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
[ 2, 23, 80, 22 ]
68
[ "22/2=11", "80-23=57", "11+57=68" ]
Current State: 68:[2, 23, 80, 22], Operations: [] Exploring Operation: 22/2=11, Resulting Numbers: [23, 80, 11] Generated Node #2: [23, 80, 11] from Operation: 22/2=11 Current State: 68:[23, 80, 11], Operations: ['22/2=11'] Exploring Operation: 80-23=57, Resulting Numbers: [11, 57] Generated Node #3: [11, 57] from Operation: 80-23=57 Current State: 68:[11, 57], Operations: ['22/2=11', '80-23=57'] Exploring Operation: 11+57=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[2, 23, 80, 22], Operations: [] Exploring Operation: 23-22=1, Resulting Numbers: [2, 80, 1] Generated Node #0,0: 68:[2, 80, 1] Operation: 23-22=1 Exploring Operation: 80-23=57, Resulting Numbers: [2, 22, 57] Generated Node #0,1: 68:[2, 22, 57] Operation: 80-23=57 Exploring Operation: 80/2=40, Resulting Numbers: [23, 22, 40] Generated Node #0,2: 68:[23, 22, 40] Operation: 80/2=40 Exploring Operation: 80-22=58, Resulting Numbers: [2, 23, 58] Generated Node #0,3: 68:[2, 23, 58] Operation: 80-22=58 Moving to Node #0,0 Current State: 68:[2, 80, 1], Operations: ['23-22=1'] Exploring Operation: 2*1=2, Resulting Numbers: [80, 2] Generated Node #0,0,0: 68:[80, 2] Operation: 2*1=2 Exploring Operation: 80-1=79, Resulting Numbers: [2, 79] Generated Node #0,0,1: 68:[2, 79] Operation: 80-1=79 Exploring Operation: 80/2=40, Resulting Numbers: [1, 40] Generated Node #0,0,2: 68:[1, 40] Operation: 80/2=40 Exploring Operation: 80-2=78, Resulting Numbers: [1, 78] Generated Node #0,0,3: 68:[1, 78] Operation: 80-2=78 Moving to Node #0,3 Current State: 68:[2, 23, 58], Operations: ['80-22=58'] Exploring Operation: 58-23=35, Resulting Numbers: [2, 35] Generated Node #0,3,0: 68:[2, 35] Operation: 58-23=35 Exploring Operation: 58/2=29, Resulting Numbers: [23, 29] Generated Node #0,3,1: 68:[23, 29] Operation: 58/2=29 Exploring Operation: 23-2=21, Resulting Numbers: [58, 21] Generated Node #0,3,2: 68:[58, 21] Operation: 23-2=21 Exploring Operation: 23+58=81, Resulting Numbers: [2, 81] Generated Node #0,3,3: 68:[2, 81] Operation: 23+58=81 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[2, 35], Operations: ['80-22=58', '58-23=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,68 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 68:[23, 29], Operations: ['80-22=58', '58/2=29'] Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,68 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 68:[2, 81], Operations: ['80-22=58', '23+58=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,68 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,68 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 68:[58, 21], Operations: ['80-22=58', '23-2=21'] Exploring Operation: 58*21=1218, Resulting Numbers: [1218] 1218,68 unequal: No Solution Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 58+21=79, Resulting Numbers: [79] 79,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 68:[2, 22, 57], Operations: ['80-23=57'] Exploring Operation: 22+57=79, Resulting Numbers: [2, 79] Generated Node #0,1,0: 68:[2, 79] Operation: 22+57=79 Exploring Operation: 2+57=59, Resulting Numbers: [22, 59] Generated Node #0,1,1: 68:[22, 59] Operation: 2+57=59 Exploring Operation: 22-2=20, Resulting Numbers: [57, 20] Generated Node #0,1,2: 68:[57, 20] Operation: 22-2=20 Exploring Operation: 57-22=35, Resulting Numbers: [2, 35] Generated Node #0,1,3: 68:[2, 35] Operation: 57-22=35 Moving to Node #0,2 Current State: 68:[23, 22, 40], Operations: ['80/2=40'] Exploring Operation: 40-22=18, Resulting Numbers: [23, 18] Generated Node #0,2,0: 68:[23, 18] Operation: 40-22=18 Exploring Operation: 23-22=1, Resulting Numbers: [40, 1] Generated Node #0,2,1: 68:[40, 1] Operation: 23-22=1 Exploring Operation: 23+40=63, Resulting Numbers: [22, 63] Generated Node #0,2,2: 68:[22, 63] Operation: 23+40=63 Exploring Operation: 40-23=17, Resulting Numbers: [22, 17] Generated Node #0,2,3: 68:[22, 17] Operation: 40-23=17 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 68:[22, 17], Operations: ['80/2=40', '40-23=17'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,68 unequal: No Solution Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[23, 18], Operations: ['80/2=40', '40-22=18'] Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,68 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[40, 1], Operations: ['80/2=40', '23-22=1'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[22, 63], Operations: ['80/2=40', '23+40=63'] Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,68 unequal: No Solution Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,68 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 68:[2, 35], Operations: ['80-23=57', '57-22=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[1, 40], Operations: ['23-22=1', '80/2=40'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[1, 78], Operations: ['23-22=1', '80-2=78'] Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,68 unequal: No Solution Exploring Operation: 1+78=79, Resulting Numbers: [79] 79,68 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 1*78=78, Resulting Numbers: [78] 78,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[2, 79], Operations: ['80-23=57', '22+57=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,68 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[2, 79], Operations: ['23-22=1', '80-1=79'] Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,68 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[80, 2], Operations: ['23-22=1', '2*1=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,68 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,68 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[57, 20], Operations: ['80-23=57', '22-2=20'] Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,68 unequal: No Solution Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[22, 59], Operations: ['80-23=57', '2+57=59'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,68 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,68 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 90, 70, 36, 29 ]
90
[ "90*29=2610", "70*36=2520", "2610-2520=90" ]
Current State: 90:[90, 70, 36, 29], Operations: [] Exploring Operation: 90*29=2610, Resulting Numbers: [70, 36, 2610] Generated Node #2: [70, 36, 2610] from Operation: 90*29=2610 Current State: 90:[70, 36, 2610], Operations: ['90*29=2610'] Exploring Operation: 70*36=2520, Resulting Numbers: [2610, 2520] Generated Node #3: [2610, 2520] from Operation: 70*36=2520 Current State: 90:[2610, 2520], Operations: ['90*29=2610', '70*36=2520'] Exploring Operation: 2610-2520=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[90, 70, 36, 29], Operations: [] Exploring Operation: 70-36=34, Resulting Numbers: [90, 29, 34] Generated Node #0,0: 90:[90, 29, 34] Operation: 70-36=34 Exploring Operation: 90-70=20, Resulting Numbers: [36, 29, 20] Generated Node #0,1: 90:[36, 29, 20] Operation: 90-70=20 Moving to Node #0,0 Current State: 90:[90, 29, 34], Operations: ['70-36=34'] Exploring Operation: 34-29=5, Resulting Numbers: [90, 5] Generated Node #0,0,0: 90:[90, 5] Operation: 34-29=5 Exploring Operation: 90-34=56, Resulting Numbers: [29, 56] Generated Node #0,0,1: 90:[29, 56] Operation: 90-34=56 Moving to Node #0,1 Current State: 90:[36, 29, 20], Operations: ['90-70=20'] Exploring Operation: 36-20=16, Resulting Numbers: [29, 16] Generated Node #0,1,0: 90:[29, 16] Operation: 36-20=16 Exploring Operation: 36-29=7, Resulting Numbers: [20, 7] Generated Node #0,1,1: 90:[20, 7] Operation: 36-29=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[29, 16], Operations: ['90-70=20', '36-20=16'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[20, 7], Operations: ['90-70=20', '36-29=7'] Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,90 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: 90:[90, 5], Operations: ['70-36=34', '34-29=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[29, 56], Operations: ['70-36=34', '90-34=56'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,90 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 60, 51, 2, 70 ]
44
[ "60-51=9", "70/2=35", "9+35=44" ]
Current State: 44:[60, 51, 2, 70], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [2, 70, 9] Generated Node #2: [2, 70, 9] from Operation: 60-51=9 Current State: 44:[2, 70, 9], Operations: ['60-51=9'] Exploring Operation: 70/2=35, Resulting Numbers: [9, 35] Generated Node #3: [9, 35] from Operation: 70/2=35 Current State: 44:[9, 35], Operations: ['60-51=9', '70/2=35'] Exploring Operation: 9+35=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[60, 51, 2, 70], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [60, 2, 19] Generated Node #0,0: 44:[60, 2, 19] Operation: 70-51=19 Exploring Operation: 60-51=9, Resulting Numbers: [2, 70, 9] Generated Node #0,1: 44:[2, 70, 9] Operation: 60-51=9 Exploring Operation: 60/2=30, Resulting Numbers: [51, 70, 30] Generated Node #0,2: 44:[51, 70, 30] Operation: 60/2=30 Exploring Operation: 70/2=35, Resulting Numbers: [60, 51, 35] Generated Node #0,3: 44:[60, 51, 35] Operation: 70/2=35 Exploring Operation: 70-60=10, Resulting Numbers: [51, 2, 10] Generated Node #0,4: 44:[51, 2, 10] Operation: 70-60=10 Moving to Node #0,4 Current State: 44:[51, 2, 10], Operations: ['70-60=10'] Exploring Operation: 2*10=20, Resulting Numbers: [51, 20] Generated Node #0,4,0: 44:[51, 20] Operation: 2*10=20 Exploring Operation: 2+10=12, Resulting Numbers: [51, 12] Generated Node #0,4,1: 44:[51, 12] Operation: 2+10=12 Exploring Operation: 10/2=5, Resulting Numbers: [51, 5] Generated Node #0,4,2: 44:[51, 5] Operation: 10/2=5 Exploring Operation: 51-10=41, Resulting Numbers: [2, 41] Generated Node #0,4,3: 44:[2, 41] Operation: 51-10=41 Exploring Operation: 51-2=49, Resulting Numbers: [10, 49] Generated Node #0,4,4: 44:[10, 49] Operation: 51-2=49 Moving to Node #0,0 Current State: 44:[60, 2, 19], Operations: ['70-51=19'] Exploring Operation: 60-19=41, Resulting Numbers: [2, 41] Generated Node #0,0,0: 44:[2, 41] Operation: 60-19=41 Exploring Operation: 60+2=62, Resulting Numbers: [19, 62] Generated Node #0,0,1: 44:[19, 62] Operation: 60+2=62 Exploring Operation: 60-2=58, Resulting Numbers: [19, 58] Generated Node #0,0,2: 44:[19, 58] Operation: 60-2=58 Exploring Operation: 2+19=21, Resulting Numbers: [60, 21] Generated Node #0,0,3: 44:[60, 21] Operation: 2+19=21 Exploring Operation: 60/2=30, Resulting Numbers: [19, 30] Generated Node #0,0,4: 44:[19, 30] Operation: 60/2=30 Moving to Node #0,1 Current State: 44:[2, 70, 9], Operations: ['60-51=9'] Exploring Operation: 2+9=11, Resulting Numbers: [70, 11] Generated Node #0,1,0: 44:[70, 11] Operation: 2+9=11 Exploring Operation: 9-2=7, Resulting Numbers: [70, 7] Generated Node #0,1,1: 44:[70, 7] Operation: 9-2=7 Exploring Operation: 70-9=61, Resulting Numbers: [2, 61] Generated Node #0,1,2: 44:[2, 61] Operation: 70-9=61 Exploring Operation: 70/2=35, Resulting Numbers: [9, 35] Generated Node #0,1,3: 44:[9, 35] Operation: 70/2=35 Exploring Operation: 70-2=68, Resulting Numbers: [9, 68] Generated Node #0,1,4: 44:[9, 68] Operation: 70-2=68 Moving to Node #0,3 Current State: 44:[60, 51, 35], Operations: ['70/2=35'] Exploring Operation: 60-35=25, Resulting Numbers: [51, 25] Generated Node #0,3,0: 44:[51, 25] Operation: 60-35=25 Exploring Operation: 51-35=16, Resulting Numbers: [60, 16] Generated Node #0,3,1: 44:[60, 16] Operation: 51-35=16 Exploring Operation: 60+35=95, Resulting Numbers: [51, 95] Generated Node #0,3,2: 44:[51, 95] Operation: 60+35=95 Exploring Operation: 60-51=9, Resulting Numbers: [35, 9] Generated Node #0,3,3: 44:[35, 9] Operation: 60-51=9 Exploring Operation: 51+35=86, Resulting Numbers: [60, 86] Generated Node #0,3,4: 44:[60, 86] Operation: 51+35=86 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 44:[51, 25], Operations: ['70/2=35', '60-35=25'] Exploring Operation: 51+25=76, Resulting Numbers: [76] 76,44 unequal: No Solution Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,44 unequal: No Solution Exploring Operation: 51*25=1275, Resulting Numbers: [1275] 1275,44 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 #0,3,3 Current State: 44:[35, 9], Operations: ['70/2=35', '60-51=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[60, 51, 2, 70], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [60, 51, 35] Generated Node #0,3: 44:[60, 51, 35] Operation: 70/2=35 Moving to Node #0,3 Current State: 44:[60, 51, 35], Operations: ['70/2=35'] Exploring Operation: 60-51=9, Resulting Numbers: [35, 9] Generated Node #0,3,3: 44:[35, 9] Operation: 60-51=9 Moving to Node #0,3,3 Current State: 44:[35, 9], Operations: ['70/2=35', '60-51=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_5
sum_heuristic
[ 94, 71, 48, 57 ]
55
[ "94+48=142", "142/71=2", "57-2=55" ]
Current State: 55:[94, 71, 48, 57], Operations: [] Exploring Operation: 94+48=142, Resulting Numbers: [71, 57, 142] Generated Node #2: [71, 57, 142] from Operation: 94+48=142 Current State: 55:[71, 57, 142], Operations: ['94+48=142'] Exploring Operation: 142/71=2, Resulting Numbers: [57, 2] Generated Node #3: [57, 2] from Operation: 142/71=2 Current State: 55:[57, 2], Operations: ['94+48=142', '142/71=2'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[94, 71, 48, 57], Operations: [] Exploring Operation: 71-48=23, Resulting Numbers: [94, 57, 23] Generated Node #0,0: 55:[94, 57, 23] Operation: 71-48=23 Exploring Operation: 94-57=37, Resulting Numbers: [71, 48, 37] Generated Node #0,1: 55:[71, 48, 37] Operation: 94-57=37 Exploring Operation: 94-71=23, Resulting Numbers: [48, 57, 23] Generated Node #0,2: 55:[48, 57, 23] Operation: 94-71=23 Exploring Operation: 71-57=14, Resulting Numbers: [94, 48, 14] Generated Node #0,3: 55:[94, 48, 14] Operation: 71-57=14 Exploring Operation: 94-48=46, Resulting Numbers: [71, 57, 46] Generated Node #0,4: 55:[71, 57, 46] Operation: 94-48=46 Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[48, 57, 23], Operations: ['94-71=23'] Exploring Operation: 57+23=80, Resulting Numbers: [48, 80] Generated Node #0,2,0: 55:[48, 80] Operation: 57+23=80 Exploring Operation: 57-48=9, Resulting Numbers: [23, 9] Generated Node #0,2,1: 55:[23, 9] Operation: 57-48=9 Exploring Operation: 48+23=71, Resulting Numbers: [57, 71] Generated Node #0,2,2: 55:[57, 71] Operation: 48+23=71 Exploring Operation: 57-23=34, Resulting Numbers: [48, 34] Generated Node #0,2,3: 55:[48, 34] Operation: 57-23=34 Exploring Operation: 48-23=25, Resulting Numbers: [57, 25] Generated Node #0,2,4: 55:[57, 25] Operation: 48-23=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[23, 9], Operations: ['94-71=23', '57-48=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 55:[57, 25], Operations: ['94-71=23', '48-23=25'] Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,55 unequal: No Solution Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[57, 71], Operations: ['94-71=23', '48+23=71'] Exploring Operation: 57*71=4047, Resulting Numbers: [4047] 4047,55 unequal: No Solution Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 57+71=128, Resulting Numbers: [128] 128,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[48, 34], Operations: ['94-71=23', '57-23=34'] Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,55 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[48, 80], Operations: ['94-71=23', '57+23=80'] Exploring Operation: 48*80=3840, Resulting Numbers: [3840] 3840,55 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 48+80=128, Resulting Numbers: [128] 128,55 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: 55:[71, 57, 46], Operations: ['94-48=46'] Exploring Operation: 57+46=103, Resulting Numbers: [71, 103] Generated Node #0,4,0: 55:[71, 103] Operation: 57+46=103 Exploring Operation: 71-57=14, Resulting Numbers: [46, 14] Generated Node #0,4,1: 55:[46, 14] Operation: 71-57=14 Exploring Operation: 57-46=11, Resulting Numbers: [71, 11] Generated Node #0,4,2: 55:[71, 11] Operation: 57-46=11 Exploring Operation: 71-46=25, Resulting Numbers: [57, 25] Generated Node #0,4,3: 55:[57, 25] Operation: 71-46=25 Exploring Operation: 71+46=117, Resulting Numbers: [57, 117] Generated Node #0,4,4: 55:[57, 117] Operation: 71+46=117 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 55:[46, 14], Operations: ['94-48=46', '71-57=14'] Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,55 unequal: No Solution Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 55:[71, 11], Operations: ['94-48=46', '57-46=11'] Exploring Operation: 71*11=781, Resulting Numbers: [781] 781,55 unequal: No Solution Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,55 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 55:[57, 25], Operations: ['94-48=46', '71-46=25'] Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,55 unequal: No Solution Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 55:[71, 103], Operations: ['94-48=46', '57+46=103'] Exploring Operation: 71*103=7313, Resulting Numbers: [7313] 7313,55 unequal: No Solution Exploring Operation: 71+103=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 103-71=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 55:[57, 117], Operations: ['94-48=46', '71+46=117'] Exploring Operation: 57+117=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 117-57=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 57*117=6669, Resulting Numbers: [6669] 6669,55 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: 55:[71, 48, 37], Operations: ['94-57=37'] Exploring Operation: 48-37=11, Resulting Numbers: [71, 11] Generated Node #0,1,0: 55:[71, 11] Operation: 48-37=11 Exploring Operation: 71-37=34, Resulting Numbers: [48, 34] Generated Node #0,1,1: 55:[48, 34] Operation: 71-37=34 Exploring Operation: 71+37=108, Resulting Numbers: [48, 108] Generated Node #0,1,2: 55:[48, 108] Operation: 71+37=108 Exploring Operation: 48+37=85, Resulting Numbers: [71, 85] Generated Node #0,1,3: 55:[71, 85] Operation: 48+37=85 Exploring Operation: 71-48=23, Resulting Numbers: [37, 23] Generated Node #0,1,4: 55:[37, 23] Operation: 71-48=23 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[71, 11], Operations: ['94-57=37', '48-37=11'] Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,55 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 71*11=781, Resulting Numbers: [781] 781,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[48, 34], Operations: ['94-57=37', '71-37=34'] Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,55 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[37, 23], Operations: ['94-57=37', '71-48=23'] Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,55 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[71, 85], Operations: ['94-57=37', '48+37=85'] Exploring Operation: 71*85=6035, Resulting Numbers: [6035] 6035,55 unequal: No Solution Exploring Operation: 71+85=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 85-71=14, Resulting Numbers: [14] 14,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[48, 108], Operations: ['94-57=37', '71+37=108'] Exploring Operation: 48+108=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 108-48=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 48*108=5184, Resulting Numbers: [5184] 5184,55 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: 55:[94, 48, 14], Operations: ['71-57=14'] Exploring Operation: 48-14=34, Resulting Numbers: [94, 34] Generated Node #0,3,0: 55:[94, 34] Operation: 48-14=34 Exploring Operation: 48+14=62, Resulting Numbers: [94, 62] Generated Node #0,3,1: 55:[94, 62] Operation: 48+14=62 Exploring Operation: 94-14=80, Resulting Numbers: [48, 80] Generated Node #0,3,2: 55:[48, 80] Operation: 94-14=80 Exploring Operation: 94-48=46, Resulting Numbers: [14, 46] Generated Node #0,3,3: 55:[14, 46] Operation: 94-48=46 Exploring Operation: 94+14=108, Resulting Numbers: [48, 108] Generated Node #0,3,4: 55:[48, 108] Operation: 94+14=108 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 55:[14, 46], Operations: ['71-57=14', '94-48=46'] Exploring Operation: 14*46=644, Resulting Numbers: [644] 644,55 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 14+46=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 55:[48, 80], Operations: ['71-57=14', '94-14=80'] Exploring Operation: 48+80=128, Resulting Numbers: [128] 128,55 unequal: No Solution Exploring Operation: 48*80=3840, Resulting Numbers: [3840] 3840,55 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[94, 62], Operations: ['71-57=14', '48+14=62'] Exploring Operation: 94+62=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 94*62=5828, Resulting Numbers: [5828] 5828,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[94, 34], Operations: ['71-57=14', '48-14=34'] Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,55 unequal: No Solution Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 55:[48, 108], Operations: ['71-57=14', '94+14=108'] Exploring Operation: 48+108=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 48*108=5184, Resulting Numbers: [5184] 5184,55 unequal: No Solution Exploring Operation: 108-48=60, Resulting Numbers: [60] 60,55 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: 55:[94, 57, 23], Operations: ['71-48=23'] Exploring Operation: 57-23=34, Resulting Numbers: [94, 34] Generated Node #0,0,0: 55:[94, 34] Operation: 57-23=34 Exploring Operation: 94+23=117, Resulting Numbers: [57, 117] Generated Node #0,0,1: 55:[57, 117] Operation: 94+23=117 Exploring Operation: 57+23=80, Resulting Numbers: [94, 80] Generated Node #0,0,2: 55:[94, 80] Operation: 57+23=80 Exploring Operation: 94-23=71, Resulting Numbers: [57, 71] Generated Node #0,0,3: 55:[57, 71] Operation: 94-23=71 Exploring Operation: 94-57=37, Resulting Numbers: [23, 37] Generated Node #0,0,4: 55:[23, 37] Operation: 94-57=37 Moving to Node #0,0,3 Current State: 55:[57, 71], Operations: ['71-48=23', '94-23=71'] Exploring Operation: 57*71=4047, Resulting Numbers: [4047] 4047,55 unequal: No Solution Exploring Operation: 57+71=128, Resulting Numbers: [128] 128,55 unequal: No Solution Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,55 unequal: No Solution Moving to Node #0,0,4 Current State: 55:[23, 37], Operations: ['71-48=23', '94-57=37'] Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,55 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,55 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[94, 34], Operations: ['71-48=23', '57-23=34'] Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,55 unequal: No Solution Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[57, 117], Operations: ['71-48=23', '94+23=117'] Exploring Operation: 117-57=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 57+117=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 57*117=6669, Resulting Numbers: [6669] 6669,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[94, 80], Operations: ['71-48=23', '57+23=80'] Exploring Operation: 94+80=174, Resulting Numbers: [174] 174,55 unequal: No Solution Exploring Operation: 94*80=7520, Resulting Numbers: [7520] 7520,55 unequal: No Solution Exploring Operation: 94-80=14, Resulting Numbers: [14] 14,55 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
[ 64, 40, 47, 85 ]
89
[ "64*85=5440", "5440/40=136", "136-47=89" ]
Current State: 89:[64, 40, 47, 85], Operations: [] Exploring Operation: 64*85=5440, Resulting Numbers: [40, 47, 5440] Generated Node #2: [40, 47, 5440] from Operation: 64*85=5440 Current State: 89:[40, 47, 5440], Operations: ['64*85=5440'] Exploring Operation: 5440/40=136, Resulting Numbers: [47, 136] Generated Node #3: [47, 136] from Operation: 5440/40=136 Current State: 89:[47, 136], Operations: ['64*85=5440', '5440/40=136'] Exploring Operation: 136-47=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[64, 40, 47, 85], Operations: [] Exploring Operation: 64+40=104, Resulting Numbers: [47, 85, 104] Generated Node #0,0: 89:[47, 85, 104] Operation: 64+40=104 Exploring Operation: 40+47=87, Resulting Numbers: [64, 85, 87] Generated Node #0,1: 89:[64, 85, 87] Operation: 40+47=87 Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[64, 85, 87], Operations: ['40+47=87'] Exploring Operation: 64+87=151, Resulting Numbers: [85, 151] Generated Node #0,1,0: 89:[85, 151] Operation: 64+87=151 Exploring Operation: 64+85=149, Resulting Numbers: [87, 149] Generated Node #0,1,1: 89:[87, 149] Operation: 64+85=149 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[87, 149], Operations: ['40+47=87', '64+85=149'] Exploring Operation: 149-87=62, Resulting Numbers: [62] 62,89 unequal: No Solution Exploring Operation: 87+149=236, Resulting Numbers: [236] 236,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[85, 151], Operations: ['40+47=87', '64+87=151'] Exploring Operation: 151-85=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 85+151=236, Resulting Numbers: [236] 236,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[47, 85, 104], Operations: ['64+40=104'] Exploring Operation: 47+85=132, Resulting Numbers: [104, 132] Generated Node #0,0,0: 89:[104, 132] Operation: 47+85=132 Exploring Operation: 104-47=57, Resulting Numbers: [85, 57] Generated Node #0,0,1: 89:[85, 57] Operation: 104-47=57 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[85, 57], Operations: ['64+40=104', '104-47=57'] Exploring Operation: 85+57=142, Resulting Numbers: [142] 142,89 unequal: No Solution Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[104, 132], Operations: ['64+40=104', '47+85=132'] Exploring Operation: 132-104=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 104+132=236, Resulting Numbers: [236] 236,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 75, 39, 7, 58 ]
15
[ "75-39=36", "58-7=51", "51-36=15" ]
Current State: 15:[75, 39, 7, 58], Operations: [] Exploring Operation: 75-39=36, Resulting Numbers: [7, 58, 36] Generated Node #2: [7, 58, 36] from Operation: 75-39=36 Current State: 15:[7, 58, 36], Operations: ['75-39=36'] Exploring Operation: 58-7=51, Resulting Numbers: [36, 51] Generated Node #3: [36, 51] from Operation: 58-7=51 Current State: 15:[36, 51], Operations: ['75-39=36', '58-7=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[75, 39, 7, 58], Operations: [] Exploring Operation: 75-58=17, Resulting Numbers: [39, 7, 17] Generated Node #0,0: 15:[39, 7, 17] Operation: 75-58=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[39, 7, 17], Operations: ['75-58=17'] Exploring Operation: 39-17=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 15:[7, 22] Operation: 39-17=22 Moving to Node #0,0,0 Current State: 15:[7, 22], Operations: ['75-58=17', '39-17=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[75, 39, 7, 58], Operations: [] Exploring Operation: 75-58=17, Resulting Numbers: [39, 7, 17] Generated Node #0,0: 15:[39, 7, 17] Operation: 75-58=17 Moving to Node #0,0 Current State: 15:[39, 7, 17], Operations: ['75-58=17'] Exploring Operation: 39-17=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 15:[7, 22] Operation: 39-17=22 Moving to Node #0,0,0 Current State: 15:[7, 22], Operations: ['75-58=17', '39-17=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 47, 6, 92, 84 ]
59
[ "92-47=45", "84/6=14", "45+14=59" ]
Current State: 59:[47, 6, 92, 84], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [6, 84, 45] Generated Node #2: [6, 84, 45] from Operation: 92-47=45 Current State: 59:[6, 84, 45], Operations: ['92-47=45'] Exploring Operation: 84/6=14, Resulting Numbers: [45, 14] Generated Node #3: [45, 14] from Operation: 84/6=14 Current State: 59:[45, 14], Operations: ['92-47=45', '84/6=14'] Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[47, 6, 92, 84], Operations: [] Exploring Operation: 47-6=41, Resulting Numbers: [92, 84, 41] Generated Node #0,0: 59:[92, 84, 41] Operation: 47-6=41 Exploring Operation: 47+6=53, Resulting Numbers: [92, 84, 53] Generated Node #0,1: 59:[92, 84, 53] Operation: 47+6=53 Exploring Operation: 92-6=86, Resulting Numbers: [47, 84, 86] Generated Node #0,2: 59:[47, 84, 86] Operation: 92-6=86 Exploring Operation: 84-6=78, Resulting Numbers: [47, 92, 78] Generated Node #0,3: 59:[47, 92, 78] Operation: 84-6=78 Moving to Node #0,1 Current State: 59:[92, 84, 53], Operations: ['47+6=53'] Exploring Operation: 92+53=145, Resulting Numbers: [84, 145] Generated Node #0,1,0: 59:[84, 145] Operation: 92+53=145 Exploring Operation: 84-53=31, Resulting Numbers: [92, 31] Generated Node #0,1,1: 59:[92, 31] Operation: 84-53=31 Exploring Operation: 92-84=8, Resulting Numbers: [53, 8] Generated Node #0,1,2: 59:[53, 8] Operation: 92-84=8 Exploring Operation: 92-53=39, Resulting Numbers: [84, 39] Generated Node #0,1,3: 59:[84, 39] Operation: 92-53=39 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[84, 39], Operations: ['47+6=53', '92-53=39'] Exploring Operation: 84*39=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 84+39=123, Resulting Numbers: [123] 123,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[53, 8], Operations: ['47+6=53', '92-84=8'] Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,59 unequal: No Solution Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[92, 31], Operations: ['47+6=53', '84-53=31'] Exploring Operation: 92-31=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 92+31=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 92*31=2852, Resulting Numbers: [2852] 2852,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[84, 145], Operations: ['47+6=53', '92+53=145'] Exploring Operation: 84*145=12180, Resulting Numbers: [12180] 12180,59 unequal: No Solution Exploring Operation: 84+145=229, Resulting Numbers: [229] 229,59 unequal: No Solution Exploring Operation: 145-84=61, Resulting Numbers: [61] 61,59 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: 59:[47, 92, 78], Operations: ['84-6=78'] Exploring Operation: 92-47=45, Resulting Numbers: [78, 45] Generated Node #0,3,0: 59:[78, 45] Operation: 92-47=45 Exploring Operation: 47+92=139, Resulting Numbers: [78, 139] Generated Node #0,3,1: 59:[78, 139] Operation: 47+92=139 Exploring Operation: 78-47=31, Resulting Numbers: [92, 31] Generated Node #0,3,2: 59:[92, 31] Operation: 78-47=31 Exploring Operation: 92-78=14, Resulting Numbers: [47, 14] Generated Node #0,3,3: 59:[47, 14] Operation: 92-78=14 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[78, 45], Operations: ['84-6=78', '92-47=45'] Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,59 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,59 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:[47, 14], Operations: ['84-6=78', '92-78=14'] Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 47*14=658, Resulting Numbers: [658] 658,59 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 #0,3,2 Current State: 59:[92, 31], Operations: ['84-6=78', '78-47=31'] Exploring Operation: 92+31=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 92*31=2852, Resulting Numbers: [2852] 2852,59 unequal: No Solution Exploring Operation: 92-31=61, Resulting Numbers: [61] 61,59 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:[78, 139], Operations: ['84-6=78', '47+92=139'] Exploring Operation: 139-78=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 78*139=10842, Resulting Numbers: [10842] 10842,59 unequal: No Solution Exploring Operation: 78+139=217, Resulting Numbers: [217] 217,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[47, 84, 86], Operations: ['92-6=86'] Exploring Operation: 47+84=131, Resulting Numbers: [86, 131] Generated Node #0,2,0: 59:[86, 131] Operation: 47+84=131 Exploring Operation: 86-47=39, Resulting Numbers: [84, 39] Generated Node #0,2,1: 59:[84, 39] Operation: 86-47=39 Exploring Operation: 86-84=2, Resulting Numbers: [47, 2] Generated Node #0,2,2: 59:[47, 2] Operation: 86-84=2 Exploring Operation: 84-47=37, Resulting Numbers: [86, 37] Generated Node #0,2,3: 59:[86, 37] Operation: 84-47=37 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[84, 39], Operations: ['92-6=86', '86-47=39'] Exploring Operation: 84+39=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 84*39=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,59 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 #0,2,3 Current State: 59:[86, 37], Operations: ['92-6=86', '84-47=37'] Exploring Operation: 86*37=3182, Resulting Numbers: [3182] 3182,59 unequal: No Solution Exploring Operation: 86+37=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 86-37=49, Resulting Numbers: [49] 49,59 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 #0,2,2 Current State: 59:[47, 2], Operations: ['92-6=86', '86-84=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,59 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 #0,2,0 Current State: 59:[86, 131], Operations: ['92-6=86', '47+84=131'] Exploring Operation: 86*131=11266, Resulting Numbers: [11266] 11266,59 unequal: No Solution Exploring Operation: 131-86=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 86+131=217, Resulting Numbers: [217] 217,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 59:[92, 84, 41], Operations: ['47-6=41'] Exploring Operation: 92-84=8, Resulting Numbers: [41, 8] Generated Node #0,0,0: 59:[41, 8] Operation: 92-84=8 Exploring Operation: 92+41=133, Resulting Numbers: [84, 133] Generated Node #0,0,1: 59:[84, 133] Operation: 92+41=133 Exploring Operation: 92-41=51, Resulting Numbers: [84, 51] Generated Node #0,0,2: 59:[84, 51] Operation: 92-41=51 Exploring Operation: 84-41=43, Resulting Numbers: [92, 43] Generated Node #0,0,3: 59:[92, 43] Operation: 84-41=43 Moving to Node #0,0,2 Current State: 59:[84, 51], Operations: ['47-6=41', '92-41=51'] Exploring Operation: 84*51=4284, Resulting Numbers: [4284] 4284,59 unequal: No Solution Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 84+51=135, Resulting Numbers: [135] 135,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[92, 43], Operations: ['47-6=41', '84-41=43'] Exploring Operation: 92+43=135, Resulting Numbers: [135] 135,59 unequal: No Solution Exploring Operation: 92-43=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 92*43=3956, Resulting Numbers: [3956] 3956,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[41, 8], Operations: ['47-6=41', '92-84=8'] Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,59 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[84, 133], Operations: ['47-6=41', '92+41=133'] Exploring Operation: 133-84=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 84+133=217, Resulting Numbers: [217] 217,59 unequal: No Solution Exploring Operation: 84*133=11172, Resulting Numbers: [11172] 11172,59 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 46, 59, 98, 36 ]
75
[ "59-46=13", "98-36=62", "13+62=75" ]
Current State: 75:[46, 59, 98, 36], Operations: [] Exploring Operation: 59-46=13, Resulting Numbers: [98, 36, 13] Generated Node #2: [98, 36, 13] from Operation: 59-46=13 Current State: 75:[98, 36, 13], Operations: ['59-46=13'] Exploring Operation: 98-36=62, Resulting Numbers: [13, 62] Generated Node #3: [13, 62] from Operation: 98-36=62 Current State: 75:[13, 62], Operations: ['59-46=13', '98-36=62'] Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[46, 59, 98, 36], Operations: [] Exploring Operation: 46+36=82, Resulting Numbers: [59, 98, 82] Generated Node #0,0: 75:[59, 98, 82] Operation: 46+36=82 Exploring Operation: 59-36=23, Resulting Numbers: [46, 98, 23] Generated Node #0,1: 75:[46, 98, 23] Operation: 59-36=23 Exploring Operation: 59-46=13, Resulting Numbers: [98, 36, 13] Generated Node #0,2: 75:[98, 36, 13] Operation: 59-46=13 Exploring Operation: 46-36=10, Resulting Numbers: [59, 98, 10] Generated Node #0,3: 75:[59, 98, 10] Operation: 46-36=10 Exploring Operation: 98-59=39, Resulting Numbers: [46, 36, 39] Generated Node #0,4: 75:[46, 36, 39] Operation: 98-59=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[98, 36, 13], Operations: ['59-46=13'] Exploring Operation: 98+13=111, Resulting Numbers: [36, 111] Generated Node #0,2,0: 75:[36, 111] Operation: 98+13=111 Exploring Operation: 98-13=85, Resulting Numbers: [36, 85] Generated Node #0,2,1: 75:[36, 85] Operation: 98-13=85 Exploring Operation: 36-13=23, Resulting Numbers: [98, 23] Generated Node #0,2,2: 75:[98, 23] Operation: 36-13=23 Exploring Operation: 36+13=49, Resulting Numbers: [98, 49] Generated Node #0,2,3: 75:[98, 49] Operation: 36+13=49 Exploring Operation: 98-36=62, Resulting Numbers: [13, 62] Generated Node #0,2,4: 75:[13, 62] Operation: 98-36=62 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 75:[13, 62], Operations: ['59-46=13', '98-36=62'] Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[46, 59, 98, 36], Operations: [] Exploring Operation: 59-46=13, Resulting Numbers: [98, 36, 13] Generated Node #0,2: 75:[98, 36, 13] Operation: 59-46=13 Moving to Node #0,2 Current State: 75:[98, 36, 13], Operations: ['59-46=13'] Exploring Operation: 98-36=62, Resulting Numbers: [13, 62] Generated Node #0,2,4: 75:[13, 62] Operation: 98-36=62 Moving to Node #0,2,4 Current State: 75:[13, 62], Operations: ['59-46=13', '98-36=62'] Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 7, 5, 7, 13 ]
89
[ "7-5=2", "7*13=91", "91-2=89" ]
Current State: 89:[7, 5, 7, 13], Operations: [] Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #2: [13, 2] from Operation: 7-5=2 Current State: 89:[13, 2], Operations: ['7-5=2'] Exploring Operation: 7*13=91, Resulting Numbers: [2, 91] Generated Node #3: [2, 91] from Operation: 7*13=91 Current State: 89:[2, 91], Operations: ['7-5=2', '7*13=91'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[7, 5, 7, 13], Operations: [] Exploring Operation: 7*13=91, Resulting Numbers: [5, 7, 91] Generated Node #0,0: 89:[5, 7, 91] Operation: 7*13=91 Exploring Operation: 7*7=49, Resulting Numbers: [5, 13, 49] Generated Node #0,1: 89:[5, 13, 49] Operation: 7*7=49 Exploring Operation: 7*13=91, Resulting Numbers: [7, 5, 91] Generated Node #0,2: 89:[7, 5, 91] Operation: 7*13=91 Exploring Operation: 5*13=65, Resulting Numbers: [7, 7, 65] Generated Node #0,3: 89:[7, 7, 65] Operation: 5*13=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[5, 7, 91], Operations: ['7*13=91'] Exploring Operation: 5+7=12, Resulting Numbers: [91, 12] Generated Node #0,0,0: 89:[91, 12] Operation: 5+7=12 Exploring Operation: 5*7=35, Resulting Numbers: [91, 35] Generated Node #0,0,1: 89:[91, 35] Operation: 5*7=35 Exploring Operation: 91-5=86, Resulting Numbers: [7, 86] Generated Node #0,0,2: 89:[7, 86] Operation: 91-5=86 Exploring Operation: 7-5=2, Resulting Numbers: [91, 2] Generated Node #0,0,3: 89:[91, 2] Operation: 7-5=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[91, 35], Operations: ['7*13=91', '5*7=35'] Exploring Operation: 91*35=3185, Resulting Numbers: [3185] 3185,89 unequal: No Solution Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,89 unequal: No Solution Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[91, 12], Operations: ['7*13=91', '5+7=12'] Exploring Operation: 91+12=103, Resulting Numbers: [103] 103,89 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,89 unequal: No Solution Exploring Operation: 91*12=1092, Resulting Numbers: [1092] 1092,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[7, 86], Operations: ['7*13=91', '91-5=86'] Exploring Operation: 7*86=602, Resulting Numbers: [602] 602,89 unequal: No Solution Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,89 unequal: No Solution Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[91, 2], Operations: ['7*13=91', '7-5=2'] Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,89 unequal: No Solution Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[7, 5, 7, 13], Operations: [] Exploring Operation: 7*13=91, Resulting Numbers: [5, 7, 91] Generated Node #0,0: 89:[5, 7, 91] Operation: 7*13=91 Moving to Node #0,0 Current State: 89:[5, 7, 91], Operations: ['7*13=91'] Exploring Operation: 7-5=2, Resulting Numbers: [91, 2] Generated Node #0,0,3: 89:[91, 2] Operation: 7-5=2 Moving to Node #0,0,3 Current State: 89:[91, 2], Operations: ['7*13=91', '7-5=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_4
mult_heuristic
[ 62, 70, 7, 48 ]
91
[ "62+70=132", "48-7=41", "132-41=91" ]
Current State: 91:[62, 70, 7, 48], Operations: [] Exploring Operation: 62+70=132, Resulting Numbers: [7, 48, 132] Generated Node #2: [7, 48, 132] from Operation: 62+70=132 Current State: 91:[7, 48, 132], Operations: ['62+70=132'] Exploring Operation: 48-7=41, Resulting Numbers: [132, 41] Generated Node #3: [132, 41] from Operation: 48-7=41 Current State: 91:[132, 41], Operations: ['62+70=132', '48-7=41'] Exploring Operation: 132-41=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[62, 70, 7, 48], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [70, 7, 14] Generated Node #0,0: 91:[70, 7, 14] Operation: 62-48=14 Moving to Node #0,0 Current State: 91:[70, 7, 14], Operations: ['62-48=14'] Exploring Operation: 70/14=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 91:[7, 5] Operation: 70/14=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[7, 5], Operations: ['62-48=14', '70/14=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,91 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
[ 55, 17, 3, 2 ]
38
[ "55-17=38", "3-2=1", "38*1=38" ]
Current State: 38:[55, 17, 3, 2], Operations: [] Exploring Operation: 55-17=38, Resulting Numbers: [3, 2, 38] Generated Node #2: [3, 2, 38] from Operation: 55-17=38 Current State: 38:[3, 2, 38], Operations: ['55-17=38'] Exploring Operation: 3-2=1, Resulting Numbers: [38, 1] Generated Node #3: [38, 1] from Operation: 3-2=1 Current State: 38:[38, 1], Operations: ['55-17=38', '3-2=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[55, 17, 3, 2], Operations: [] Exploring Operation: 55-17=38, Resulting Numbers: [3, 2, 38] Generated Node #0,0: 38:[3, 2, 38] Operation: 55-17=38 Moving to Node #0,0 Current State: 38:[3, 2, 38], Operations: ['55-17=38'] Exploring Operation: 3-2=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 3-2=1 Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['55-17=38', '3-2=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[55, 17, 3, 2], Operations: [] Exploring Operation: 55-17=38, Resulting Numbers: [3, 2, 38] Generated Node #0,0: 38:[3, 2, 38] Operation: 55-17=38 Moving to Node #0,0 Current State: 38:[3, 2, 38], Operations: ['55-17=38'] Exploring Operation: 3-2=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 3-2=1 Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['55-17=38', '3-2=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 60, 20, 87, 46 ]
53
[ "60+20=80", "87+46=133", "133-80=53" ]
Current State: 53:[60, 20, 87, 46], Operations: [] Exploring Operation: 60+20=80, Resulting Numbers: [87, 46, 80] Generated Node #2: [87, 46, 80] from Operation: 60+20=80 Current State: 53:[87, 46, 80], Operations: ['60+20=80'] Exploring Operation: 87+46=133, Resulting Numbers: [80, 133] Generated Node #3: [80, 133] from Operation: 87+46=133 Current State: 53:[80, 133], Operations: ['60+20=80', '87+46=133'] Exploring Operation: 133-80=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[60, 20, 87, 46], Operations: [] Exploring Operation: 87-46=41, Resulting Numbers: [60, 20, 41] Generated Node #0,0: 53:[60, 20, 41] Operation: 87-46=41 Exploring Operation: 60-20=40, Resulting Numbers: [87, 46, 40] Generated Node #0,1: 53:[87, 46, 40] Operation: 60-20=40 Exploring Operation: 87-20=67, Resulting Numbers: [60, 46, 67] Generated Node #0,2: 53:[60, 46, 67] Operation: 87-20=67 Exploring Operation: 20+46=66, Resulting Numbers: [60, 87, 66] Generated Node #0,3: 53:[60, 87, 66] Operation: 20+46=66 Moving to Node #0,2 Current State: 53:[60, 46, 67], Operations: ['87-20=67'] Exploring Operation: 67-46=21, Resulting Numbers: [60, 21] Generated Node #0,2,0: 53:[60, 21] Operation: 67-46=21 Exploring Operation: 67-60=7, Resulting Numbers: [46, 7] Generated Node #0,2,1: 53:[46, 7] Operation: 67-60=7 Exploring Operation: 60-46=14, Resulting Numbers: [67, 14] Generated Node #0,2,2: 53:[67, 14] Operation: 60-46=14 Exploring Operation: 60+46=106, Resulting Numbers: [67, 106] Generated Node #0,2,3: 53:[67, 106] Operation: 60+46=106 Moving to Node #0,0 Current State: 53:[60, 20, 41], Operations: ['87-46=41'] Exploring Operation: 60+20=80, Resulting Numbers: [41, 80] Generated Node #0,0,0: 53:[41, 80] Operation: 60+20=80 Exploring Operation: 41-20=21, Resulting Numbers: [60, 21] Generated Node #0,0,1: 53:[60, 21] Operation: 41-20=21 Exploring Operation: 20+41=61, Resulting Numbers: [60, 61] Generated Node #0,0,2: 53:[60, 61] Operation: 20+41=61 Exploring Operation: 60-20=40, Resulting Numbers: [41, 40] Generated Node #0,0,3: 53:[41, 40] Operation: 60-20=40 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[60, 61], Operations: ['87-46=41', '20+41=61'] Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 60*61=3660, Resulting Numbers: [3660] 3660,53 unequal: No Solution Exploring Operation: 60+61=121, Resulting Numbers: [121] 121,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 53:[41, 40], Operations: ['87-46=41', '60-20=40'] Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,53 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[41, 80], Operations: ['87-46=41', '60+20=80'] Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 41+80=121, Resulting Numbers: [121] 121,53 unequal: No Solution Exploring Operation: 41*80=3280, Resulting Numbers: [3280] 3280,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[60, 21], Operations: ['87-46=41', '41-20=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,53 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,53 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: 53:[60, 87, 66], Operations: ['20+46=66'] Exploring Operation: 60+87=147, Resulting Numbers: [66, 147] Generated Node #0,3,0: 53:[66, 147] Operation: 60+87=147 Exploring Operation: 66-60=6, Resulting Numbers: [87, 6] Generated Node #0,3,1: 53:[87, 6] Operation: 66-60=6 Exploring Operation: 87-60=27, Resulting Numbers: [66, 27] Generated Node #0,3,2: 53:[66, 27] Operation: 87-60=27 Exploring Operation: 87-66=21, Resulting Numbers: [60, 21] Generated Node #0,3,3: 53:[60, 21] Operation: 87-66=21 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[66, 27], Operations: ['20+46=66', '87-60=27'] Exploring Operation: 66+27=93, Resulting Numbers: [93] 93,53 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 66*27=1782, Resulting Numbers: [1782] 1782,53 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 #0,3,3 Current State: 53:[60, 21], Operations: ['20+46=66', '87-66=21'] Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,53 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 #0,3,1 Current State: 53:[87, 6], Operations: ['20+46=66', '66-60=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,53 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,53 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 #0,3,0 Current State: 53:[66, 147], Operations: ['20+46=66', '60+87=147'] Exploring Operation: 66+147=213, Resulting Numbers: [213] 213,53 unequal: No Solution Exploring Operation: 66*147=9702, Resulting Numbers: [9702] 9702,53 unequal: No Solution Exploring Operation: 147-66=81, Resulting Numbers: [81] 81,53 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: 53:[87, 46, 40], Operations: ['60-20=40'] Exploring Operation: 87+40=127, Resulting Numbers: [46, 127] Generated Node #0,1,0: 53:[46, 127] Operation: 87+40=127 Exploring Operation: 87-46=41, Resulting Numbers: [40, 41] Generated Node #0,1,1: 53:[40, 41] Operation: 87-46=41 Exploring Operation: 87-40=47, Resulting Numbers: [46, 47] Generated Node #0,1,2: 53:[46, 47] Operation: 87-40=47 Exploring Operation: 46+40=86, Resulting Numbers: [87, 86] Generated Node #0,1,3: 53:[87, 86] Operation: 46+40=86 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[46, 47], Operations: ['60-20=40', '87-40=47'] Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,53 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 46*47=2162, Resulting Numbers: [2162] 2162,53 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 #0,1,1 Current State: 53:[40, 41], Operations: ['60-20=40', '87-46=41'] Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,53 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,53 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 #0,1,3 Current State: 53:[87, 86], Operations: ['60-20=40', '46+40=86'] Exploring Operation: 87-86=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 87+86=173, Resulting Numbers: [173] 173,53 unequal: No Solution Exploring Operation: 87*86=7482, Resulting Numbers: [7482] 7482,53 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 #0,1,0 Current State: 53:[46, 127], Operations: ['60-20=40', '87+40=127'] Exploring Operation: 46*127=5842, Resulting Numbers: [5842] 5842,53 unequal: No Solution Exploring Operation: 46+127=173, Resulting Numbers: [173] 173,53 unequal: No Solution Exploring Operation: 127-46=81, Resulting Numbers: [81] 81,53 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: 53:[60, 21], Operations: ['87-20=67', '67-46=21'] Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,53 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[67, 14], Operations: ['87-20=67', '60-46=14'] Exploring Operation: 67+14=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 67*14=938, Resulting Numbers: [938] 938,53 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[60, 20, 87, 46], Operations: [] Exploring Operation: 87-20=67, Resulting Numbers: [60, 46, 67] Generated Node #0,2: 53:[60, 46, 67] Operation: 87-20=67 Moving to Node #0,2 Current State: 53:[60, 46, 67], Operations: ['87-20=67'] Exploring Operation: 60-46=14, Resulting Numbers: [67, 14] Generated Node #0,2,2: 53:[67, 14] Operation: 60-46=14 Moving to Node #0,2,2 Current State: 53:[67, 14], Operations: ['87-20=67', '60-46=14'] Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
0.942708
hs_4
sum_heuristic
[ 57, 66, 11, 20 ]
59
[ "57+20=77", "77/11=7", "66-7=59" ]
Current State: 59:[57, 66, 11, 20], Operations: [] Exploring Operation: 57+20=77, Resulting Numbers: [66, 11, 77] Generated Node #2: [66, 11, 77] from Operation: 57+20=77 Current State: 59:[66, 11, 77], Operations: ['57+20=77'] Exploring Operation: 77/11=7, Resulting Numbers: [66, 7] Generated Node #3: [66, 7] from Operation: 77/11=7 Current State: 59:[66, 7], Operations: ['57+20=77', '77/11=7'] Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[57, 66, 11, 20], Operations: [] Exploring Operation: 57+11=68, Resulting Numbers: [66, 20, 68] Generated Node #0,0: 59:[66, 20, 68] Operation: 57+11=68 Exploring Operation: 66-11=55, Resulting Numbers: [57, 20, 55] Generated Node #0,1: 59:[57, 20, 55] Operation: 66-11=55 Exploring Operation: 11+20=31, Resulting Numbers: [57, 66, 31] Generated Node #0,2: 59:[57, 66, 31] Operation: 11+20=31 Exploring Operation: 57-11=46, Resulting Numbers: [66, 20, 46] Generated Node #0,3: 59:[66, 20, 46] Operation: 57-11=46 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[57, 66, 31], Operations: ['11+20=31'] Exploring Operation: 66-31=35, Resulting Numbers: [57, 35] Generated Node #0,2,0: 59:[57, 35] Operation: 66-31=35 Exploring Operation: 66+31=97, Resulting Numbers: [57, 97] Generated Node #0,2,1: 59:[57, 97] Operation: 66+31=97 Exploring Operation: 57-31=26, Resulting Numbers: [66, 26] Generated Node #0,2,2: 59:[66, 26] Operation: 57-31=26 Exploring Operation: 57+31=88, Resulting Numbers: [66, 88] Generated Node #0,2,3: 59:[66, 88] Operation: 57+31=88 Moving to Node #0,2,0 Current State: 59:[57, 35], Operations: ['11+20=31', '66-31=35'] Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[66, 88], Operations: ['11+20=31', '57+31=88'] Exploring Operation: 66*88=5808, Resulting Numbers: [5808] 5808,59 unequal: No Solution Exploring Operation: 88-66=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 66+88=154, Resulting Numbers: [154] 154,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[66, 26], Operations: ['11+20=31', '57-31=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[57, 97], Operations: ['11+20=31', '66+31=97'] Exploring Operation: 57*97=5529, Resulting Numbers: [5529] 5529,59 unequal: No Solution Exploring Operation: 57+97=154, Resulting Numbers: [154] 154,59 unequal: No Solution Exploring Operation: 97-57=40, Resulting Numbers: [40] 40,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[57, 20, 55], Operations: ['66-11=55'] Exploring Operation: 55-20=35, Resulting Numbers: [57, 35] Generated Node #0,1,0: 59:[57, 35] Operation: 55-20=35 Exploring Operation: 57-20=37, Resulting Numbers: [55, 37] Generated Node #0,1,1: 59:[55, 37] Operation: 57-20=37 Exploring Operation: 20+55=75, Resulting Numbers: [57, 75] Generated Node #0,1,2: 59:[57, 75] Operation: 20+55=75 Exploring Operation: 57+20=77, Resulting Numbers: [55, 77] Generated Node #0,1,3: 59:[55, 77] Operation: 57+20=77 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[57, 75], Operations: ['66-11=55', '20+55=75'] Exploring Operation: 57+75=132, Resulting Numbers: [132] 132,59 unequal: No Solution Exploring Operation: 57*75=4275, Resulting Numbers: [4275] 4275,59 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 59:[55, 77], Operations: ['66-11=55', '57+20=77'] Exploring Operation: 55*77=4235, Resulting Numbers: [4235] 4235,59 unequal: No Solution Exploring Operation: 55+77=132, Resulting Numbers: [132] 132,59 unequal: No Solution Exploring Operation: 77-55=22, Resulting Numbers: [22] 22,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[57, 35], Operations: ['66-11=55', '55-20=35'] Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,59 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[55, 37], Operations: ['66-11=55', '57-20=37'] Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[66, 20, 68], Operations: ['57+11=68'] Exploring Operation: 66+20=86, Resulting Numbers: [68, 86] Generated Node #0,0,0: 59:[68, 86] Operation: 66+20=86 Exploring Operation: 68-20=48, Resulting Numbers: [66, 48] Generated Node #0,0,1: 59:[66, 48] Operation: 68-20=48 Exploring Operation: 20+68=88, Resulting Numbers: [66, 88] Generated Node #0,0,2: 59:[66, 88] Operation: 20+68=88 Exploring Operation: 66-20=46, Resulting Numbers: [68, 46] Generated Node #0,0,3: 59:[68, 46] Operation: 66-20=46 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[66, 48], Operations: ['57+11=68', '68-20=48'] Exploring Operation: 66+48=114, Resulting Numbers: [114] 114,59 unequal: No Solution Exploring Operation: 66*48=3168, Resulting Numbers: [3168] 3168,59 unequal: No Solution Exploring Operation: 66-48=18, Resulting Numbers: [18] 18,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 59:[68, 46], Operations: ['57+11=68', '66-20=46'] Exploring Operation: 68+46=114, Resulting Numbers: [114] 114,59 unequal: No Solution Exploring Operation: 68-46=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 68*46=3128, Resulting Numbers: [3128] 3128,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[68, 86], Operations: ['57+11=68', '66+20=86'] Exploring Operation: 68*86=5848, Resulting Numbers: [5848] 5848,59 unequal: No Solution Exploring Operation: 86-68=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 68+86=154, Resulting Numbers: [154] 154,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[66, 88], Operations: ['57+11=68', '20+68=88'] Exploring Operation: 66*88=5808, Resulting Numbers: [5808] 5808,59 unequal: No Solution Exploring Operation: 88-66=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 66+88=154, Resulting Numbers: [154] 154,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[66, 20, 46], Operations: ['57-11=46'] Exploring Operation: 46-20=26, Resulting Numbers: [66, 26] Generated Node #0,3,0: 59:[66, 26] Operation: 46-20=26 Exploring Operation: 20+46=66, Resulting Numbers: [66, 66] Generated Node #0,3,1: 59:[66, 66] Operation: 20+46=66 Exploring Operation: 66+20=86, Resulting Numbers: [46, 86] Generated Node #0,3,2: 59:[46, 86] Operation: 66+20=86 Exploring Operation: 66-20=46, Resulting Numbers: [46, 46] Generated Node #0,3,3: 59:[46, 46] Operation: 66-20=46 Moving to Node #0,3,1 Current State: 59:[66, 66], Operations: ['57-11=46', '20+46=66'] Exploring Operation: 66/66=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 66-66=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 66+66=132, Resulting Numbers: [132] 132,59 unequal: No Solution Exploring Operation: 66*66=4356, Resulting Numbers: [4356] 4356,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[46, 46], Operations: ['57-11=46', '66-20=46'] Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,59 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[46, 86], Operations: ['57-11=46', '66+20=86'] Exploring Operation: 46+86=132, Resulting Numbers: [132] 132,59 unequal: No Solution Exploring Operation: 86-46=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 46*86=3956, Resulting Numbers: [3956] 3956,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[66, 26], Operations: ['57-11=46', '46-20=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,59 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,59 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
[ 41, 43, 4, 3 ]
92
[ "41+4=45", "3*45=135", "135-43=92" ]
Current State: 92:[41, 43, 4, 3], Operations: [] Exploring Operation: 41+4=45, Resulting Numbers: [43, 3, 45] Generated Node #2: [43, 3, 45] from Operation: 41+4=45 Current State: 92:[43, 3, 45], Operations: ['41+4=45'] Exploring Operation: 3*45=135, Resulting Numbers: [43, 135] Generated Node #3: [43, 135] from Operation: 3*45=135 Current State: 92:[43, 135], Operations: ['41+4=45', '3*45=135'] Exploring Operation: 135-43=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[41, 43, 4, 3], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [4, 3, 2] Generated Node #0,0: 92:[4, 3, 2] Operation: 43-41=2 Exploring Operation: 41+3=44, Resulting Numbers: [43, 4, 44] Generated Node #0,1: 92:[43, 4, 44] Operation: 41+3=44 Exploring Operation: 41+4=45, Resulting Numbers: [43, 3, 45] Generated Node #0,2: 92:[43, 3, 45] Operation: 41+4=45 Moving to Node #0,0 Current State: 92:[4, 3, 2], Operations: ['43-41=2'] Exploring Operation: 4/2=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 92:[3, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 92:[3, 2] Operation: 4-2=2 Exploring Operation: 4-3=1, Resulting Numbers: [2, 1] Generated Node #0,0,2: 92:[2, 1] Operation: 4-3=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[3, 2], Operations: ['43-41=2', '4/2=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[3, 2], Operations: ['43-41=2', '4-2=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 92:[2, 1], Operations: ['43-41=2', '4-3=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 92:[43, 4, 44], Operations: ['41+3=44'] Exploring Operation: 43+44=87, Resulting Numbers: [4, 87] Generated Node #0,1,0: 92:[4, 87] Operation: 43+44=87 Exploring Operation: 43+4=47, Resulting Numbers: [44, 47] Generated Node #0,1,1: 92:[44, 47] Operation: 43+4=47 Exploring Operation: 44-43=1, Resulting Numbers: [4, 1] Generated Node #0,1,2: 92:[4, 1] Operation: 44-43=1 Moving to Node #0,2 Current State: 92:[43, 3, 45], Operations: ['41+4=45'] Exploring Operation: 45-43=2, Resulting Numbers: [3, 2] Generated Node #0,2,0: 92:[3, 2] Operation: 45-43=2 Exploring Operation: 43+45=88, Resulting Numbers: [3, 88] Generated Node #0,2,1: 92:[3, 88] Operation: 43+45=88 Exploring Operation: 43+3=46, Resulting Numbers: [45, 46] Generated Node #0,2,2: 92:[45, 46] Operation: 43+3=46 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[3, 2], Operations: ['41+4=45', '45-43=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[45, 46], Operations: ['41+4=45', '43+3=46'] Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,92 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[3, 88], Operations: ['41+4=45', '43+45=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,92 unequal: No Solution Exploring Operation: 3*88=264, Resulting Numbers: [264] 264,92 unequal: No Solution Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 92:[4, 1], Operations: ['41+3=44', '44-43=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[44, 47], Operations: ['41+3=44', '43+4=47'] Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,92 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[4, 87], Operations: ['41+3=44', '43+44=87'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,92 unequal: No Solution Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 4*87=348, Resulting Numbers: [348] 348,92 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 82, 91, 75, 5 ]
30
[ "91-82=9", "5*9=45", "75-45=30" ]
Current State: 30:[82, 91, 75, 5], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [75, 5, 9] Generated Node #2: [75, 5, 9] from Operation: 91-82=9 Current State: 30:[75, 5, 9], Operations: ['91-82=9'] Exploring Operation: 5*9=45, Resulting Numbers: [75, 45] Generated Node #3: [75, 45] from Operation: 5*9=45 Current State: 30:[75, 45], Operations: ['91-82=9', '5*9=45'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[82, 91, 75, 5], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [75, 5, 9] Generated Node #0,0: 30:[75, 5, 9] Operation: 91-82=9 Exploring Operation: 82-75=7, Resulting Numbers: [91, 5, 7] Generated Node #0,1: 30:[91, 5, 7] Operation: 82-75=7 Exploring Operation: 82-5=77, Resulting Numbers: [91, 75, 77] Generated Node #0,2: 30:[91, 75, 77] Operation: 82-5=77 Exploring Operation: 75/5=15, Resulting Numbers: [82, 91, 15] Generated Node #0,3: 30:[82, 91, 15] Operation: 75/5=15 Exploring Operation: 91-75=16, Resulting Numbers: [82, 5, 16] Generated Node #0,4: 30:[82, 5, 16] Operation: 91-75=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[75, 5, 9], Operations: ['91-82=9'] Exploring Operation: 9-5=4, Resulting Numbers: [75, 4] Generated Node #0,0,0: 30:[75, 4] Operation: 9-5=4 Exploring Operation: 75/5=15, Resulting Numbers: [9, 15] Generated Node #0,0,1: 30:[9, 15] Operation: 75/5=15 Exploring Operation: 5+9=14, Resulting Numbers: [75, 14] Generated Node #0,0,2: 30:[75, 14] Operation: 5+9=14 Exploring Operation: 75-5=70, Resulting Numbers: [9, 70] Generated Node #0,0,3: 30:[9, 70] Operation: 75-5=70 Exploring Operation: 75-9=66, Resulting Numbers: [5, 66] Generated Node #0,0,4: 30:[5, 66] Operation: 75-9=66 Moving to Node #0,0,1 Current State: 30:[9, 15], Operations: ['91-82=9', '75/5=15'] Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,30 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,30 unequal: No Solution Moving to Node #0,0,4 Current State: 30:[5, 66], Operations: ['91-82=9', '75-9=66'] Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,30 unequal: No Solution Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,30 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,30 unequal: No Solution Moving to Node #0,0,3 Current State: 30:[9, 70], Operations: ['91-82=9', '75-5=70'] Exploring Operation: 9+70=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 9*70=630, Resulting Numbers: [630] 630,30 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[75, 4], Operations: ['91-82=9', '9-5=4'] Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 75*4=300, Resulting Numbers: [300] 300,30 unequal: No Solution Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[75, 14], Operations: ['91-82=9', '5+9=14'] Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,30 unequal: No Solution Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 30:[82, 5, 16], Operations: ['91-75=16'] Exploring Operation: 82-16=66, Resulting Numbers: [5, 66] Generated Node #0,4,0: 30:[5, 66] Operation: 82-16=66 Exploring Operation: 82-5=77, Resulting Numbers: [16, 77] Generated Node #0,4,1: 30:[16, 77] Operation: 82-5=77 Exploring Operation: 82+5=87, Resulting Numbers: [16, 87] Generated Node #0,4,2: 30:[16, 87] Operation: 82+5=87 Exploring Operation: 5+16=21, Resulting Numbers: [82, 21] Generated Node #0,4,3: 30:[82, 21] Operation: 5+16=21 Exploring Operation: 16-5=11, Resulting Numbers: [82, 11] Generated Node #0,4,4: 30:[82, 11] Operation: 16-5=11 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 30:[5, 66], Operations: ['91-75=16', '82-16=66'] Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,30 unequal: No Solution Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,30 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 #0,4,1 Current State: 30:[16, 77], Operations: ['91-75=16', '82-5=77'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,30 unequal: No Solution Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,30 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 #0,4,4 Current State: 30:[82, 11], Operations: ['91-75=16', '16-5=11'] Exploring Operation: 82*11=902, Resulting Numbers: [902] 902,30 unequal: No Solution Exploring Operation: 82+11=93, Resulting Numbers: [93] 93,30 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,30 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 #0,4,2 Current State: 30:[16, 87], Operations: ['91-75=16', '82+5=87'] Exploring Operation: 16+87=103, Resulting Numbers: [103] 103,30 unequal: No Solution Exploring Operation: 87-16=71, Resulting Numbers: [71] 71,30 unequal: No Solution Exploring Operation: 16*87=1392, Resulting Numbers: [1392] 1392,30 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 #0,4,3 Current State: 30:[82, 21], Operations: ['91-75=16', '5+16=21'] Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,30 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[91, 5, 7], Operations: ['82-75=7'] Exploring Operation: 5+7=12, Resulting Numbers: [91, 12] Generated Node #0,1,0: 30:[91, 12] Operation: 5+7=12 Exploring Operation: 7-5=2, Resulting Numbers: [91, 2] Generated Node #0,1,1: 30:[91, 2] Operation: 7-5=2 Exploring Operation: 91-5=86, Resulting Numbers: [7, 86] Generated Node #0,1,2: 30:[7, 86] Operation: 91-5=86 Exploring Operation: 91/7=13, Resulting Numbers: [5, 13] Generated Node #0,1,3: 30:[5, 13] Operation: 91/7=13 Exploring Operation: 91-7=84, Resulting Numbers: [5, 84] Generated Node #0,1,4: 30:[5, 84] Operation: 91-7=84 Moving to Node #0,1,3 Current State: 30:[5, 13], Operations: ['82-75=7', '91/7=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,30 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,30 unequal: No Solution Moving to Node #0,1,4 Current State: 30:[5, 84], Operations: ['82-75=7', '91-7=84'] Exploring Operation: 5+84=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 5*84=420, Resulting Numbers: [420] 420,30 unequal: No Solution Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[7, 86], Operations: ['82-75=7', '91-5=86'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,30 unequal: No Solution Exploring Operation: 7*86=602, Resulting Numbers: [602] 602,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[91, 2], Operations: ['82-75=7', '7-5=2'] Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,30 unequal: No Solution Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,30 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[91, 12], Operations: ['82-75=7', '5+7=12'] Exploring Operation: 91*12=1092, Resulting Numbers: [1092] 1092,30 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,30 unequal: No Solution Exploring Operation: 91+12=103, Resulting Numbers: [103] 103,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[82, 91, 15], Operations: ['75/5=15'] Exploring Operation: 91-82=9, Resulting Numbers: [15, 9] Generated Node #0,3,0: 30:[15, 9] Operation: 91-82=9 Exploring Operation: 82+15=97, Resulting Numbers: [91, 97] Generated Node #0,3,1: 30:[91, 97] Operation: 82+15=97 Exploring Operation: 91-15=76, Resulting Numbers: [82, 76] Generated Node #0,3,2: 30:[82, 76] Operation: 91-15=76 Exploring Operation: 91+15=106, Resulting Numbers: [82, 106] Generated Node #0,3,3: 30:[82, 106] Operation: 91+15=106 Exploring Operation: 82-15=67, Resulting Numbers: [91, 67] Generated Node #0,3,4: 30:[91, 67] Operation: 82-15=67 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 30:[15, 9], Operations: ['75/5=15', '91-82=9'] Exploring Operation: 15*9=135, Resulting Numbers: [135] 135,30 unequal: No Solution Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,30 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 #0,3,2 Current State: 30:[82, 76], Operations: ['75/5=15', '91-15=76'] Exploring Operation: 82*76=6232, Resulting Numbers: [6232] 6232,30 unequal: No Solution Exploring Operation: 82+76=158, Resulting Numbers: [158] 158,30 unequal: No Solution Exploring Operation: 82-76=6, Resulting Numbers: [6] 6,30 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 #0,3,4 Current State: 30:[91, 67], Operations: ['75/5=15', '82-15=67'] Exploring Operation: 91+67=158, Resulting Numbers: [158] 158,30 unequal: No Solution Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 91*67=6097, Resulting Numbers: [6097] 6097,30 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 #0,3,1 Current State: 30:[91, 97], Operations: ['75/5=15', '82+15=97'] Exploring Operation: 91+97=188, Resulting Numbers: [188] 188,30 unequal: No Solution Exploring Operation: 97-91=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 91*97=8827, Resulting Numbers: [8827] 8827,30 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 #0,3,3 Current State: 30:[82, 106], Operations: ['75/5=15', '91+15=106'] Exploring Operation: 82+106=188, Resulting Numbers: [188] 188,30 unequal: No Solution Exploring Operation: 106-82=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 82*106=8692, Resulting Numbers: [8692] 8692,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[91, 75, 77], Operations: ['82-5=77'] Exploring Operation: 91+77=168, Resulting Numbers: [75, 168] Generated Node #0,2,0: 30:[75, 168] Operation: 91+77=168 Exploring Operation: 91-77=14, Resulting Numbers: [75, 14] Generated Node #0,2,1: 30:[75, 14] Operation: 91-77=14 Exploring Operation: 91+75=166, Resulting Numbers: [77, 166] Generated Node #0,2,2: 30:[77, 166] Operation: 91+75=166 Exploring Operation: 91-75=16, Resulting Numbers: [77, 16] Generated Node #0,2,3: 30:[77, 16] Operation: 91-75=16 Exploring Operation: 77-75=2, Resulting Numbers: [91, 2] Generated Node #0,2,4: 30:[91, 2] Operation: 77-75=2 Moving to Node #0,2,1 Current State: 30:[75, 14], Operations: ['82-5=77', '91-77=14'] Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[77, 16], Operations: ['82-5=77', '91-75=16'] Exploring Operation: 77*16=1232, Resulting Numbers: [1232] 1232,30 unequal: No Solution Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 77+16=93, Resulting Numbers: [93] 93,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[91, 2], Operations: ['82-5=77', '77-75=2'] Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,30 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[75, 168], Operations: ['82-5=77', '91+77=168'] Exploring Operation: 75*168=12600, Resulting Numbers: [12600] 12600,30 unequal: No Solution Exploring Operation: 75+168=243, Resulting Numbers: [243] 243,30 unequal: No Solution Exploring Operation: 168-75=93, Resulting Numbers: [93] 93,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[77, 166], Operations: ['82-5=77', '91+75=166'] Exploring Operation: 166-77=89, Resulting Numbers: [89] 89,30 unequal: No Solution Exploring Operation: 77*166=12782, Resulting Numbers: [12782] 12782,30 unequal: No Solution Exploring Operation: 77+166=243, Resulting Numbers: [243] 243,30 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
[ 46, 85, 2, 61 ]
11
[ "85-46=39", "61-39=22", "22/2=11" ]
Current State: 11:[46, 85, 2, 61], Operations: [] Exploring Operation: 85-46=39, Resulting Numbers: [2, 61, 39] Generated Node #2: [2, 61, 39] from Operation: 85-46=39 Current State: 11:[2, 61, 39], Operations: ['85-46=39'] Exploring Operation: 61-39=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 61-39=22 Current State: 11:[2, 22], Operations: ['85-46=39', '61-39=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[46, 85, 2, 61], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [46, 2, 24] Generated Node #0,0: 11:[46, 2, 24] Operation: 85-61=24 Moving to Node #0,0 Current State: 11:[46, 2, 24], Operations: ['85-61=24'] Exploring Operation: 46-24=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 11:[2, 22] Operation: 46-24=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[2, 22], Operations: ['85-61=24', '46-24=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[46, 85, 2, 61], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [46, 2, 24] Generated Node #0,0: 11:[46, 2, 24] Operation: 85-61=24 Moving to Node #0,0 Current State: 11:[46, 2, 24], Operations: ['85-61=24'] Exploring Operation: 46-24=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 11:[2, 22] Operation: 46-24=22 Moving to Node #0,0,0 Current State: 11:[2, 22], Operations: ['85-61=24', '46-24=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 28, 32, 35, 2 ]
34
[ "35-32=3", "2*3=6", "28+6=34" ]
Current State: 34:[28, 32, 35, 2], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [28, 2, 3] Generated Node #2: [28, 2, 3] from Operation: 35-32=3 Current State: 34:[28, 2, 3], Operations: ['35-32=3'] Exploring Operation: 2*3=6, Resulting Numbers: [28, 6] Generated Node #3: [28, 6] from Operation: 2*3=6 Current State: 34:[28, 6], Operations: ['35-32=3', '2*3=6'] Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[28, 32, 35, 2], Operations: [] Exploring Operation: 35-28=7, Resulting Numbers: [32, 2, 7] Generated Node #0,0: 34:[32, 2, 7] Operation: 35-28=7 Exploring Operation: 32-28=4, Resulting Numbers: [35, 2, 4] Generated Node #0,1: 34:[35, 2, 4] Operation: 32-28=4 Exploring Operation: 35-32=3, Resulting Numbers: [28, 2, 3] Generated Node #0,2: 34:[28, 2, 3] Operation: 35-32=3 Exploring Operation: 28+2=30, Resulting Numbers: [32, 35, 30] Generated Node #0,3: 34:[32, 35, 30] Operation: 28+2=30 Exploring Operation: 28/2=14, Resulting Numbers: [32, 35, 14] Generated Node #0,4: 34:[32, 35, 14] Operation: 28/2=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[35, 2, 4], Operations: ['32-28=4'] Exploring Operation: 4/2=2, Resulting Numbers: [35, 2] Generated Node #0,1,0: 34:[35, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [35, 2] Generated Node #0,1,1: 34:[35, 2] Operation: 4-2=2 Exploring Operation: 35+2=37, Resulting Numbers: [4, 37] Generated Node #0,1,2: 34:[4, 37] Operation: 35+2=37 Exploring Operation: 35-2=33, Resulting Numbers: [4, 33] Generated Node #0,1,3: 34:[4, 33] Operation: 35-2=33 Exploring Operation: 35-4=31, Resulting Numbers: [2, 31] Generated Node #0,1,4: 34:[2, 31] Operation: 35-4=31 Moving to Node #0,1,0 Current State: 34:[35, 2], Operations: ['32-28=4', '4/2=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[35, 2], Operations: ['32-28=4', '4-2=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,34 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[4, 33], Operations: ['32-28=4', '35-2=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 4*33=132, Resulting Numbers: [132] 132,34 unequal: No Solution Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,34 unequal: No Solution Moving to Node #0,1,4 Current State: 34:[2, 31], Operations: ['32-28=4', '35-4=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,34 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[4, 37], Operations: ['32-28=4', '35+2=37'] Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,34 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 4*37=148, Resulting Numbers: [148] 148,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 34:[32, 35, 14], Operations: ['28/2=14'] Exploring Operation: 35-32=3, Resulting Numbers: [14, 3] Generated Node #0,4,0: 34:[14, 3] Operation: 35-32=3 Exploring Operation: 35-14=21, Resulting Numbers: [32, 21] Generated Node #0,4,1: 34:[32, 21] Operation: 35-14=21 Exploring Operation: 35+14=49, Resulting Numbers: [32, 49] Generated Node #0,4,2: 34:[32, 49] Operation: 35+14=49 Exploring Operation: 32+14=46, Resulting Numbers: [35, 46] Generated Node #0,4,3: 34:[35, 46] Operation: 32+14=46 Exploring Operation: 32-14=18, Resulting Numbers: [35, 18] Generated Node #0,4,4: 34:[35, 18] Operation: 32-14=18 Moving to Node #0,4,4 Current State: 34:[35, 18], Operations: ['28/2=14', '32-14=18'] Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,34 unequal: No Solution Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,34 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,34 unequal: No Solution Moving to Node #0,4,0 Current State: 34:[14, 3], Operations: ['28/2=14', '35-32=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,34 unequal: No Solution Moving to Node #0,4,1 Current State: 34:[32, 21], Operations: ['28/2=14', '35-14=21'] Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,34 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,34 unequal: No Solution Moving to Node #0,4,3 Current State: 34:[35, 46], Operations: ['28/2=14', '32+14=46'] Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,34 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,34 unequal: No Solution Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,34 unequal: No Solution Moving to Node #0,4,2 Current State: 34:[32, 49], Operations: ['28/2=14', '35+14=49'] Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,34 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[32, 2, 7], Operations: ['35-28=7'] Exploring Operation: 32+7=39, Resulting Numbers: [2, 39] Generated Node #0,0,0: 34:[2, 39] Operation: 32+7=39 Exploring Operation: 32+2=34, Resulting Numbers: [7, 34] Generated Node #0,0,1: 34:[7, 34] Operation: 32+2=34 Exploring Operation: 7-2=5, Resulting Numbers: [32, 5] Generated Node #0,0,2: 34:[32, 5] Operation: 7-2=5 Exploring Operation: 32/2=16, Resulting Numbers: [7, 16] Generated Node #0,0,3: 34:[7, 16] Operation: 32/2=16 Exploring Operation: 2*7=14, Resulting Numbers: [32, 14] Generated Node #0,0,4: 34:[32, 14] Operation: 2*7=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[2, 39], Operations: ['35-28=7', '32+7=39'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[7, 34], Operations: ['35-28=7', '32+2=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,34 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[32, 5], Operations: ['35-28=7', '7-2=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,34 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 34:[32, 14], Operations: ['35-28=7', '2*7=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,34 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,34 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 34:[7, 16], Operations: ['35-28=7', '32/2=16'] Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,34 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,34 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: 34:[28, 2, 3], Operations: ['35-32=3'] Exploring Operation: 3-2=1, Resulting Numbers: [28, 1] Generated Node #0,2,0: 34:[28, 1] Operation: 3-2=1 Exploring Operation: 28+2=30, Resulting Numbers: [3, 30] Generated Node #0,2,1: 34:[3, 30] Operation: 28+2=30 Exploring Operation: 28/2=14, Resulting Numbers: [3, 14] Generated Node #0,2,2: 34:[3, 14] Operation: 28/2=14 Exploring Operation: 28+3=31, Resulting Numbers: [2, 31] Generated Node #0,2,3: 34:[2, 31] Operation: 28+3=31 Exploring Operation: 28-3=25, Resulting Numbers: [2, 25] Generated Node #0,2,4: 34:[2, 25] Operation: 28-3=25 Moving to Node #0,2,3 Current State: 34:[2, 31], Operations: ['35-32=3', '28+3=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[3, 14], Operations: ['35-32=3', '28/2=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[3, 30], Operations: ['35-32=3', '28+2=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,34 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[28, 1], Operations: ['35-32=3', '3-2=1'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,34 unequal: No Solution Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[2, 25], Operations: ['35-32=3', '28-3=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,34 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[32, 35, 30], Operations: ['28+2=30'] Exploring Operation: 35-30=5, Resulting Numbers: [32, 5] Generated Node #0,3,0: 34:[32, 5] Operation: 35-30=5 Exploring Operation: 32+30=62, Resulting Numbers: [35, 62] Generated Node #0,3,1: 34:[35, 62] Operation: 32+30=62 Exploring Operation: 35-32=3, Resulting Numbers: [30, 3] Generated Node #0,3,2: 34:[30, 3] Operation: 35-32=3 Exploring Operation: 32-30=2, Resulting Numbers: [35, 2] Generated Node #0,3,3: 34:[35, 2] Operation: 32-30=2 Exploring Operation: 35+30=65, Resulting Numbers: [32, 65] Generated Node #0,3,4: 34:[32, 65] Operation: 35+30=65 Moving to Node #0,3,3 Current State: 34:[35, 2], Operations: ['28+2=30', '32-30=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[30, 3], Operations: ['28+2=30', '35-32=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,34 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,34 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[32, 5], Operations: ['28+2=30', '35-30=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,34 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[35, 62], Operations: ['28+2=30', '32+30=62'] Exploring Operation: 35+62=97, Resulting Numbers: [97] 97,34 unequal: No Solution Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,34 unequal: No Solution Exploring Operation: 35*62=2170, Resulting Numbers: [2170] 2170,34 unequal: No Solution Moving to Node #0,3,4 Current State: 34:[32, 65], Operations: ['28+2=30', '35+30=65'] Exploring Operation: 32*65=2080, Resulting Numbers: [2080] 2080,34 unequal: No Solution Exploring Operation: 32+65=97, Resulting Numbers: [97] 97,34 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,34 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
[ 7, 25, 81, 2 ]
76
[ "7-2=5", "25/5=5", "81-5=76" ]
Current State: 76:[7, 25, 81, 2], Operations: [] Exploring Operation: 7-2=5, Resulting Numbers: [25, 81, 5] Generated Node #2: [25, 81, 5] from Operation: 7-2=5 Current State: 76:[25, 81, 5], Operations: ['7-2=5'] Exploring Operation: 25/5=5, Resulting Numbers: [81, 5] Generated Node #3: [81, 5] from Operation: 25/5=5 Current State: 76:[81, 5], Operations: ['7-2=5', '25/5=5'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[7, 25, 81, 2], Operations: [] Exploring Operation: 25-7=18, Resulting Numbers: [81, 2, 18] Generated Node #0,0: 76:[81, 2, 18] Operation: 25-7=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[81, 2, 18], Operations: ['25-7=18'] Exploring Operation: 81-2=79, Resulting Numbers: [18, 79] Generated Node #0,0,0: 76:[18, 79] Operation: 81-2=79 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[18, 79], Operations: ['25-7=18', '81-2=79'] Exploring Operation: 79-18=61, Resulting Numbers: [61] 61,76 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 No solution found.
0
hs_1
mult_heuristic
[ 2, 80, 74, 42 ]
16
[ "74/2=37", "42-37=5", "80/5=16" ]
Current State: 16:[2, 80, 74, 42], Operations: [] Exploring Operation: 74/2=37, Resulting Numbers: [80, 42, 37] Generated Node #2: [80, 42, 37] from Operation: 74/2=37 Current State: 16:[80, 42, 37], Operations: ['74/2=37'] Exploring Operation: 42-37=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 42-37=5 Current State: 16:[80, 5], Operations: ['74/2=37', '42-37=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[2, 80, 74, 42], Operations: [] Exploring Operation: 80-42=38, Resulting Numbers: [2, 74, 38] Generated Node #0,0: 16:[2, 74, 38] Operation: 80-42=38 Exploring Operation: 74-42=32, Resulting Numbers: [2, 80, 32] Generated Node #0,1: 16:[2, 80, 32] Operation: 74-42=32 Exploring Operation: 80-74=6, Resulting Numbers: [2, 42, 6] Generated Node #0,2: 16:[2, 42, 6] Operation: 80-74=6 Moving to Node #0,2 Current State: 16:[2, 42, 6], Operations: ['80-74=6'] Exploring Operation: 42/2=21, Resulting Numbers: [6, 21] Generated Node #0,2,0: 16:[6, 21] Operation: 42/2=21 Exploring Operation: 42-6=36, Resulting Numbers: [2, 36] Generated Node #0,2,1: 16:[2, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [2, 7] Generated Node #0,2,2: 16:[2, 7] Operation: 42/6=7 Moving to Node #0,0 Current State: 16:[2, 74, 38], Operations: ['80-42=38'] Exploring Operation: 74-38=36, Resulting Numbers: [2, 36] Generated Node #0,0,0: 16:[2, 36] Operation: 74-38=36 Exploring Operation: 38/2=19, Resulting Numbers: [74, 19] Generated Node #0,0,1: 16:[74, 19] Operation: 38/2=19 Exploring Operation: 74/2=37, Resulting Numbers: [38, 37] Generated Node #0,0,2: 16:[38, 37] Operation: 74/2=37 Moving to Node #0,1 Current State: 16:[2, 80, 32], Operations: ['74-42=32'] Exploring Operation: 32/2=16, Resulting Numbers: [80, 16] Generated Node #0,1,0: 16:[80, 16] Operation: 32/2=16 Exploring Operation: 80/2=40, Resulting Numbers: [32, 40] Generated Node #0,1,1: 16:[32, 40] Operation: 80/2=40 Exploring Operation: 80-32=48, Resulting Numbers: [2, 48] Generated Node #0,1,2: 16:[2, 48] Operation: 80-32=48 Moving to Node #0,2,2 Current State: 16:[2, 7], Operations: ['80-74=6', '42/6=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,16 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[6, 21], Operations: ['80-74=6', '42/2=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,16 unequal: No Solution Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[2, 36], Operations: ['80-74=6', '42-6=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[2, 36], Operations: ['80-42=38', '74-38=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,16 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[2, 48], Operations: ['74-42=32', '80-32=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,16 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,16 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[32, 40], Operations: ['74-42=32', '80/2=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,16 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[38, 37], Operations: ['80-42=38', '74/2=37'] Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 38+37=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 38*37=1406, Resulting Numbers: [1406] 1406,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[74, 19], Operations: ['80-42=38', '38/2=19'] Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,16 unequal: No Solution Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[80, 16], Operations: ['74-42=32', '32/2=16'] Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,16 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 80+16=96, Resulting Numbers: [96] 96,16 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 4, 29, 61, 83 ]
94
[ "4*29=116", "83-61=22", "116-22=94" ]
Current State: 94:[4, 29, 61, 83], Operations: [] Exploring Operation: 4*29=116, Resulting Numbers: [61, 83, 116] Generated Node #2: [61, 83, 116] from Operation: 4*29=116 Current State: 94:[61, 83, 116], Operations: ['4*29=116'] Exploring Operation: 83-61=22, Resulting Numbers: [116, 22] Generated Node #3: [116, 22] from Operation: 83-61=22 Current State: 94:[116, 22], Operations: ['4*29=116', '83-61=22'] Exploring Operation: 116-22=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[4, 29, 61, 83], Operations: [] Exploring Operation: 29+61=90, Resulting Numbers: [4, 83, 90] Generated Node #0,0: 94:[4, 83, 90] Operation: 29+61=90 Exploring Operation: 61-29=32, Resulting Numbers: [4, 83, 32] Generated Node #0,1: 94:[4, 83, 32] Operation: 61-29=32 Exploring Operation: 83-29=54, Resulting Numbers: [4, 61, 54] Generated Node #0,2: 94:[4, 61, 54] Operation: 83-29=54 Moving to Node #0,0 Current State: 94:[4, 83, 90], Operations: ['29+61=90'] Exploring Operation: 90-83=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 94:[4, 7] Operation: 90-83=7 Exploring Operation: 4+90=94, Resulting Numbers: [83, 94] Generated Node #0,0,1: 94:[83, 94] Operation: 4+90=94 Exploring Operation: 4+83=87, Resulting Numbers: [90, 87] Generated Node #0,0,2: 94:[90, 87] Operation: 4+83=87 Moving to Node #0,2 Current State: 94:[4, 61, 54], Operations: ['83-29=54'] Exploring Operation: 61-4=57, Resulting Numbers: [54, 57] Generated Node #0,2,0: 94:[54, 57] Operation: 61-4=57 Exploring Operation: 54-4=50, Resulting Numbers: [61, 50] Generated Node #0,2,1: 94:[61, 50] Operation: 54-4=50 Exploring Operation: 61-54=7, Resulting Numbers: [4, 7] Generated Node #0,2,2: 94:[4, 7] Operation: 61-54=7 Moving to Node #0,1 Current State: 94:[4, 83, 32], Operations: ['61-29=32'] Exploring Operation: 4+83=87, Resulting Numbers: [32, 87] Generated Node #0,1,0: 94:[32, 87] Operation: 4+83=87 Exploring Operation: 83-32=51, Resulting Numbers: [4, 51] Generated Node #0,1,1: 94:[4, 51] Operation: 83-32=51 Exploring Operation: 32/4=8, Resulting Numbers: [83, 8] Generated Node #0,1,2: 94:[83, 8] Operation: 32/4=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[4, 51], Operations: ['61-29=32', '83-32=51'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,94 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 94:[83, 8], Operations: ['61-29=32', '32/4=8'] Exploring Operation: 83+8=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 83*8=664, Resulting Numbers: [664] 664,94 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[32, 87], Operations: ['61-29=32', '4+83=87'] Exploring Operation: 32+87=119, Resulting Numbers: [119] 119,94 unequal: No Solution Exploring Operation: 32*87=2784, Resulting Numbers: [2784] 2784,94 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,94 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: 94:[4, 7], Operations: ['29+61=90', '90-83=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[4, 7], Operations: ['83-29=54', '61-54=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[90, 87], Operations: ['29+61=90', '4+83=87'] Exploring Operation: 90*87=7830, Resulting Numbers: [7830] 7830,94 unequal: No Solution Exploring Operation: 90+87=177, Resulting Numbers: [177] 177,94 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[83, 94], Operations: ['29+61=90', '4+90=94'] Exploring Operation: 94-83=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 83*94=7802, Resulting Numbers: [7802] 7802,94 unequal: No Solution Exploring Operation: 83+94=177, Resulting Numbers: [177] 177,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[61, 50], Operations: ['83-29=54', '54-4=50'] Exploring Operation: 61-50=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 61+50=111, Resulting Numbers: [111] 111,94 unequal: No Solution Exploring Operation: 61*50=3050, Resulting Numbers: [3050] 3050,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[54, 57], Operations: ['83-29=54', '61-4=57'] Exploring Operation: 54+57=111, Resulting Numbers: [111] 111,94 unequal: No Solution Exploring Operation: 54*57=3078, Resulting Numbers: [3078] 3078,94 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,94 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 21, 42, 44, 42 ]
61
[ "21+42=63", "44-42=2", "63-2=61" ]
Current State: 61:[21, 42, 44, 42], Operations: [] Exploring Operation: 21+42=63, Resulting Numbers: [44, 63] Generated Node #2: [44, 63] from Operation: 21+42=63 Current State: 61:[44, 63], Operations: ['21+42=63'] Exploring Operation: 44-42=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 44-42=2 Current State: 61:[63, 2], Operations: ['21+42=63', '44-42=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[21, 42, 44, 42], Operations: [] Exploring Operation: 21+42=63, Resulting Numbers: [44, 42, 63] Generated Node #0,0: 61:[44, 42, 63] Operation: 21+42=63 Exploring Operation: 21+42=63, Resulting Numbers: [42, 44, 63] Generated Node #0,1: 61:[42, 44, 63] Operation: 21+42=63 Moving to Node #0,0 Current State: 61:[44, 42, 63], Operations: ['21+42=63'] Exploring Operation: 44+42=86, Resulting Numbers: [63, 86] Generated Node #0,0,0: 61:[63, 86] Operation: 44+42=86 Exploring Operation: 63-42=21, Resulting Numbers: [44, 21] Generated Node #0,0,1: 61:[44, 21] Operation: 63-42=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[63, 86], Operations: ['21+42=63', '44+42=86'] Exploring Operation: 86-63=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 63+86=149, Resulting Numbers: [149] 149,61 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 #0,0,1 Current State: 61:[44, 21], Operations: ['21+42=63', '63-42=21'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[42, 44, 63], Operations: ['21+42=63'] Exploring Operation: 42+44=86, Resulting Numbers: [63, 86] Generated Node #0,1,0: 61:[63, 86] Operation: 42+44=86 Exploring Operation: 63-42=21, Resulting Numbers: [44, 21] Generated Node #0,1,1: 61:[44, 21] Operation: 63-42=21 Moving to Node #0,1,0 Current State: 61:[63, 86], Operations: ['21+42=63', '42+44=86'] Exploring Operation: 63+86=149, Resulting Numbers: [149] 149,61 unequal: No Solution Exploring Operation: 86-63=23, Resulting Numbers: [23] 23,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[44, 21], Operations: ['21+42=63', '63-42=21'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,61 unequal: No Solution Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,61 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 54, 41, 6, 87 ]
37
[ "54/6=9", "87-41=46", "46-9=37" ]
Current State: 37:[54, 41, 6, 87], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [41, 87, 9] Generated Node #2: [41, 87, 9] from Operation: 54/6=9 Current State: 37:[41, 87, 9], Operations: ['54/6=9'] Exploring Operation: 87-41=46, Resulting Numbers: [9, 46] Generated Node #3: [9, 46] from Operation: 87-41=46 Current State: 37:[9, 46], Operations: ['54/6=9', '87-41=46'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[54, 41, 6, 87], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [41, 6, 33] Generated Node #0,0: 37:[41, 6, 33] Operation: 87-54=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[41, 6, 33], Operations: ['87-54=33'] Exploring Operation: 41-6=35, Resulting Numbers: [33, 35] Generated Node #0,0,0: 37:[33, 35] Operation: 41-6=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[33, 35], Operations: ['87-54=33', '41-6=35'] Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,37 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
[ 14, 76, 92, 13 ]
26
[ "14+76=90", "92-90=2", "13*2=26" ]
Current State: 26:[14, 76, 92, 13], Operations: [] Exploring Operation: 14+76=90, Resulting Numbers: [92, 13, 90] Generated Node #2: [92, 13, 90] from Operation: 14+76=90 Current State: 26:[92, 13, 90], Operations: ['14+76=90'] Exploring Operation: 92-90=2, Resulting Numbers: [13, 2] Generated Node #3: [13, 2] from Operation: 92-90=2 Current State: 26:[13, 2], Operations: ['14+76=90', '92-90=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[14, 76, 92, 13], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [14, 13, 16] Generated Node #0,0: 26:[14, 13, 16] Operation: 92-76=16 Moving to Node #0,0 Current State: 26:[14, 13, 16], Operations: ['92-76=16'] Exploring Operation: 16-14=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 26:[13, 2] Operation: 16-14=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[13, 2], Operations: ['92-76=16', '16-14=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[14, 76, 92, 13], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [14, 13, 16] Generated Node #0,0: 26:[14, 13, 16] Operation: 92-76=16 Moving to Node #0,0 Current State: 26:[14, 13, 16], Operations: ['92-76=16'] Exploring Operation: 16-14=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 26:[13, 2] Operation: 16-14=2 Moving to Node #0,0,0 Current State: 26:[13, 2], Operations: ['92-76=16', '16-14=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 62, 99, 66, 27 ]
18
[ "66-62=4", "99-27=72", "72/4=18" ]
Current State: 18:[62, 99, 66, 27], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [99, 27, 4] Generated Node #2: [99, 27, 4] from Operation: 66-62=4 Current State: 18:[99, 27, 4], Operations: ['66-62=4'] Exploring Operation: 99-27=72, Resulting Numbers: [4, 72] Generated Node #3: [4, 72] from Operation: 99-27=72 Current State: 18:[4, 72], Operations: ['66-62=4', '99-27=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[62, 99, 66, 27], Operations: [] Exploring Operation: 99-62=37, Resulting Numbers: [66, 27, 37] Generated Node #0,0: 18:[66, 27, 37] Operation: 99-62=37 Exploring Operation: 99-27=72, Resulting Numbers: [62, 66, 72] Generated Node #0,1: 18:[62, 66, 72] Operation: 99-27=72 Exploring Operation: 66-62=4, Resulting Numbers: [99, 27, 4] Generated Node #0,2: 18:[99, 27, 4] Operation: 66-62=4 Exploring Operation: 62-27=35, Resulting Numbers: [99, 66, 35] Generated Node #0,3: 18:[99, 66, 35] Operation: 62-27=35 Exploring Operation: 99-66=33, Resulting Numbers: [62, 27, 33] Generated Node #0,4: 18:[62, 27, 33] Operation: 99-66=33 Start Sub Search at level 1: Moving to Node #0,4 Current State: 18:[62, 27, 33], Operations: ['99-66=33'] Exploring Operation: 62+27=89, Resulting Numbers: [33, 89] Generated Node #0,4,0: 18:[33, 89] Operation: 62+27=89 Exploring Operation: 62-27=35, Resulting Numbers: [33, 35] Generated Node #0,4,1: 18:[33, 35] Operation: 62-27=35 Exploring Operation: 62-33=29, Resulting Numbers: [27, 29] Generated Node #0,4,2: 18:[27, 29] Operation: 62-33=29 Exploring Operation: 62+33=95, Resulting Numbers: [27, 95] Generated Node #0,4,3: 18:[27, 95] Operation: 62+33=95 Exploring Operation: 33-27=6, Resulting Numbers: [62, 6] Generated Node #0,4,4: 18:[62, 6] Operation: 33-27=6 Moving to Node #0,4,2 Current State: 18:[27, 29], Operations: ['99-66=33', '62-33=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,18 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,4,1 Current State: 18:[33, 35], Operations: ['99-66=33', '62-27=35'] Exploring Operation: 33*35=1155, Resulting Numbers: [1155] 1155,18 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[62, 6], Operations: ['99-66=33', '33-27=6'] Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,18 unequal: No Solution Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[33, 89], Operations: ['99-66=33', '62+27=89'] Exploring Operation: 89-33=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 33+89=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 33*89=2937, Resulting Numbers: [2937] 2937,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[27, 95], Operations: ['99-66=33', '62+33=95'] Exploring Operation: 95-27=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 27+95=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 27*95=2565, Resulting Numbers: [2565] 2565,18 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 Current State: 18:[66, 27, 37], Operations: ['99-62=37'] Exploring Operation: 66-27=39, Resulting Numbers: [37, 39] Generated Node #0,0,0: 18:[37, 39] Operation: 66-27=39 Exploring Operation: 66-37=29, Resulting Numbers: [27, 29] Generated Node #0,0,1: 18:[27, 29] Operation: 66-37=29 Exploring Operation: 66+37=103, Resulting Numbers: [27, 103] Generated Node #0,0,2: 18:[27, 103] Operation: 66+37=103 Exploring Operation: 66+27=93, Resulting Numbers: [37, 93] Generated Node #0,0,3: 18:[37, 93] Operation: 66+27=93 Exploring Operation: 37-27=10, Resulting Numbers: [66, 10] Generated Node #0,0,4: 18:[66, 10] Operation: 37-27=10 Moving to Node #0,0,1 Current State: 18:[27, 29], Operations: ['99-62=37', '66-37=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[37, 39], Operations: ['99-62=37', '66-27=39'] Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 37+39=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 37*39=1443, Resulting Numbers: [1443] 1443,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[66, 10], Operations: ['99-62=37', '37-27=10'] Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 66*10=660, Resulting Numbers: [660] 660,18 unequal: No Solution Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[27, 103], Operations: ['99-62=37', '66+37=103'] Exploring Operation: 27*103=2781, Resulting Numbers: [2781] 2781,18 unequal: No Solution Exploring Operation: 27+103=130, Resulting Numbers: [130] 130,18 unequal: No Solution Exploring Operation: 103-27=76, Resulting Numbers: [76] 76,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[37, 93], Operations: ['99-62=37', '66+27=93'] Exploring Operation: 37+93=130, Resulting Numbers: [130] 130,18 unequal: No Solution Exploring Operation: 37*93=3441, Resulting Numbers: [3441] 3441,18 unequal: No Solution Exploring Operation: 93-37=56, Resulting Numbers: [56] 56,18 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 Current State: 18:[99, 27, 4], Operations: ['66-62=4'] Exploring Operation: 27-4=23, Resulting Numbers: [99, 23] Generated Node #0,2,0: 18:[99, 23] Operation: 27-4=23 Exploring Operation: 99-4=95, Resulting Numbers: [27, 95] Generated Node #0,2,1: 18:[27, 95] Operation: 99-4=95 Exploring Operation: 27+4=31, Resulting Numbers: [99, 31] Generated Node #0,2,2: 18:[99, 31] Operation: 27+4=31 Exploring Operation: 99+4=103, Resulting Numbers: [27, 103] Generated Node #0,2,3: 18:[27, 103] Operation: 99+4=103 Exploring Operation: 99-27=72, Resulting Numbers: [4, 72] Generated Node #0,2,4: 18:[4, 72] Operation: 99-27=72 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 18:[4, 72], Operations: ['66-62=4', '99-27=72'] Exploring Operation: 4+72=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,18 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[62, 99, 66, 27], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [99, 27, 4] Generated Node #0,2: 18:[99, 27, 4] Operation: 66-62=4 Moving to Node #0,2 Current State: 18:[99, 27, 4], Operations: ['66-62=4'] Exploring Operation: 99-27=72, Resulting Numbers: [4, 72] Generated Node #0,2,4: 18:[4, 72] Operation: 99-27=72 Moving to Node #0,2,4 Current State: 18:[4, 72], Operations: ['66-62=4', '99-27=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
mult_heuristic
[ 41, 93, 26, 95 ]
30
[ "41-26=15", "95-93=2", "15*2=30" ]
Current State: 30:[41, 93, 26, 95], Operations: [] Exploring Operation: 41-26=15, Resulting Numbers: [93, 95, 15] Generated Node #2: [93, 95, 15] from Operation: 41-26=15 Current State: 30:[93, 95, 15], Operations: ['41-26=15'] Exploring Operation: 95-93=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 95-93=2 Current State: 30:[15, 2], Operations: ['41-26=15', '95-93=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[41, 93, 26, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [41, 26, 2] Generated Node #0,0: 30:[41, 26, 2] Operation: 95-93=2 Exploring Operation: 93-26=67, Resulting Numbers: [41, 95, 67] Generated Node #0,1: 30:[41, 95, 67] Operation: 93-26=67 Exploring Operation: 95-41=54, Resulting Numbers: [93, 26, 54] Generated Node #0,2: 30:[93, 26, 54] Operation: 95-41=54 Exploring Operation: 93-41=52, Resulting Numbers: [26, 95, 52] Generated Node #0,3: 30:[26, 95, 52] Operation: 93-41=52 Moving to Node #0,0 Current State: 30:[41, 26, 2], Operations: ['95-93=2'] Exploring Operation: 41-2=39, Resulting Numbers: [26, 39] Generated Node #0,0,0: 30:[26, 39] Operation: 41-2=39 Exploring Operation: 26+2=28, Resulting Numbers: [41, 28] Generated Node #0,0,1: 30:[41, 28] Operation: 26+2=28 Exploring Operation: 41-26=15, Resulting Numbers: [2, 15] Generated Node #0,0,2: 30:[2, 15] Operation: 41-26=15 Exploring Operation: 26/2=13, Resulting Numbers: [41, 13] Generated Node #0,0,3: 30:[41, 13] Operation: 26/2=13 Moving to Node #0,3 Current State: 30:[26, 95, 52], Operations: ['93-41=52'] Exploring Operation: 52-26=26, Resulting Numbers: [95, 26] Generated Node #0,3,0: 30:[95, 26] Operation: 52-26=26 Exploring Operation: 52/26=2, Resulting Numbers: [95, 2] Generated Node #0,3,1: 30:[95, 2] Operation: 52/26=2 Exploring Operation: 95-52=43, Resulting Numbers: [26, 43] Generated Node #0,3,2: 30:[26, 43] Operation: 95-52=43 Exploring Operation: 95-26=69, Resulting Numbers: [52, 69] Generated Node #0,3,3: 30:[52, 69] Operation: 95-26=69 Moving to Node #0,2 Current State: 30:[93, 26, 54], Operations: ['95-41=54'] Exploring Operation: 54-26=28, Resulting Numbers: [93, 28] Generated Node #0,2,0: 30:[93, 28] Operation: 54-26=28 Exploring Operation: 93-54=39, Resulting Numbers: [26, 39] Generated Node #0,2,1: 30:[26, 39] Operation: 93-54=39 Exploring Operation: 93-26=67, Resulting Numbers: [54, 67] Generated Node #0,2,2: 30:[54, 67] Operation: 93-26=67 Exploring Operation: 93+26=119, Resulting Numbers: [54, 119] Generated Node #0,2,3: 30:[54, 119] Operation: 93+26=119 Moving to Node #0,1 Current State: 30:[41, 95, 67], Operations: ['93-26=67'] Exploring Operation: 95-67=28, Resulting Numbers: [41, 28] Generated Node #0,1,0: 30:[41, 28] Operation: 95-67=28 Exploring Operation: 67-41=26, Resulting Numbers: [95, 26] Generated Node #0,1,1: 30:[95, 26] Operation: 67-41=26 Exploring Operation: 95-41=54, Resulting Numbers: [67, 54] Generated Node #0,1,2: 30:[67, 54] Operation: 95-41=54 Exploring Operation: 41+95=136, Resulting Numbers: [67, 136] Generated Node #0,1,3: 30:[67, 136] Operation: 41+95=136 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[41, 28], Operations: ['93-26=67', '95-67=28'] Exploring Operation: 41*28=1148, Resulting Numbers: [1148] 1148,30 unequal: No Solution Exploring Operation: 41+28=69, Resulting Numbers: [69] 69,30 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[67, 54], Operations: ['93-26=67', '95-41=54'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[95, 26], Operations: ['93-26=67', '67-41=26'] Exploring Operation: 95*26=2470, Resulting Numbers: [2470] 2470,30 unequal: No Solution Exploring Operation: 95+26=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 95-26=69, Resulting Numbers: [69] 69,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 30:[67, 136], Operations: ['93-26=67', '41+95=136'] Exploring Operation: 67+136=203, Resulting Numbers: [203] 203,30 unequal: No Solution Exploring Operation: 67*136=9112, Resulting Numbers: [9112] 9112,30 unequal: No Solution Exploring Operation: 136-67=69, Resulting Numbers: [69] 69,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 30:[2, 15], Operations: ['95-93=2', '41-26=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[41, 93, 26, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [41, 26, 2] Generated Node #0,0: 30:[41, 26, 2] Operation: 95-93=2 Moving to Node #0,0 Current State: 30:[41, 26, 2], Operations: ['95-93=2'] Exploring Operation: 41-26=15, Resulting Numbers: [2, 15] Generated Node #0,0,2: 30:[2, 15] Operation: 41-26=15 Moving to Node #0,0,2 Current State: 30:[2, 15], Operations: ['95-93=2', '41-26=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 82, 46, 21, 95 ]
38
[ "82-46=36", "95-21=74", "74-36=38" ]
Current State: 38:[82, 46, 21, 95], Operations: [] Exploring Operation: 82-46=36, Resulting Numbers: [21, 95, 36] Generated Node #2: [21, 95, 36] from Operation: 82-46=36 Current State: 38:[21, 95, 36], Operations: ['82-46=36'] Exploring Operation: 95-21=74, Resulting Numbers: [36, 74] Generated Node #3: [36, 74] from Operation: 95-21=74 Current State: 38:[36, 74], Operations: ['82-46=36', '95-21=74'] Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[82, 46, 21, 95], Operations: [] Exploring Operation: 95-82=13, Resulting Numbers: [46, 21, 13] Generated Node #0,0: 38:[46, 21, 13] Operation: 95-82=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[46, 21, 13], Operations: ['95-82=13'] Exploring Operation: 46-13=33, Resulting Numbers: [21, 33] Generated Node #0,0,0: 38:[21, 33] Operation: 46-13=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[21, 33], Operations: ['95-82=13', '46-13=33'] Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 29, 86, 17, 23 ]
75
[ "29+86=115", "17+23=40", "115-40=75" ]
Current State: 75:[29, 86, 17, 23], Operations: [] Exploring Operation: 29+86=115, Resulting Numbers: [17, 23, 115] Generated Node #2: [17, 23, 115] from Operation: 29+86=115 Current State: 75:[17, 23, 115], Operations: ['29+86=115'] Exploring Operation: 17+23=40, Resulting Numbers: [115, 40] Generated Node #3: [115, 40] from Operation: 17+23=40 Current State: 75:[115, 40], Operations: ['29+86=115', '17+23=40'] Exploring Operation: 115-40=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[29, 86, 17, 23], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [29, 23, 69] Generated Node #0,0: 75:[29, 23, 69] Operation: 86-17=69 Exploring Operation: 29-23=6, Resulting Numbers: [86, 17, 6] Generated Node #0,1: 75:[86, 17, 6] Operation: 29-23=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[29, 23, 69], Operations: ['86-17=69'] Exploring Operation: 29-23=6, Resulting Numbers: [69, 6] Generated Node #0,0,0: 75:[69, 6] Operation: 29-23=6 Exploring Operation: 69/23=3, Resulting Numbers: [29, 3] Generated Node #0,0,1: 75:[29, 3] Operation: 69/23=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[29, 3], Operations: ['86-17=69', '69/23=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,75 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,75 unequal: No Solution No 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: 75:[69, 6], Operations: ['86-17=69', '29-23=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[29, 86, 17, 23], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [29, 23, 69] Generated Node #0,0: 75:[29, 23, 69] Operation: 86-17=69 Moving to Node #0,0 Current State: 75:[29, 23, 69], Operations: ['86-17=69'] Exploring Operation: 29-23=6, Resulting Numbers: [69, 6] Generated Node #0,0,0: 75:[69, 6] Operation: 29-23=6 Moving to Node #0,0,0 Current State: 75:[69, 6], Operations: ['86-17=69', '29-23=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 12, 17, 7, 7 ]
94
[ "12*7=84", "17-7=10", "84+10=94" ]
Current State: 94:[12, 17, 7, 7], Operations: [] Exploring Operation: 12*7=84, Resulting Numbers: [17, 84] Generated Node #2: [17, 84] from Operation: 12*7=84 Current State: 94:[17, 84], Operations: ['12*7=84'] Exploring Operation: 17-7=10, Resulting Numbers: [84, 10] Generated Node #3: [84, 10] from Operation: 17-7=10 Current State: 94:[84, 10], Operations: ['12*7=84', '17-7=10'] Exploring Operation: 84+10=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[12, 17, 7, 7], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [7, 7, 5] Generated Node #0,0: 94:[7, 7, 5] Operation: 17-12=5 Moving to Node #0,0 Current State: 94:[7, 7, 5], Operations: ['17-12=5'] Exploring Operation: 7/7=1, Resulting Numbers: [5, 1] Generated Node #0,0,0: 94:[5, 1] Operation: 7/7=1 Moving to Node #0,0,0 Current State: 94:[5, 1], Operations: ['17-12=5', '7/7=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 35, 28, 33, 55 ]
81
[ "35-28=7", "33+55=88", "88-7=81" ]
Current State: 81:[35, 28, 33, 55], Operations: [] Exploring Operation: 35-28=7, Resulting Numbers: [33, 55, 7] Generated Node #2: [33, 55, 7] from Operation: 35-28=7 Current State: 81:[33, 55, 7], Operations: ['35-28=7'] Exploring Operation: 33+55=88, Resulting Numbers: [7, 88] Generated Node #3: [7, 88] from Operation: 33+55=88 Current State: 81:[7, 88], Operations: ['35-28=7', '33+55=88'] Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[35, 28, 33, 55], Operations: [] Exploring Operation: 28+55=83, Resulting Numbers: [35, 33, 83] Generated Node #0,0: 81:[35, 33, 83] Operation: 28+55=83 Exploring Operation: 55-28=27, Resulting Numbers: [35, 33, 27] Generated Node #0,1: 81:[35, 33, 27] Operation: 55-28=27 Exploring Operation: 35+55=90, Resulting Numbers: [28, 33, 90] Generated Node #0,2: 81:[28, 33, 90] Operation: 35+55=90 Exploring Operation: 55-35=20, Resulting Numbers: [28, 33, 20] Generated Node #0,3: 81:[28, 33, 20] Operation: 55-35=20 Exploring Operation: 55-33=22, Resulting Numbers: [35, 28, 22] Generated Node #0,4: 81:[35, 28, 22] Operation: 55-33=22 Moving to Node #0,1 Current State: 81:[35, 33, 27], Operations: ['55-28=27'] Exploring Operation: 33-27=6, Resulting Numbers: [35, 6] Generated Node #0,1,0: 81:[35, 6] Operation: 33-27=6 Exploring Operation: 35+27=62, Resulting Numbers: [33, 62] Generated Node #0,1,1: 81:[33, 62] Operation: 35+27=62 Exploring Operation: 35+33=68, Resulting Numbers: [27, 68] Generated Node #0,1,2: 81:[27, 68] Operation: 35+33=68 Exploring Operation: 35-27=8, Resulting Numbers: [33, 8] Generated Node #0,1,3: 81:[33, 8] Operation: 35-27=8 Exploring Operation: 35-33=2, Resulting Numbers: [27, 2] Generated Node #0,1,4: 81:[27, 2] Operation: 35-33=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 81:[27, 2], Operations: ['55-28=27', '35-33=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,81 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 81:[33, 8], Operations: ['55-28=27', '35-27=8'] Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 33*8=264, Resulting Numbers: [264] 264,81 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[35, 6], Operations: ['55-28=27', '33-27=6'] Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,81 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 81:[27, 68], Operations: ['55-28=27', '35+33=68'] Exploring Operation: 27+68=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 27*68=1836, Resulting Numbers: [1836] 1836,81 unequal: No Solution Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[33, 62], Operations: ['55-28=27', '35+27=62'] Exploring Operation: 33*62=2046, Resulting Numbers: [2046] 2046,81 unequal: No Solution Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 33+62=95, Resulting Numbers: [95] 95,81 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: 81:[35, 28, 22], Operations: ['55-33=22'] Exploring Operation: 28-22=6, Resulting Numbers: [35, 6] Generated Node #0,4,0: 81:[35, 6] Operation: 28-22=6 Exploring Operation: 35-28=7, Resulting Numbers: [22, 7] Generated Node #0,4,1: 81:[22, 7] Operation: 35-28=7 Exploring Operation: 35+22=57, Resulting Numbers: [28, 57] Generated Node #0,4,2: 81:[28, 57] Operation: 35+22=57 Exploring Operation: 35+28=63, Resulting Numbers: [22, 63] Generated Node #0,4,3: 81:[22, 63] Operation: 35+28=63 Exploring Operation: 35-22=13, Resulting Numbers: [28, 13] Generated Node #0,4,4: 81:[28, 13] Operation: 35-22=13 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 81:[28, 13], Operations: ['55-33=22', '35-22=13'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,81 unequal: No Solution Exploring Operation: 28+13=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 28*13=364, Resulting Numbers: [364] 364,81 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 #0,4,1 Current State: 81:[22, 7], Operations: ['55-33=22', '35-28=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 22*7=154, Resulting Numbers: [154] 154,81 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,81 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 #0,4,0 Current State: 81:[35, 6], Operations: ['55-33=22', '28-22=6'] Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,81 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,81 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 #0,4,3 Current State: 81:[22, 63], Operations: ['55-33=22', '35+28=63'] Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,81 unequal: No Solution Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,81 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 #0,4,2 Current State: 81:[28, 57], Operations: ['55-33=22', '35+22=57'] Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,81 unequal: No Solution Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 81:[28, 33, 20], Operations: ['55-35=20'] Exploring Operation: 28-20=8, Resulting Numbers: [33, 8] Generated Node #0,3,0: 81:[33, 8] Operation: 28-20=8 Exploring Operation: 28+20=48, Resulting Numbers: [33, 48] Generated Node #0,3,1: 81:[33, 48] Operation: 28+20=48 Exploring Operation: 33-20=13, Resulting Numbers: [28, 13] Generated Node #0,3,2: 81:[28, 13] Operation: 33-20=13 Exploring Operation: 28+33=61, Resulting Numbers: [20, 61] Generated Node #0,3,3: 81:[20, 61] Operation: 28+33=61 Exploring Operation: 33-28=5, Resulting Numbers: [20, 5] Generated Node #0,3,4: 81:[20, 5] Operation: 33-28=5 Moving to Node #0,0 Current State: 81:[35, 33, 83], Operations: ['28+55=83'] Exploring Operation: 35-33=2, Resulting Numbers: [83, 2] Generated Node #0,0,0: 81:[83, 2] Operation: 35-33=2 Exploring Operation: 35+33=68, Resulting Numbers: [83, 68] Generated Node #0,0,1: 81:[83, 68] Operation: 35+33=68 Exploring Operation: 83-35=48, Resulting Numbers: [33, 48] Generated Node #0,0,2: 81:[33, 48] Operation: 83-35=48 Exploring Operation: 35+83=118, Resulting Numbers: [33, 118] Generated Node #0,0,3: 81:[33, 118] Operation: 35+83=118 Exploring Operation: 83-33=50, Resulting Numbers: [35, 50] Generated Node #0,0,4: 81:[35, 50] Operation: 83-33=50 Moving to Node #0,2 Current State: 81:[28, 33, 90], Operations: ['35+55=90'] Exploring Operation: 28+33=61, Resulting Numbers: [90, 61] Generated Node #0,2,0: 81:[90, 61] Operation: 28+33=61 Exploring Operation: 90-28=62, Resulting Numbers: [33, 62] Generated Node #0,2,1: 81:[33, 62] Operation: 90-28=62 Exploring Operation: 28+90=118, Resulting Numbers: [33, 118] Generated Node #0,2,2: 81:[33, 118] Operation: 28+90=118 Exploring Operation: 33-28=5, Resulting Numbers: [90, 5] Generated Node #0,2,3: 81:[90, 5] Operation: 33-28=5 Exploring Operation: 90-33=57, Resulting Numbers: [28, 57] Generated Node #0,2,4: 81:[28, 57] Operation: 90-33=57 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 81:[90, 5], Operations: ['35+55=90', '33-28=5'] Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,81 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,81 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[33, 62], Operations: ['35+55=90', '90-28=62'] Exploring Operation: 33*62=2046, Resulting Numbers: [2046] 2046,81 unequal: No Solution Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 33+62=95, Resulting Numbers: [95] 95,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 81:[28, 57], Operations: ['35+55=90', '90-33=57'] Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,81 unequal: No Solution Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[90, 61], Operations: ['35+55=90', '28+33=61'] Exploring Operation: 90+61=151, Resulting Numbers: [151] 151,81 unequal: No Solution Exploring Operation: 90-61=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 90*61=5490, Resulting Numbers: [5490] 5490,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[33, 118], Operations: ['35+55=90', '28+90=118'] Exploring Operation: 33+118=151, Resulting Numbers: [151] 151,81 unequal: No Solution Exploring Operation: 33*118=3894, Resulting Numbers: [3894] 3894,81 unequal: No Solution Exploring Operation: 118-33=85, Resulting Numbers: [85] 85,81 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: 81:[83, 2], Operations: ['28+55=83', '35-33=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[35, 28, 33, 55], Operations: [] Exploring Operation: 28+55=83, Resulting Numbers: [35, 33, 83] Generated Node #0,0: 81:[35, 33, 83] Operation: 28+55=83 Moving to Node #0,0 Current State: 81:[35, 33, 83], Operations: ['28+55=83'] Exploring Operation: 35-33=2, Resulting Numbers: [83, 2] Generated Node #0,0,0: 81:[83, 2] Operation: 35-33=2 Moving to Node #0,0,0 Current State: 81:[83, 2], Operations: ['28+55=83', '35-33=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
0.929688
hs_5
sum_heuristic
[ 30, 72, 12, 16 ]
74
[ "30+72=102", "12+16=28", "102-28=74" ]
Current State: 74:[30, 72, 12, 16], Operations: [] Exploring Operation: 30+72=102, Resulting Numbers: [12, 16, 102] Generated Node #2: [12, 16, 102] from Operation: 30+72=102 Current State: 74:[12, 16, 102], Operations: ['30+72=102'] Exploring Operation: 12+16=28, Resulting Numbers: [102, 28] Generated Node #3: [102, 28] from Operation: 12+16=28 Current State: 74:[102, 28], Operations: ['30+72=102', '12+16=28'] Exploring Operation: 102-28=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[30, 72, 12, 16], Operations: [] Exploring Operation: 16-12=4, Resulting Numbers: [30, 72, 4] Generated Node #0,0: 74:[30, 72, 4] Operation: 16-12=4 Exploring Operation: 12+16=28, Resulting Numbers: [30, 72, 28] Generated Node #0,1: 74:[30, 72, 28] Operation: 12+16=28 Exploring Operation: 30+12=42, Resulting Numbers: [72, 16, 42] Generated Node #0,2: 74:[72, 16, 42] Operation: 30+12=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[30, 72, 4], Operations: ['16-12=4'] Exploring Operation: 30+4=34, Resulting Numbers: [72, 34] Generated Node #0,0,0: 74:[72, 34] Operation: 30+4=34 Exploring Operation: 72-30=42, Resulting Numbers: [4, 42] Generated Node #0,0,1: 74:[4, 42] Operation: 72-30=42 Exploring Operation: 72+4=76, Resulting Numbers: [30, 76] Generated Node #0,0,2: 74:[30, 76] Operation: 72+4=76 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[72, 34], Operations: ['16-12=4', '30+4=34'] Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 72*34=2448, Resulting Numbers: [2448] 2448,74 unequal: No Solution Exploring Operation: 72+34=106, Resulting Numbers: [106] 106,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[4, 42], Operations: ['16-12=4', '72-30=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,74 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 74:[30, 76], Operations: ['16-12=4', '72+4=76'] Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,74 unequal: No Solution Exploring Operation: 30*76=2280, Resulting Numbers: [2280] 2280,74 unequal: No Solution Exploring Operation: 30+76=106, Resulting Numbers: [106] 106,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[30, 72, 28], Operations: ['12+16=28'] Exploring Operation: 30-28=2, Resulting Numbers: [72, 2] Generated Node #0,1,0: 74:[72, 2] Operation: 30-28=2 Exploring Operation: 72-30=42, Resulting Numbers: [28, 42] Generated Node #0,1,1: 74:[28, 42] Operation: 72-30=42 Exploring Operation: 72-28=44, Resulting Numbers: [30, 44] Generated Node #0,1,2: 74:[30, 44] Operation: 72-28=44 Moving to Node #0,1,0 Current State: 74:[72, 2], Operations: ['12+16=28', '30-28=2'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[30, 72, 12, 16], Operations: [] Exploring Operation: 12+16=28, Resulting Numbers: [30, 72, 28] Generated Node #0,1: 74:[30, 72, 28] Operation: 12+16=28 Moving to Node #0,1 Current State: 74:[30, 72, 28], Operations: ['12+16=28'] Exploring Operation: 30-28=2, Resulting Numbers: [72, 2] Generated Node #0,1,0: 74:[72, 2] Operation: 30-28=2 Moving to Node #0,1,0 Current State: 74:[72, 2], Operations: ['12+16=28', '30-28=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 23, 1, 10, 57 ]
71
[ "23+1=24", "57-10=47", "24+47=71" ]
Current State: 71:[23, 1, 10, 57], Operations: [] Exploring Operation: 23+1=24, Resulting Numbers: [10, 57, 24] Generated Node #2: [10, 57, 24] from Operation: 23+1=24 Current State: 71:[10, 57, 24], Operations: ['23+1=24'] Exploring Operation: 57-10=47, Resulting Numbers: [24, 47] Generated Node #3: [24, 47] from Operation: 57-10=47 Current State: 71:[24, 47], Operations: ['23+1=24', '57-10=47'] Exploring Operation: 24+47=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[23, 1, 10, 57], Operations: [] Exploring Operation: 1+10=11, Resulting Numbers: [23, 57, 11] Generated Node #0,0: 71:[23, 57, 11] Operation: 1+10=11 Exploring Operation: 23+1=24, Resulting Numbers: [10, 57, 24] Generated Node #0,1: 71:[10, 57, 24] Operation: 23+1=24 Exploring Operation: 23+10=33, Resulting Numbers: [1, 57, 33] Generated Node #0,2: 71:[1, 57, 33] Operation: 23+10=33 Exploring Operation: 1+57=58, Resulting Numbers: [23, 10, 58] Generated Node #0,3: 71:[23, 10, 58] Operation: 1+57=58 Moving to Node #0,0 Current State: 71:[23, 57, 11], Operations: ['1+10=11'] Exploring Operation: 23+11=34, Resulting Numbers: [57, 34] Generated Node #0,0,0: 71:[57, 34] Operation: 23+11=34 Exploring Operation: 23+57=80, Resulting Numbers: [11, 80] Generated Node #0,0,1: 71:[11, 80] Operation: 23+57=80 Exploring Operation: 57+11=68, Resulting Numbers: [23, 68] Generated Node #0,0,2: 71:[23, 68] Operation: 57+11=68 Exploring Operation: 23-11=12, Resulting Numbers: [57, 12] Generated Node #0,0,3: 71:[57, 12] Operation: 23-11=12 Moving to Node #0,2 Current State: 71:[1, 57, 33], Operations: ['23+10=33'] Exploring Operation: 1*57=57, Resulting Numbers: [33, 57] Generated Node #0,2,0: 71:[33, 57] Operation: 1*57=57 Exploring Operation: 57/1=57, Resulting Numbers: [33, 57] Generated Node #0,2,1: 71:[33, 57] Operation: 57/1=57 Exploring Operation: 1+57=58, Resulting Numbers: [33, 58] Generated Node #0,2,2: 71:[33, 58] Operation: 1+57=58 Exploring Operation: 1+33=34, Resulting Numbers: [57, 34] Generated Node #0,2,3: 71:[57, 34] Operation: 1+33=34 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[33, 58], Operations: ['23+10=33', '1+57=58'] Exploring Operation: 33+58=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,71 unequal: No Solution Exploring Operation: 33*58=1914, Resulting Numbers: [1914] 1914,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 71:[57, 34], Operations: ['23+10=33', '1+33=34'] Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[33, 57], Operations: ['23+10=33', '1*57=57'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[33, 57], Operations: ['23+10=33', '57/1=57'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,71 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: 71:[10, 57, 24], Operations: ['23+1=24'] Exploring Operation: 24-10=14, Resulting Numbers: [57, 14] Generated Node #0,1,0: 71:[57, 14] Operation: 24-10=14 Exploring Operation: 10+57=67, Resulting Numbers: [24, 67] Generated Node #0,1,1: 71:[24, 67] Operation: 10+57=67 Exploring Operation: 57-10=47, Resulting Numbers: [24, 47] Generated Node #0,1,2: 71:[24, 47] Operation: 57-10=47 Exploring Operation: 10+24=34, Resulting Numbers: [57, 34] Generated Node #0,1,3: 71:[57, 34] Operation: 10+24=34 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[24, 67], Operations: ['23+1=24', '10+57=67'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,71 unequal: No Solution Exploring Operation: 24+67=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 24*67=1608, Resulting Numbers: [1608] 1608,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 71:[57, 34], Operations: ['23+1=24', '10+24=34'] Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[57, 14], Operations: ['23+1=24', '24-10=14'] Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[23, 1, 10, 57], Operations: [] Exploring Operation: 23+1=24, Resulting Numbers: [10, 57, 24] Generated Node #0,1: 71:[10, 57, 24] Operation: 23+1=24 Moving to Node #0,1 Current State: 71:[10, 57, 24], Operations: ['23+1=24'] Exploring Operation: 24-10=14, Resulting Numbers: [57, 14] Generated Node #0,1,0: 71:[57, 14] Operation: 24-10=14 Moving to Node #0,1,0 Current State: 71:[57, 14], Operations: ['23+1=24', '24-10=14'] Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 25, 31, 13, 49 ]
92
[ "25+31=56", "49-13=36", "56+36=92" ]
Current State: 92:[25, 31, 13, 49], Operations: [] Exploring Operation: 25+31=56, Resulting Numbers: [13, 49, 56] Generated Node #2: [13, 49, 56] from Operation: 25+31=56 Current State: 92:[13, 49, 56], Operations: ['25+31=56'] Exploring Operation: 49-13=36, Resulting Numbers: [56, 36] Generated Node #3: [56, 36] from Operation: 49-13=36 Current State: 92:[56, 36], Operations: ['25+31=56', '49-13=36'] Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[25, 31, 13, 49], Operations: [] Exploring Operation: 31+13=44, Resulting Numbers: [25, 49, 44] Generated Node #0,0: 92:[25, 49, 44] Operation: 31+13=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[25, 49, 44], Operations: ['31+13=44'] Exploring Operation: 49-25=24, Resulting Numbers: [44, 24] Generated Node #0,0,0: 92:[44, 24] Operation: 49-25=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[44, 24], Operations: ['31+13=44', '49-25=24'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,92 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
[ 1, 31, 5, 19 ]
17
[ "1*31=31", "19-5=14", "31-14=17" ]
Current State: 17:[1, 31, 5, 19], Operations: [] Exploring Operation: 1*31=31, Resulting Numbers: [5, 19, 31] Generated Node #2: [5, 19, 31] from Operation: 1*31=31 Current State: 17:[5, 19, 31], Operations: ['1*31=31'] Exploring Operation: 19-5=14, Resulting Numbers: [31, 14] Generated Node #3: [31, 14] from Operation: 19-5=14 Current State: 17:[31, 14], Operations: ['1*31=31', '19-5=14'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[1, 31, 5, 19], Operations: [] Exploring Operation: 19-1=18, Resulting Numbers: [31, 5, 18] Generated Node #0,0: 17:[31, 5, 18] Operation: 19-1=18 Exploring Operation: 1+5=6, Resulting Numbers: [31, 19, 6] Generated Node #0,1: 17:[31, 19, 6] Operation: 1+5=6 Exploring Operation: 1*31=31, Resulting Numbers: [5, 19, 31] Generated Node #0,2: 17:[5, 19, 31] Operation: 1*31=31 Exploring Operation: 31-1=30, Resulting Numbers: [5, 19, 30] Generated Node #0,3: 17:[5, 19, 30] Operation: 31-1=30 Exploring Operation: 31-5=26, Resulting Numbers: [1, 19, 26] Generated Node #0,4: 17:[1, 19, 26] Operation: 31-5=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[31, 5, 18], Operations: ['19-1=18'] Exploring Operation: 31-18=13, Resulting Numbers: [5, 13] Generated Node #0,0,0: 17:[5, 13] Operation: 31-18=13 Exploring Operation: 5+18=23, Resulting Numbers: [31, 23] Generated Node #0,0,1: 17:[31, 23] Operation: 5+18=23 Exploring Operation: 31+5=36, Resulting Numbers: [18, 36] Generated Node #0,0,2: 17:[18, 36] Operation: 31+5=36 Exploring Operation: 31-5=26, Resulting Numbers: [18, 26] Generated Node #0,0,3: 17:[18, 26] Operation: 31-5=26 Exploring Operation: 18-5=13, Resulting Numbers: [31, 13] Generated Node #0,0,4: 17:[31, 13] Operation: 18-5=13 Moving to Node #0,0,3 Current State: 17:[18, 26], Operations: ['19-1=18', '31-5=26'] Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[5, 13], Operations: ['19-1=18', '31-18=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,17 unequal: No Solution Moving to Node #0,0,4 Current State: 17:[31, 13], Operations: ['19-1=18', '18-5=13'] Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,17 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[31, 23], Operations: ['19-1=18', '5+18=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[18, 36], Operations: ['19-1=18', '31+5=36'] Exploring Operation: 18+36=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 18*36=648, Resulting Numbers: [648] 648,17 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:[31, 19, 6], Operations: ['1+5=6'] Exploring Operation: 31-19=12, Resulting Numbers: [6, 12] Generated Node #0,1,0: 17:[6, 12] Operation: 31-19=12 Exploring Operation: 19-6=13, Resulting Numbers: [31, 13] Generated Node #0,1,1: 17:[31, 13] Operation: 19-6=13 Exploring Operation: 31-6=25, Resulting Numbers: [19, 25] Generated Node #0,1,2: 17:[19, 25] Operation: 31-6=25 Exploring Operation: 31+6=37, Resulting Numbers: [19, 37] Generated Node #0,1,3: 17:[19, 37] Operation: 31+6=37 Exploring Operation: 19+6=25, Resulting Numbers: [31, 25] Generated Node #0,1,4: 17:[31, 25] Operation: 19+6=25 Moving to Node #0,1,2 Current State: 17:[19, 25], Operations: ['1+5=6', '31-6=25'] Exploring Operation: 19*25=475, Resulting Numbers: [475] 475,17 unequal: No Solution Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[6, 12], Operations: ['1+5=6', '31-19=12'] Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[31, 13], Operations: ['1+5=6', '19-6=13'] Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,17 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[19, 37], Operations: ['1+5=6', '31+6=37'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,17 unequal: No Solution Exploring Operation: 19+37=56, Resulting Numbers: [56] 56,17 unequal: No Solution Exploring Operation: 19*37=703, Resulting Numbers: [703] 703,17 unequal: No Solution Moving to Node #0,1,4 Current State: 17:[31, 25], Operations: ['1+5=6', '19+6=25'] Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 31*25=775, Resulting Numbers: [775] 775,17 unequal: No Solution Exploring Operation: 31+25=56, Resulting Numbers: [56] 56,17 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 #0,3 Current State: 17:[5, 19, 30], Operations: ['31-1=30'] Exploring Operation: 30-19=11, Resulting Numbers: [5, 11] Generated Node #0,3,0: 17:[5, 11] Operation: 30-19=11 Exploring Operation: 19-5=14, Resulting Numbers: [30, 14] Generated Node #0,3,1: 17:[30, 14] Operation: 19-5=14 Exploring Operation: 30/5=6, Resulting Numbers: [19, 6] Generated Node #0,3,2: 17:[19, 6] Operation: 30/5=6 Exploring Operation: 5+19=24, Resulting Numbers: [30, 24] Generated Node #0,3,3: 17:[30, 24] Operation: 5+19=24 Exploring Operation: 30-5=25, Resulting Numbers: [19, 25] Generated Node #0,3,4: 17:[19, 25] Operation: 30-5=25 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 17:[19, 25], Operations: ['31-1=30', '30-5=25'] Exploring Operation: 19*25=475, Resulting Numbers: [475] 475,17 unequal: No Solution Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,17 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:[19, 6], Operations: ['31-1=30', '30/5=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,17 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,17 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,17 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 #0,3,1 Current State: 17:[30, 14], Operations: ['31-1=30', '19-5=14'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,17 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:[5, 11], Operations: ['31-1=30', '30-19=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,17 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:[30, 24], Operations: ['31-1=30', '5+19=24'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 30*24=720, Resulting Numbers: [720] 720,17 unequal: No Solution Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,17 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 #0,4 Current State: 17:[1, 19, 26], Operations: ['31-5=26'] Exploring Operation: 19-1=18, Resulting Numbers: [26, 18] Generated Node #0,4,0: 17:[26, 18] Operation: 19-1=18 Exploring Operation: 1*19=19, Resulting Numbers: [26, 19] Generated Node #0,4,1: 17:[26, 19] Operation: 1*19=19 Exploring Operation: 1*26=26, Resulting Numbers: [19, 26] Generated Node #0,4,2: 17:[19, 26] Operation: 1*26=26 Exploring Operation: 26-1=25, Resulting Numbers: [19, 25] Generated Node #0,4,3: 17:[19, 25] Operation: 26-1=25 Exploring Operation: 19/1=19, Resulting Numbers: [26, 19] Generated Node #0,4,4: 17:[26, 19] Operation: 19/1=19 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 17:[26, 18], Operations: ['31-5=26', '19-1=18'] Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 26*18=468, Resulting Numbers: [468] 468,17 unequal: No Solution Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,17 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 #0,4,3 Current State: 17:[19, 25], Operations: ['31-5=26', '26-1=25'] Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 19*25=475, Resulting Numbers: [475] 475,17 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 #0,4,1 Current State: 17:[26, 19], Operations: ['31-5=26', '1*19=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,17 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 #0,4,2 Current State: 17:[19, 26], Operations: ['31-5=26', '1*26=26'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,17 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 #0,4,4 Current State: 17:[26, 19], Operations: ['31-5=26', '19/1=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,17 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:[5, 19, 31], Operations: ['1*31=31'] Exploring Operation: 19-5=14, Resulting Numbers: [31, 14] Generated Node #0,2,0: 17:[31, 14] Operation: 19-5=14 Exploring Operation: 31-5=26, Resulting Numbers: [19, 26] Generated Node #0,2,1: 17:[19, 26] Operation: 31-5=26 Exploring Operation: 31-19=12, Resulting Numbers: [5, 12] Generated Node #0,2,2: 17:[5, 12] Operation: 31-19=12 Exploring Operation: 5+19=24, Resulting Numbers: [31, 24] Generated Node #0,2,3: 17:[31, 24] Operation: 5+19=24 Exploring Operation: 5+31=36, Resulting Numbers: [19, 36] Generated Node #0,2,4: 17:[19, 36] Operation: 5+31=36 Moving to Node #0,2,1 Current State: 17:[19, 26], Operations: ['1*31=31', '31-5=26'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[5, 12], Operations: ['1*31=31', '31-19=12'] Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[1, 31, 5, 19], Operations: [] Exploring Operation: 1*31=31, Resulting Numbers: [5, 19, 31] Generated Node #0,2: 17:[5, 19, 31] Operation: 1*31=31 Moving to Node #0,2 Current State: 17:[5, 19, 31], Operations: ['1*31=31'] Exploring Operation: 31-19=12, Resulting Numbers: [5, 12] Generated Node #0,2,2: 17:[5, 12] Operation: 31-19=12 Moving to Node #0,2,2 Current State: 17:[5, 12], Operations: ['1*31=31', '31-19=12'] Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.913194
hs_5
sum_heuristic
[ 53, 19, 64, 38 ]
68
[ "53-19=34", "64+38=102", "102-34=68" ]
Current State: 68:[53, 19, 64, 38], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [64, 38, 34] Generated Node #2: [64, 38, 34] from Operation: 53-19=34 Current State: 68:[64, 38, 34], Operations: ['53-19=34'] Exploring Operation: 64+38=102, Resulting Numbers: [34, 102] Generated Node #3: [34, 102] from Operation: 64+38=102 Current State: 68:[34, 102], Operations: ['53-19=34', '64+38=102'] Exploring Operation: 102-34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[53, 19, 64, 38], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [64, 38, 34] Generated Node #0,0: 68:[64, 38, 34] Operation: 53-19=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[64, 38, 34], Operations: ['53-19=34'] Exploring Operation: 38-34=4, Resulting Numbers: [64, 4] Generated Node #0,0,0: 68:[64, 4] Operation: 38-34=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[64, 4], Operations: ['53-19=34', '38-34=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[53, 19, 64, 38], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [64, 38, 34] Generated Node #0,0: 68:[64, 38, 34] Operation: 53-19=34 Moving to Node #0,0 Current State: 68:[64, 38, 34], Operations: ['53-19=34'] Exploring Operation: 38-34=4, Resulting Numbers: [64, 4] Generated Node #0,0,0: 68:[64, 4] Operation: 38-34=4 Moving to Node #0,0,0 Current State: 68:[64, 4], Operations: ['53-19=34', '38-34=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 37, 64, 5, 19 ]
46
[ "64-19=45", "45/5=9", "37+9=46" ]
Current State: 46:[37, 64, 5, 19], Operations: [] Exploring Operation: 64-19=45, Resulting Numbers: [37, 5, 45] Generated Node #2: [37, 5, 45] from Operation: 64-19=45 Current State: 46:[37, 5, 45], Operations: ['64-19=45'] Exploring Operation: 45/5=9, Resulting Numbers: [37, 9] Generated Node #3: [37, 9] from Operation: 45/5=9 Current State: 46:[37, 9], Operations: ['64-19=45', '45/5=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[37, 64, 5, 19], Operations: [] Exploring Operation: 64-19=45, Resulting Numbers: [37, 5, 45] Generated Node #0,0: 46:[37, 5, 45] Operation: 64-19=45 Exploring Operation: 64-37=27, Resulting Numbers: [5, 19, 27] Generated Node #0,1: 46:[5, 19, 27] Operation: 64-37=27 Moving to Node #0,1 Current State: 46:[5, 19, 27], Operations: ['64-37=27'] Exploring Operation: 5+19=24, Resulting Numbers: [27, 24] Generated Node #0,1,0: 46:[27, 24] Operation: 5+19=24 Exploring Operation: 19+27=46, Resulting Numbers: [5, 46] Generated Node #0,1,1: 46:[5, 46] Operation: 19+27=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[5, 46], Operations: ['64-37=27', '19+27=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,46 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 #0,1,0 Current State: 46:[27, 24], Operations: ['64-37=27', '5+19=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,46 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: 46:[37, 5, 45], Operations: ['64-19=45'] Exploring Operation: 37+5=42, Resulting Numbers: [45, 42] Generated Node #0,0,0: 46:[45, 42] Operation: 37+5=42 Exploring Operation: 45-37=8, Resulting Numbers: [5, 8] Generated Node #0,0,1: 46:[5, 8] Operation: 45-37=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[45, 42], Operations: ['64-19=45', '37+5=42'] Exploring Operation: 45-42=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 45+42=87, Resulting Numbers: [87] 87,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 46:[5, 8], Operations: ['64-19=45', '45-37=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,46 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 45, 26, 85, 26 ]
92
[ "45-26=19", "85+26=111", "111-19=92" ]
Current State: 92:[45, 26, 85, 26], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [85, 19] Generated Node #2: [85, 19] from Operation: 45-26=19 Current State: 92:[85, 19], Operations: ['45-26=19'] Exploring Operation: 85+26=111, Resulting Numbers: [19, 111] Generated Node #3: [19, 111] from Operation: 85+26=111 Current State: 92:[19, 111], Operations: ['45-26=19', '85+26=111'] Exploring Operation: 111-19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[45, 26, 85, 26], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [26, 26, 40] Generated Node #0,0: 92:[26, 26, 40] Operation: 85-45=40 Exploring Operation: 45-26=19, Resulting Numbers: [85, 26, 19] Generated Node #0,1: 92:[85, 26, 19] Operation: 45-26=19 Exploring Operation: 26-26=0, Resulting Numbers: [45, 85, 0] Generated Node #0,2: 92:[45, 85, 0] Operation: 26-26=0 Exploring Operation: 26/26=1, Resulting Numbers: [45, 85, 1] Generated Node #0,3: 92:[45, 85, 1] Operation: 26/26=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[45, 85, 1], Operations: ['26/26=1'] Exploring Operation: 45*1=45, Resulting Numbers: [85, 45] Generated Node #0,3,0: 92:[85, 45] Operation: 45*1=45 Exploring Operation: 85-45=40, Resulting Numbers: [1, 40] Generated Node #0,3,1: 92:[1, 40] Operation: 85-45=40 Exploring Operation: 45+1=46, Resulting Numbers: [85, 46] Generated Node #0,3,2: 92:[85, 46] Operation: 45+1=46 Exploring Operation: 85+1=86, Resulting Numbers: [45, 86] Generated Node #0,3,3: 92:[45, 86] Operation: 85+1=86 Moving to Node #0,3,1 Current State: 92:[1, 40], Operations: ['26/26=1', '85-45=40'] Exploring Operation: 1+40=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 1*40=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[45, 86], Operations: ['26/26=1', '85+1=86'] Exploring Operation: 45*86=3870, Resulting Numbers: [3870] 3870,92 unequal: No Solution Exploring Operation: 45+86=131, Resulting Numbers: [131] 131,92 unequal: No Solution Exploring Operation: 86-45=41, Resulting Numbers: [41] 41,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[85, 46], Operations: ['26/26=1', '45+1=46'] Exploring Operation: 85+46=131, Resulting Numbers: [131] 131,92 unequal: No Solution Exploring Operation: 85*46=3910, Resulting Numbers: [3910] 3910,92 unequal: No Solution Exploring Operation: 85-46=39, Resulting Numbers: [39] 39,92 unequal: No Solution Moving to Node #0,3,0 Current State: 92:[85, 45], Operations: ['26/26=1', '45*1=45'] Exploring Operation: 85+45=130, Resulting Numbers: [130] 130,92 unequal: No Solution Exploring Operation: 85*45=3825, Resulting Numbers: [3825] 3825,92 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[45, 85, 0], Operations: ['26-26=0'] Exploring Operation: 45+0=45, Resulting Numbers: [85, 45] Generated Node #0,2,0: 92:[85, 45] Operation: 45+0=45 Exploring Operation: 85*0=0, Resulting Numbers: [45, 0] Generated Node #0,2,1: 92:[45, 0] Operation: 85*0=0 Exploring Operation: 45-0=45, Resulting Numbers: [85, 45] Generated Node #0,2,2: 92:[85, 45] Operation: 45-0=45 Exploring Operation: 85-45=40, Resulting Numbers: [0, 40] Generated Node #0,2,3: 92:[0, 40] Operation: 85-45=40 Moving to Node #0,2,1 Current State: 92:[45, 0], Operations: ['26-26=0', '85*0=0'] Exploring Operation: 45-0=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 45+0=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 45*0=0, Resulting Numbers: [0] 0,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[85, 45], Operations: ['26-26=0', '45-0=45'] Exploring Operation: 85*45=3825, Resulting Numbers: [3825] 3825,92 unequal: No Solution Exploring Operation: 85+45=130, Resulting Numbers: [130] 130,92 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,2,0 Current State: 92:[85, 45], Operations: ['26-26=0', '45+0=45'] Exploring Operation: 85+45=130, Resulting Numbers: [130] 130,92 unequal: No Solution Exploring Operation: 85*45=3825, Resulting Numbers: [3825] 3825,92 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[0, 40], Operations: ['26-26=0', '85-45=40'] Exploring Operation: 0*40=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 40-0=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 0+40=40, Resulting Numbers: [40] 40,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[26, 26, 40], Operations: ['85-45=40'] Exploring Operation: 26+26=52, Resulting Numbers: [40, 52] Generated Node #0,0,0: 92:[40, 52] Operation: 26+26=52 Exploring Operation: 26/26=1, Resulting Numbers: [40, 1] Generated Node #0,0,1: 92:[40, 1] Operation: 26/26=1 Exploring Operation: 26-26=0, Resulting Numbers: [40, 0] Generated Node #0,0,2: 92:[40, 0] Operation: 26-26=0 Exploring Operation: 40-26=14, Resulting Numbers: [26, 14] Generated Node #0,0,3: 92:[26, 14] Operation: 40-26=14 Moving to Node #0,0,1 Current State: 92:[40, 1], Operations: ['85-45=40', '26/26=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[40, 0], Operations: ['85-45=40', '26-26=0'] Exploring Operation: 40*0=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 40-0=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,0,3 Current State: 92:[26, 14], Operations: ['85-45=40', '40-26=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,92 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[40, 52], Operations: ['85-45=40', '26+26=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[45, 26, 85, 26], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [26, 26, 40] Generated Node #0,0: 92:[26, 26, 40] Operation: 85-45=40 Moving to Node #0,0 Current State: 92:[26, 26, 40], Operations: ['85-45=40'] Exploring Operation: 26+26=52, Resulting Numbers: [40, 52] Generated Node #0,0,0: 92:[40, 52] Operation: 26+26=52 Moving to Node #0,0,0 Current State: 92:[40, 52], Operations: ['85-45=40', '26+26=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_4
mult_heuristic
[ 54, 1, 34, 21 ]
41
[ "54*1=54", "34-21=13", "54-13=41" ]
Current State: 41:[54, 1, 34, 21], Operations: [] Exploring Operation: 54*1=54, Resulting Numbers: [34, 21, 54] Generated Node #2: [34, 21, 54] from Operation: 54*1=54 Current State: 41:[34, 21, 54], Operations: ['54*1=54'] Exploring Operation: 34-21=13, Resulting Numbers: [54, 13] Generated Node #3: [54, 13] from Operation: 34-21=13 Current State: 41:[54, 13], Operations: ['54*1=54', '34-21=13'] Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[54, 1, 34, 21], Operations: [] Exploring Operation: 54-1=53, Resulting Numbers: [34, 21, 53] Generated Node #0,0: 41:[34, 21, 53] Operation: 54-1=53 Exploring Operation: 1+34=35, Resulting Numbers: [54, 21, 35] Generated Node #0,1: 41:[54, 21, 35] Operation: 1+34=35 Exploring Operation: 1+21=22, Resulting Numbers: [54, 34, 22] Generated Node #0,2: 41:[54, 34, 22] Operation: 1+21=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[34, 21, 53], Operations: ['54-1=53'] Exploring Operation: 34+21=55, Resulting Numbers: [53, 55] Generated Node #0,0,0: 41:[53, 55] Operation: 34+21=55 Exploring Operation: 53-21=32, Resulting Numbers: [34, 32] Generated Node #0,0,1: 41:[34, 32] Operation: 53-21=32 Exploring Operation: 34-21=13, Resulting Numbers: [53, 13] Generated Node #0,0,2: 41:[53, 13] Operation: 34-21=13 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[34, 32], Operations: ['54-1=53', '53-21=32'] Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 34*32=1088, Resulting Numbers: [1088] 1088,41 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[53, 55], Operations: ['54-1=53', '34+21=55'] Exploring Operation: 53*55=2915, Resulting Numbers: [2915] 2915,41 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 53+55=108, Resulting Numbers: [108] 108,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[53, 13], Operations: ['54-1=53', '34-21=13'] Exploring Operation: 53+13=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 53*13=689, Resulting Numbers: [689] 689,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[54, 21, 35], Operations: ['1+34=35'] Exploring Operation: 54-21=33, Resulting Numbers: [35, 33] Generated Node #0,1,0: 41:[35, 33] Operation: 54-21=33 Exploring Operation: 54+21=75, Resulting Numbers: [35, 75] Generated Node #0,1,1: 41:[35, 75] Operation: 54+21=75 Exploring Operation: 21+35=56, Resulting Numbers: [54, 56] Generated Node #0,1,2: 41:[54, 56] Operation: 21+35=56 Moving to Node #0,1,0 Current State: 41:[35, 33], Operations: ['1+34=35', '54-21=33'] Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,41 unequal: No Solution Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[54, 56], Operations: ['1+34=35', '21+35=56'] Exploring Operation: 54*56=3024, Resulting Numbers: [3024] 3024,41 unequal: No Solution Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 54+56=110, Resulting Numbers: [110] 110,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[35, 75], Operations: ['1+34=35', '54+21=75'] Exploring Operation: 35*75=2625, Resulting Numbers: [2625] 2625,41 unequal: No Solution Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[54, 34, 22], Operations: ['1+21=22'] Exploring Operation: 54-34=20, Resulting Numbers: [22, 20] Generated Node #0,2,0: 41:[22, 20] Operation: 54-34=20 Exploring Operation: 54-22=32, Resulting Numbers: [34, 32] Generated Node #0,2,1: 41:[34, 32] Operation: 54-22=32 Exploring Operation: 34+22=56, Resulting Numbers: [54, 56] Generated Node #0,2,2: 41:[54, 56] Operation: 34+22=56 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 41:[34, 32], Operations: ['1+21=22', '54-22=32'] Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,41 unequal: No Solution Exploring Operation: 34*32=1088, Resulting Numbers: [1088] 1088,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[54, 56], Operations: ['1+21=22', '34+22=56'] Exploring Operation: 54*56=3024, Resulting Numbers: [3024] 3024,41 unequal: No Solution Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 54+56=110, Resulting Numbers: [110] 110,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[22, 20], Operations: ['1+21=22', '54-34=20'] Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,41 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 90, 24, 34, 73 ]
27
[ "90-24=66", "73-34=39", "66-39=27" ]
Current State: 27:[90, 24, 34, 73], Operations: [] Exploring Operation: 90-24=66, Resulting Numbers: [34, 73, 66] Generated Node #2: [34, 73, 66] from Operation: 90-24=66 Current State: 27:[34, 73, 66], Operations: ['90-24=66'] Exploring Operation: 73-34=39, Resulting Numbers: [66, 39] Generated Node #3: [66, 39] from Operation: 73-34=39 Current State: 27:[66, 39], Operations: ['90-24=66', '73-34=39'] Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[90, 24, 34, 73], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [24, 34, 17] Generated Node #0,0: 27:[24, 34, 17] Operation: 90-73=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[24, 34, 17], Operations: ['90-73=17'] Exploring Operation: 34/17=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 27:[24, 2] Operation: 34/17=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[24, 2], Operations: ['90-73=17', '34/17=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 36, 5, 20, 94 ]
62
[ "94-36=58", "20/5=4", "58+4=62" ]
Current State: 62:[36, 5, 20, 94], Operations: [] Exploring Operation: 94-36=58, Resulting Numbers: [5, 20, 58] Generated Node #2: [5, 20, 58] from Operation: 94-36=58 Current State: 62:[5, 20, 58], Operations: ['94-36=58'] Exploring Operation: 20/5=4, Resulting Numbers: [58, 4] Generated Node #3: [58, 4] from Operation: 20/5=4 Current State: 62:[58, 4], Operations: ['94-36=58', '20/5=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[36, 5, 20, 94], Operations: [] Exploring Operation: 94-36=58, Resulting Numbers: [5, 20, 58] Generated Node #0,0: 62:[5, 20, 58] Operation: 94-36=58 Moving to Node #0,0 Current State: 62:[5, 20, 58], Operations: ['94-36=58'] Exploring Operation: 20/5=4, Resulting Numbers: [58, 4] Generated Node #0,0,0: 62:[58, 4] Operation: 20/5=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[58, 4], Operations: ['94-36=58', '20/5=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[36, 5, 20, 94], Operations: [] Exploring Operation: 94-36=58, Resulting Numbers: [5, 20, 58] Generated Node #0,0: 62:[5, 20, 58] Operation: 94-36=58 Moving to Node #0,0 Current State: 62:[5, 20, 58], Operations: ['94-36=58'] Exploring Operation: 20/5=4, Resulting Numbers: [58, 4] Generated Node #0,0,0: 62:[58, 4] Operation: 20/5=4 Moving to Node #0,0,0 Current State: 62:[58, 4], Operations: ['94-36=58', '20/5=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 80, 78, 81 ]
62
[ "80-15=65", "81-78=3", "65-3=62" ]
Current State: 62:[15, 80, 78, 81], Operations: [] Exploring Operation: 80-15=65, Resulting Numbers: [78, 81, 65] Generated Node #2: [78, 81, 65] from Operation: 80-15=65 Current State: 62:[78, 81, 65], Operations: ['80-15=65'] Exploring Operation: 81-78=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 81-78=3 Current State: 62:[65, 3], Operations: ['80-15=65', '81-78=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[15, 80, 78, 81], Operations: [] Exploring Operation: 81-80=1, Resulting Numbers: [15, 78, 1] Generated Node #0,0: 62:[15, 78, 1] Operation: 81-80=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[15, 78, 1], Operations: ['81-80=1'] Exploring Operation: 78-15=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 62:[1, 63] Operation: 78-15=63 Moving to Node #0,0,0 Current State: 62:[1, 63], Operations: ['81-80=1', '78-15=63'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[15, 80, 78, 81], Operations: [] Exploring Operation: 81-80=1, Resulting Numbers: [15, 78, 1] Generated Node #0,0: 62:[15, 78, 1] Operation: 81-80=1 Moving to Node #0,0 Current State: 62:[15, 78, 1], Operations: ['81-80=1'] Exploring Operation: 78-15=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 62:[1, 63] Operation: 78-15=63 Moving to Node #0,0,0 Current State: 62:[1, 63], Operations: ['81-80=1', '78-15=63'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 93, 85, 51, 1 ]
42
[ "93-85=8", "51-1=50", "50-8=42" ]
Current State: 42:[93, 85, 51, 1], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [51, 1, 8] Generated Node #2: [51, 1, 8] from Operation: 93-85=8 Current State: 42:[51, 1, 8], Operations: ['93-85=8'] Exploring Operation: 51-1=50, Resulting Numbers: [8, 50] Generated Node #3: [8, 50] from Operation: 51-1=50 Current State: 42:[8, 50], Operations: ['93-85=8', '51-1=50'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[93, 85, 51, 1], Operations: [] Exploring Operation: 93-51=42, Resulting Numbers: [85, 1, 42] Generated Node #0,0: 42:[85, 1, 42] Operation: 93-51=42 Exploring Operation: 93-1=92, Resulting Numbers: [85, 51, 92] Generated Node #0,1: 42:[85, 51, 92] Operation: 93-1=92 Exploring Operation: 93-85=8, Resulting Numbers: [51, 1, 8] Generated Node #0,2: 42:[51, 1, 8] Operation: 93-85=8 Exploring Operation: 85-51=34, Resulting Numbers: [93, 1, 34] Generated Node #0,3: 42:[93, 1, 34] Operation: 85-51=34 Exploring Operation: 85-1=84, Resulting Numbers: [93, 51, 84] Generated Node #0,4: 42:[93, 51, 84] Operation: 85-1=84 Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[51, 1, 8], Operations: ['93-85=8'] Exploring Operation: 51*1=51, Resulting Numbers: [8, 51] Generated Node #0,2,0: 42:[8, 51] Operation: 51*1=51 Exploring Operation: 8-1=7, Resulting Numbers: [51, 7] Generated Node #0,2,1: 42:[51, 7] Operation: 8-1=7 Exploring Operation: 51-1=50, Resulting Numbers: [8, 50] Generated Node #0,2,2: 42:[8, 50] Operation: 51-1=50 Exploring Operation: 51/1=51, Resulting Numbers: [8, 51] Generated Node #0,2,3: 42:[8, 51] Operation: 51/1=51 Exploring Operation: 51-8=43, Resulting Numbers: [1, 43] Generated Node #0,2,4: 42:[1, 43] Operation: 51-8=43 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 42:[1, 43], Operations: ['93-85=8', '51-8=43'] Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,42 unequal: No Solution Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,42 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[93, 85, 51, 1], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [51, 1, 8] Generated Node #0,2: 42:[51, 1, 8] Operation: 93-85=8 Moving to Node #0,2 Current State: 42:[51, 1, 8], Operations: ['93-85=8'] Exploring Operation: 51-8=43, Resulting Numbers: [1, 43] Generated Node #0,2,4: 42:[1, 43] Operation: 51-8=43 Moving to Node #0,2,4 Current State: 42:[1, 43], Operations: ['93-85=8', '51-8=43'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 57, 26, 72, 5 ]
98
[ "57-26=31", "72-5=67", "31+67=98" ]
Current State: 98:[57, 26, 72, 5], Operations: [] Exploring Operation: 57-26=31, Resulting Numbers: [72, 5, 31] Generated Node #2: [72, 5, 31] from Operation: 57-26=31 Current State: 98:[72, 5, 31], Operations: ['57-26=31'] Exploring Operation: 72-5=67, Resulting Numbers: [31, 67] Generated Node #3: [31, 67] from Operation: 72-5=67 Current State: 98:[31, 67], Operations: ['57-26=31', '72-5=67'] Exploring Operation: 31+67=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[57, 26, 72, 5], Operations: [] Exploring Operation: 26+72=98, Resulting Numbers: [57, 5, 98] Generated Node #0,0: 98:[57, 5, 98] Operation: 26+72=98 Moving to Node #0,0 Current State: 98:[57, 5, 98], Operations: ['26+72=98'] Exploring Operation: 57-5=52, Resulting Numbers: [98, 52] Generated Node #0,0,0: 98:[98, 52] Operation: 57-5=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[98, 52], Operations: ['26+72=98', '57-5=52'] Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 32, 16, 14, 79 ]
49
[ "32-16=16", "79-14=65", "65-16=49" ]
Current State: 49:[32, 16, 14, 79], Operations: [] Exploring Operation: 32-16=16, Resulting Numbers: [14, 79, 16] Generated Node #2: [14, 79, 16] from Operation: 32-16=16 Current State: 49:[14, 79, 16], Operations: ['32-16=16'] Exploring Operation: 79-14=65, Resulting Numbers: [16, 65] Generated Node #3: [16, 65] from Operation: 79-14=65 Current State: 49:[16, 65], Operations: ['32-16=16', '79-14=65'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[32, 16, 14, 79], Operations: [] Exploring Operation: 79-32=47, Resulting Numbers: [16, 14, 47] Generated Node #0,0: 49:[16, 14, 47] Operation: 79-32=47 Moving to Node #0,0 Current State: 49:[16, 14, 47], Operations: ['79-32=47'] Exploring Operation: 16-14=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 49:[47, 2] Operation: 16-14=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[47, 2], Operations: ['79-32=47', '16-14=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[32, 16, 14, 79], Operations: [] Exploring Operation: 79-32=47, Resulting Numbers: [16, 14, 47] Generated Node #0,0: 49:[16, 14, 47] Operation: 79-32=47 Moving to Node #0,0 Current State: 49:[16, 14, 47], Operations: ['79-32=47'] Exploring Operation: 16-14=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 49:[47, 2] Operation: 16-14=2 Moving to Node #0,0,0 Current State: 49:[47, 2], Operations: ['79-32=47', '16-14=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 8, 61, 10, 20 ]
55
[ "61-8=53", "20/10=2", "53+2=55" ]
Current State: 55:[8, 61, 10, 20], Operations: [] Exploring Operation: 61-8=53, Resulting Numbers: [10, 20, 53] Generated Node #2: [10, 20, 53] from Operation: 61-8=53 Current State: 55:[10, 20, 53], Operations: ['61-8=53'] Exploring Operation: 20/10=2, Resulting Numbers: [53, 2] Generated Node #3: [53, 2] from Operation: 20/10=2 Current State: 55:[53, 2], Operations: ['61-8=53', '20/10=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[8, 61, 10, 20], Operations: [] Exploring Operation: 20-8=12, Resulting Numbers: [61, 10, 12] Generated Node #0,0: 55:[61, 10, 12] Operation: 20-8=12 Exploring Operation: 61-8=53, Resulting Numbers: [10, 20, 53] Generated Node #0,1: 55:[10, 20, 53] Operation: 61-8=53 Exploring Operation: 20-10=10, Resulting Numbers: [8, 61, 10] Generated Node #0,2: 55:[8, 61, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[61, 10, 12], Operations: ['20-8=12'] Exploring Operation: 12-10=2, Resulting Numbers: [61, 2] Generated Node #0,0,0: 55:[61, 2] Operation: 12-10=2 Exploring Operation: 61-12=49, Resulting Numbers: [10, 49] Generated Node #0,0,1: 55:[10, 49] Operation: 61-12=49 Exploring Operation: 61-10=51, Resulting Numbers: [12, 51] Generated Node #0,0,2: 55:[12, 51] Operation: 61-10=51 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[12, 51], Operations: ['20-8=12', '61-10=51'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,55 unequal: No Solution Exploring Operation: 12+51=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 12*51=612, Resulting Numbers: [612] 612,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[10, 49], Operations: ['20-8=12', '61-12=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,55 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[61, 2], Operations: ['20-8=12', '12-10=2'] Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,55 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: 55:[8, 61, 10], Operations: ['20-10=10'] Exploring Operation: 61-10=51, Resulting Numbers: [8, 51] Generated Node #0,2,0: 55:[8, 51] Operation: 61-10=51 Exploring Operation: 61-8=53, Resulting Numbers: [10, 53] Generated Node #0,2,1: 55:[10, 53] Operation: 61-8=53 Exploring Operation: 10-8=2, Resulting Numbers: [61, 2] Generated Node #0,2,2: 55:[61, 2] Operation: 10-8=2 Moving to Node #0,2,1 Current State: 55:[10, 53], Operations: ['20-10=10', '61-8=53'] Exploring Operation: 10*53=530, Resulting Numbers: [530] 530,55 unequal: No Solution Exploring Operation: 10+53=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[8, 51], Operations: ['20-10=10', '61-10=51'] Exploring Operation: 8*51=408, Resulting Numbers: [408] 408,55 unequal: No Solution Exploring Operation: 8+51=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[61, 2], Operations: ['20-10=10', '10-8=2'] Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,55 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,55 unequal: No Solution No 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: 55:[10, 20, 53], Operations: ['61-8=53'] Exploring Operation: 20/10=2, Resulting Numbers: [53, 2] Generated Node #0,1,0: 55:[53, 2] Operation: 20/10=2 Exploring Operation: 10+53=63, Resulting Numbers: [20, 63] Generated Node #0,1,1: 55:[20, 63] Operation: 10+53=63 Exploring Operation: 20-10=10, Resulting Numbers: [53, 10] Generated Node #0,1,2: 55:[53, 10] Operation: 20-10=10 Moving to Node #0,1,2 Current State: 55:[53, 10], Operations: ['61-8=53', '20-10=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,55 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[53, 2], Operations: ['61-8=53', '20/10=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,55 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[8, 61, 10, 20], Operations: [] Exploring Operation: 61-8=53, Resulting Numbers: [10, 20, 53] Generated Node #0,1: 55:[10, 20, 53] Operation: 61-8=53 Moving to Node #0,1 Current State: 55:[10, 20, 53], Operations: ['61-8=53'] Exploring Operation: 20/10=2, Resulting Numbers: [53, 2] Generated Node #0,1,0: 55:[53, 2] Operation: 20/10=2 Moving to Node #0,1,0 Current State: 55:[53, 2], Operations: ['61-8=53', '20/10=2'] Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_3
mult_heuristic
[ 63, 30, 60, 90 ]
64
[ "30+60=90", "90/90=1", "63+1=64" ]
Current State: 64:[63, 30, 60, 90], Operations: [] Exploring Operation: 30+60=90, Resulting Numbers: [63, 90, 90] Generated Node #2: [63, 90, 90] from Operation: 30+60=90 Current State: 64:[63, 90, 90], Operations: ['30+60=90'] Exploring Operation: 90/90=1, Resulting Numbers: [63, 1] Generated Node #3: [63, 1] from Operation: 90/90=1 Current State: 64:[63, 1], Operations: ['30+60=90', '90/90=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[63, 30, 60, 90], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [63, 60, 3] Generated Node #0,0: 64:[63, 60, 3] Operation: 90/30=3 Exploring Operation: 90-60=30, Resulting Numbers: [63, 30, 30] Generated Node #0,1: 64:[63, 30, 30] Operation: 90-60=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[63, 30, 30], Operations: ['90-60=30'] Exploring Operation: 30/30=1, Resulting Numbers: [63, 1] Generated Node #0,1,0: 64:[63, 1] Operation: 30/30=1 Exploring Operation: 63-30=33, Resulting Numbers: [30, 33] Generated Node #0,1,1: 64:[30, 33] Operation: 63-30=33 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[63, 1], Operations: ['90-60=30', '30/30=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[63, 30, 60, 90], Operations: [] Exploring Operation: 90-60=30, Resulting Numbers: [63, 30, 30] Generated Node #0,1: 64:[63, 30, 30] Operation: 90-60=30 Moving to Node #0,1 Current State: 64:[63, 30, 30], Operations: ['90-60=30'] Exploring Operation: 30/30=1, Resulting Numbers: [63, 1] Generated Node #0,1,0: 64:[63, 1] Operation: 30/30=1 Moving to Node #0,1,0 Current State: 64:[63, 1], Operations: ['90-60=30', '30/30=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 10, 30, 9, 24 ]
72
[ "30/10=3", "9*24=216", "216/3=72" ]
Current State: 72:[10, 30, 9, 24], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [9, 24, 3] Generated Node #2: [9, 24, 3] from Operation: 30/10=3 Current State: 72:[9, 24, 3], Operations: ['30/10=3'] Exploring Operation: 9*24=216, Resulting Numbers: [3, 216] Generated Node #3: [3, 216] from Operation: 9*24=216 Current State: 72:[3, 216], Operations: ['30/10=3', '9*24=216'] Exploring Operation: 216/3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[10, 30, 9, 24], Operations: [] Exploring Operation: 30-10=20, Resulting Numbers: [9, 24, 20] Generated Node #0,0: 72:[9, 24, 20] Operation: 30-10=20 Exploring Operation: 30/10=3, Resulting Numbers: [9, 24, 3] Generated Node #0,1: 72:[9, 24, 3] Operation: 30/10=3 Exploring Operation: 30-24=6, Resulting Numbers: [10, 9, 6] Generated Node #0,2: 72:[10, 9, 6] Operation: 30-24=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[9, 24, 3], Operations: ['30/10=3'] Exploring Operation: 9+3=12, Resulting Numbers: [24, 12] Generated Node #0,1,0: 72:[24, 12] Operation: 9+3=12 Exploring Operation: 9-3=6, Resulting Numbers: [24, 6] Generated Node #0,1,1: 72:[24, 6] Operation: 9-3=6 Exploring Operation: 9/3=3, Resulting Numbers: [24, 3] Generated Node #0,1,2: 72:[24, 3] Operation: 9/3=3 Moving to Node #0,1,0 Current State: 72:[24, 12], Operations: ['30/10=3', '9+3=12'] Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[24, 6], Operations: ['30/10=3', '9-3=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,72 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[24, 3], Operations: ['30/10=3', '9/3=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[10, 30, 9, 24], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [9, 24, 3] Generated Node #0,1: 72:[9, 24, 3] Operation: 30/10=3 Moving to Node #0,1 Current State: 72:[9, 24, 3], Operations: ['30/10=3'] Exploring Operation: 9/3=3, Resulting Numbers: [24, 3] Generated Node #0,1,2: 72:[24, 3] Operation: 9/3=3 Moving to Node #0,1,2 Current State: 72:[24, 3], Operations: ['30/10=3', '9/3=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 30, 43, 49, 54 ]
18
[ "43-30=13", "54-49=5", "13+5=18" ]
Current State: 18:[30, 43, 49, 54], Operations: [] Exploring Operation: 43-30=13, Resulting Numbers: [49, 54, 13] Generated Node #2: [49, 54, 13] from Operation: 43-30=13 Current State: 18:[49, 54, 13], Operations: ['43-30=13'] Exploring Operation: 54-49=5, Resulting Numbers: [13, 5] Generated Node #3: [13, 5] from Operation: 54-49=5 Current State: 18:[13, 5], Operations: ['43-30=13', '54-49=5'] Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[30, 43, 49, 54], Operations: [] Exploring Operation: 54-43=11, Resulting Numbers: [30, 49, 11] Generated Node #0,0: 18:[30, 49, 11] Operation: 54-43=11 Exploring Operation: 54-49=5, Resulting Numbers: [30, 43, 5] Generated Node #0,1: 18:[30, 43, 5] Operation: 54-49=5 Exploring Operation: 54-30=24, Resulting Numbers: [43, 49, 24] Generated Node #0,2: 18:[43, 49, 24] Operation: 54-30=24 Exploring Operation: 49-30=19, Resulting Numbers: [43, 54, 19] Generated Node #0,3: 18:[43, 54, 19] Operation: 49-30=19 Exploring Operation: 49-43=6, Resulting Numbers: [30, 54, 6] Generated Node #0,4: 18:[30, 54, 6] Operation: 49-43=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[30, 43, 5], Operations: ['54-49=5'] Exploring Operation: 43-5=38, Resulting Numbers: [30, 38] Generated Node #0,1,0: 18:[30, 38] Operation: 43-5=38 Exploring Operation: 43-30=13, Resulting Numbers: [5, 13] Generated Node #0,1,1: 18:[5, 13] Operation: 43-30=13 Exploring Operation: 30-5=25, Resulting Numbers: [43, 25] Generated Node #0,1,2: 18:[43, 25] Operation: 30-5=25 Exploring Operation: 30/5=6, Resulting Numbers: [43, 6] Generated Node #0,1,3: 18:[43, 6] Operation: 30/5=6 Exploring Operation: 30+5=35, Resulting Numbers: [43, 35] Generated Node #0,1,4: 18:[43, 35] Operation: 30+5=35 Moving to Node #0,1,1 Current State: 18:[5, 13], Operations: ['54-49=5', '43-30=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[30, 43, 49, 54], Operations: [] Exploring Operation: 54-49=5, Resulting Numbers: [30, 43, 5] Generated Node #0,1: 18:[30, 43, 5] Operation: 54-49=5 Moving to Node #0,1 Current State: 18:[30, 43, 5], Operations: ['54-49=5'] Exploring Operation: 43-30=13, Resulting Numbers: [5, 13] Generated Node #0,1,1: 18:[5, 13] Operation: 43-30=13 Moving to Node #0,1,1 Current State: 18:[5, 13], Operations: ['54-49=5', '43-30=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 6, 6, 42, 20 ]
18
[ "6*42=252", "20-6=14", "252/14=18" ]
Current State: 18:[6, 6, 42, 20], Operations: [] Exploring Operation: 6*42=252, Resulting Numbers: [20, 252] Generated Node #2: [20, 252] from Operation: 6*42=252 Current State: 18:[20, 252], Operations: ['6*42=252'] Exploring Operation: 20-6=14, Resulting Numbers: [252, 14] Generated Node #3: [252, 14] from Operation: 20-6=14 Current State: 18:[252, 14], Operations: ['6*42=252', '20-6=14'] Exploring Operation: 252/14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[6, 6, 42, 20], Operations: [] Exploring Operation: 42-20=22, Resulting Numbers: [6, 6, 22] Generated Node #0,0: 18:[6, 6, 22] Operation: 42-20=22 Exploring Operation: 42-6=36, Resulting Numbers: [6, 20, 36] Generated Node #0,1: 18:[6, 20, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [6, 20, 7] Generated Node #0,2: 18:[6, 20, 7] Operation: 42/6=7 Exploring Operation: 42/6=7, Resulting Numbers: [6, 20, 7] Generated Node #0,3: 18:[6, 20, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [6, 20, 36] Generated Node #0,4: 18:[6, 20, 36] Operation: 42-6=36 Moving to Node #0,2 Current State: 18:[6, 20, 7], Operations: ['42/6=7'] Exploring Operation: 6+7=13, Resulting Numbers: [20, 13] Generated Node #0,2,0: 18:[20, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [20, 1] Generated Node #0,2,1: 18:[20, 1] Operation: 7-6=1 Exploring Operation: 6+20=26, Resulting Numbers: [7, 26] Generated Node #0,2,2: 18:[7, 26] Operation: 6+20=26 Exploring Operation: 20-7=13, Resulting Numbers: [6, 13] Generated Node #0,2,3: 18:[6, 13] Operation: 20-7=13 Exploring Operation: 20-6=14, Resulting Numbers: [7, 14] Generated Node #0,2,4: 18:[7, 14] Operation: 20-6=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[20, 1], Operations: ['42/6=7', '7-6=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,18 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:[6, 13], Operations: ['42/6=7', '20-7=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,18 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:[7, 14], Operations: ['42/6=7', '20-6=14'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,18 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[20, 13], Operations: ['42/6=7', '6+7=13'] Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,18 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:[7, 26], Operations: ['42/6=7', '6+20=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,18 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:[6, 20, 7], Operations: ['42/6=7'] Exploring Operation: 7-6=1, Resulting Numbers: [20, 1] Generated Node #0,3,0: 18:[20, 1] Operation: 7-6=1 Exploring Operation: 20-7=13, Resulting Numbers: [6, 13] Generated Node #0,3,1: 18:[6, 13] Operation: 20-7=13 Exploring Operation: 6+7=13, Resulting Numbers: [20, 13] Generated Node #0,3,2: 18:[20, 13] Operation: 6+7=13 Exploring Operation: 6+20=26, Resulting Numbers: [7, 26] Generated Node #0,3,3: 18:[7, 26] Operation: 6+20=26 Exploring Operation: 20-6=14, Resulting Numbers: [7, 14] Generated Node #0,3,4: 18:[7, 14] Operation: 20-6=14 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[20, 1], Operations: ['42/6=7', '7-6=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,18 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:[6, 13], Operations: ['42/6=7', '20-7=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,18 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,18 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:[7, 14], Operations: ['42/6=7', '20-6=14'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,18 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[20, 13], Operations: ['42/6=7', '6+7=13'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,18 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,18 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 #0,3,3 Current State: 18:[7, 26], Operations: ['42/6=7', '6+20=26'] Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,18 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:[6, 6, 22], Operations: ['42-20=22'] Exploring Operation: 22-6=16, Resulting Numbers: [6, 16] Generated Node #0,0,0: 18:[6, 16] Operation: 22-6=16 Exploring Operation: 6+6=12, Resulting Numbers: [22, 12] Generated Node #0,0,1: 18:[22, 12] Operation: 6+6=12 Exploring Operation: 6-6=0, Resulting Numbers: [22, 0] Generated Node #0,0,2: 18:[22, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [22, 1] Generated Node #0,0,3: 18:[22, 1] Operation: 6/6=1 Exploring Operation: 22-6=16, Resulting Numbers: [6, 16] Generated Node #0,0,4: 18:[6, 16] Operation: 22-6=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[6, 16], Operations: ['42-20=22', '22-6=16'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,18 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:[6, 16], Operations: ['42-20=22', '22-6=16'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,18 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 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:[22, 1], Operations: ['42-20=22', '6/6=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 22+1=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[22, 0], Operations: ['42-20=22', '6-6=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 22*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[22, 12], Operations: ['42-20=22', '6+6=12'] Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,18 unequal: No Solution Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,18 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:[6, 20, 36], Operations: ['42-6=36'] Exploring Operation: 36-6=30, Resulting Numbers: [20, 30] Generated Node #0,1,0: 18:[20, 30] Operation: 36-6=30 Exploring Operation: 36/6=6, Resulting Numbers: [20, 6] Generated Node #0,1,1: 18:[20, 6] Operation: 36/6=6 Exploring Operation: 36-20=16, Resulting Numbers: [6, 16] Generated Node #0,1,2: 18:[6, 16] Operation: 36-20=16 Exploring Operation: 20-6=14, Resulting Numbers: [36, 14] Generated Node #0,1,3: 18:[36, 14] Operation: 20-6=14 Exploring Operation: 6+20=26, Resulting Numbers: [36, 26] Generated Node #0,1,4: 18:[36, 26] Operation: 6+20=26 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[20, 6], Operations: ['42-6=36', '36/6=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,18 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:[6, 16], Operations: ['42-6=36', '36-20=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,18 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:[20, 30], Operations: ['42-6=36', '36-6=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,18 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:[36, 14], Operations: ['42-6=36', '20-6=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,18 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 #0,1,4 Current State: 18:[36, 26], Operations: ['42-6=36', '6+20=26'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,18 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: 18:[6, 20, 36], Operations: ['42-6=36'] Exploring Operation: 36-20=16, Resulting Numbers: [6, 16] Generated Node #0,4,0: 18:[6, 16] Operation: 36-20=16 Exploring Operation: 36-6=30, Resulting Numbers: [20, 30] Generated Node #0,4,1: 18:[20, 30] Operation: 36-6=30 Exploring Operation: 20-6=14, Resulting Numbers: [36, 14] Generated Node #0,4,2: 18:[36, 14] Operation: 20-6=14 Exploring Operation: 36/6=6, Resulting Numbers: [20, 6] Generated Node #0,4,3: 18:[20, 6] Operation: 36/6=6 Exploring Operation: 6+20=26, Resulting Numbers: [36, 26] Generated Node #0,4,4: 18:[36, 26] Operation: 6+20=26 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 18:[6, 16], Operations: ['42-6=36', '36-20=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,18 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 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:[20, 6], Operations: ['42-6=36', '36/6=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 18:[20, 30], Operations: ['42-6=36', '36-6=30'] Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,18 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,18 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:[36, 14], Operations: ['42-6=36', '20-6=14'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,18 unequal: No Solution Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,18 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 #0,4,4 Current State: 18:[36, 26], Operations: ['42-6=36', '6+20=26'] Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,18 unequal: No Solution Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 55, 18, 31, 40 ]
30
[ "55-31=24", "18*40=720", "720/24=30" ]
Current State: 30:[55, 18, 31, 40], Operations: [] Exploring Operation: 55-31=24, Resulting Numbers: [18, 40, 24] Generated Node #2: [18, 40, 24] from Operation: 55-31=24 Current State: 30:[18, 40, 24], Operations: ['55-31=24'] Exploring Operation: 18*40=720, Resulting Numbers: [24, 720] Generated Node #3: [24, 720] from Operation: 18*40=720 Current State: 30:[24, 720], Operations: ['55-31=24', '18*40=720'] Exploring Operation: 720/24=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[55, 18, 31, 40], Operations: [] Exploring Operation: 55-18=37, Resulting Numbers: [31, 40, 37] Generated Node #0,0: 30:[31, 40, 37] Operation: 55-18=37 Exploring Operation: 55-40=15, Resulting Numbers: [18, 31, 15] Generated Node #0,1: 30:[18, 31, 15] Operation: 55-40=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[18, 31, 15], Operations: ['55-40=15'] Exploring Operation: 18-15=3, Resulting Numbers: [31, 3] Generated Node #0,1,0: 30:[31, 3] Operation: 18-15=3 Exploring Operation: 31-18=13, Resulting Numbers: [15, 13] Generated Node #0,1,1: 30:[15, 13] Operation: 31-18=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[31, 3], Operations: ['55-40=15', '18-15=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[15, 13], Operations: ['55-40=15', '31-18=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[31, 40, 37], Operations: ['55-18=37'] Exploring Operation: 40-31=9, Resulting Numbers: [37, 9] Generated Node #0,0,0: 30:[37, 9] Operation: 40-31=9 Exploring Operation: 40-37=3, Resulting Numbers: [31, 3] Generated Node #0,0,1: 30:[31, 3] Operation: 40-37=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[31, 3], Operations: ['55-18=37', '40-37=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,30 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 #0,0,0 Current State: 30:[37, 9], Operations: ['55-18=37', '40-31=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 29, 61, 62, 4 ]
26
[ "61-29=32", "62-4=58", "58-32=26" ]
Current State: 26:[29, 61, 62, 4], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [62, 4, 32] Generated Node #2: [62, 4, 32] from Operation: 61-29=32 Current State: 26:[62, 4, 32], Operations: ['61-29=32'] Exploring Operation: 62-4=58, Resulting Numbers: [32, 58] Generated Node #3: [32, 58] from Operation: 62-4=58 Current State: 26:[32, 58], Operations: ['61-29=32', '62-4=58'] Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[29, 61, 62, 4], Operations: [] Exploring Operation: 62-29=33, Resulting Numbers: [61, 4, 33] Generated Node #0,0: 26:[61, 4, 33] Operation: 62-29=33 Exploring Operation: 61-4=57, Resulting Numbers: [29, 62, 57] Generated Node #0,1: 26:[29, 62, 57] Operation: 61-4=57 Exploring Operation: 62-61=1, Resulting Numbers: [29, 4, 1] Generated Node #0,2: 26:[29, 4, 1] Operation: 62-61=1 Exploring Operation: 61-29=32, Resulting Numbers: [62, 4, 32] Generated Node #0,3: 26:[62, 4, 32] Operation: 61-29=32 Moving to Node #0,2 Current State: 26:[29, 4, 1], Operations: ['62-61=1'] Exploring Operation: 29-1=28, Resulting Numbers: [4, 28] Generated Node #0,2,0: 26:[4, 28] Operation: 29-1=28 Exploring Operation: 29-4=25, Resulting Numbers: [1, 25] Generated Node #0,2,1: 26:[1, 25] Operation: 29-4=25 Exploring Operation: 29*1=29, Resulting Numbers: [4, 29] Generated Node #0,2,2: 26:[4, 29] Operation: 29*1=29 Exploring Operation: 4-1=3, Resulting Numbers: [29, 3] Generated Node #0,2,3: 26:[29, 3] Operation: 4-1=3 Moving to Node #0,3 Current State: 26:[62, 4, 32], Operations: ['61-29=32'] Exploring Operation: 32-4=28, Resulting Numbers: [62, 28] Generated Node #0,3,0: 26:[62, 28] Operation: 32-4=28 Exploring Operation: 62-32=30, Resulting Numbers: [4, 30] Generated Node #0,3,1: 26:[4, 30] Operation: 62-32=30 Exploring Operation: 62-4=58, Resulting Numbers: [32, 58] Generated Node #0,3,2: 26:[32, 58] Operation: 62-4=58 Exploring Operation: 32/4=8, Resulting Numbers: [62, 8] Generated Node #0,3,3: 26:[62, 8] Operation: 32/4=8 Moving to Node #0,0 Current State: 26:[61, 4, 33], Operations: ['62-29=33'] Exploring Operation: 61+4=65, Resulting Numbers: [33, 65] Generated Node #0,0,0: 26:[33, 65] Operation: 61+4=65 Exploring Operation: 33-4=29, Resulting Numbers: [61, 29] Generated Node #0,0,1: 26:[61, 29] Operation: 33-4=29 Exploring Operation: 61-33=28, Resulting Numbers: [4, 28] Generated Node #0,0,2: 26:[4, 28] Operation: 61-33=28 Exploring Operation: 61-4=57, Resulting Numbers: [33, 57] Generated Node #0,0,3: 26:[33, 57] Operation: 61-4=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[4, 28], Operations: ['62-29=33', '61-33=28'] Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,26 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,26 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[61, 29], Operations: ['62-29=33', '33-4=29'] Exploring Operation: 61*29=1769, Resulting Numbers: [1769] 1769,26 unequal: No Solution Exploring Operation: 61+29=90, Resulting Numbers: [90] 90,26 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 26:[33, 57], Operations: ['62-29=33', '61-4=57'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,26 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[33, 65], Operations: ['62-29=33', '61+4=65'] Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,26 unequal: No Solution Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,26 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,26 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: 26:[29, 62, 57], Operations: ['61-4=57'] Exploring Operation: 62-57=5, Resulting Numbers: [29, 5] Generated Node #0,1,0: 26:[29, 5] Operation: 62-57=5 Exploring Operation: 57-29=28, Resulting Numbers: [62, 28] Generated Node #0,1,1: 26:[62, 28] Operation: 57-29=28 Exploring Operation: 29+62=91, Resulting Numbers: [57, 91] Generated Node #0,1,2: 26:[57, 91] Operation: 29+62=91 Exploring Operation: 62-29=33, Resulting Numbers: [57, 33] Generated Node #0,1,3: 26:[57, 33] Operation: 62-29=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[29, 5], Operations: ['61-4=57', '62-57=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,26 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[62, 28], Operations: ['61-4=57', '57-29=28'] Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,26 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 26:[57, 33], Operations: ['61-4=57', '62-29=33'] Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,26 unequal: No Solution Exploring Operation: 57*33=1881, Resulting Numbers: [1881] 1881,26 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[57, 91], Operations: ['61-4=57', '29+62=91'] Exploring Operation: 57*91=5187, Resulting Numbers: [5187] 5187,26 unequal: No Solution Exploring Operation: 91-57=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 57+91=148, Resulting Numbers: [148] 148,26 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: 26:[1, 25], Operations: ['62-61=1', '29-4=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[29, 61, 62, 4], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [29, 4, 1] Generated Node #0,2: 26:[29, 4, 1] Operation: 62-61=1 Moving to Node #0,2 Current State: 26:[29, 4, 1], Operations: ['62-61=1'] Exploring Operation: 29-4=25, Resulting Numbers: [1, 25] Generated Node #0,2,1: 26:[1, 25] Operation: 29-4=25 Moving to Node #0,2,1 Current State: 26:[1, 25], Operations: ['62-61=1', '29-4=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.956597
hs_4
sum_heuristic
[ 48, 24, 60, 2 ]
86
[ "48-24=24", "60+2=62", "24+62=86" ]
Current State: 86:[48, 24, 60, 2], Operations: [] Exploring Operation: 48-24=24, Resulting Numbers: [60, 2, 24] Generated Node #2: [60, 2, 24] from Operation: 48-24=24 Current State: 86:[60, 2, 24], Operations: ['48-24=24'] Exploring Operation: 60+2=62, Resulting Numbers: [24, 62] Generated Node #3: [24, 62] from Operation: 60+2=62 Current State: 86:[24, 62], Operations: ['48-24=24', '60+2=62'] Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[48, 24, 60, 2], Operations: [] Exploring Operation: 60-48=12, Resulting Numbers: [24, 2, 12] Generated Node #0,0: 86:[24, 2, 12] Operation: 60-48=12 Exploring Operation: 24+60=84, Resulting Numbers: [48, 2, 84] Generated Node #0,1: 86:[48, 2, 84] Operation: 24+60=84 Exploring Operation: 48/24=2, Resulting Numbers: [60, 2, 2] Generated Node #0,2: 86:[60, 2, 2] Operation: 48/24=2 Exploring Operation: 60-24=36, Resulting Numbers: [48, 2, 36] Generated Node #0,3: 86:[48, 2, 36] Operation: 60-24=36 Exploring Operation: 24*2=48, Resulting Numbers: [48, 60, 48] Generated Node #0,4: 86:[48, 60, 48] Operation: 24*2=48 Moving to Node #0,1 Current State: 86:[48, 2, 84], Operations: ['24+60=84'] Exploring Operation: 2+84=86, Resulting Numbers: [48, 86] Generated Node #0,1,0: 86:[48, 86] Operation: 2+84=86 Exploring Operation: 48-2=46, Resulting Numbers: [84, 46] Generated Node #0,1,1: 86:[84, 46] Operation: 48-2=46 Exploring Operation: 84-48=36, Resulting Numbers: [2, 36] Generated Node #0,1,2: 86:[2, 36] Operation: 84-48=36 Exploring Operation: 48+2=50, Resulting Numbers: [84, 50] Generated Node #0,1,3: 86:[84, 50] Operation: 48+2=50 Exploring Operation: 84/2=42, Resulting Numbers: [48, 42] Generated Node #0,1,4: 86:[48, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[48, 86], Operations: ['24+60=84', '2+84=86'] Exploring Operation: 48+86=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 48*86=4128, Resulting Numbers: [4128] 4128,86 unequal: No Solution Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,86 unequal: No Solution No 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: 86:[84, 46], Operations: ['24+60=84', '48-2=46'] Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,86 unequal: No Solution Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,86 unequal: No Solution No 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: 86:[48, 42], Operations: ['24+60=84', '84/2=42'] Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,86 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,86 unequal: No Solution No 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: 86:[2, 36], Operations: ['24+60=84', '84-48=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,86 unequal: No Solution No 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: 86:[84, 50], Operations: ['24+60=84', '48+2=50'] Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,86 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,86 unequal: No Solution Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,86 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: 86:[48, 2, 36], Operations: ['60-24=36'] Exploring Operation: 48-2=46, Resulting Numbers: [36, 46] Generated Node #0,3,0: 86:[36, 46] Operation: 48-2=46 Exploring Operation: 48-36=12, Resulting Numbers: [2, 12] Generated Node #0,3,1: 86:[2, 12] Operation: 48-36=12 Exploring Operation: 48+36=84, Resulting Numbers: [2, 84] Generated Node #0,3,2: 86:[2, 84] Operation: 48+36=84 Exploring Operation: 48+2=50, Resulting Numbers: [36, 50] Generated Node #0,3,3: 86:[36, 50] Operation: 48+2=50 Exploring Operation: 2+36=38, Resulting Numbers: [48, 38] Generated Node #0,3,4: 86:[48, 38] Operation: 2+36=38 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 86:[2, 84], Operations: ['60-24=36', '48+36=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,86 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[48, 24, 60, 2], Operations: [] Exploring Operation: 60-24=36, Resulting Numbers: [48, 2, 36] Generated Node #0,3: 86:[48, 2, 36] Operation: 60-24=36 Moving to Node #0,3 Current State: 86:[48, 2, 36], Operations: ['60-24=36'] Exploring Operation: 48+36=84, Resulting Numbers: [2, 84] Generated Node #0,3,2: 86:[2, 84] Operation: 48+36=84 Moving to Node #0,3,2 Current State: 86:[2, 84], Operations: ['60-24=36', '48+36=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 60, 97, 28, 62 ]
71
[ "97-60=37", "62-28=34", "37+34=71" ]
Current State: 71:[60, 97, 28, 62], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [28, 62, 37] Generated Node #2: [28, 62, 37] from Operation: 97-60=37 Current State: 71:[28, 62, 37], Operations: ['97-60=37'] Exploring Operation: 62-28=34, Resulting Numbers: [37, 34] Generated Node #3: [37, 34] from Operation: 62-28=34 Current State: 71:[37, 34], Operations: ['97-60=37', '62-28=34'] Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[60, 97, 28, 62], Operations: [] Exploring Operation: 28+62=90, Resulting Numbers: [60, 97, 90] Generated Node #0,0: 71:[60, 97, 90] Operation: 28+62=90 Exploring Operation: 60+28=88, Resulting Numbers: [97, 62, 88] Generated Node #0,1: 71:[97, 62, 88] Operation: 60+28=88 Exploring Operation: 97-28=69, Resulting Numbers: [60, 62, 69] Generated Node #0,2: 71:[60, 62, 69] Operation: 97-28=69 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[60, 62, 69], Operations: ['97-28=69'] Exploring Operation: 60+62=122, Resulting Numbers: [69, 122] Generated Node #0,2,0: 71:[69, 122] Operation: 60+62=122 Exploring Operation: 60+69=129, Resulting Numbers: [62, 129] Generated Node #0,2,1: 71:[62, 129] Operation: 60+69=129 Exploring Operation: 62-60=2, Resulting Numbers: [69, 2] Generated Node #0,2,2: 71:[69, 2] Operation: 62-60=2 Moving to Node #0,2,0 Current State: 71:[69, 122], Operations: ['97-28=69', '60+62=122'] Exploring Operation: 69*122=8418, Resulting Numbers: [8418] 8418,71 unequal: No Solution Exploring Operation: 122-69=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 69+122=191, Resulting Numbers: [191] 191,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[62, 129], Operations: ['97-28=69', '60+69=129'] Exploring Operation: 62+129=191, Resulting Numbers: [191] 191,71 unequal: No Solution Exploring Operation: 129-62=67, Resulting Numbers: [67] 67,71 unequal: No Solution Exploring Operation: 62*129=7998, Resulting Numbers: [7998] 7998,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[69, 2], Operations: ['97-28=69', '62-60=2'] Exploring Operation: 69*2=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,71 unequal: No Solution Exploring Operation: 69+2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[60, 97, 28, 62], Operations: [] Exploring Operation: 97-28=69, Resulting Numbers: [60, 62, 69] Generated Node #0,2: 71:[60, 62, 69] Operation: 97-28=69 Moving to Node #0,2 Current State: 71:[60, 62, 69], Operations: ['97-28=69'] Exploring Operation: 62-60=2, Resulting Numbers: [69, 2] Generated Node #0,2,2: 71:[69, 2] Operation: 62-60=2 Moving to Node #0,2,2 Current State: 71:[69, 2], Operations: ['97-28=69', '62-60=2'] Exploring Operation: 69+2=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 25, 43, 76, 38 ]
81
[ "43-38=5", "25/5=5", "76+5=81" ]
Current State: 81:[25, 43, 76, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [25, 76, 5] Generated Node #2: [25, 76, 5] from Operation: 43-38=5 Current State: 81:[25, 76, 5], Operations: ['43-38=5'] Exploring Operation: 25/5=5, Resulting Numbers: [76, 5] Generated Node #3: [76, 5] from Operation: 25/5=5 Current State: 81:[76, 5], Operations: ['43-38=5', '25/5=5'] Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[25, 43, 76, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [25, 76, 5] Generated Node #0,0: 81:[25, 76, 5] Operation: 43-38=5 Exploring Operation: 76-43=33, Resulting Numbers: [25, 38, 33] Generated Node #0,1: 81:[25, 38, 33] Operation: 76-43=33 Exploring Operation: 43+38=81, Resulting Numbers: [25, 76, 81] Generated Node #0,2: 81:[25, 76, 81] Operation: 43+38=81 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[25, 76, 81], Operations: ['43+38=81'] Exploring Operation: 81-76=5, Resulting Numbers: [25, 5] Generated Node #0,2,0: 81:[25, 5] Operation: 81-76=5 Exploring Operation: 76-25=51, Resulting Numbers: [81, 51] Generated Node #0,2,1: 81:[81, 51] Operation: 76-25=51 Exploring Operation: 25+76=101, Resulting Numbers: [81, 101] Generated Node #0,2,2: 81:[81, 101] Operation: 25+76=101 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[25, 5], Operations: ['43+38=81', '81-76=5'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 81:[81, 101], Operations: ['43+38=81', '25+76=101'] Exploring Operation: 81+101=182, Resulting Numbers: [182] 182,81 unequal: No Solution Exploring Operation: 101-81=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 81*101=8181, Resulting Numbers: [8181] 8181,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 81:[81, 51], Operations: ['43+38=81', '76-25=51'] Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 81+51=132, Resulting Numbers: [132] 132,81 unequal: No Solution Exploring Operation: 81*51=4131, Resulting Numbers: [4131] 4131,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[25, 76, 5], Operations: ['43-38=5'] Exploring Operation: 25/5=5, Resulting Numbers: [76, 5] Generated Node #0,0,0: 81:[76, 5] Operation: 25/5=5 Exploring Operation: 76+5=81, Resulting Numbers: [25, 81] Generated Node #0,0,1: 81:[25, 81] Operation: 76+5=81 Exploring Operation: 25+5=30, Resulting Numbers: [76, 30] Generated Node #0,0,2: 81:[76, 30] Operation: 25+5=30 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[25, 81], Operations: ['43-38=5', '76+5=81'] Exploring Operation: 25+81=106, Resulting Numbers: [106] 106,81 unequal: No Solution Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 25*81=2025, Resulting Numbers: [2025] 2025,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[76, 5], Operations: ['43-38=5', '25/5=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[25, 43, 76, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [25, 76, 5] Generated Node #0,0: 81:[25, 76, 5] Operation: 43-38=5 Moving to Node #0,0 Current State: 81:[25, 76, 5], Operations: ['43-38=5'] Exploring Operation: 25/5=5, Resulting Numbers: [76, 5] Generated Node #0,0,0: 81:[76, 5] Operation: 25/5=5 Moving to Node #0,0,0 Current State: 81:[76, 5], Operations: ['43-38=5', '25/5=5'] Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 6, 44, 22, 35 ]
63
[ "6+44=50", "35-22=13", "50+13=63" ]
Current State: 63:[6, 44, 22, 35], Operations: [] Exploring Operation: 6+44=50, Resulting Numbers: [22, 35, 50] Generated Node #2: [22, 35, 50] from Operation: 6+44=50 Current State: 63:[22, 35, 50], Operations: ['6+44=50'] Exploring Operation: 35-22=13, Resulting Numbers: [50, 13] Generated Node #3: [50, 13] from Operation: 35-22=13 Current State: 63:[50, 13], Operations: ['6+44=50', '35-22=13'] Exploring Operation: 50+13=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[6, 44, 22, 35], Operations: [] Exploring Operation: 44-22=22, Resulting Numbers: [6, 35, 22] Generated Node #0,0: 63:[6, 35, 22] Operation: 44-22=22 Exploring Operation: 44-35=9, Resulting Numbers: [6, 22, 9] Generated Node #0,1: 63:[6, 22, 9] Operation: 44-35=9 Exploring Operation: 44+22=66, Resulting Numbers: [6, 35, 66] Generated Node #0,2: 63:[6, 35, 66] Operation: 44+22=66 Exploring Operation: 44/22=2, Resulting Numbers: [6, 35, 2] Generated Node #0,3: 63:[6, 35, 2] Operation: 44/22=2 Moving to Node #0,1 Current State: 63:[6, 22, 9], Operations: ['44-35=9'] Exploring Operation: 22-6=16, Resulting Numbers: [9, 16] Generated Node #0,1,0: 63:[9, 16] Operation: 22-6=16 Exploring Operation: 9-6=3, Resulting Numbers: [22, 3] Generated Node #0,1,1: 63:[22, 3] Operation: 9-6=3 Exploring Operation: 6+22=28, Resulting Numbers: [9, 28] Generated Node #0,1,2: 63:[9, 28] Operation: 6+22=28 Exploring Operation: 22-9=13, Resulting Numbers: [6, 13] Generated Node #0,1,3: 63:[6, 13] Operation: 22-9=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[22, 3], Operations: ['44-35=9', '9-6=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[9, 16], Operations: ['44-35=9', '22-6=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,63 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 63:[6, 13], Operations: ['44-35=9', '22-9=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[9, 28], Operations: ['44-35=9', '6+22=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,63 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,63 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: 63:[6, 35, 2], Operations: ['44/22=2'] Exploring Operation: 35-6=29, Resulting Numbers: [2, 29] Generated Node #0,3,0: 63:[2, 29] Operation: 35-6=29 Exploring Operation: 35*2=70, Resulting Numbers: [6, 70] Generated Node #0,3,1: 63:[6, 70] Operation: 35*2=70 Exploring Operation: 35-2=33, Resulting Numbers: [6, 33] Generated Node #0,3,2: 63:[6, 33] Operation: 35-2=33 Exploring Operation: 6/2=3, Resulting Numbers: [35, 3] Generated Node #0,3,3: 63:[35, 3] Operation: 6/2=3 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 63:[6, 70], Operations: ['44/22=2', '35*2=70'] Exploring Operation: 6+70=76, Resulting Numbers: [76] 76,63 unequal: No Solution Exploring Operation: 6*70=420, Resulting Numbers: [420] 420,63 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 63:[2, 29], Operations: ['44/22=2', '35-6=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,63 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,63 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[6, 33], Operations: ['44/22=2', '35-2=33'] Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,63 unequal: No Solution Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,63 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 63:[35, 3], Operations: ['44/22=2', '6/2=3'] Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,63 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,63 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: 63:[6, 35, 22], Operations: ['44-22=22'] Exploring Operation: 35-6=29, Resulting Numbers: [22, 29] Generated Node #0,0,0: 63:[22, 29] Operation: 35-6=29 Exploring Operation: 35+22=57, Resulting Numbers: [6, 57] Generated Node #0,0,1: 63:[6, 57] Operation: 35+22=57 Exploring Operation: 22-6=16, Resulting Numbers: [35, 16] Generated Node #0,0,2: 63:[35, 16] Operation: 22-6=16 Exploring Operation: 35-22=13, Resulting Numbers: [6, 13] Generated Node #0,0,3: 63:[6, 13] Operation: 35-22=13 Moving to Node #0,2 Current State: 63:[6, 35, 66], Operations: ['44+22=66'] Exploring Operation: 66-35=31, Resulting Numbers: [6, 31] Generated Node #0,2,0: 63:[6, 31] Operation: 66-35=31 Exploring Operation: 35-6=29, Resulting Numbers: [66, 29] Generated Node #0,2,1: 63:[66, 29] Operation: 35-6=29 Exploring Operation: 66-6=60, Resulting Numbers: [35, 60] Generated Node #0,2,2: 63:[35, 60] Operation: 66-6=60 Exploring Operation: 66/6=11, Resulting Numbers: [35, 11] Generated Node #0,2,3: 63:[35, 11] Operation: 66/6=11 Moving to Node #0,0,3 Current State: 63:[6, 13], Operations: ['44-22=22', '35-22=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,63 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[6, 57], Operations: ['44-22=22', '35+22=57'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,63 unequal: No Solution Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[6, 44, 22, 35], Operations: [] Exploring Operation: 44-22=22, Resulting Numbers: [6, 35, 22] Generated Node #0,0: 63:[6, 35, 22] Operation: 44-22=22 Moving to Node #0,0 Current State: 63:[6, 35, 22], Operations: ['44-22=22'] Exploring Operation: 35+22=57, Resulting Numbers: [6, 57] Generated Node #0,0,1: 63:[6, 57] Operation: 35+22=57 Moving to Node #0,0,1 Current State: 63:[6, 57], Operations: ['44-22=22', '35+22=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.953993
hs_4
mult_heuristic
[ 45, 32, 5, 37 ]
28
[ "45-32=13", "5*13=65", "65-37=28" ]
Current State: 28:[45, 32, 5, 37], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [5, 37, 13] Generated Node #2: [5, 37, 13] from Operation: 45-32=13 Current State: 28:[5, 37, 13], Operations: ['45-32=13'] Exploring Operation: 5*13=65, Resulting Numbers: [37, 65] Generated Node #3: [37, 65] from Operation: 5*13=65 Current State: 28:[37, 65], Operations: ['45-32=13', '5*13=65'] Exploring Operation: 65-37=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[45, 32, 5, 37], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [5, 37, 13] Generated Node #0,0: 28:[5, 37, 13] Operation: 45-32=13 Exploring Operation: 37-32=5, Resulting Numbers: [45, 5, 5] Generated Node #0,1: 28:[45, 5, 5] Operation: 37-32=5 Exploring Operation: 45-37=8, Resulting Numbers: [32, 5, 8] Generated Node #0,2: 28:[32, 5, 8] Operation: 45-37=8 Exploring Operation: 45/5=9, Resulting Numbers: [32, 37, 9] Generated Node #0,3: 28:[32, 37, 9] Operation: 45/5=9 Moving to Node #0,2 Current State: 28:[32, 5, 8], Operations: ['45-37=8'] Exploring Operation: 32-8=24, Resulting Numbers: [5, 24] Generated Node #0,2,0: 28:[5, 24] Operation: 32-8=24 Exploring Operation: 32/8=4, Resulting Numbers: [5, 4] Generated Node #0,2,1: 28:[5, 4] Operation: 32/8=4 Exploring Operation: 32-5=27, Resulting Numbers: [8, 27] Generated Node #0,2,2: 28:[8, 27] Operation: 32-5=27 Exploring Operation: 5+8=13, Resulting Numbers: [32, 13] Generated Node #0,2,3: 28:[32, 13] Operation: 5+8=13 Moving to Node #0,0 Current State: 28:[5, 37, 13], Operations: ['45-32=13'] Exploring Operation: 5+13=18, Resulting Numbers: [37, 18] Generated Node #0,0,0: 28:[37, 18] Operation: 5+13=18 Exploring Operation: 13-5=8, Resulting Numbers: [37, 8] Generated Node #0,0,1: 28:[37, 8] Operation: 13-5=8 Exploring Operation: 37-13=24, Resulting Numbers: [5, 24] Generated Node #0,0,2: 28:[5, 24] Operation: 37-13=24 Exploring Operation: 37-5=32, Resulting Numbers: [13, 32] Generated Node #0,0,3: 28:[13, 32] Operation: 37-5=32 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 28:[5, 24], Operations: ['45-32=13', '37-13=24'] Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,28 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 28:[13, 32], Operations: ['45-32=13', '37-5=32'] Exploring Operation: 13*32=416, Resulting Numbers: [416] 416,28 unequal: No Solution Exploring Operation: 13+32=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[37, 8], Operations: ['45-32=13', '13-5=8'] Exploring Operation: 37*8=296, Resulting Numbers: [296] 296,28 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 37+8=45, Resulting Numbers: [45] 45,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[37, 18], Operations: ['45-32=13', '5+13=18'] Exploring Operation: 37+18=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 37*18=666, Resulting Numbers: [666] 666,28 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: 28:[32, 37, 9], Operations: ['45/5=9'] Exploring Operation: 32-9=23, Resulting Numbers: [37, 23] Generated Node #0,3,0: 28:[37, 23] Operation: 32-9=23 Exploring Operation: 37-9=28, Resulting Numbers: [32, 28] Generated Node #0,3,1: 28:[32, 28] Operation: 37-9=28 Exploring Operation: 32+9=41, Resulting Numbers: [37, 41] Generated Node #0,3,2: 28:[37, 41] Operation: 32+9=41 Exploring Operation: 37-32=5, Resulting Numbers: [9, 5] Generated Node #0,3,3: 28:[9, 5] Operation: 37-32=5 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 28:[9, 5], Operations: ['45/5=9', '37-32=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 28:[32, 28], Operations: ['45/5=9', '37-9=28'] Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,28 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 28:[37, 23], Operations: ['45/5=9', '32-9=23'] Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,28 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 28:[37, 41], Operations: ['45/5=9', '32+9=41'] Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 37+41=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 37*41=1517, Resulting Numbers: [1517] 1517,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 28:[45, 5, 5], Operations: ['37-32=5'] Exploring Operation: 45/5=9, Resulting Numbers: [5, 9] Generated Node #0,1,0: 28:[5, 9] Operation: 45/5=9 Exploring Operation: 45-5=40, Resulting Numbers: [5, 40] Generated Node #0,1,1: 28:[5, 40] Operation: 45-5=40 Exploring Operation: 45/5=9, Resulting Numbers: [5, 9] Generated Node #0,1,2: 28:[5, 9] Operation: 45/5=9 Exploring Operation: 45-5=40, Resulting Numbers: [5, 40] Generated Node #0,1,3: 28:[5, 40] Operation: 45-5=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[5, 9], Operations: ['37-32=5', '45/5=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[5, 9], Operations: ['37-32=5', '45/5=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[5, 40], Operations: ['37-32=5', '45-5=40'] Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,28 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 28:[5, 40], Operations: ['37-32=5', '45-5=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,28 unequal: No Solution Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,28 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: 28:[5, 4], Operations: ['45-37=8', '32/8=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,28 unequal: No Solution Moving to Node #0,2,2 Current State: 28:[8, 27], Operations: ['45-37=8', '32-5=27'] Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,28 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,28 unequal: No Solution Moving to Node #0,2,3 Current State: 28:[32, 13], Operations: ['45-37=8', '5+8=13'] Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,28 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[5, 24], Operations: ['45-37=8', '32-8=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,28 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 79, 69, 12, 6 ]
48
[ "79-69=10", "6*10=60", "60-12=48" ]
Current State: 48:[79, 69, 12, 6], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [12, 6, 10] Generated Node #2: [12, 6, 10] from Operation: 79-69=10 Current State: 48:[12, 6, 10], Operations: ['79-69=10'] Exploring Operation: 6*10=60, Resulting Numbers: [12, 60] Generated Node #3: [12, 60] from Operation: 6*10=60 Current State: 48:[12, 60], Operations: ['79-69=10', '6*10=60'] Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[79, 69, 12, 6], Operations: [] Exploring Operation: 79-6=73, Resulting Numbers: [69, 12, 73] Generated Node #0,0: 48:[69, 12, 73] Operation: 79-6=73 Exploring Operation: 79-69=10, Resulting Numbers: [12, 6, 10] Generated Node #0,1: 48:[12, 6, 10] Operation: 79-69=10 Exploring Operation: 69-6=63, Resulting Numbers: [79, 12, 63] Generated Node #0,2: 48:[79, 12, 63] Operation: 69-6=63 Exploring Operation: 79-12=67, Resulting Numbers: [69, 6, 67] Generated Node #0,3: 48:[69, 6, 67] Operation: 79-12=67 Exploring Operation: 69-12=57, Resulting Numbers: [79, 6, 57] Generated Node #0,4: 48:[79, 6, 57] Operation: 69-12=57 Moving to Node #0,1 Current State: 48:[12, 6, 10], Operations: ['79-69=10'] Exploring Operation: 12-10=2, Resulting Numbers: [6, 2] Generated Node #0,1,0: 48:[6, 2] Operation: 12-10=2 Exploring Operation: 12-6=6, Resulting Numbers: [10, 6] Generated Node #0,1,1: 48:[10, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [10, 2] Generated Node #0,1,2: 48:[10, 2] Operation: 12/6=2 Exploring Operation: 6+10=16, Resulting Numbers: [12, 16] Generated Node #0,1,3: 48:[12, 16] Operation: 6+10=16 Exploring Operation: 10-6=4, Resulting Numbers: [12, 4] Generated Node #0,1,4: 48:[12, 4] Operation: 10-6=4 Moving to Node #0,4 Current State: 48:[79, 6, 57], Operations: ['69-12=57'] Exploring Operation: 6+57=63, Resulting Numbers: [79, 63] Generated Node #0,4,0: 48:[79, 63] Operation: 6+57=63 Exploring Operation: 79-57=22, Resulting Numbers: [6, 22] Generated Node #0,4,1: 48:[6, 22] Operation: 79-57=22 Exploring Operation: 57-6=51, Resulting Numbers: [79, 51] Generated Node #0,4,2: 48:[79, 51] Operation: 57-6=51 Exploring Operation: 79+6=85, Resulting Numbers: [57, 85] Generated Node #0,4,3: 48:[57, 85] Operation: 79+6=85 Exploring Operation: 79-6=73, Resulting Numbers: [57, 73] Generated Node #0,4,4: 48:[57, 73] Operation: 79-6=73 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 48:[6, 22], Operations: ['69-12=57', '79-57=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 48:[79, 51], Operations: ['69-12=57', '57-6=51'] Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,48 unequal: No Solution Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 48:[57, 73], Operations: ['69-12=57', '79-6=73'] Exploring Operation: 57+73=130, Resulting Numbers: [130] 130,48 unequal: No Solution Exploring Operation: 57*73=4161, Resulting Numbers: [4161] 4161,48 unequal: No Solution Exploring Operation: 73-57=16, Resulting Numbers: [16] 16,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 48:[79, 63], Operations: ['69-12=57', '6+57=63'] Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 79*63=4977, Resulting Numbers: [4977] 4977,48 unequal: No Solution Exploring Operation: 79+63=142, Resulting Numbers: [142] 142,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 48:[57, 85], Operations: ['69-12=57', '79+6=85'] Exploring Operation: 57*85=4845, Resulting Numbers: [4845] 4845,48 unequal: No Solution Exploring Operation: 57+85=142, Resulting Numbers: [142] 142,48 unequal: No Solution Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,48 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: 48:[69, 6, 67], Operations: ['79-12=67'] Exploring Operation: 6+67=73, Resulting Numbers: [69, 73] Generated Node #0,3,0: 48:[69, 73] Operation: 6+67=73 Exploring Operation: 69+6=75, Resulting Numbers: [67, 75] Generated Node #0,3,1: 48:[67, 75] Operation: 69+6=75 Exploring Operation: 69-67=2, Resulting Numbers: [6, 2] Generated Node #0,3,2: 48:[6, 2] Operation: 69-67=2 Exploring Operation: 69-6=63, Resulting Numbers: [67, 63] Generated Node #0,3,3: 48:[67, 63] Operation: 69-6=63 Exploring Operation: 67-6=61, Resulting Numbers: [69, 61] Generated Node #0,3,4: 48:[69, 61] Operation: 67-6=61 Moving to Node #0,0 Current State: 48:[69, 12, 73], Operations: ['79-6=73'] Exploring Operation: 69-12=57, Resulting Numbers: [73, 57] Generated Node #0,0,0: 48:[73, 57] Operation: 69-12=57 Exploring Operation: 73-12=61, Resulting Numbers: [69, 61] Generated Node #0,0,1: 48:[69, 61] Operation: 73-12=61 Exploring Operation: 69+12=81, Resulting Numbers: [73, 81] Generated Node #0,0,2: 48:[73, 81] Operation: 69+12=81 Exploring Operation: 12+73=85, Resulting Numbers: [69, 85] Generated Node #0,0,3: 48:[69, 85] Operation: 12+73=85 Exploring Operation: 73-69=4, Resulting Numbers: [12, 4] Generated Node #0,0,4: 48:[12, 4] Operation: 73-69=4 Moving to Node #0,2 Current State: 48:[79, 12, 63], Operations: ['69-6=63'] Exploring Operation: 79-63=16, Resulting Numbers: [12, 16] Generated Node #0,2,0: 48:[12, 16] Operation: 79-63=16 Exploring Operation: 63-12=51, Resulting Numbers: [79, 51] Generated Node #0,2,1: 48:[79, 51] Operation: 63-12=51 Exploring Operation: 12+63=75, Resulting Numbers: [79, 75] Generated Node #0,2,2: 48:[79, 75] Operation: 12+63=75 Exploring Operation: 79+12=91, Resulting Numbers: [63, 91] Generated Node #0,2,3: 48:[63, 91] Operation: 79+12=91 Exploring Operation: 79-12=67, Resulting Numbers: [63, 67] Generated Node #0,2,4: 48:[63, 67] Operation: 79-12=67 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[12, 16], Operations: ['69-6=63', '79-63=16'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,48 unequal: No Solution Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[79, 51], Operations: ['69-6=63', '63-12=51'] Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,48 unequal: No Solution Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 48:[63, 67], Operations: ['69-6=63', '79-12=67'] Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,48 unequal: No Solution Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[79, 75], Operations: ['69-6=63', '12+63=75'] Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,48 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 48:[63, 91], Operations: ['69-6=63', '79+12=91'] Exploring Operation: 63+91=154, Resulting Numbers: [154] 154,48 unequal: No Solution Exploring Operation: 63*91=5733, Resulting Numbers: [5733] 5733,48 unequal: No Solution Exploring Operation: 91-63=28, Resulting Numbers: [28] 28,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 48:[6, 2], Operations: ['79-69=10', '12-10=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,48 unequal: No Solution Moving to Node #0,1,4 Current State: 48:[12, 4], Operations: ['79-69=10', '10-6=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[79, 69, 12, 6], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [12, 6, 10] Generated Node #0,1: 48:[12, 6, 10] Operation: 79-69=10 Moving to Node #0,1 Current State: 48:[12, 6, 10], Operations: ['79-69=10'] Exploring Operation: 10-6=4, Resulting Numbers: [12, 4] Generated Node #0,1,4: 48:[12, 4] Operation: 10-6=4 Moving to Node #0,1,4 Current State: 48:[12, 4], Operations: ['79-69=10', '10-6=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.940104
hs_5
mult_heuristic
[ 78, 73, 3, 47 ]
94
[ "78-73=5", "5-3=2", "47*2=94" ]
Current State: 94:[78, 73, 3, 47], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [3, 47, 5] Generated Node #2: [3, 47, 5] from Operation: 78-73=5 Current State: 94:[3, 47, 5], Operations: ['78-73=5'] Exploring Operation: 5-3=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 5-3=2 Current State: 94:[47, 2], Operations: ['78-73=5', '5-3=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[78, 73, 3, 47], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [3, 47, 5] Generated Node #0,0: 94:[3, 47, 5] Operation: 78-73=5 Moving to Node #0,0 Current State: 94:[3, 47, 5], Operations: ['78-73=5'] Exploring Operation: 5-3=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 94:[47, 2] Operation: 5-3=2 Moving to Node #0,0,0 Current State: 94:[47, 2], Operations: ['78-73=5', '5-3=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[78, 73, 3, 47], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [3, 47, 5] Generated Node #0,0: 94:[3, 47, 5] Operation: 78-73=5 Moving to Node #0,0 Current State: 94:[3, 47, 5], Operations: ['78-73=5'] Exploring Operation: 5-3=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 94:[47, 2] Operation: 5-3=2 Moving to Node #0,0,0 Current State: 94:[47, 2], Operations: ['78-73=5', '5-3=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 82, 68, 39, 89 ]
64
[ "82-68=14", "89-39=50", "14+50=64" ]
Current State: 64:[82, 68, 39, 89], Operations: [] Exploring Operation: 82-68=14, Resulting Numbers: [39, 89, 14] Generated Node #2: [39, 89, 14] from Operation: 82-68=14 Current State: 64:[39, 89, 14], Operations: ['82-68=14'] Exploring Operation: 89-39=50, Resulting Numbers: [14, 50] Generated Node #3: [14, 50] from Operation: 89-39=50 Current State: 64:[14, 50], Operations: ['82-68=14', '89-39=50'] Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[82, 68, 39, 89], Operations: [] Exploring Operation: 89-39=50, Resulting Numbers: [82, 68, 50] Generated Node #0,0: 64:[82, 68, 50] Operation: 89-39=50 Exploring Operation: 89-68=21, Resulting Numbers: [82, 39, 21] Generated Node #0,1: 64:[82, 39, 21] Operation: 89-68=21 Exploring Operation: 89-82=7, Resulting Numbers: [68, 39, 7] Generated Node #0,2: 64:[68, 39, 7] Operation: 89-82=7 Exploring Operation: 82-68=14, Resulting Numbers: [39, 89, 14] Generated Node #0,3: 64:[39, 89, 14] Operation: 82-68=14 Moving to Node #0,2 Current State: 64:[68, 39, 7], Operations: ['89-82=7'] Exploring Operation: 39-7=32, Resulting Numbers: [68, 32] Generated Node #0,2,0: 64:[68, 32] Operation: 39-7=32 Exploring Operation: 68-7=61, Resulting Numbers: [39, 61] Generated Node #0,2,1: 64:[39, 61] Operation: 68-7=61 Exploring Operation: 68+7=75, Resulting Numbers: [39, 75] Generated Node #0,2,2: 64:[39, 75] Operation: 68+7=75 Exploring Operation: 68-39=29, Resulting Numbers: [7, 29] Generated Node #0,2,3: 64:[7, 29] Operation: 68-39=29 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[68, 32], Operations: ['89-82=7', '39-7=32'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,64 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,64 unequal: No Solution Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,64 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 #0,2,3 Current State: 64:[7, 29], Operations: ['89-82=7', '68-39=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,64 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,64 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,64 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 #0,2,1 Current State: 64:[39, 61], Operations: ['89-82=7', '68-7=61'] Exploring Operation: 39+61=100, Resulting Numbers: [100] 100,64 unequal: No Solution Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,64 unequal: No Solution Exploring Operation: 39*61=2379, Resulting Numbers: [2379] 2379,64 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 #0,2,2 Current State: 64:[39, 75], Operations: ['89-82=7', '68+7=75'] Exploring Operation: 39+75=114, Resulting Numbers: [114] 114,64 unequal: No Solution Exploring Operation: 39*75=2925, Resulting Numbers: [2925] 2925,64 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,64 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: 64:[82, 39, 21], Operations: ['89-68=21'] Exploring Operation: 82-21=61, Resulting Numbers: [39, 61] Generated Node #0,1,0: 64:[39, 61] Operation: 82-21=61 Exploring Operation: 39-21=18, Resulting Numbers: [82, 18] Generated Node #0,1,1: 64:[82, 18] Operation: 39-21=18 Exploring Operation: 82-39=43, Resulting Numbers: [21, 43] Generated Node #0,1,2: 64:[21, 43] Operation: 82-39=43 Exploring Operation: 39+21=60, Resulting Numbers: [82, 60] Generated Node #0,1,3: 64:[82, 60] Operation: 39+21=60 Moving to Node #0,3 Current State: 64:[39, 89, 14], Operations: ['82-68=14'] Exploring Operation: 89-14=75, Resulting Numbers: [39, 75] Generated Node #0,3,0: 64:[39, 75] Operation: 89-14=75 Exploring Operation: 39+14=53, Resulting Numbers: [89, 53] Generated Node #0,3,1: 64:[89, 53] Operation: 39+14=53 Exploring Operation: 89-39=50, Resulting Numbers: [14, 50] Generated Node #0,3,2: 64:[14, 50] Operation: 89-39=50 Exploring Operation: 39-14=25, Resulting Numbers: [89, 25] Generated Node #0,3,3: 64:[89, 25] Operation: 39-14=25 Moving to Node #0,0 Current State: 64:[82, 68, 50], Operations: ['89-39=50'] Exploring Operation: 82+50=132, Resulting Numbers: [68, 132] Generated Node #0,0,0: 64:[68, 132] Operation: 82+50=132 Exploring Operation: 68-50=18, Resulting Numbers: [82, 18] Generated Node #0,0,1: 64:[82, 18] Operation: 68-50=18 Exploring Operation: 82-68=14, Resulting Numbers: [50, 14] Generated Node #0,0,2: 64:[50, 14] Operation: 82-68=14 Exploring Operation: 82-50=32, Resulting Numbers: [68, 32] Generated Node #0,0,3: 64:[68, 32] Operation: 82-50=32 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 64:[68, 32], Operations: ['89-39=50', '82-50=32'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,64 unequal: No Solution Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,64 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,64 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 #0,0,2 Current State: 64:[50, 14], Operations: ['89-39=50', '82-68=14'] Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[82, 68, 39, 89], Operations: [] Exploring Operation: 89-39=50, Resulting Numbers: [82, 68, 50] Generated Node #0,0: 64:[82, 68, 50] Operation: 89-39=50 Moving to Node #0,0 Current State: 64:[82, 68, 50], Operations: ['89-39=50'] Exploring Operation: 82-68=14, Resulting Numbers: [50, 14] Generated Node #0,0,2: 64:[50, 14] Operation: 82-68=14 Moving to Node #0,0,2 Current State: 64:[50, 14], Operations: ['89-39=50', '82-68=14'] Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
sum_heuristic
[ 99, 7, 73, 6 ]
83
[ "99*6=594", "7*73=511", "594-511=83" ]
Current State: 83:[99, 7, 73, 6], Operations: [] Exploring Operation: 99*6=594, Resulting Numbers: [7, 73, 594] Generated Node #2: [7, 73, 594] from Operation: 99*6=594 Current State: 83:[7, 73, 594], Operations: ['99*6=594'] Exploring Operation: 7*73=511, Resulting Numbers: [594, 511] Generated Node #3: [594, 511] from Operation: 7*73=511 Current State: 83:[594, 511], Operations: ['99*6=594', '7*73=511'] Exploring Operation: 594-511=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[99, 7, 73, 6], Operations: [] Exploring Operation: 7*6=42, Resulting Numbers: [99, 73, 42] Generated Node #0,0: 83:[99, 73, 42] Operation: 7*6=42 Exploring Operation: 99-7=92, Resulting Numbers: [73, 6, 92] Generated Node #0,1: 83:[73, 6, 92] Operation: 99-7=92 Moving to Node #0,0 Current State: 83:[99, 73, 42], Operations: ['7*6=42'] Exploring Operation: 99-42=57, Resulting Numbers: [73, 57] Generated Node #0,0,0: 83:[73, 57] Operation: 99-42=57 Exploring Operation: 73+42=115, Resulting Numbers: [99, 115] Generated Node #0,0,1: 83:[99, 115] Operation: 73+42=115 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[73, 57], Operations: ['7*6=42', '99-42=57'] Exploring Operation: 73+57=130, Resulting Numbers: [130] 130,83 unequal: No Solution Exploring Operation: 73-57=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[99, 115], Operations: ['7*6=42', '73+42=115'] Exploring Operation: 115-99=16, Resulting Numbers: [16] 16,83 unequal: No Solution Exploring Operation: 99+115=214, Resulting Numbers: [214] 214,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[73, 6, 92], Operations: ['99-7=92'] Exploring Operation: 73+6=79, Resulting Numbers: [92, 79] Generated Node #0,1,0: 83:[92, 79] Operation: 73+6=79 Exploring Operation: 92-6=86, Resulting Numbers: [73, 86] Generated Node #0,1,1: 83:[73, 86] Operation: 92-6=86 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[92, 79], Operations: ['99-7=92', '73+6=79'] Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[73, 86], Operations: ['99-7=92', '92-6=86'] Exploring Operation: 73+86=159, Resulting Numbers: [159] 159,83 unequal: No Solution Exploring Operation: 86-73=13, Resulting Numbers: [13] 13,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 32, 99, 21, 17 ]
93
[ "32+99=131", "21+17=38", "131-38=93" ]
Current State: 93:[32, 99, 21, 17], Operations: [] Exploring Operation: 32+99=131, Resulting Numbers: [21, 17, 131] Generated Node #2: [21, 17, 131] from Operation: 32+99=131 Current State: 93:[21, 17, 131], Operations: ['32+99=131'] Exploring Operation: 21+17=38, Resulting Numbers: [131, 38] Generated Node #3: [131, 38] from Operation: 21+17=38 Current State: 93:[131, 38], Operations: ['32+99=131', '21+17=38'] Exploring Operation: 131-38=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[32, 99, 21, 17], Operations: [] Exploring Operation: 21+17=38, Resulting Numbers: [32, 99, 38] Generated Node #0,0: 93:[32, 99, 38] Operation: 21+17=38 Exploring Operation: 21-17=4, Resulting Numbers: [32, 99, 4] Generated Node #0,1: 93:[32, 99, 4] Operation: 21-17=4 Exploring Operation: 99-17=82, Resulting Numbers: [32, 21, 82] Generated Node #0,2: 93:[32, 21, 82] Operation: 99-17=82 Moving to Node #0,1 Current State: 93:[32, 99, 4], Operations: ['21-17=4'] Exploring Operation: 99-4=95, Resulting Numbers: [32, 95] Generated Node #0,1,0: 93:[32, 95] Operation: 99-4=95 Exploring Operation: 32+4=36, Resulting Numbers: [99, 36] Generated Node #0,1,1: 93:[99, 36] Operation: 32+4=36 Exploring Operation: 32-4=28, Resulting Numbers: [99, 28] Generated Node #0,1,2: 93:[99, 28] Operation: 32-4=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[32, 95], Operations: ['21-17=4', '99-4=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 32*95=3040, Resulting Numbers: [3040] 3040,93 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 93:[99, 28], Operations: ['21-17=4', '32-4=28'] Exploring Operation: 99*28=2772, Resulting Numbers: [2772] 2772,93 unequal: No Solution Exploring Operation: 99+28=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[99, 36], Operations: ['21-17=4', '32+4=36'] Exploring Operation: 99*36=3564, Resulting Numbers: [3564] 3564,93 unequal: No Solution Exploring Operation: 99+36=135, Resulting Numbers: [135] 135,93 unequal: No Solution Exploring Operation: 99-36=63, Resulting Numbers: [63] 63,93 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: 93:[32, 99, 38], Operations: ['21+17=38'] Exploring Operation: 38-32=6, Resulting Numbers: [99, 6] Generated Node #0,0,0: 93:[99, 6] Operation: 38-32=6 Exploring Operation: 32+38=70, Resulting Numbers: [99, 70] Generated Node #0,0,1: 93:[99, 70] Operation: 32+38=70 Exploring Operation: 99-38=61, Resulting Numbers: [32, 61] Generated Node #0,0,2: 93:[32, 61] Operation: 99-38=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[99, 6], Operations: ['21+17=38', '38-32=6'] Exploring Operation: 99*6=594, Resulting Numbers: [594] 594,93 unequal: No Solution Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[32, 99, 21, 17], Operations: [] Exploring Operation: 21+17=38, Resulting Numbers: [32, 99, 38] Generated Node #0,0: 93:[32, 99, 38] Operation: 21+17=38 Moving to Node #0,0 Current State: 93:[32, 99, 38], Operations: ['21+17=38'] Exploring Operation: 38-32=6, Resulting Numbers: [99, 6] Generated Node #0,0,0: 93:[99, 6] Operation: 38-32=6 Moving to Node #0,0,0 Current State: 93:[99, 6], Operations: ['21+17=38', '38-32=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 52, 89, 69, 26 ]
98
[ "52+89=141", "69-26=43", "141-43=98" ]
Current State: 98:[52, 89, 69, 26], Operations: [] Exploring Operation: 52+89=141, Resulting Numbers: [69, 26, 141] Generated Node #2: [69, 26, 141] from Operation: 52+89=141 Current State: 98:[69, 26, 141], Operations: ['52+89=141'] Exploring Operation: 69-26=43, Resulting Numbers: [141, 43] Generated Node #3: [141, 43] from Operation: 69-26=43 Current State: 98:[141, 43], Operations: ['52+89=141', '69-26=43'] Exploring Operation: 141-43=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[52, 89, 69, 26], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [89, 26, 17] Generated Node #0,0: 98:[89, 26, 17] Operation: 69-52=17 Exploring Operation: 69-26=43, Resulting Numbers: [52, 89, 43] Generated Node #0,1: 98:[52, 89, 43] Operation: 69-26=43 Exploring Operation: 89-69=20, Resulting Numbers: [52, 26, 20] Generated Node #0,2: 98:[52, 26, 20] Operation: 89-69=20 Exploring Operation: 69+26=95, Resulting Numbers: [52, 89, 95] Generated Node #0,3: 98:[52, 89, 95] Operation: 69+26=95 Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[52, 89, 95], Operations: ['69+26=95'] Exploring Operation: 95-89=6, Resulting Numbers: [52, 6] Generated Node #0,3,0: 98:[52, 6] Operation: 95-89=6 Exploring Operation: 89-52=37, Resulting Numbers: [95, 37] Generated Node #0,3,1: 98:[95, 37] Operation: 89-52=37 Exploring Operation: 52+89=141, Resulting Numbers: [95, 141] Generated Node #0,3,2: 98:[95, 141] Operation: 52+89=141 Exploring Operation: 95-52=43, Resulting Numbers: [89, 43] Generated Node #0,3,3: 98:[89, 43] Operation: 95-52=43 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 98:[52, 6], Operations: ['69+26=95', '95-89=6'] Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,98 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 98:[95, 37], Operations: ['69+26=95', '89-52=37'] Exploring Operation: 95-37=58, Resulting Numbers: [58] 58,98 unequal: No Solution Exploring Operation: 95+37=132, Resulting Numbers: [132] 132,98 unequal: No Solution Exploring Operation: 95*37=3515, Resulting Numbers: [3515] 3515,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 98:[89, 43], Operations: ['69+26=95', '95-52=43'] Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 89+43=132, Resulting Numbers: [132] 132,98 unequal: No Solution Exploring Operation: 89*43=3827, Resulting Numbers: [3827] 3827,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 98:[95, 141], Operations: ['69+26=95', '52+89=141'] Exploring Operation: 95*141=13395, Resulting Numbers: [13395] 13395,98 unequal: No Solution Exploring Operation: 141-95=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 95+141=236, Resulting Numbers: [236] 236,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[52, 89, 43], Operations: ['69-26=43'] Exploring Operation: 52+43=95, Resulting Numbers: [89, 95] Generated Node #0,1,0: 98:[89, 95] Operation: 52+43=95 Exploring Operation: 52-43=9, Resulting Numbers: [89, 9] Generated Node #0,1,1: 98:[89, 9] Operation: 52-43=9 Exploring Operation: 89-52=37, Resulting Numbers: [43, 37] Generated Node #0,1,2: 98:[43, 37] Operation: 89-52=37 Exploring Operation: 89-43=46, Resulting Numbers: [52, 46] Generated Node #0,1,3: 98:[52, 46] Operation: 89-43=46 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 98:[52, 46], Operations: ['69-26=43', '89-43=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,98 unequal: No Solution Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[52, 89, 69, 26], Operations: [] Exploring Operation: 69-26=43, Resulting Numbers: [52, 89, 43] Generated Node #0,1: 98:[52, 89, 43] Operation: 69-26=43 Moving to Node #0,1 Current State: 98:[52, 89, 43], Operations: ['69-26=43'] Exploring Operation: 89-43=46, Resulting Numbers: [52, 46] Generated Node #0,1,3: 98:[52, 46] Operation: 89-43=46 Moving to Node #0,1,3 Current State: 98:[52, 46], Operations: ['69-26=43', '89-43=46'] Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 84, 10, 18, 69 ]
66
[ "10+18=28", "84/28=3", "69-3=66" ]
Current State: 66:[84, 10, 18, 69], Operations: [] Exploring Operation: 10+18=28, Resulting Numbers: [84, 69, 28] Generated Node #2: [84, 69, 28] from Operation: 10+18=28 Current State: 66:[84, 69, 28], Operations: ['10+18=28'] Exploring Operation: 84/28=3, Resulting Numbers: [69, 3] Generated Node #3: [69, 3] from Operation: 84/28=3 Current State: 66:[69, 3], Operations: ['10+18=28', '84/28=3'] Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[84, 10, 18, 69], Operations: [] Exploring Operation: 84-18=66, Resulting Numbers: [10, 69, 66] Generated Node #0,0: 66:[10, 69, 66] Operation: 84-18=66 Exploring Operation: 84-10=74, Resulting Numbers: [18, 69, 74] Generated Node #0,1: 66:[18, 69, 74] Operation: 84-10=74 Exploring Operation: 84-69=15, Resulting Numbers: [10, 18, 15] Generated Node #0,2: 66:[10, 18, 15] Operation: 84-69=15 Moving to Node #0,0 Current State: 66:[10, 69, 66], Operations: ['84-18=66'] Exploring Operation: 10+69=79, Resulting Numbers: [66, 79] Generated Node #0,0,0: 66:[66, 79] Operation: 10+69=79 Exploring Operation: 69-66=3, Resulting Numbers: [10, 3] Generated Node #0,0,1: 66:[10, 3] Operation: 69-66=3 Exploring Operation: 69-10=59, Resulting Numbers: [66, 59] Generated Node #0,0,2: 66:[66, 59] Operation: 69-10=59 Moving to Node #0,2 Current State: 66:[10, 18, 15], Operations: ['84-69=15'] Exploring Operation: 18+15=33, Resulting Numbers: [10, 33] Generated Node #0,2,0: 66:[10, 33] Operation: 18+15=33 Exploring Operation: 15-10=5, Resulting Numbers: [18, 5] Generated Node #0,2,1: 66:[18, 5] Operation: 15-10=5 Exploring Operation: 18-15=3, Resulting Numbers: [10, 3] Generated Node #0,2,2: 66:[10, 3] Operation: 18-15=3 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[10, 33], Operations: ['84-69=15', '18+15=33'] Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,66 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,66 unequal: No Solution No 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: 66:[10, 3], Operations: ['84-69=15', '18-15=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,66 unequal: No Solution No 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: 66:[18, 5], Operations: ['84-69=15', '15-10=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,66 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: 66:[18, 69, 74], Operations: ['84-10=74'] Exploring Operation: 69-18=51, Resulting Numbers: [74, 51] Generated Node #0,1,0: 66:[74, 51] Operation: 69-18=51 Exploring Operation: 74-69=5, Resulting Numbers: [18, 5] Generated Node #0,1,1: 66:[18, 5] Operation: 74-69=5 Exploring Operation: 74-18=56, Resulting Numbers: [69, 56] Generated Node #0,1,2: 66:[69, 56] Operation: 74-18=56 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[18, 5], Operations: ['84-10=74', '74-69=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,66 unequal: No Solution No 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: 66:[69, 56], Operations: ['84-10=74', '74-18=56'] Exploring Operation: 69*56=3864, Resulting Numbers: [3864] 3864,66 unequal: No Solution Exploring Operation: 69+56=125, Resulting Numbers: [125] 125,66 unequal: No Solution Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,66 unequal: No Solution No 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: 66:[74, 51], Operations: ['84-10=74', '69-18=51'] Exploring Operation: 74+51=125, Resulting Numbers: [125] 125,66 unequal: No Solution Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 74*51=3774, Resulting Numbers: [3774] 3774,66 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: 66:[10, 3], Operations: ['84-18=66', '69-66=3'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[66, 59], Operations: ['84-18=66', '69-10=59'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,66 unequal: No Solution Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,66 unequal: No Solution Exploring Operation: 66*59=3894, Resulting Numbers: [3894] 3894,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[66, 79], Operations: ['84-18=66', '10+69=79'] Exploring Operation: 66+79=145, Resulting Numbers: [145] 145,66 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 66*79=5214, Resulting Numbers: [5214] 5214,66 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 75, 56, 3, 74 ]
58
[ "75-56=19", "3+74=77", "77-19=58" ]
Current State: 58:[75, 56, 3, 74], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [3, 74, 19] Generated Node #2: [3, 74, 19] from Operation: 75-56=19 Current State: 58:[3, 74, 19], Operations: ['75-56=19'] Exploring Operation: 3+74=77, Resulting Numbers: [19, 77] Generated Node #3: [19, 77] from Operation: 3+74=77 Current State: 58:[19, 77], Operations: ['75-56=19', '3+74=77'] Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[75, 56, 3, 74], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [3, 74, 19] Generated Node #0,0: 58:[3, 74, 19] Operation: 75-56=19 Exploring Operation: 75-74=1, Resulting Numbers: [56, 3, 1] Generated Node #0,1: 58:[56, 3, 1] Operation: 75-74=1 Exploring Operation: 75/3=25, Resulting Numbers: [56, 74, 25] Generated Node #0,2: 58:[56, 74, 25] Operation: 75/3=25 Exploring Operation: 74-56=18, Resulting Numbers: [75, 3, 18] Generated Node #0,3: 58:[75, 3, 18] Operation: 74-56=18 Moving to Node #0,1 Current State: 58:[56, 3, 1], Operations: ['75-74=1'] Exploring Operation: 3-1=2, Resulting Numbers: [56, 2] Generated Node #0,1,0: 58:[56, 2] Operation: 3-1=2 Exploring Operation: 56+3=59, Resulting Numbers: [1, 59] Generated Node #0,1,1: 58:[1, 59] Operation: 56+3=59 Exploring Operation: 56+1=57, Resulting Numbers: [3, 57] Generated Node #0,1,2: 58:[3, 57] Operation: 56+1=57 Exploring Operation: 56*1=56, Resulting Numbers: [3, 56] Generated Node #0,1,3: 58:[3, 56] Operation: 56*1=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 58:[56, 2], Operations: ['75-74=1', '3-1=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,58 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,58 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[75, 56, 3, 74], Operations: [] Exploring Operation: 75-74=1, Resulting Numbers: [56, 3, 1] Generated Node #0,1: 58:[56, 3, 1] Operation: 75-74=1 Moving to Node #0,1 Current State: 58:[56, 3, 1], Operations: ['75-74=1'] Exploring Operation: 3-1=2, Resulting Numbers: [56, 2] Generated Node #0,1,0: 58:[56, 2] Operation: 3-1=2 Moving to Node #0,1,0 Current State: 58:[56, 2], Operations: ['75-74=1', '3-1=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 74, 1, 50, 10 ]
69
[ "74*1=74", "50/10=5", "74-5=69" ]
Current State: 69:[74, 1, 50, 10], Operations: [] Exploring Operation: 74*1=74, Resulting Numbers: [50, 10, 74] Generated Node #2: [50, 10, 74] from Operation: 74*1=74 Current State: 69:[50, 10, 74], Operations: ['74*1=74'] Exploring Operation: 50/10=5, Resulting Numbers: [74, 5] Generated Node #3: [74, 5] from Operation: 50/10=5 Current State: 69:[74, 5], Operations: ['74*1=74', '50/10=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[74, 1, 50, 10], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [74, 1, 5] Generated Node #0,0: 69:[74, 1, 5] Operation: 50/10=5 Exploring Operation: 50+10=60, Resulting Numbers: [74, 1, 60] Generated Node #0,1: 69:[74, 1, 60] Operation: 50+10=60 Exploring Operation: 74-50=24, Resulting Numbers: [1, 10, 24] Generated Node #0,2: 69:[1, 10, 24] Operation: 74-50=24 Exploring Operation: 50-10=40, Resulting Numbers: [74, 1, 40] Generated Node #0,3: 69:[74, 1, 40] Operation: 50-10=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[74, 1, 5], Operations: ['50/10=5'] Exploring Operation: 74-5=69, Resulting Numbers: [1, 69] Generated Node #0,0,0: 69:[1, 69] Operation: 74-5=69 Exploring Operation: 5-1=4, Resulting Numbers: [74, 4] Generated Node #0,0,1: 69:[74, 4] Operation: 5-1=4 Exploring Operation: 74-1=73, Resulting Numbers: [5, 73] Generated Node #0,0,2: 69:[5, 73] Operation: 74-1=73 Exploring Operation: 74*1=74, Resulting Numbers: [5, 74] Generated Node #0,0,3: 69:[5, 74] Operation: 74*1=74 Moving to Node #0,0,0 Current State: 69:[1, 69], Operations: ['50/10=5', '74-5=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[74, 1, 50, 10], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [74, 1, 5] Generated Node #0,0: 69:[74, 1, 5] Operation: 50/10=5 Moving to Node #0,0 Current State: 69:[74, 1, 5], Operations: ['50/10=5'] Exploring Operation: 74-5=69, Resulting Numbers: [1, 69] Generated Node #0,0,0: 69:[1, 69] Operation: 74-5=69 Moving to Node #0,0,0 Current State: 69:[1, 69], Operations: ['50/10=5', '74-5=69'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 22, 84, 69, 3 ]
83
[ "22+84=106", "69/3=23", "106-23=83" ]
Current State: 83:[22, 84, 69, 3], Operations: [] Exploring Operation: 22+84=106, Resulting Numbers: [69, 3, 106] Generated Node #2: [69, 3, 106] from Operation: 22+84=106 Current State: 83:[69, 3, 106], Operations: ['22+84=106'] Exploring Operation: 69/3=23, Resulting Numbers: [106, 23] Generated Node #3: [106, 23] from Operation: 69/3=23 Current State: 83:[106, 23], Operations: ['22+84=106', '69/3=23'] Exploring Operation: 106-23=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[22, 84, 69, 3], Operations: [] Exploring Operation: 22*3=66, Resulting Numbers: [84, 69, 66] Generated Node #0,0: 83:[84, 69, 66] Operation: 22*3=66 Exploring Operation: 22+3=25, Resulting Numbers: [84, 69, 25] Generated Node #0,1: 83:[84, 69, 25] Operation: 22+3=25 Exploring Operation: 69+3=72, Resulting Numbers: [22, 84, 72] Generated Node #0,2: 83:[22, 84, 72] Operation: 69+3=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[84, 69, 66], Operations: ['22*3=66'] Exploring Operation: 84+66=150, Resulting Numbers: [69, 150] Generated Node #0,0,0: 83:[69, 150] Operation: 84+66=150 Exploring Operation: 84-66=18, Resulting Numbers: [69, 18] Generated Node #0,0,1: 83:[69, 18] Operation: 84-66=18 Exploring Operation: 69+66=135, Resulting Numbers: [84, 135] Generated Node #0,0,2: 83:[84, 135] Operation: 69+66=135 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[84, 135], Operations: ['22*3=66', '69+66=135'] Exploring Operation: 84*135=11340, Resulting Numbers: [11340] 11340,83 unequal: No Solution Exploring Operation: 84+135=219, Resulting Numbers: [219] 219,83 unequal: No Solution Exploring Operation: 135-84=51, Resulting Numbers: [51] 51,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[69, 18], Operations: ['22*3=66', '84-66=18'] Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,83 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[69, 150], Operations: ['22*3=66', '84+66=150'] Exploring Operation: 69*150=10350, Resulting Numbers: [10350] 10350,83 unequal: No Solution Exploring Operation: 69+150=219, Resulting Numbers: [219] 219,83 unequal: No Solution Exploring Operation: 150-69=81, Resulting Numbers: [81] 81,83 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: 83:[84, 69, 25], Operations: ['22+3=25'] Exploring Operation: 69+25=94, Resulting Numbers: [84, 94] Generated Node #0,1,0: 83:[84, 94] Operation: 69+25=94 Exploring Operation: 84+25=109, Resulting Numbers: [69, 109] Generated Node #0,1,1: 83:[69, 109] Operation: 84+25=109 Exploring Operation: 84-25=59, Resulting Numbers: [69, 59] Generated Node #0,1,2: 83:[69, 59] Operation: 84-25=59 Moving to Node #0,1,0 Current State: 83:[84, 94], Operations: ['22+3=25', '69+25=94'] Exploring Operation: 94-84=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 84*94=7896, Resulting Numbers: [7896] 7896,83 unequal: No Solution Exploring Operation: 84+94=178, Resulting Numbers: [178] 178,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[69, 59], Operations: ['22+3=25', '84-25=59'] Exploring Operation: 69*59=4071, Resulting Numbers: [4071] 4071,83 unequal: No Solution Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 69+59=128, Resulting Numbers: [128] 128,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[69, 109], Operations: ['22+3=25', '84+25=109'] Exploring Operation: 109-69=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 69*109=7521, Resulting Numbers: [7521] 7521,83 unequal: No Solution Exploring Operation: 69+109=178, Resulting Numbers: [178] 178,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[22, 84, 72], Operations: ['69+3=72'] Exploring Operation: 22+84=106, Resulting Numbers: [72, 106] Generated Node #0,2,0: 83:[72, 106] Operation: 22+84=106 Exploring Operation: 84-22=62, Resulting Numbers: [72, 62] Generated Node #0,2,1: 83:[72, 62] Operation: 84-22=62 Exploring Operation: 22+72=94, Resulting Numbers: [84, 94] Generated Node #0,2,2: 83:[84, 94] Operation: 22+72=94 Moving to Node #0,2,2 Current State: 83:[84, 94], Operations: ['69+3=72', '22+72=94'] Exploring Operation: 84*94=7896, Resulting Numbers: [7896] 7896,83 unequal: No Solution Exploring Operation: 94-84=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 84+94=178, Resulting Numbers: [178] 178,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[72, 62], Operations: ['69+3=72', '84-22=62'] Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,83 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[72, 106], Operations: ['69+3=72', '22+84=106'] Exploring Operation: 72+106=178, Resulting Numbers: [178] 178,83 unequal: No Solution Exploring Operation: 72*106=7632, Resulting Numbers: [7632] 7632,83 unequal: No Solution Exploring Operation: 106-72=34, Resulting Numbers: [34] 34,83 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
[ 55, 80, 51, 61 ]
77
[ "51+61=112", "55*112=6160", "6160/80=77" ]
Current State: 77:[55, 80, 51, 61], Operations: [] Exploring Operation: 51+61=112, Resulting Numbers: [55, 80, 112] Generated Node #2: [55, 80, 112] from Operation: 51+61=112 Current State: 77:[55, 80, 112], Operations: ['51+61=112'] Exploring Operation: 55*112=6160, Resulting Numbers: [80, 6160] Generated Node #3: [80, 6160] from Operation: 55*112=6160 Current State: 77:[80, 6160], Operations: ['51+61=112', '55*112=6160'] Exploring Operation: 6160/80=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[55, 80, 51, 61], Operations: [] Exploring Operation: 55+51=106, Resulting Numbers: [80, 61, 106] Generated Node #0,0: 77:[80, 61, 106] Operation: 55+51=106 Exploring Operation: 61-51=10, Resulting Numbers: [55, 80, 10] Generated Node #0,1: 77:[55, 80, 10] Operation: 61-51=10 Exploring Operation: 80-55=25, Resulting Numbers: [51, 61, 25] Generated Node #0,2: 77:[51, 61, 25] Operation: 80-55=25 Exploring Operation: 55-51=4, Resulting Numbers: [80, 61, 4] Generated Node #0,3: 77:[80, 61, 4] Operation: 55-51=4 Exploring Operation: 61-55=6, Resulting Numbers: [80, 51, 6] Generated Node #0,4: 77:[80, 51, 6] Operation: 61-55=6 Moving to Node #0,3 Current State: 77:[80, 61, 4], Operations: ['55-51=4'] Exploring Operation: 80+4=84, Resulting Numbers: [61, 84] Generated Node #0,3,0: 77:[61, 84] Operation: 80+4=84 Exploring Operation: 80-61=19, Resulting Numbers: [4, 19] Generated Node #0,3,1: 77:[4, 19] Operation: 80-61=19 Exploring Operation: 61+4=65, Resulting Numbers: [80, 65] Generated Node #0,3,2: 77:[80, 65] Operation: 61+4=65 Exploring Operation: 80-4=76, Resulting Numbers: [61, 76] Generated Node #0,3,3: 77:[61, 76] Operation: 80-4=76 Exploring Operation: 61-4=57, Resulting Numbers: [80, 57] Generated Node #0,3,4: 77:[80, 57] Operation: 61-4=57 Moving to Node #0,1 Current State: 77:[55, 80, 10], Operations: ['61-51=10'] Exploring Operation: 55-10=45, Resulting Numbers: [80, 45] Generated Node #0,1,0: 77:[80, 45] Operation: 55-10=45 Exploring Operation: 80/10=8, Resulting Numbers: [55, 8] Generated Node #0,1,1: 77:[55, 8] Operation: 80/10=8 Exploring Operation: 55+10=65, Resulting Numbers: [80, 65] Generated Node #0,1,2: 77:[80, 65] Operation: 55+10=65 Exploring Operation: 80-10=70, Resulting Numbers: [55, 70] Generated Node #0,1,3: 77:[55, 70] Operation: 80-10=70 Exploring Operation: 80-55=25, Resulting Numbers: [10, 25] Generated Node #0,1,4: 77:[10, 25] Operation: 80-55=25 Moving to Node #0,4 Current State: 77:[80, 51, 6], Operations: ['61-55=6'] Exploring Operation: 80-6=74, Resulting Numbers: [51, 74] Generated Node #0,4,0: 77:[51, 74] Operation: 80-6=74 Exploring Operation: 80-51=29, Resulting Numbers: [6, 29] Generated Node #0,4,1: 77:[6, 29] Operation: 80-51=29 Exploring Operation: 51-6=45, Resulting Numbers: [80, 45] Generated Node #0,4,2: 77:[80, 45] Operation: 51-6=45 Exploring Operation: 51+6=57, Resulting Numbers: [80, 57] Generated Node #0,4,3: 77:[80, 57] Operation: 51+6=57 Exploring Operation: 80+6=86, Resulting Numbers: [51, 86] Generated Node #0,4,4: 77:[51, 86] Operation: 80+6=86 Moving to Node #0,0 Current State: 77:[80, 61, 106], Operations: ['55+51=106'] Exploring Operation: 61+106=167, Resulting Numbers: [80, 167] Generated Node #0,0,0: 77:[80, 167] Operation: 61+106=167 Exploring Operation: 106-80=26, Resulting Numbers: [61, 26] Generated Node #0,0,1: 77:[61, 26] Operation: 106-80=26 Exploring Operation: 106-61=45, Resulting Numbers: [80, 45] Generated Node #0,0,2: 77:[80, 45] Operation: 106-61=45 Exploring Operation: 80-61=19, Resulting Numbers: [106, 19] Generated Node #0,0,3: 77:[106, 19] Operation: 80-61=19 Exploring Operation: 80+61=141, Resulting Numbers: [106, 141] Generated Node #0,0,4: 77:[106, 141] Operation: 80+61=141 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[61, 26], Operations: ['55+51=106', '106-80=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,77 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 77:[80, 45], Operations: ['55+51=106', '106-61=45'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[106, 19], Operations: ['55+51=106', '80-61=19'] Exploring Operation: 106+19=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 106*19=2014, Resulting Numbers: [2014] 2014,77 unequal: No Solution Exploring Operation: 106-19=87, Resulting Numbers: [87] 87,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[80, 167], Operations: ['55+51=106', '61+106=167'] Exploring Operation: 80+167=247, Resulting Numbers: [247] 247,77 unequal: No Solution Exploring Operation: 167-80=87, Resulting Numbers: [87] 87,77 unequal: No Solution Exploring Operation: 80*167=13360, Resulting Numbers: [13360] 13360,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 77:[106, 141], Operations: ['55+51=106', '80+61=141'] Exploring Operation: 106+141=247, Resulting Numbers: [247] 247,77 unequal: No Solution Exploring Operation: 141-106=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 106*141=14946, Resulting Numbers: [14946] 14946,77 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: 77:[51, 61, 25], Operations: ['80-55=25'] Exploring Operation: 61-51=10, Resulting Numbers: [25, 10] Generated Node #0,2,0: 77:[25, 10] Operation: 61-51=10 Exploring Operation: 51+25=76, Resulting Numbers: [61, 76] Generated Node #0,2,1: 77:[61, 76] Operation: 51+25=76 Exploring Operation: 61+25=86, Resulting Numbers: [51, 86] Generated Node #0,2,2: 77:[51, 86] Operation: 61+25=86 Exploring Operation: 51-25=26, Resulting Numbers: [61, 26] Generated Node #0,2,3: 77:[61, 26] Operation: 51-25=26 Exploring Operation: 51+61=112, Resulting Numbers: [25, 112] Generated Node #0,2,4: 77:[25, 112] Operation: 51+61=112 Moving to Node #0,3,1 Current State: 77:[4, 19], Operations: ['55-51=4', '80-61=19'] Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,77 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[80, 65], Operations: ['61-51=10', '55+10=65'] Exploring Operation: 80+65=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 80*65=5200, Resulting Numbers: [5200] 5200,77 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,77 unequal: No Solution Moving to Node #0,1,4 Current State: 77:[10, 25], Operations: ['61-51=10', '80-55=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[80, 65], Operations: ['55-51=4', '61+4=65'] Exploring Operation: 80+65=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 80*65=5200, Resulting Numbers: [5200] 5200,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[25, 10], Operations: ['80-55=25', '61-51=10'] Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[61, 76], Operations: ['55-51=4', '80-4=76'] Exploring Operation: 61*76=4636, Resulting Numbers: [4636] 4636,77 unequal: No Solution Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 61+76=137, Resulting Numbers: [137] 137,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[61, 76], Operations: ['80-55=25', '51+25=76'] Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 61*76=4636, Resulting Numbers: [4636] 4636,77 unequal: No Solution Exploring Operation: 61+76=137, Resulting Numbers: [137] 137,77 unequal: No Solution Moving to Node #0,4,1 Current State: 77:[6, 29], Operations: ['61-55=6', '80-51=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,77 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,77 unequal: No Solution Moving to Node #0,4,3 Current State: 77:[80, 57], Operations: ['61-55=6', '51+6=57'] Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,77 unequal: No Solution Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,77 unequal: No Solution Moving to Node #0,3,4 Current State: 77:[80, 57], Operations: ['55-51=4', '61-4=57'] Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,77 unequal: No Solution Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[61, 84], Operations: ['55-51=4', '80+4=84'] Exploring Operation: 61+84=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 84-61=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 61*84=5124, Resulting Numbers: [5124] 5124,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[55, 8], Operations: ['61-51=10', '80/10=8'] Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,77 unequal: No Solution Exploring Operation: 55*8=440, Resulting Numbers: [440] 440,77 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,77 unequal: No Solution Moving to Node #0,4,0 Current State: 77:[51, 74], Operations: ['61-55=6', '80-6=74'] Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 51+74=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 51*74=3774, Resulting Numbers: [3774] 3774,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[55, 70], Operations: ['61-51=10', '80-10=70'] Exploring Operation: 55+70=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 55*70=3850, Resulting Numbers: [3850] 3850,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[61, 26], Operations: ['80-55=25', '51-25=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,77 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,77 unequal: No Solution Moving to Node #0,4,4 Current State: 77:[51, 86], Operations: ['61-55=6', '80+6=86'] Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,77 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,77 unequal: No Solution Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[80, 45], Operations: ['61-51=10', '55-10=45'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[51, 86], Operations: ['80-55=25', '61+25=86'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,77 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,77 unequal: No Solution Moving to Node #0,4,2 Current State: 77:[80, 45], Operations: ['61-55=6', '51-6=45'] Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,77 unequal: No Solution Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,77 unequal: No Solution Moving to Node #0,2,4 Current State: 77:[25, 112], Operations: ['80-55=25', '51+61=112'] Exploring Operation: 25*112=2800, Resulting Numbers: [2800] 2800,77 unequal: No Solution Exploring Operation: 112-25=87, Resulting Numbers: [87] 87,77 unequal: No Solution Exploring Operation: 25+112=137, Resulting Numbers: [137] 137,77 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 45, 91, 50, 58 ]
43
[ "58-45=13", "91/13=7", "50-7=43" ]
Current State: 43:[45, 91, 50, 58], Operations: [] Exploring Operation: 58-45=13, Resulting Numbers: [91, 50, 13] Generated Node #2: [91, 50, 13] from Operation: 58-45=13 Current State: 43:[91, 50, 13], Operations: ['58-45=13'] Exploring Operation: 91/13=7, Resulting Numbers: [50, 7] Generated Node #3: [50, 7] from Operation: 91/13=7 Current State: 43:[50, 7], Operations: ['58-45=13', '91/13=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[45, 91, 50, 58], Operations: [] Exploring Operation: 91-58=33, Resulting Numbers: [45, 50, 33] Generated Node #0,0: 43:[45, 50, 33] Operation: 91-58=33 Exploring Operation: 91-50=41, Resulting Numbers: [45, 58, 41] Generated Node #0,1: 43:[45, 58, 41] Operation: 91-50=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[45, 50, 33], Operations: ['91-58=33'] Exploring Operation: 50-33=17, Resulting Numbers: [45, 17] Generated Node #0,0,0: 43:[45, 17] Operation: 50-33=17 Exploring Operation: 45-33=12, Resulting Numbers: [50, 12] Generated Node #0,0,1: 43:[50, 12] Operation: 45-33=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[45, 17], Operations: ['91-58=33', '50-33=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,43 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[50, 12], Operations: ['91-58=33', '45-33=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,43 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[45, 58, 41], Operations: ['91-50=41'] Exploring Operation: 58-45=13, Resulting Numbers: [41, 13] Generated Node #0,1,0: 43:[41, 13] Operation: 58-45=13 Exploring Operation: 58-41=17, Resulting Numbers: [45, 17] Generated Node #0,1,1: 43:[45, 17] Operation: 58-41=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[45, 17], Operations: ['91-50=41', '58-41=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,43 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[41, 13], Operations: ['91-50=41', '58-45=13'] Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 7, 10, 10, 92 ]
100
[ "7+92=99", "10/10=1", "99+1=100" ]
Current State: 100:[7, 10, 10, 92], Operations: [] Exploring Operation: 7+92=99, Resulting Numbers: [10, 10, 99] Generated Node #2: [10, 10, 99] from Operation: 7+92=99 Current State: 100:[10, 10, 99], Operations: ['7+92=99'] Exploring Operation: 10/10=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 10/10=1 Current State: 100:[99, 1], Operations: ['7+92=99', '10/10=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[7, 10, 10, 92], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [10, 92, 3] Generated Node #0,0: 100:[10, 92, 3] Operation: 10-7=3 Exploring Operation: 7+92=99, Resulting Numbers: [10, 10, 99] Generated Node #0,1: 100:[10, 10, 99] Operation: 7+92=99 Exploring Operation: 10+92=102, Resulting Numbers: [7, 10, 102] Generated Node #0,2: 100:[7, 10, 102] Operation: 10+92=102 Exploring Operation: 10+92=102, Resulting Numbers: [7, 10, 102] Generated Node #0,3: 100:[7, 10, 102] Operation: 10+92=102 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[10, 10, 99], Operations: ['7+92=99'] Exploring Operation: 10-10=0, Resulting Numbers: [99, 0] Generated Node #0,1,0: 100:[99, 0] Operation: 10-10=0 Exploring Operation: 10+10=20, Resulting Numbers: [99, 20] Generated Node #0,1,1: 100:[99, 20] Operation: 10+10=20 Exploring Operation: 10/10=1, Resulting Numbers: [99, 1] Generated Node #0,1,2: 100:[99, 1] Operation: 10/10=1 Exploring Operation: 10*10=100, Resulting Numbers: [99, 100] Generated Node #0,1,3: 100:[99, 100] Operation: 10*10=100 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[99, 20], Operations: ['7+92=99', '10+10=20'] Exploring Operation: 99+20=119, Resulting Numbers: [119] 119,100 unequal: No Solution Exploring Operation: 99*20=1980, Resulting Numbers: [1980] 1980,100 unequal: No Solution Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,100 unequal: No Solution No 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: 100:[99, 100], Operations: ['7+92=99', '10*10=100'] Exploring Operation: 99*100=9900, Resulting Numbers: [9900] 9900,100 unequal: No Solution Exploring Operation: 100-99=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 99+100=199, Resulting Numbers: [199] 199,100 unequal: No Solution No 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: 100:[99, 1], Operations: ['7+92=99', '10/10=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[7, 10, 10, 92], Operations: [] Exploring Operation: 7+92=99, Resulting Numbers: [10, 10, 99] Generated Node #0,1: 100:[10, 10, 99] Operation: 7+92=99 Moving to Node #0,1 Current State: 100:[10, 10, 99], Operations: ['7+92=99'] Exploring Operation: 10/10=1, Resulting Numbers: [99, 1] Generated Node #0,1,2: 100:[99, 1] Operation: 10/10=1 Moving to Node #0,1,2 Current State: 100:[99, 1], Operations: ['7+92=99', '10/10=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 98, 26, 62, 46 ]
44
[ "98+26=124", "124/62=2", "46-2=44" ]
Current State: 44:[98, 26, 62, 46], Operations: [] Exploring Operation: 98+26=124, Resulting Numbers: [62, 46, 124] Generated Node #2: [62, 46, 124] from Operation: 98+26=124 Current State: 44:[62, 46, 124], Operations: ['98+26=124'] Exploring Operation: 124/62=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 124/62=2 Current State: 44:[46, 2], Operations: ['98+26=124', '124/62=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[98, 26, 62, 46], Operations: [] Exploring Operation: 62-46=16, Resulting Numbers: [98, 26, 16] Generated Node #0,0: 44:[98, 26, 16] Operation: 62-46=16 Exploring Operation: 98-46=52, Resulting Numbers: [26, 62, 52] Generated Node #0,1: 44:[26, 62, 52] Operation: 98-46=52 Exploring Operation: 98-62=36, Resulting Numbers: [26, 46, 36] Generated Node #0,2: 44:[26, 46, 36] Operation: 98-62=36 Exploring Operation: 98-26=72, Resulting Numbers: [62, 46, 72] Generated Node #0,3: 44:[62, 46, 72] Operation: 98-26=72 Exploring Operation: 62-26=36, Resulting Numbers: [98, 46, 36] Generated Node #0,4: 44:[98, 46, 36] Operation: 62-26=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[26, 46, 36], Operations: ['98-62=36'] Exploring Operation: 36-26=10, Resulting Numbers: [46, 10] Generated Node #0,2,0: 44:[46, 10] Operation: 36-26=10 Exploring Operation: 26+46=72, Resulting Numbers: [36, 72] Generated Node #0,2,1: 44:[36, 72] Operation: 26+46=72 Exploring Operation: 26+36=62, Resulting Numbers: [46, 62] Generated Node #0,2,2: 44:[46, 62] Operation: 26+36=62 Exploring Operation: 46-26=20, Resulting Numbers: [36, 20] Generated Node #0,2,3: 44:[36, 20] Operation: 46-26=20 Exploring Operation: 46-36=10, Resulting Numbers: [26, 10] Generated Node #0,2,4: 44:[26, 10] Operation: 46-36=10 Moving to Node #0,2,0 Current State: 44:[46, 10], Operations: ['98-62=36', '36-26=10'] Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,44 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,44 unequal: No Solution Moving to Node #0,2,4 Current State: 44:[26, 10], Operations: ['98-62=36', '46-36=10'] Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,44 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[36, 20], Operations: ['98-62=36', '46-26=20'] Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,44 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[46, 62], Operations: ['98-62=36', '26+36=62'] Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,44 unequal: No Solution Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[36, 72], Operations: ['98-62=36', '26+46=72'] Exploring Operation: 36*72=2592, Resulting Numbers: [2592] 2592,44 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,44 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 Current State: 44:[26, 62, 52], Operations: ['98-46=52'] Exploring Operation: 26+62=88, Resulting Numbers: [52, 88] Generated Node #0,1,0: 44:[52, 88] Operation: 26+62=88 Exploring Operation: 52/26=2, Resulting Numbers: [62, 2] Generated Node #0,1,1: 44:[62, 2] Operation: 52/26=2 Exploring Operation: 62-26=36, Resulting Numbers: [52, 36] Generated Node #0,1,2: 44:[52, 36] Operation: 62-26=36 Exploring Operation: 52-26=26, Resulting Numbers: [62, 26] Generated Node #0,1,3: 44:[62, 26] Operation: 52-26=26 Exploring Operation: 62-52=10, Resulting Numbers: [26, 10] Generated Node #0,1,4: 44:[26, 10] Operation: 62-52=10 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 44:[26, 10], Operations: ['98-46=52', '62-52=10'] Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 44:[52, 36], Operations: ['98-46=52', '62-26=36'] Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 52+36=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 52*36=1872, Resulting Numbers: [1872] 1872,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 44:[62, 2], Operations: ['98-46=52', '52/26=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,44 unequal: No Solution Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,44 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,44 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 44:[62, 26], Operations: ['98-46=52', '52-26=26'] Exploring Operation: 62*26=1612, Resulting Numbers: [1612] 1612,44 unequal: No Solution Exploring Operation: 62+26=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 62-26=36, Resulting Numbers: [36] 36,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 44:[52, 88], Operations: ['98-46=52', '26+62=88'] Exploring Operation: 88-52=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 52*88=4576, Resulting Numbers: [4576] 4576,44 unequal: No Solution Exploring Operation: 52+88=140, Resulting Numbers: [140] 140,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[62, 46, 72], Operations: ['98-26=72'] Exploring Operation: 62+46=108, Resulting Numbers: [72, 108] Generated Node #0,3,0: 44:[72, 108] Operation: 62+46=108 Exploring Operation: 72-46=26, Resulting Numbers: [62, 26] Generated Node #0,3,1: 44:[62, 26] Operation: 72-46=26 Exploring Operation: 62-46=16, Resulting Numbers: [72, 16] Generated Node #0,3,2: 44:[72, 16] Operation: 62-46=16 Exploring Operation: 72-62=10, Resulting Numbers: [46, 10] Generated Node #0,3,3: 44:[46, 10] Operation: 72-62=10 Exploring Operation: 62+72=134, Resulting Numbers: [46, 134] Generated Node #0,3,4: 44:[46, 134] Operation: 62+72=134 Moving to Node #0,3,3 Current State: 44:[46, 10], Operations: ['98-26=72', '72-62=10'] Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,44 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[62, 26], Operations: ['98-26=72', '72-46=26'] Exploring Operation: 62+26=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 62-26=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 62*26=1612, Resulting Numbers: [1612] 1612,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[72, 16], Operations: ['98-26=72', '62-46=16'] Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[72, 108], Operations: ['98-26=72', '62+46=108'] Exploring Operation: 72+108=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 108-72=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 72*108=7776, Resulting Numbers: [7776] 7776,44 unequal: No Solution Moving to Node #0,3,4 Current State: 44:[46, 134], Operations: ['98-26=72', '62+72=134'] Exploring Operation: 134-46=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 46+134=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 46*134=6164, Resulting Numbers: [6164] 6164,44 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 Current State: 44:[98, 26, 16], Operations: ['62-46=16'] Exploring Operation: 26-16=10, Resulting Numbers: [98, 10] Generated Node #0,0,0: 44:[98, 10] Operation: 26-16=10 Exploring Operation: 98-26=72, Resulting Numbers: [16, 72] Generated Node #0,0,1: 44:[16, 72] Operation: 98-26=72 Exploring Operation: 98-16=82, Resulting Numbers: [26, 82] Generated Node #0,0,2: 44:[26, 82] Operation: 98-16=82 Exploring Operation: 98+16=114, Resulting Numbers: [26, 114] Generated Node #0,0,3: 44:[26, 114] Operation: 98+16=114 Exploring Operation: 26+16=42, Resulting Numbers: [98, 42] Generated Node #0,0,4: 44:[98, 42] Operation: 26+16=42 Moving to Node #0,0,1 Current State: 44:[16, 72], Operations: ['62-46=16', '98-26=72'] Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 16*72=1152, Resulting Numbers: [1152] 1152,44 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[26, 82], Operations: ['62-46=16', '98-16=82'] Exploring Operation: 26+82=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 26*82=2132, Resulting Numbers: [2132] 2132,44 unequal: No Solution Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[98, 10], Operations: ['62-46=16', '26-16=10'] Exploring Operation: 98-10=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 98+10=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 98*10=980, Resulting Numbers: [980] 980,44 unequal: No Solution Moving to Node #0,0,4 Current State: 44:[98, 42], Operations: ['62-46=16', '26+16=42'] Exploring Operation: 98+42=140, Resulting Numbers: [140] 140,44 unequal: No Solution Exploring Operation: 98-42=56, Resulting Numbers: [56] 56,44 unequal: No Solution Exploring Operation: 98*42=4116, Resulting Numbers: [4116] 4116,44 unequal: No Solution Moving to Node #0,0,3 Current State: 44:[26, 114], Operations: ['62-46=16', '98+16=114'] Exploring Operation: 114-26=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 26+114=140, Resulting Numbers: [140] 140,44 unequal: No Solution Exploring Operation: 26*114=2964, Resulting Numbers: [2964] 2964,44 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 #0,4 Current State: 44:[98, 46, 36], Operations: ['62-26=36'] Exploring Operation: 98+36=134, Resulting Numbers: [46, 134] Generated Node #0,4,0: 44:[46, 134] Operation: 98+36=134 Exploring Operation: 46-36=10, Resulting Numbers: [98, 10] Generated Node #0,4,1: 44:[98, 10] Operation: 46-36=10 Exploring Operation: 98-46=52, Resulting Numbers: [36, 52] Generated Node #0,4,2: 44:[36, 52] Operation: 98-46=52 Exploring Operation: 46+36=82, Resulting Numbers: [98, 82] Generated Node #0,4,3: 44:[98, 82] Operation: 46+36=82 Exploring Operation: 98-36=62, Resulting Numbers: [46, 62] Generated Node #0,4,4: 44:[46, 62] Operation: 98-36=62 Moving to Node #0,4,2 Current State: 44:[36, 52], Operations: ['62-26=36', '98-46=52'] Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 36+52=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 36*52=1872, Resulting Numbers: [1872] 1872,44 unequal: No Solution Moving to Node #0,4,4 Current State: 44:[46, 62], Operations: ['62-26=36', '98-36=62'] Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,44 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,44 unequal: No Solution Moving to Node #0,4,1 Current State: 44:[98, 10], Operations: ['62-26=36', '46-36=10'] Exploring Operation: 98+10=108, Resulting Numbers: [108] 108,44 unequal: No Solution Exploring Operation: 98*10=980, Resulting Numbers: [980] 980,44 unequal: No Solution Exploring Operation: 98-10=88, Resulting Numbers: [88] 88,44 unequal: No Solution Moving to Node #0,4,0 Current State: 44:[46, 134], Operations: ['62-26=36', '98+36=134'] Exploring Operation: 134-46=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 46*134=6164, Resulting Numbers: [6164] 6164,44 unequal: No Solution Exploring Operation: 46+134=180, Resulting Numbers: [180] 180,44 unequal: No Solution Moving to Node #0,4,3 Current State: 44:[98, 82], Operations: ['62-26=36', '46+36=82'] Exploring Operation: 98+82=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 98*82=8036, Resulting Numbers: [8036] 8036,44 unequal: No Solution Exploring Operation: 98-82=16, Resulting Numbers: [16] 16,44 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
[ 6, 46, 11, 61 ]
90
[ "46-6=40", "61-11=50", "40+50=90" ]
Current State: 90:[6, 46, 11, 61], Operations: [] Exploring Operation: 46-6=40, Resulting Numbers: [11, 61, 40] Generated Node #2: [11, 61, 40] from Operation: 46-6=40 Current State: 90:[11, 61, 40], Operations: ['46-6=40'] Exploring Operation: 61-11=50, Resulting Numbers: [40, 50] Generated Node #3: [40, 50] from Operation: 61-11=50 Current State: 90:[40, 50], Operations: ['46-6=40', '61-11=50'] Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[6, 46, 11, 61], Operations: [] Exploring Operation: 61-46=15, Resulting Numbers: [6, 11, 15] Generated Node #0,0: 90:[6, 11, 15] Operation: 61-46=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[6, 11, 15], Operations: ['61-46=15'] Exploring Operation: 11-6=5, Resulting Numbers: [15, 5] Generated Node #0,0,0: 90:[15, 5] Operation: 11-6=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[15, 5], Operations: ['61-46=15', '11-6=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,90 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
[ 46, 44, 13, 14 ]
41
[ "46-44=2", "14*2=28", "13+28=41" ]
Current State: 41:[46, 44, 13, 14], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [13, 14, 2] Generated Node #2: [13, 14, 2] from Operation: 46-44=2 Current State: 41:[13, 14, 2], Operations: ['46-44=2'] Exploring Operation: 14*2=28, Resulting Numbers: [13, 28] Generated Node #3: [13, 28] from Operation: 14*2=28 Current State: 41:[13, 28], Operations: ['46-44=2', '14*2=28'] Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[46, 44, 13, 14], Operations: [] Exploring Operation: 13+14=27, Resulting Numbers: [46, 44, 27] Generated Node #0,0: 41:[46, 44, 27] Operation: 13+14=27 Exploring Operation: 44-14=30, Resulting Numbers: [46, 13, 30] Generated Node #0,1: 41:[46, 13, 30] Operation: 44-14=30 Exploring Operation: 46-14=32, Resulting Numbers: [44, 13, 32] Generated Node #0,2: 41:[44, 13, 32] Operation: 46-14=32 Exploring Operation: 44-13=31, Resulting Numbers: [46, 14, 31] Generated Node #0,3: 41:[46, 14, 31] Operation: 44-13=31 Exploring Operation: 46-13=33, Resulting Numbers: [44, 14, 33] Generated Node #0,4: 41:[44, 14, 33] Operation: 46-13=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[46, 44, 27], Operations: ['13+14=27'] Exploring Operation: 46-27=19, Resulting Numbers: [44, 19] Generated Node #0,0,0: 41:[44, 19] Operation: 46-27=19 Exploring Operation: 44+27=71, Resulting Numbers: [46, 71] Generated Node #0,0,1: 41:[46, 71] Operation: 44+27=71 Exploring Operation: 44-27=17, Resulting Numbers: [46, 17] Generated Node #0,0,2: 41:[46, 17] Operation: 44-27=17 Exploring Operation: 46+27=73, Resulting Numbers: [44, 73] Generated Node #0,0,3: 41:[44, 73] Operation: 46+27=73 Exploring Operation: 46-44=2, Resulting Numbers: [27, 2] Generated Node #0,0,4: 41:[27, 2] Operation: 46-44=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[44, 19], Operations: ['13+14=27', '46-27=19'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,41 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[46, 17], Operations: ['13+14=27', '44-27=17'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[46, 71], Operations: ['13+14=27', '44+27=71'] Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 46+71=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 46*71=3266, Resulting Numbers: [3266] 3266,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[44, 73], Operations: ['13+14=27', '46+27=73'] Exploring Operation: 44+73=117, Resulting Numbers: [117] 117,41 unequal: No Solution Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 44*73=3212, Resulting Numbers: [3212] 3212,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 41:[27, 2], Operations: ['13+14=27', '46-44=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 41:[44, 14, 33], Operations: ['46-13=33'] Exploring Operation: 14+33=47, Resulting Numbers: [44, 47] Generated Node #0,4,0: 41:[44, 47] Operation: 14+33=47 Exploring Operation: 44-14=30, Resulting Numbers: [33, 30] Generated Node #0,4,1: 41:[33, 30] Operation: 44-14=30 Exploring Operation: 33-14=19, Resulting Numbers: [44, 19] Generated Node #0,4,2: 41:[44, 19] Operation: 33-14=19 Exploring Operation: 44+14=58, Resulting Numbers: [33, 58] Generated Node #0,4,3: 41:[33, 58] Operation: 44+14=58 Exploring Operation: 44-33=11, Resulting Numbers: [14, 11] Generated Node #0,4,4: 41:[14, 11] Operation: 44-33=11 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 41:[44, 47], Operations: ['46-13=33', '14+33=47'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 41:[33, 30], Operations: ['46-13=33', '44-14=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,41 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 41:[44, 19], Operations: ['46-13=33', '33-14=19'] Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,41 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 41:[33, 58], Operations: ['46-13=33', '44+14=58'] Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 33+58=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 33*58=1914, Resulting Numbers: [1914] 1914,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 41:[14, 11], Operations: ['46-13=33', '44-33=11'] Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,41 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[44, 13, 32], Operations: ['46-14=32'] Exploring Operation: 13+32=45, Resulting Numbers: [44, 45] Generated Node #0,2,0: 41:[44, 45] Operation: 13+32=45 Exploring Operation: 44-32=12, Resulting Numbers: [13, 12] Generated Node #0,2,1: 41:[13, 12] Operation: 44-32=12 Exploring Operation: 32-13=19, Resulting Numbers: [44, 19] Generated Node #0,2,2: 41:[44, 19] Operation: 32-13=19 Exploring Operation: 44-13=31, Resulting Numbers: [32, 31] Generated Node #0,2,3: 41:[32, 31] Operation: 44-13=31 Exploring Operation: 44+13=57, Resulting Numbers: [32, 57] Generated Node #0,2,4: 41:[32, 57] Operation: 44+13=57 Moving to Node #0,2,0 Current State: 41:[44, 45], Operations: ['46-14=32', '13+32=45'] Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 44*45=1980, Resulting Numbers: [1980] 1980,41 unequal: No Solution Exploring Operation: 44+45=89, Resulting Numbers: [89] 89,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[32, 31], Operations: ['46-14=32', '44-13=31'] Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[44, 19], Operations: ['46-14=32', '32-13=19'] Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,41 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,41 unequal: No Solution Moving to Node #0,2,4 Current State: 41:[32, 57], Operations: ['46-14=32', '44+13=57'] Exploring Operation: 32*57=1824, Resulting Numbers: [1824] 1824,41 unequal: No Solution Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[13, 12], Operations: ['46-14=32', '44-32=12'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,41 unequal: No Solution Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[46, 14, 31], Operations: ['44-13=31'] Exploring Operation: 46-31=15, Resulting Numbers: [14, 15] Generated Node #0,3,0: 41:[14, 15] Operation: 46-31=15 Exploring Operation: 31-14=17, Resulting Numbers: [46, 17] Generated Node #0,3,1: 41:[46, 17] Operation: 31-14=17 Exploring Operation: 14+31=45, Resulting Numbers: [46, 45] Generated Node #0,3,2: 41:[46, 45] Operation: 14+31=45 Exploring Operation: 46-14=32, Resulting Numbers: [31, 32] Generated Node #0,3,3: 41:[31, 32] Operation: 46-14=32 Exploring Operation: 46+14=60, Resulting Numbers: [31, 60] Generated Node #0,3,4: 41:[31, 60] Operation: 46+14=60 Moving to Node #0,3,2 Current State: 41:[46, 45], Operations: ['44-13=31', '14+31=45'] Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[31, 32], Operations: ['44-13=31', '46-14=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[46, 17], Operations: ['44-13=31', '31-14=17'] Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,41 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,41 unequal: No Solution Moving to Node #0,3,4 Current State: 41:[31, 60], Operations: ['44-13=31', '46+14=60'] Exploring Operation: 31*60=1860, Resulting Numbers: [1860] 1860,41 unequal: No Solution Exploring Operation: 31+60=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[14, 15], Operations: ['44-13=31', '46-31=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,41 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[46, 13, 30], Operations: ['44-14=30'] Exploring Operation: 46-30=16, Resulting Numbers: [13, 16] Generated Node #0,1,0: 41:[13, 16] Operation: 46-30=16 Exploring Operation: 46-13=33, Resulting Numbers: [30, 33] Generated Node #0,1,1: 41:[30, 33] Operation: 46-13=33 Exploring Operation: 46+13=59, Resulting Numbers: [30, 59] Generated Node #0,1,2: 41:[30, 59] Operation: 46+13=59 Exploring Operation: 13+30=43, Resulting Numbers: [46, 43] Generated Node #0,1,3: 41:[46, 43] Operation: 13+30=43 Exploring Operation: 30-13=17, Resulting Numbers: [46, 17] Generated Node #0,1,4: 41:[46, 17] Operation: 30-13=17 Moving to Node #0,1,3 Current State: 41:[46, 43], Operations: ['44-14=30', '13+30=43'] Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[30, 33], Operations: ['44-14=30', '46-13=33'] Exploring Operation: 30*33=990, Resulting Numbers: [990] 990,41 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 30+33=63, Resulting Numbers: [63] 63,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[30, 59], Operations: ['44-14=30', '46+13=59'] Exploring Operation: 30*59=1770, Resulting Numbers: [1770] 1770,41 unequal: No Solution Exploring Operation: 30+59=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,41 unequal: No Solution Moving to Node #0,1,4 Current State: 41:[46, 17], Operations: ['44-14=30', '30-13=17'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,41 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[13, 16], Operations: ['44-14=30', '46-30=16'] Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 13*16=208, Resulting Numbers: [208] 208,41 unequal: No Solution Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,41 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
[ 45, 5, 48, 44 ]
53
[ "45-44=1", "5+48=53", "1*53=53" ]
Current State: 53:[45, 5, 48, 44], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [5, 48, 1] Generated Node #2: [5, 48, 1] from Operation: 45-44=1 Current State: 53:[5, 48, 1], Operations: ['45-44=1'] Exploring Operation: 5+48=53, Resulting Numbers: [1, 53] Generated Node #3: [1, 53] from Operation: 5+48=53 Current State: 53:[1, 53], Operations: ['45-44=1', '5+48=53'] Exploring Operation: 1*53=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[45, 5, 48, 44], Operations: [] Exploring Operation: 5+48=53, Resulting Numbers: [45, 44, 53] Generated Node #0,0: 53:[45, 44, 53] Operation: 5+48=53 Exploring Operation: 45+5=50, Resulting Numbers: [48, 44, 50] Generated Node #0,1: 53:[48, 44, 50] Operation: 45+5=50 Exploring Operation: 5+44=49, Resulting Numbers: [45, 48, 49] Generated Node #0,2: 53:[45, 48, 49] Operation: 5+44=49 Moving to Node #0,0 Current State: 53:[45, 44, 53], Operations: ['5+48=53'] Exploring Operation: 44+53=97, Resulting Numbers: [45, 97] Generated Node #0,0,0: 53:[45, 97] Operation: 44+53=97 Exploring Operation: 45+44=89, Resulting Numbers: [53, 89] Generated Node #0,0,1: 53:[53, 89] Operation: 45+44=89 Exploring Operation: 45-44=1, Resulting Numbers: [53, 1] Generated Node #0,0,2: 53:[53, 1] Operation: 45-44=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[53, 89], Operations: ['5+48=53', '45+44=89'] Exploring Operation: 53*89=4717, Resulting Numbers: [4717] 4717,53 unequal: No Solution Exploring Operation: 89-53=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 53+89=142, Resulting Numbers: [142] 142,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[45, 97], Operations: ['5+48=53', '44+53=97'] Exploring Operation: 97-45=52, Resulting Numbers: [52] 52,53 unequal: No Solution Exploring Operation: 45+97=142, Resulting Numbers: [142] 142,53 unequal: No Solution Exploring Operation: 45*97=4365, Resulting Numbers: [4365] 4365,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[53, 1], Operations: ['5+48=53', '45-44=1'] Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[45, 5, 48, 44], Operations: [] Exploring Operation: 5+48=53, Resulting Numbers: [45, 44, 53] Generated Node #0,0: 53:[45, 44, 53] Operation: 5+48=53 Moving to Node #0,0 Current State: 53:[45, 44, 53], Operations: ['5+48=53'] Exploring Operation: 45-44=1, Resulting Numbers: [53, 1] Generated Node #0,0,2: 53:[53, 1] Operation: 45-44=1 Moving to Node #0,0,2 Current State: 53:[53, 1], Operations: ['5+48=53', '45-44=1'] Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 2, 43, 28, 42 ]
55
[ "43-2=41", "42-28=14", "41+14=55" ]
Current State: 55:[2, 43, 28, 42], Operations: [] Exploring Operation: 43-2=41, Resulting Numbers: [28, 42, 41] Generated Node #2: [28, 42, 41] from Operation: 43-2=41 Current State: 55:[28, 42, 41], Operations: ['43-2=41'] Exploring Operation: 42-28=14, Resulting Numbers: [41, 14] Generated Node #3: [41, 14] from Operation: 42-28=14 Current State: 55:[41, 14], Operations: ['43-2=41', '42-28=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[2, 43, 28, 42], Operations: [] Exploring Operation: 2*28=56, Resulting Numbers: [43, 42, 56] Generated Node #0,0: 55:[43, 42, 56] Operation: 2*28=56 Exploring Operation: 43-28=15, Resulting Numbers: [2, 42, 15] Generated Node #0,1: 55:[2, 42, 15] Operation: 43-28=15 Exploring Operation: 43-42=1, Resulting Numbers: [2, 28, 1] Generated Node #0,2: 55:[2, 28, 1] Operation: 43-42=1 Exploring Operation: 42-28=14, Resulting Numbers: [2, 43, 14] Generated Node #0,3: 55:[2, 43, 14] Operation: 42-28=14 Moving to Node #0,3 Current State: 55:[2, 43, 14], Operations: ['42-28=14'] Exploring Operation: 14/2=7, Resulting Numbers: [43, 7] Generated Node #0,3,0: 55:[43, 7] Operation: 14/2=7 Exploring Operation: 43+14=57, Resulting Numbers: [2, 57] Generated Node #0,3,1: 55:[2, 57] Operation: 43+14=57 Exploring Operation: 2+43=45, Resulting Numbers: [14, 45] Generated Node #0,3,2: 55:[14, 45] Operation: 2+43=45 Exploring Operation: 14-2=12, Resulting Numbers: [43, 12] Generated Node #0,3,3: 55:[43, 12] Operation: 14-2=12 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 55:[2, 57], Operations: ['42-28=14', '43+14=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[2, 43, 28, 42], Operations: [] Exploring Operation: 42-28=14, Resulting Numbers: [2, 43, 14] Generated Node #0,3: 55:[2, 43, 14] Operation: 42-28=14 Moving to Node #0,3 Current State: 55:[2, 43, 14], Operations: ['42-28=14'] Exploring Operation: 43+14=57, Resulting Numbers: [2, 57] Generated Node #0,3,1: 55:[2, 57] Operation: 43+14=57 Moving to Node #0,3,1 Current State: 55:[2, 57], Operations: ['42-28=14', '43+14=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 53, 12, 42, 6 ]
78
[ "53-42=11", "6*11=66", "12+66=78" ]
Current State: 78:[53, 12, 42, 6], Operations: [] Exploring Operation: 53-42=11, Resulting Numbers: [12, 6, 11] Generated Node #2: [12, 6, 11] from Operation: 53-42=11 Current State: 78:[12, 6, 11], Operations: ['53-42=11'] Exploring Operation: 6*11=66, Resulting Numbers: [12, 66] Generated Node #3: [12, 66] from Operation: 6*11=66 Current State: 78:[12, 66], Operations: ['53-42=11', '6*11=66'] Exploring Operation: 12+66=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[53, 12, 42, 6], Operations: [] Exploring Operation: 53-6=47, Resulting Numbers: [12, 42, 47] Generated Node #0,0: 78:[12, 42, 47] Operation: 53-6=47 Exploring Operation: 53-12=41, Resulting Numbers: [42, 6, 41] Generated Node #0,1: 78:[42, 6, 41] Operation: 53-12=41 Exploring Operation: 42/6=7, Resulting Numbers: [53, 12, 7] Generated Node #0,2: 78:[53, 12, 7] Operation: 42/6=7 Exploring Operation: 53+12=65, Resulting Numbers: [42, 6, 65] Generated Node #0,3: 78:[42, 6, 65] Operation: 53+12=65 Exploring Operation: 53-42=11, Resulting Numbers: [12, 6, 11] Generated Node #0,4: 78:[12, 6, 11] Operation: 53-42=11 Start Sub Search at level 1: Moving to Node #0,4 Current State: 78:[12, 6, 11], Operations: ['53-42=11'] Exploring Operation: 11-6=5, Resulting Numbers: [12, 5] Generated Node #0,4,0: 78:[12, 5] Operation: 11-6=5 Exploring Operation: 12+11=23, Resulting Numbers: [6, 23] Generated Node #0,4,1: 78:[6, 23] Operation: 12+11=23 Exploring Operation: 12/6=2, Resulting Numbers: [11, 2] Generated Node #0,4,2: 78:[11, 2] Operation: 12/6=2 Exploring Operation: 12-11=1, Resulting Numbers: [6, 1] Generated Node #0,4,3: 78:[6, 1] Operation: 12-11=1 Exploring Operation: 12-6=6, Resulting Numbers: [11, 6] Generated Node #0,4,4: 78:[11, 6] Operation: 12-6=6 Moving to Node #0,4,3 Current State: 78:[6, 1], Operations: ['53-42=11', '12-11=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,4,2 Current State: 78:[11, 2], Operations: ['53-42=11', '12/6=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,78 unequal: No Solution Moving to Node #0,4,0 Current State: 78:[12, 5], Operations: ['53-42=11', '11-6=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,78 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,78 unequal: No Solution Moving to Node #0,4,4 Current State: 78:[11, 6], Operations: ['53-42=11', '12-6=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,78 unequal: No Solution Moving to Node #0,4,1 Current State: 78:[6, 23], Operations: ['53-42=11', '12+11=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,78 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[42, 6, 41], Operations: ['53-12=41'] Exploring Operation: 42-41=1, Resulting Numbers: [6, 1] Generated Node #0,1,0: 78:[6, 1] Operation: 42-41=1 Exploring Operation: 42/6=7, Resulting Numbers: [41, 7] Generated Node #0,1,1: 78:[41, 7] Operation: 42/6=7 Exploring Operation: 41-6=35, Resulting Numbers: [42, 35] Generated Node #0,1,2: 78:[42, 35] Operation: 41-6=35 Exploring Operation: 42+41=83, Resulting Numbers: [6, 83] Generated Node #0,1,3: 78:[6, 83] Operation: 42+41=83 Exploring Operation: 42-6=36, Resulting Numbers: [41, 36] Generated Node #0,1,4: 78:[41, 36] Operation: 42-6=36 Moving to Node #0,1,0 Current State: 78:[6, 1], Operations: ['53-12=41', '42-41=1'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[41, 7], Operations: ['53-12=41', '42/6=7'] Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,78 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[6, 83], Operations: ['53-12=41', '42+41=83'] Exploring Operation: 6*83=498, Resulting Numbers: [498] 498,78 unequal: No Solution Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,78 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,78 unequal: No Solution Moving to Node #0,1,4 Current State: 78:[41, 36], Operations: ['53-12=41', '42-6=36'] Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,78 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[42, 35], Operations: ['53-12=41', '41-6=35'] Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,78 unequal: No Solution Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,78 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[12, 42, 47], Operations: ['53-6=47'] Exploring Operation: 42+47=89, Resulting Numbers: [12, 89] Generated Node #0,0,0: 78:[12, 89] Operation: 42+47=89 Exploring Operation: 47-42=5, Resulting Numbers: [12, 5] Generated Node #0,0,1: 78:[12, 5] Operation: 47-42=5 Exploring Operation: 42-12=30, Resulting Numbers: [47, 30] Generated Node #0,0,2: 78:[47, 30] Operation: 42-12=30 Exploring Operation: 47-12=35, Resulting Numbers: [42, 35] Generated Node #0,0,3: 78:[42, 35] Operation: 47-12=35 Exploring Operation: 12+47=59, Resulting Numbers: [42, 59] Generated Node #0,0,4: 78:[42, 59] Operation: 12+47=59 Moving to Node #0,0,1 Current State: 78:[12, 5], Operations: ['53-6=47', '47-42=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,78 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[42, 35], Operations: ['53-6=47', '47-12=35'] Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,78 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[12, 89], Operations: ['53-6=47', '42+47=89'] Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,78 unequal: No Solution Exploring Operation: 12*89=1068, Resulting Numbers: [1068] 1068,78 unequal: No Solution Exploring Operation: 12+89=101, Resulting Numbers: [101] 101,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[47, 30], Operations: ['53-6=47', '42-12=30'] Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,78 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,78 unequal: No Solution Moving to Node #0,0,4 Current State: 78:[42, 59], Operations: ['53-6=47', '12+47=59'] Exploring Operation: 42*59=2478, Resulting Numbers: [2478] 2478,78 unequal: No Solution Exploring Operation: 42+59=101, Resulting Numbers: [101] 101,78 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,78 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 Current State: 78:[53, 12, 7], Operations: ['42/6=7'] Exploring Operation: 12-7=5, Resulting Numbers: [53, 5] Generated Node #0,2,0: 78:[53, 5] Operation: 12-7=5 Exploring Operation: 53+12=65, Resulting Numbers: [7, 65] Generated Node #0,2,1: 78:[7, 65] Operation: 53+12=65 Exploring Operation: 53+7=60, Resulting Numbers: [12, 60] Generated Node #0,2,2: 78:[12, 60] Operation: 53+7=60 Exploring Operation: 53-7=46, Resulting Numbers: [12, 46] Generated Node #0,2,3: 78:[12, 46] Operation: 53-7=46 Exploring Operation: 53-12=41, Resulting Numbers: [7, 41] Generated Node #0,2,4: 78:[7, 41] Operation: 53-12=41 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 78:[7, 41], Operations: ['42/6=7', '53-12=41'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 7*41=287, Resulting Numbers: [287] 287,78 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:[12, 46], Operations: ['42/6=7', '53-7=46'] Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 12*46=552, Resulting Numbers: [552] 552,78 unequal: No Solution Exploring Operation: 12+46=58, Resulting Numbers: [58] 58,78 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:[7, 65], Operations: ['42/6=7', '53+12=65'] Exploring Operation: 7*65=455, Resulting Numbers: [455] 455,78 unequal: No Solution Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,78 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 #0,2,0 Current State: 78:[53, 5], Operations: ['42/6=7', '12-7=5'] Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,78 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,78 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,78 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 #0,2,2 Current State: 78:[12, 60], Operations: ['42/6=7', '53+7=60'] Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,78 unequal: No Solution Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,78 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 #0,3 Current State: 78:[42, 6, 65], Operations: ['53+12=65'] Exploring Operation: 42+6=48, Resulting Numbers: [65, 48] Generated Node #0,3,0: 78:[65, 48] Operation: 42+6=48 Exploring Operation: 65-42=23, Resulting Numbers: [6, 23] Generated Node #0,3,1: 78:[6, 23] Operation: 65-42=23 Exploring Operation: 42/6=7, Resulting Numbers: [65, 7] Generated Node #0,3,2: 78:[65, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [65, 36] Generated Node #0,3,3: 78:[65, 36] Operation: 42-6=36 Exploring Operation: 6+65=71, Resulting Numbers: [42, 71] Generated Node #0,3,4: 78:[42, 71] Operation: 6+65=71 Moving to Node #0,3,1 Current State: 78:[6, 23], Operations: ['53+12=65', '65-42=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,78 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,78 unequal: No Solution Moving to Node #0,3,4 Current State: 78:[42, 71], Operations: ['53+12=65', '6+65=71'] Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 42*71=2982, Resulting Numbers: [2982] 2982,78 unequal: No Solution Exploring Operation: 42+71=113, Resulting Numbers: [113] 113,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[65, 7], Operations: ['53+12=65', '42/6=7'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,78 unequal: No Solution Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 65*7=455, Resulting Numbers: [455] 455,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[65, 36], Operations: ['53+12=65', '42-6=36'] Exploring Operation: 65*36=2340, Resulting Numbers: [2340] 2340,78 unequal: No Solution Exploring Operation: 65+36=101, Resulting Numbers: [101] 101,78 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,78 unequal: No Solution Moving to Node #0,3,0 Current State: 78:[65, 48], Operations: ['53+12=65', '42+6=48'] Exploring Operation: 65*48=3120, Resulting Numbers: [3120] 3120,78 unequal: No Solution Exploring Operation: 65+48=113, Resulting Numbers: [113] 113,78 unequal: No Solution Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,78 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
[ 25, 65, 20, 51 ]
59
[ "25+65=90", "51-20=31", "90-31=59" ]
Current State: 59:[25, 65, 20, 51], Operations: [] Exploring Operation: 25+65=90, Resulting Numbers: [20, 51, 90] Generated Node #2: [20, 51, 90] from Operation: 25+65=90 Current State: 59:[20, 51, 90], Operations: ['25+65=90'] Exploring Operation: 51-20=31, Resulting Numbers: [90, 31] Generated Node #3: [90, 31] from Operation: 51-20=31 Current State: 59:[90, 31], Operations: ['25+65=90', '51-20=31'] Exploring Operation: 90-31=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[25, 65, 20, 51], Operations: [] Exploring Operation: 20+51=71, Resulting Numbers: [25, 65, 71] Generated Node #0,0: 59:[25, 65, 71] Operation: 20+51=71 Exploring Operation: 25+20=45, Resulting Numbers: [65, 51, 45] Generated Node #0,1: 59:[65, 51, 45] Operation: 25+20=45 Exploring Operation: 25+51=76, Resulting Numbers: [65, 20, 76] Generated Node #0,2: 59:[65, 20, 76] Operation: 25+51=76 Exploring Operation: 65-20=45, Resulting Numbers: [25, 51, 45] Generated Node #0,3: 59:[25, 51, 45] Operation: 65-20=45 Moving to Node #0,1 Current State: 59:[65, 51, 45], Operations: ['25+20=45'] Exploring Operation: 65+45=110, Resulting Numbers: [51, 110] Generated Node #0,1,0: 59:[51, 110] Operation: 65+45=110 Exploring Operation: 65-45=20, Resulting Numbers: [51, 20] Generated Node #0,1,1: 59:[51, 20] Operation: 65-45=20 Exploring Operation: 51+45=96, Resulting Numbers: [65, 96] Generated Node #0,1,2: 59:[65, 96] Operation: 51+45=96 Exploring Operation: 65-51=14, Resulting Numbers: [45, 14] Generated Node #0,1,3: 59:[45, 14] Operation: 65-51=14 Moving to Node #0,0 Current State: 59:[25, 65, 71], Operations: ['20+51=71'] Exploring Operation: 25+71=96, Resulting Numbers: [65, 96] Generated Node #0,0,0: 59:[65, 96] Operation: 25+71=96 Exploring Operation: 71-25=46, Resulting Numbers: [65, 46] Generated Node #0,0,1: 59:[65, 46] Operation: 71-25=46 Exploring Operation: 25+65=90, Resulting Numbers: [71, 90] Generated Node #0,0,2: 59:[71, 90] Operation: 25+65=90 Exploring Operation: 65-25=40, Resulting Numbers: [71, 40] Generated Node #0,0,3: 59:[71, 40] Operation: 65-25=40 Moving to Node #0,3 Current State: 59:[25, 51, 45], Operations: ['65-20=45'] Exploring Operation: 51-25=26, Resulting Numbers: [45, 26] Generated Node #0,3,0: 59:[45, 26] Operation: 51-25=26 Exploring Operation: 25+45=70, Resulting Numbers: [51, 70] Generated Node #0,3,1: 59:[51, 70] Operation: 25+45=70 Exploring Operation: 45-25=20, Resulting Numbers: [51, 20] Generated Node #0,3,2: 59:[51, 20] Operation: 45-25=20 Exploring Operation: 25+51=76, Resulting Numbers: [45, 76] Generated Node #0,3,3: 59:[45, 76] Operation: 25+51=76 Moving to Node #0,2 Current State: 59:[65, 20, 76], Operations: ['25+51=76'] Exploring Operation: 65+20=85, Resulting Numbers: [76, 85] Generated Node #0,2,0: 59:[76, 85] Operation: 65+20=85 Exploring Operation: 65-20=45, Resulting Numbers: [76, 45] Generated Node #0,2,1: 59:[76, 45] Operation: 65-20=45 Exploring Operation: 76-20=56, Resulting Numbers: [65, 56] Generated Node #0,2,2: 59:[65, 56] Operation: 76-20=56 Exploring Operation: 20+76=96, Resulting Numbers: [65, 96] Generated Node #0,2,3: 59:[65, 96] Operation: 20+76=96 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[65, 56], Operations: ['25+51=76', '76-20=56'] Exploring Operation: 65*56=3640, Resulting Numbers: [3640] 3640,59 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 65+56=121, Resulting Numbers: [121] 121,59 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 #0,2,1 Current State: 59:[76, 45], Operations: ['25+51=76', '65-20=45'] Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,59 unequal: No Solution Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,59 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 #0,2,0 Current State: 59:[76, 85], Operations: ['25+51=76', '65+20=85'] Exploring Operation: 76*85=6460, Resulting Numbers: [6460] 6460,59 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 76+85=161, Resulting Numbers: [161] 161,59 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 #0,2,3 Current State: 59:[65, 96], Operations: ['25+51=76', '20+76=96'] Exploring Operation: 65*96=6240, Resulting Numbers: [6240] 6240,59 unequal: No Solution Exploring Operation: 65+96=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 96-65=31, Resulting Numbers: [31] 31,59 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: 59:[65, 46], Operations: ['20+51=71', '71-25=46'] Exploring Operation: 65*46=2990, Resulting Numbers: [2990] 2990,59 unequal: No Solution Exploring Operation: 65+46=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 65-46=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[51, 70], Operations: ['65-20=45', '25+45=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,59 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[71, 40], Operations: ['20+51=71', '65-25=40'] Exploring Operation: 71+40=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 71*40=2840, Resulting Numbers: [2840] 2840,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[45, 76], Operations: ['65-20=45', '25+51=76'] Exploring Operation: 45+76=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 45*76=3420, Resulting Numbers: [3420] 3420,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[65, 96], Operations: ['20+51=71', '25+71=96'] Exploring Operation: 65+96=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 96-65=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 65*96=6240, Resulting Numbers: [6240] 6240,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[65, 96], Operations: ['25+20=45', '51+45=96'] Exploring Operation: 65+96=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 96-65=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 65*96=6240, Resulting Numbers: [6240] 6240,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[71, 90], Operations: ['20+51=71', '25+65=90'] Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,59 unequal: No Solution Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[51, 20], Operations: ['65-20=45', '45-25=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[51, 20], Operations: ['25+20=45', '65-45=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,59 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[45, 26], Operations: ['65-20=45', '51-25=26'] Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,59 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[45, 14], Operations: ['25+20=45', '65-51=14'] Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[25, 65, 20, 51], Operations: [] Exploring Operation: 25+20=45, Resulting Numbers: [65, 51, 45] Generated Node #0,1: 59:[65, 51, 45] Operation: 25+20=45 Moving to Node #0,1 Current State: 59:[65, 51, 45], Operations: ['25+20=45'] Exploring Operation: 65-51=14, Resulting Numbers: [45, 14] Generated Node #0,1,3: 59:[45, 14] Operation: 65-51=14 Moving to Node #0,1,3 Current State: 59:[45, 14], Operations: ['25+20=45', '65-51=14'] Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.94184
hs_4
mult_heuristic
[ 38, 40, 32, 25 ]
20
[ "32*25=800", "800-40=760", "760/38=20" ]
Current State: 20:[38, 40, 32, 25], Operations: [] Exploring Operation: 32*25=800, Resulting Numbers: [38, 40, 800] Generated Node #2: [38, 40, 800] from Operation: 32*25=800 Current State: 20:[38, 40, 800], Operations: ['32*25=800'] Exploring Operation: 800-40=760, Resulting Numbers: [38, 760] Generated Node #3: [38, 760] from Operation: 800-40=760 Current State: 20:[38, 760], Operations: ['32*25=800', '800-40=760'] Exploring Operation: 760/38=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[38, 40, 32, 25], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [32, 25, 2] Generated Node #0,0: 20:[32, 25, 2] Operation: 40-38=2 Exploring Operation: 38-32=6, Resulting Numbers: [40, 25, 6] Generated Node #0,1: 20:[40, 25, 6] Operation: 38-32=6 Exploring Operation: 40-32=8, Resulting Numbers: [38, 25, 8] Generated Node #0,2: 20:[38, 25, 8] Operation: 40-32=8 Moving to Node #0,0 Current State: 20:[32, 25, 2], Operations: ['40-38=2'] Exploring Operation: 32-25=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 20:[2, 7] Operation: 32-25=7 Exploring Operation: 32/2=16, Resulting Numbers: [25, 16] Generated Node #0,0,1: 20:[25, 16] Operation: 32/2=16 Exploring Operation: 32-2=30, Resulting Numbers: [25, 30] Generated Node #0,0,2: 20:[25, 30] Operation: 32-2=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[2, 7], Operations: ['40-38=2', '32-25=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,20 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,20 unequal: No Solution No 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: 20:[25, 16], Operations: ['40-38=2', '32/2=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,20 unequal: No Solution No 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: 20:[25, 30], Operations: ['40-38=2', '32-2=30'] Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,20 unequal: No Solution Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,20 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: 20:[38, 25, 8], Operations: ['40-32=8'] Exploring Operation: 25-8=17, Resulting Numbers: [38, 17] Generated Node #0,2,0: 20:[38, 17] Operation: 25-8=17 Exploring Operation: 38-25=13, Resulting Numbers: [8, 13] Generated Node #0,2,1: 20:[8, 13] Operation: 38-25=13 Exploring Operation: 38-8=30, Resulting Numbers: [25, 30] Generated Node #0,2,2: 20:[25, 30] Operation: 38-8=30 Moving to Node #0,1 Current State: 20:[40, 25, 6], Operations: ['38-32=6'] Exploring Operation: 40-6=34, Resulting Numbers: [25, 34] Generated Node #0,1,0: 20:[25, 34] Operation: 40-6=34 Exploring Operation: 25-6=19, Resulting Numbers: [40, 19] Generated Node #0,1,1: 20:[40, 19] Operation: 25-6=19 Exploring Operation: 40-25=15, Resulting Numbers: [6, 15] Generated Node #0,1,2: 20:[6, 15] Operation: 40-25=15 Moving to Node #0,2,1 Current State: 20:[8, 13], Operations: ['40-32=8', '38-25=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,20 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[6, 15], Operations: ['38-32=6', '40-25=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,20 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,20 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[25, 30], Operations: ['40-32=8', '38-8=30'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,20 unequal: No Solution Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[25, 34], Operations: ['38-32=6', '40-6=34'] Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[40, 19], Operations: ['38-32=6', '25-6=19'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,20 unequal: No Solution Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,20 unequal: No Solution Exploring Operation: 40*19=760, Resulting Numbers: [760] 760,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[38, 17], Operations: ['40-32=8', '25-8=17'] Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,20 unequal: No Solution Exploring Operation: 38*17=646, Resulting Numbers: [646] 646,20 unequal: No Solution Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 22, 89, 59, 57 ]
65
[ "89-22=67", "59-57=2", "67-2=65" ]
Current State: 65:[22, 89, 59, 57], Operations: [] Exploring Operation: 89-22=67, Resulting Numbers: [59, 57, 67] Generated Node #2: [59, 57, 67] from Operation: 89-22=67 Current State: 65:[59, 57, 67], Operations: ['89-22=67'] Exploring Operation: 59-57=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 59-57=2 Current State: 65:[67, 2], Operations: ['89-22=67', '59-57=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[22, 89, 59, 57], Operations: [] Exploring Operation: 89-59=30, Resulting Numbers: [22, 57, 30] Generated Node #0,0: 65:[22, 57, 30] Operation: 89-59=30 Exploring Operation: 59-57=2, Resulting Numbers: [22, 89, 2] Generated Node #0,1: 65:[22, 89, 2] Operation: 59-57=2 Exploring Operation: 89-22=67, Resulting Numbers: [59, 57, 67] Generated Node #0,2: 65:[59, 57, 67] Operation: 89-22=67 Exploring Operation: 89-57=32, Resulting Numbers: [22, 59, 32] Generated Node #0,3: 65:[22, 59, 32] Operation: 89-57=32 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[59, 57, 67], Operations: ['89-22=67'] Exploring Operation: 59-57=2, Resulting Numbers: [67, 2] Generated Node #0,2,0: 65:[67, 2] Operation: 59-57=2 Exploring Operation: 67-57=10, Resulting Numbers: [59, 10] Generated Node #0,2,1: 65:[59, 10] Operation: 67-57=10 Exploring Operation: 67-59=8, Resulting Numbers: [57, 8] Generated Node #0,2,2: 65:[57, 8] Operation: 67-59=8 Exploring Operation: 59+57=116, Resulting Numbers: [67, 116] Generated Node #0,2,3: 65:[67, 116] Operation: 59+57=116 Moving to Node #0,2,0 Current State: 65:[67, 2], Operations: ['89-22=67', '59-57=2'] Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,65 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,65 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[22, 89, 59, 57], Operations: [] Exploring Operation: 89-22=67, Resulting Numbers: [59, 57, 67] Generated Node #0,2: 65:[59, 57, 67] Operation: 89-22=67 Moving to Node #0,2 Current State: 65:[59, 57, 67], Operations: ['89-22=67'] Exploring Operation: 59-57=2, Resulting Numbers: [67, 2] Generated Node #0,2,0: 65:[67, 2] Operation: 59-57=2 Moving to Node #0,2,0 Current State: 65:[67, 2], Operations: ['89-22=67', '59-57=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 88, 32, 77, 1 ]
20
[ "88-32=56", "77-1=76", "76-56=20" ]
Current State: 20:[88, 32, 77, 1], Operations: [] Exploring Operation: 88-32=56, Resulting Numbers: [77, 1, 56] Generated Node #2: [77, 1, 56] from Operation: 88-32=56 Current State: 20:[77, 1, 56], Operations: ['88-32=56'] Exploring Operation: 77-1=76, Resulting Numbers: [56, 76] Generated Node #3: [56, 76] from Operation: 77-1=76 Current State: 20:[56, 76], Operations: ['88-32=56', '77-1=76'] Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[88, 32, 77, 1], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [32, 1, 11] Generated Node #0,0: 20:[32, 1, 11] Operation: 88-77=11 Exploring Operation: 88-1=87, Resulting Numbers: [32, 77, 87] Generated Node #0,1: 20:[32, 77, 87] Operation: 88-1=87 Exploring Operation: 77-32=45, Resulting Numbers: [88, 1, 45] Generated Node #0,2: 20:[88, 1, 45] Operation: 77-32=45 Exploring Operation: 88-32=56, Resulting Numbers: [77, 1, 56] Generated Node #0,3: 20:[77, 1, 56] Operation: 88-32=56 Moving to Node #0,0 Current State: 20:[32, 1, 11], Operations: ['88-77=11'] Exploring Operation: 11-1=10, Resulting Numbers: [32, 10] Generated Node #0,0,0: 20:[32, 10] Operation: 11-1=10 Exploring Operation: 32-11=21, Resulting Numbers: [1, 21] Generated Node #0,0,1: 20:[1, 21] Operation: 32-11=21 Exploring Operation: 32*1=32, Resulting Numbers: [11, 32] Generated Node #0,0,2: 20:[11, 32] Operation: 32*1=32 Exploring Operation: 32-1=31, Resulting Numbers: [11, 31] Generated Node #0,0,3: 20:[11, 31] Operation: 32-1=31 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[1, 21], Operations: ['88-77=11', '32-11=21'] Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,20 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,20 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[88, 32, 77, 1], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [32, 1, 11] Generated Node #0,0: 20:[32, 1, 11] Operation: 88-77=11 Moving to Node #0,0 Current State: 20:[32, 1, 11], Operations: ['88-77=11'] Exploring Operation: 32-11=21, Resulting Numbers: [1, 21] Generated Node #0,0,1: 20:[1, 21] Operation: 32-11=21 Moving to Node #0,0,1 Current State: 20:[1, 21], Operations: ['88-77=11', '32-11=21'] Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 12, 86, 5, 23 ]
41
[ "86-12=74", "5*23=115", "115-74=41" ]
Current State: 41:[12, 86, 5, 23], Operations: [] Exploring Operation: 86-12=74, Resulting Numbers: [5, 23, 74] Generated Node #2: [5, 23, 74] from Operation: 86-12=74 Current State: 41:[5, 23, 74], Operations: ['86-12=74'] Exploring Operation: 5*23=115, Resulting Numbers: [74, 115] Generated Node #3: [74, 115] from Operation: 5*23=115 Current State: 41:[74, 115], Operations: ['86-12=74', '5*23=115'] Exploring Operation: 115-74=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[12, 86, 5, 23], Operations: [] Exploring Operation: 86-12=74, Resulting Numbers: [5, 23, 74] Generated Node #0,0: 41:[5, 23, 74] Operation: 86-12=74 Exploring Operation: 12*5=60, Resulting Numbers: [86, 23, 60] Generated Node #0,1: 41:[86, 23, 60] Operation: 12*5=60 Exploring Operation: 12+5=17, Resulting Numbers: [86, 23, 17] Generated Node #0,2: 41:[86, 23, 17] Operation: 12+5=17 Exploring Operation: 12+23=35, Resulting Numbers: [86, 5, 35] Generated Node #0,3: 41:[86, 5, 35] Operation: 12+23=35 Moving to Node #0,1 Current State: 41:[86, 23, 60], Operations: ['12*5=60'] Exploring Operation: 86-23=63, Resulting Numbers: [60, 63] Generated Node #0,1,0: 41:[60, 63] Operation: 86-23=63 Exploring Operation: 60-23=37, Resulting Numbers: [86, 37] Generated Node #0,1,1: 41:[86, 37] Operation: 60-23=37 Exploring Operation: 86-60=26, Resulting Numbers: [23, 26] Generated Node #0,1,2: 41:[23, 26] Operation: 86-60=26 Exploring Operation: 86+23=109, Resulting Numbers: [60, 109] Generated Node #0,1,3: 41:[60, 109] Operation: 86+23=109 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[23, 26], Operations: ['12*5=60', '86-60=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,41 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[60, 63], Operations: ['12*5=60', '86-23=63'] Exploring Operation: 60*63=3780, Resulting Numbers: [3780] 3780,41 unequal: No Solution Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 60+63=123, Resulting Numbers: [123] 123,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[86, 37], Operations: ['12*5=60', '60-23=37'] Exploring Operation: 86-37=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 86*37=3182, Resulting Numbers: [3182] 3182,41 unequal: No Solution Exploring Operation: 86+37=123, Resulting Numbers: [123] 123,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[60, 109], Operations: ['12*5=60', '86+23=109'] Exploring Operation: 60+109=169, Resulting Numbers: [169] 169,41 unequal: No Solution Exploring Operation: 109-60=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 60*109=6540, Resulting Numbers: [6540] 6540,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 41:[86, 23, 17], Operations: ['12+5=17'] Exploring Operation: 23+17=40, Resulting Numbers: [86, 40] Generated Node #0,2,0: 41:[86, 40] Operation: 23+17=40 Exploring Operation: 86+17=103, Resulting Numbers: [23, 103] Generated Node #0,2,1: 41:[23, 103] Operation: 86+17=103 Exploring Operation: 86-23=63, Resulting Numbers: [17, 63] Generated Node #0,2,2: 41:[17, 63] Operation: 86-23=63 Exploring Operation: 86-17=69, Resulting Numbers: [23, 69] Generated Node #0,2,3: 41:[23, 69] Operation: 86-17=69 Moving to Node #0,0 Current State: 41:[5, 23, 74], Operations: ['86-12=74'] Exploring Operation: 74-5=69, Resulting Numbers: [23, 69] Generated Node #0,0,0: 41:[23, 69] Operation: 74-5=69 Exploring Operation: 23-5=18, Resulting Numbers: [74, 18] Generated Node #0,0,1: 41:[74, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [74, 28] Generated Node #0,0,2: 41:[74, 28] Operation: 5+23=28 Exploring Operation: 74-23=51, Resulting Numbers: [5, 51] Generated Node #0,0,3: 41:[5, 51] Operation: 74-23=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[23, 69], Operations: ['86-12=74', '74-5=69'] Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 23*69=1587, Resulting Numbers: [1587] 1587,41 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[74, 28], Operations: ['86-12=74', '5+23=28'] Exploring Operation: 74*28=2072, Resulting Numbers: [2072] 2072,41 unequal: No Solution Exploring Operation: 74+28=102, Resulting Numbers: [102] 102,41 unequal: No Solution Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 41:[5, 51], Operations: ['86-12=74', '74-23=51'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[74, 18], Operations: ['86-12=74', '23-5=18'] Exploring Operation: 74-18=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 74*18=1332, Resulting Numbers: [1332] 1332,41 unequal: No Solution Exploring Operation: 74+18=92, Resulting Numbers: [92] 92,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 41:[86, 5, 35], Operations: ['12+23=35'] Exploring Operation: 5+35=40, Resulting Numbers: [86, 40] Generated Node #0,3,0: 41:[86, 40] Operation: 5+35=40 Exploring Operation: 86+5=91, Resulting Numbers: [35, 91] Generated Node #0,3,1: 41:[35, 91] Operation: 86+5=91 Exploring Operation: 86-35=51, Resulting Numbers: [5, 51] Generated Node #0,3,2: 41:[5, 51] Operation: 86-35=51 Exploring Operation: 86-5=81, Resulting Numbers: [35, 81] Generated Node #0,3,3: 41:[35, 81] Operation: 86-5=81 Moving to Node #0,2,0 Current State: 41:[86, 40], Operations: ['12+5=17', '23+17=40'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,41 unequal: No Solution Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[23, 69], Operations: ['12+5=17', '86-17=69'] Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 23+69=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 23*69=1587, Resulting Numbers: [1587] 1587,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[35, 81], Operations: ['12+23=35', '86-5=81'] Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,41 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[5, 51], Operations: ['12+23=35', '86-35=51'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[17, 63], Operations: ['12+5=17', '86-23=63'] Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,41 unequal: No Solution Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[86, 40], Operations: ['12+23=35', '5+35=40'] Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[35, 91], Operations: ['12+23=35', '86+5=91'] Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,41 unequal: No Solution Exploring Operation: 35+91=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 35*91=3185, Resulting Numbers: [3185] 3185,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[23, 103], Operations: ['12+5=17', '86+17=103'] Exploring Operation: 103-23=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 23+103=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 23*103=2369, Resulting Numbers: [2369] 2369,41 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 69, 68, 70, 63 ]
66
[ "69+63=132", "70-68=2", "132/2=66" ]
Current State: 66:[69, 68, 70, 63], Operations: [] Exploring Operation: 69+63=132, Resulting Numbers: [68, 70, 132] Generated Node #2: [68, 70, 132] from Operation: 69+63=132 Current State: 66:[68, 70, 132], Operations: ['69+63=132'] Exploring Operation: 70-68=2, Resulting Numbers: [132, 2] Generated Node #3: [132, 2] from Operation: 70-68=2 Current State: 66:[132, 2], Operations: ['69+63=132', '70-68=2'] Exploring Operation: 132/2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[69, 68, 70, 63], Operations: [] Exploring Operation: 69-63=6, Resulting Numbers: [68, 70, 6] Generated Node #0,0: 66:[68, 70, 6] Operation: 69-63=6 Exploring Operation: 70-69=1, Resulting Numbers: [68, 63, 1] Generated Node #0,1: 66:[68, 63, 1] Operation: 70-69=1 Exploring Operation: 70-68=2, Resulting Numbers: [69, 63, 2] Generated Node #0,2: 66:[69, 63, 2] Operation: 70-68=2 Moving to Node #0,0 Current State: 66:[68, 70, 6], Operations: ['69-63=6'] Exploring Operation: 70-6=64, Resulting Numbers: [68, 64] Generated Node #0,0,0: 66:[68, 64] Operation: 70-6=64 Exploring Operation: 68-6=62, Resulting Numbers: [70, 62] Generated Node #0,0,1: 66:[70, 62] Operation: 68-6=62 Exploring Operation: 70-68=2, Resulting Numbers: [6, 2] Generated Node #0,0,2: 66:[6, 2] Operation: 70-68=2 Moving to Node #0,1 Current State: 66:[68, 63, 1], Operations: ['70-69=1'] Exploring Operation: 68-63=5, Resulting Numbers: [1, 5] Generated Node #0,1,0: 66:[1, 5] Operation: 68-63=5 Exploring Operation: 68-1=67, Resulting Numbers: [63, 67] Generated Node #0,1,1: 66:[63, 67] Operation: 68-1=67 Exploring Operation: 63+1=64, Resulting Numbers: [68, 64] Generated Node #0,1,2: 66:[68, 64] Operation: 63+1=64 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[1, 5], Operations: ['70-69=1', '68-63=5'] Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,66 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,66 unequal: No Solution No 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: 66:[63, 67], Operations: ['70-69=1', '68-1=67'] Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,66 unequal: No Solution Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,66 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,66 unequal: No Solution No 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: 66:[68, 64], Operations: ['70-69=1', '63+1=64'] Exploring Operation: 68*64=4352, Resulting Numbers: [4352] 4352,66 unequal: No Solution Exploring Operation: 68+64=132, Resulting Numbers: [132] 132,66 unequal: No Solution Exploring Operation: 68-64=4, Resulting Numbers: [4] 4,66 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: 66:[69, 63, 2], Operations: ['70-68=2'] Exploring Operation: 69-63=6, Resulting Numbers: [2, 6] Generated Node #0,2,0: 66:[2, 6] Operation: 69-63=6 Exploring Operation: 69-2=67, Resulting Numbers: [63, 67] Generated Node #0,2,1: 66:[63, 67] Operation: 69-2=67 Exploring Operation: 63+2=65, Resulting Numbers: [69, 65] Generated Node #0,2,2: 66:[69, 65] Operation: 63+2=65 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[2, 6], Operations: ['70-68=2', '69-63=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,66 unequal: No Solution No 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: 66:[63, 67], Operations: ['70-68=2', '69-2=67'] Exploring Operation: 63*67=4221, Resulting Numbers: [4221] 4221,66 unequal: No Solution Exploring Operation: 63+67=130, Resulting Numbers: [130] 130,66 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,66 unequal: No Solution No 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: 66:[69, 65], Operations: ['70-68=2', '63+2=65'] Exploring Operation: 69*65=4485, Resulting Numbers: [4485] 4485,66 unequal: No Solution Exploring Operation: 69-65=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 69+65=134, Resulting Numbers: [134] 134,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 66:[6, 2], Operations: ['69-63=6', '70-68=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,66 unequal: No Solution Moving to Node #0,0,0 Current State: 66:[68, 64], Operations: ['69-63=6', '70-6=64'] Exploring Operation: 68*64=4352, Resulting Numbers: [4352] 4352,66 unequal: No Solution Exploring Operation: 68-64=4, Resulting Numbers: [4] 4,66 unequal: No Solution Exploring Operation: 68+64=132, Resulting Numbers: [132] 132,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[70, 62], Operations: ['69-63=6', '68-6=62'] Exploring Operation: 70*62=4340, Resulting Numbers: [4340] 4340,66 unequal: No Solution Exploring Operation: 70+62=132, Resulting Numbers: [132] 132,66 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,66 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 86, 4, 22, 19 ]
86
[ "22-4=18", "19-18=1", "86*1=86" ]
Current State: 86:[86, 4, 22, 19], Operations: [] Exploring Operation: 22-4=18, Resulting Numbers: [86, 19, 18] Generated Node #2: [86, 19, 18] from Operation: 22-4=18 Current State: 86:[86, 19, 18], Operations: ['22-4=18'] Exploring Operation: 19-18=1, Resulting Numbers: [86, 1] Generated Node #3: [86, 1] from Operation: 19-18=1 Current State: 86:[86, 1], Operations: ['22-4=18', '19-18=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[86, 4, 22, 19], Operations: [] Exploring Operation: 22-19=3, Resulting Numbers: [86, 4, 3] Generated Node #0,0: 86:[86, 4, 3] Operation: 22-19=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[86, 4, 3], Operations: ['22-19=3'] Exploring Operation: 4-3=1, Resulting Numbers: [86, 1] Generated Node #0,0,0: 86:[86, 1] Operation: 4-3=1 Moving to Node #0,0,0 Current State: 86:[86, 1], Operations: ['22-19=3', '4-3=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[86, 4, 22, 19], Operations: [] Exploring Operation: 22-19=3, Resulting Numbers: [86, 4, 3] Generated Node #0,0: 86:[86, 4, 3] Operation: 22-19=3 Moving to Node #0,0 Current State: 86:[86, 4, 3], Operations: ['22-19=3'] Exploring Operation: 4-3=1, Resulting Numbers: [86, 1] Generated Node #0,0,0: 86:[86, 1] Operation: 4-3=1 Moving to Node #0,0,0 Current State: 86:[86, 1], Operations: ['22-19=3', '4-3=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 87, 4, 21, 13 ]
10
[ "87-13=74", "4*21=84", "84-74=10" ]
Current State: 10:[87, 4, 21, 13], Operations: [] Exploring Operation: 87-13=74, Resulting Numbers: [4, 21, 74] Generated Node #2: [4, 21, 74] from Operation: 87-13=74 Current State: 10:[4, 21, 74], Operations: ['87-13=74'] Exploring Operation: 4*21=84, Resulting Numbers: [74, 84] Generated Node #3: [74, 84] from Operation: 4*21=84 Current State: 10:[74, 84], Operations: ['87-13=74', '4*21=84'] Exploring Operation: 84-74=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[87, 4, 21, 13], Operations: [] Exploring Operation: 87-21=66, Resulting Numbers: [4, 13, 66] Generated Node #0,0: 10:[4, 13, 66] Operation: 87-21=66 Exploring Operation: 87-13=74, Resulting Numbers: [4, 21, 74] Generated Node #0,1: 10:[4, 21, 74] Operation: 87-13=74 Exploring Operation: 21-13=8, Resulting Numbers: [87, 4, 8] Generated Node #0,2: 10:[87, 4, 8] Operation: 21-13=8 Moving to Node #0,0 Current State: 10:[4, 13, 66], Operations: ['87-21=66'] Exploring Operation: 66-4=62, Resulting Numbers: [13, 62] Generated Node #0,0,0: 10:[13, 62] Operation: 66-4=62 Exploring Operation: 66-13=53, Resulting Numbers: [4, 53] Generated Node #0,0,1: 10:[4, 53] Operation: 66-13=53 Exploring Operation: 13-4=9, Resulting Numbers: [66, 9] Generated Node #0,0,2: 10:[66, 9] Operation: 13-4=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 10:[4, 53], Operations: ['87-21=66', '66-13=53'] Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 4*53=212, Resulting Numbers: [212] 212,10 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[13, 62], Operations: ['87-21=66', '66-4=62'] Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 13*62=806, Resulting Numbers: [806] 806,10 unequal: No Solution Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[66, 9], Operations: ['87-21=66', '13-4=9'] Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 66+9=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 66*9=594, Resulting Numbers: [594] 594,10 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: 10:[4, 21, 74], Operations: ['87-13=74'] Exploring Operation: 74-21=53, Resulting Numbers: [4, 53] Generated Node #0,1,0: 10:[4, 53] Operation: 74-21=53 Exploring Operation: 74-4=70, Resulting Numbers: [21, 70] Generated Node #0,1,1: 10:[21, 70] Operation: 74-4=70 Exploring Operation: 21-4=17, Resulting Numbers: [74, 17] Generated Node #0,1,2: 10:[74, 17] Operation: 21-4=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[4, 53], Operations: ['87-13=74', '74-21=53'] Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 4*53=212, Resulting Numbers: [212] 212,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[21, 70], Operations: ['87-13=74', '74-4=70'] Exploring Operation: 21*70=1470, Resulting Numbers: [1470] 1470,10 unequal: No Solution Exploring Operation: 70-21=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 21+70=91, Resulting Numbers: [91] 91,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[74, 17], Operations: ['87-13=74', '21-4=17'] Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,10 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,10 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: 10:[87, 4, 8], Operations: ['21-13=8'] Exploring Operation: 87-8=79, Resulting Numbers: [4, 79] Generated Node #0,2,0: 10:[4, 79] Operation: 87-8=79 Exploring Operation: 87-4=83, Resulting Numbers: [8, 83] Generated Node #0,2,1: 10:[8, 83] Operation: 87-4=83 Exploring Operation: 8/4=2, Resulting Numbers: [87, 2] Generated Node #0,2,2: 10:[87, 2] Operation: 8/4=2 Moving to Node #0,2,0 Current State: 10:[4, 79], Operations: ['21-13=8', '87-8=79'] Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,10 unequal: No Solution Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[8, 83], Operations: ['21-13=8', '87-4=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,10 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,10 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[87, 2], Operations: ['21-13=8', '8/4=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,10 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,10 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,10 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 91, 2, 65, 67 ]
91
[ "91+2=93", "67-65=2", "93-2=91" ]
Current State: 91:[91, 2, 65, 67], Operations: [] Exploring Operation: 91+2=93, Resulting Numbers: [65, 67, 93] Generated Node #2: [65, 67, 93] from Operation: 91+2=93 Current State: 91:[65, 67, 93], Operations: ['91+2=93'] Exploring Operation: 67-65=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 67-65=2 Current State: 91:[93, 2], Operations: ['91+2=93', '67-65=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[91, 2, 65, 67], Operations: [] Exploring Operation: 91-65=26, Resulting Numbers: [2, 67, 26] Generated Node #0,0: 91:[2, 67, 26] Operation: 91-65=26 Exploring Operation: 2+65=67, Resulting Numbers: [91, 67, 67] Generated Node #0,1: 91:[91, 67, 67] Operation: 2+65=67 Exploring Operation: 67-65=2, Resulting Numbers: [91, 2, 2] Generated Node #0,2: 91:[91, 2, 2] Operation: 67-65=2 Exploring Operation: 65+67=132, Resulting Numbers: [91, 2, 132] Generated Node #0,3: 91:[91, 2, 132] Operation: 65+67=132 Exploring Operation: 91-67=24, Resulting Numbers: [2, 65, 24] Generated Node #0,4: 91:[2, 65, 24] Operation: 91-67=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[91, 2, 2], Operations: ['67-65=2'] Exploring Operation: 2*2=4, Resulting Numbers: [91, 4] Generated Node #0,2,0: 91:[91, 4] Operation: 2*2=4 Exploring Operation: 2/2=1, Resulting Numbers: [91, 1] Generated Node #0,2,1: 91:[91, 1] Operation: 2/2=1 Exploring Operation: 2+2=4, Resulting Numbers: [91, 4] Generated Node #0,2,2: 91:[91, 4] Operation: 2+2=4 Exploring Operation: 91-2=89, Resulting Numbers: [2, 89] Generated Node #0,2,3: 91:[2, 89] Operation: 91-2=89 Exploring Operation: 91+2=93, Resulting Numbers: [2, 93] Generated Node #0,2,4: 91:[2, 93] Operation: 91+2=93 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[91, 4], Operations: ['67-65=2', '2*2=4'] Exploring Operation: 91+4=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 91*4=364, Resulting Numbers: [364] 364,91 unequal: No Solution Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,91 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 #0,2,2 Current State: 91:[91, 4], Operations: ['67-65=2', '2+2=4'] Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,91 unequal: No Solution Exploring Operation: 91*4=364, Resulting Numbers: [364] 364,91 unequal: No Solution Exploring Operation: 91+4=95, Resulting Numbers: [95] 95,91 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:[91, 1], Operations: ['67-65=2', '2/2=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,91 unequal: No Solution Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[91, 2, 65, 67], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [91, 2, 2] Generated Node #0,2: 91:[91, 2, 2] Operation: 67-65=2 Moving to Node #0,2 Current State: 91:[91, 2, 2], Operations: ['67-65=2'] Exploring Operation: 2/2=1, Resulting Numbers: [91, 1] Generated Node #0,2,1: 91:[91, 1] Operation: 2/2=1 Moving to Node #0,2,1 Current State: 91:[91, 1], Operations: ['67-65=2', '2/2=1'] Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 68, 33, 32, 23 ]
20
[ "68-33=35", "32+23=55", "55-35=20" ]
Current State: 20:[68, 33, 32, 23], Operations: [] Exploring Operation: 68-33=35, Resulting Numbers: [32, 23, 35] Generated Node #2: [32, 23, 35] from Operation: 68-33=35 Current State: 20:[32, 23, 35], Operations: ['68-33=35'] Exploring Operation: 32+23=55, Resulting Numbers: [35, 55] Generated Node #3: [35, 55] from Operation: 32+23=55 Current State: 20:[35, 55], Operations: ['68-33=35', '32+23=55'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[68, 33, 32, 23], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [33, 32, 45] Generated Node #0,0: 20:[33, 32, 45] Operation: 68-23=45 Exploring Operation: 68-33=35, Resulting Numbers: [32, 23, 35] Generated Node #0,1: 20:[32, 23, 35] Operation: 68-33=35 Exploring Operation: 33-32=1, Resulting Numbers: [68, 23, 1] Generated Node #0,2: 20:[68, 23, 1] Operation: 33-32=1 Exploring Operation: 68-32=36, Resulting Numbers: [33, 23, 36] Generated Node #0,3: 20:[33, 23, 36] Operation: 68-32=36 Moving to Node #0,1 Current State: 20:[32, 23, 35], Operations: ['68-33=35'] Exploring Operation: 32+23=55, Resulting Numbers: [35, 55] Generated Node #0,1,0: 20:[35, 55] Operation: 32+23=55 Exploring Operation: 35-32=3, Resulting Numbers: [23, 3] Generated Node #0,1,1: 20:[23, 3] Operation: 35-32=3 Exploring Operation: 35-23=12, Resulting Numbers: [32, 12] Generated Node #0,1,2: 20:[32, 12] Operation: 35-23=12 Exploring Operation: 32-23=9, Resulting Numbers: [35, 9] Generated Node #0,1,3: 20:[35, 9] Operation: 32-23=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[23, 3], Operations: ['68-33=35', '35-32=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,20 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[68, 33, 32, 23], Operations: [] Exploring Operation: 68-33=35, Resulting Numbers: [32, 23, 35] Generated Node #0,1: 20:[32, 23, 35] Operation: 68-33=35 Moving to Node #0,1 Current State: 20:[32, 23, 35], Operations: ['68-33=35'] Exploring Operation: 35-32=3, Resulting Numbers: [23, 3] Generated Node #0,1,1: 20:[23, 3] Operation: 35-32=3 Moving to Node #0,1,1 Current State: 20:[23, 3], Operations: ['68-33=35', '35-32=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 69, 60, 39, 26 ]
56
[ "69-60=9", "39+26=65", "65-9=56" ]
Current State: 56:[69, 60, 39, 26], Operations: [] Exploring Operation: 69-60=9, Resulting Numbers: [39, 26, 9] Generated Node #2: [39, 26, 9] from Operation: 69-60=9 Current State: 56:[39, 26, 9], Operations: ['69-60=9'] Exploring Operation: 39+26=65, Resulting Numbers: [9, 65] Generated Node #3: [9, 65] from Operation: 39+26=65 Current State: 56:[9, 65], Operations: ['69-60=9', '39+26=65'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[69, 60, 39, 26], Operations: [] Exploring Operation: 60-39=21, Resulting Numbers: [69, 26, 21] Generated Node #0,0: 56:[69, 26, 21] Operation: 60-39=21 Exploring Operation: 69-60=9, Resulting Numbers: [39, 26, 9] Generated Node #0,1: 56:[39, 26, 9] Operation: 69-60=9 Exploring Operation: 39-26=13, Resulting Numbers: [69, 60, 13] Generated Node #0,2: 56:[69, 60, 13] Operation: 39-26=13 Exploring Operation: 39+26=65, Resulting Numbers: [69, 60, 65] Generated Node #0,3: 56:[69, 60, 65] Operation: 39+26=65 Exploring Operation: 69-39=30, Resulting Numbers: [60, 26, 30] Generated Node #0,4: 56:[60, 26, 30] Operation: 69-39=30 Moving to Node #0,4 Current State: 56:[60, 26, 30], Operations: ['69-39=30'] Exploring Operation: 60/30=2, Resulting Numbers: [26, 2] Generated Node #0,4,0: 56:[26, 2] Operation: 60/30=2 Exploring Operation: 60-30=30, Resulting Numbers: [26, 30] Generated Node #0,4,1: 56:[26, 30] Operation: 60-30=30 Exploring Operation: 30-26=4, Resulting Numbers: [60, 4] Generated Node #0,4,2: 56:[60, 4] Operation: 30-26=4 Exploring Operation: 26+30=56, Resulting Numbers: [60, 56] Generated Node #0,4,3: 56:[60, 56] Operation: 26+30=56 Exploring Operation: 60-26=34, Resulting Numbers: [30, 34] Generated Node #0,4,4: 56:[30, 34] Operation: 60-26=34 Moving to Node #0,1 Current State: 56:[39, 26, 9], Operations: ['69-60=9'] Exploring Operation: 39-26=13, Resulting Numbers: [9, 13] Generated Node #0,1,0: 56:[9, 13] Operation: 39-26=13 Exploring Operation: 39-9=30, Resulting Numbers: [26, 30] Generated Node #0,1,1: 56:[26, 30] Operation: 39-9=30 Exploring Operation: 39+26=65, Resulting Numbers: [9, 65] Generated Node #0,1,2: 56:[9, 65] Operation: 39+26=65 Exploring Operation: 39+9=48, Resulting Numbers: [26, 48] Generated Node #0,1,3: 56:[26, 48] Operation: 39+9=48 Exploring Operation: 26-9=17, Resulting Numbers: [39, 17] Generated Node #0,1,4: 56:[39, 17] Operation: 26-9=17 Moving to Node #0,2 Current State: 56:[69, 60, 13], Operations: ['39-26=13'] Exploring Operation: 69+13=82, Resulting Numbers: [60, 82] Generated Node #0,2,0: 56:[60, 82] Operation: 69+13=82 Exploring Operation: 69-60=9, Resulting Numbers: [13, 9] Generated Node #0,2,1: 56:[13, 9] Operation: 69-60=9 Exploring Operation: 60+13=73, Resulting Numbers: [69, 73] Generated Node #0,2,2: 56:[69, 73] Operation: 60+13=73 Exploring Operation: 69-13=56, Resulting Numbers: [60, 56] Generated Node #0,2,3: 56:[60, 56] Operation: 69-13=56 Exploring Operation: 60-13=47, Resulting Numbers: [69, 47] Generated Node #0,2,4: 56:[69, 47] Operation: 60-13=47 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[13, 9], Operations: ['39-26=13', '69-60=9'] Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,56 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,56 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 #0,2,3 Current State: 56:[60, 56], Operations: ['39-26=13', '69-13=56'] Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,56 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,56 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,56 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 #0,2,4 Current State: 56:[69, 47], Operations: ['39-26=13', '60-13=47'] Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 69+47=116, Resulting Numbers: [116] 116,56 unequal: No Solution Exploring Operation: 69*47=3243, Resulting Numbers: [3243] 3243,56 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 #0,2,0 Current State: 56:[60, 82], Operations: ['39-26=13', '69+13=82'] Exploring Operation: 60*82=4920, Resulting Numbers: [4920] 4920,56 unequal: No Solution Exploring Operation: 82-60=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 60+82=142, Resulting Numbers: [142] 142,56 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 #0,2,2 Current State: 56:[69, 73], Operations: ['39-26=13', '60+13=73'] Exploring Operation: 73-69=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 69+73=142, Resulting Numbers: [142] 142,56 unequal: No Solution Exploring Operation: 69*73=5037, Resulting Numbers: [5037] 5037,56 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:[69, 26, 21], Operations: ['60-39=21'] Exploring Operation: 69-21=48, Resulting Numbers: [26, 48] Generated Node #0,0,0: 56:[26, 48] Operation: 69-21=48 Exploring Operation: 26-21=5, Resulting Numbers: [69, 5] Generated Node #0,0,1: 56:[69, 5] Operation: 26-21=5 Exploring Operation: 26+21=47, Resulting Numbers: [69, 47] Generated Node #0,0,2: 56:[69, 47] Operation: 26+21=47 Exploring Operation: 69+21=90, Resulting Numbers: [26, 90] Generated Node #0,0,3: 56:[26, 90] Operation: 69+21=90 Exploring Operation: 69-26=43, Resulting Numbers: [21, 43] Generated Node #0,0,4: 56:[21, 43] Operation: 69-26=43 Moving to Node #0,3 Current State: 56:[69, 60, 65], Operations: ['39+26=65'] Exploring Operation: 69-60=9, Resulting Numbers: [65, 9] Generated Node #0,3,0: 56:[65, 9] Operation: 69-60=9 Exploring Operation: 69-65=4, Resulting Numbers: [60, 4] Generated Node #0,3,1: 56:[60, 4] Operation: 69-65=4 Exploring Operation: 69+60=129, Resulting Numbers: [65, 129] Generated Node #0,3,2: 56:[65, 129] Operation: 69+60=129 Exploring Operation: 69+65=134, Resulting Numbers: [60, 134] Generated Node #0,3,3: 56:[60, 134] Operation: 69+65=134 Exploring Operation: 65-60=5, Resulting Numbers: [69, 5] Generated Node #0,3,4: 56:[69, 5] Operation: 65-60=5 Moving to Node #0,4,0 Current State: 56:[26, 2], Operations: ['69-39=30', '60/30=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,56 unequal: No Solution Moving to Node #0,1,0 Current State: 56:[9, 13], Operations: ['69-60=9', '39-26=13'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[26, 30], Operations: ['69-60=9', '39-9=30'] Exploring Operation: 26+30=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[69, 60, 39, 26], Operations: [] Exploring Operation: 69-60=9, Resulting Numbers: [39, 26, 9] Generated Node #0,1: 56:[39, 26, 9] Operation: 69-60=9 Moving to Node #0,1 Current State: 56:[39, 26, 9], Operations: ['69-60=9'] Exploring Operation: 39-9=30, Resulting Numbers: [26, 30] Generated Node #0,1,1: 56:[26, 30] Operation: 39-9=30 Moving to Node #0,1,1 Current State: 56:[26, 30], Operations: ['69-60=9', '39-9=30'] Exploring Operation: 26+30=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.950521
hs_5
sum_heuristic
[ 97, 40, 61, 87 ]
31
[ "97-40=57", "87-61=26", "57-26=31" ]
Current State: 31:[97, 40, 61, 87], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [61, 87, 57] Generated Node #2: [61, 87, 57] from Operation: 97-40=57 Current State: 31:[61, 87, 57], Operations: ['97-40=57'] Exploring Operation: 87-61=26, Resulting Numbers: [57, 26] Generated Node #3: [57, 26] from Operation: 87-61=26 Current State: 31:[57, 26], Operations: ['97-40=57', '87-61=26'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[97, 40, 61, 87], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [40, 87, 36] Generated Node #0,0: 31:[40, 87, 36] Operation: 97-61=36 Exploring Operation: 97-87=10, Resulting Numbers: [40, 61, 10] Generated Node #0,1: 31:[40, 61, 10] Operation: 97-87=10 Moving to Node #0,1 Current State: 31:[40, 61, 10], Operations: ['97-87=10'] Exploring Operation: 61-40=21, Resulting Numbers: [10, 21] Generated Node #0,1,0: 31:[10, 21] Operation: 61-40=21 Exploring Operation: 61-10=51, Resulting Numbers: [40, 51] Generated Node #0,1,1: 31:[40, 51] Operation: 61-10=51 Moving to Node #0,0 Current State: 31:[40, 87, 36], Operations: ['97-61=36'] Exploring Operation: 87-40=47, Resulting Numbers: [36, 47] Generated Node #0,0,0: 31:[36, 47] Operation: 87-40=47 Exploring Operation: 87-36=51, Resulting Numbers: [40, 51] Generated Node #0,0,1: 31:[40, 51] Operation: 87-36=51 Moving to Node #0,0,0 Current State: 31:[36, 47], Operations: ['97-61=36', '87-40=47'] Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 36+47=83, Resulting Numbers: [83] 83,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[40, 51], Operations: ['97-87=10', '61-10=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[40, 51], Operations: ['97-61=36', '87-36=51'] Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[10, 21], Operations: ['97-87=10', '61-40=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[97, 40, 61, 87], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [40, 61, 10] Generated Node #0,1: 31:[40, 61, 10] Operation: 97-87=10 Moving to Node #0,1 Current State: 31:[40, 61, 10], Operations: ['97-87=10'] Exploring Operation: 61-40=21, Resulting Numbers: [10, 21] Generated Node #0,1,0: 31:[10, 21] Operation: 61-40=21 Moving to Node #0,1,0 Current State: 31:[10, 21], Operations: ['97-87=10', '61-40=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 12, 30, 19, 48 ]
17
[ "12+48=60", "60/30=2", "19-2=17" ]
Current State: 17:[12, 30, 19, 48], Operations: [] Exploring Operation: 12+48=60, Resulting Numbers: [30, 19, 60] Generated Node #2: [30, 19, 60] from Operation: 12+48=60 Current State: 17:[30, 19, 60], Operations: ['12+48=60'] Exploring Operation: 60/30=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 60/30=2 Current State: 17:[19, 2], Operations: ['12+48=60', '60/30=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[12, 30, 19, 48], Operations: [] Exploring Operation: 48-19=29, Resulting Numbers: [12, 30, 29] Generated Node #0,0: 17:[12, 30, 29] Operation: 48-19=29 Exploring Operation: 48-30=18, Resulting Numbers: [12, 19, 18] Generated Node #0,1: 17:[12, 19, 18] Operation: 48-30=18 Exploring Operation: 48/12=4, Resulting Numbers: [30, 19, 4] Generated Node #0,2: 17:[30, 19, 4] Operation: 48/12=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[12, 19, 18], Operations: ['48-30=18'] Exploring Operation: 12+19=31, Resulting Numbers: [18, 31] Generated Node #0,1,0: 17:[18, 31] Operation: 12+19=31 Exploring Operation: 18-12=6, Resulting Numbers: [19, 6] Generated Node #0,1,1: 17:[19, 6] Operation: 18-12=6 Exploring Operation: 19-12=7, Resulting Numbers: [18, 7] Generated Node #0,1,2: 17:[18, 7] Operation: 19-12=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 17:[18, 7], Operations: ['48-30=18', '19-12=7'] Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,17 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,17 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:[19, 6], Operations: ['48-30=18', '18-12=6'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 19*6=114, Resulting Numbers: [114] 114,17 unequal: No Solution Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,17 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 #0,1,0 Current State: 17:[18, 31], Operations: ['48-30=18', '12+19=31'] Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,17 unequal: No Solution Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,17 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:[30, 19, 4], Operations: ['48/12=4'] Exploring Operation: 30-19=11, Resulting Numbers: [4, 11] Generated Node #0,2,0: 17:[4, 11] Operation: 30-19=11 Exploring Operation: 19-4=15, Resulting Numbers: [30, 15] Generated Node #0,2,1: 17:[30, 15] Operation: 19-4=15 Exploring Operation: 30-4=26, Resulting Numbers: [19, 26] Generated Node #0,2,2: 17:[19, 26] Operation: 30-4=26 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[19, 26], Operations: ['48/12=4', '30-4=26'] Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,17 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,17 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:[30, 15], Operations: ['48/12=4', '19-4=15'] Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,17 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[4, 11], Operations: ['48/12=4', '30-19=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,17 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:[12, 30, 29], Operations: ['48-19=29'] Exploring Operation: 29-12=17, Resulting Numbers: [30, 17] Generated Node #0,0,0: 17:[30, 17] Operation: 29-12=17 Exploring Operation: 30-12=18, Resulting Numbers: [29, 18] Generated Node #0,0,1: 17:[29, 18] Operation: 30-12=18 Exploring Operation: 30-29=1, Resulting Numbers: [12, 1] Generated Node #0,0,2: 17:[12, 1] Operation: 30-29=1 Moving to Node #0,0,0 Current State: 17:[30, 17], Operations: ['48-19=29', '29-12=17'] Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,17 unequal: No Solution Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[29, 18], Operations: ['48-19=29', '30-12=18'] Exploring Operation: 29*18=522, Resulting Numbers: [522] 522,17 unequal: No Solution Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,17 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[12, 1], Operations: ['48-19=29', '30-29=1'] Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,17 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
[ 47, 49, 48, 69 ]
20
[ "48-47=1", "69-49=20", "1*20=20" ]
Current State: 20:[47, 49, 48, 69], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [49, 69, 1] Generated Node #2: [49, 69, 1] from Operation: 48-47=1 Current State: 20:[49, 69, 1], Operations: ['48-47=1'] Exploring Operation: 69-49=20, Resulting Numbers: [1, 20] Generated Node #3: [1, 20] from Operation: 69-49=20 Current State: 20:[1, 20], Operations: ['48-47=1', '69-49=20'] Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[47, 49, 48, 69], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [47, 48, 20] Generated Node #0,0: 20:[47, 48, 20] Operation: 69-49=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[47, 48, 20], Operations: ['69-49=20'] Exploring Operation: 48-47=1, Resulting Numbers: [20, 1] Generated Node #0,0,0: 20:[20, 1] Operation: 48-47=1 Moving to Node #0,0,0 Current State: 20:[20, 1], Operations: ['69-49=20', '48-47=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[47, 49, 48, 69], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [47, 48, 20] Generated Node #0,0: 20:[47, 48, 20] Operation: 69-49=20 Moving to Node #0,0 Current State: 20:[47, 48, 20], Operations: ['69-49=20'] Exploring Operation: 48-47=1, Resulting Numbers: [20, 1] Generated Node #0,0,0: 20:[20, 1] Operation: 48-47=1 Moving to Node #0,0,0 Current State: 20:[20, 1], Operations: ['69-49=20', '48-47=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 84, 46, 51, 63 ]
53
[ "63-51=12", "84/12=7", "46+7=53" ]
Current State: 53:[84, 46, 51, 63], Operations: [] Exploring Operation: 63-51=12, Resulting Numbers: [84, 46, 12] Generated Node #2: [84, 46, 12] from Operation: 63-51=12 Current State: 53:[84, 46, 12], Operations: ['63-51=12'] Exploring Operation: 84/12=7, Resulting Numbers: [46, 7] Generated Node #3: [46, 7] from Operation: 84/12=7 Current State: 53:[46, 7], Operations: ['63-51=12', '84/12=7'] Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[84, 46, 51, 63], Operations: [] Exploring Operation: 84-51=33, Resulting Numbers: [46, 63, 33] Generated Node #0,0: 53:[46, 63, 33] Operation: 84-51=33 Exploring Operation: 84-46=38, Resulting Numbers: [51, 63, 38] Generated Node #0,1: 53:[51, 63, 38] Operation: 84-46=38 Moving to Node #0,1 Current State: 53:[51, 63, 38], Operations: ['84-46=38'] Exploring Operation: 51+38=89, Resulting Numbers: [63, 89] Generated Node #0,1,0: 53:[63, 89] Operation: 51+38=89 Exploring Operation: 63-38=25, Resulting Numbers: [51, 25] Generated Node #0,1,1: 53:[51, 25] Operation: 63-38=25 Moving to Node #0,0 Current State: 53:[46, 63, 33], Operations: ['84-51=33'] Exploring Operation: 63-33=30, Resulting Numbers: [46, 30] Generated Node #0,0,0: 53:[46, 30] Operation: 63-33=30 Exploring Operation: 46+33=79, Resulting Numbers: [63, 79] Generated Node #0,0,1: 53:[63, 79] Operation: 46+33=79 Moving to Node #0,1,1 Current State: 53:[51, 25], Operations: ['84-46=38', '63-38=25'] Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,53 unequal: No Solution Exploring Operation: 51+25=76, Resulting Numbers: [76] 76,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[46, 30], Operations: ['84-51=33', '63-33=30'] Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[63, 79], Operations: ['84-51=33', '46+33=79'] Exploring Operation: 63+79=142, Resulting Numbers: [142] 142,53 unequal: No Solution Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[63, 89], Operations: ['84-46=38', '51+38=89'] Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,53 unequal: No Solution Exploring Operation: 63+89=152, Resulting Numbers: [152] 152,53 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 21, 59, 4 ]
29
[ "4*21=84", "59-4=55", "84-55=29" ]
Current State: 29:[4, 21, 59, 4], Operations: [] Exploring Operation: 4*21=84, Resulting Numbers: [59, 84] Generated Node #2: [59, 84] from Operation: 4*21=84 Current State: 29:[59, 84], Operations: ['4*21=84'] Exploring Operation: 59-4=55, Resulting Numbers: [84, 55] Generated Node #3: [84, 55] from Operation: 59-4=55 Current State: 29:[84, 55], Operations: ['4*21=84', '59-4=55'] Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[4, 21, 59, 4], Operations: [] Exploring Operation: 4+21=25, Resulting Numbers: [59, 4, 25] Generated Node #0,0: 29:[59, 4, 25] Operation: 4+21=25 Exploring Operation: 59-4=55, Resulting Numbers: [21, 4, 55] Generated Node #0,1: 29:[21, 4, 55] Operation: 59-4=55 Exploring Operation: 4*4=16, Resulting Numbers: [21, 59, 16] Generated Node #0,2: 29:[21, 59, 16] Operation: 4*4=16 Moving to Node #0,2 Current State: 29:[21, 59, 16], Operations: ['4*4=16'] Exploring Operation: 59-16=43, Resulting Numbers: [21, 43] Generated Node #0,2,0: 29:[21, 43] Operation: 59-16=43 Exploring Operation: 59-21=38, Resulting Numbers: [16, 38] Generated Node #0,2,1: 29:[16, 38] Operation: 59-21=38 Exploring Operation: 21+16=37, Resulting Numbers: [59, 37] Generated Node #0,2,2: 29:[59, 37] Operation: 21+16=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[21, 43], Operations: ['4*4=16', '59-16=43'] Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,29 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 #0,2,1 Current State: 29:[16, 38], Operations: ['4*4=16', '59-21=38'] Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,29 unequal: No Solution Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,29 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,29 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:[59, 37], Operations: ['4*4=16', '21+16=37'] Exploring Operation: 59+37=96, Resulting Numbers: [96] 96,29 unequal: No Solution Exploring Operation: 59*37=2183, Resulting Numbers: [2183] 2183,29 unequal: No Solution Exploring Operation: 59-37=22, Resulting Numbers: [22] 22,29 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: 29:[59, 4, 25], Operations: ['4+21=25'] Exploring Operation: 59-25=34, Resulting Numbers: [4, 34] Generated Node #0,0,0: 29:[4, 34] Operation: 59-25=34 Exploring Operation: 59-4=55, Resulting Numbers: [25, 55] Generated Node #0,0,1: 29:[25, 55] Operation: 59-4=55 Exploring Operation: 4+25=29, Resulting Numbers: [59, 29] Generated Node #0,0,2: 29:[59, 29] Operation: 4+25=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[4, 34], Operations: ['4+21=25', '59-25=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,29 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 4+34=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 #0,0,1 Current State: 29:[25, 55], Operations: ['4+21=25', '59-4=55'] Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 25*55=1375, Resulting Numbers: [1375] 1375,29 unequal: No Solution Exploring Operation: 25+55=80, Resulting Numbers: [80] 80,29 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 #0,0,2 Current State: 29:[59, 29], Operations: ['4+21=25', '4+25=29'] Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,29 unequal: No Solution Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,29 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:[21, 4, 55], Operations: ['59-4=55'] Exploring Operation: 55-21=34, Resulting Numbers: [4, 34] Generated Node #0,1,0: 29:[4, 34] Operation: 55-21=34 Exploring Operation: 55-4=51, Resulting Numbers: [21, 51] Generated Node #0,1,1: 29:[21, 51] Operation: 55-4=51 Exploring Operation: 21+4=25, Resulting Numbers: [55, 25] Generated Node #0,1,2: 29:[55, 25] Operation: 21+4=25 Moving to Node #0,1,0 Current State: 29:[4, 34], Operations: ['59-4=55', '55-21=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,29 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[21, 51], Operations: ['59-4=55', '55-4=51'] Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 21*51=1071, Resulting Numbers: [1071] 1071,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[55, 25], Operations: ['59-4=55', '21+4=25'] Exploring Operation: 55+25=80, Resulting Numbers: [80] 80,29 unequal: No Solution Exploring Operation: 55*25=1375, Resulting Numbers: [1375] 1375,29 unequal: No Solution Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,29 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 79, 24, 33, 57 ]
36
[ "79-57=22", "24*33=792", "792/22=36" ]
Current State: 36:[79, 24, 33, 57], Operations: [] Exploring Operation: 79-57=22, Resulting Numbers: [24, 33, 22] Generated Node #2: [24, 33, 22] from Operation: 79-57=22 Current State: 36:[24, 33, 22], Operations: ['79-57=22'] Exploring Operation: 24*33=792, Resulting Numbers: [22, 792] Generated Node #3: [22, 792] from Operation: 24*33=792 Current State: 36:[22, 792], Operations: ['79-57=22', '24*33=792'] Exploring Operation: 792/22=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[79, 24, 33, 57], Operations: [] Exploring Operation: 79-57=22, Resulting Numbers: [24, 33, 22] Generated Node #0,0: 36:[24, 33, 22] Operation: 79-57=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[24, 33, 22], Operations: ['79-57=22'] Exploring Operation: 24-22=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 36:[33, 2] Operation: 24-22=2 Moving to Node #0,0,0 Current State: 36:[33, 2], Operations: ['79-57=22', '24-22=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,36 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
[ 50, 62, 57, 32 ]
23
[ "50+62=112", "57+32=89", "112-89=23" ]
Current State: 23:[50, 62, 57, 32], Operations: [] Exploring Operation: 50+62=112, Resulting Numbers: [57, 32, 112] Generated Node #2: [57, 32, 112] from Operation: 50+62=112 Current State: 23:[57, 32, 112], Operations: ['50+62=112'] Exploring Operation: 57+32=89, Resulting Numbers: [112, 89] Generated Node #3: [112, 89] from Operation: 57+32=89 Current State: 23:[112, 89], Operations: ['50+62=112', '57+32=89'] Exploring Operation: 112-89=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[50, 62, 57, 32], Operations: [] Exploring Operation: 62-50=12, Resulting Numbers: [57, 32, 12] Generated Node #0,0: 23:[57, 32, 12] Operation: 62-50=12 Moving to Node #0,0 Current State: 23:[57, 32, 12], Operations: ['62-50=12'] Exploring Operation: 57-32=25, Resulting Numbers: [12, 25] Generated Node #0,0,0: 23:[12, 25] Operation: 57-32=25 Moving to Node #0,0,0 Current State: 23:[12, 25], Operations: ['62-50=12', '57-32=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,23 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 82, 57, 27, 84 ]
15
[ "84-82=2", "57-27=30", "30/2=15" ]
Current State: 15:[82, 57, 27, 84], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [57, 27, 2] Generated Node #2: [57, 27, 2] from Operation: 84-82=2 Current State: 15:[57, 27, 2], Operations: ['84-82=2'] Exploring Operation: 57-27=30, Resulting Numbers: [2, 30] Generated Node #3: [2, 30] from Operation: 57-27=30 Current State: 15:[2, 30], Operations: ['84-82=2', '57-27=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[82, 57, 27, 84], Operations: [] Exploring Operation: 82-57=25, Resulting Numbers: [27, 84, 25] Generated Node #0,0: 15:[27, 84, 25] Operation: 82-57=25 Exploring Operation: 84-82=2, Resulting Numbers: [57, 27, 2] Generated Node #0,1: 15:[57, 27, 2] Operation: 84-82=2 Exploring Operation: 84-57=27, Resulting Numbers: [82, 27, 27] Generated Node #0,2: 15:[82, 27, 27] Operation: 84-57=27 Exploring Operation: 82-27=55, Resulting Numbers: [57, 84, 55] Generated Node #0,3: 15:[57, 84, 55] Operation: 82-27=55 Moving to Node #0,1 Current State: 15:[57, 27, 2], Operations: ['84-82=2'] Exploring Operation: 57-27=30, Resulting Numbers: [2, 30] Generated Node #0,1,0: 15:[2, 30] Operation: 57-27=30 Exploring Operation: 57-2=55, Resulting Numbers: [27, 55] Generated Node #0,1,1: 15:[27, 55] Operation: 57-2=55 Exploring Operation: 27-2=25, Resulting Numbers: [57, 25] Generated Node #0,1,2: 15:[57, 25] Operation: 27-2=25 Exploring Operation: 57+2=59, Resulting Numbers: [27, 59] Generated Node #0,1,3: 15:[27, 59] Operation: 57+2=59 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[2, 30], Operations: ['84-82=2', '57-27=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,15 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,15 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[82, 57, 27, 84], Operations: [] Exploring Operation: 84-82=2, Resulting Numbers: [57, 27, 2] Generated Node #0,1: 15:[57, 27, 2] Operation: 84-82=2 Moving to Node #0,1 Current State: 15:[57, 27, 2], Operations: ['84-82=2'] Exploring Operation: 57-27=30, Resulting Numbers: [2, 30] Generated Node #0,1,0: 15:[2, 30] Operation: 57-27=30 Moving to Node #0,1,0 Current State: 15:[2, 30], Operations: ['84-82=2', '57-27=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 5, 53, 53, 31 ]
31
[ "53-53=0", "5*0=0", "31+0=31" ]
Current State: 31:[5, 53, 53, 31], Operations: [] Exploring Operation: 53-53=0, Resulting Numbers: [5, 31, 0] Generated Node #2: [5, 31, 0] from Operation: 53-53=0 Current State: 31:[5, 31, 0], Operations: ['53-53=0'] Exploring Operation: 5*0=0, Resulting Numbers: [31, 0] Generated Node #3: [31, 0] from Operation: 5*0=0 Current State: 31:[31, 0], Operations: ['53-53=0', '5*0=0'] Exploring Operation: 31+0=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[5, 53, 53, 31], Operations: [] Exploring Operation: 53-5=48, Resulting Numbers: [53, 31, 48] Generated Node #0,0: 31:[53, 31, 48] Operation: 53-5=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[53, 31, 48], Operations: ['53-5=48'] Exploring Operation: 53-31=22, Resulting Numbers: [48, 22] Generated Node #0,0,0: 31:[48, 22] Operation: 53-31=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[48, 22], Operations: ['53-5=48', '53-31=22'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 71, 65, 74, 90 ]
89
[ "71-65=6", "90/6=15", "74+15=89" ]
Current State: 89:[71, 65, 74, 90], Operations: [] Exploring Operation: 71-65=6, Resulting Numbers: [74, 90, 6] Generated Node #2: [74, 90, 6] from Operation: 71-65=6 Current State: 89:[74, 90, 6], Operations: ['71-65=6'] Exploring Operation: 90/6=15, Resulting Numbers: [74, 15] Generated Node #3: [74, 15] from Operation: 90/6=15 Current State: 89:[74, 15], Operations: ['71-65=6', '90/6=15'] Exploring Operation: 74+15=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[71, 65, 74, 90], Operations: [] Exploring Operation: 90-65=25, Resulting Numbers: [71, 74, 25] Generated Node #0,0: 89:[71, 74, 25] Operation: 90-65=25 Exploring Operation: 71+74=145, Resulting Numbers: [65, 90, 145] Generated Node #0,1: 89:[65, 90, 145] Operation: 71+74=145 Exploring Operation: 65+74=139, Resulting Numbers: [71, 90, 139] Generated Node #0,2: 89:[71, 90, 139] Operation: 65+74=139 Exploring Operation: 71+65=136, Resulting Numbers: [74, 90, 136] Generated Node #0,3: 89:[74, 90, 136] Operation: 71+65=136 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[74, 90, 136], Operations: ['71+65=136'] Exploring Operation: 136-74=62, Resulting Numbers: [90, 62] Generated Node #0,3,0: 89:[90, 62] Operation: 136-74=62 Exploring Operation: 136-90=46, Resulting Numbers: [74, 46] Generated Node #0,3,1: 89:[74, 46] Operation: 136-90=46 Exploring Operation: 74+90=164, Resulting Numbers: [136, 164] Generated Node #0,3,2: 89:[136, 164] Operation: 74+90=164 Exploring Operation: 90-74=16, Resulting Numbers: [136, 16] Generated Node #0,3,3: 89:[136, 16] Operation: 90-74=16 Moving to Node #0,3,0 Current State: 89:[90, 62], Operations: ['71+65=136', '136-74=62'] Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 90*62=5580, Resulting Numbers: [5580] 5580,89 unequal: No Solution Exploring Operation: 90+62=152, Resulting Numbers: [152] 152,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[74, 46], Operations: ['71+65=136', '136-90=46'] Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[136, 16], Operations: ['71+65=136', '90-74=16'] Exploring Operation: 136+16=152, Resulting Numbers: [152] 152,89 unequal: No Solution Exploring Operation: 136-16=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 136*16=2176, Resulting Numbers: [2176] 2176,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[136, 164], Operations: ['71+65=136', '74+90=164'] Exploring Operation: 164-136=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 136+164=300, Resulting Numbers: [300] 300,89 unequal: No Solution Exploring Operation: 136*164=22304, Resulting Numbers: [22304] 22304,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[71, 90, 139], Operations: ['65+74=139'] Exploring Operation: 71+90=161, Resulting Numbers: [139, 161] Generated Node #0,2,0: 89:[139, 161] Operation: 71+90=161 Exploring Operation: 90-71=19, Resulting Numbers: [139, 19] Generated Node #0,2,1: 89:[139, 19] Operation: 90-71=19 Exploring Operation: 139-71=68, Resulting Numbers: [90, 68] Generated Node #0,2,2: 89:[90, 68] Operation: 139-71=68 Exploring Operation: 139-90=49, Resulting Numbers: [71, 49] Generated Node #0,2,3: 89:[71, 49] Operation: 139-90=49 Moving to Node #0,2,2 Current State: 89:[90, 68], Operations: ['65+74=139', '139-71=68'] Exploring Operation: 90*68=6120, Resulting Numbers: [6120] 6120,89 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 90+68=158, Resulting Numbers: [158] 158,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[71, 49], Operations: ['65+74=139', '139-90=49'] Exploring Operation: 71+49=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 71-49=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 71*49=3479, Resulting Numbers: [3479] 3479,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[139, 19], Operations: ['65+74=139', '90-71=19'] Exploring Operation: 139*19=2641, Resulting Numbers: [2641] 2641,89 unequal: No Solution Exploring Operation: 139+19=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 139-19=120, Resulting Numbers: [120] 120,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[139, 161], Operations: ['65+74=139', '71+90=161'] Exploring Operation: 139*161=22379, Resulting Numbers: [22379] 22379,89 unequal: No Solution Exploring Operation: 161-139=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 139+161=300, Resulting Numbers: [300] 300,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[65, 90, 145], Operations: ['71+74=145'] Exploring Operation: 145-65=80, Resulting Numbers: [90, 80] Generated Node #0,1,0: 89:[90, 80] Operation: 145-65=80 Exploring Operation: 90-65=25, Resulting Numbers: [145, 25] Generated Node #0,1,1: 89:[145, 25] Operation: 90-65=25 Exploring Operation: 65+90=155, Resulting Numbers: [145, 155] Generated Node #0,1,2: 89:[145, 155] Operation: 65+90=155 Exploring Operation: 145-90=55, Resulting Numbers: [65, 55] Generated Node #0,1,3: 89:[65, 55] Operation: 145-90=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[90, 80], Operations: ['71+74=145', '145-65=80'] Exploring Operation: 90*80=7200, Resulting Numbers: [7200] 7200,89 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 90+80=170, Resulting Numbers: [170] 170,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 89:[65, 55], Operations: ['71+74=145', '145-90=55'] Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,89 unequal: No Solution Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[145, 25], Operations: ['71+74=145', '90-65=25'] Exploring Operation: 145+25=170, Resulting Numbers: [170] 170,89 unequal: No Solution Exploring Operation: 145-25=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 145*25=3625, Resulting Numbers: [3625] 3625,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[145, 155], Operations: ['71+74=145', '65+90=155'] Exploring Operation: 145+155=300, Resulting Numbers: [300] 300,89 unequal: No Solution Exploring Operation: 145*155=22475, Resulting Numbers: [22475] 22475,89 unequal: No Solution Exploring Operation: 155-145=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[71, 74, 25], Operations: ['90-65=25'] Exploring Operation: 74-25=49, Resulting Numbers: [71, 49] Generated Node #0,0,0: 89:[71, 49] Operation: 74-25=49 Exploring Operation: 71-25=46, Resulting Numbers: [74, 46] Generated Node #0,0,1: 89:[74, 46] Operation: 71-25=46 Exploring Operation: 74+25=99, Resulting Numbers: [71, 99] Generated Node #0,0,2: 89:[71, 99] Operation: 74+25=99 Exploring Operation: 71+25=96, Resulting Numbers: [74, 96] Generated Node #0,0,3: 89:[74, 96] Operation: 71+25=96 Moving to Node #0,0,3 Current State: 89:[74, 96], Operations: ['90-65=25', '71+25=96'] Exploring Operation: 74+96=170, Resulting Numbers: [170] 170,89 unequal: No Solution Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 74*96=7104, Resulting Numbers: [7104] 7104,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[71, 99], Operations: ['90-65=25', '74+25=99'] Exploring Operation: 71+99=170, Resulting Numbers: [170] 170,89 unequal: No Solution Exploring Operation: 71*99=7029, Resulting Numbers: [7029] 7029,89 unequal: No Solution Exploring Operation: 99-71=28, Resulting Numbers: [28] 28,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[74, 46], Operations: ['90-65=25', '71-25=46'] Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,89 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[71, 49], Operations: ['90-65=25', '74-25=49'] Exploring Operation: 71*49=3479, Resulting Numbers: [3479] 3479,89 unequal: No Solution Exploring Operation: 71-49=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 71+49=120, Resulting Numbers: [120] 120,89 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
[ 88, 90, 92, 22 ]
22
[ "92-90=2", "88/2=44", "44-22=22" ]
Current State: 22:[88, 90, 92, 22], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [88, 22, 2] Generated Node #2: [88, 22, 2] from Operation: 92-90=2 Current State: 22:[88, 22, 2], Operations: ['92-90=2'] Exploring Operation: 88/2=44, Resulting Numbers: [22, 44] Generated Node #3: [22, 44] from Operation: 88/2=44 Current State: 22:[22, 44], Operations: ['92-90=2', '88/2=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[88, 90, 92, 22], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [92, 22, 2] Generated Node #0,0: 22:[92, 22, 2] Operation: 90-88=2 Exploring Operation: 92-90=2, Resulting Numbers: [88, 22, 2] Generated Node #0,1: 22:[88, 22, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[88, 22, 2], Operations: ['92-90=2'] Exploring Operation: 88/22=4, Resulting Numbers: [2, 4] Generated Node #0,1,0: 22:[2, 4] Operation: 88/22=4 Exploring Operation: 88/2=44, Resulting Numbers: [22, 44] Generated Node #0,1,1: 22:[22, 44] Operation: 88/2=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[2, 4], Operations: ['92-90=2', '88/22=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[22, 44], Operations: ['92-90=2', '88/2=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[88, 90, 92, 22], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [88, 22, 2] Generated Node #0,1: 22:[88, 22, 2] Operation: 92-90=2 Moving to Node #0,1 Current State: 22:[88, 22, 2], Operations: ['92-90=2'] Exploring Operation: 88/2=44, Resulting Numbers: [22, 44] Generated Node #0,1,1: 22:[22, 44] Operation: 88/2=44 Moving to Node #0,1,1 Current State: 22:[22, 44], Operations: ['92-90=2', '88/2=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 4, 38, 15, 28 ]
30
[ "4+15=19", "38/19=2", "28+2=30" ]
Current State: 30:[4, 38, 15, 28], Operations: [] Exploring Operation: 4+15=19, Resulting Numbers: [38, 28, 19] Generated Node #2: [38, 28, 19] from Operation: 4+15=19 Current State: 30:[38, 28, 19], Operations: ['4+15=19'] Exploring Operation: 38/19=2, Resulting Numbers: [28, 2] Generated Node #3: [28, 2] from Operation: 38/19=2 Current State: 30:[28, 2], Operations: ['4+15=19', '38/19=2'] Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 38, 15, 28], Operations: [] Exploring Operation: 38-4=34, Resulting Numbers: [15, 28, 34] Generated Node #0,0: 30:[15, 28, 34] Operation: 38-4=34 Exploring Operation: 38-28=10, Resulting Numbers: [4, 15, 10] Generated Node #0,1: 30:[4, 15, 10] Operation: 38-28=10 Exploring Operation: 28/4=7, Resulting Numbers: [38, 15, 7] Generated Node #0,2: 30:[38, 15, 7] Operation: 28/4=7 Moving to Node #0,1 Current State: 30:[4, 15, 10], Operations: ['38-28=10'] Exploring Operation: 10-4=6, Resulting Numbers: [15, 6] Generated Node #0,1,0: 30:[15, 6] Operation: 10-4=6 Exploring Operation: 4+10=14, Resulting Numbers: [15, 14] Generated Node #0,1,1: 30:[15, 14] Operation: 4+10=14 Exploring Operation: 15-4=11, Resulting Numbers: [10, 11] Generated Node #0,1,2: 30:[10, 11] Operation: 15-4=11 Moving to Node #0,0 Current State: 30:[15, 28, 34], Operations: ['38-4=34'] Exploring Operation: 28-15=13, Resulting Numbers: [34, 13] Generated Node #0,0,0: 30:[34, 13] Operation: 28-15=13 Exploring Operation: 34-15=19, Resulting Numbers: [28, 19] Generated Node #0,0,1: 30:[28, 19] Operation: 34-15=19 Exploring Operation: 34-28=6, Resulting Numbers: [15, 6] Generated Node #0,0,2: 30:[15, 6] Operation: 34-28=6 Moving to Node #0,2 Current State: 30:[38, 15, 7], Operations: ['28/4=7'] Exploring Operation: 38-7=31, Resulting Numbers: [15, 31] Generated Node #0,2,0: 30:[15, 31] Operation: 38-7=31 Exploring Operation: 38-15=23, Resulting Numbers: [7, 23] Generated Node #0,2,1: 30:[7, 23] Operation: 38-15=23 Exploring Operation: 15-7=8, Resulting Numbers: [38, 8] Generated Node #0,2,2: 30:[38, 8] Operation: 15-7=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[15, 31], Operations: ['28/4=7', '38-7=31'] Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,30 unequal: No Solution Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[7, 23], Operations: ['28/4=7', '38-15=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[4, 38, 15, 28], Operations: [] Exploring Operation: 28/4=7, Resulting Numbers: [38, 15, 7] Generated Node #0,2: 30:[38, 15, 7] Operation: 28/4=7 Moving to Node #0,2 Current State: 30:[38, 15, 7], Operations: ['28/4=7'] Exploring Operation: 38-15=23, Resulting Numbers: [7, 23] Generated Node #0,2,1: 30:[7, 23] Operation: 38-15=23 Moving to Node #0,2,1 Current State: 30:[7, 23], Operations: ['28/4=7', '38-15=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
mult_heuristic
[ 96, 48, 91, 67 ]
23
[ "96-91=5", "48+67=115", "115/5=23" ]
Current State: 23:[96, 48, 91, 67], Operations: [] Exploring Operation: 96-91=5, Resulting Numbers: [48, 67, 5] Generated Node #2: [48, 67, 5] from Operation: 96-91=5 Current State: 23:[48, 67, 5], Operations: ['96-91=5'] Exploring Operation: 48+67=115, Resulting Numbers: [5, 115] Generated Node #3: [5, 115] from Operation: 48+67=115 Current State: 23:[5, 115], Operations: ['96-91=5', '48+67=115'] Exploring Operation: 115/5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[96, 48, 91, 67], Operations: [] Exploring Operation: 96-91=5, Resulting Numbers: [48, 67, 5] Generated Node #0,0: 23:[48, 67, 5] Operation: 96-91=5 Exploring Operation: 91-67=24, Resulting Numbers: [96, 48, 24] Generated Node #0,1: 23:[96, 48, 24] Operation: 91-67=24 Exploring Operation: 96-67=29, Resulting Numbers: [48, 91, 29] Generated Node #0,2: 23:[48, 91, 29] Operation: 96-67=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[48, 67, 5], Operations: ['96-91=5'] Exploring Operation: 67-5=62, Resulting Numbers: [48, 62] Generated Node #0,0,0: 23:[48, 62] Operation: 67-5=62 Exploring Operation: 48-5=43, Resulting Numbers: [67, 43] Generated Node #0,0,1: 23:[67, 43] Operation: 48-5=43 Exploring Operation: 67-48=19, Resulting Numbers: [5, 19] Generated Node #0,0,2: 23:[5, 19] Operation: 67-48=19 Moving to Node #0,0,2 Current State: 23:[5, 19], Operations: ['96-91=5', '67-48=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,23 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[48, 62], Operations: ['96-91=5', '67-5=62'] Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,23 unequal: No Solution Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,23 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[67, 43], Operations: ['96-91=5', '48-5=43'] Exploring Operation: 67*43=2881, Resulting Numbers: [2881] 2881,23 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 67+43=110, Resulting Numbers: [110] 110,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[96, 48, 24], Operations: ['91-67=24'] Exploring Operation: 96/24=4, Resulting Numbers: [48, 4] Generated Node #0,1,0: 23:[48, 4] Operation: 96/24=4 Exploring Operation: 96-48=48, Resulting Numbers: [24, 48] Generated Node #0,1,1: 23:[24, 48] Operation: 96-48=48 Exploring Operation: 96/48=2, Resulting Numbers: [24, 2] Generated Node #0,1,2: 23:[24, 2] Operation: 96/48=2 Moving to Node #0,1,2 Current State: 23:[24, 2], Operations: ['91-67=24', '96/48=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,23 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[24, 48], Operations: ['91-67=24', '96-48=48'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[48, 4], Operations: ['91-67=24', '96/24=4'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,23 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:[48, 91, 29], Operations: ['96-67=29'] Exploring Operation: 91-48=43, Resulting Numbers: [29, 43] Generated Node #0,2,0: 23:[29, 43] Operation: 91-48=43 Exploring Operation: 91-29=62, Resulting Numbers: [48, 62] Generated Node #0,2,1: 23:[48, 62] Operation: 91-29=62 Exploring Operation: 48-29=19, Resulting Numbers: [91, 19] Generated Node #0,2,2: 23:[91, 19] Operation: 48-29=19 Moving to Node #0,2,0 Current State: 23:[29, 43], Operations: ['96-67=29', '91-48=43'] Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,23 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,23 unequal: No Solution Exploring Operation: 29*43=1247, Resulting Numbers: [1247] 1247,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[48, 62], Operations: ['96-67=29', '91-29=62'] Exploring Operation: 48*62=2976, Resulting Numbers: [2976] 2976,23 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,23 unequal: No Solution Exploring Operation: 48+62=110, Resulting Numbers: [110] 110,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[91, 19], Operations: ['96-67=29', '48-29=19'] Exploring Operation: 91+19=110, Resulting Numbers: [110] 110,23 unequal: No Solution Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,23 unequal: No Solution Exploring Operation: 91*19=1729, Resulting Numbers: [1729] 1729,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 81, 27, 85, 45 ]
30
[ "27*85=2295", "2295/45=51", "81-51=30" ]
Current State: 30:[81, 27, 85, 45], Operations: [] Exploring Operation: 27*85=2295, Resulting Numbers: [81, 45, 2295] Generated Node #2: [81, 45, 2295] from Operation: 27*85=2295 Current State: 30:[81, 45, 2295], Operations: ['27*85=2295'] Exploring Operation: 2295/45=51, Resulting Numbers: [81, 51] Generated Node #3: [81, 51] from Operation: 2295/45=51 Current State: 30:[81, 51], Operations: ['27*85=2295', '2295/45=51'] Exploring Operation: 81-51=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[81, 27, 85, 45], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [85, 45, 3] Generated Node #0,0: 30:[85, 45, 3] Operation: 81/27=3 Exploring Operation: 85-45=40, Resulting Numbers: [81, 27, 40] Generated Node #0,1: 30:[81, 27, 40] Operation: 85-45=40 Exploring Operation: 81-27=54, Resulting Numbers: [85, 45, 54] Generated Node #0,2: 30:[85, 45, 54] Operation: 81-27=54 Exploring Operation: 85-81=4, Resulting Numbers: [27, 45, 4] Generated Node #0,3: 30:[27, 45, 4] Operation: 85-81=4 Exploring Operation: 81-45=36, Resulting Numbers: [27, 85, 36] Generated Node #0,4: 30:[27, 85, 36] Operation: 81-45=36 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[27, 45, 4], Operations: ['85-81=4'] Exploring Operation: 27-4=23, Resulting Numbers: [45, 23] Generated Node #0,3,0: 30:[45, 23] Operation: 27-4=23 Exploring Operation: 45-27=18, Resulting Numbers: [4, 18] Generated Node #0,3,1: 30:[4, 18] Operation: 45-27=18 Exploring Operation: 45-4=41, Resulting Numbers: [27, 41] Generated Node #0,3,2: 30:[27, 41] Operation: 45-4=41 Exploring Operation: 27+4=31, Resulting Numbers: [45, 31] Generated Node #0,3,3: 30:[45, 31] Operation: 27+4=31 Exploring Operation: 45+4=49, Resulting Numbers: [27, 49] Generated Node #0,3,4: 30:[27, 49] Operation: 45+4=49 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 30:[4, 18], Operations: ['85-81=4', '45-27=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,30 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,30 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 #0,3,2 Current State: 30:[27, 41], Operations: ['85-81=4', '45-4=41'] Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,30 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,30 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 #0,3,3 Current State: 30:[45, 31], Operations: ['85-81=4', '27+4=31'] Exploring Operation: 45+31=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 45*31=1395, Resulting Numbers: [1395] 1395,30 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 #0,3,0 Current State: 30:[45, 23], Operations: ['85-81=4', '27-4=23'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,30 unequal: No Solution Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,30 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 #0,3,4 Current State: 30:[27, 49], Operations: ['85-81=4', '45+4=49'] Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[81, 27, 40], Operations: ['85-45=40'] Exploring Operation: 81+27=108, Resulting Numbers: [40, 108] Generated Node #0,1,0: 30:[40, 108] Operation: 81+27=108 Exploring Operation: 81-27=54, Resulting Numbers: [40, 54] Generated Node #0,1,1: 30:[40, 54] Operation: 81-27=54 Exploring Operation: 81/27=3, Resulting Numbers: [40, 3] Generated Node #0,1,2: 30:[40, 3] Operation: 81/27=3 Exploring Operation: 81-40=41, Resulting Numbers: [27, 41] Generated Node #0,1,3: 30:[27, 41] Operation: 81-40=41 Exploring Operation: 40-27=13, Resulting Numbers: [81, 13] Generated Node #0,1,4: 30:[81, 13] Operation: 40-27=13 Moving to Node #0,1,2 Current State: 30:[40, 3], Operations: ['85-45=40', '81/27=3'] Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,30 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[27, 41], Operations: ['85-45=40', '81-40=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,30 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[40, 54], Operations: ['85-45=40', '81-27=54'] Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,30 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,30 unequal: No Solution Moving to Node #0,1,4 Current State: 30:[81, 13], Operations: ['85-45=40', '40-27=13'] Exploring Operation: 81*13=1053, Resulting Numbers: [1053] 1053,30 unequal: No Solution Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[40, 108], Operations: ['85-45=40', '81+27=108'] Exploring Operation: 40+108=148, Resulting Numbers: [148] 148,30 unequal: No Solution Exploring Operation: 108-40=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 40*108=4320, Resulting Numbers: [4320] 4320,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 30:[27, 85, 36], Operations: ['81-45=36'] Exploring Operation: 27+85=112, Resulting Numbers: [36, 112] Generated Node #0,4,0: 30:[36, 112] Operation: 27+85=112 Exploring Operation: 27+36=63, Resulting Numbers: [85, 63] Generated Node #0,4,1: 30:[85, 63] Operation: 27+36=63 Exploring Operation: 36-27=9, Resulting Numbers: [85, 9] Generated Node #0,4,2: 30:[85, 9] Operation: 36-27=9 Exploring Operation: 85-27=58, Resulting Numbers: [36, 58] Generated Node #0,4,3: 30:[36, 58] Operation: 85-27=58 Exploring Operation: 85-36=49, Resulting Numbers: [27, 49] Generated Node #0,4,4: 30:[27, 49] Operation: 85-36=49 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 30:[27, 49], Operations: ['81-45=36', '85-36=49'] Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,30 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 #0,4,3 Current State: 30:[36, 58], Operations: ['81-45=36', '85-27=58'] Exploring Operation: 36*58=2088, Resulting Numbers: [2088] 2088,30 unequal: No Solution Exploring Operation: 36+58=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 58-36=22, Resulting Numbers: [22] 22,30 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 #0,4,2 Current State: 30:[85, 9], Operations: ['81-45=36', '36-27=9'] Exploring Operation: 85*9=765, Resulting Numbers: [765] 765,30 unequal: No Solution Exploring Operation: 85+9=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,30 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 #0,4,0 Current State: 30:[36, 112], Operations: ['81-45=36', '27+85=112'] Exploring Operation: 112-36=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 36*112=4032, Resulting Numbers: [4032] 4032,30 unequal: No Solution Exploring Operation: 36+112=148, Resulting Numbers: [148] 148,30 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 #0,4,1 Current State: 30:[85, 63], Operations: ['81-45=36', '27+36=63'] Exploring Operation: 85+63=148, Resulting Numbers: [148] 148,30 unequal: No Solution Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,30 unequal: No Solution Exploring Operation: 85*63=5355, Resulting Numbers: [5355] 5355,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[85, 45, 3], Operations: ['81/27=3'] Exploring Operation: 85-45=40, Resulting Numbers: [3, 40] Generated Node #0,0,0: 30:[3, 40] Operation: 85-45=40 Exploring Operation: 45/3=15, Resulting Numbers: [85, 15] Generated Node #0,0,1: 30:[85, 15] Operation: 45/3=15 Exploring Operation: 45-3=42, Resulting Numbers: [85, 42] Generated Node #0,0,2: 30:[85, 42] Operation: 45-3=42 Exploring Operation: 85-3=82, Resulting Numbers: [45, 82] Generated Node #0,0,3: 30:[45, 82] Operation: 85-3=82 Exploring Operation: 85+3=88, Resulting Numbers: [45, 88] Generated Node #0,0,4: 30:[45, 88] Operation: 85+3=88 Moving to Node #0,0,0 Current State: 30:[3, 40], Operations: ['81/27=3', '85-45=40'] Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,30 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[85, 15], Operations: ['81/27=3', '45/3=15'] Exploring Operation: 85-15=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 85+15=100, Resulting Numbers: [100] 100,30 unequal: No Solution Exploring Operation: 85*15=1275, Resulting Numbers: [1275] 1275,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[85, 42], Operations: ['81/27=3', '45-3=42'] Exploring Operation: 85+42=127, Resulting Numbers: [127] 127,30 unequal: No Solution Exploring Operation: 85*42=3570, Resulting Numbers: [3570] 3570,30 unequal: No Solution Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,30 unequal: No Solution Moving to Node #0,0,3 Current State: 30:[45, 82], Operations: ['81/27=3', '85-3=82'] Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,30 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,30 unequal: No Solution Moving to Node #0,0,4 Current State: 30:[45, 88], Operations: ['81/27=3', '85+3=88'] Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,30 unequal: No Solution Exploring Operation: 45*88=3960, Resulting Numbers: [3960] 3960,30 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[85, 45, 54], Operations: ['81-27=54'] Exploring Operation: 85+45=130, Resulting Numbers: [54, 130] Generated Node #0,2,0: 30:[54, 130] Operation: 85+45=130 Exploring Operation: 54-45=9, Resulting Numbers: [85, 9] Generated Node #0,2,1: 30:[85, 9] Operation: 54-45=9 Exploring Operation: 85-54=31, Resulting Numbers: [45, 31] Generated Node #0,2,2: 30:[45, 31] Operation: 85-54=31 Exploring Operation: 85+54=139, Resulting Numbers: [45, 139] Generated Node #0,2,3: 30:[45, 139] Operation: 85+54=139 Exploring Operation: 85-45=40, Resulting Numbers: [54, 40] Generated Node #0,2,4: 30:[54, 40] Operation: 85-45=40 Moving to Node #0,2,2 Current State: 30:[45, 31], Operations: ['81-27=54', '85-54=31'] Exploring Operation: 45*31=1395, Resulting Numbers: [1395] 1395,30 unequal: No Solution Exploring Operation: 45+31=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[54, 40], Operations: ['81-27=54', '85-45=40'] Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 54+40=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 54*40=2160, Resulting Numbers: [2160] 2160,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[85, 9], Operations: ['81-27=54', '54-45=9'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,30 unequal: No Solution Exploring Operation: 85*9=765, Resulting Numbers: [765] 765,30 unequal: No Solution Exploring Operation: 85+9=94, Resulting Numbers: [94] 94,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[54, 130], Operations: ['81-27=54', '85+45=130'] Exploring Operation: 54*130=7020, Resulting Numbers: [7020] 7020,30 unequal: No Solution Exploring Operation: 54+130=184, Resulting Numbers: [184] 184,30 unequal: No Solution Exploring Operation: 130-54=76, Resulting Numbers: [76] 76,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[45, 139], Operations: ['81-27=54', '85+54=139'] Exploring Operation: 139-45=94, Resulting Numbers: [94] 94,30 unequal: No Solution Exploring Operation: 45+139=184, Resulting Numbers: [184] 184,30 unequal: No Solution Exploring Operation: 45*139=6255, Resulting Numbers: [6255] 6255,30 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
[ 84, 39, 19, 24 ]
40
[ "84-39=45", "24-19=5", "45-5=40" ]
Current State: 40:[84, 39, 19, 24], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [19, 24, 45] Generated Node #2: [19, 24, 45] from Operation: 84-39=45 Current State: 40:[19, 24, 45], Operations: ['84-39=45'] Exploring Operation: 24-19=5, Resulting Numbers: [45, 5] Generated Node #3: [45, 5] from Operation: 24-19=5 Current State: 40:[45, 5], Operations: ['84-39=45', '24-19=5'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[84, 39, 19, 24], Operations: [] Exploring Operation: 24-19=5, Resulting Numbers: [84, 39, 5] Generated Node #0,0: 40:[84, 39, 5] Operation: 24-19=5 Exploring Operation: 84-39=45, Resulting Numbers: [19, 24, 45] Generated Node #0,1: 40:[19, 24, 45] Operation: 84-39=45 Exploring Operation: 84-24=60, Resulting Numbers: [39, 19, 60] Generated Node #0,2: 40:[39, 19, 60] Operation: 84-24=60 Exploring Operation: 39-19=20, Resulting Numbers: [84, 24, 20] Generated Node #0,3: 40:[84, 24, 20] Operation: 39-19=20 Exploring Operation: 84-19=65, Resulting Numbers: [39, 24, 65] Generated Node #0,4: 40:[39, 24, 65] Operation: 84-19=65 Moving to Node #0,1 Current State: 40:[19, 24, 45], Operations: ['84-39=45'] Exploring Operation: 24-19=5, Resulting Numbers: [45, 5] Generated Node #0,1,0: 40:[45, 5] Operation: 24-19=5 Exploring Operation: 45-19=26, Resulting Numbers: [24, 26] Generated Node #0,1,1: 40:[24, 26] Operation: 45-19=26 Exploring Operation: 19+45=64, Resulting Numbers: [24, 64] Generated Node #0,1,2: 40:[24, 64] Operation: 19+45=64 Exploring Operation: 45-24=21, Resulting Numbers: [19, 21] Generated Node #0,1,3: 40:[19, 21] Operation: 45-24=21 Exploring Operation: 19+24=43, Resulting Numbers: [45, 43] Generated Node #0,1,4: 40:[45, 43] Operation: 19+24=43 Moving to Node #0,2 Current State: 40:[39, 19, 60], Operations: ['84-24=60'] Exploring Operation: 39-19=20, Resulting Numbers: [60, 20] Generated Node #0,2,0: 40:[60, 20] Operation: 39-19=20 Exploring Operation: 60-39=21, Resulting Numbers: [19, 21] Generated Node #0,2,1: 40:[19, 21] Operation: 60-39=21 Exploring Operation: 60-19=41, Resulting Numbers: [39, 41] Generated Node #0,2,2: 40:[39, 41] Operation: 60-19=41 Exploring Operation: 39+19=58, Resulting Numbers: [60, 58] Generated Node #0,2,3: 40:[60, 58] Operation: 39+19=58 Exploring Operation: 19+60=79, Resulting Numbers: [39, 79] Generated Node #0,2,4: 40:[39, 79] Operation: 19+60=79 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[19, 21], Operations: ['84-24=60', '60-39=21'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[84, 39, 19, 24], Operations: [] Exploring Operation: 84-24=60, Resulting Numbers: [39, 19, 60] Generated Node #0,2: 40:[39, 19, 60] Operation: 84-24=60 Moving to Node #0,2 Current State: 40:[39, 19, 60], Operations: ['84-24=60'] Exploring Operation: 60-39=21, Resulting Numbers: [19, 21] Generated Node #0,2,1: 40:[19, 21] Operation: 60-39=21 Moving to Node #0,2,1 Current State: 40:[19, 21], Operations: ['84-24=60', '60-39=21'] Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic