[28, 1], Operations: ['73-51=22', '22/22=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 33, 40, 93, 26 ]
39
[ "93-33=60", "26*60=1560", "1560/40=39" ]
Current State: 39:[33, 40, 93, 26], Operations: [] Exploring Operation: 93-33=60, Resulting Numbers: [40, 26, 60] Generated Node #2: [40, 26, 60] from Operation: 93-33=60 Current State: 39:[40, 26, 60], Operations: ['93-33=60'] Exploring Operation: 26*60=1560, Resulting Numbers: [40, 1560] Generated Node #3: [40, 1560] from Operation: 26*60=1560 Current State: 39:[40, 1560], Operations: ['93-33=60', '26*60=1560'] Exploring Operation: 1560/40=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[33, 40, 93, 26], Operations: [] Exploring Operation: 40-26=14, Resulting Numbers: [33, 93, 14] Generated Node #0,0: 39:[33, 93, 14] Operation: 40-26=14 Exploring Operation: 93-26=67, Resulting Numbers: [33, 40, 67] Generated Node #0,1: 39:[33, 40, 67] Operation: 93-26=67 Exploring Operation: 93-40=53, Resulting Numbers: [33, 26, 53] Generated Node #0,2: 39:[33, 26, 53] Operation: 93-40=53 Exploring Operation: 93-33=60, Resulting Numbers: [40, 26, 60] Generated Node #0,3: 39:[40, 26, 60] Operation: 93-33=60 Exploring Operation: 33-26=7, Resulting Numbers: [40, 93, 7] Generated Node #0,4: 39:[40, 93, 7] Operation: 33-26=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[33, 26, 53], Operations: ['93-40=53'] Exploring Operation: 53-26=27, Resulting Numbers: [33, 27] Generated Node #0,2,0: 39:[33, 27] Operation: 53-26=27 Exploring Operation: 26+53=79, Resulting Numbers: [33, 79] Generated Node #0,2,1: 39:[33, 79] Operation: 26+53=79 Exploring Operation: 33-26=7, Resulting Numbers: [53, 7] Generated Node #0,2,2: 39:[53, 7] Operation: 33-26=7 Exploring Operation: 33+26=59, Resulting Numbers: [53, 59] Generated Node #0,2,3: 39:[53, 59] Operation: 33+26=59 Exploring Operation: 53-33=20, Resulting Numbers: [26, 20] Generated Node #0,2,4: 39:[26, 20] Operation: 53-33=20 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[33, 27], Operations: ['93-40=53', '53-26=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,39 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[53, 7], Operations: ['93-40=53', '33-26=7'] Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,39 unequal: No Solution No 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: 39:[26, 20], Operations: ['93-40=53', '53-33=20'] Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,39 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[53, 59], Operations: ['93-40=53', '33+26=59'] Exploring Operation: 53*59=3127, Resulting Numbers: [3127] 3127,39 unequal: No Solution Exploring Operation: 59-53=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 53+59=112, Resulting Numbers: [112] 112,39 unequal: No Solution No 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: 39:[33, 79], Operations: ['93-40=53', '26+53=79'] Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,39 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,39 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: 39:[33, 40, 67], Operations: ['93-26=67'] Exploring Operation: 67-40=27, Resulting Numbers: [33, 27] Generated Node #0,1,0: 39:[33, 27] Operation: 67-40=27 Exploring Operation: 40-33=7, Resulting Numbers: [67, 7] Generated Node #0,1,1: 39:[67, 7] Operation: 40-33=7 Exploring Operation: 33+67=100, Resulting Numbers: [40, 100] Generated Node #0,1,2: 39:[40, 100] Operation: 33+67=100 Exploring Operation: 67-33=34, Resulting Numbers: [40, 34] Generated Node #0,1,3: 39:[40, 34] Operation: 67-33=34 Exploring Operation: 33+40=73, Resulting Numbers: [67, 73] Generated Node #0,1,4: 39:[67, 73] Operation: 33+40=73 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 39:[40, 34], Operations: ['93-26=67', '67-33=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[33, 27], Operations: ['93-26=67', '67-40=27'] Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,39 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[67, 7], Operations: ['93-26=67', '40-33=7'] Exploring Operation: 67*7=469, Resulting Numbers: [469] 469,39 unequal: No Solution Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 67+7=74, Resulting Numbers: [74] 74,39 unequal: No Solution No 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: 39:[40, 100], Operations: ['93-26=67', '33+67=100'] Exploring Operation: 100-40=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 40*100=4000, Resulting Numbers: [4000] 4000,39 unequal: No Solution Exploring Operation: 40+100=140, Resulting Numbers: [140] 140,39 unequal: No Solution No 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: 39:[67, 73], Operations: ['93-26=67', '33+40=73'] Exploring Operation: 73-67=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 67*73=4891, Resulting Numbers: [4891] 4891,39 unequal: No Solution Exploring Operation: 67+73=140, Resulting Numbers: [140] 140,39 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: 39:[40, 26, 60], Operations: ['93-33=60'] Exploring Operation: 40-26=14, Resulting Numbers: [60, 14] Generated Node #0,3,0: 39:[60, 14] Operation: 40-26=14 Exploring Operation: 40+26=66, Resulting Numbers: [60, 66] Generated Node #0,3,1: 39:[60, 66] Operation: 40+26=66 Exploring Operation: 60-40=20, Resulting Numbers: [26, 20] Generated Node #0,3,2: 39:[26, 20] Operation: 60-40=20 Exploring Operation: 26+60=86, Resulting Numbers: [40, 86] Generated Node #0,3,3: 39:[40, 86] Operation: 26+60=86 Exploring Operation: 60-26=34, Resulting Numbers: [40, 34] Generated Node #0,3,4: 39:[40, 34] Operation: 60-26=34 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 39:[40, 34], Operations: ['93-33=60', '60-26=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[26, 20], Operations: ['93-33=60', '60-40=20'] Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,39 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,39 unequal: No Solution No 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: 39:[60, 14], Operations: ['93-33=60', '40-26=14'] Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,39 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,39 unequal: No Solution No 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: 39:[60, 66], Operations: ['93-33=60', '40+26=66'] Exploring Operation: 66-60=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 60*66=3960, Resulting Numbers: [3960] 3960,39 unequal: No Solution Exploring Operation: 60+66=126, Resulting Numbers: [126] 126,39 unequal: No Solution No 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: 39:[40, 86], Operations: ['93-33=60', '26+60=86'] Exploring Operation: 40+86=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 40*86=3440, Resulting Numbers: [3440] 3440,39 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,39 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: 39:[40, 93, 7], Operations: ['33-26=7'] Exploring Operation: 40-7=33, Resulting Numbers: [93, 33] Generated Node #0,4,0: 39:[93, 33] Operation: 40-7=33 Exploring Operation: 40+7=47, Resulting Numbers: [93, 47] Generated Node #0,4,1: 39:[93, 47] Operation: 40+7=47 Exploring Operation: 93-40=53, Resulting Numbers: [7, 53] Generated Node #0,4,2: 39:[7, 53] Operation: 93-40=53 Exploring Operation: 93+7=100, Resulting Numbers: [40, 100] Generated Node #0,4,3: 39:[40, 100] Operation: 93+7=100 Exploring Operation: 93-7=86, Resulting Numbers: [40, 86] Generated Node #0,4,4: 39:[40, 86] Operation: 93-7=86 Moving to Node #0,4,2 Current State: 39:[7, 53], Operations: ['33-26=7', '93-40=53'] Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,39 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,39 unequal: No Solution Moving to Node #0,4,4 Current State: 39:[40, 86], Operations: ['33-26=7', '93-7=86'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 40+86=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 40*86=3440, Resulting Numbers: [3440] 3440,39 unequal: No Solution Moving to Node #0,4,0 Current State: 39:[93, 33], Operations: ['33-26=7', '40-7=33'] Exploring Operation: 93+33=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 93*33=3069, Resulting Numbers: [3069] 3069,39 unequal: No Solution Moving to Node #0,4,1 Current State: 39:[93, 47], Operations: ['33-26=7', '40+7=47'] Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,39 unequal: No Solution Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,39 unequal: No Solution Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[40, 100], Operations: ['33-26=7', '93+7=100'] Exploring Operation: 40*100=4000, Resulting Numbers: [4000] 4000,39 unequal: No Solution Exploring Operation: 40+100=140, Resulting Numbers: [140] 140,39 unequal: No Solution Exploring Operation: 100-40=60, Resulting Numbers: [60] 60,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[33, 93, 14], Operations: ['40-26=14'] Exploring Operation: 93-33=60, Resulting Numbers: [14, 60] Generated Node #0,0,0: 39:[14, 60] Operation: 93-33=60 Exploring Operation: 93-14=79, Resulting Numbers: [33, 79] Generated Node #0,0,1: 39:[33, 79] Operation: 93-14=79 Exploring Operation: 33-14=19, Resulting Numbers: [93, 19] Generated Node #0,0,2: 39:[93, 19] Operation: 33-14=19 Exploring Operation: 93+14=107, Resulting Numbers: [33, 107] Generated Node #0,0,3: 39:[33, 107] Operation: 93+14=107 Exploring Operation: 33+14=47, Resulting Numbers: [93, 47] Generated Node #0,0,4: 39:[93, 47] Operation: 33+14=47 Moving to Node #0,0,0 Current State: 39:[14, 60], Operations: ['40-26=14', '93-33=60'] Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 14*60=840, Resulting Numbers: [840] 840,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[33, 79], Operations: ['40-26=14', '93-14=79'] Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,39 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,39 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[93, 19], Operations: ['40-26=14', '33-14=19'] Exploring Operation: 93+19=112, Resulting Numbers: [112] 112,39 unequal: No Solution Exploring Operation: 93*19=1767, Resulting Numbers: [1767] 1767,39 unequal: No Solution Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[93, 47], Operations: ['40-26=14', '33+14=47'] Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,39 unequal: No Solution Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[33, 107], Operations: ['40-26=14', '93+14=107'] Exploring Operation: 33*107=3531, Resulting Numbers: [3531] 3531,39 unequal: No Solution Exploring Operation: 107-33=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 33+107=140, Resulting Numbers: [140] 140,39 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
[ 1, 58, 81, 81 ]
56
[ "58-1=57", "81/81=1", "57-1=56" ]
Current State: 56:[1, 58, 81, 81], Operations: [] Exploring Operation: 58-1=57, Resulting Numbers: [81, 81, 57] Generated Node #2: [81, 81, 57] from Operation: 58-1=57 Current State: 56:[81, 81, 57], Operations: ['58-1=57'] Exploring Operation: 81/81=1, Resulting Numbers: [57, 1] Generated Node #3: [57, 1] from Operation: 81/81=1 Current State: 56:[57, 1], Operations: ['58-1=57', '81/81=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[1, 58, 81, 81], Operations: [] Exploring Operation: 81-58=23, Resulting Numbers: [1, 81, 23] Generated Node #0,0: 56:[1, 81, 23] Operation: 81-58=23 Exploring Operation: 81-81=0, Resulting Numbers: [1, 58, 0] Generated Node #0,1: 56:[1, 58, 0] Operation: 81-81=0 Exploring Operation: 58-1=57, Resulting Numbers: [81, 81, 57] Generated Node #0,2: 56:[81, 81, 57] Operation: 58-1=57 Exploring Operation: 81/81=1, Resulting Numbers: [1, 58, 1] Generated Node #0,3: 56:[1, 58, 1] Operation: 81/81=1 Exploring Operation: 81-58=23, Resulting Numbers: [1, 81, 23] Generated Node #0,4: 56:[1, 81, 23] Operation: 81-58=23 Moving to Node #0,3 Current State: 56:[1, 58, 1], Operations: ['81/81=1'] Exploring Operation: 58/1=58, Resulting Numbers: [1, 58] Generated Node #0,3,0: 56:[1, 58] Operation: 58/1=58 Exploring Operation: 1*58=58, Resulting Numbers: [1, 58] Generated Node #0,3,1: 56:[1, 58] Operation: 1*58=58 Exploring Operation: 58-1=57, Resulting Numbers: [1, 57] Generated Node #0,3,2: 56:[1, 57] Operation: 58-1=57 Exploring Operation: 1+1=2, Resulting Numbers: [58, 2] Generated Node #0,3,3: 56:[58, 2] Operation: 1+1=2 Exploring Operation: 58-1=57, Resulting Numbers: [1, 57] Generated Node #0,3,4: 56:[1, 57] Operation: 58-1=57 Moving to Node #0,1 Current State: 56:[1, 58, 0], Operations: ['81-81=0'] Exploring Operation: 1+0=1, Resulting Numbers: [58, 1] Generated Node #0,1,0: 56:[58, 1] Operation: 1+0=1 Exploring Operation: 58+0=58, Resulting Numbers: [1, 58] Generated Node #0,1,1: 56:[1, 58] Operation: 58+0=58 Exploring Operation: 58-1=57, Resulting Numbers: [0, 57] Generated Node #0,1,2: 56:[0, 57] Operation: 58-1=57 Exploring Operation: 58*0=0, Resulting Numbers: [1, 0] Generated Node #0,1,3: 56:[1, 0] Operation: 58*0=0 Exploring Operation: 1-0=1, Resulting Numbers: [58, 1] Generated Node #0,1,4: 56:[58, 1] Operation: 1-0=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[58, 1], Operations: ['81-81=0', '1+0=1'] Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,56 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[1, 58], Operations: ['81-81=0', '58+0=58'] Exploring Operation: 1*58=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 1+58=59, Resulting Numbers: [59] 59,56 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[0, 57], Operations: ['81-81=0', '58-1=57'] Exploring Operation: 57-0=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 0*57=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 0+57=57, Resulting Numbers: [57] 57,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[1, 0], Operations: ['81-81=0', '58*0=0'] Exploring Operation: 1*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 1-0=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 1+0=1, Resulting Numbers: [1] 1,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 56:[58, 1], Operations: ['81-81=0', '1-0=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,56 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: 56:[1, 81, 23], Operations: ['81-58=23'] Exploring Operation: 1+23=24, Resulting Numbers: [81, 24] Generated Node #0,0,0: 56:[81, 24] Operation: 1+23=24 Exploring Operation: 1*81=81, Resulting Numbers: [23, 81] Generated Node #0,0,1: 56:[23, 81] Operation: 1*81=81 Exploring Operation: 81-1=80, Resulting Numbers: [23, 80] Generated Node #0,0,2: 56:[23, 80] Operation: 81-1=80 Exploring Operation: 81/1=81, Resulting Numbers: [23, 81] Generated Node #0,0,3: 56:[23, 81] Operation: 81/1=81 Exploring Operation: 81-23=58, Resulting Numbers: [1, 58] Generated Node #0,0,4: 56:[1, 58] Operation: 81-23=58 Moving to Node #0,4 Current State: 56:[1, 81, 23], Operations: ['81-58=23'] Exploring Operation: 81-1=80, Resulting Numbers: [23, 80] Generated Node #0,4,0: 56:[23, 80] Operation: 81-1=80 Exploring Operation: 1*81=81, Resulting Numbers: [23, 81] Generated Node #0,4,1: 56:[23, 81] Operation: 1*81=81 Exploring Operation: 81/1=81, Resulting Numbers: [23, 81] Generated Node #0,4,2: 56:[23, 81] Operation: 81/1=81 Exploring Operation: 81-23=58, Resulting Numbers: [1, 58] Generated Node #0,4,3: 56:[1, 58] Operation: 81-23=58 Exploring Operation: 1+23=24, Resulting Numbers: [81, 24] Generated Node #0,4,4: 56:[81, 24] Operation: 1+23=24 Moving to Node #0,2 Current State: 56:[81, 81, 57], Operations: ['58-1=57'] Exploring Operation: 81-57=24, Resulting Numbers: [81, 24] Generated Node #0,2,0: 56:[81, 24] Operation: 81-57=24 Exploring Operation: 81-57=24, Resulting Numbers: [81, 24] Generated Node #0,2,1: 56:[81, 24] Operation: 81-57=24 Exploring Operation: 81+81=162, Resulting Numbers: [57, 162] Generated Node #0,2,2: 56:[57, 162] Operation: 81+81=162 Exploring Operation: 81-81=0, Resulting Numbers: [57, 0] Generated Node #0,2,3: 56:[57, 0] Operation: 81-81=0 Exploring Operation: 81/81=1, Resulting Numbers: [57, 1] Generated Node #0,2,4: 56:[57, 1] Operation: 81/81=1 Moving to Node #0,3,2 Current State: 56:[1, 57], Operations: ['81/81=1', '58-1=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[1, 58, 81, 81], Operations: [] Exploring Operation: 81/81=1, Resulting Numbers: [1, 58, 1] Generated Node #0,3: 56:[1, 58, 1] Operation: 81/81=1 Moving to Node #0,3 Current State: 56:[1, 58, 1], Operations: ['81/81=1'] Exploring Operation: 58-1=57, Resulting Numbers: [1, 57] Generated Node #0,3,2: 56:[1, 57] Operation: 58-1=57 Moving to Node #0,3,2 Current State: 56:[1, 57], Operations: ['81/81=1', '58-1=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.951389
hs_5
mult_heuristic
[ 76, 58, 54, 88 ]
54
[ "76-54=22", "88/22=4", "58-4=54" ]
Current State: 54:[76, 58, 54, 88], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [58, 88, 22] Generated Node #2: [58, 88, 22] from Operation: 76-54=22 Current State: 54:[58, 88, 22], Operations: ['76-54=22'] Exploring Operation: 88/22=4, Resulting Numbers: [58, 4] Generated Node #3: [58, 4] from Operation: 88/22=4 Current State: 54:[58, 4], Operations: ['76-54=22', '88/22=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[76, 58, 54, 88], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [58, 54, 12] Generated Node #0,0: 54:[58, 54, 12] Operation: 88-76=12 Moving to Node #0,0 Current State: 54:[58, 54, 12], Operations: ['88-76=12'] Exploring Operation: 58-54=4, Resulting Numbers: [12, 4] Generated Node #0,0,0: 54:[12, 4] Operation: 58-54=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[12, 4], Operations: ['88-76=12', '58-54=4'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,54 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
[ 68, 73, 28, 67 ]
46
[ "68+73=141", "28+67=95", "141-95=46" ]
Current State: 46:[68, 73, 28, 67], Operations: [] Exploring Operation: 68+73=141, Resulting Numbers: [28, 67, 141] Generated Node #2: [28, 67, 141] from Operation: 68+73=141 Current State: 46:[28, 67, 141], Operations: ['68+73=141'] Exploring Operation: 28+67=95, Resulting Numbers: [141, 95] Generated Node #3: [141, 95] from Operation: 28+67=95 Current State: 46:[141, 95], Operations: ['68+73=141', '28+67=95'] Exploring Operation: 141-95=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[68, 73, 28, 67], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [28, 67, 5] Generated Node #0,0: 46:[28, 67, 5] Operation: 73-68=5 Exploring Operation: 73-28=45, Resulting Numbers: [68, 67, 45] Generated Node #0,1: 46:[68, 67, 45] Operation: 73-28=45 Exploring Operation: 68-28=40, Resulting Numbers: [73, 67, 40] Generated Node #0,2: 46:[73, 67, 40] Operation: 68-28=40 Exploring Operation: 73-67=6, Resulting Numbers: [68, 28, 6] Generated Node #0,3: 46:[68, 28, 6] Operation: 73-67=6 Exploring Operation: 68-67=1, Resulting Numbers: [73, 28, 1] Generated Node #0,4: 46:[73, 28, 1] Operation: 68-67=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[28, 67, 5], Operations: ['73-68=5'] Exploring Operation: 28+5=33, Resulting Numbers: [67, 33] Generated Node #0,0,0: 46:[67, 33] Operation: 28+5=33 Exploring Operation: 67-5=62, Resulting Numbers: [28, 62] Generated Node #0,0,1: 46:[28, 62] Operation: 67-5=62 Exploring Operation: 67-28=39, Resulting Numbers: [5, 39] Generated Node #0,0,2: 46:[5, 39] Operation: 67-28=39 Exploring Operation: 67+5=72, Resulting Numbers: [28, 72] Generated Node #0,0,3: 46:[28, 72] Operation: 67+5=72 Exploring Operation: 28-5=23, Resulting Numbers: [67, 23] Generated Node #0,0,4: 46:[67, 23] Operation: 28-5=23 Moving to Node #0,0,2 Current State: 46:[5, 39], Operations: ['73-68=5', '67-28=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,46 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,46 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[67, 23], Operations: ['73-68=5', '28-5=23'] Exploring Operation: 67+23=90, Resulting Numbers: [90] 90,46 unequal: No Solution Exploring Operation: 67-23=44, Resulting Numbers: [44] 44,46 unequal: No Solution Exploring Operation: 67*23=1541, Resulting Numbers: [1541] 1541,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[28, 62], Operations: ['73-68=5', '67-5=62'] Exploring Operation: 28*62=1736, Resulting Numbers: [1736] 1736,46 unequal: No Solution Exploring Operation: 28+62=90, Resulting Numbers: [90] 90,46 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[67, 33], Operations: ['73-68=5', '28+5=33'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,46 unequal: No Solution Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,46 unequal: No Solution Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[28, 72], Operations: ['73-68=5', '67+5=72'] Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,46 unequal: No Solution Exploring Operation: 28*72=2016, Resulting Numbers: [2016] 2016,46 unequal: No Solution Exploring Operation: 28+72=100, Resulting Numbers: [100] 100,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[68, 28, 6], Operations: ['73-67=6'] Exploring Operation: 68+6=74, Resulting Numbers: [28, 74] Generated Node #0,3,0: 46:[28, 74] Operation: 68+6=74 Exploring Operation: 28-6=22, Resulting Numbers: [68, 22] Generated Node #0,3,1: 46:[68, 22] Operation: 28-6=22 Exploring Operation: 68-6=62, Resulting Numbers: [28, 62] Generated Node #0,3,2: 46:[28, 62] Operation: 68-6=62 Exploring Operation: 68-28=40, Resulting Numbers: [6, 40] Generated Node #0,3,3: 46:[6, 40] Operation: 68-28=40 Exploring Operation: 28+6=34, Resulting Numbers: [68, 34] Generated Node #0,3,4: 46:[68, 34] Operation: 28+6=34 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 46:[6, 40], Operations: ['73-67=6', '68-28=40'] Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[68, 73, 28, 67], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [68, 28, 6] Generated Node #0,3: 46:[68, 28, 6] Operation: 73-67=6 Moving to Node #0,3 Current State: 46:[68, 28, 6], Operations: ['73-67=6'] Exploring Operation: 68-28=40, Resulting Numbers: [6, 40] Generated Node #0,3,3: 46:[6, 40] Operation: 68-28=40 Moving to Node #0,3,3 Current State: 46:[6, 40], Operations: ['73-67=6', '68-28=40'] Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 95, 43, 71, 88 ]
35
[ "95-43=52", "88-71=17", "52-17=35" ]
Current State: 35:[95, 43, 71, 88], Operations: [] Exploring Operation: 95-43=52, Resulting Numbers: [71, 88, 52] Generated Node #2: [71, 88, 52] from Operation: 95-43=52 Current State: 35:[71, 88, 52], Operations: ['95-43=52'] Exploring Operation: 88-71=17, Resulting Numbers: [52, 17] Generated Node #3: [52, 17] from Operation: 88-71=17 Current State: 35:[52, 17], Operations: ['95-43=52', '88-71=17'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[95, 43, 71, 88], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [43, 71, 7] Generated Node #0,0: 35:[43, 71, 7] Operation: 95-88=7 Moving to Node #0,0 Current State: 35:[43, 71, 7], Operations: ['95-88=7'] Exploring Operation: 71-43=28, Resulting Numbers: [7, 28] Generated Node #0,0,0: 35:[7, 28] Operation: 71-43=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[7, 28], Operations: ['95-88=7', '71-43=28'] Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[95, 43, 71, 88], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [43, 71, 7] Generated Node #0,0: 35:[43, 71, 7] Operation: 95-88=7 Moving to Node #0,0 Current State: 35:[43, 71, 7], Operations: ['95-88=7'] Exploring Operation: 71-43=28, Resulting Numbers: [7, 28] Generated Node #0,0,0: 35:[7, 28] Operation: 71-43=28 Moving to Node #0,0,0 Current State: 35:[7, 28], Operations: ['95-88=7', '71-43=28'] Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 51, 64, 18, 8 ]
25
[ "51-18=33", "64/8=8", "33-8=25" ]
Current State: 25:[51, 64, 18, 8], Operations: [] Exploring Operation: 51-18=33, Resulting Numbers: [64, 8, 33] Generated Node #2: [64, 8, 33] from Operation: 51-18=33 Current State: 25:[64, 8, 33], Operations: ['51-18=33'] Exploring Operation: 64/8=8, Resulting Numbers: [33, 8] Generated Node #3: [33, 8] from Operation: 64/8=8 Current State: 25:[33, 8], Operations: ['51-18=33', '64/8=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[51, 64, 18, 8], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [51, 18, 8] Generated Node #0,0: 25:[51, 18, 8] Operation: 64/8=8 Exploring Operation: 51-18=33, Resulting Numbers: [64, 8, 33] Generated Node #0,1: 25:[64, 8, 33] Operation: 51-18=33 Exploring Operation: 64-18=46, Resulting Numbers: [51, 8, 46] Generated Node #0,2: 25:[51, 8, 46] Operation: 64-18=46 Exploring Operation: 64-51=13, Resulting Numbers: [18, 8, 13] Generated Node #0,3: 25:[18, 8, 13] Operation: 64-51=13 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[18, 8, 13], Operations: ['64-51=13'] Exploring Operation: 18+8=26, Resulting Numbers: [13, 26] Generated Node #0,3,0: 25:[13, 26] Operation: 18+8=26 Exploring Operation: 18+13=31, Resulting Numbers: [8, 31] Generated Node #0,3,1: 25:[8, 31] Operation: 18+13=31 Exploring Operation: 13-8=5, Resulting Numbers: [18, 5] Generated Node #0,3,2: 25:[18, 5] Operation: 13-8=5 Exploring Operation: 18-13=5, Resulting Numbers: [8, 5] Generated Node #0,3,3: 25:[8, 5] Operation: 18-13=5 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 25:[8, 5], Operations: ['64-51=13', '18-13=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,25 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,25 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 25:[18, 5], Operations: ['64-51=13', '13-8=5'] Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 25:[13, 26], Operations: ['64-51=13', '18+8=26'] Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,25 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,25 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 25:[8, 31], Operations: ['64-51=13', '18+13=31'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,25 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[51, 18, 8], Operations: ['64/8=8'] Exploring Operation: 51-8=43, Resulting Numbers: [18, 43] Generated Node #0,0,0: 25:[18, 43] Operation: 51-8=43 Exploring Operation: 51-18=33, Resulting Numbers: [8, 33] Generated Node #0,0,1: 25:[8, 33] Operation: 51-18=33 Exploring Operation: 18+8=26, Resulting Numbers: [51, 26] Generated Node #0,0,2: 25:[51, 26] Operation: 18+8=26 Exploring Operation: 18-8=10, Resulting Numbers: [51, 10] Generated Node #0,0,3: 25:[51, 10] Operation: 18-8=10 Moving to Node #0,0,1 Current State: 25:[8, 33], Operations: ['64/8=8', '51-18=33'] Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,25 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[51, 64, 18, 8], Operations: [] Exploring Operation: 64/8=8, Resulting Numbers: [51, 18, 8] Generated Node #0,0: 25:[51, 18, 8] Operation: 64/8=8 Moving to Node #0,0 Current State: 25:[51, 18, 8], Operations: ['64/8=8'] Exploring Operation: 51-18=33, Resulting Numbers: [8, 33] Generated Node #0,0,1: 25:[8, 33] Operation: 51-18=33 Moving to Node #0,0,1 Current State: 25:[8, 33], Operations: ['64/8=8', '51-18=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 8, 55, 57, 59 ]
51
[ "59-57=2", "8/2=4", "55-4=51" ]
Current State: 51:[8, 55, 57, 59], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [8, 55, 2] Generated Node #2: [8, 55, 2] from Operation: 59-57=2 Current State: 51:[8, 55, 2], Operations: ['59-57=2'] Exploring Operation: 8/2=4, Resulting Numbers: [55, 4] Generated Node #3: [55, 4] from Operation: 8/2=4 Current State: 51:[55, 4], Operations: ['59-57=2', '8/2=4'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[8, 55, 57, 59], Operations: [] Exploring Operation: 59-8=51, Resulting Numbers: [55, 57, 51] Generated Node #0,0: 51:[55, 57, 51] Operation: 59-8=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[55, 57, 51], Operations: ['59-8=51'] Exploring Operation: 57-55=2, Resulting Numbers: [51, 2] Generated Node #0,0,0: 51:[51, 2] Operation: 57-55=2 Moving to Node #0,0,0 Current State: 51:[51, 2], Operations: ['59-8=51', '57-55=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,51 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
[ 78, 79, 72, 97 ]
24
[ "79-78=1", "97-72=25", "25-1=24" ]
Current State: 24:[78, 79, 72, 97], Operations: [] Exploring Operation: 79-78=1, Resulting Numbers: [72, 97, 1] Generated Node #2: [72, 97, 1] from Operation: 79-78=1 Current State: 24:[72, 97, 1], Operations: ['79-78=1'] Exploring Operation: 97-72=25, Resulting Numbers: [1, 25] Generated Node #3: [1, 25] from Operation: 97-72=25 Current State: 24:[1, 25], Operations: ['79-78=1', '97-72=25'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[78, 79, 72, 97], Operations: [] Exploring Operation: 97-72=25, Resulting Numbers: [78, 79, 25] Generated Node #0,0: 24:[78, 79, 25] Operation: 97-72=25 Exploring Operation: 97-78=19, Resulting Numbers: [79, 72, 19] Generated Node #0,1: 24:[79, 72, 19] Operation: 97-78=19 Exploring Operation: 97-79=18, Resulting Numbers: [78, 72, 18] Generated Node #0,2: 24:[78, 72, 18] Operation: 97-79=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[79, 72, 19], Operations: ['97-78=19'] Exploring Operation: 79-72=7, Resulting Numbers: [19, 7] Generated Node #0,1,0: 24:[19, 7] Operation: 79-72=7 Exploring Operation: 72-19=53, Resulting Numbers: [79, 53] Generated Node #0,1,1: 24:[79, 53] Operation: 72-19=53 Exploring Operation: 79-19=60, Resulting Numbers: [72, 60] Generated Node #0,1,2: 24:[72, 60] Operation: 79-19=60 Moving to Node #0,1,0 Current State: 24:[19, 7], Operations: ['97-78=19', '79-72=7'] Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,24 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[79, 53], Operations: ['97-78=19', '72-19=53'] Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,24 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,24 unequal: No Solution Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[72, 60], Operations: ['97-78=19', '79-19=60'] Exploring Operation: 72*60=4320, Resulting Numbers: [4320] 4320,24 unequal: No Solution Exploring Operation: 72+60=132, Resulting Numbers: [132] 132,24 unequal: No Solution Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[78, 72, 18], Operations: ['97-79=18'] Exploring Operation: 72/18=4, Resulting Numbers: [78, 4] Generated Node #0,2,0: 24:[78, 4] Operation: 72/18=4 Exploring Operation: 78-18=60, Resulting Numbers: [72, 60] Generated Node #0,2,1: 24:[72, 60] Operation: 78-18=60 Exploring Operation: 78-72=6, Resulting Numbers: [18, 6] Generated Node #0,2,2: 24:[18, 6] Operation: 78-72=6 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[18, 6], Operations: ['97-79=18', '78-72=6'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[78, 79, 72, 97], Operations: [] Exploring Operation: 97-79=18, Resulting Numbers: [78, 72, 18] Generated Node #0,2: 24:[78, 72, 18] Operation: 97-79=18 Moving to Node #0,2 Current State: 24:[78, 72, 18], Operations: ['97-79=18'] Exploring Operation: 78-72=6, Resulting Numbers: [18, 6] Generated Node #0,2,2: 24:[18, 6] Operation: 78-72=6 Moving to Node #0,2,2 Current State: 24:[18, 6], Operations: ['97-79=18', '78-72=6'] Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 4, 2, 9, 47 ]
99
[ "9-4=5", "2*47=94", "5+94=99" ]
Current State: 99:[4, 2, 9, 47], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [2, 47, 5] Generated Node #2: [2, 47, 5] from Operation: 9-4=5 Current State: 99:[2, 47, 5], Operations: ['9-4=5'] Exploring Operation: 2*47=94, Resulting Numbers: [5, 94] Generated Node #3: [5, 94] from Operation: 2*47=94 Current State: 99:[5, 94], Operations: ['9-4=5', '2*47=94'] Exploring Operation: 5+94=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[4, 2, 9, 47], Operations: [] Exploring Operation: 47-9=38, Resulting Numbers: [4, 2, 38] Generated Node #0,0: 99:[4, 2, 38] Operation: 47-9=38 Exploring Operation: 2*47=94, Resulting Numbers: [4, 9, 94] Generated Node #0,1: 99:[4, 9, 94] Operation: 2*47=94 Exploring Operation: 4*2=8, Resulting Numbers: [9, 47, 8] Generated Node #0,2: 99:[9, 47, 8] Operation: 4*2=8 Exploring Operation: 47-4=43, Resulting Numbers: [2, 9, 43] Generated Node #0,3: 99:[2, 9, 43] Operation: 47-4=43 Exploring Operation: 47-2=45, Resulting Numbers: [4, 9, 45] Generated Node #0,4: 99:[4, 9, 45] Operation: 47-2=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[4, 9, 94], Operations: ['2*47=94'] Exploring Operation: 4+9=13, Resulting Numbers: [94, 13] Generated Node #0,1,0: 99:[94, 13] Operation: 4+9=13 Exploring Operation: 4+94=98, Resulting Numbers: [9, 98] Generated Node #0,1,1: 99:[9, 98] Operation: 4+94=98 Exploring Operation: 4*9=36, Resulting Numbers: [94, 36] Generated Node #0,1,2: 99:[94, 36] Operation: 4*9=36 Exploring Operation: 9-4=5, Resulting Numbers: [94, 5] Generated Node #0,1,3: 99:[94, 5] Operation: 9-4=5 Exploring Operation: 9+94=103, Resulting Numbers: [4, 103] Generated Node #0,1,4: 99:[4, 103] Operation: 9+94=103 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[9, 98], Operations: ['2*47=94', '4+94=98'] Exploring Operation: 9*98=882, Resulting Numbers: [882] 882,99 unequal: No Solution Exploring Operation: 9+98=107, Resulting Numbers: [107] 107,99 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,99 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 #0,1,4 Current State: 99:[4, 103], Operations: ['2*47=94', '9+94=103'] Exploring Operation: 4*103=412, Resulting Numbers: [412] 412,99 unequal: No Solution Exploring Operation: 103-4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[4, 2, 9, 47], Operations: [] Exploring Operation: 2*47=94, Resulting Numbers: [4, 9, 94] Generated Node #0,1: 99:[4, 9, 94] Operation: 2*47=94 Moving to Node #0,1 Current State: 99:[4, 9, 94], Operations: ['2*47=94'] Exploring Operation: 9+94=103, Resulting Numbers: [4, 103] Generated Node #0,1,4: 99:[4, 103] Operation: 9+94=103 Moving to Node #0,1,4 Current State: 99:[4, 103], Operations: ['2*47=94', '9+94=103'] Exploring Operation: 103-4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 50, 57, 6, 21 ]
53
[ "57+6=63", "63/21=3", "50+3=53" ]
Current State: 53:[50, 57, 6, 21], Operations: [] Exploring Operation: 57+6=63, Resulting Numbers: [50, 21, 63] Generated Node #2: [50, 21, 63] from Operation: 57+6=63 Current State: 53:[50, 21, 63], Operations: ['57+6=63'] Exploring Operation: 63/21=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 63/21=3 Current State: 53:[50, 3], Operations: ['57+6=63', '63/21=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[50, 57, 6, 21], Operations: [] Exploring Operation: 6+21=27, Resulting Numbers: [50, 57, 27] Generated Node #0,0: 53:[50, 57, 27] Operation: 6+21=27 Exploring Operation: 57-6=51, Resulting Numbers: [50, 21, 51] Generated Node #0,1: 53:[50, 21, 51] Operation: 57-6=51 Exploring Operation: 50+6=56, Resulting Numbers: [57, 21, 56] Generated Node #0,2: 53:[57, 21, 56] Operation: 50+6=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[50, 57, 27], Operations: ['6+21=27'] Exploring Operation: 50+27=77, Resulting Numbers: [57, 77] Generated Node #0,0,0: 53:[57, 77] Operation: 50+27=77 Exploring Operation: 50-27=23, Resulting Numbers: [57, 23] Generated Node #0,0,1: 53:[57, 23] Operation: 50-27=23 Exploring Operation: 57-27=30, Resulting Numbers: [50, 30] Generated Node #0,0,2: 53:[50, 30] Operation: 57-27=30 Moving to Node #0,0,2 Current State: 53:[50, 30], Operations: ['6+21=27', '57-27=30'] Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[57, 77], Operations: ['6+21=27', '50+27=77'] Exploring Operation: 57*77=4389, Resulting Numbers: [4389] 4389,53 unequal: No Solution Exploring Operation: 77-57=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 57+77=134, Resulting Numbers: [134] 134,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[57, 23], Operations: ['6+21=27', '50-27=23'] Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,53 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[50, 21, 51], Operations: ['57-6=51'] Exploring Operation: 50-21=29, Resulting Numbers: [51, 29] Generated Node #0,1,0: 53:[51, 29] Operation: 50-21=29 Exploring Operation: 21+51=72, Resulting Numbers: [50, 72] Generated Node #0,1,1: 53:[50, 72] Operation: 21+51=72 Exploring Operation: 50+21=71, Resulting Numbers: [51, 71] Generated Node #0,1,2: 53:[51, 71] Operation: 50+21=71 Moving to Node #0,1,2 Current State: 53:[51, 71], Operations: ['57-6=51', '50+21=71'] Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,53 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[50, 72], Operations: ['57-6=51', '21+51=72'] Exploring Operation: 50+72=122, Resulting Numbers: [122] 122,53 unequal: No Solution Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 50*72=3600, Resulting Numbers: [3600] 3600,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[51, 29], Operations: ['57-6=51', '50-21=29'] Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 51*29=1479, Resulting Numbers: [1479] 1479,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[57, 21, 56], Operations: ['50+6=56'] Exploring Operation: 57-21=36, Resulting Numbers: [56, 36] Generated Node #0,2,0: 53:[56, 36] Operation: 57-21=36 Exploring Operation: 57+21=78, Resulting Numbers: [56, 78] Generated Node #0,2,1: 53:[56, 78] Operation: 57+21=78 Exploring Operation: 56-21=35, Resulting Numbers: [57, 35] Generated Node #0,2,2: 53:[57, 35] Operation: 56-21=35 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[56, 36], Operations: ['50+6=56', '57-21=36'] Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,53 unequal: No Solution Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,53 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 #0,2,2 Current State: 53:[57, 35], Operations: ['50+6=56', '56-21=35'] Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,53 unequal: No Solution Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,53 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,53 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 #0,2,1 Current State: 53:[56, 78], Operations: ['50+6=56', '57+21=78'] Exploring Operation: 78-56=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 56*78=4368, Resulting Numbers: [4368] 4368,53 unequal: No Solution Exploring Operation: 56+78=134, Resulting Numbers: [134] 134,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 31, 19, 52, 77 ]
79
[ "31+19=50", "52+77=129", "129-50=79" ]
Current State: 79:[31, 19, 52, 77], Operations: [] Exploring Operation: 31+19=50, Resulting Numbers: [52, 77, 50] Generated Node #2: [52, 77, 50] from Operation: 31+19=50 Current State: 79:[52, 77, 50], Operations: ['31+19=50'] Exploring Operation: 52+77=129, Resulting Numbers: [50, 129] Generated Node #3: [50, 129] from Operation: 52+77=129 Current State: 79:[50, 129], Operations: ['31+19=50', '52+77=129'] Exploring Operation: 129-50=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[31, 19, 52, 77], Operations: [] Exploring Operation: 31+19=50, Resulting Numbers: [52, 77, 50] Generated Node #0,0: 79:[52, 77, 50] Operation: 31+19=50 Exploring Operation: 19+52=71, Resulting Numbers: [31, 77, 71] Generated Node #0,1: 79:[31, 77, 71] Operation: 19+52=71 Moving to Node #0,0 Current State: 79:[52, 77, 50], Operations: ['31+19=50'] Exploring Operation: 52+50=102, Resulting Numbers: [77, 102] Generated Node #0,0,0: 79:[77, 102] Operation: 52+50=102 Exploring Operation: 77+50=127, Resulting Numbers: [52, 127] Generated Node #0,0,1: 79:[52, 127] Operation: 77+50=127 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[77, 102], Operations: ['31+19=50', '52+50=102'] Exploring Operation: 77+102=179, Resulting Numbers: [179] 179,79 unequal: No Solution Exploring Operation: 102-77=25, Resulting Numbers: [25] 25,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[52, 127], Operations: ['31+19=50', '77+50=127'] Exploring Operation: 127-52=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 52+127=179, Resulting Numbers: [179] 179,79 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: 79:[31, 77, 71], Operations: ['19+52=71'] Exploring Operation: 31+71=102, Resulting Numbers: [77, 102] Generated Node #0,1,0: 79:[77, 102] Operation: 31+71=102 Exploring Operation: 31+77=108, Resulting Numbers: [71, 108] Generated Node #0,1,1: 79:[71, 108] Operation: 31+77=108 Moving to Node #0,1,0 Current State: 79:[77, 102], Operations: ['19+52=71', '31+71=102'] Exploring Operation: 102-77=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 77+102=179, Resulting Numbers: [179] 179,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[71, 108], Operations: ['19+52=71', '31+77=108'] Exploring Operation: 108-71=37, Resulting Numbers: [37] 37,79 unequal: No Solution Exploring Operation: 71+108=179, Resulting Numbers: [179] 179,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 42, 48, 11, 63 ]
80
[ "48-42=6", "11+63=74", "6+74=80" ]
Current State: 80:[42, 48, 11, 63], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [11, 63, 6] Generated Node #2: [11, 63, 6] from Operation: 48-42=6 Current State: 80:[11, 63, 6], Operations: ['48-42=6'] Exploring Operation: 11+63=74, Resulting Numbers: [6, 74] Generated Node #3: [6, 74] from Operation: 11+63=74 Current State: 80:[6, 74], Operations: ['48-42=6', '11+63=74'] Exploring Operation: 6+74=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[42, 48, 11, 63], Operations: [] Exploring Operation: 63-42=21, Resulting Numbers: [48, 11, 21] Generated Node #0,0: 80:[48, 11, 21] Operation: 63-42=21 Exploring Operation: 63-48=15, Resulting Numbers: [42, 11, 15] Generated Node #0,1: 80:[42, 11, 15] Operation: 63-48=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[42, 11, 15], Operations: ['63-48=15'] Exploring Operation: 42-15=27, Resulting Numbers: [11, 27] Generated Node #0,1,0: 80:[11, 27] Operation: 42-15=27 Exploring Operation: 15-11=4, Resulting Numbers: [42, 4] Generated Node #0,1,1: 80:[42, 4] Operation: 15-11=4 Moving to Node #0,1,1 Current State: 80:[42, 4], Operations: ['63-48=15', '15-11=4'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[11, 27], Operations: ['63-48=15', '42-15=27'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[48, 11, 21], Operations: ['63-42=21'] Exploring Operation: 48-11=37, Resulting Numbers: [21, 37] Generated Node #0,0,0: 80:[21, 37] Operation: 48-11=37 Exploring Operation: 48-21=27, Resulting Numbers: [11, 27] Generated Node #0,0,1: 80:[11, 27] Operation: 48-21=27 Moving to Node #0,0,0 Current State: 80:[21, 37], Operations: ['63-42=21', '48-11=37'] Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[11, 27], Operations: ['63-42=21', '48-21=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 22, 21, 9, 49 ]
43
[ "9*49=441", "441/21=21", "22+21=43" ]
Current State: 43:[22, 21, 9, 49], Operations: [] Exploring Operation: 9*49=441, Resulting Numbers: [22, 21, 441] Generated Node #2: [22, 21, 441] from Operation: 9*49=441 Current State: 43:[22, 21, 441], Operations: ['9*49=441'] Exploring Operation: 441/21=21, Resulting Numbers: [22, 21] Generated Node #3: [22, 21] from Operation: 441/21=21 Current State: 43:[22, 21], Operations: ['9*49=441', '441/21=21'] Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[22, 21, 9, 49], Operations: [] Exploring Operation: 21+9=30, Resulting Numbers: [22, 49, 30] Generated Node #0,0: 43:[22, 49, 30] Operation: 21+9=30 Exploring Operation: 22-9=13, Resulting Numbers: [21, 49, 13] Generated Node #0,1: 43:[21, 49, 13] Operation: 22-9=13 Exploring Operation: 49-9=40, Resulting Numbers: [22, 21, 40] Generated Node #0,2: 43:[22, 21, 40] Operation: 49-9=40 Exploring Operation: 22+21=43, Resulting Numbers: [9, 49, 43] Generated Node #0,3: 43:[9, 49, 43] Operation: 22+21=43 Exploring Operation: 22+9=31, Resulting Numbers: [21, 49, 31] Generated Node #0,4: 43:[21, 49, 31] Operation: 22+9=31 Moving to Node #0,0 Current State: 43:[22, 49, 30], Operations: ['21+9=30'] Exploring Operation: 49-30=19, Resulting Numbers: [22, 19] Generated Node #0,0,0: 43:[22, 19] Operation: 49-30=19 Exploring Operation: 49-22=27, Resulting Numbers: [30, 27] Generated Node #0,0,1: 43:[30, 27] Operation: 49-22=27 Exploring Operation: 22+49=71, Resulting Numbers: [30, 71] Generated Node #0,0,2: 43:[30, 71] Operation: 22+49=71 Exploring Operation: 22+30=52, Resulting Numbers: [49, 52] Generated Node #0,0,3: 43:[49, 52] Operation: 22+30=52 Exploring Operation: 30-22=8, Resulting Numbers: [49, 8] Generated Node #0,0,4: 43:[49, 8] Operation: 30-22=8 Moving to Node #0,4 Current State: 43:[21, 49, 31], Operations: ['22+9=31'] Exploring Operation: 31-21=10, Resulting Numbers: [49, 10] Generated Node #0,4,0: 43:[49, 10] Operation: 31-21=10 Exploring Operation: 21+31=52, Resulting Numbers: [49, 52] Generated Node #0,4,1: 43:[49, 52] Operation: 21+31=52 Exploring Operation: 49-31=18, Resulting Numbers: [21, 18] Generated Node #0,4,2: 43:[21, 18] Operation: 49-31=18 Exploring Operation: 21+49=70, Resulting Numbers: [31, 70] Generated Node #0,4,3: 43:[31, 70] Operation: 21+49=70 Exploring Operation: 49-21=28, Resulting Numbers: [31, 28] Generated Node #0,4,4: 43:[31, 28] Operation: 49-21=28 Moving to Node #0,3 Current State: 43:[9, 49, 43], Operations: ['22+21=43'] Exploring Operation: 49-43=6, Resulting Numbers: [9, 6] Generated Node #0,3,0: 43:[9, 6] Operation: 49-43=6 Exploring Operation: 9+43=52, Resulting Numbers: [49, 52] Generated Node #0,3,1: 43:[49, 52] Operation: 9+43=52 Exploring Operation: 9+49=58, Resulting Numbers: [43, 58] Generated Node #0,3,2: 43:[43, 58] Operation: 9+49=58 Exploring Operation: 43-9=34, Resulting Numbers: [49, 34] Generated Node #0,3,3: 43:[49, 34] Operation: 43-9=34 Exploring Operation: 49-9=40, Resulting Numbers: [43, 40] Generated Node #0,3,4: 43:[43, 40] Operation: 49-9=40 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 43:[43, 40], Operations: ['22+21=43', '49-9=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 43*40=1720, Resulting Numbers: [1720] 1720,43 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,43 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 #0,3,1 Current State: 43:[49, 52], Operations: ['22+21=43', '9+43=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,43 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,43 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,43 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 #0,3,2 Current State: 43:[43, 58], Operations: ['22+21=43', '9+49=58'] Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 43+58=101, Resulting Numbers: [101] 101,43 unequal: No Solution Exploring Operation: 43*58=2494, Resulting Numbers: [2494] 2494,43 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 #0,3,3 Current State: 43:[49, 34], Operations: ['22+21=43', '43-9=34'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,43 unequal: No Solution Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,43 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 #0,3,0 Current State: 43:[9, 6], Operations: ['22+21=43', '49-43=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 43:[22, 21, 40], Operations: ['49-9=40'] Exploring Operation: 21+40=61, Resulting Numbers: [22, 61] Generated Node #0,2,0: 43:[22, 61] Operation: 21+40=61 Exploring Operation: 22+40=62, Resulting Numbers: [21, 62] Generated Node #0,2,1: 43:[21, 62] Operation: 22+40=62 Exploring Operation: 22+21=43, Resulting Numbers: [40, 43] Generated Node #0,2,2: 43:[40, 43] Operation: 22+21=43 Exploring Operation: 40-21=19, Resulting Numbers: [22, 19] Generated Node #0,2,3: 43:[22, 19] Operation: 40-21=19 Exploring Operation: 22-21=1, Resulting Numbers: [40, 1] Generated Node #0,2,4: 43:[40, 1] Operation: 22-21=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[40, 43], Operations: ['49-9=40', '22+21=43'] Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,43 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 #0,2,0 Current State: 43:[22, 61], Operations: ['49-9=40', '21+40=61'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 22+61=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 22*61=1342, Resulting Numbers: [1342] 1342,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[21, 62], Operations: ['49-9=40', '22+40=62'] Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,43 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,43 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 43:[22, 19], Operations: ['49-9=40', '40-21=19'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,43 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,43 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 #0,2,4 Current State: 43:[40, 1], Operations: ['49-9=40', '22-21=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,43 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: 43:[21, 49, 13], Operations: ['22-9=13'] Exploring Operation: 21+13=34, Resulting Numbers: [49, 34] Generated Node #0,1,0: 43:[49, 34] Operation: 21+13=34 Exploring Operation: 49-13=36, Resulting Numbers: [21, 36] Generated Node #0,1,1: 43:[21, 36] Operation: 49-13=36 Exploring Operation: 49-21=28, Resulting Numbers: [13, 28] Generated Node #0,1,2: 43:[13, 28] Operation: 49-21=28 Exploring Operation: 49+13=62, Resulting Numbers: [21, 62] Generated Node #0,1,3: 43:[21, 62] Operation: 49+13=62 Exploring Operation: 21-13=8, Resulting Numbers: [49, 8] Generated Node #0,1,4: 43:[49, 8] Operation: 21-13=8 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[49, 34], Operations: ['22-9=13', '21+13=34'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,43 unequal: No Solution Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[21, 36], Operations: ['22-9=13', '49-13=36'] Exploring Operation: 21*36=756, Resulting Numbers: [756] 756,43 unequal: No Solution Exploring Operation: 21+36=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 43:[21, 62], Operations: ['22-9=13', '49+13=62'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,43 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 43:[49, 8], Operations: ['22-9=13', '21-13=8'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,43 unequal: No Solution Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[13, 28], Operations: ['22-9=13', '49-21=28'] Exploring Operation: 13*28=364, Resulting Numbers: [364] 364,43 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 43:[49, 52], Operations: ['21+9=30', '22+30=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,43 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[49, 52], Operations: ['22+9=31', '21+31=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,43 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,43 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[31, 28], Operations: ['22+9=31', '49-21=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,43 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[30, 27], Operations: ['21+9=30', '49-22=27'] Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,43 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,43 unequal: No Solution Moving to Node #0,4,3 Current State: 43:[31, 70], Operations: ['22+9=31', '21+49=70'] Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,43 unequal: No Solution Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[49, 10], Operations: ['22+9=31', '31-21=10'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,43 unequal: No Solution Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[30, 71], Operations: ['21+9=30', '22+49=71'] 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 Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[49, 8], Operations: ['21+9=30', '30-22=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 49*8=392, Resulting Numbers: [392] 392,43 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[22, 19], Operations: ['21+9=30', '49-30=19'] Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,43 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[21, 18], Operations: ['22+9=31', '49-31=18'] Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,43 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,43 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 11, 97, 12, 66 ]
99
[ "11*12=132", "132/66=2", "97+2=99" ]
Current State: 99:[11, 97, 12, 66], Operations: [] Exploring Operation: 11*12=132, Resulting Numbers: [97, 66, 132] Generated Node #2: [97, 66, 132] from Operation: 11*12=132 Current State: 99:[97, 66, 132], Operations: ['11*12=132'] Exploring Operation: 132/66=2, Resulting Numbers: [97, 2] Generated Node #3: [97, 2] from Operation: 132/66=2 Current State: 99:[97, 2], Operations: ['11*12=132', '132/66=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[11, 97, 12, 66], Operations: [] Exploring Operation: 12+66=78, Resulting Numbers: [11, 97, 78] Generated Node #0,0: 99:[11, 97, 78] Operation: 12+66=78 Exploring Operation: 66/11=6, Resulting Numbers: [97, 12, 6] Generated Node #0,1: 99:[97, 12, 6] Operation: 66/11=6 Exploring Operation: 97-66=31, Resulting Numbers: [11, 12, 31] Generated Node #0,2: 99:[11, 12, 31] Operation: 97-66=31 Exploring Operation: 66-12=54, Resulting Numbers: [11, 97, 54] Generated Node #0,3: 99:[11, 97, 54] Operation: 66-12=54 Moving to Node #0,2 Current State: 99:[11, 12, 31], Operations: ['97-66=31'] Exploring Operation: 31-12=19, Resulting Numbers: [11, 19] Generated Node #0,2,0: 99:[11, 19] Operation: 31-12=19 Exploring Operation: 31-11=20, Resulting Numbers: [12, 20] Generated Node #0,2,1: 99:[12, 20] Operation: 31-11=20 Exploring Operation: 12-11=1, Resulting Numbers: [31, 1] Generated Node #0,2,2: 99:[31, 1] Operation: 12-11=1 Exploring Operation: 11+31=42, Resulting Numbers: [12, 42] Generated Node #0,2,3: 99:[12, 42] Operation: 11+31=42 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[31, 1], Operations: ['97-66=31', '12-11=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,99 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:[11, 19], Operations: ['97-66=31', '31-12=19'] Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,99 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,99 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:[12, 20], Operations: ['97-66=31', '31-11=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,99 unequal: No Solution Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 99:[12, 42], Operations: ['97-66=31', '11+31=42'] Exploring Operation: 12+42=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 12*42=504, Resulting Numbers: [504] 504,99 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:[97, 12, 6], Operations: ['66/11=6'] Exploring Operation: 97-6=91, Resulting Numbers: [12, 91] Generated Node #0,1,0: 99:[12, 91] Operation: 97-6=91 Exploring Operation: 12/6=2, Resulting Numbers: [97, 2] Generated Node #0,1,1: 99:[97, 2] Operation: 12/6=2 Exploring Operation: 12-6=6, Resulting Numbers: [97, 6] Generated Node #0,1,2: 99:[97, 6] Operation: 12-6=6 Exploring Operation: 97+6=103, Resulting Numbers: [12, 103] Generated Node #0,1,3: 99:[12, 103] Operation: 97+6=103 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[97, 2], Operations: ['66/11=6', '12/6=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[11, 97, 12, 66], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [97, 12, 6] Generated Node #0,1: 99:[97, 12, 6] Operation: 66/11=6 Moving to Node #0,1 Current State: 99:[97, 12, 6], Operations: ['66/11=6'] Exploring Operation: 12/6=2, Resulting Numbers: [97, 2] Generated Node #0,1,1: 99:[97, 2] Operation: 12/6=2 Moving to Node #0,1,1 Current State: 99:[97, 2], Operations: ['66/11=6', '12/6=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 98, 94, 51, 88 ]
29
[ "98-94=4", "88/4=22", "51-22=29" ]
Current State: 29:[98, 94, 51, 88], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [51, 88, 4] Generated Node #2: [51, 88, 4] from Operation: 98-94=4 Current State: 29:[51, 88, 4], Operations: ['98-94=4'] Exploring Operation: 88/4=22, Resulting Numbers: [51, 22] Generated Node #3: [51, 22] from Operation: 88/4=22 Current State: 29:[51, 22], Operations: ['98-94=4', '88/4=22'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[98, 94, 51, 88], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [94, 51, 10] Generated Node #0,0: 29:[94, 51, 10] Operation: 98-88=10 Exploring Operation: 98-94=4, Resulting Numbers: [51, 88, 4] Generated Node #0,1: 29:[51, 88, 4] Operation: 98-94=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[94, 51, 10], Operations: ['98-88=10'] Exploring Operation: 94-51=43, Resulting Numbers: [10, 43] Generated Node #0,0,0: 29:[10, 43] Operation: 94-51=43 Exploring Operation: 94-10=84, Resulting Numbers: [51, 84] Generated Node #0,0,1: 29:[51, 84] Operation: 94-10=84 Moving to Node #0,0,0 Current State: 29:[10, 43], Operations: ['98-88=10', '94-51=43'] Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,29 unequal: No Solution Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[51, 84], Operations: ['98-88=10', '94-10=84'] Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,29 unequal: No Solution Exploring Operation: 51+84=135, Resulting Numbers: [135] 135,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[51, 88, 4], Operations: ['98-94=4'] Exploring Operation: 88/4=22, Resulting Numbers: [51, 22] Generated Node #0,1,0: 29:[51, 22] Operation: 88/4=22 Exploring Operation: 88-51=37, Resulting Numbers: [4, 37] Generated Node #0,1,1: 29:[4, 37] Operation: 88-51=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[51, 22], Operations: ['98-94=4', '88/4=22'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[98, 94, 51, 88], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [51, 88, 4] Generated Node #0,1: 29:[51, 88, 4] Operation: 98-94=4 Moving to Node #0,1 Current State: 29:[51, 88, 4], Operations: ['98-94=4'] Exploring Operation: 88/4=22, Resulting Numbers: [51, 22] Generated Node #0,1,0: 29:[51, 22] Operation: 88/4=22 Moving to Node #0,1,0 Current State: 29:[51, 22], Operations: ['98-94=4', '88/4=22'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 43, 48, 77, 4 ]
57
[ "48-43=5", "4*5=20", "77-20=57" ]
Current State: 57:[43, 48, 77, 4], Operations: [] Exploring Operation: 48-43=5, Resulting Numbers: [77, 4, 5] Generated Node #2: [77, 4, 5] from Operation: 48-43=5 Current State: 57:[77, 4, 5], Operations: ['48-43=5'] Exploring Operation: 4*5=20, Resulting Numbers: [77, 20] Generated Node #3: [77, 20] from Operation: 4*5=20 Current State: 57:[77, 20], Operations: ['48-43=5', '4*5=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[43, 48, 77, 4], Operations: [] Exploring Operation: 48-43=5, Resulting Numbers: [77, 4, 5] Generated Node #0,0: 57:[77, 4, 5] Operation: 48-43=5 Moving to Node #0,0 Current State: 57:[77, 4, 5], Operations: ['48-43=5'] Exploring Operation: 77-5=72, Resulting Numbers: [4, 72] Generated Node #0,0,0: 57:[4, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[4, 72], Operations: ['48-43=5', '77-5=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 12, 20, 89, 40 ]
99
[ "12+89=101", "40/20=2", "101-2=99" ]
Current State: 99:[12, 20, 89, 40], Operations: [] Exploring Operation: 12+89=101, Resulting Numbers: [20, 40, 101] Generated Node #2: [20, 40, 101] from Operation: 12+89=101 Current State: 99:[20, 40, 101], Operations: ['12+89=101'] Exploring Operation: 40/20=2, Resulting Numbers: [101, 2] Generated Node #3: [101, 2] from Operation: 40/20=2 Current State: 99:[101, 2], Operations: ['12+89=101', '40/20=2'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[12, 20, 89, 40], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [12, 89, 2] Generated Node #0,0: 99:[12, 89, 2] Operation: 40/20=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[12, 89, 2], Operations: ['40/20=2'] Exploring Operation: 12+89=101, Resulting Numbers: [2, 101] Generated Node #0,0,0: 99:[2, 101] Operation: 12+89=101 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[2, 101], Operations: ['40/20=2', '12+89=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[12, 20, 89, 40], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [12, 89, 2] Generated Node #0,0: 99:[12, 89, 2] Operation: 40/20=2 Moving to Node #0,0 Current State: 99:[12, 89, 2], Operations: ['40/20=2'] Exploring Operation: 12+89=101, Resulting Numbers: [2, 101] Generated Node #0,0,0: 99:[2, 101] Operation: 12+89=101 Moving to Node #0,0,0 Current State: 99:[2, 101], Operations: ['40/20=2', '12+89=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 63, 64, 21, 15 ]
37
[ "64-63=1", "21+15=36", "1+36=37" ]
Current State: 37:[63, 64, 21, 15], Operations: [] Exploring Operation: 64-63=1, Resulting Numbers: [21, 15, 1] Generated Node #2: [21, 15, 1] from Operation: 64-63=1 Current State: 37:[21, 15, 1], Operations: ['64-63=1'] Exploring Operation: 21+15=36, Resulting Numbers: [1, 36] Generated Node #3: [1, 36] from Operation: 21+15=36 Current State: 37:[1, 36], Operations: ['64-63=1', '21+15=36'] Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[63, 64, 21, 15], Operations: [] Exploring Operation: 63-21=42, Resulting Numbers: [64, 15, 42] Generated Node #0,0: 37:[64, 15, 42] Operation: 63-21=42 Moving to Node #0,0 Current State: 37:[64, 15, 42], Operations: ['63-21=42'] Exploring Operation: 64-15=49, Resulting Numbers: [42, 49] Generated Node #0,0,0: 37:[42, 49] Operation: 64-15=49 Moving to Node #0,0,0 Current State: 37:[42, 49], Operations: ['63-21=42', '64-15=49'] Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,37 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 2, 58, 55, 99 ]
28
[ "58+55=113", "113-99=14", "2*14=28" ]
Current State: 28:[2, 58, 55, 99], Operations: [] Exploring Operation: 58+55=113, Resulting Numbers: [2, 99, 113] Generated Node #2: [2, 99, 113] from Operation: 58+55=113 Current State: 28:[2, 99, 113], Operations: ['58+55=113'] Exploring Operation: 113-99=14, Resulting Numbers: [2, 14] Generated Node #3: [2, 14] from Operation: 113-99=14 Current State: 28:[2, 14], Operations: ['58+55=113', '113-99=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[2, 58, 55, 99], Operations: [] Exploring Operation: 99-58=41, Resulting Numbers: [2, 55, 41] Generated Node #0,0: 28:[2, 55, 41] Operation: 99-58=41 Exploring Operation: 99-55=44, Resulting Numbers: [2, 58, 44] Generated Node #0,1: 28:[2, 58, 44] Operation: 99-55=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[2, 55, 41], Operations: ['99-58=41'] Exploring Operation: 55-2=53, Resulting Numbers: [41, 53] Generated Node #0,0,0: 28:[41, 53] Operation: 55-2=53 Exploring Operation: 55-41=14, Resulting Numbers: [2, 14] Generated Node #0,0,1: 28:[2, 14] Operation: 55-41=14 Moving to Node #0,0,1 Current State: 28:[2, 14], Operations: ['99-58=41', '55-41=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[2, 58, 55, 99], Operations: [] Exploring Operation: 99-58=41, Resulting Numbers: [2, 55, 41] Generated Node #0,0: 28:[2, 55, 41] Operation: 99-58=41 Moving to Node #0,0 Current State: 28:[2, 55, 41], Operations: ['99-58=41'] Exploring Operation: 55-41=14, Resulting Numbers: [2, 14] Generated Node #0,0,1: 28:[2, 14] Operation: 55-41=14 Moving to Node #0,0,1 Current State: 28:[2, 14], Operations: ['99-58=41', '55-41=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 84, 80, 74, 26 ]
44
[ "84-80=4", "74-26=48", "48-4=44" ]
Current State: 44:[84, 80, 74, 26], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [74, 26, 4] Generated Node #2: [74, 26, 4] from Operation: 84-80=4 Current State: 44:[74, 26, 4], Operations: ['84-80=4'] Exploring Operation: 74-26=48, Resulting Numbers: [4, 48] Generated Node #3: [4, 48] from Operation: 74-26=48 Current State: 44:[4, 48], Operations: ['84-80=4', '74-26=48'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[84, 80, 74, 26], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [74, 26, 4] Generated Node #0,0: 44:[74, 26, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[74, 26, 4], Operations: ['84-80=4'] Exploring Operation: 74-26=48, Resulting Numbers: [4, 48] Generated Node #0,0,0: 44:[4, 48] Operation: 74-26=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[4, 48], Operations: ['84-80=4', '74-26=48'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[84, 80, 74, 26], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [74, 26, 4] Generated Node #0,0: 44:[74, 26, 4] Operation: 84-80=4 Moving to Node #0,0 Current State: 44:[74, 26, 4], Operations: ['84-80=4'] Exploring Operation: 74-26=48, Resulting Numbers: [4, 48] Generated Node #0,0,0: 44:[4, 48] Operation: 74-26=48 Moving to Node #0,0,0 Current State: 44:[4, 48], Operations: ['84-80=4', '74-26=48'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 97, 18, 31, 49 ]
35
[ "97+18=115", "31+49=80", "115-80=35" ]
Current State: 35:[97, 18, 31, 49], Operations: [] Exploring Operation: 97+18=115, Resulting Numbers: [31, 49, 115] Generated Node #2: [31, 49, 115] from Operation: 97+18=115 Current State: 35:[31, 49, 115], Operations: ['97+18=115'] Exploring Operation: 31+49=80, Resulting Numbers: [115, 80] Generated Node #3: [115, 80] from Operation: 31+49=80 Current State: 35:[115, 80], Operations: ['97+18=115', '31+49=80'] Exploring Operation: 115-80=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[97, 18, 31, 49], Operations: [] Exploring Operation: 97-49=48, Resulting Numbers: [18, 31, 48] Generated Node #0,0: 35:[18, 31, 48] Operation: 97-49=48 Exploring Operation: 97-31=66, Resulting Numbers: [18, 49, 66] Generated Node #0,1: 35:[18, 49, 66] Operation: 97-31=66 Moving to Node #0,0 Current State: 35:[18, 31, 48], Operations: ['97-49=48'] Exploring Operation: 48-18=30, Resulting Numbers: [31, 30] Generated Node #0,0,0: 35:[31, 30] Operation: 48-18=30 Exploring Operation: 31-18=13, Resulting Numbers: [48, 13] Generated Node #0,0,1: 35:[48, 13] Operation: 31-18=13 Moving to Node #0,1 Current State: 35:[18, 49, 66], Operations: ['97-31=66'] Exploring Operation: 66-49=17, Resulting Numbers: [18, 17] Generated Node #0,1,0: 35:[18, 17] Operation: 66-49=17 Exploring Operation: 66-18=48, Resulting Numbers: [49, 48] Generated Node #0,1,1: 35:[49, 48] Operation: 66-18=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[18, 17], Operations: ['97-31=66', '66-49=17'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,35 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[97, 18, 31, 49], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [18, 49, 66] Generated Node #0,1: 35:[18, 49, 66] Operation: 97-31=66 Moving to Node #0,1 Current State: 35:[18, 49, 66], Operations: ['97-31=66'] Exploring Operation: 66-49=17, Resulting Numbers: [18, 17] Generated Node #0,1,0: 35:[18, 17] Operation: 66-49=17 Moving to Node #0,1,0 Current State: 35:[18, 17], Operations: ['97-31=66', '66-49=17'] Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 64, 23, 15, 87 ]
61
[ "64-23=41", "15+87=102", "102-41=61" ]
Current State: 61:[64, 23, 15, 87], Operations: [] Exploring Operation: 64-23=41, Resulting Numbers: [15, 87, 41] Generated Node #2: [15, 87, 41] from Operation: 64-23=41 Current State: 61:[15, 87, 41], Operations: ['64-23=41'] Exploring Operation: 15+87=102, Resulting Numbers: [41, 102] Generated Node #3: [41, 102] from Operation: 15+87=102 Current State: 61:[41, 102], Operations: ['64-23=41', '15+87=102'] Exploring Operation: 102-41=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[64, 23, 15, 87], Operations: [] Exploring Operation: 64-15=49, Resulting Numbers: [23, 87, 49] Generated Node #0,0: 61:[23, 87, 49] Operation: 64-15=49 Exploring Operation: 23+15=38, Resulting Numbers: [64, 87, 38] Generated Node #0,1: 61:[64, 87, 38] Operation: 23+15=38 Exploring Operation: 87-23=64, Resulting Numbers: [64, 15, 64] Generated Node #0,2: 61:[64, 15, 64] Operation: 87-23=64 Exploring Operation: 87-15=72, Resulting Numbers: [64, 23, 72] Generated Node #0,3: 61:[64, 23, 72] Operation: 87-15=72 Exploring Operation: 64+15=79, Resulting Numbers: [23, 87, 79] Generated Node #0,4: 61:[23, 87, 79] Operation: 64+15=79 Moving to Node #0,1 Current State: 61:[64, 87, 38], Operations: ['23+15=38'] Exploring Operation: 64+38=102, Resulting Numbers: [87, 102] Generated Node #0,1,0: 61:[87, 102] Operation: 64+38=102 Exploring Operation: 87-64=23, Resulting Numbers: [38, 23] Generated Node #0,1,1: 61:[38, 23] Operation: 87-64=23 Exploring Operation: 64-38=26, Resulting Numbers: [87, 26] Generated Node #0,1,2: 61:[87, 26] Operation: 64-38=26 Exploring Operation: 87-38=49, Resulting Numbers: [64, 49] Generated Node #0,1,3: 61:[64, 49] Operation: 87-38=49 Exploring Operation: 87+38=125, Resulting Numbers: [64, 125] Generated Node #0,1,4: 61:[64, 125] Operation: 87+38=125 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 61:[64, 49], Operations: ['23+15=38', '87-38=49'] Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,61 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,61 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:[38, 23], Operations: ['23+15=38', '87-64=23'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 38*23=874, Resulting Numbers: [874] 874,61 unequal: No Solution Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[64, 23, 15, 87], Operations: [] Exploring Operation: 23+15=38, Resulting Numbers: [64, 87, 38] Generated Node #0,1: 61:[64, 87, 38] Operation: 23+15=38 Moving to Node #0,1 Current State: 61:[64, 87, 38], Operations: ['23+15=38'] Exploring Operation: 87-64=23, Resulting Numbers: [38, 23] Generated Node #0,1,1: 61:[38, 23] Operation: 87-64=23 Moving to Node #0,1,1 Current State: 61:[38, 23], Operations: ['23+15=38', '87-64=23'] Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 11, 85, 25, 78 ]
88
[ "85+25=110", "110/11=10", "78+10=88" ]
Current State: 88:[11, 85, 25, 78], Operations: [] Exploring Operation: 85+25=110, Resulting Numbers: [11, 78, 110] Generated Node #2: [11, 78, 110] from Operation: 85+25=110 Current State: 88:[11, 78, 110], Operations: ['85+25=110'] Exploring Operation: 110/11=10, Resulting Numbers: [78, 10] Generated Node #3: [78, 10] from Operation: 110/11=10 Current State: 88:[78, 10], Operations: ['85+25=110', '110/11=10'] Exploring Operation: 78+10=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[11, 85, 25, 78], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [11, 25, 7] Generated Node #0,0: 88:[11, 25, 7] Operation: 85-78=7 Moving to Node #0,0 Current State: 88:[11, 25, 7], Operations: ['85-78=7'] Exploring Operation: 11-7=4, Resulting Numbers: [25, 4] Generated Node #0,0,0: 88:[25, 4] Operation: 11-7=4 Moving to Node #0,0,0 Current State: 88:[25, 4], Operations: ['85-78=7', '11-7=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,88 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 1, 71, 7, 67 ]
23
[ "7-1=6", "71+67=138", "138/6=23" ]
Current State: 23:[1, 71, 7, 67], Operations: [] Exploring Operation: 7-1=6, Resulting Numbers: [71, 67, 6] Generated Node #2: [71, 67, 6] from Operation: 7-1=6 Current State: 23:[71, 67, 6], Operations: ['7-1=6'] Exploring Operation: 71+67=138, Resulting Numbers: [6, 138] Generated Node #3: [6, 138] from Operation: 71+67=138 Current State: 23:[6, 138], Operations: ['7-1=6', '71+67=138'] Exploring Operation: 138/6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[1, 71, 7, 67], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [1, 7, 4] Generated Node #0,0: 23:[1, 7, 4] Operation: 71-67=4 Exploring Operation: 1+7=8, Resulting Numbers: [71, 67, 8] Generated Node #0,1: 23:[71, 67, 8] Operation: 1+7=8 Exploring Operation: 71-1=70, Resulting Numbers: [7, 67, 70] Generated Node #0,2: 23:[7, 67, 70] Operation: 71-1=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[1, 7, 4], Operations: ['71-67=4'] Exploring Operation: 7*4=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 23:[1, 28] Operation: 7*4=28 Exploring Operation: 1+7=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 23:[4, 8] Operation: 1+7=8 Exploring Operation: 1+4=5, Resulting Numbers: [7, 5] Generated Node #0,0,2: 23:[7, 5] Operation: 1+4=5 Moving to Node #0,0,0 Current State: 23:[1, 28], Operations: ['71-67=4', '7*4=28'] Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,23 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,23 unequal: No Solution Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[4, 8], Operations: ['71-67=4', '1+7=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[7, 5], Operations: ['71-67=4', '1+4=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[71, 67, 8], Operations: ['1+7=8'] Exploring Operation: 71-8=63, Resulting Numbers: [67, 63] Generated Node #0,1,0: 23:[67, 63] Operation: 71-8=63 Exploring Operation: 71-67=4, Resulting Numbers: [8, 4] Generated Node #0,1,1: 23:[8, 4] Operation: 71-67=4 Exploring Operation: 67-8=59, Resulting Numbers: [71, 59] Generated Node #0,1,2: 23:[71, 59] Operation: 67-8=59 Moving to Node #0,1,1 Current State: 23:[8, 4], Operations: ['1+7=8', '71-67=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[67, 63], Operations: ['1+7=8', '71-8=63'] Exploring Operation: 67*63=4221, Resulting Numbers: [4221] 4221,23 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 67+63=130, Resulting Numbers: [130] 130,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[71, 59], Operations: ['1+7=8', '67-8=59'] Exploring Operation: 71-59=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 71+59=130, Resulting Numbers: [130] 130,23 unequal: No Solution Exploring Operation: 71*59=4189, Resulting Numbers: [4189] 4189,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[7, 67, 70], Operations: ['71-1=70'] Exploring Operation: 67-7=60, Resulting Numbers: [70, 60] Generated Node #0,2,0: 23:[70, 60] Operation: 67-7=60 Exploring Operation: 70/7=10, Resulting Numbers: [67, 10] Generated Node #0,2,1: 23:[67, 10] Operation: 70/7=10 Exploring Operation: 70-67=3, Resulting Numbers: [7, 3] Generated Node #0,2,2: 23:[7, 3] Operation: 70-67=3 Moving to Node #0,2,2 Current State: 23:[7, 3], Operations: ['71-1=70', '70-67=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,23 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[67, 10], Operations: ['71-1=70', '70/7=10'] Exploring Operation: 67*10=670, Resulting Numbers: [670] 670,23 unequal: No Solution Exploring Operation: 67+10=77, Resulting Numbers: [77] 77,23 unequal: No Solution Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[70, 60], Operations: ['71-1=70', '67-7=60'] Exploring Operation: 70*60=4200, Resulting Numbers: [4200] 4200,23 unequal: No Solution Exploring Operation: 70-60=10, Resulting Numbers: [10] 10,23 unequal: No Solution Exploring Operation: 70+60=130, Resulting Numbers: [130] 130,23 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
[ 93, 79, 10, 23 ]
90
[ "93-79=14", "23-14=9", "10*9=90" ]
Current State: 90:[93, 79, 10, 23], Operations: [] Exploring Operation: 93-79=14, Resulting Numbers: [10, 23, 14] Generated Node #2: [10, 23, 14] from Operation: 93-79=14 Current State: 90:[10, 23, 14], Operations: ['93-79=14'] Exploring Operation: 23-14=9, Resulting Numbers: [10, 9] Generated Node #3: [10, 9] from Operation: 23-14=9 Current State: 90:[10, 9], Operations: ['93-79=14', '23-14=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[93, 79, 10, 23], Operations: [] Exploring Operation: 79+10=89, Resulting Numbers: [93, 23, 89] Generated Node #0,0: 90:[93, 23, 89] Operation: 79+10=89 Exploring Operation: 93-79=14, Resulting Numbers: [10, 23, 14] Generated Node #0,1: 90:[10, 23, 14] Operation: 93-79=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[10, 23, 14], Operations: ['93-79=14'] Exploring Operation: 23-10=13, Resulting Numbers: [14, 13] Generated Node #0,1,0: 90:[14, 13] Operation: 23-10=13 Exploring Operation: 23-14=9, Resulting Numbers: [10, 9] Generated Node #0,1,1: 90:[10, 9] Operation: 23-14=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[10, 9], Operations: ['93-79=14', '23-14=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[93, 79, 10, 23], Operations: [] Exploring Operation: 93-79=14, Resulting Numbers: [10, 23, 14] Generated Node #0,1: 90:[10, 23, 14] Operation: 93-79=14 Moving to Node #0,1 Current State: 90:[10, 23, 14], Operations: ['93-79=14'] Exploring Operation: 23-14=9, Resulting Numbers: [10, 9] Generated Node #0,1,1: 90:[10, 9] Operation: 23-14=9 Moving to Node #0,1,1 Current State: 90:[10, 9], Operations: ['93-79=14', '23-14=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 74, 9, 6, 15 ]
92
[ "74+9=83", "15-6=9", "83+9=92" ]
Current State: 92:[74, 9, 6, 15], Operations: [] Exploring Operation: 74+9=83, Resulting Numbers: [6, 15, 83] Generated Node #2: [6, 15, 83] from Operation: 74+9=83 Current State: 92:[6, 15, 83], Operations: ['74+9=83'] Exploring Operation: 15-6=9, Resulting Numbers: [83, 9] Generated Node #3: [83, 9] from Operation: 15-6=9 Current State: 92:[83, 9], Operations: ['74+9=83', '15-6=9'] Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[74, 9, 6, 15], Operations: [] Exploring Operation: 74+15=89, Resulting Numbers: [9, 6, 89] Generated Node #0,0: 92:[9, 6, 89] Operation: 74+15=89 Moving to Node #0,0 Current State: 92:[9, 6, 89], Operations: ['74+15=89'] Exploring Operation: 9-6=3, Resulting Numbers: [89, 3] Generated Node #0,0,0: 92:[89, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 92:[89, 3], Operations: ['74+15=89', '9-6=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[74, 9, 6, 15], Operations: [] Exploring Operation: 74+15=89, Resulting Numbers: [9, 6, 89] Generated Node #0,0: 92:[9, 6, 89] Operation: 74+15=89 Moving to Node #0,0 Current State: 92:[9, 6, 89], Operations: ['74+15=89'] Exploring Operation: 9-6=3, Resulting Numbers: [89, 3] Generated Node #0,0,0: 92:[89, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 92:[89, 3], Operations: ['74+15=89', '9-6=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 1, 97, 20, 2 ]
38
[ "97-1=96", "96-20=76", "76/2=38" ]
Current State: 38:[1, 97, 20, 2], Operations: [] Exploring Operation: 97-1=96, Resulting Numbers: [20, 2, 96] Generated Node #2: [20, 2, 96] from Operation: 97-1=96 Current State: 38:[20, 2, 96], Operations: ['97-1=96'] Exploring Operation: 96-20=76, Resulting Numbers: [2, 76] Generated Node #3: [2, 76] from Operation: 96-20=76 Current State: 38:[2, 76], Operations: ['97-1=96', '96-20=76'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[1, 97, 20, 2], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [1, 2, 77] Generated Node #0,0: 38:[1, 2, 77] Operation: 97-20=77 Moving to Node #0,0 Current State: 38:[1, 2, 77], Operations: ['97-20=77'] Exploring Operation: 77-1=76, Resulting Numbers: [2, 76] Generated Node #0,0,0: 38:[2, 76] Operation: 77-1=76 Moving to Node #0,0,0 Current State: 38:[2, 76], Operations: ['97-20=77', '77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[1, 97, 20, 2], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [1, 2, 77] Generated Node #0,0: 38:[1, 2, 77] Operation: 97-20=77 Moving to Node #0,0 Current State: 38:[1, 2, 77], Operations: ['97-20=77'] Exploring Operation: 77-1=76, Resulting Numbers: [2, 76] Generated Node #0,0,0: 38:[2, 76] Operation: 77-1=76 Moving to Node #0,0,0 Current State: 38:[2, 76], Operations: ['97-20=77', '77-1=76'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 2, 98, 97, 8 ]
17
[ "2*8=16", "98-97=1", "16+1=17" ]
Current State: 17:[2, 98, 97, 8], Operations: [] Exploring Operation: 2*8=16, Resulting Numbers: [98, 97, 16] Generated Node #2: [98, 97, 16] from Operation: 2*8=16 Current State: 17:[98, 97, 16], Operations: ['2*8=16'] Exploring Operation: 98-97=1, Resulting Numbers: [16, 1] Generated Node #3: [16, 1] from Operation: 98-97=1 Current State: 17:[16, 1], Operations: ['2*8=16', '98-97=1'] Exploring Operation: 16+1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[2, 98, 97, 8], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [2, 8, 1] Generated Node #0,0: 17:[2, 8, 1] Operation: 98-97=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[2, 8, 1], Operations: ['98-97=1'] Exploring Operation: 2*8=16, Resulting Numbers: [1, 16] Generated Node #0,0,0: 17:[1, 16] Operation: 2*8=16 Moving to Node #0,0,0 Current State: 17:[1, 16], Operations: ['98-97=1', '2*8=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[2, 98, 97, 8], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [2, 8, 1] Generated Node #0,0: 17:[2, 8, 1] Operation: 98-97=1 Moving to Node #0,0 Current State: 17:[2, 8, 1], Operations: ['98-97=1'] Exploring Operation: 2*8=16, Resulting Numbers: [1, 16] Generated Node #0,0,0: 17:[1, 16] Operation: 2*8=16 Moving to Node #0,0,0 Current State: 17:[1, 16], Operations: ['98-97=1', '2*8=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 50, 23, 78, 18 ]
52
[ "50-23=27", "78*18=1404", "1404/27=52" ]
Current State: 52:[50, 23, 78, 18], Operations: [] Exploring Operation: 50-23=27, Resulting Numbers: [78, 18, 27] Generated Node #2: [78, 18, 27] from Operation: 50-23=27 Current State: 52:[78, 18, 27], Operations: ['50-23=27'] Exploring Operation: 78*18=1404, Resulting Numbers: [27, 1404] Generated Node #3: [27, 1404] from Operation: 78*18=1404 Current State: 52:[27, 1404], Operations: ['50-23=27', '78*18=1404'] Exploring Operation: 1404/27=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[50, 23, 78, 18], Operations: [] Exploring Operation: 78-23=55, Resulting Numbers: [50, 18, 55] Generated Node #0,0: 52:[50, 18, 55] Operation: 78-23=55 Exploring Operation: 78-50=28, Resulting Numbers: [23, 18, 28] Generated Node #0,1: 52:[23, 18, 28] Operation: 78-50=28 Moving to Node #0,0 Current State: 52:[50, 18, 55], Operations: ['78-23=55'] Exploring Operation: 55-50=5, Resulting Numbers: [18, 5] Generated Node #0,0,0: 52:[18, 5] Operation: 55-50=5 Exploring Operation: 50-18=32, Resulting Numbers: [55, 32] Generated Node #0,0,1: 52:[55, 32] Operation: 50-18=32 Moving to Node #0,1 Current State: 52:[23, 18, 28], Operations: ['78-50=28'] Exploring Operation: 23+28=51, Resulting Numbers: [18, 51] Generated Node #0,1,0: 52:[18, 51] Operation: 23+28=51 Exploring Operation: 23-18=5, Resulting Numbers: [28, 5] Generated Node #0,1,1: 52:[28, 5] Operation: 23-18=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[28, 5], Operations: ['78-50=28', '23-18=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,52 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 #0,1,0 Current State: 52:[18, 51], Operations: ['78-50=28', '23+28=51'] Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,52 unequal: No Solution Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,52 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: 52:[18, 5], Operations: ['78-23=55', '55-50=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[55, 32], Operations: ['78-23=55', '50-18=32'] Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 55+32=87, Resulting Numbers: [87] 87,52 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 12, 51, 40, 50 ]
49
[ "51-12=39", "50-40=10", "39+10=49" ]
Current State: 49:[12, 51, 40, 50], Operations: [] Exploring Operation: 51-12=39, Resulting Numbers: [40, 50, 39] Generated Node #2: [40, 50, 39] from Operation: 51-12=39 Current State: 49:[40, 50, 39], Operations: ['51-12=39'] Exploring Operation: 50-40=10, Resulting Numbers: [39, 10] Generated Node #3: [39, 10] from Operation: 50-40=10 Current State: 49:[39, 10], Operations: ['51-12=39', '50-40=10'] Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[12, 51, 40, 50], Operations: [] Exploring Operation: 51-40=11, Resulting Numbers: [12, 50, 11] Generated Node #0,0: 49:[12, 50, 11] Operation: 51-40=11 Exploring Operation: 12+40=52, Resulting Numbers: [51, 50, 52] Generated Node #0,1: 49:[51, 50, 52] Operation: 12+40=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[51, 50, 52], Operations: ['12+40=52'] Exploring Operation: 52-51=1, Resulting Numbers: [50, 1] Generated Node #0,1,0: 49:[50, 1] Operation: 52-51=1 Exploring Operation: 52-50=2, Resulting Numbers: [51, 2] Generated Node #0,1,1: 49:[51, 2] Operation: 52-50=2 Moving to Node #0,1,0 Current State: 49:[50, 1], Operations: ['12+40=52', '52-51=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[12, 51, 40, 50], Operations: [] Exploring Operation: 12+40=52, Resulting Numbers: [51, 50, 52] Generated Node #0,1: 49:[51, 50, 52] Operation: 12+40=52 Moving to Node #0,1 Current State: 49:[51, 50, 52], Operations: ['12+40=52'] Exploring Operation: 52-51=1, Resulting Numbers: [50, 1] Generated Node #0,1,0: 49:[50, 1] Operation: 52-51=1 Moving to Node #0,1,0 Current State: 49:[50, 1], Operations: ['12+40=52', '52-51=1'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 22, 81, 15, 2 ]
59
[ "22+81=103", "15+103=118", "118/2=59" ]
Current State: 59:[22, 81, 15, 2], Operations: [] Exploring Operation: 22+81=103, Resulting Numbers: [15, 2, 103] Generated Node #2: [15, 2, 103] from Operation: 22+81=103 Current State: 59:[15, 2, 103], Operations: ['22+81=103'] Exploring Operation: 15+103=118, Resulting Numbers: [2, 118] Generated Node #3: [2, 118] from Operation: 15+103=118 Current State: 59:[2, 118], Operations: ['22+81=103', '15+103=118'] Exploring Operation: 118/2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[22, 81, 15, 2], Operations: [] Exploring Operation: 81-22=59, Resulting Numbers: [15, 2, 59] Generated Node #0,0: 59:[15, 2, 59] Operation: 81-22=59 Exploring Operation: 22+15=37, Resulting Numbers: [81, 2, 37] Generated Node #0,1: 59:[81, 2, 37] Operation: 22+15=37 Exploring Operation: 22*2=44, Resulting Numbers: [81, 15, 44] Generated Node #0,2: 59:[81, 15, 44] Operation: 22*2=44 Exploring Operation: 15*2=30, Resulting Numbers: [22, 81, 30] Generated Node #0,3: 59:[22, 81, 30] Operation: 15*2=30 Moving to Node #0,2 Current State: 59:[81, 15, 44], Operations: ['22*2=44'] Exploring Operation: 15+44=59, Resulting Numbers: [81, 59] Generated Node #0,2,0: 59:[81, 59] Operation: 15+44=59 Exploring Operation: 81-15=66, Resulting Numbers: [44, 66] Generated Node #0,2,1: 59:[44, 66] Operation: 81-15=66 Exploring Operation: 81+15=96, Resulting Numbers: [44, 96] Generated Node #0,2,2: 59:[44, 96] Operation: 81+15=96 Exploring Operation: 44-15=29, Resulting Numbers: [81, 29] Generated Node #0,2,3: 59:[81, 29] Operation: 44-15=29 Moving to Node #0,3 Current State: 59:[22, 81, 30], Operations: ['15*2=30'] Exploring Operation: 81-30=51, Resulting Numbers: [22, 51] Generated Node #0,3,0: 59:[22, 51] Operation: 81-30=51 Exploring Operation: 22+81=103, Resulting Numbers: [30, 103] Generated Node #0,3,1: 59:[30, 103] Operation: 22+81=103 Exploring Operation: 81-22=59, Resulting Numbers: [30, 59] Generated Node #0,3,2: 59:[30, 59] Operation: 81-22=59 Exploring Operation: 22+30=52, Resulting Numbers: [81, 52] Generated Node #0,3,3: 59:[81, 52] Operation: 22+30=52 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[30, 59], Operations: ['15*2=30', '81-22=59'] Exploring Operation: 30+59=89, Resulting Numbers: [89] 89,59 unequal: No Solution Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,59 unequal: No Solution Exploring Operation: 30*59=1770, Resulting Numbers: [1770] 1770,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[81, 52], Operations: ['15*2=30', '22+30=52'] Exploring Operation: 81+52=133, Resulting Numbers: [133] 133,59 unequal: No Solution Exploring Operation: 81-52=29, Resulting Numbers: [29] 29,59 unequal: No Solution Exploring Operation: 81*52=4212, Resulting Numbers: [4212] 4212,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[22, 51], Operations: ['15*2=30', '81-30=51'] Exploring Operation: 22+51=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 22*51=1122, Resulting Numbers: [1122] 1122,59 unequal: No Solution Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[30, 103], Operations: ['15*2=30', '22+81=103'] Exploring Operation: 30+103=133, Resulting Numbers: [133] 133,59 unequal: No Solution Exploring Operation: 30*103=3090, Resulting Numbers: [3090] 3090,59 unequal: No Solution Exploring Operation: 103-30=73, Resulting Numbers: [73] 73,59 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: 59:[81, 2, 37], Operations: ['22+15=37'] Exploring Operation: 2*37=74, Resulting Numbers: [81, 74] Generated Node #0,1,0: 59:[81, 74] Operation: 2*37=74 Exploring Operation: 2+37=39, Resulting Numbers: [81, 39] Generated Node #0,1,1: 59:[81, 39] Operation: 2+37=39 Exploring Operation: 81+2=83, Resulting Numbers: [37, 83] Generated Node #0,1,2: 59:[37, 83] Operation: 81+2=83 Exploring Operation: 81-2=79, Resulting Numbers: [37, 79] Generated Node #0,1,3: 59:[37, 79] Operation: 81-2=79 Moving to Node #0,0 Current State: 59:[15, 2, 59], Operations: ['81-22=59'] Exploring Operation: 15+2=17, Resulting Numbers: [59, 17] Generated Node #0,0,0: 59:[59, 17] Operation: 15+2=17 Exploring Operation: 15*2=30, Resulting Numbers: [59, 30] Generated Node #0,0,1: 59:[59, 30] Operation: 15*2=30 Exploring Operation: 15-2=13, Resulting Numbers: [59, 13] Generated Node #0,0,2: 59:[59, 13] Operation: 15-2=13 Exploring Operation: 2+59=61, Resulting Numbers: [15, 61] Generated Node #0,0,3: 59:[15, 61] Operation: 2+59=61 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[59, 30], Operations: ['81-22=59', '15*2=30'] Exploring Operation: 59+30=89, Resulting Numbers: [89] 89,59 unequal: No Solution Exploring Operation: 59*30=1770, Resulting Numbers: [1770] 1770,59 unequal: No Solution Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,59 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 #0,0,0 Current State: 59:[59, 17], Operations: ['81-22=59', '15+2=17'] Exploring Operation: 59+17=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 59*17=1003, Resulting Numbers: [1003] 1003,59 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,59 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 #0,0,2 Current State: 59:[59, 13], Operations: ['81-22=59', '15-2=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,59 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,59 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 #0,0,3 Current State: 59:[15, 61], Operations: ['81-22=59', '2+59=61'] Exploring Operation: 15+61=76, Resulting Numbers: [76] 76,59 unequal: No Solution Exploring Operation: 15*61=915, Resulting Numbers: [915] 915,59 unequal: No Solution Exploring Operation: 61-15=46, Resulting Numbers: [46] 46,59 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: 59:[81, 59], Operations: ['22*2=44', '15+44=59'] Exploring Operation: 81*59=4779, Resulting Numbers: [4779] 4779,59 unequal: No Solution Exploring Operation: 81-59=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 81+59=140, Resulting Numbers: [140] 140,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[44, 66], Operations: ['22*2=44', '81-15=66'] Exploring Operation: 44*66=2904, Resulting Numbers: [2904] 2904,59 unequal: No Solution Exploring Operation: 66-44=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 44+66=110, Resulting Numbers: [110] 110,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[81, 74], Operations: ['22+15=37', '2*37=74'] Exploring Operation: 81+74=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 81*74=5994, Resulting Numbers: [5994] 5994,59 unequal: No Solution Exploring Operation: 81-74=7, Resulting Numbers: [7] 7,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[81, 39], Operations: ['22+15=37', '2+37=39'] Exploring Operation: 81-39=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 81+39=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 81*39=3159, Resulting Numbers: [3159] 3159,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[37, 79], Operations: ['22+15=37', '81-2=79'] Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,59 unequal: No Solution Exploring Operation: 37*79=2923, Resulting Numbers: [2923] 2923,59 unequal: No Solution Exploring Operation: 37+79=116, Resulting Numbers: [116] 116,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[37, 83], Operations: ['22+15=37', '81+2=83'] Exploring Operation: 37+83=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 37*83=3071, Resulting Numbers: [3071] 3071,59 unequal: No Solution Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[81, 29], Operations: ['22*2=44', '44-15=29'] Exploring Operation: 81*29=2349, Resulting Numbers: [2349] 2349,59 unequal: No Solution Exploring Operation: 81+29=110, Resulting Numbers: [110] 110,59 unequal: No Solution Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[44, 96], Operations: ['22*2=44', '81+15=96'] Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,59 unequal: No Solution Exploring Operation: 44*96=4224, Resulting Numbers: [4224] 4224,59 unequal: No Solution Exploring Operation: 44+96=140, Resulting Numbers: [140] 140,59 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 71, 47, 28, 9 ]
61
[ "71-47=24", "28+9=37", "24+37=61" ]
Current State: 61:[71, 47, 28, 9], Operations: [] Exploring Operation: 71-47=24, Resulting Numbers: [28, 9, 24] Generated Node #2: [28, 9, 24] from Operation: 71-47=24 Current State: 61:[28, 9, 24], Operations: ['71-47=24'] Exploring Operation: 28+9=37, Resulting Numbers: [24, 37] Generated Node #3: [24, 37] from Operation: 28+9=37 Current State: 61:[24, 37], Operations: ['71-47=24', '28+9=37'] Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[71, 47, 28, 9], Operations: [] Exploring Operation: 28+9=37, Resulting Numbers: [71, 47, 37] Generated Node #0,0: 61:[71, 47, 37] Operation: 28+9=37 Exploring Operation: 71-9=62, Resulting Numbers: [47, 28, 62] Generated Node #0,1: 61:[47, 28, 62] Operation: 71-9=62 Exploring Operation: 47+9=56, Resulting Numbers: [71, 28, 56] Generated Node #0,2: 61:[71, 28, 56] Operation: 47+9=56 Moving to Node #0,0 Current State: 61:[71, 47, 37], Operations: ['28+9=37'] Exploring Operation: 71-47=24, Resulting Numbers: [37, 24] Generated Node #0,0,0: 61:[37, 24] Operation: 71-47=24 Exploring Operation: 47+37=84, Resulting Numbers: [71, 84] Generated Node #0,0,1: 61:[71, 84] Operation: 47+37=84 Exploring Operation: 71-37=34, Resulting Numbers: [47, 34] Generated Node #0,0,2: 61:[47, 34] Operation: 71-37=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[71, 84], Operations: ['28+9=37', '47+37=84'] Exploring Operation: 71+84=155, Resulting Numbers: [155] 155,61 unequal: No Solution Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 71*84=5964, Resulting Numbers: [5964] 5964,61 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 #0,0,2 Current State: 61:[47, 34], Operations: ['28+9=37', '71-37=34'] Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,61 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,61 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:[37, 24], Operations: ['28+9=37', '71-47=24'] Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,61 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[71, 47, 28, 9], Operations: [] Exploring Operation: 28+9=37, Resulting Numbers: [71, 47, 37] Generated Node #0,0: 61:[71, 47, 37] Operation: 28+9=37 Moving to Node #0,0 Current State: 61:[71, 47, 37], Operations: ['28+9=37'] Exploring Operation: 71-47=24, Resulting Numbers: [37, 24] Generated Node #0,0,0: 61:[37, 24] Operation: 71-47=24 Moving to Node #0,0,0 Current State: 61:[37, 24], Operations: ['28+9=37', '71-47=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 24, 22, 28, 68 ]
54
[ "24-22=2", "28/2=14", "68-14=54" ]
Current State: 54:[24, 22, 28, 68], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [28, 68, 2] Generated Node #2: [28, 68, 2] from Operation: 24-22=2 Current State: 54:[28, 68, 2], Operations: ['24-22=2'] Exploring Operation: 28/2=14, Resulting Numbers: [68, 14] Generated Node #3: [68, 14] from Operation: 28/2=14 Current State: 54:[68, 14], Operations: ['24-22=2', '28/2=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[24, 22, 28, 68], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [24, 28, 46] Generated Node #0,0: 54:[24, 28, 46] Operation: 68-22=46 Exploring Operation: 68-24=44, Resulting Numbers: [22, 28, 44] Generated Node #0,1: 54:[22, 28, 44] Operation: 68-24=44 Exploring Operation: 24-22=2, Resulting Numbers: [28, 68, 2] Generated Node #0,2: 54:[28, 68, 2] Operation: 24-22=2 Moving to Node #0,0 Current State: 54:[24, 28, 46], Operations: ['68-22=46'] Exploring Operation: 46-24=22, Resulting Numbers: [28, 22] Generated Node #0,0,0: 54:[28, 22] Operation: 46-24=22 Exploring Operation: 28-24=4, Resulting Numbers: [46, 4] Generated Node #0,0,1: 54:[46, 4] Operation: 28-24=4 Exploring Operation: 46-28=18, Resulting Numbers: [24, 18] Generated Node #0,0,2: 54:[24, 18] Operation: 46-28=18 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[24, 18], Operations: ['68-22=46', '46-28=18'] Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,54 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,54 unequal: No Solution No 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: 54:[28, 22], Operations: ['68-22=46', '46-24=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,54 unequal: No Solution No 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: 54:[46, 4], Operations: ['68-22=46', '28-24=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,54 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: 54:[22, 28, 44], Operations: ['68-24=44'] Exploring Operation: 44/22=2, Resulting Numbers: [28, 2] Generated Node #0,1,0: 54:[28, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [28, 22] Generated Node #0,1,1: 54:[28, 22] Operation: 44-22=22 Exploring Operation: 44-28=16, Resulting Numbers: [22, 16] Generated Node #0,1,2: 54:[22, 16] Operation: 44-28=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[28, 2], Operations: ['68-24=44', '44/22=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,54 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,54 unequal: No Solution No 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: 54:[28, 22], Operations: ['68-24=44', '44-22=22'] Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,54 unequal: No Solution No 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: 54:[22, 16], Operations: ['68-24=44', '44-28=16'] Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,54 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,54 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: 54:[28, 68, 2], Operations: ['24-22=2'] Exploring Operation: 68-28=40, Resulting Numbers: [2, 40] Generated Node #0,2,0: 54:[2, 40] Operation: 68-28=40 Exploring Operation: 68-2=66, Resulting Numbers: [28, 66] Generated Node #0,2,1: 54:[28, 66] Operation: 68-2=66 Exploring Operation: 68/2=34, Resulting Numbers: [28, 34] Generated Node #0,2,2: 54:[28, 34] Operation: 68/2=34 Moving to Node #0,2,2 Current State: 54:[28, 34], Operations: ['24-22=2', '68/2=34'] Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,54 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[2, 40], Operations: ['24-22=2', '68-28=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,54 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,54 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[28, 66], Operations: ['24-22=2', '68-2=66'] Exploring Operation: 66-28=38, Resulting Numbers: [38] 38,54 unequal: No Solution Exploring Operation: 28*66=1848, Resulting Numbers: [1848] 1848,54 unequal: No Solution Exploring Operation: 28+66=94, Resulting Numbers: [94] 94,54 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 3, 6, 75, 11 ]
30
[ "75/3=25", "11-6=5", "25+5=30" ]
Current State: 30:[3, 6, 75, 11], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [6, 11, 25] Generated Node #2: [6, 11, 25] from Operation: 75/3=25 Current State: 30:[6, 11, 25], Operations: ['75/3=25'] Exploring Operation: 11-6=5, Resulting Numbers: [25, 5] Generated Node #3: [25, 5] from Operation: 11-6=5 Current State: 30:[25, 5], Operations: ['75/3=25', '11-6=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[3, 6, 75, 11], Operations: [] Exploring Operation: 75-11=64, Resulting Numbers: [3, 6, 64] Generated Node #0,0: 30:[3, 6, 64] Operation: 75-11=64 Exploring Operation: 75/3=25, Resulting Numbers: [6, 11, 25] Generated Node #0,1: 30:[6, 11, 25] Operation: 75/3=25 Exploring Operation: 75-6=69, Resulting Numbers: [3, 11, 69] Generated Node #0,2: 30:[3, 11, 69] Operation: 75-6=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[6, 11, 25], Operations: ['75/3=25'] Exploring Operation: 11-6=5, Resulting Numbers: [25, 5] Generated Node #0,1,0: 30:[25, 5] Operation: 11-6=5 Exploring Operation: 25-11=14, Resulting Numbers: [6, 14] Generated Node #0,1,1: 30:[6, 14] Operation: 25-11=14 Exploring Operation: 6+25=31, Resulting Numbers: [11, 31] Generated Node #0,1,2: 30:[11, 31] Operation: 6+25=31 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[6, 14], Operations: ['75/3=25', '25-11=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,30 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,30 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 30:[11, 31], Operations: ['75/3=25', '6+25=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,30 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[25, 5], Operations: ['75/3=25', '11-6=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[3, 6, 75, 11], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [6, 11, 25] Generated Node #0,1: 30:[6, 11, 25] Operation: 75/3=25 Moving to Node #0,1 Current State: 30:[6, 11, 25], Operations: ['75/3=25'] Exploring Operation: 11-6=5, Resulting Numbers: [25, 5] Generated Node #0,1,0: 30:[25, 5] Operation: 11-6=5 Moving to Node #0,1,0 Current State: 30:[25, 5], Operations: ['75/3=25', '11-6=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 86, 48, 4, 89 ]
47
[ "86-48=38", "89-4=85", "85-38=47" ]
Current State: 47:[86, 48, 4, 89], Operations: [] Exploring Operation: 86-48=38, Resulting Numbers: [4, 89, 38] Generated Node #2: [4, 89, 38] from Operation: 86-48=38 Current State: 47:[4, 89, 38], Operations: ['86-48=38'] Exploring Operation: 89-4=85, Resulting Numbers: [38, 85] Generated Node #3: [38, 85] from Operation: 89-4=85 Current State: 47:[38, 85], Operations: ['86-48=38', '89-4=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[86, 48, 4, 89], Operations: [] Exploring Operation: 86-4=82, Resulting Numbers: [48, 89, 82] Generated Node #0,0: 47:[48, 89, 82] Operation: 86-4=82 Exploring Operation: 48-4=44, Resulting Numbers: [86, 89, 44] Generated Node #0,1: 47:[86, 89, 44] Operation: 48-4=44 Exploring Operation: 89-4=85, Resulting Numbers: [86, 48, 85] Generated Node #0,2: 47:[86, 48, 85] Operation: 89-4=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[48, 89, 82], Operations: ['86-4=82'] Exploring Operation: 82-48=34, Resulting Numbers: [89, 34] Generated Node #0,0,0: 47:[89, 34] Operation: 82-48=34 Exploring Operation: 89-48=41, Resulting Numbers: [82, 41] Generated Node #0,0,1: 47:[82, 41] Operation: 89-48=41 Exploring Operation: 89-82=7, Resulting Numbers: [48, 7] Generated Node #0,0,2: 47:[48, 7] Operation: 89-82=7 Moving to Node #0,0,1 Current State: 47:[82, 41], Operations: ['86-4=82', '89-48=41'] Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[48, 7], Operations: ['86-4=82', '89-82=7'] Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 48+7=55, Resulting Numbers: [55] 55,47 unequal: No Solution Exploring Operation: 48*7=336, Resulting Numbers: [336] 336,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[89, 34], Operations: ['86-4=82', '82-48=34'] Exploring Operation: 89+34=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 89-34=55, Resulting Numbers: [55] 55,47 unequal: No Solution Exploring Operation: 89*34=3026, Resulting Numbers: [3026] 3026,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[86, 48, 85], Operations: ['89-4=85'] Exploring Operation: 85-48=37, Resulting Numbers: [86, 37] Generated Node #0,2,0: 47:[86, 37] Operation: 85-48=37 Exploring Operation: 86-85=1, Resulting Numbers: [48, 1] Generated Node #0,2,1: 47:[48, 1] Operation: 86-85=1 Exploring Operation: 86-48=38, Resulting Numbers: [85, 38] Generated Node #0,2,2: 47:[85, 38] Operation: 86-48=38 Moving to Node #0,2,1 Current State: 47:[48, 1], Operations: ['89-4=85', '86-85=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[86, 48, 4, 89], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [86, 48, 85] Generated Node #0,2: 47:[86, 48, 85] Operation: 89-4=85 Moving to Node #0,2 Current State: 47:[86, 48, 85], Operations: ['89-4=85'] Exploring Operation: 86-85=1, Resulting Numbers: [48, 1] Generated Node #0,2,1: 47:[48, 1] Operation: 86-85=1 Moving to Node #0,2,1 Current State: 47:[48, 1], Operations: ['89-4=85', '86-85=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 58, 61, 52, 98 ]
73
[ "58+61=119", "98-52=46", "119-46=73" ]
Current State: 73:[58, 61, 52, 98], Operations: [] Exploring Operation: 58+61=119, Resulting Numbers: [52, 98, 119] Generated Node #2: [52, 98, 119] from Operation: 58+61=119 Current State: 73:[52, 98, 119], Operations: ['58+61=119'] Exploring Operation: 98-52=46, Resulting Numbers: [119, 46] Generated Node #3: [119, 46] from Operation: 98-52=46 Current State: 73:[119, 46], Operations: ['58+61=119', '98-52=46'] Exploring Operation: 119-46=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[58, 61, 52, 98], Operations: [] Exploring Operation: 98-52=46, Resulting Numbers: [58, 61, 46] Generated Node #0,0: 73:[58, 61, 46] Operation: 98-52=46 Moving to Node #0,0 Current State: 73:[58, 61, 46], Operations: ['98-52=46'] Exploring Operation: 58+46=104, Resulting Numbers: [61, 104] Generated Node #0,0,0: 73:[61, 104] Operation: 58+46=104 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[61, 104], Operations: ['98-52=46', '58+46=104'] Exploring Operation: 104-61=43, Resulting Numbers: [43] 43,73 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
[ 10, 31, 49, 18 ]
88
[ "31-10=21", "49+18=67", "21+67=88" ]
Current State: 88:[10, 31, 49, 18], Operations: [] Exploring Operation: 31-10=21, Resulting Numbers: [49, 18, 21] Generated Node #2: [49, 18, 21] from Operation: 31-10=21 Current State: 88:[49, 18, 21], Operations: ['31-10=21'] Exploring Operation: 49+18=67, Resulting Numbers: [21, 67] Generated Node #3: [21, 67] from Operation: 49+18=67 Current State: 88:[21, 67], Operations: ['31-10=21', '49+18=67'] Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[10, 31, 49, 18], Operations: [] Exploring Operation: 31-18=13, Resulting Numbers: [10, 49, 13] Generated Node #0,0: 88:[10, 49, 13] Operation: 31-18=13 Exploring Operation: 31-10=21, Resulting Numbers: [49, 18, 21] Generated Node #0,1: 88:[49, 18, 21] Operation: 31-10=21 Exploring Operation: 49-31=18, Resulting Numbers: [10, 18, 18] Generated Node #0,2: 88:[10, 18, 18] Operation: 49-31=18 Moving to Node #0,0 Current State: 88:[10, 49, 13], Operations: ['31-18=13'] Exploring Operation: 13-10=3, Resulting Numbers: [49, 3] Generated Node #0,0,0: 88:[49, 3] Operation: 13-10=3 Exploring Operation: 49-10=39, Resulting Numbers: [13, 39] Generated Node #0,0,1: 88:[13, 39] Operation: 49-10=39 Exploring Operation: 10+13=23, Resulting Numbers: [49, 23] Generated Node #0,0,2: 88:[49, 23] Operation: 10+13=23 Moving to Node #0,2 Current State: 88:[10, 18, 18], Operations: ['49-31=18'] Exploring Operation: 18-10=8, Resulting Numbers: [18, 8] Generated Node #0,2,0: 88:[18, 8] Operation: 18-10=8 Exploring Operation: 18-18=0, Resulting Numbers: [10, 0] Generated Node #0,2,1: 88:[10, 0] Operation: 18-18=0 Exploring Operation: 18/18=1, Resulting Numbers: [10, 1] Generated Node #0,2,2: 88:[10, 1] Operation: 18/18=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[10, 1], Operations: ['49-31=18', '18/18=1'] Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,88 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 #0,2,1 Current State: 88:[10, 0], Operations: ['49-31=18', '18-18=0'] Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,88 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 #0,2,0 Current State: 88:[18, 8], Operations: ['49-31=18', '18-10=8'] Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,88 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 88:[49, 18, 21], Operations: ['31-10=21'] Exploring Operation: 49-21=28, Resulting Numbers: [18, 28] Generated Node #0,1,0: 88:[18, 28] Operation: 49-21=28 Exploring Operation: 49-18=31, Resulting Numbers: [21, 31] Generated Node #0,1,1: 88:[21, 31] Operation: 49-18=31 Exploring Operation: 21-18=3, Resulting Numbers: [49, 3] Generated Node #0,1,2: 88:[49, 3] Operation: 21-18=3 Moving to Node #0,0,0 Current State: 88:[49, 3], Operations: ['31-18=13', '13-10=3'] Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,88 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[49, 23], Operations: ['31-18=13', '10+13=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[49, 3], Operations: ['31-10=21', '21-18=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[13, 39], Operations: ['31-18=13', '49-10=39'] Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 13+39=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[21, 31], Operations: ['31-10=21', '49-18=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[18, 28], Operations: ['31-10=21', '49-21=28'] Exploring Operation: 18+28=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 18*28=504, Resulting Numbers: [504] 504,88 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 68, 98, 48, 52 ]
81
[ "52-48=4", "68/4=17", "98-17=81" ]
Current State: 81:[68, 98, 48, 52], Operations: [] Exploring Operation: 52-48=4, Resulting Numbers: [68, 98, 4] Generated Node #2: [68, 98, 4] from Operation: 52-48=4 Current State: 81:[68, 98, 4], Operations: ['52-48=4'] Exploring Operation: 68/4=17, Resulting Numbers: [98, 17] Generated Node #3: [98, 17] from Operation: 68/4=17 Current State: 81:[98, 17], Operations: ['52-48=4', '68/4=17'] Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[68, 98, 48, 52], Operations: [] Exploring Operation: 52-48=4, Resulting Numbers: [68, 98, 4] Generated Node #0,0: 81:[68, 98, 4] Operation: 52-48=4 Exploring Operation: 68-52=16, Resulting Numbers: [98, 48, 16] Generated Node #0,1: 81:[98, 48, 16] Operation: 68-52=16 Moving to Node #0,0 Current State: 81:[68, 98, 4], Operations: ['52-48=4'] Exploring Operation: 68/4=17, Resulting Numbers: [98, 17] Generated Node #0,0,0: 81:[98, 17] Operation: 68/4=17 Exploring Operation: 98-68=30, Resulting Numbers: [4, 30] Generated Node #0,0,1: 81:[4, 30] Operation: 98-68=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[4, 30], Operations: ['52-48=4', '98-68=30'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[98, 17], Operations: ['52-48=4', '68/4=17'] Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[68, 98, 48, 52], Operations: [] Exploring Operation: 52-48=4, Resulting Numbers: [68, 98, 4] Generated Node #0,0: 81:[68, 98, 4] Operation: 52-48=4 Moving to Node #0,0 Current State: 81:[68, 98, 4], Operations: ['52-48=4'] Exploring Operation: 68/4=17, Resulting Numbers: [98, 17] Generated Node #0,0,0: 81:[98, 17] Operation: 68/4=17 Moving to Node #0,0,0 Current State: 81:[98, 17], Operations: ['52-48=4', '68/4=17'] Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 55, 23, 30, 17 ]
11
[ "23-17=6", "55*6=330", "330/30=11" ]
Current State: 11:[55, 23, 30, 17], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [55, 30, 6] Generated Node #2: [55, 30, 6] from Operation: 23-17=6 Current State: 11:[55, 30, 6], Operations: ['23-17=6'] Exploring Operation: 55*6=330, Resulting Numbers: [30, 330] Generated Node #3: [30, 330] from Operation: 55*6=330 Current State: 11:[30, 330], Operations: ['23-17=6', '55*6=330'] Exploring Operation: 330/30=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[55, 23, 30, 17], Operations: [] Exploring Operation: 55-30=25, Resulting Numbers: [23, 17, 25] Generated Node #0,0: 11:[23, 17, 25] Operation: 55-30=25 Exploring Operation: 55-23=32, Resulting Numbers: [30, 17, 32] Generated Node #0,1: 11:[30, 17, 32] Operation: 55-23=32 Exploring Operation: 55-17=38, Resulting Numbers: [23, 30, 38] Generated Node #0,2: 11:[23, 30, 38] Operation: 55-17=38 Exploring Operation: 30-23=7, Resulting Numbers: [55, 17, 7] Generated Node #0,3: 11:[55, 17, 7] Operation: 30-23=7 Moving to Node #0,0 Current State: 11:[23, 17, 25], Operations: ['55-30=25'] Exploring Operation: 25-17=8, Resulting Numbers: [23, 8] Generated Node #0,0,0: 11:[23, 8] Operation: 25-17=8 Exploring Operation: 23-17=6, Resulting Numbers: [25, 6] Generated Node #0,0,1: 11:[25, 6] Operation: 23-17=6 Exploring Operation: 23+17=40, Resulting Numbers: [25, 40] Generated Node #0,0,2: 11:[25, 40] Operation: 23+17=40 Exploring Operation: 25-23=2, Resulting Numbers: [17, 2] Generated Node #0,0,3: 11:[17, 2] Operation: 25-23=2 Moving to Node #0,1 Current State: 11:[30, 17, 32], Operations: ['55-23=32'] Exploring Operation: 32-17=15, Resulting Numbers: [30, 15] Generated Node #0,1,0: 11:[30, 15] Operation: 32-17=15 Exploring Operation: 32-30=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 11:[17, 2] Operation: 32-30=2 Exploring Operation: 30-17=13, Resulting Numbers: [32, 13] Generated Node #0,1,2: 11:[32, 13] Operation: 30-17=13 Exploring Operation: 30+17=47, Resulting Numbers: [32, 47] Generated Node #0,1,3: 11:[32, 47] Operation: 30+17=47 Moving to Node #0,3 Current State: 11:[55, 17, 7], Operations: ['30-23=7'] Exploring Operation: 17-7=10, Resulting Numbers: [55, 10] Generated Node #0,3,0: 11:[55, 10] Operation: 17-7=10 Exploring Operation: 55-17=38, Resulting Numbers: [7, 38] Generated Node #0,3,1: 11:[7, 38] Operation: 55-17=38 Exploring Operation: 55-7=48, Resulting Numbers: [17, 48] Generated Node #0,3,2: 11:[17, 48] Operation: 55-7=48 Exploring Operation: 55+7=62, Resulting Numbers: [17, 62] Generated Node #0,3,3: 11:[17, 62] Operation: 55+7=62 Moving to Node #0,2 Current State: 11:[23, 30, 38], Operations: ['55-17=38'] Exploring Operation: 23+30=53, Resulting Numbers: [38, 53] Generated Node #0,2,0: 11:[38, 53] Operation: 23+30=53 Exploring Operation: 38-30=8, Resulting Numbers: [23, 8] Generated Node #0,2,1: 11:[23, 8] Operation: 38-30=8 Exploring Operation: 30-23=7, Resulting Numbers: [38, 7] Generated Node #0,2,2: 11:[38, 7] Operation: 30-23=7 Exploring Operation: 38-23=15, Resulting Numbers: [30, 15] Generated Node #0,2,3: 11:[30, 15] Operation: 38-23=15 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[23, 8], Operations: ['55-17=38', '38-30=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,11 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,11 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:[30, 15], Operations: ['55-17=38', '38-23=15'] Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,11 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,11 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:[38, 7], Operations: ['55-17=38', '30-23=7'] Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,11 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:[38, 53], Operations: ['55-17=38', '23+30=53'] Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,11 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,11 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,11 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: 11:[23, 8], Operations: ['55-30=25', '25-17=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[17, 2], Operations: ['55-30=25', '25-23=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[17, 2], Operations: ['55-23=32', '32-30=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[25, 6], Operations: ['55-30=25', '23-17=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[32, 13], Operations: ['55-23=32', '30-17=13'] Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,11 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[30, 15], Operations: ['55-23=32', '32-17=15'] Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[7, 38], Operations: ['30-23=7', '55-17=38'] Exploring Operation: 7+38=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 7*38=266, Resulting Numbers: [266] 266,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[17, 48], Operations: ['30-23=7', '55-7=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,11 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[25, 40], Operations: ['55-30=25', '23+17=40'] Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[55, 10], Operations: ['30-23=7', '17-7=10'] Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,11 unequal: No Solution Exploring Operation: 55*10=550, Resulting Numbers: [550] 550,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[32, 47], Operations: ['55-23=32', '30+17=47'] Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,11 unequal: No Solution Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,11 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[17, 62], Operations: ['30-23=7', '55+7=62'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 17*62=1054, Resulting Numbers: [1054] 1054,11 unequal: No Solution Exploring Operation: 17+62=79, Resulting Numbers: [79] 79,11 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 9, 29, 3, 30 ]
77
[ "9*29=261", "261-30=231", "231/3=77" ]
Current State: 77:[9, 29, 3, 30], Operations: [] Exploring Operation: 9*29=261, Resulting Numbers: [3, 30, 261] Generated Node #2: [3, 30, 261] from Operation: 9*29=261 Current State: 77:[3, 30, 261], Operations: ['9*29=261'] Exploring Operation: 261-30=231, Resulting Numbers: [3, 231] Generated Node #3: [3, 231] from Operation: 261-30=231 Current State: 77:[3, 231], Operations: ['9*29=261', '261-30=231'] Exploring Operation: 231/3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[9, 29, 3, 30], Operations: [] Exploring Operation: 30-29=1, Resulting Numbers: [9, 3, 1] Generated Node #0,0: 77:[9, 3, 1] Operation: 30-29=1 Exploring Operation: 29+30=59, Resulting Numbers: [9, 3, 59] Generated Node #0,1: 77:[9, 3, 59] Operation: 29+30=59 Exploring Operation: 30/3=10, Resulting Numbers: [9, 29, 10] Generated Node #0,2: 77:[9, 29, 10] Operation: 30/3=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[9, 3, 1], Operations: ['30-29=1'] Exploring Operation: 3+1=4, Resulting Numbers: [9, 4] Generated Node #0,0,0: 77:[9, 4] Operation: 3+1=4 Exploring Operation: 9-1=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 77:[3, 8] Operation: 9-1=8 Exploring Operation: 9+1=10, Resulting Numbers: [3, 10] Generated Node #0,0,2: 77:[3, 10] Operation: 9+1=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[9, 4], Operations: ['30-29=1', '3+1=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[3, 8], Operations: ['30-29=1', '9-1=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[3, 10], Operations: ['30-29=1', '9+1=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[9, 29, 10], Operations: ['30/3=10'] Exploring Operation: 29-10=19, Resulting Numbers: [9, 19] Generated Node #0,2,0: 77:[9, 19] Operation: 29-10=19 Exploring Operation: 10-9=1, Resulting Numbers: [29, 1] Generated Node #0,2,1: 77:[29, 1] Operation: 10-9=1 Exploring Operation: 29-9=20, Resulting Numbers: [10, 20] Generated Node #0,2,2: 77:[10, 20] Operation: 29-9=20 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[9, 19], Operations: ['30/3=10', '29-10=19'] Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,77 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,77 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[10, 20], Operations: ['30/3=10', '29-9=20'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[29, 1], Operations: ['30/3=10', '10-9=1'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,77 unequal: No Solution Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,77 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[9, 3, 59], Operations: ['29+30=59'] Exploring Operation: 9+59=68, Resulting Numbers: [3, 68] Generated Node #0,1,0: 77:[3, 68] Operation: 9+59=68 Exploring Operation: 9+3=12, Resulting Numbers: [59, 12] Generated Node #0,1,1: 77:[59, 12] Operation: 9+3=12 Exploring Operation: 3+59=62, Resulting Numbers: [9, 62] Generated Node #0,1,2: 77:[9, 62] Operation: 3+59=62 Moving to Node #0,1,0 Current State: 77:[3, 68], Operations: ['29+30=59', '9+59=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,77 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,77 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[9, 62], Operations: ['29+30=59', '3+59=62'] Exploring Operation: 9+62=71, Resulting Numbers: [71] 71,77 unequal: No Solution Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,77 unequal: No Solution Exploring Operation: 9*62=558, Resulting Numbers: [558] 558,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[59, 12], Operations: ['29+30=59', '9+3=12'] Exploring Operation: 59*12=708, Resulting Numbers: [708] 708,77 unequal: No Solution Exploring Operation: 59+12=71, Resulting Numbers: [71] 71,77 unequal: No Solution Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 82, 70, 72, 91 ]
78
[ "91-82=9", "72/9=8", "70+8=78" ]
Current State: 78:[82, 70, 72, 91], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [70, 72, 9] Generated Node #2: [70, 72, 9] from Operation: 91-82=9 Current State: 78:[70, 72, 9], Operations: ['91-82=9'] Exploring Operation: 72/9=8, Resulting Numbers: [70, 8] Generated Node #3: [70, 8] from Operation: 72/9=8 Current State: 78:[70, 8], Operations: ['91-82=9', '72/9=8'] Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[82, 70, 72, 91], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [70, 72, 9] Generated Node #0,0: 78:[70, 72, 9] Operation: 91-82=9 Exploring Operation: 91-70=21, Resulting Numbers: [82, 72, 21] Generated Node #0,1: 78:[82, 72, 21] Operation: 91-70=21 Exploring Operation: 72-70=2, Resulting Numbers: [82, 91, 2] Generated Node #0,2: 78:[82, 91, 2] Operation: 72-70=2 Moving to Node #0,1 Current State: 78:[82, 72, 21], Operations: ['91-70=21'] Exploring Operation: 72-21=51, Resulting Numbers: [82, 51] Generated Node #0,1,0: 78:[82, 51] Operation: 72-21=51 Exploring Operation: 72+21=93, Resulting Numbers: [82, 93] Generated Node #0,1,1: 78:[82, 93] Operation: 72+21=93 Exploring Operation: 82-72=10, Resulting Numbers: [21, 10] Generated Node #0,1,2: 78:[21, 10] Operation: 82-72=10 Moving to Node #0,0 Current State: 78:[70, 72, 9], Operations: ['91-82=9'] Exploring Operation: 72/9=8, Resulting Numbers: [70, 8] Generated Node #0,0,0: 78:[70, 8] Operation: 72/9=8 Exploring Operation: 72-70=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 78:[9, 2] Operation: 72-70=2 Exploring Operation: 70+9=79, Resulting Numbers: [72, 79] Generated Node #0,0,2: 78:[72, 79] Operation: 70+9=79 Moving to Node #0,2 Current State: 78:[82, 91, 2], Operations: ['72-70=2'] Exploring Operation: 82/2=41, Resulting Numbers: [91, 41] Generated Node #0,2,0: 78:[91, 41] Operation: 82/2=41 Exploring Operation: 82-2=80, Resulting Numbers: [91, 80] Generated Node #0,2,1: 78:[91, 80] Operation: 82-2=80 Exploring Operation: 91-82=9, Resulting Numbers: [2, 9] Generated Node #0,2,2: 78:[2, 9] Operation: 91-82=9 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[2, 9], Operations: ['72-70=2', '91-82=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,78 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[91, 41], Operations: ['72-70=2', '82/2=41'] Exploring Operation: 91+41=132, Resulting Numbers: [132] 132,78 unequal: No Solution Exploring Operation: 91*41=3731, Resulting Numbers: [3731] 3731,78 unequal: No Solution Exploring Operation: 91-41=50, Resulting Numbers: [50] 50,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[91, 80], Operations: ['72-70=2', '82-2=80'] Exploring Operation: 91*80=7280, Resulting Numbers: [7280] 7280,78 unequal: No Solution Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 91+80=171, Resulting Numbers: [171] 171,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 78:[9, 2], Operations: ['91-82=9', '72-70=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,78 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[72, 79], Operations: ['91-82=9', '70+9=79'] Exploring Operation: 72+79=151, Resulting Numbers: [151] 151,78 unequal: No Solution Exploring Operation: 79-72=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 72*79=5688, Resulting Numbers: [5688] 5688,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[21, 10], Operations: ['91-70=21', '82-72=10'] Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,78 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[70, 8], Operations: ['91-82=9', '72/9=8'] Exploring Operation: 70*8=560, Resulting Numbers: [560] 560,78 unequal: No Solution Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[82, 70, 72, 91], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [70, 72, 9] Generated Node #0,0: 78:[70, 72, 9] Operation: 91-82=9 Moving to Node #0,0 Current State: 78:[70, 72, 9], Operations: ['91-82=9'] Exploring Operation: 72/9=8, Resulting Numbers: [70, 8] Generated Node #0,0,0: 78:[70, 8] Operation: 72/9=8 Moving to Node #0,0,0 Current State: 78:[70, 8], Operations: ['91-82=9', '72/9=8'] Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 43, 85, 37, 89 ]
84
[ "85-43=42", "37+89=126", "126-42=84" ]
Current State: 84:[43, 85, 37, 89], Operations: [] Exploring Operation: 85-43=42, Resulting Numbers: [37, 89, 42] Generated Node #2: [37, 89, 42] from Operation: 85-43=42 Current State: 84:[37, 89, 42], Operations: ['85-43=42'] Exploring Operation: 37+89=126, Resulting Numbers: [42, 126] Generated Node #3: [42, 126] from Operation: 37+89=126 Current State: 84:[42, 126], Operations: ['85-43=42', '37+89=126'] Exploring Operation: 126-42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[43, 85, 37, 89], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [43, 37, 4] Generated Node #0,0: 84:[43, 37, 4] Operation: 89-85=4 Exploring Operation: 43-37=6, Resulting Numbers: [85, 89, 6] Generated Node #0,1: 84:[85, 89, 6] Operation: 43-37=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[43, 37, 4], Operations: ['89-85=4'] Exploring Operation: 43-37=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 84:[4, 6] Operation: 43-37=6 Exploring Operation: 37+4=41, Resulting Numbers: [43, 41] Generated Node #0,0,1: 84:[43, 41] Operation: 37+4=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[4, 6], Operations: ['89-85=4', '43-37=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,84 unequal: No Solution No 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: 84:[43, 41], Operations: ['89-85=4', '37+4=41'] Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[43, 85, 37, 89], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [43, 37, 4] Generated Node #0,0: 84:[43, 37, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 84:[43, 37, 4], Operations: ['89-85=4'] Exploring Operation: 37+4=41, Resulting Numbers: [43, 41] Generated Node #0,0,1: 84:[43, 41] Operation: 37+4=41 Moving to Node #0,0,1 Current State: 84:[43, 41], Operations: ['89-85=4', '37+4=41'] Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 55, 68, 89, 60 ]
42
[ "68-55=13", "89-60=29", "13+29=42" ]
Current State: 42:[55, 68, 89, 60], Operations: [] Exploring Operation: 68-55=13, Resulting Numbers: [89, 60, 13] Generated Node #2: [89, 60, 13] from Operation: 68-55=13 Current State: 42:[89, 60, 13], Operations: ['68-55=13'] Exploring Operation: 89-60=29, Resulting Numbers: [13, 29] Generated Node #3: [13, 29] from Operation: 89-60=29 Current State: 42:[13, 29], Operations: ['68-55=13', '89-60=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[55, 68, 89, 60], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [55, 60, 21] Generated Node #0,0: 42:[55, 60, 21] Operation: 89-68=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[55, 60, 21], Operations: ['89-68=21'] Exploring Operation: 60-55=5, Resulting Numbers: [21, 5] Generated Node #0,0,0: 42:[21, 5] Operation: 60-55=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[21, 5], Operations: ['89-68=21', '60-55=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 8, 87, 10, 11 ]
10
[ "8*11=88", "88-87=1", "10*1=10" ]
Current State: 10:[8, 87, 10, 11], Operations: [] Exploring Operation: 8*11=88, Resulting Numbers: [87, 10, 88] Generated Node #2: [87, 10, 88] from Operation: 8*11=88 Current State: 10:[87, 10, 88], Operations: ['8*11=88'] Exploring Operation: 88-87=1, Resulting Numbers: [10, 1] Generated Node #3: [10, 1] from Operation: 88-87=1 Current State: 10:[10, 1], Operations: ['8*11=88', '88-87=1'] Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[8, 87, 10, 11], Operations: [] Exploring Operation: 87-11=76, Resulting Numbers: [8, 10, 76] Generated Node #0,0: 10:[8, 10, 76] Operation: 87-11=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[8, 10, 76], Operations: ['87-11=76'] Exploring Operation: 76-8=68, Resulting Numbers: [10, 68] Generated Node #0,0,0: 10:[10, 68] Operation: 76-8=68 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[10, 68], Operations: ['87-11=76', '76-8=68'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 46, 43, 14, 46 ]
14
[ "46-46=0", "43*0=0", "14+0=14" ]
Current State: 14:[46, 43, 14, 46], Operations: [] Exploring Operation: 46-46=0, Resulting Numbers: [43, 14, 0] Generated Node #2: [43, 14, 0] from Operation: 46-46=0 Current State: 14:[43, 14, 0], Operations: ['46-46=0'] Exploring Operation: 43*0=0, Resulting Numbers: [14, 0] Generated Node #3: [14, 0] from Operation: 43*0=0 Current State: 14:[14, 0], Operations: ['46-46=0', '43*0=0'] Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[46, 43, 14, 46], Operations: [] Exploring Operation: 46-43=3, Resulting Numbers: [46, 14, 3] Generated Node #0,0: 14:[46, 14, 3] Operation: 46-43=3 Exploring Operation: 46-14=32, Resulting Numbers: [43, 46, 32] Generated Node #0,1: 14:[43, 46, 32] Operation: 46-14=32 Exploring Operation: 46-46=0, Resulting Numbers: [43, 14, 0] Generated Node #0,2: 14:[43, 14, 0] Operation: 46-46=0 Exploring Operation: 46/46=1, Resulting Numbers: [43, 14, 1] Generated Node #0,3: 14:[43, 14, 1] Operation: 46/46=1 Exploring Operation: 46-43=3, Resulting Numbers: [14, 46, 3] Generated Node #0,4: 14:[14, 46, 3] Operation: 46-43=3 Moving to Node #0,3 Current State: 14:[43, 14, 1], Operations: ['46/46=1'] Exploring Operation: 43-14=29, Resulting Numbers: [1, 29] Generated Node #0,3,0: 14:[1, 29] Operation: 43-14=29 Exploring Operation: 14*1=14, Resulting Numbers: [43, 14] Generated Node #0,3,1: 14:[43, 14] Operation: 14*1=14 Exploring Operation: 43*1=43, Resulting Numbers: [14, 43] Generated Node #0,3,2: 14:[14, 43] Operation: 43*1=43 Exploring Operation: 43/1=43, Resulting Numbers: [14, 43] Generated Node #0,3,3: 14:[14, 43] Operation: 43/1=43 Exploring Operation: 43-1=42, Resulting Numbers: [14, 42] Generated Node #0,3,4: 14:[14, 42] Operation: 43-1=42 Moving to Node #0,2 Current State: 14:[43, 14, 0], Operations: ['46-46=0'] Exploring Operation: 43+0=43, Resulting Numbers: [14, 43] Generated Node #0,2,0: 14:[14, 43] Operation: 43+0=43 Exploring Operation: 43-14=29, Resulting Numbers: [0, 29] Generated Node #0,2,1: 14:[0, 29] Operation: 43-14=29 Exploring Operation: 43*0=0, Resulting Numbers: [14, 0] Generated Node #0,2,2: 14:[14, 0] Operation: 43*0=0 Exploring Operation: 14+0=14, Resulting Numbers: [43, 14] Generated Node #0,2,3: 14:[43, 14] Operation: 14+0=14 Exploring Operation: 43-0=43, Resulting Numbers: [14, 43] Generated Node #0,2,4: 14:[14, 43] Operation: 43-0=43 Moving to Node #0,0 Current State: 14:[46, 14, 3], Operations: ['46-43=3'] Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #0,0,0: 14:[3, 32] Operation: 46-14=32 Exploring Operation: 46+3=49, Resulting Numbers: [14, 49] Generated Node #0,0,1: 14:[14, 49] Operation: 46+3=49 Exploring Operation: 14-3=11, Resulting Numbers: [46, 11] Generated Node #0,0,2: 14:[46, 11] Operation: 14-3=11 Exploring Operation: 14+3=17, Resulting Numbers: [46, 17] Generated Node #0,0,3: 14:[46, 17] Operation: 14+3=17 Exploring Operation: 46-3=43, Resulting Numbers: [14, 43] Generated Node #0,0,4: 14:[14, 43] Operation: 46-3=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[3, 32], Operations: ['46-43=3', '46-14=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,14 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 #0,0,4 Current State: 14:[14, 43], Operations: ['46-43=3', '46-3=43'] Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,14 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,14 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 #0,0,1 Current State: 14:[14, 49], Operations: ['46-43=3', '46+3=49'] Exploring Operation: 14*49=686, Resulting Numbers: [686] 686,14 unequal: No Solution Exploring Operation: 14+49=63, Resulting Numbers: [63] 63,14 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,14 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 #0,0,2 Current State: 14:[46, 11], Operations: ['46-43=3', '14-3=11'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 46*11=506, Resulting Numbers: [506] 506,14 unequal: No Solution Exploring Operation: 46+11=57, Resulting Numbers: [57] 57,14 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 #0,0,3 Current State: 14:[46, 17], Operations: ['46-43=3', '14+3=17'] Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,14 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,14 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,14 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: 14:[14, 46, 3], Operations: ['46-43=3'] Exploring Operation: 46+3=49, Resulting Numbers: [14, 49] Generated Node #0,4,0: 14:[14, 49] Operation: 46+3=49 Exploring Operation: 14+3=17, Resulting Numbers: [46, 17] Generated Node #0,4,1: 14:[46, 17] Operation: 14+3=17 Exploring Operation: 46-3=43, Resulting Numbers: [14, 43] Generated Node #0,4,2: 14:[14, 43] Operation: 46-3=43 Exploring Operation: 46-14=32, Resulting Numbers: [3, 32] Generated Node #0,4,3: 14:[3, 32] Operation: 46-14=32 Exploring Operation: 14-3=11, Resulting Numbers: [46, 11] Generated Node #0,4,4: 14:[46, 11] Operation: 14-3=11 Moving to Node #0,1 Current State: 14:[43, 46, 32], Operations: ['46-14=32'] Exploring Operation: 43+32=75, Resulting Numbers: [46, 75] Generated Node #0,1,0: 14:[46, 75] Operation: 43+32=75 Exploring Operation: 46-43=3, Resulting Numbers: [32, 3] Generated Node #0,1,1: 14:[32, 3] Operation: 46-43=3 Exploring Operation: 43-32=11, Resulting Numbers: [46, 11] Generated Node #0,1,2: 14:[46, 11] Operation: 43-32=11 Exploring Operation: 46-32=14, Resulting Numbers: [43, 14] Generated Node #0,1,3: 14:[43, 14] Operation: 46-32=14 Exploring Operation: 43+46=89, Resulting Numbers: [32, 89] Generated Node #0,1,4: 14:[32, 89] Operation: 43+46=89 Moving to Node #0,2,2 Current State: 14:[14, 0], Operations: ['46-46=0', '43*0=0'] Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[46, 43, 14, 46], Operations: [] Exploring Operation: 46-46=0, Resulting Numbers: [43, 14, 0] Generated Node #0,2: 14:[43, 14, 0] Operation: 46-46=0 Moving to Node #0,2 Current State: 14:[43, 14, 0], Operations: ['46-46=0'] Exploring Operation: 43*0=0, Resulting Numbers: [14, 0] Generated Node #0,2,2: 14:[14, 0] Operation: 43*0=0 Moving to Node #0,2,2 Current State: 14:[14, 0], Operations: ['46-46=0', '43*0=0'] Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.956597
hs_5
mult_heuristic
[ 8, 27, 99, 81 ]
37
[ "27-8=19", "99-81=18", "19+18=37" ]
Current State: 37:[8, 27, 99, 81], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [99, 81, 19] Generated Node #2: [99, 81, 19] from Operation: 27-8=19 Current State: 37:[99, 81, 19], Operations: ['27-8=19'] Exploring Operation: 99-81=18, Resulting Numbers: [19, 18] Generated Node #3: [19, 18] from Operation: 99-81=18 Current State: 37:[19, 18], Operations: ['27-8=19', '99-81=18'] Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[8, 27, 99, 81], Operations: [] Exploring Operation: 99-81=18, Resulting Numbers: [8, 27, 18] Generated Node #0,0: 37:[8, 27, 18] Operation: 99-81=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[8, 27, 18], Operations: ['99-81=18'] Exploring Operation: 8+27=35, Resulting Numbers: [18, 35] Generated Node #0,0,0: 37:[18, 35] Operation: 8+27=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[18, 35], Operations: ['99-81=18', '8+27=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 30, 76, 3, 36 ]
78
[ "36-30=6", "6/3=2", "76+2=78" ]
Current State: 78:[30, 76, 3, 36], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [76, 3, 6] Generated Node #2: [76, 3, 6] from Operation: 36-30=6 Current State: 78:[76, 3, 6], Operations: ['36-30=6'] Exploring Operation: 6/3=2, Resulting Numbers: [76, 2] Generated Node #3: [76, 2] from Operation: 6/3=2 Current State: 78:[76, 2], Operations: ['36-30=6', '6/3=2'] Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[30, 76, 3, 36], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [76, 3, 6] Generated Node #0,0: 78:[76, 3, 6] Operation: 36-30=6 Moving to Node #0,0 Current State: 78:[76, 3, 6], Operations: ['36-30=6'] Exploring Operation: 76+3=79, Resulting Numbers: [6, 79] Generated Node #0,0,0: 78:[6, 79] Operation: 76+3=79 Moving to Node #0,0,0 Current State: 78:[6, 79], Operations: ['36-30=6', '76+3=79'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,78 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 10, 26, 70, 61 ]
64
[ "70-61=9", "10*9=90", "90-26=64" ]
Current State: 64:[10, 26, 70, 61], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [10, 26, 9] Generated Node #2: [10, 26, 9] from Operation: 70-61=9 Current State: 64:[10, 26, 9], Operations: ['70-61=9'] Exploring Operation: 10*9=90, Resulting Numbers: [26, 90] Generated Node #3: [26, 90] from Operation: 10*9=90 Current State: 64:[26, 90], Operations: ['70-61=9', '10*9=90'] Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[10, 26, 70, 61], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [10, 26, 9] Generated Node #0,0: 64:[10, 26, 9] Operation: 70-61=9 Exploring Operation: 26-10=16, Resulting Numbers: [70, 61, 16] Generated Node #0,1: 64:[70, 61, 16] Operation: 26-10=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[10, 26, 9], Operations: ['70-61=9'] Exploring Operation: 26-10=16, Resulting Numbers: [9, 16] Generated Node #0,0,0: 64:[9, 16] Operation: 26-10=16 Exploring Operation: 26-9=17, Resulting Numbers: [10, 17] Generated Node #0,0,1: 64:[10, 17] Operation: 26-9=17 Moving to Node #0,0,0 Current State: 64:[9, 16], Operations: ['70-61=9', '26-10=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,64 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[10, 17], Operations: ['70-61=9', '26-9=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[70, 61, 16], Operations: ['26-10=16'] Exploring Operation: 70-16=54, Resulting Numbers: [61, 54] Generated Node #0,1,0: 64:[61, 54] Operation: 70-16=54 Exploring Operation: 70-61=9, Resulting Numbers: [16, 9] Generated Node #0,1,1: 64:[16, 9] Operation: 70-61=9 Moving to Node #0,1,1 Current State: 64:[16, 9], Operations: ['26-10=16', '70-61=9'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[61, 54], Operations: ['26-10=16', '70-16=54'] Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 61+54=115, Resulting Numbers: [115] 115,64 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
[ 57, 94, 11, 31 ]
17
[ "94-57=37", "31-11=20", "37-20=17" ]
Current State: 17:[57, 94, 11, 31], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [11, 31, 37] Generated Node #2: [11, 31, 37] from Operation: 94-57=37 Current State: 17:[11, 31, 37], Operations: ['94-57=37'] Exploring Operation: 31-11=20, Resulting Numbers: [37, 20] Generated Node #3: [37, 20] from Operation: 31-11=20 Current State: 17:[37, 20], Operations: ['94-57=37', '31-11=20'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[57, 94, 11, 31], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [11, 31, 37] Generated Node #0,0: 17:[11, 31, 37] Operation: 94-57=37 Exploring Operation: 57-31=26, Resulting Numbers: [94, 11, 26] Generated Node #0,1: 17:[94, 11, 26] Operation: 57-31=26 Moving to Node #0,0 Current State: 17:[11, 31, 37], Operations: ['94-57=37'] Exploring Operation: 31-11=20, Resulting Numbers: [37, 20] Generated Node #0,0,0: 17:[37, 20] Operation: 31-11=20 Exploring Operation: 37-31=6, Resulting Numbers: [11, 6] Generated Node #0,0,1: 17:[11, 6] Operation: 37-31=6 Moving to Node #0,1 Current State: 17:[94, 11, 26], Operations: ['57-31=26'] Exploring Operation: 94-11=83, Resulting Numbers: [26, 83] Generated Node #0,1,0: 17:[26, 83] Operation: 94-11=83 Exploring Operation: 94-26=68, Resulting Numbers: [11, 68] Generated Node #0,1,1: 17:[11, 68] Operation: 94-26=68 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[11, 68], Operations: ['57-31=26', '94-26=68'] Exploring Operation: 11+68=79, Resulting Numbers: [79] 79,17 unequal: No Solution Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,17 unequal: No Solution No 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: 17:[26, 83], Operations: ['57-31=26', '94-11=83'] Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,17 unequal: No Solution Exploring Operation: 26+83=109, Resulting Numbers: [109] 109,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 17:[11, 6], Operations: ['94-57=37', '37-31=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[57, 94, 11, 31], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [11, 31, 37] Generated Node #0,0: 17:[11, 31, 37] Operation: 94-57=37 Moving to Node #0,0 Current State: 17:[11, 31, 37], Operations: ['94-57=37'] Exploring Operation: 37-31=6, Resulting Numbers: [11, 6] Generated Node #0,0,1: 17:[11, 6] Operation: 37-31=6 Moving to Node #0,0,1 Current State: 17:[11, 6], Operations: ['94-57=37', '37-31=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 34, 51, 2, 71 ]
46
[ "71-2=69", "34*69=2346", "2346/51=46" ]
Current State: 46:[34, 51, 2, 71], Operations: [] Exploring Operation: 71-2=69, Resulting Numbers: [34, 51, 69] Generated Node #2: [34, 51, 69] from Operation: 71-2=69 Current State: 46:[34, 51, 69], Operations: ['71-2=69'] Exploring Operation: 34*69=2346, Resulting Numbers: [51, 2346] Generated Node #3: [51, 2346] from Operation: 34*69=2346 Current State: 46:[51, 2346], Operations: ['71-2=69', '34*69=2346'] Exploring Operation: 2346/51=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[34, 51, 2, 71], Operations: [] Exploring Operation: 71-34=37, Resulting Numbers: [51, 2, 37] Generated Node #0,0: 46:[51, 2, 37] Operation: 71-34=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[51, 2, 37], Operations: ['71-34=37'] Exploring Operation: 51-37=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 46:[2, 14] Operation: 51-37=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[2, 14], Operations: ['71-34=37', '51-37=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 7, 58, 62, 39 ]
13
[ "7+58=65", "65-62=3", "39/3=13" ]
Current State: 13:[7, 58, 62, 39], Operations: [] Exploring Operation: 7+58=65, Resulting Numbers: [62, 39, 65] Generated Node #2: [62, 39, 65] from Operation: 7+58=65 Current State: 13:[62, 39, 65], Operations: ['7+58=65'] Exploring Operation: 65-62=3, Resulting Numbers: [39, 3] Generated Node #3: [39, 3] from Operation: 65-62=3 Current State: 13:[39, 3], Operations: ['7+58=65', '65-62=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[7, 58, 62, 39], Operations: [] Exploring Operation: 58-39=19, Resulting Numbers: [7, 62, 19] Generated Node #0,0: 13:[7, 62, 19] Operation: 58-39=19 Exploring Operation: 62-58=4, Resulting Numbers: [7, 39, 4] Generated Node #0,1: 13:[7, 39, 4] Operation: 62-58=4 Exploring Operation: 62-39=23, Resulting Numbers: [7, 58, 23] Generated Node #0,2: 13:[7, 58, 23] Operation: 62-39=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[7, 39, 4], Operations: ['62-58=4'] Exploring Operation: 7+4=11, Resulting Numbers: [39, 11] Generated Node #0,1,0: 13:[39, 11] Operation: 7+4=11 Exploring Operation: 39-7=32, Resulting Numbers: [4, 32] Generated Node #0,1,1: 13:[4, 32] Operation: 39-7=32 Exploring Operation: 39-4=35, Resulting Numbers: [7, 35] Generated Node #0,1,2: 13:[7, 35] Operation: 39-4=35 Moving to Node #0,1,0 Current State: 13:[39, 11], Operations: ['62-58=4', '7+4=11'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,13 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[4, 32], Operations: ['62-58=4', '39-7=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[7, 35], Operations: ['62-58=4', '39-4=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[7, 62, 19], Operations: ['58-39=19'] Exploring Operation: 62-7=55, Resulting Numbers: [19, 55] Generated Node #0,0,0: 13:[19, 55] Operation: 62-7=55 Exploring Operation: 19-7=12, Resulting Numbers: [62, 12] Generated Node #0,0,1: 13:[62, 12] Operation: 19-7=12 Exploring Operation: 62-19=43, Resulting Numbers: [7, 43] Generated Node #0,0,2: 13:[7, 43] Operation: 62-19=43 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[7, 43], Operations: ['58-39=19', '62-19=43'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,13 unequal: No Solution Exploring Operation: 7*43=301, Resulting Numbers: [301] 301,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[19, 55], Operations: ['58-39=19', '62-7=55'] Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,13 unequal: No Solution Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[62, 12], Operations: ['58-39=19', '19-7=12'] Exploring Operation: 62-12=50, Resulting Numbers: [50] 50,13 unequal: No Solution Exploring Operation: 62+12=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 62*12=744, Resulting Numbers: [744] 744,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[7, 58, 23], Operations: ['62-39=23'] Exploring Operation: 58-23=35, Resulting Numbers: [7, 35] Generated Node #0,2,0: 13:[7, 35] Operation: 58-23=35 Exploring Operation: 23-7=16, Resulting Numbers: [58, 16] Generated Node #0,2,1: 13:[58, 16] Operation: 23-7=16 Exploring Operation: 58-7=51, Resulting Numbers: [23, 51] Generated Node #0,2,2: 13:[23, 51] Operation: 58-7=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[7, 35], Operations: ['62-39=23', '58-23=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,13 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[58, 16], Operations: ['62-39=23', '23-7=16'] Exploring Operation: 58*16=928, Resulting Numbers: [928] 928,13 unequal: No Solution Exploring Operation: 58+16=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[23, 51], Operations: ['62-39=23', '58-7=51'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,13 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 46, 19, 7, 4 ]
91
[ "46-4=42", "19*7=133", "133-42=91" ]
Current State: 91:[46, 19, 7, 4], Operations: [] Exploring Operation: 46-4=42, Resulting Numbers: [19, 7, 42] Generated Node #2: [19, 7, 42] from Operation: 46-4=42 Current State: 91:[19, 7, 42], Operations: ['46-4=42'] Exploring Operation: 19*7=133, Resulting Numbers: [42, 133] Generated Node #3: [42, 133] from Operation: 19*7=133 Current State: 91:[42, 133], Operations: ['46-4=42', '19*7=133'] Exploring Operation: 133-42=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[46, 19, 7, 4], Operations: [] Exploring Operation: 46+19=65, Resulting Numbers: [7, 4, 65] Generated Node #0,0: 91:[7, 4, 65] Operation: 46+19=65 Exploring Operation: 46-7=39, Resulting Numbers: [19, 4, 39] Generated Node #0,1: 91:[19, 4, 39] Operation: 46-7=39 Exploring Operation: 46-19=27, Resulting Numbers: [7, 4, 27] Generated Node #0,2: 91:[7, 4, 27] Operation: 46-19=27 Exploring Operation: 46-4=42, Resulting Numbers: [19, 7, 42] Generated Node #0,3: 91:[19, 7, 42] Operation: 46-4=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[7, 4, 27], Operations: ['46-19=27'] Exploring Operation: 7+4=11, Resulting Numbers: [27, 11] Generated Node #0,2,0: 91:[27, 11] Operation: 7+4=11 Exploring Operation: 4*27=108, Resulting Numbers: [7, 108] Generated Node #0,2,1: 91:[7, 108] Operation: 4*27=108 Exploring Operation: 27-4=23, Resulting Numbers: [7, 23] Generated Node #0,2,2: 91:[7, 23] Operation: 27-4=23 Exploring Operation: 27-7=20, Resulting Numbers: [4, 20] Generated Node #0,2,3: 91:[4, 20] Operation: 27-7=20 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[7, 23], Operations: ['46-19=27', '27-4=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,91 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,91 unequal: No Solution No 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: 91:[4, 20], Operations: ['46-19=27', '27-7=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,91 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,91 unequal: No Solution No 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: 91:[27, 11], Operations: ['46-19=27', '7+4=11'] Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,91 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,91 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,91 unequal: No Solution No 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: 91:[7, 108], Operations: ['46-19=27', '4*27=108'] Exploring Operation: 108-7=101, Resulting Numbers: [101] 101,91 unequal: No Solution Exploring Operation: 7+108=115, Resulting Numbers: [115] 115,91 unequal: No Solution Exploring Operation: 7*108=756, Resulting Numbers: [756] 756,91 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: 91:[7, 4, 65], Operations: ['46+19=65'] Exploring Operation: 7+65=72, Resulting Numbers: [4, 72] Generated Node #0,0,0: 91:[4, 72] Operation: 7+65=72 Exploring Operation: 4+65=69, Resulting Numbers: [7, 69] Generated Node #0,0,1: 91:[7, 69] Operation: 4+65=69 Exploring Operation: 7+4=11, Resulting Numbers: [65, 11] Generated Node #0,0,2: 91:[65, 11] Operation: 7+4=11 Exploring Operation: 7-4=3, Resulting Numbers: [65, 3] Generated Node #0,0,3: 91:[65, 3] Operation: 7-4=3 Moving to Node #0,0,0 Current State: 91:[4, 72], Operations: ['46+19=65', '7+65=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,91 unequal: No Solution Exploring Operation: 4*72=288, Resulting Numbers: [288] 288,91 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 4+72=76, Resulting Numbers: [76] 76,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[7, 69], Operations: ['46+19=65', '4+65=69'] Exploring Operation: 7+69=76, Resulting Numbers: [76] 76,91 unequal: No Solution Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 7*69=483, Resulting Numbers: [483] 483,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[65, 11], Operations: ['46+19=65', '7+4=11'] Exploring Operation: 65+11=76, Resulting Numbers: [76] 76,91 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 65*11=715, Resulting Numbers: [715] 715,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[65, 3], Operations: ['46+19=65', '7-4=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[19, 4, 39], Operations: ['46-7=39'] Exploring Operation: 39-4=35, Resulting Numbers: [19, 35] Generated Node #0,1,0: 91:[19, 35] Operation: 39-4=35 Exploring Operation: 39-19=20, Resulting Numbers: [4, 20] Generated Node #0,1,1: 91:[4, 20] Operation: 39-19=20 Exploring Operation: 19+4=23, Resulting Numbers: [39, 23] Generated Node #0,1,2: 91:[39, 23] Operation: 19+4=23 Exploring Operation: 19-4=15, Resulting Numbers: [39, 15] Generated Node #0,1,3: 91:[39, 15] Operation: 19-4=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[4, 20], Operations: ['46-7=39', '39-19=20'] Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,91 unequal: No Solution No 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: 91:[19, 35], Operations: ['46-7=39', '39-4=35'] Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 19*35=665, Resulting Numbers: [665] 665,91 unequal: No Solution No 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: 91:[39, 15], Operations: ['46-7=39', '19-4=15'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,91 unequal: No Solution Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,91 unequal: No Solution No 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: 91:[39, 23], Operations: ['46-7=39', '19+4=23'] Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,91 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,91 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: 91:[19, 7, 42], Operations: ['46-4=42'] Exploring Operation: 42/7=6, Resulting Numbers: [19, 6] Generated Node #0,3,0: 91:[19, 6] Operation: 42/7=6 Exploring Operation: 19-7=12, Resulting Numbers: [42, 12] Generated Node #0,3,1: 91:[42, 12] Operation: 19-7=12 Exploring Operation: 42-19=23, Resulting Numbers: [7, 23] Generated Node #0,3,2: 91:[7, 23] Operation: 42-19=23 Exploring Operation: 42-7=35, Resulting Numbers: [19, 35] Generated Node #0,3,3: 91:[19, 35] Operation: 42-7=35 Moving to Node #0,3,0 Current State: 91:[19, 6], Operations: ['46-4=42', '42/7=6'] Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,91 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,91 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[7, 23], Operations: ['46-4=42', '42-19=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,91 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[19, 35], Operations: ['46-4=42', '42-7=35'] Exploring Operation: 19*35=665, Resulting Numbers: [665] 665,91 unequal: No Solution Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[42, 12], Operations: ['46-4=42', '19-7=12'] Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,91 unequal: No Solution Exploring Operation: 42*12=504, Resulting Numbers: [504] 504,91 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
[ 13, 36, 41, 75 ]
44
[ "75-36=39", "39/13=3", "41+3=44" ]
Current State: 44:[13, 36, 41, 75], Operations: [] Exploring Operation: 75-36=39, Resulting Numbers: [13, 41, 39] Generated Node #2: [13, 41, 39] from Operation: 75-36=39 Current State: 44:[13, 41, 39], Operations: ['75-36=39'] Exploring Operation: 39/13=3, Resulting Numbers: [41, 3] Generated Node #3: [41, 3] from Operation: 39/13=3 Current State: 44:[41, 3], Operations: ['75-36=39', '39/13=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[13, 36, 41, 75], Operations: [] Exploring Operation: 75-41=34, Resulting Numbers: [13, 36, 34] Generated Node #0,0: 44:[13, 36, 34] Operation: 75-41=34 Exploring Operation: 75-36=39, Resulting Numbers: [13, 41, 39] Generated Node #0,1: 44:[13, 41, 39] Operation: 75-36=39 Exploring Operation: 75-13=62, Resulting Numbers: [36, 41, 62] Generated Node #0,2: 44:[36, 41, 62] Operation: 75-13=62 Exploring Operation: 41-36=5, Resulting Numbers: [13, 75, 5] Generated Node #0,3: 44:[13, 75, 5] Operation: 41-36=5 Exploring Operation: 36-13=23, Resulting Numbers: [41, 75, 23] Generated Node #0,4: 44:[41, 75, 23] Operation: 36-13=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[13, 41, 39], Operations: ['75-36=39'] Exploring Operation: 41-39=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 44:[13, 2] Operation: 41-39=2 Exploring Operation: 39-13=26, Resulting Numbers: [41, 26] Generated Node #0,1,1: 44:[41, 26] Operation: 39-13=26 Exploring Operation: 41-13=28, Resulting Numbers: [39, 28] Generated Node #0,1,2: 44:[39, 28] Operation: 41-13=28 Exploring Operation: 39/13=3, Resulting Numbers: [41, 3] Generated Node #0,1,3: 44:[41, 3] Operation: 39/13=3 Exploring Operation: 13+39=52, Resulting Numbers: [41, 52] Generated Node #0,1,4: 44:[41, 52] Operation: 13+39=52 Moving to Node #0,1,0 Current State: 44:[13, 2], Operations: ['75-36=39', '41-39=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[41, 3], Operations: ['75-36=39', '39/13=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,44 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[13, 36, 41, 75], Operations: [] Exploring Operation: 75-36=39, Resulting Numbers: [13, 41, 39] Generated Node #0,1: 44:[13, 41, 39] Operation: 75-36=39 Moving to Node #0,1 Current State: 44:[13, 41, 39], Operations: ['75-36=39'] Exploring Operation: 39/13=3, Resulting Numbers: [41, 3] Generated Node #0,1,3: 44:[41, 3] Operation: 39/13=3 Moving to Node #0,1,3 Current State: 44:[41, 3], Operations: ['75-36=39', '39/13=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 87, 56, 68, 18 ]
19
[ "87-56=31", "68-18=50", "50-31=19" ]
Current State: 19:[87, 56, 68, 18], Operations: [] Exploring Operation: 87-56=31, Resulting Numbers: [68, 18, 31] Generated Node #2: [68, 18, 31] from Operation: 87-56=31 Current State: 19:[68, 18, 31], Operations: ['87-56=31'] Exploring Operation: 68-18=50, Resulting Numbers: [31, 50] Generated Node #3: [31, 50] from Operation: 68-18=50 Current State: 19:[31, 50], Operations: ['87-56=31', '68-18=50'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[87, 56, 68, 18], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [56, 18, 19] Generated Node #0,0: 19:[56, 18, 19] Operation: 87-68=19 Exploring Operation: 68-56=12, Resulting Numbers: [87, 18, 12] Generated Node #0,1: 19:[87, 18, 12] Operation: 68-56=12 Exploring Operation: 87-56=31, Resulting Numbers: [68, 18, 31] Generated Node #0,2: 19:[68, 18, 31] Operation: 87-56=31 Moving to Node #0,0 Current State: 19:[56, 18, 19], Operations: ['87-68=19'] Exploring Operation: 56+18=74, Resulting Numbers: [19, 74] Generated Node #0,0,0: 19:[19, 74] Operation: 56+18=74 Exploring Operation: 56-18=38, Resulting Numbers: [19, 38] Generated Node #0,0,1: 19:[19, 38] Operation: 56-18=38 Exploring Operation: 56-19=37, Resulting Numbers: [18, 37] Generated Node #0,0,2: 19:[18, 37] Operation: 56-19=37 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 19:[19, 38], Operations: ['87-68=19', '56-18=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[87, 56, 68, 18], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [56, 18, 19] Generated Node #0,0: 19:[56, 18, 19] Operation: 87-68=19 Moving to Node #0,0 Current State: 19:[56, 18, 19], Operations: ['87-68=19'] Exploring Operation: 56-18=38, Resulting Numbers: [19, 38] Generated Node #0,0,1: 19:[19, 38] Operation: 56-18=38 Moving to Node #0,0,1 Current State: 19:[19, 38], Operations: ['87-68=19', '56-18=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 13, 16, 29, 23 ]
87
[ "16+23=39", "39/13=3", "29*3=87" ]
Current State: 87:[13, 16, 29, 23], Operations: [] Exploring Operation: 16+23=39, Resulting Numbers: [13, 29, 39] Generated Node #2: [13, 29, 39] from Operation: 16+23=39 Current State: 87:[13, 29, 39], Operations: ['16+23=39'] Exploring Operation: 39/13=3, Resulting Numbers: [29, 3] Generated Node #3: [29, 3] from Operation: 39/13=3 Current State: 87:[29, 3], Operations: ['16+23=39', '39/13=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[13, 16, 29, 23], Operations: [] Exploring Operation: 13+16=29, Resulting Numbers: [29, 23, 29] Generated Node #0,0: 87:[29, 23, 29] Operation: 13+16=29 Moving to Node #0,0 Current State: 87:[29, 23, 29], Operations: ['13+16=29'] Exploring Operation: 29-23=6, Resulting Numbers: [29, 6] Generated Node #0,0,0: 87:[29, 6] Operation: 29-23=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[29, 6], Operations: ['13+16=29', '29-23=6'] Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,87 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
[ 90, 15, 46, 30 ]
90
[ "46-15=31", "31-30=1", "90*1=90" ]
Current State: 90:[90, 15, 46, 30], Operations: [] Exploring Operation: 46-15=31, Resulting Numbers: [90, 30, 31] Generated Node #2: [90, 30, 31] from Operation: 46-15=31 Current State: 90:[90, 30, 31], Operations: ['46-15=31'] Exploring Operation: 31-30=1, Resulting Numbers: [90, 1] Generated Node #3: [90, 1] from Operation: 31-30=1 Current State: 90:[90, 1], Operations: ['46-15=31', '31-30=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[90, 15, 46, 30], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [15, 46, 3] Generated Node #0,0: 90:[15, 46, 3] Operation: 90/30=3 Exploring Operation: 90-46=44, Resulting Numbers: [15, 30, 44] Generated Node #0,1: 90:[15, 30, 44] Operation: 90-46=44 Exploring Operation: 90/15=6, Resulting Numbers: [46, 30, 6] Generated Node #0,2: 90:[46, 30, 6] Operation: 90/15=6 Exploring Operation: 46-15=31, Resulting Numbers: [90, 30, 31] Generated Node #0,3: 90:[90, 30, 31] Operation: 46-15=31 Moving to Node #0,0 Current State: 90:[15, 46, 3], Operations: ['90/30=3'] Exploring Operation: 15*3=45, Resulting Numbers: [46, 45] Generated Node #0,0,0: 90:[46, 45] Operation: 15*3=45 Exploring Operation: 15/3=5, Resulting Numbers: [46, 5] Generated Node #0,0,1: 90:[46, 5] Operation: 15/3=5 Exploring Operation: 15+3=18, Resulting Numbers: [46, 18] Generated Node #0,0,2: 90:[46, 18] Operation: 15+3=18 Exploring Operation: 46-15=31, Resulting Numbers: [3, 31] Generated Node #0,0,3: 90:[3, 31] Operation: 46-15=31 Moving to Node #0,2 Current State: 90:[46, 30, 6], Operations: ['90/15=6'] Exploring Operation: 46-30=16, Resulting Numbers: [6, 16] Generated Node #0,2,0: 90:[6, 16] Operation: 46-30=16 Exploring Operation: 46+6=52, Resulting Numbers: [30, 52] Generated Node #0,2,1: 90:[30, 52] Operation: 46+6=52 Exploring Operation: 30/6=5, Resulting Numbers: [46, 5] Generated Node #0,2,2: 90:[46, 5] Operation: 30/6=5 Exploring Operation: 46-6=40, Resulting Numbers: [30, 40] Generated Node #0,2,3: 90:[30, 40] Operation: 46-6=40 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[6, 16], Operations: ['90/15=6', '46-30=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,90 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[46, 5], Operations: ['90/15=6', '30/6=5'] Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[30, 40], Operations: ['90/15=6', '46-6=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,90 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[30, 52], Operations: ['90/15=6', '46+6=52'] Exploring Operation: 52-30=22, Resulting Numbers: [22] 22,90 unequal: No Solution Exploring Operation: 30*52=1560, Resulting Numbers: [1560] 1560,90 unequal: No Solution Exploring Operation: 30+52=82, Resulting Numbers: [82] 82,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 90:[15, 30, 44], Operations: ['90-46=44'] Exploring Operation: 15+30=45, Resulting Numbers: [44, 45] Generated Node #0,1,0: 90:[44, 45] Operation: 15+30=45 Exploring Operation: 30/15=2, Resulting Numbers: [44, 2] Generated Node #0,1,1: 90:[44, 2] Operation: 30/15=2 Exploring Operation: 44-15=29, Resulting Numbers: [30, 29] Generated Node #0,1,2: 90:[30, 29] Operation: 44-15=29 Exploring Operation: 30-15=15, Resulting Numbers: [44, 15] Generated Node #0,1,3: 90:[44, 15] Operation: 30-15=15 Moving to Node #0,3 Current State: 90:[90, 30, 31], Operations: ['46-15=31'] Exploring Operation: 90-31=59, Resulting Numbers: [30, 59] Generated Node #0,3,0: 90:[30, 59] Operation: 90-31=59 Exploring Operation: 31-30=1, Resulting Numbers: [90, 1] Generated Node #0,3,1: 90:[90, 1] Operation: 31-30=1 Exploring Operation: 90-30=60, Resulting Numbers: [31, 60] Generated Node #0,3,2: 90:[31, 60] Operation: 90-30=60 Exploring Operation: 90/30=3, Resulting Numbers: [31, 3] Generated Node #0,3,3: 90:[31, 3] Operation: 90/30=3 Moving to Node #0,0,0 Current State: 90:[46, 45], Operations: ['90/30=3', '15*3=45'] Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,90 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,90 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[46, 18], Operations: ['90/30=3', '15+3=18'] Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,90 unequal: No Solution Exploring Operation: 46*18=828, Resulting Numbers: [828] 828,90 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[30, 29], Operations: ['90-46=44', '44-15=29'] Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,90 unequal: No Solution Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[44, 2], Operations: ['90-46=44', '30/15=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,90 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[31, 3], Operations: ['46-15=31', '90/30=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[90, 1], Operations: ['46-15=31', '31-30=1'] Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[90, 15, 46, 30], Operations: [] Exploring Operation: 46-15=31, Resulting Numbers: [90, 30, 31] Generated Node #0,3: 90:[90, 30, 31] Operation: 46-15=31 Moving to Node #0,3 Current State: 90:[90, 30, 31], Operations: ['46-15=31'] Exploring Operation: 31-30=1, Resulting Numbers: [90, 1] Generated Node #0,3,1: 90:[90, 1] Operation: 31-30=1 Moving to Node #0,3,1 Current State: 90:[90, 1], Operations: ['46-15=31', '31-30=1'] Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.953993
hs_4
sum_heuristic
[ 30, 9, 73, 84 ]
50
[ "30+9=39", "84-73=11", "39+11=50" ]
Current State: 50:[30, 9, 73, 84], Operations: [] Exploring Operation: 30+9=39, Resulting Numbers: [73, 84, 39] Generated Node #2: [73, 84, 39] from Operation: 30+9=39 Current State: 50:[73, 84, 39], Operations: ['30+9=39'] Exploring Operation: 84-73=11, Resulting Numbers: [39, 11] Generated Node #3: [39, 11] from Operation: 84-73=11 Current State: 50:[39, 11], Operations: ['30+9=39', '84-73=11'] Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[30, 9, 73, 84], Operations: [] Exploring Operation: 84-9=75, Resulting Numbers: [30, 73, 75] Generated Node #0,0: 50:[30, 73, 75] Operation: 84-9=75 Exploring Operation: 73-30=43, Resulting Numbers: [9, 84, 43] Generated Node #0,1: 50:[9, 84, 43] Operation: 73-30=43 Exploring Operation: 84-30=54, Resulting Numbers: [9, 73, 54] Generated Node #0,2: 50:[9, 73, 54] Operation: 84-30=54 Exploring Operation: 84-73=11, Resulting Numbers: [30, 9, 11] Generated Node #0,3: 50:[30, 9, 11] Operation: 84-73=11 Exploring Operation: 73-9=64, Resulting Numbers: [30, 84, 64] Generated Node #0,4: 50:[30, 84, 64] Operation: 73-9=64 Start Sub Search at level 1: Moving to Node #0,3 Current State: 50:[30, 9, 11], Operations: ['84-73=11'] Exploring Operation: 11-9=2, Resulting Numbers: [30, 2] Generated Node #0,3,0: 50:[30, 2] Operation: 11-9=2 Exploring Operation: 30+11=41, Resulting Numbers: [9, 41] Generated Node #0,3,1: 50:[9, 41] Operation: 30+11=41 Exploring Operation: 30-11=19, Resulting Numbers: [9, 19] Generated Node #0,3,2: 50:[9, 19] Operation: 30-11=19 Exploring Operation: 30-9=21, Resulting Numbers: [11, 21] Generated Node #0,3,3: 50:[11, 21] Operation: 30-9=21 Exploring Operation: 9+11=20, Resulting Numbers: [30, 20] Generated Node #0,3,4: 50:[30, 20] Operation: 9+11=20 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 50:[30, 2], Operations: ['84-73=11', '11-9=2'] Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,50 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 30*2=60, Resulting Numbers: [60] 60,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 50:[11, 21], Operations: ['84-73=11', '30-9=21'] Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,50 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 50:[9, 19], Operations: ['84-73=11', '30-11=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,50 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 50:[9, 41], Operations: ['84-73=11', '30+11=41'] Exploring Operation: 9+41=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[30, 9, 73, 84], Operations: [] Exploring Operation: 84-73=11, Resulting Numbers: [30, 9, 11] Generated Node #0,3: 50:[30, 9, 11] Operation: 84-73=11 Moving to Node #0,3 Current State: 50:[30, 9, 11], Operations: ['84-73=11'] Exploring Operation: 30+11=41, Resulting Numbers: [9, 41] Generated Node #0,3,1: 50:[9, 41] Operation: 30+11=41 Moving to Node #0,3,1 Current State: 50:[9, 41], Operations: ['84-73=11', '30+11=41'] Exploring Operation: 9+41=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 38, 87, 10, 72 ]
76
[ "38+72=110", "110/10=11", "87-11=76" ]
Current State: 76:[38, 87, 10, 72], Operations: [] Exploring Operation: 38+72=110, Resulting Numbers: [87, 10, 110] Generated Node #2: [87, 10, 110] from Operation: 38+72=110 Current State: 76:[87, 10, 110], Operations: ['38+72=110'] Exploring Operation: 110/10=11, Resulting Numbers: [87, 11] Generated Node #3: [87, 11] from Operation: 110/10=11 Current State: 76:[87, 11], Operations: ['38+72=110', '110/10=11'] Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[38, 87, 10, 72], Operations: [] Exploring Operation: 87-10=77, Resulting Numbers: [38, 72, 77] Generated Node #0,0: 76:[38, 72, 77] Operation: 87-10=77 Exploring Operation: 87-72=15, Resulting Numbers: [38, 10, 15] Generated Node #0,1: 76:[38, 10, 15] Operation: 87-72=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[38, 72, 77], Operations: ['87-10=77'] Exploring Operation: 72-38=34, Resulting Numbers: [77, 34] Generated Node #0,0,0: 76:[77, 34] Operation: 72-38=34 Exploring Operation: 77-72=5, Resulting Numbers: [38, 5] Generated Node #0,0,1: 76:[38, 5] Operation: 77-72=5 Moving to Node #0,0,1 Current State: 76:[38, 5], Operations: ['87-10=77', '77-72=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[77, 34], Operations: ['87-10=77', '72-38=34'] Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,76 unequal: No Solution Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,76 unequal: No Solution No 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: 76:[38, 10, 15], Operations: ['87-72=15'] Exploring Operation: 10+15=25, Resulting Numbers: [38, 25] Generated Node #0,1,0: 76:[38, 25] Operation: 10+15=25 Exploring Operation: 15-10=5, Resulting Numbers: [38, 5] Generated Node #0,1,1: 76:[38, 5] Operation: 15-10=5 Moving to Node #0,1,1 Current State: 76:[38, 5], Operations: ['87-72=15', '15-10=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[38, 25], Operations: ['87-72=15', '10+15=25'] Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 38+25=63, Resulting Numbers: [63] 63,76 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
[ 35, 11, 41, 23 ]
82
[ "35+11=46", "41*46=1886", "1886/23=82" ]
Current State: 82:[35, 11, 41, 23], Operations: [] Exploring Operation: 35+11=46, Resulting Numbers: [41, 23, 46] Generated Node #2: [41, 23, 46] from Operation: 35+11=46 Current State: 82:[41, 23, 46], Operations: ['35+11=46'] Exploring Operation: 41*46=1886, Resulting Numbers: [23, 1886] Generated Node #3: [23, 1886] from Operation: 41*46=1886 Current State: 82:[23, 1886], Operations: ['35+11=46', '41*46=1886'] Exploring Operation: 1886/23=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[35, 11, 41, 23], Operations: [] Exploring Operation: 35+23=58, Resulting Numbers: [11, 41, 58] Generated Node #0,0: 82:[11, 41, 58] Operation: 35+23=58 Exploring Operation: 11+23=34, Resulting Numbers: [35, 41, 34] Generated Node #0,1: 82:[35, 41, 34] Operation: 11+23=34 Exploring Operation: 35+11=46, Resulting Numbers: [41, 23, 46] Generated Node #0,2: 82:[41, 23, 46] Operation: 35+11=46 Exploring Operation: 23-11=12, Resulting Numbers: [35, 41, 12] Generated Node #0,3: 82:[35, 41, 12] Operation: 23-11=12 Exploring Operation: 35-23=12, Resulting Numbers: [11, 41, 12] Generated Node #0,4: 82:[11, 41, 12] Operation: 35-23=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[35, 41, 34], Operations: ['11+23=34'] Exploring Operation: 35+34=69, Resulting Numbers: [41, 69] Generated Node #0,1,0: 82:[41, 69] Operation: 35+34=69 Exploring Operation: 35+41=76, Resulting Numbers: [34, 76] Generated Node #0,1,1: 82:[34, 76] Operation: 35+41=76 Exploring Operation: 35-34=1, Resulting Numbers: [41, 1] Generated Node #0,1,2: 82:[41, 1] Operation: 35-34=1 Exploring Operation: 41-35=6, Resulting Numbers: [34, 6] Generated Node #0,1,3: 82:[34, 6] Operation: 41-35=6 Exploring Operation: 41-34=7, Resulting Numbers: [35, 7] Generated Node #0,1,4: 82:[35, 7] Operation: 41-34=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[41, 1], Operations: ['11+23=34', '35-34=1'] Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,82 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,82 unequal: No Solution No 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: 82:[34, 6], Operations: ['11+23=34', '41-35=6'] Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,82 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,82 unequal: No Solution No 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: 82:[35, 7], Operations: ['11+23=34', '41-34=7'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 35*7=245, Resulting Numbers: [245] 245,82 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,82 unequal: No Solution No 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: 82:[41, 69], Operations: ['11+23=34', '35+34=69'] Exploring Operation: 41+69=110, Resulting Numbers: [110] 110,82 unequal: No Solution Exploring Operation: 69-41=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 41*69=2829, Resulting Numbers: [2829] 2829,82 unequal: No Solution No 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: 82:[34, 76], Operations: ['11+23=34', '35+41=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,82 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,82 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: 82:[35, 41, 12], Operations: ['23-11=12'] Exploring Operation: 41-35=6, Resulting Numbers: [12, 6] Generated Node #0,3,0: 82:[12, 6] Operation: 41-35=6 Exploring Operation: 41+12=53, Resulting Numbers: [35, 53] Generated Node #0,3,1: 82:[35, 53] Operation: 41+12=53 Exploring Operation: 35+41=76, Resulting Numbers: [12, 76] Generated Node #0,3,2: 82:[12, 76] Operation: 35+41=76 Exploring Operation: 35-12=23, Resulting Numbers: [41, 23] Generated Node #0,3,3: 82:[41, 23] Operation: 35-12=23 Exploring Operation: 35+12=47, Resulting Numbers: [41, 47] Generated Node #0,3,4: 82:[41, 47] Operation: 35+12=47 Moving to Node #0,3,4 Current State: 82:[41, 47], Operations: ['23-11=12', '35+12=47'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[12, 6], Operations: ['23-11=12', '41-35=6'] Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[12, 76], Operations: ['23-11=12', '35+41=76'] Exploring Operation: 12+76=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 12*76=912, Resulting Numbers: [912] 912,82 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[35, 53], Operations: ['23-11=12', '41+12=53'] Exploring Operation: 35*53=1855, Resulting Numbers: [1855] 1855,82 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 35+53=88, Resulting Numbers: [88] 88,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[41, 23], Operations: ['23-11=12', '35-12=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,82 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,82 unequal: No Solution No 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: 82:[11, 41, 12], Operations: ['35-23=12'] Exploring Operation: 11+41=52, Resulting Numbers: [12, 52] Generated Node #0,4,0: 82:[12, 52] Operation: 11+41=52 Exploring Operation: 11+12=23, Resulting Numbers: [41, 23] Generated Node #0,4,1: 82:[41, 23] Operation: 11+12=23 Exploring Operation: 12-11=1, Resulting Numbers: [41, 1] Generated Node #0,4,2: 82:[41, 1] Operation: 12-11=1 Exploring Operation: 41+12=53, Resulting Numbers: [11, 53] Generated Node #0,4,3: 82:[11, 53] Operation: 41+12=53 Exploring Operation: 41-11=30, Resulting Numbers: [12, 30] Generated Node #0,4,4: 82:[12, 30] Operation: 41-11=30 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 82:[41, 1], Operations: ['35-23=12', '12-11=1'] Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,82 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,82 unequal: No Solution No 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: 82:[41, 23], Operations: ['35-23=12', '11+12=23'] Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,82 unequal: No Solution No 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: 82:[12, 52], Operations: ['35-23=12', '11+41=52'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,82 unequal: No Solution Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,82 unequal: No Solution No 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: 82:[11, 53], Operations: ['35-23=12', '41+12=53'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,82 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 82:[12, 30], Operations: ['35-23=12', '41-11=30'] Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 12*30=360, Resulting Numbers: [360] 360,82 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,82 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: 82:[41, 23, 46], Operations: ['35+11=46'] Exploring Operation: 46-23=23, Resulting Numbers: [41, 23] Generated Node #0,2,0: 82:[41, 23] Operation: 46-23=23 Exploring Operation: 41-23=18, Resulting Numbers: [46, 18] Generated Node #0,2,1: 82:[46, 18] Operation: 41-23=18 Exploring Operation: 46/23=2, Resulting Numbers: [41, 2] Generated Node #0,2,2: 82:[41, 2] Operation: 46/23=2 Exploring Operation: 46-41=5, Resulting Numbers: [23, 5] Generated Node #0,2,3: 82:[23, 5] Operation: 46-41=5 Exploring Operation: 23+46=69, Resulting Numbers: [41, 69] Generated Node #0,2,4: 82:[41, 69] Operation: 23+46=69 Moving to Node #0,2,2 Current State: 82:[41, 2], Operations: ['35+11=46', '46/23=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[35, 11, 41, 23], Operations: [] Exploring Operation: 35+11=46, Resulting Numbers: [41, 23, 46] Generated Node #0,2: 82:[41, 23, 46] Operation: 35+11=46 Moving to Node #0,2 Current State: 82:[41, 23, 46], Operations: ['35+11=46'] Exploring Operation: 46/23=2, Resulting Numbers: [41, 2] Generated Node #0,2,2: 82:[41, 2] Operation: 46/23=2 Moving to Node #0,2,2 Current State: 82:[41, 2], Operations: ['35+11=46', '46/23=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.929688
hs_5
mult_heuristic
[ 81, 95, 67, 27 ]
80
[ "95-81=14", "67+27=94", "94-14=80" ]
Current State: 80:[81, 95, 67, 27], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [67, 27, 14] Generated Node #2: [67, 27, 14] from Operation: 95-81=14 Current State: 80:[67, 27, 14], Operations: ['95-81=14'] Exploring Operation: 67+27=94, Resulting Numbers: [14, 94] Generated Node #3: [14, 94] from Operation: 67+27=94 Current State: 80:[14, 94], Operations: ['95-81=14', '67+27=94'] Exploring Operation: 94-14=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[81, 95, 67, 27], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [81, 27, 28] Generated Node #0,0: 80:[81, 27, 28] Operation: 95-67=28 Moving to Node #0,0 Current State: 80:[81, 27, 28], Operations: ['95-67=28'] Exploring Operation: 28-27=1, Resulting Numbers: [81, 1] Generated Node #0,0,0: 80:[81, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[81, 1], Operations: ['95-67=28', '28-27=1'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[81, 95, 67, 27], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [81, 27, 28] Generated Node #0,0: 80:[81, 27, 28] Operation: 95-67=28 Moving to Node #0,0 Current State: 80:[81, 27, 28], Operations: ['95-67=28'] Exploring Operation: 28-27=1, Resulting Numbers: [81, 1] Generated Node #0,0,0: 80:[81, 1] Operation: 28-27=1 Moving to Node #0,0,0 Current State: 80:[81, 1], Operations: ['95-67=28', '28-27=1'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 90, 42, 2, 67 ]
40
[ "67-42=25", "2*25=50", "90-50=40" ]
Current State: 40:[90, 42, 2, 67], Operations: [] Exploring Operation: 67-42=25, Resulting Numbers: [90, 2, 25] Generated Node #2: [90, 2, 25] from Operation: 67-42=25 Current State: 40:[90, 2, 25], Operations: ['67-42=25'] Exploring Operation: 2*25=50, Resulting Numbers: [90, 50] Generated Node #3: [90, 50] from Operation: 2*25=50 Current State: 40:[90, 50], Operations: ['67-42=25', '2*25=50'] Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[90, 42, 2, 67], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [42, 67, 45] Generated Node #0,0: 40:[42, 67, 45] Operation: 90/2=45 Exploring Operation: 90-67=23, Resulting Numbers: [42, 2, 23] Generated Node #0,1: 40:[42, 2, 23] Operation: 90-67=23 Exploring Operation: 90-42=48, Resulting Numbers: [2, 67, 48] Generated Node #0,2: 40:[2, 67, 48] Operation: 90-42=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[42, 2, 23], Operations: ['90-67=23'] Exploring Operation: 23-2=21, Resulting Numbers: [42, 21] Generated Node #0,1,0: 40:[42, 21] Operation: 23-2=21 Exploring Operation: 42-23=19, Resulting Numbers: [2, 19] Generated Node #0,1,1: 40:[2, 19] Operation: 42-23=19 Exploring Operation: 42-2=40, Resulting Numbers: [23, 40] Generated Node #0,1,2: 40:[23, 40] Operation: 42-2=40 Moving to Node #0,1,1 Current State: 40:[2, 19], Operations: ['90-67=23', '42-23=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[42, 21], Operations: ['90-67=23', '23-2=21'] Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,40 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[23, 40], Operations: ['90-67=23', '42-2=40'] Exploring Operation: 23+40=63, Resulting Numbers: [63] 63,40 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 23*40=920, Resulting Numbers: [920] 920,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[42, 67, 45], Operations: ['90/2=45'] Exploring Operation: 67-45=22, Resulting Numbers: [42, 22] Generated Node #0,0,0: 40:[42, 22] Operation: 67-45=22 Exploring Operation: 67-42=25, Resulting Numbers: [45, 25] Generated Node #0,0,1: 40:[45, 25] Operation: 67-42=25 Exploring Operation: 45-42=3, Resulting Numbers: [67, 3] Generated Node #0,0,2: 40:[67, 3] Operation: 45-42=3 Moving to Node #0,0,0 Current State: 40:[42, 22], Operations: ['90/2=45', '67-45=22'] Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,40 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[45, 25], Operations: ['90/2=45', '67-42=25'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[67, 3], Operations: ['90/2=45', '45-42=3'] Exploring Operation: 67+3=70, Resulting Numbers: [70] 70,40 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,40 unequal: No Solution Exploring Operation: 67*3=201, Resulting Numbers: [201] 201,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[2, 67, 48], Operations: ['90-42=48'] Exploring Operation: 67-2=65, Resulting Numbers: [48, 65] Generated Node #0,2,0: 40:[48, 65] Operation: 67-2=65 Exploring Operation: 48/2=24, Resulting Numbers: [67, 24] Generated Node #0,2,1: 40:[67, 24] Operation: 48/2=24 Exploring Operation: 67-48=19, Resulting Numbers: [2, 19] Generated Node #0,2,2: 40:[2, 19] Operation: 67-48=19 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 40:[2, 19], Operations: ['90-42=48', '67-48=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,40 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 #0,2,1 Current State: 40:[67, 24], Operations: ['90-42=48', '48/2=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,40 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,40 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,40 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 #0,2,0 Current State: 40:[48, 65], Operations: ['90-42=48', '67-2=65'] Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 48+65=113, Resulting Numbers: [113] 113,40 unequal: No Solution Exploring Operation: 48*65=3120, Resulting Numbers: [3120] 3120,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 3, 14, 98, 98 ]
43
[ "3*14=42", "98/98=1", "42+1=43" ]
Current State: 43:[3, 14, 98, 98], Operations: [] Exploring Operation: 3*14=42, Resulting Numbers: [98, 98, 42] Generated Node #2: [98, 98, 42] from Operation: 3*14=42 Current State: 43:[98, 98, 42], Operations: ['3*14=42'] Exploring Operation: 98/98=1, Resulting Numbers: [42, 1] Generated Node #3: [42, 1] from Operation: 98/98=1 Current State: 43:[42, 1], Operations: ['3*14=42', '98/98=1'] Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[3, 14, 98, 98], Operations: [] Exploring Operation: 3*14=42, Resulting Numbers: [98, 98, 42] Generated Node #0,0: 43:[98, 98, 42] Operation: 3*14=42 Exploring Operation: 98/98=1, Resulting Numbers: [3, 14, 1] Generated Node #0,1: 43:[3, 14, 1] Operation: 98/98=1 Moving to Node #0,0 Current State: 43:[98, 98, 42], Operations: ['3*14=42'] Exploring Operation: 98/98=1, Resulting Numbers: [42, 1] Generated Node #0,0,0: 43:[42, 1] Operation: 98/98=1 Exploring Operation: 98-98=0, Resulting Numbers: [42, 0] Generated Node #0,0,1: 43:[42, 0] Operation: 98-98=0 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[42, 1], Operations: ['3*14=42', '98/98=1'] Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[3, 14, 98, 98], Operations: [] Exploring Operation: 3*14=42, Resulting Numbers: [98, 98, 42] Generated Node #0,0: 43:[98, 98, 42] Operation: 3*14=42 Moving to Node #0,0 Current State: 43:[98, 98, 42], Operations: ['3*14=42'] Exploring Operation: 98/98=1, Resulting Numbers: [42, 1] Generated Node #0,0,0: 43:[42, 1] Operation: 98/98=1 Moving to Node #0,0,0 Current State: 43:[42, 1], Operations: ['3*14=42', '98/98=1'] Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 91, 3, 21, 68 ]
92
[ "91+21=112", "3*68=204", "204-112=92" ]
Current State: 92:[91, 3, 21, 68], Operations: [] Exploring Operation: 91+21=112, Resulting Numbers: [3, 68, 112] Generated Node #2: [3, 68, 112] from Operation: 91+21=112 Current State: 92:[3, 68, 112], Operations: ['91+21=112'] Exploring Operation: 3*68=204, Resulting Numbers: [112, 204] Generated Node #3: [112, 204] from Operation: 3*68=204 Current State: 92:[112, 204], Operations: ['91+21=112', '3*68=204'] Exploring Operation: 204-112=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[91, 3, 21, 68], Operations: [] Exploring Operation: 91-68=23, Resulting Numbers: [3, 21, 23] Generated Node #0,0: 92:[3, 21, 23] Operation: 91-68=23 Moving to Node #0,0 Current State: 92:[3, 21, 23], Operations: ['91-68=23'] Exploring Operation: 3+21=24, Resulting Numbers: [23, 24] Generated Node #0,0,0: 92:[23, 24] Operation: 3+21=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[23, 24], Operations: ['91-68=23', '3+21=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 27, 2, 20, 50 ]
24
[ "27*2=54", "50-20=30", "54-30=24" ]
Current State: 24:[27, 2, 20, 50], Operations: [] Exploring Operation: 27*2=54, Resulting Numbers: [20, 50, 54] Generated Node #2: [20, 50, 54] from Operation: 27*2=54 Current State: 24:[20, 50, 54], Operations: ['27*2=54'] Exploring Operation: 50-20=30, Resulting Numbers: [54, 30] Generated Node #3: [54, 30] from Operation: 50-20=30 Current State: 24:[54, 30], Operations: ['27*2=54', '50-20=30'] Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[27, 2, 20, 50], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [27, 20, 25] Generated Node #0,0: 24:[27, 20, 25] Operation: 50/2=25 Exploring Operation: 50-20=30, Resulting Numbers: [27, 2, 30] Generated Node #0,1: 24:[27, 2, 30] Operation: 50-20=30 Exploring Operation: 50-27=23, Resulting Numbers: [2, 20, 23] Generated Node #0,2: 24:[2, 20, 23] Operation: 50-27=23 Exploring Operation: 27-20=7, Resulting Numbers: [2, 50, 7] Generated Node #0,3: 24:[2, 50, 7] Operation: 27-20=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[2, 20, 23], Operations: ['50-27=23'] Exploring Operation: 2+23=25, Resulting Numbers: [20, 25] Generated Node #0,2,0: 24:[20, 25] Operation: 2+23=25 Exploring Operation: 20/2=10, Resulting Numbers: [23, 10] Generated Node #0,2,1: 24:[23, 10] Operation: 20/2=10 Exploring Operation: 23-20=3, Resulting Numbers: [2, 3] Generated Node #0,2,2: 24:[2, 3] Operation: 23-20=3 Exploring Operation: 2+20=22, Resulting Numbers: [23, 22] Generated Node #0,2,3: 24:[23, 22] Operation: 2+20=22 Moving to Node #0,2,2 Current State: 24:[2, 3], Operations: ['50-27=23', '23-20=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[23, 22], Operations: ['50-27=23', '2+20=22'] Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,24 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[23, 10], Operations: ['50-27=23', '20/2=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,24 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,24 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[20, 25], Operations: ['50-27=23', '2+23=25'] Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,24 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[27, 20, 25], Operations: ['50/2=25'] Exploring Operation: 27-20=7, Resulting Numbers: [25, 7] Generated Node #0,0,0: 24:[25, 7] Operation: 27-20=7 Exploring Operation: 27+20=47, Resulting Numbers: [25, 47] Generated Node #0,0,1: 24:[25, 47] Operation: 27+20=47 Exploring Operation: 25-20=5, Resulting Numbers: [27, 5] Generated Node #0,0,2: 24:[27, 5] Operation: 25-20=5 Exploring Operation: 27-25=2, Resulting Numbers: [20, 2] Generated Node #0,0,3: 24:[20, 2] Operation: 27-25=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[25, 7], Operations: ['50/2=25', '27-20=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,24 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 #0,0,2 Current State: 24:[27, 5], Operations: ['50/2=25', '25-20=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,24 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 24:[20, 2], Operations: ['50/2=25', '27-25=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,24 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 #0,0,1 Current State: 24:[25, 47], Operations: ['50/2=25', '27+20=47'] Exploring Operation: 25+47=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 25*47=1175, Resulting Numbers: [1175] 1175,24 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,24 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 #0,1 Current State: 24:[27, 2, 30], Operations: ['50-20=30'] Exploring Operation: 30/2=15, Resulting Numbers: [27, 15] Generated Node #0,1,0: 24:[27, 15] Operation: 30/2=15 Exploring Operation: 30-2=28, Resulting Numbers: [27, 28] Generated Node #0,1,1: 24:[27, 28] Operation: 30-2=28 Exploring Operation: 30-27=3, Resulting Numbers: [2, 3] Generated Node #0,1,2: 24:[2, 3] Operation: 30-27=3 Exploring Operation: 27-2=25, Resulting Numbers: [30, 25] Generated Node #0,1,3: 24:[30, 25] Operation: 27-2=25 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[2, 3], Operations: ['50-20=30', '30-27=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,24 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 #0,1,0 Current State: 24:[27, 15], Operations: ['50-20=30', '30/2=15'] Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,24 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,24 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:[27, 28], Operations: ['50-20=30', '30-2=28'] Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,24 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,24 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:[30, 25], Operations: ['50-20=30', '27-2=25'] Exploring Operation: 30*25=750, Resulting Numbers: [750] 750,24 unequal: No Solution Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[2, 50, 7], Operations: ['27-20=7'] Exploring Operation: 50/2=25, Resulting Numbers: [7, 25] Generated Node #0,3,0: 24:[7, 25] Operation: 50/2=25 Exploring Operation: 50-2=48, Resulting Numbers: [7, 48] Generated Node #0,3,1: 24:[7, 48] Operation: 50-2=48 Exploring Operation: 2+7=9, Resulting Numbers: [50, 9] Generated Node #0,3,2: 24:[50, 9] Operation: 2+7=9 Exploring Operation: 50-7=43, Resulting Numbers: [2, 43] Generated Node #0,3,3: 24:[2, 43] Operation: 50-7=43 Moving to Node #0,3,0 Current State: 24:[7, 25], Operations: ['27-20=7', '50/2=25'] Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,24 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[2, 43], Operations: ['27-20=7', '50-7=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[7, 48], Operations: ['27-20=7', '50-2=48'] Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,24 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[50, 9], Operations: ['27-20=7', '2+7=9'] Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,24 unequal: No Solution Exploring Operation: 50*9=450, Resulting Numbers: [450] 450,24 unequal: No Solution Exploring Operation: 50+9=59, Resulting Numbers: [59] 59,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 53, 61, 6, 38 ]
18
[ "53+61=114", "6*114=684", "684/38=18" ]
Current State: 18:[53, 61, 6, 38], Operations: [] Exploring Operation: 53+61=114, Resulting Numbers: [6, 38, 114] Generated Node #2: [6, 38, 114] from Operation: 53+61=114 Current State: 18:[6, 38, 114], Operations: ['53+61=114'] Exploring Operation: 6*114=684, Resulting Numbers: [38, 684] Generated Node #3: [38, 684] from Operation: 6*114=684 Current State: 18:[38, 684], Operations: ['53+61=114', '6*114=684'] Exploring Operation: 684/38=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[53, 61, 6, 38], Operations: [] Exploring Operation: 61-38=23, Resulting Numbers: [53, 6, 23] Generated Node #0,0: 18:[53, 6, 23] Operation: 61-38=23 Exploring Operation: 53-38=15, Resulting Numbers: [61, 6, 15] Generated Node #0,1: 18:[61, 6, 15] Operation: 53-38=15 Exploring Operation: 53-6=47, Resulting Numbers: [61, 38, 47] Generated Node #0,2: 18:[61, 38, 47] Operation: 53-6=47 Exploring Operation: 61-6=55, Resulting Numbers: [53, 38, 55] Generated Node #0,3: 18:[53, 38, 55] Operation: 61-6=55 Exploring Operation: 61-53=8, Resulting Numbers: [6, 38, 8] Generated Node #0,4: 18:[6, 38, 8] Operation: 61-53=8 Moving to Node #0,4 Current State: 18:[6, 38, 8], Operations: ['61-53=8'] Exploring Operation: 6+38=44, Resulting Numbers: [8, 44] Generated Node #0,4,0: 18:[8, 44] Operation: 6+38=44 Exploring Operation: 6+8=14, Resulting Numbers: [38, 14] Generated Node #0,4,1: 18:[38, 14] Operation: 6+8=14 Exploring Operation: 38-6=32, Resulting Numbers: [8, 32] Generated Node #0,4,2: 18:[8, 32] Operation: 38-6=32 Exploring Operation: 8-6=2, Resulting Numbers: [38, 2] Generated Node #0,4,3: 18:[38, 2] Operation: 8-6=2 Exploring Operation: 38-8=30, Resulting Numbers: [6, 30] Generated Node #0,4,4: 18:[6, 30] Operation: 38-8=30 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 18:[6, 30], Operations: ['61-53=8', '38-8=30'] Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 18:[8, 32], Operations: ['61-53=8', '38-6=32'] Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 8*32=256, Resulting Numbers: [256] 256,18 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 18:[38, 2], Operations: ['61-53=8', '8-6=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 18:[38, 14], Operations: ['61-53=8', '6+8=14'] Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,18 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 18:[8, 44], Operations: ['61-53=8', '6+38=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,18 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: 18:[53, 6, 23], Operations: ['61-38=23'] Exploring Operation: 53+6=59, Resulting Numbers: [23, 59] Generated Node #0,0,0: 18:[23, 59] Operation: 53+6=59 Exploring Operation: 53-23=30, Resulting Numbers: [6, 30] Generated Node #0,0,1: 18:[6, 30] Operation: 53-23=30 Exploring Operation: 23-6=17, Resulting Numbers: [53, 17] Generated Node #0,0,2: 18:[53, 17] Operation: 23-6=17 Exploring Operation: 53-6=47, Resulting Numbers: [23, 47] Generated Node #0,0,3: 18:[23, 47] Operation: 53-6=47 Exploring Operation: 6+23=29, Resulting Numbers: [53, 29] Generated Node #0,0,4: 18:[53, 29] Operation: 6+23=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[6, 30], Operations: ['61-38=23', '53-23=30'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[23, 47], Operations: ['61-38=23', '53-6=47'] Exploring Operation: 23+47=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 23*47=1081, Resulting Numbers: [1081] 1081,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[53, 17], Operations: ['61-38=23', '23-6=17'] Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[23, 59], Operations: ['61-38=23', '53+6=59'] Exploring Operation: 23+59=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 23*59=1357, Resulting Numbers: [1357] 1357,18 unequal: No Solution Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 18:[53, 29], Operations: ['61-38=23', '6+23=29'] Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 53+29=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 53*29=1537, Resulting Numbers: [1537] 1537,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[61, 6, 15], Operations: ['53-38=15'] Exploring Operation: 15-6=9, Resulting Numbers: [61, 9] Generated Node #0,1,0: 18:[61, 9] Operation: 15-6=9 Exploring Operation: 61-6=55, Resulting Numbers: [15, 55] Generated Node #0,1,1: 18:[15, 55] Operation: 61-6=55 Exploring Operation: 61+6=67, Resulting Numbers: [15, 67] Generated Node #0,1,2: 18:[15, 67] Operation: 61+6=67 Exploring Operation: 6+15=21, Resulting Numbers: [61, 21] Generated Node #0,1,3: 18:[61, 21] Operation: 6+15=21 Exploring Operation: 61-15=46, Resulting Numbers: [6, 46] Generated Node #0,1,4: 18:[6, 46] Operation: 61-15=46 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[6, 46], Operations: ['53-38=15', '61-15=46'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 6*46=276, Resulting Numbers: [276] 276,18 unequal: No Solution Exploring Operation: 6+46=52, Resulting Numbers: [52] 52,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[15, 55], Operations: ['53-38=15', '61-6=55'] Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 15+55=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 15*55=825, Resulting Numbers: [825] 825,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[61, 9], Operations: ['53-38=15', '15-6=9'] Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,18 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[61, 21], Operations: ['53-38=15', '6+15=21'] Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 61*21=1281, Resulting Numbers: [1281] 1281,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[15, 67], Operations: ['53-38=15', '61+6=67'] Exploring Operation: 15+67=82, Resulting Numbers: [82] 82,18 unequal: No Solution Exploring Operation: 67-15=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 15*67=1005, Resulting Numbers: [1005] 1005,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[61, 38, 47], Operations: ['53-6=47'] Exploring Operation: 47-38=9, Resulting Numbers: [61, 9] Generated Node #0,2,0: 18:[61, 9] Operation: 47-38=9 Exploring Operation: 61-47=14, Resulting Numbers: [38, 14] Generated Node #0,2,1: 18:[38, 14] Operation: 61-47=14 Exploring Operation: 61-38=23, Resulting Numbers: [47, 23] Generated Node #0,2,2: 18:[47, 23] Operation: 61-38=23 Exploring Operation: 61+38=99, Resulting Numbers: [47, 99] Generated Node #0,2,3: 18:[47, 99] Operation: 61+38=99 Exploring Operation: 61+47=108, Resulting Numbers: [38, 108] Generated Node #0,2,4: 18:[38, 108] Operation: 61+47=108 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[38, 14], Operations: ['53-6=47', '61-47=14'] Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,18 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[47, 23], Operations: ['53-6=47', '61-38=23'] Exploring Operation: 47+23=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 47*23=1081, Resulting Numbers: [1081] 1081,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[61, 9], Operations: ['53-6=47', '47-38=9'] Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[47, 99], Operations: ['53-6=47', '61+38=99'] Exploring Operation: 47+99=146, Resulting Numbers: [146] 146,18 unequal: No Solution Exploring Operation: 47*99=4653, Resulting Numbers: [4653] 4653,18 unequal: No Solution Exploring Operation: 99-47=52, Resulting Numbers: [52] 52,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[38, 108], Operations: ['53-6=47', '61+47=108'] Exploring Operation: 108-38=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 38+108=146, Resulting Numbers: [146] 146,18 unequal: No Solution Exploring Operation: 38*108=4104, Resulting Numbers: [4104] 4104,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 18:[53, 38, 55], Operations: ['61-6=55'] Exploring Operation: 55-38=17, Resulting Numbers: [53, 17] Generated Node #0,3,0: 18:[53, 17] Operation: 55-38=17 Exploring Operation: 53-38=15, Resulting Numbers: [55, 15] Generated Node #0,3,1: 18:[55, 15] Operation: 53-38=15 Exploring Operation: 53+38=91, Resulting Numbers: [55, 91] Generated Node #0,3,2: 18:[55, 91] Operation: 53+38=91 Exploring Operation: 55-53=2, Resulting Numbers: [38, 2] Generated Node #0,3,3: 18:[38, 2] Operation: 55-53=2 Exploring Operation: 53+55=108, Resulting Numbers: [38, 108] Generated Node #0,3,4: 18:[38, 108] Operation: 53+55=108 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[38, 2], Operations: ['61-6=55', '55-53=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[53, 17], Operations: ['61-6=55', '55-38=17'] Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[55, 15], Operations: ['61-6=55', '53-38=15'] Exploring Operation: 55+15=70, Resulting Numbers: [70] 70,18 unequal: No Solution Exploring Operation: 55-15=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 55*15=825, Resulting Numbers: [825] 825,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[55, 91], Operations: ['61-6=55', '53+38=91'] Exploring Operation: 91-55=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 55+91=146, Resulting Numbers: [146] 146,18 unequal: No Solution Exploring Operation: 55*91=5005, Resulting Numbers: [5005] 5005,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 18:[38, 108], Operations: ['61-6=55', '53+55=108'] Exploring Operation: 38+108=146, Resulting Numbers: [146] 146,18 unequal: No Solution Exploring Operation: 38*108=4104, Resulting Numbers: [4104] 4104,18 unequal: No Solution Exploring Operation: 108-38=70, Resulting Numbers: [70] 70,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 4, 88, 80, 57 ]
45
[ "4+88=92", "80+57=137", "137-92=45" ]
Current State: 45:[4, 88, 80, 57], Operations: [] Exploring Operation: 4+88=92, Resulting Numbers: [80, 57, 92] Generated Node #2: [80, 57, 92] from Operation: 4+88=92 Current State: 45:[80, 57, 92], Operations: ['4+88=92'] Exploring Operation: 80+57=137, Resulting Numbers: [92, 137] Generated Node #3: [92, 137] from Operation: 80+57=137 Current State: 45:[92, 137], Operations: ['4+88=92', '80+57=137'] Exploring Operation: 137-92=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[4, 88, 80, 57], Operations: [] Exploring Operation: 88-57=31, Resulting Numbers: [4, 80, 31] Generated Node #0,0: 45:[4, 80, 31] Operation: 88-57=31 Exploring Operation: 88-80=8, Resulting Numbers: [4, 57, 8] Generated Node #0,1: 45:[4, 57, 8] Operation: 88-80=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[4, 57, 8], Operations: ['88-80=8'] Exploring Operation: 57-4=53, Resulting Numbers: [8, 53] Generated Node #0,1,0: 45:[8, 53] Operation: 57-4=53 Exploring Operation: 57-8=49, Resulting Numbers: [4, 49] Generated Node #0,1,1: 45:[4, 49] Operation: 57-8=49 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[4, 49], Operations: ['88-80=8', '57-8=49'] Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,45 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[4, 88, 80, 57], Operations: [] Exploring Operation: 88-80=8, Resulting Numbers: [4, 57, 8] Generated Node #0,1: 45:[4, 57, 8] Operation: 88-80=8 Moving to Node #0,1 Current State: 45:[4, 57, 8], Operations: ['88-80=8'] Exploring Operation: 57-8=49, Resulting Numbers: [4, 49] Generated Node #0,1,1: 45:[4, 49] Operation: 57-8=49 Moving to Node #0,1,1 Current State: 45:[4, 49], Operations: ['88-80=8', '57-8=49'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 43, 87, 46, 11 ]
40
[ "46-43=3", "87/3=29", "11+29=40" ]
Current State: 40:[43, 87, 46, 11], Operations: [] Exploring Operation: 46-43=3, Resulting Numbers: [87, 11, 3] Generated Node #2: [87, 11, 3] from Operation: 46-43=3 Current State: 40:[87, 11, 3], Operations: ['46-43=3'] Exploring Operation: 87/3=29, Resulting Numbers: [11, 29] Generated Node #3: [11, 29] from Operation: 87/3=29 Current State: 40:[11, 29], Operations: ['46-43=3', '87/3=29'] Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[43, 87, 46, 11], Operations: [] Exploring Operation: 87-46=41, Resulting Numbers: [43, 11, 41] Generated Node #0,0: 40:[43, 11, 41] Operation: 87-46=41 Moving to Node #0,0 Current State: 40:[43, 11, 41], Operations: ['87-46=41'] Exploring Operation: 43-41=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 40:[11, 2] Operation: 43-41=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[11, 2], Operations: ['87-46=41', '43-41=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 9, 16, 35, 48 ]
29
[ "35-9=26", "48/16=3", "26+3=29" ]
Current State: 29:[9, 16, 35, 48], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [16, 48, 26] Generated Node #2: [16, 48, 26] from Operation: 35-9=26 Current State: 29:[16, 48, 26], Operations: ['35-9=26'] Exploring Operation: 48/16=3, Resulting Numbers: [26, 3] Generated Node #3: [26, 3] from Operation: 48/16=3 Current State: 29:[26, 3], Operations: ['35-9=26', '48/16=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[9, 16, 35, 48], Operations: [] Exploring Operation: 9+16=25, Resulting Numbers: [35, 48, 25] Generated Node #0,0: 29:[35, 48, 25] Operation: 9+16=25 Exploring Operation: 48-9=39, Resulting Numbers: [16, 35, 39] Generated Node #0,1: 29:[16, 35, 39] Operation: 48-9=39 Exploring Operation: 48-16=32, Resulting Numbers: [9, 35, 32] Generated Node #0,2: 29:[9, 35, 32] Operation: 48-16=32 Exploring Operation: 35-9=26, Resulting Numbers: [16, 48, 26] Generated Node #0,3: 29:[16, 48, 26] Operation: 35-9=26 Moving to Node #0,0 Current State: 29:[35, 48, 25], Operations: ['9+16=25'] Exploring Operation: 35+25=60, Resulting Numbers: [48, 60] Generated Node #0,0,0: 29:[48, 60] Operation: 35+25=60 Exploring Operation: 35-25=10, Resulting Numbers: [48, 10] Generated Node #0,0,1: 29:[48, 10] Operation: 35-25=10 Exploring Operation: 48-25=23, Resulting Numbers: [35, 23] Generated Node #0,0,2: 29:[35, 23] Operation: 48-25=23 Exploring Operation: 48-35=13, Resulting Numbers: [25, 13] Generated Node #0,0,3: 29:[25, 13] Operation: 48-35=13 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[35, 23], Operations: ['9+16=25', '48-25=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,29 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 29:[25, 13], Operations: ['9+16=25', '48-35=13'] Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,29 unequal: No Solution Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[48, 10], Operations: ['9+16=25', '35-25=10'] Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 48*10=480, Resulting Numbers: [480] 480,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[48, 60], Operations: ['9+16=25', '35+25=60'] Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,29 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,29 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,29 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: 29:[9, 35, 32], Operations: ['48-16=32'] Exploring Operation: 32-9=23, Resulting Numbers: [35, 23] Generated Node #0,2,0: 29:[35, 23] Operation: 32-9=23 Exploring Operation: 35-9=26, Resulting Numbers: [32, 26] Generated Node #0,2,1: 29:[32, 26] Operation: 35-9=26 Exploring Operation: 9+35=44, Resulting Numbers: [32, 44] Generated Node #0,2,2: 29:[32, 44] Operation: 9+35=44 Exploring Operation: 9+32=41, Resulting Numbers: [35, 41] Generated Node #0,2,3: 29:[35, 41] Operation: 9+32=41 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[32, 26], Operations: ['48-16=32', '35-9=26'] Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 32*26=832, Resulting Numbers: [832] 832,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[35, 23], Operations: ['48-16=32', '32-9=23'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,29 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[32, 44], Operations: ['48-16=32', '9+35=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,29 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[35, 41], Operations: ['48-16=32', '9+32=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 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: 29:[16, 35, 39], Operations: ['48-9=39'] Exploring Operation: 16+35=51, Resulting Numbers: [39, 51] Generated Node #0,1,0: 29:[39, 51] Operation: 16+35=51 Exploring Operation: 39-16=23, Resulting Numbers: [35, 23] Generated Node #0,1,1: 29:[35, 23] Operation: 39-16=23 Exploring Operation: 35-16=19, Resulting Numbers: [39, 19] Generated Node #0,1,2: 29:[39, 19] Operation: 35-16=19 Exploring Operation: 16+39=55, Resulting Numbers: [35, 55] Generated Node #0,1,3: 29:[35, 55] Operation: 16+39=55 Moving to Node #0,3 Current State: 29:[16, 48, 26], Operations: ['35-9=26'] Exploring Operation: 48-26=22, Resulting Numbers: [16, 22] Generated Node #0,3,0: 29:[16, 22] Operation: 48-26=22 Exploring Operation: 16+26=42, Resulting Numbers: [48, 42] Generated Node #0,3,1: 29:[48, 42] Operation: 16+26=42 Exploring Operation: 48-16=32, Resulting Numbers: [26, 32] Generated Node #0,3,2: 29:[26, 32] Operation: 48-16=32 Exploring Operation: 48/16=3, Resulting Numbers: [26, 3] Generated Node #0,3,3: 29:[26, 3] Operation: 48/16=3 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 29:[26, 32], Operations: ['35-9=26', '48-16=32'] Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 26+32=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 26*32=832, Resulting Numbers: [832] 832,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 29:[16, 22], Operations: ['35-9=26', '48-26=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,29 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 29:[26, 3], Operations: ['35-9=26', '48/16=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,29 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,29 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[9, 16, 35, 48], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [16, 48, 26] Generated Node #0,3: 29:[16, 48, 26] Operation: 35-9=26 Moving to Node #0,3 Current State: 29:[16, 48, 26], Operations: ['35-9=26'] Exploring Operation: 48/16=3, Resulting Numbers: [26, 3] Generated Node #0,3,3: 29:[26, 3] Operation: 48/16=3 Moving to Node #0,3,3 Current State: 29:[26, 3], Operations: ['35-9=26', '48/16=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_4
sum_heuristic
[ 36, 59, 47, 51 ]
68
[ "51-47=4", "36/4=9", "59+9=68" ]
Current State: 68:[36, 59, 47, 51], Operations: [] Exploring Operation: 51-47=4, Resulting Numbers: [36, 59, 4] Generated Node #2: [36, 59, 4] from Operation: 51-47=4 Current State: 68:[36, 59, 4], Operations: ['51-47=4'] Exploring Operation: 36/4=9, Resulting Numbers: [59, 9] Generated Node #3: [59, 9] from Operation: 36/4=9 Current State: 68:[59, 9], Operations: ['51-47=4', '36/4=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[36, 59, 47, 51], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [59, 47, 15] Generated Node #0,0: 68:[59, 47, 15] Operation: 51-36=15 Exploring Operation: 59-51=8, Resulting Numbers: [36, 47, 8] Generated Node #0,1: 68:[36, 47, 8] Operation: 59-51=8 Exploring Operation: 51-47=4, Resulting Numbers: [36, 59, 4] Generated Node #0,2: 68:[36, 59, 4] Operation: 51-47=4 Exploring Operation: 59-47=12, Resulting Numbers: [36, 51, 12] Generated Node #0,3: 68:[36, 51, 12] Operation: 59-47=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[36, 59, 4], Operations: ['51-47=4'] Exploring Operation: 36-4=32, Resulting Numbers: [59, 32] Generated Node #0,2,0: 68:[59, 32] Operation: 36-4=32 Exploring Operation: 36/4=9, Resulting Numbers: [59, 9] Generated Node #0,2,1: 68:[59, 9] Operation: 36/4=9 Exploring Operation: 59-36=23, Resulting Numbers: [4, 23] Generated Node #0,2,2: 68:[4, 23] Operation: 59-36=23 Exploring Operation: 59+4=63, Resulting Numbers: [36, 63] Generated Node #0,2,3: 68:[36, 63] Operation: 59+4=63 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[4, 23], Operations: ['51-47=4', '59-36=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,68 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,68 unequal: No Solution No 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: 68:[36, 63], Operations: ['51-47=4', '59+4=63'] Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,68 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,68 unequal: No Solution No 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: 68:[59, 32], Operations: ['51-47=4', '36-4=32'] Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 59*32=1888, Resulting Numbers: [1888] 1888,68 unequal: No Solution Exploring Operation: 59+32=91, Resulting Numbers: [91] 91,68 unequal: No Solution No 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: 68:[59, 9], Operations: ['51-47=4', '36/4=9'] Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,68 unequal: No Solution Exploring Operation: 59*9=531, Resulting Numbers: [531] 531,68 unequal: No Solution Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[36, 59, 47, 51], Operations: [] Exploring Operation: 51-47=4, Resulting Numbers: [36, 59, 4] Generated Node #0,2: 68:[36, 59, 4] Operation: 51-47=4 Moving to Node #0,2 Current State: 68:[36, 59, 4], Operations: ['51-47=4'] Exploring Operation: 36/4=9, Resulting Numbers: [59, 9] Generated Node #0,2,1: 68:[59, 9] Operation: 36/4=9 Moving to Node #0,2,1 Current State: 68:[59, 9], Operations: ['51-47=4', '36/4=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 81, 64, 19, 47 ]
79
[ "81+64=145", "19+47=66", "145-66=79" ]
Current State: 79:[81, 64, 19, 47], Operations: [] Exploring Operation: 81+64=145, Resulting Numbers: [19, 47, 145] Generated Node #2: [19, 47, 145] from Operation: 81+64=145 Current State: 79:[19, 47, 145], Operations: ['81+64=145'] Exploring Operation: 19+47=66, Resulting Numbers: [145, 66] Generated Node #3: [145, 66] from Operation: 19+47=66 Current State: 79:[145, 66], Operations: ['81+64=145', '19+47=66'] Exploring Operation: 145-66=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[81, 64, 19, 47], Operations: [] Exploring Operation: 81+19=100, Resulting Numbers: [64, 47, 100] Generated Node #0,0: 79:[64, 47, 100] Operation: 81+19=100 Exploring Operation: 64+19=83, Resulting Numbers: [81, 47, 83] Generated Node #0,1: 79:[81, 47, 83] Operation: 64+19=83 Exploring Operation: 19+47=66, Resulting Numbers: [81, 64, 66] Generated Node #0,2: 79:[81, 64, 66] Operation: 19+47=66 Exploring Operation: 81-19=62, Resulting Numbers: [64, 47, 62] Generated Node #0,3: 79:[64, 47, 62] Operation: 81-19=62 Moving to Node #0,2 Current State: 79:[81, 64, 66], Operations: ['19+47=66'] Exploring Operation: 64+66=130, Resulting Numbers: [81, 130] Generated Node #0,2,0: 79:[81, 130] Operation: 64+66=130 Exploring Operation: 81-66=15, Resulting Numbers: [64, 15] Generated Node #0,2,1: 79:[64, 15] Operation: 81-66=15 Exploring Operation: 81+64=145, Resulting Numbers: [66, 145] Generated Node #0,2,2: 79:[66, 145] Operation: 81+64=145 Exploring Operation: 81-64=17, Resulting Numbers: [66, 17] Generated Node #0,2,3: 79:[66, 17] Operation: 81-64=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[81, 130], Operations: ['19+47=66', '64+66=130'] Exploring Operation: 81*130=10530, Resulting Numbers: [10530] 10530,79 unequal: No Solution Exploring Operation: 81+130=211, Resulting Numbers: [211] 211,79 unequal: No Solution Exploring Operation: 130-81=49, Resulting Numbers: [49] 49,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[66, 17], Operations: ['19+47=66', '81-64=17'] Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,79 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,79 unequal: No Solution Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[64, 15], Operations: ['19+47=66', '81-66=15'] Exploring Operation: 64*15=960, Resulting Numbers: [960] 960,79 unequal: No Solution Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[81, 64, 19, 47], Operations: [] Exploring Operation: 19+47=66, Resulting Numbers: [81, 64, 66] Generated Node #0,2: 79:[81, 64, 66] Operation: 19+47=66 Moving to Node #0,2 Current State: 79:[81, 64, 66], Operations: ['19+47=66'] Exploring Operation: 81-66=15, Resulting Numbers: [64, 15] Generated Node #0,2,1: 79:[64, 15] Operation: 81-66=15 Moving to Node #0,2,1 Current State: 79:[64, 15], Operations: ['19+47=66', '81-66=15'] Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 90, 63, 16, 96 ]
73
[ "90+63=153", "96-16=80", "153-80=73" ]
Current State: 73:[90, 63, 16, 96], Operations: [] Exploring Operation: 90+63=153, Resulting Numbers: [16, 96, 153] Generated Node #2: [16, 96, 153] from Operation: 90+63=153 Current State: 73:[16, 96, 153], Operations: ['90+63=153'] Exploring Operation: 96-16=80, Resulting Numbers: [153, 80] Generated Node #3: [153, 80] from Operation: 96-16=80 Current State: 73:[153, 80], Operations: ['90+63=153', '96-16=80'] Exploring Operation: 153-80=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[90, 63, 16, 96], Operations: [] Exploring Operation: 63+16=79, Resulting Numbers: [90, 96, 79] Generated Node #0,0: 73:[90, 96, 79] Operation: 63+16=79 Exploring Operation: 96-16=80, Resulting Numbers: [90, 63, 80] Generated Node #0,1: 73:[90, 63, 80] Operation: 96-16=80 Exploring Operation: 63-16=47, Resulting Numbers: [90, 96, 47] Generated Node #0,2: 73:[90, 96, 47] Operation: 63-16=47 Exploring Operation: 90+16=106, Resulting Numbers: [63, 96, 106] Generated Node #0,3: 73:[63, 96, 106] Operation: 90+16=106 Exploring Operation: 90-16=74, Resulting Numbers: [63, 96, 74] Generated Node #0,4: 73:[63, 96, 74] Operation: 90-16=74 Moving to Node #0,1 Current State: 73:[90, 63, 80], Operations: ['96-16=80'] Exploring Operation: 90-63=27, Resulting Numbers: [80, 27] Generated Node #0,1,0: 73:[80, 27] Operation: 90-63=27 Exploring Operation: 90+63=153, Resulting Numbers: [80, 153] Generated Node #0,1,1: 73:[80, 153] Operation: 90+63=153 Exploring Operation: 80-63=17, Resulting Numbers: [90, 17] Generated Node #0,1,2: 73:[90, 17] Operation: 80-63=17 Exploring Operation: 90-80=10, Resulting Numbers: [63, 10] Generated Node #0,1,3: 73:[63, 10] Operation: 90-80=10 Exploring Operation: 63+80=143, Resulting Numbers: [90, 143] Generated Node #0,1,4: 73:[90, 143] Operation: 63+80=143 Moving to Node #0,4 Current State: 73:[63, 96, 74], Operations: ['90-16=74'] Exploring Operation: 96-63=33, Resulting Numbers: [74, 33] Generated Node #0,4,0: 73:[74, 33] Operation: 96-63=33 Exploring Operation: 74-63=11, Resulting Numbers: [96, 11] Generated Node #0,4,1: 73:[96, 11] Operation: 74-63=11 Exploring Operation: 63+74=137, Resulting Numbers: [96, 137] Generated Node #0,4,2: 73:[96, 137] Operation: 63+74=137 Exploring Operation: 63+96=159, Resulting Numbers: [74, 159] Generated Node #0,4,3: 73:[74, 159] Operation: 63+96=159 Exploring Operation: 96-74=22, Resulting Numbers: [63, 22] Generated Node #0,4,4: 73:[63, 22] Operation: 96-74=22 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 73:[74, 33], Operations: ['90-16=74', '96-63=33'] Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,73 unequal: No Solution Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,73 unequal: No Solution Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,73 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 #0,4,4 Current State: 73:[63, 22], Operations: ['90-16=74', '96-74=22'] Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,73 unequal: No Solution Exploring Operation: 63+22=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 63*22=1386, Resulting Numbers: [1386] 1386,73 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 #0,4,1 Current State: 73:[96, 11], Operations: ['90-16=74', '74-63=11'] Exploring Operation: 96-11=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 96*11=1056, Resulting Numbers: [1056] 1056,73 unequal: No Solution Exploring Operation: 96+11=107, Resulting Numbers: [107] 107,73 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 #0,4,2 Current State: 73:[96, 137], Operations: ['90-16=74', '63+74=137'] Exploring Operation: 96+137=233, Resulting Numbers: [233] 233,73 unequal: No Solution Exploring Operation: 137-96=41, Resulting Numbers: [41] 41,73 unequal: No Solution Exploring Operation: 96*137=13152, Resulting Numbers: [13152] 13152,73 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 #0,4,3 Current State: 73:[74, 159], Operations: ['90-16=74', '63+96=159'] Exploring Operation: 159-74=85, Resulting Numbers: [85] 85,73 unequal: No Solution Exploring Operation: 74*159=11766, Resulting Numbers: [11766] 11766,73 unequal: No Solution Exploring Operation: 74+159=233, Resulting Numbers: [233] 233,73 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: 73:[90, 96, 79], Operations: ['63+16=79'] Exploring Operation: 90-79=11, Resulting Numbers: [96, 11] Generated Node #0,0,0: 73:[96, 11] Operation: 90-79=11 Exploring Operation: 96-79=17, Resulting Numbers: [90, 17] Generated Node #0,0,1: 73:[90, 17] Operation: 96-79=17 Exploring Operation: 96-90=6, Resulting Numbers: [79, 6] Generated Node #0,0,2: 73:[79, 6] Operation: 96-90=6 Exploring Operation: 90+96=186, Resulting Numbers: [79, 186] Generated Node #0,0,3: 73:[79, 186] Operation: 90+96=186 Exploring Operation: 90+79=169, Resulting Numbers: [96, 169] Generated Node #0,0,4: 73:[96, 169] Operation: 90+79=169 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[90, 17], Operations: ['63+16=79', '96-79=17'] Exploring Operation: 90-17=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[90, 63, 16, 96], Operations: [] Exploring Operation: 63+16=79, Resulting Numbers: [90, 96, 79] Generated Node #0,0: 73:[90, 96, 79] Operation: 63+16=79 Moving to Node #0,0 Current State: 73:[90, 96, 79], Operations: ['63+16=79'] Exploring Operation: 96-79=17, Resulting Numbers: [90, 17] Generated Node #0,0,1: 73:[90, 17] Operation: 96-79=17 Moving to Node #0,0,1 Current State: 73:[90, 17], Operations: ['63+16=79', '96-79=17'] Exploring Operation: 90-17=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_5
mult_heuristic
[ 36, 79, 67, 97 ]
94
[ "79-67=12", "36/12=3", "97-3=94" ]
Current State: 94:[36, 79, 67, 97], Operations: [] Exploring Operation: 79-67=12, Resulting Numbers: [36, 97, 12] Generated Node #2: [36, 97, 12] from Operation: 79-67=12 Current State: 94:[36, 97, 12], Operations: ['79-67=12'] Exploring Operation: 36/12=3, Resulting Numbers: [97, 3] Generated Node #3: [97, 3] from Operation: 36/12=3 Current State: 94:[97, 3], Operations: ['79-67=12', '36/12=3'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[36, 79, 67, 97], Operations: [] Exploring Operation: 97-67=30, Resulting Numbers: [36, 79, 30] Generated Node #0,0: 94:[36, 79, 30] Operation: 97-67=30 Exploring Operation: 79-67=12, Resulting Numbers: [36, 97, 12] Generated Node #0,1: 94:[36, 97, 12] Operation: 79-67=12 Exploring Operation: 79-36=43, Resulting Numbers: [67, 97, 43] Generated Node #0,2: 94:[67, 97, 43] Operation: 79-36=43 Exploring Operation: 67-36=31, Resulting Numbers: [79, 97, 31] Generated Node #0,3: 94:[79, 97, 31] Operation: 67-36=31 Exploring Operation: 36+67=103, Resulting Numbers: [79, 97, 103] Generated Node #0,4: 94:[79, 97, 103] Operation: 36+67=103 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[36, 97, 12], Operations: ['79-67=12'] Exploring Operation: 36-12=24, Resulting Numbers: [97, 24] Generated Node #0,1,0: 94:[97, 24] Operation: 36-12=24 Exploring Operation: 36+12=48, Resulting Numbers: [97, 48] Generated Node #0,1,1: 94:[97, 48] Operation: 36+12=48 Exploring Operation: 97-36=61, Resulting Numbers: [12, 61] Generated Node #0,1,2: 94:[12, 61] Operation: 97-36=61 Exploring Operation: 97-12=85, Resulting Numbers: [36, 85] Generated Node #0,1,3: 94:[36, 85] Operation: 97-12=85 Exploring Operation: 36/12=3, Resulting Numbers: [97, 3] Generated Node #0,1,4: 94:[97, 3] Operation: 36/12=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[97, 48], Operations: ['79-67=12', '36+12=48'] Exploring Operation: 97+48=145, Resulting Numbers: [145] 145,94 unequal: No Solution Exploring Operation: 97-48=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 97*48=4656, Resulting Numbers: [4656] 4656,94 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 #0,1,4 Current State: 94:[97, 3], Operations: ['79-67=12', '36/12=3'] Exploring Operation: 97*3=291, Resulting Numbers: [291] 291,94 unequal: No Solution Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,94 unequal: No Solution Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[36, 79, 67, 97], Operations: [] Exploring Operation: 79-67=12, Resulting Numbers: [36, 97, 12] Generated Node #0,1: 94:[36, 97, 12] Operation: 79-67=12 Moving to Node #0,1 Current State: 94:[36, 97, 12], Operations: ['79-67=12'] Exploring Operation: 36/12=3, Resulting Numbers: [97, 3] Generated Node #0,1,4: 94:[97, 3] Operation: 36/12=3 Moving to Node #0,1,4 Current State: 94:[97, 3], Operations: ['79-67=12', '36/12=3'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 7, 31, 32, 92 ]
36
[ "31-7=24", "92-32=60", "60-24=36" ]
Current State: 36:[7, 31, 32, 92], Operations: [] Exploring Operation: 31-7=24, Resulting Numbers: [32, 92, 24] Generated Node #2: [32, 92, 24] from Operation: 31-7=24 Current State: 36:[32, 92, 24], Operations: ['31-7=24'] Exploring Operation: 92-32=60, Resulting Numbers: [24, 60] Generated Node #3: [24, 60] from Operation: 92-32=60 Current State: 36:[24, 60], Operations: ['31-7=24', '92-32=60'] Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[7, 31, 32, 92], Operations: [] Exploring Operation: 92-31=61, Resulting Numbers: [7, 32, 61] Generated Node #0,0: 36:[7, 32, 61] Operation: 92-31=61 Moving to Node #0,0 Current State: 36:[7, 32, 61], Operations: ['92-31=61'] Exploring Operation: 61-32=29, Resulting Numbers: [7, 29] Generated Node #0,0,0: 36:[7, 29] Operation: 61-32=29 Moving to Node #0,0,0 Current State: 36:[7, 29], Operations: ['92-31=61', '61-32=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[7, 31, 32, 92], Operations: [] Exploring Operation: 92-31=61, Resulting Numbers: [7, 32, 61] Generated Node #0,0: 36:[7, 32, 61] Operation: 92-31=61 Moving to Node #0,0 Current State: 36:[7, 32, 61], Operations: ['92-31=61'] Exploring Operation: 61-32=29, Resulting Numbers: [7, 29] Generated Node #0,0,0: 36:[7, 29] Operation: 61-32=29 Moving to Node #0,0,0 Current State: 36:[7, 29], Operations: ['92-31=61', '61-32=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 2, 32, 7, 30 ]
36
[ "30-2=28", "28/7=4", "32+4=36" ]
Current State: 36:[2, 32, 7, 30], Operations: [] Exploring Operation: 30-2=28, Resulting Numbers: [32, 7, 28] Generated Node #2: [32, 7, 28] from Operation: 30-2=28 Current State: 36:[32, 7, 28], Operations: ['30-2=28'] Exploring Operation: 28/7=4, Resulting Numbers: [32, 4] Generated Node #3: [32, 4] from Operation: 28/7=4 Current State: 36:[32, 4], Operations: ['30-2=28', '28/7=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[2, 32, 7, 30], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [2, 7, 2] Generated Node #0,0: 36:[2, 7, 2] Operation: 32-30=2 Exploring Operation: 7+30=37, Resulting Numbers: [2, 32, 37] Generated Node #0,1: 36:[2, 32, 37] Operation: 7+30=37 Exploring Operation: 30/2=15, Resulting Numbers: [32, 7, 15] Generated Node #0,2: 36:[32, 7, 15] Operation: 30/2=15 Exploring Operation: 2+32=34, Resulting Numbers: [7, 30, 34] Generated Node #0,3: 36:[7, 30, 34] Operation: 2+32=34 Exploring Operation: 32/2=16, Resulting Numbers: [7, 30, 16] Generated Node #0,4: 36:[7, 30, 16] Operation: 32/2=16 Moving to Node #0,0 Current State: 36:[2, 7, 2], Operations: ['32-30=2'] Exploring Operation: 7-2=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 36:[2, 5] Operation: 7-2=5 Exploring Operation: 7+2=9, Resulting Numbers: [2, 9] Generated Node #0,0,1: 36:[2, 9] Operation: 7+2=9 Exploring Operation: 2+7=9, Resulting Numbers: [2, 9] Generated Node #0,0,2: 36:[2, 9] Operation: 2+7=9 Exploring Operation: 2*2=4, Resulting Numbers: [7, 4] Generated Node #0,0,3: 36:[7, 4] Operation: 2*2=4 Exploring Operation: 2+2=4, Resulting Numbers: [7, 4] Generated Node #0,0,4: 36:[7, 4] Operation: 2+2=4 Moving to Node #0,1 Current State: 36:[2, 32, 37], Operations: ['7+30=37'] Exploring Operation: 32-2=30, Resulting Numbers: [37, 30] Generated Node #0,1,0: 36:[37, 30] Operation: 32-2=30 Exploring Operation: 2+32=34, Resulting Numbers: [37, 34] Generated Node #0,1,1: 36:[37, 34] Operation: 2+32=34 Exploring Operation: 37-2=35, Resulting Numbers: [32, 35] Generated Node #0,1,2: 36:[32, 35] Operation: 37-2=35 Exploring Operation: 32/2=16, Resulting Numbers: [37, 16] Generated Node #0,1,3: 36:[37, 16] Operation: 32/2=16 Exploring Operation: 37-32=5, Resulting Numbers: [2, 5] Generated Node #0,1,4: 36:[2, 5] Operation: 37-32=5 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 36:[2, 5], Operations: ['7+30=37', '37-32=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[37, 34], Operations: ['7+30=37', '2+32=34'] Exploring Operation: 37*34=1258, Resulting Numbers: [1258] 1258,36 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 36:[37, 16], Operations: ['7+30=37', '32/2=16'] Exploring Operation: 37+16=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 37*16=592, Resulting Numbers: [592] 592,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 36:[32, 35], Operations: ['7+30=37', '37-2=35'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,36 unequal: No Solution Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[37, 30], Operations: ['7+30=37', '32-2=30'] Exploring Operation: 37*30=1110, Resulting Numbers: [1110] 1110,36 unequal: No Solution Exploring Operation: 37+30=67, Resulting Numbers: [67] 67,36 unequal: No Solution Exploring Operation: 37-30=7, Resulting Numbers: [7] 7,36 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: 36:[32, 7, 15], Operations: ['30/2=15'] Exploring Operation: 7+15=22, Resulting Numbers: [32, 22] Generated Node #0,2,0: 36:[32, 22] Operation: 7+15=22 Exploring Operation: 32+7=39, Resulting Numbers: [15, 39] Generated Node #0,2,1: 36:[15, 39] Operation: 32+7=39 Exploring Operation: 32-15=17, Resulting Numbers: [7, 17] Generated Node #0,2,2: 36:[7, 17] Operation: 32-15=17 Exploring Operation: 15-7=8, Resulting Numbers: [32, 8] Generated Node #0,2,3: 36:[32, 8] Operation: 15-7=8 Exploring Operation: 32-7=25, Resulting Numbers: [15, 25] Generated Node #0,2,4: 36:[15, 25] Operation: 32-7=25 Moving to Node #0,3 Current State: 36:[7, 30, 34], Operations: ['2+32=34'] Exploring Operation: 34-7=27, Resulting Numbers: [30, 27] Generated Node #0,3,0: 36:[30, 27] Operation: 34-7=27 Exploring Operation: 34-30=4, Resulting Numbers: [7, 4] Generated Node #0,3,1: 36:[7, 4] Operation: 34-30=4 Exploring Operation: 30-7=23, Resulting Numbers: [34, 23] Generated Node #0,3,2: 36:[34, 23] Operation: 30-7=23 Exploring Operation: 7+34=41, Resulting Numbers: [30, 41] Generated Node #0,3,3: 36:[30, 41] Operation: 7+34=41 Exploring Operation: 7+30=37, Resulting Numbers: [34, 37] Generated Node #0,3,4: 36:[34, 37] Operation: 7+30=37 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[7, 4], Operations: ['2+32=34', '34-30=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 36:[34, 37], Operations: ['2+32=34', '7+30=37'] Exploring Operation: 34+37=71, Resulting Numbers: [71] 71,36 unequal: No Solution Exploring Operation: 34*37=1258, Resulting Numbers: [1258] 1258,36 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[34, 23], Operations: ['2+32=34', '30-7=23'] Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 34*23=782, Resulting Numbers: [782] 782,36 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[30, 41], Operations: ['2+32=34', '7+34=41'] Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 30+41=71, Resulting Numbers: [71] 71,36 unequal: No Solution Exploring Operation: 30*41=1230, Resulting Numbers: [1230] 1230,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[30, 27], Operations: ['2+32=34', '34-7=27'] Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,36 unequal: No Solution Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,36 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: 36:[7, 30, 16], Operations: ['32/2=16'] Exploring Operation: 16-7=9, Resulting Numbers: [30, 9] Generated Node #0,4,0: 36:[30, 9] Operation: 16-7=9 Exploring Operation: 30-16=14, Resulting Numbers: [7, 14] Generated Node #0,4,1: 36:[7, 14] Operation: 30-16=14 Exploring Operation: 7+16=23, Resulting Numbers: [30, 23] Generated Node #0,4,2: 36:[30, 23] Operation: 7+16=23 Exploring Operation: 30-7=23, Resulting Numbers: [16, 23] Generated Node #0,4,3: 36:[16, 23] Operation: 30-7=23 Exploring Operation: 7+30=37, Resulting Numbers: [16, 37] Generated Node #0,4,4: 36:[16, 37] Operation: 7+30=37 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 36:[7, 14], Operations: ['32/2=16', '30-16=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,36 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 36:[16, 37], Operations: ['32/2=16', '7+30=37'] Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,36 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 36:[30, 9], Operations: ['32/2=16', '16-7=9'] Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,36 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 36:[16, 23], Operations: ['32/2=16', '30-7=23'] Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,36 unequal: No Solution Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 36:[30, 23], Operations: ['32/2=16', '7+16=23'] Exploring Operation: 30*23=690, Resulting Numbers: [690] 690,36 unequal: No Solution Exploring Operation: 30+23=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 36:[2, 9], Operations: ['32-30=2', '7+2=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,36 unequal: No Solution Moving to Node #0,0,2 Current State: 36:[2, 9], Operations: ['32-30=2', '2+7=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[2, 5], Operations: ['32-30=2', '7-2=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,36 unequal: No Solution Moving to Node #0,0,4 Current State: 36:[7, 4], Operations: ['32-30=2', '2+2=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,36 unequal: No Solution Moving to Node #0,0,3 Current State: 36:[7, 4], Operations: ['32-30=2', '2*2=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[7, 17], Operations: ['30/2=15', '32-15=17'] Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,36 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,36 unequal: No Solution Moving to Node #0,2,3 Current State: 36:[32, 8], Operations: ['30/2=15', '15-7=8'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,36 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[15, 39], Operations: ['30/2=15', '32+7=39'] Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,36 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,36 unequal: No Solution Moving to Node #0,2,0 Current State: 36:[32, 22], Operations: ['30/2=15', '7+15=22'] Exploring Operation: 32*22=704, Resulting Numbers: [704] 704,36 unequal: No Solution Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,36 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,36 unequal: No Solution Moving to Node #0,2,4 Current State: 36:[15, 25], Operations: ['30/2=15', '32-7=25'] Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,36 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,36 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,36 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 86, 72, 81, 30 ]
78
[ "86-81=5", "30*5=150", "150-72=78" ]
Current State: 78:[86, 72, 81, 30], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [72, 30, 5] Generated Node #2: [72, 30, 5] from Operation: 86-81=5 Current State: 78:[72, 30, 5], Operations: ['86-81=5'] Exploring Operation: 30*5=150, Resulting Numbers: [72, 150] Generated Node #3: [72, 150] from Operation: 30*5=150 Current State: 78:[72, 150], Operations: ['86-81=5', '30*5=150'] Exploring Operation: 150-72=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[86, 72, 81, 30], Operations: [] Exploring Operation: 81-72=9, Resulting Numbers: [86, 30, 9] Generated Node #0,0: 78:[86, 30, 9] Operation: 81-72=9 Exploring Operation: 86-30=56, Resulting Numbers: [72, 81, 56] Generated Node #0,1: 78:[72, 81, 56] Operation: 86-30=56 Exploring Operation: 86-81=5, Resulting Numbers: [72, 30, 5] Generated Node #0,2: 78:[72, 30, 5] Operation: 86-81=5 Exploring Operation: 72-30=42, Resulting Numbers: [86, 81, 42] Generated Node #0,3: 78:[86, 81, 42] Operation: 72-30=42 Exploring Operation: 86-72=14, Resulting Numbers: [81, 30, 14] Generated Node #0,4: 78:[81, 30, 14] Operation: 86-72=14 Start Sub Search at level 1: Moving to Node #0,4 Current State: 78:[81, 30, 14], Operations: ['86-72=14'] Exploring Operation: 81-30=51, Resulting Numbers: [14, 51] Generated Node #0,4,0: 78:[14, 51] Operation: 81-30=51 Exploring Operation: 30-14=16, Resulting Numbers: [81, 16] Generated Node #0,4,1: 78:[81, 16] Operation: 30-14=16 Exploring Operation: 81-14=67, Resulting Numbers: [30, 67] Generated Node #0,4,2: 78:[30, 67] Operation: 81-14=67 Exploring Operation: 30+14=44, Resulting Numbers: [81, 44] Generated Node #0,4,3: 78:[81, 44] Operation: 30+14=44 Exploring Operation: 81+14=95, Resulting Numbers: [30, 95] Generated Node #0,4,4: 78:[30, 95] Operation: 81+14=95 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 78:[81, 16], Operations: ['86-72=14', '30-14=16'] Exploring Operation: 81+16=97, Resulting Numbers: [97] 97,78 unequal: No Solution Exploring Operation: 81*16=1296, Resulting Numbers: [1296] 1296,78 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,78 unequal: No Solution No 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: 78:[81, 44], Operations: ['86-72=14', '30+14=44'] Exploring Operation: 81+44=125, Resulting Numbers: [125] 125,78 unequal: No Solution Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 81*44=3564, Resulting Numbers: [3564] 3564,78 unequal: No Solution No 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: 78:[14, 51], Operations: ['86-72=14', '81-30=51'] Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,78 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,78 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,78 unequal: No Solution No 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: 78:[30, 67], Operations: ['86-72=14', '81-14=67'] Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,78 unequal: No Solution Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,78 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 78:[30, 95], Operations: ['86-72=14', '81+14=95'] Exploring Operation: 30*95=2850, Resulting Numbers: [2850] 2850,78 unequal: No Solution Exploring Operation: 30+95=125, Resulting Numbers: [125] 125,78 unequal: No Solution Exploring Operation: 95-30=65, Resulting Numbers: [65] 65,78 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: 78:[72, 30, 5], Operations: ['86-81=5'] Exploring Operation: 30-5=25, Resulting Numbers: [72, 25] Generated Node #0,2,0: 78:[72, 25] Operation: 30-5=25 Exploring Operation: 72+5=77, Resulting Numbers: [30, 77] Generated Node #0,2,1: 78:[30, 77] Operation: 72+5=77 Exploring Operation: 30+5=35, Resulting Numbers: [72, 35] Generated Node #0,2,2: 78:[72, 35] Operation: 30+5=35 Exploring Operation: 30/5=6, Resulting Numbers: [72, 6] Generated Node #0,2,3: 78:[72, 6] Operation: 30/5=6 Exploring Operation: 72-30=42, Resulting Numbers: [5, 42] Generated Node #0,2,4: 78:[5, 42] Operation: 72-30=42 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 78:[5, 42], Operations: ['86-81=5', '72-30=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,78 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 5*42=210, Resulting Numbers: [210] 210,78 unequal: No Solution No 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: 78:[30, 77], Operations: ['86-81=5', '72+5=77'] Exploring Operation: 77-30=47, Resulting Numbers: [47] 47,78 unequal: No Solution Exploring Operation: 30*77=2310, Resulting Numbers: [2310] 2310,78 unequal: No Solution Exploring Operation: 30+77=107, Resulting Numbers: [107] 107,78 unequal: No Solution No 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: 78:[72, 6], Operations: ['86-81=5', '30/5=6'] Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[86, 72, 81, 30], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [72, 30, 5] Generated Node #0,2: 78:[72, 30, 5] Operation: 86-81=5 Moving to Node #0,2 Current State: 78:[72, 30, 5], Operations: ['86-81=5'] Exploring Operation: 30/5=6, Resulting Numbers: [72, 6] Generated Node #0,2,3: 78:[72, 6] Operation: 30/5=6 Moving to Node #0,2,3 Current State: 78:[72, 6], Operations: ['86-81=5', '30/5=6'] Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 10, 55, 16, 19 ]
69
[ "55*16=880", "880/10=88", "88-19=69" ]
Current State: 69:[10, 55, 16, 19], Operations: [] Exploring Operation: 55*16=880, Resulting Numbers: [10, 19, 880] Generated Node #2: [10, 19, 880] from Operation: 55*16=880 Current State: 69:[10, 19, 880], Operations: ['55*16=880'] Exploring Operation: 880/10=88, Resulting Numbers: [19, 88] Generated Node #3: [19, 88] from Operation: 880/10=88 Current State: 69:[19, 88], Operations: ['55*16=880', '880/10=88'] Exploring Operation: 88-19=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[10, 55, 16, 19], Operations: [] Exploring Operation: 10+55=65, Resulting Numbers: [16, 19, 65] Generated Node #0,0: 69:[16, 19, 65] Operation: 10+55=65 Exploring Operation: 55+16=71, Resulting Numbers: [10, 19, 71] Generated Node #0,1: 69:[10, 19, 71] Operation: 55+16=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[10, 19, 71], Operations: ['55+16=71'] Exploring Operation: 19-10=9, Resulting Numbers: [71, 9] Generated Node #0,1,0: 69:[71, 9] Operation: 19-10=9 Exploring Operation: 10+19=29, Resulting Numbers: [71, 29] Generated Node #0,1,1: 69:[71, 29] Operation: 10+19=29 Moving to Node #0,1,0 Current State: 69:[71, 9], Operations: ['55+16=71', '19-10=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[71, 29], Operations: ['55+16=71', '10+19=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[16, 19, 65], Operations: ['10+55=65'] Exploring Operation: 19-16=3, Resulting Numbers: [65, 3] Generated Node #0,0,0: 69:[65, 3] Operation: 19-16=3 Exploring Operation: 16+19=35, Resulting Numbers: [65, 35] Generated Node #0,0,1: 69:[65, 35] Operation: 16+19=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[65, 3], Operations: ['10+55=65', '19-16=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,69 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[65, 35], Operations: ['10+55=65', '16+19=35'] Exploring Operation: 65+35=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 2, 76, 11, 60 ]
35
[ "60/2=30", "76-11=65", "65-30=35" ]
Current State: 35:[2, 76, 11, 60], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [76, 11, 30] Generated Node #2: [76, 11, 30] from Operation: 60/2=30 Current State: 35:[76, 11, 30], Operations: ['60/2=30'] Exploring Operation: 76-11=65, Resulting Numbers: [30, 65] Generated Node #3: [30, 65] from Operation: 76-11=65 Current State: 35:[30, 65], Operations: ['60/2=30', '76-11=65'] Exploring Operation: 65-30=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[2, 76, 11, 60], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [11, 60, 38] Generated Node #0,0: 35:[11, 60, 38] Operation: 76/2=38 Exploring Operation: 76-11=65, Resulting Numbers: [2, 60, 65] Generated Node #0,1: 35:[2, 60, 65] Operation: 76-11=65 Exploring Operation: 60/2=30, Resulting Numbers: [76, 11, 30] Generated Node #0,2: 35:[76, 11, 30] Operation: 60/2=30 Exploring Operation: 60-11=49, Resulting Numbers: [2, 76, 49] Generated Node #0,3: 35:[2, 76, 49] Operation: 60-11=49 Exploring Operation: 76-60=16, Resulting Numbers: [2, 11, 16] Generated Node #0,4: 35:[2, 11, 16] Operation: 76-60=16 Moving to Node #0,4 Current State: 35:[2, 11, 16], Operations: ['76-60=16'] Exploring Operation: 2*16=32, Resulting Numbers: [11, 32] Generated Node #0,4,0: 35:[11, 32] Operation: 2*16=32 Exploring Operation: 16-2=14, Resulting Numbers: [11, 14] Generated Node #0,4,1: 35:[11, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [11, 8] Generated Node #0,4,2: 35:[11, 8] Operation: 16/2=8 Exploring Operation: 11-2=9, Resulting Numbers: [16, 9] Generated Node #0,4,3: 35:[16, 9] Operation: 11-2=9 Exploring Operation: 16-11=5, Resulting Numbers: [2, 5] Generated Node #0,4,4: 35:[2, 5] Operation: 16-11=5 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 35:[2, 5], Operations: ['76-60=16', '16-11=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,35 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 #0,4,2 Current State: 35:[11, 8], Operations: ['76-60=16', '16/2=8'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 11+8=19, Resulting Numbers: [19] 19,35 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 #0,4,0 Current State: 35:[11, 32], Operations: ['76-60=16', '2*16=32'] Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,35 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 #0,4,1 Current State: 35:[11, 14], Operations: ['76-60=16', '16-2=14'] Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,35 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,35 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 #0,4,3 Current State: 35:[16, 9], Operations: ['76-60=16', '11-2=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,35 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,35 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: 35:[11, 60, 38], Operations: ['76/2=38'] Exploring Operation: 60-38=22, Resulting Numbers: [11, 22] Generated Node #0,0,0: 35:[11, 22] Operation: 60-38=22 Exploring Operation: 11+60=71, Resulting Numbers: [38, 71] Generated Node #0,0,1: 35:[38, 71] Operation: 11+60=71 Exploring Operation: 38-11=27, Resulting Numbers: [60, 27] Generated Node #0,0,2: 35:[60, 27] Operation: 38-11=27 Exploring Operation: 11+38=49, Resulting Numbers: [60, 49] Generated Node #0,0,3: 35:[60, 49] Operation: 11+38=49 Exploring Operation: 60-11=49, Resulting Numbers: [38, 49] Generated Node #0,0,4: 35:[38, 49] Operation: 60-11=49 Moving to Node #0,2 Current State: 35:[76, 11, 30], Operations: ['60/2=30'] Exploring Operation: 76+11=87, Resulting Numbers: [30, 87] Generated Node #0,2,0: 35:[30, 87] Operation: 76+11=87 Exploring Operation: 30-11=19, Resulting Numbers: [76, 19] Generated Node #0,2,1: 35:[76, 19] Operation: 30-11=19 Exploring Operation: 11+30=41, Resulting Numbers: [76, 41] Generated Node #0,2,2: 35:[76, 41] Operation: 11+30=41 Exploring Operation: 76-11=65, Resulting Numbers: [30, 65] Generated Node #0,2,3: 35:[30, 65] Operation: 76-11=65 Exploring Operation: 76-30=46, Resulting Numbers: [11, 46] Generated Node #0,2,4: 35:[11, 46] Operation: 76-30=46 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 35:[11, 46], Operations: ['60/2=30', '76-30=46'] Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,35 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,35 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[2, 76, 11, 60], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [76, 11, 30] Generated Node #0,2: 35:[76, 11, 30] Operation: 60/2=30 Moving to Node #0,2 Current State: 35:[76, 11, 30], Operations: ['60/2=30'] Exploring Operation: 76-30=46, Resulting Numbers: [11, 46] Generated Node #0,2,4: 35:[11, 46] Operation: 76-30=46 Moving to Node #0,2,4 Current State: 35:[11, 46], Operations: ['60/2=30', '76-30=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic