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
[ 61, 11, 23, 9 ]
61
[ "61-23=38", "11*9=99", "99-38=61" ]
Current State: 61:[61, 11, 23, 9], Operations: [] Exploring Operation: 61-23=38, Resulting Numbers: [11, 9, 38] Generated Node #2: [11, 9, 38] from Operation: 61-23=38 Current State: 61:[11, 9, 38], Operations: ['61-23=38'] Exploring Operation: 11*9=99, Resulting Numbers: [38, 99] Generated Node #3: [38, 99] from Operation: 11*9=99 Current State: 61:[38, 99], Operations: ['61-23=38', '11*9=99'] Exploring Operation: 99-38=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[61, 11, 23, 9], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [61, 23, 99] Generated Node #0,0: 61:[61, 23, 99] Operation: 11*9=99 Exploring Operation: 11+23=34, Resulting Numbers: [61, 9, 34] Generated Node #0,1: 61:[61, 9, 34] Operation: 11+23=34 Moving to Node #0,0 Current State: 61:[61, 23, 99], Operations: ['11*9=99'] Exploring Operation: 61+23=84, Resulting Numbers: [99, 84] Generated Node #0,0,0: 61:[99, 84] Operation: 61+23=84 Exploring Operation: 99-23=76, Resulting Numbers: [61, 76] Generated Node #0,0,1: 61:[61, 76] Operation: 99-23=76 Moving to Node #0,1 Current State: 61:[61, 9, 34], Operations: ['11+23=34'] Exploring Operation: 61+9=70, Resulting Numbers: [34, 70] Generated Node #0,1,0: 61:[34, 70] Operation: 61+9=70 Exploring Operation: 9+34=43, Resulting Numbers: [61, 43] Generated Node #0,1,1: 61:[61, 43] Operation: 9+34=43 Moving to Node #0,0,1 Current State: 61:[61, 76], Operations: ['11*9=99', '99-23=76'] Exploring Operation: 61+76=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[61, 43], Operations: ['11+23=34', '9+34=43'] Exploring Operation: 61+43=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[34, 70], Operations: ['11+23=34', '61+9=70'] Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 34+70=104, Resulting Numbers: [104] 104,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[99, 84], Operations: ['11*9=99', '61+23=84'] Exploring Operation: 99-84=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 99+84=183, Resulting Numbers: [183] 183,61 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 47, 20, 56, 43 ]
32
[ "47+20=67", "56+43=99", "99-67=32" ]
Current State: 32:[47, 20, 56, 43], Operations: [] Exploring Operation: 47+20=67, Resulting Numbers: [56, 43, 67] Generated Node #2: [56, 43, 67] from Operation: 47+20=67 Current State: 32:[56, 43, 67], Operations: ['47+20=67'] Exploring Operation: 56+43=99, Resulting Numbers: [67, 99] Generated Node #3: [67, 99] from Operation: 56+43=99 Current State: 32:[67, 99], Operations: ['47+20=67', '56+43=99'] Exploring Operation: 99-67=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[47, 20, 56, 43], Operations: [] Exploring Operation: 56-47=9, Resulting Numbers: [20, 43, 9] Generated Node #0,0: 32:[20, 43, 9] Operation: 56-47=9 Exploring Operation: 56-43=13, Resulting Numbers: [47, 20, 13] Generated Node #0,1: 32:[47, 20, 13] Operation: 56-43=13 Exploring Operation: 47-20=27, Resulting Numbers: [56, 43, 27] Generated Node #0,2: 32:[56, 43, 27] Operation: 47-20=27 Exploring Operation: 56-20=36, Resulting Numbers: [47, 43, 36] Generated Node #0,3: 32:[47, 43, 36] Operation: 56-20=36 Exploring Operation: 47-43=4, Resulting Numbers: [20, 56, 4] Generated Node #0,4: 32:[20, 56, 4] Operation: 47-43=4 Moving to Node #0,0 Current State: 32:[20, 43, 9], Operations: ['56-47=9'] Exploring Operation: 20+9=29, Resulting Numbers: [43, 29] Generated Node #0,0,0: 32:[43, 29] Operation: 20+9=29 Exploring Operation: 20-9=11, Resulting Numbers: [43, 11] Generated Node #0,0,1: 32:[43, 11] Operation: 20-9=11 Exploring Operation: 43-20=23, Resulting Numbers: [9, 23] Generated Node #0,0,2: 32:[9, 23] Operation: 43-20=23 Exploring Operation: 43-9=34, Resulting Numbers: [20, 34] Generated Node #0,0,3: 32:[20, 34] Operation: 43-9=34 Exploring Operation: 43+9=52, Resulting Numbers: [20, 52] Generated Node #0,0,4: 32:[20, 52] Operation: 43+9=52 Moving to Node #0,1 Current State: 32:[47, 20, 13], Operations: ['56-43=13'] Exploring Operation: 20+13=33, Resulting Numbers: [47, 33] Generated Node #0,1,0: 32:[47, 33] Operation: 20+13=33 Exploring Operation: 47+13=60, Resulting Numbers: [20, 60] Generated Node #0,1,1: 32:[20, 60] Operation: 47+13=60 Exploring Operation: 47-20=27, Resulting Numbers: [13, 27] Generated Node #0,1,2: 32:[13, 27] Operation: 47-20=27 Exploring Operation: 47-13=34, Resulting Numbers: [20, 34] Generated Node #0,1,3: 32:[20, 34] Operation: 47-13=34 Exploring Operation: 20-13=7, Resulting Numbers: [47, 7] Generated Node #0,1,4: 32:[47, 7] Operation: 20-13=7 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[20, 34], Operations: ['56-43=13', '47-13=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,32 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[13, 27], Operations: ['56-43=13', '47-20=27'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[47, 33], Operations: ['56-43=13', '20+13=33'] Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 47+33=80, Resulting Numbers: [80] 80,32 unequal: No Solution Exploring Operation: 47*33=1551, Resulting Numbers: [1551] 1551,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 32:[47, 7], Operations: ['56-43=13', '20-13=7'] Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,32 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[20, 60], Operations: ['56-43=13', '47+13=60'] Exploring Operation: 60-20=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 60/20=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 20+60=80, Resulting Numbers: [80] 80,32 unequal: No Solution Exploring Operation: 20*60=1200, Resulting Numbers: [1200] 1200,32 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: 32:[20, 56, 4], Operations: ['47-43=4'] Exploring Operation: 20/4=5, Resulting Numbers: [56, 5] Generated Node #0,4,0: 32:[56, 5] Operation: 20/4=5 Exploring Operation: 56-4=52, Resulting Numbers: [20, 52] Generated Node #0,4,1: 32:[20, 52] Operation: 56-4=52 Exploring Operation: 20-4=16, Resulting Numbers: [56, 16] Generated Node #0,4,2: 32:[56, 16] Operation: 20-4=16 Exploring Operation: 56/4=14, Resulting Numbers: [20, 14] Generated Node #0,4,3: 32:[20, 14] Operation: 56/4=14 Exploring Operation: 56-20=36, Resulting Numbers: [4, 36] Generated Node #0,4,4: 32:[4, 36] Operation: 56-20=36 Moving to Node #0,3 Current State: 32:[47, 43, 36], Operations: ['56-20=36'] Exploring Operation: 43-36=7, Resulting Numbers: [47, 7] Generated Node #0,3,0: 32:[47, 7] Operation: 43-36=7 Exploring Operation: 47+43=90, Resulting Numbers: [36, 90] Generated Node #0,3,1: 32:[36, 90] Operation: 47+43=90 Exploring Operation: 47+36=83, Resulting Numbers: [43, 83] Generated Node #0,3,2: 32:[43, 83] Operation: 47+36=83 Exploring Operation: 47-36=11, Resulting Numbers: [43, 11] Generated Node #0,3,3: 32:[43, 11] Operation: 47-36=11 Exploring Operation: 47-43=4, Resulting Numbers: [36, 4] Generated Node #0,3,4: 32:[36, 4] Operation: 47-43=4 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 32:[36, 4], Operations: ['56-20=36', '47-43=4'] Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,32 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[47, 20, 56, 43], Operations: [] Exploring Operation: 56-20=36, Resulting Numbers: [47, 43, 36] Generated Node #0,3: 32:[47, 43, 36] Operation: 56-20=36 Moving to Node #0,3 Current State: 32:[47, 43, 36], Operations: ['56-20=36'] Exploring Operation: 47-43=4, Resulting Numbers: [36, 4] Generated Node #0,3,4: 32:[36, 4] Operation: 47-43=4 Moving to Node #0,3,4 Current State: 32:[36, 4], Operations: ['56-20=36', '47-43=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_5
sum_heuristic
[ 50, 2, 4, 40 ]
43
[ "50-4=46", "40+46=86", "86/2=43" ]
Current State: 43:[50, 2, 4, 40], Operations: [] Exploring Operation: 50-4=46, Resulting Numbers: [2, 40, 46] Generated Node #2: [2, 40, 46] from Operation: 50-4=46 Current State: 43:[2, 40, 46], Operations: ['50-4=46'] Exploring Operation: 40+46=86, Resulting Numbers: [2, 86] Generated Node #3: [2, 86] from Operation: 40+46=86 Current State: 43:[2, 86], Operations: ['50-4=46', '40+46=86'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[50, 2, 4, 40], Operations: [] Exploring Operation: 50-2=48, Resulting Numbers: [4, 40, 48] Generated Node #0,0: 43:[4, 40, 48] Operation: 50-2=48 Exploring Operation: 2*4=8, Resulting Numbers: [50, 40, 8] Generated Node #0,1: 43:[50, 40, 8] Operation: 2*4=8 Exploring Operation: 2+4=6, Resulting Numbers: [50, 40, 6] Generated Node #0,2: 43:[50, 40, 6] Operation: 2+4=6 Exploring Operation: 50-4=46, Resulting Numbers: [2, 40, 46] Generated Node #0,3: 43:[2, 40, 46] Operation: 50-4=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[50, 40, 8], Operations: ['2*4=8'] Exploring Operation: 40-8=32, Resulting Numbers: [50, 32] Generated Node #0,1,0: 43:[50, 32] Operation: 40-8=32 Exploring Operation: 50+8=58, Resulting Numbers: [40, 58] Generated Node #0,1,1: 43:[40, 58] Operation: 50+8=58 Exploring Operation: 50-8=42, Resulting Numbers: [40, 42] Generated Node #0,1,2: 43:[40, 42] Operation: 50-8=42 Exploring Operation: 40+8=48, Resulting Numbers: [50, 48] Generated Node #0,1,3: 43:[50, 48] Operation: 40+8=48 Moving to Node #0,1,2 Current State: 43:[40, 42], Operations: ['2*4=8', '50-8=42'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,43 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[50, 48], Operations: ['2*4=8', '40+8=48'] Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,43 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[40, 58], Operations: ['2*4=8', '50+8=58'] Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 40+58=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 40*58=2320, Resulting Numbers: [2320] 2320,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[50, 32], Operations: ['2*4=8', '40-8=32'] Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,43 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[4, 40, 48], Operations: ['50-2=48'] Exploring Operation: 48-4=44, Resulting Numbers: [40, 44] Generated Node #0,0,0: 43:[40, 44] Operation: 48-4=44 Exploring Operation: 4+48=52, Resulting Numbers: [40, 52] Generated Node #0,0,1: 43:[40, 52] Operation: 4+48=52 Exploring Operation: 4+40=44, Resulting Numbers: [48, 44] Generated Node #0,0,2: 43:[48, 44] Operation: 4+40=44 Exploring Operation: 40-4=36, Resulting Numbers: [48, 36] Generated Node #0,0,3: 43:[48, 36] Operation: 40-4=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[40, 44], Operations: ['50-2=48', '48-4=44'] Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,43 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,43 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 #0,0,2 Current State: 43:[48, 44], Operations: ['50-2=48', '4+40=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 48*44=2112, Resulting Numbers: [2112] 2112,43 unequal: No Solution Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,43 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:[40, 52], Operations: ['50-2=48', '4+48=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,43 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,43 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 #0,0,3 Current State: 43:[48, 36], Operations: ['50-2=48', '40-4=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,43 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,43 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 #0,2 Current State: 43:[50, 40, 6], Operations: ['2+4=6'] Exploring Operation: 40-6=34, Resulting Numbers: [50, 34] Generated Node #0,2,0: 43:[50, 34] Operation: 40-6=34 Exploring Operation: 50+6=56, Resulting Numbers: [40, 56] Generated Node #0,2,1: 43:[40, 56] Operation: 50+6=56 Exploring Operation: 50-6=44, Resulting Numbers: [40, 44] Generated Node #0,2,2: 43:[40, 44] Operation: 50-6=44 Exploring Operation: 40+6=46, Resulting Numbers: [50, 46] Generated Node #0,2,3: 43:[50, 46] Operation: 40+6=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 43:[40, 44], Operations: ['2+4=6', '50-6=44'] Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 43:[50, 46], Operations: ['2+4=6', '40+6=46'] Exploring Operation: 50*46=2300, Resulting Numbers: [2300] 2300,43 unequal: No Solution Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,43 unequal: No Solution Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[50, 34], Operations: ['2+4=6', '40-6=34'] Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[40, 56], Operations: ['2+4=6', '50+6=56'] Exploring Operation: 56-40=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 40*56=2240, Resulting Numbers: [2240] 2240,43 unequal: No Solution Exploring Operation: 40+56=96, Resulting Numbers: [96] 96,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[2, 40, 46], Operations: ['50-4=46'] Exploring Operation: 2+46=48, Resulting Numbers: [40, 48] Generated Node #0,3,0: 43:[40, 48] Operation: 2+46=48 Exploring Operation: 46-2=44, Resulting Numbers: [40, 44] Generated Node #0,3,1: 43:[40, 44] Operation: 46-2=44 Exploring Operation: 40-2=38, Resulting Numbers: [46, 38] Generated Node #0,3,2: 43:[46, 38] Operation: 40-2=38 Exploring Operation: 2+40=42, Resulting Numbers: [46, 42] Generated Node #0,3,3: 43:[46, 42] Operation: 2+40=42 Moving to Node #0,3,1 Current State: 43:[40, 44], Operations: ['50-4=46', '46-2=44'] Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,43 unequal: No Solution Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[46, 42], Operations: ['50-4=46', '2+40=42'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,43 unequal: No Solution Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,43 unequal: No Solution Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[46, 38], Operations: ['50-4=46', '40-2=38'] Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,43 unequal: No Solution Exploring Operation: 46+38=84, Resulting Numbers: [84] 84,43 unequal: No Solution Exploring Operation: 46*38=1748, Resulting Numbers: [1748] 1748,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[40, 48], Operations: ['50-4=46', '2+46=48'] Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,43 unequal: No Solution Exploring Operation: 40*48=1920, Resulting Numbers: [1920] 1920,43 unequal: No Solution Exploring Operation: 40+48=88, Resulting Numbers: [88] 88,43 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
[ 45, 24, 95, 1 ]
75
[ "45-24=21", "95+1=96", "96-21=75" ]
Current State: 75:[45, 24, 95, 1], Operations: [] Exploring Operation: 45-24=21, Resulting Numbers: [95, 1, 21] Generated Node #2: [95, 1, 21] from Operation: 45-24=21 Current State: 75:[95, 1, 21], Operations: ['45-24=21'] Exploring Operation: 95+1=96, Resulting Numbers: [21, 96] Generated Node #3: [21, 96] from Operation: 95+1=96 Current State: 75:[21, 96], Operations: ['45-24=21', '95+1=96'] Exploring Operation: 96-21=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[45, 24, 95, 1], Operations: [] Exploring Operation: 95-24=71, Resulting Numbers: [45, 1, 71] Generated Node #0,0: 75:[45, 1, 71] Operation: 95-24=71 Exploring Operation: 45-24=21, Resulting Numbers: [95, 1, 21] Generated Node #0,1: 75:[95, 1, 21] Operation: 45-24=21 Exploring Operation: 95-45=50, Resulting Numbers: [24, 1, 50] Generated Node #0,2: 75:[24, 1, 50] Operation: 95-45=50 Exploring Operation: 45+24=69, Resulting Numbers: [95, 1, 69] Generated Node #0,3: 75:[95, 1, 69] Operation: 45+24=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[45, 1, 71], Operations: ['95-24=71'] Exploring Operation: 45-1=44, Resulting Numbers: [71, 44] Generated Node #0,0,0: 75:[71, 44] Operation: 45-1=44 Exploring Operation: 45*1=45, Resulting Numbers: [71, 45] Generated Node #0,0,1: 75:[71, 45] Operation: 45*1=45 Exploring Operation: 71-45=26, Resulting Numbers: [1, 26] Generated Node #0,0,2: 75:[1, 26] Operation: 71-45=26 Exploring Operation: 1+71=72, Resulting Numbers: [45, 72] Generated Node #0,0,3: 75:[45, 72] Operation: 1+71=72 Moving to Node #0,0,2 Current State: 75:[1, 26], Operations: ['95-24=71', '71-45=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,75 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[45, 72], Operations: ['95-24=71', '1+71=72'] Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,75 unequal: No Solution Exploring Operation: 45+72=117, Resulting Numbers: [117] 117,75 unequal: No Solution Exploring Operation: 45*72=3240, Resulting Numbers: [3240] 3240,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[71, 44], Operations: ['95-24=71', '45-1=44'] Exploring Operation: 71-44=27, Resulting Numbers: [27] 27,75 unequal: No Solution Exploring Operation: 71*44=3124, Resulting Numbers: [3124] 3124,75 unequal: No Solution Exploring Operation: 71+44=115, Resulting Numbers: [115] 115,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[71, 45], Operations: ['95-24=71', '45*1=45'] Exploring Operation: 71+45=116, Resulting Numbers: [116] 116,75 unequal: No Solution Exploring Operation: 71*45=3195, Resulting Numbers: [3195] 3195,75 unequal: No Solution Exploring Operation: 71-45=26, Resulting Numbers: [26] 26,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[95, 1, 21], Operations: ['45-24=21'] Exploring Operation: 95-21=74, Resulting Numbers: [1, 74] Generated Node #0,1,0: 75:[1, 74] Operation: 95-21=74 Exploring Operation: 1+21=22, Resulting Numbers: [95, 22] Generated Node #0,1,1: 75:[95, 22] Operation: 1+21=22 Exploring Operation: 95*1=95, Resulting Numbers: [21, 95] Generated Node #0,1,2: 75:[21, 95] Operation: 95*1=95 Exploring Operation: 95-1=94, Resulting Numbers: [21, 94] Generated Node #0,1,3: 75:[21, 94] Operation: 95-1=94 Moving to Node #0,1,0 Current State: 75:[1, 74], Operations: ['45-24=21', '95-21=74'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,75 unequal: No Solution Exploring Operation: 1*74=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 1+74=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[45, 24, 95, 1], Operations: [] Exploring Operation: 45-24=21, Resulting Numbers: [95, 1, 21] Generated Node #0,1: 75:[95, 1, 21] Operation: 45-24=21 Moving to Node #0,1 Current State: 75:[95, 1, 21], Operations: ['45-24=21'] Exploring Operation: 95-21=74, Resulting Numbers: [1, 74] Generated Node #0,1,0: 75:[1, 74] Operation: 95-21=74 Moving to Node #0,1,0 Current State: 75:[1, 74], Operations: ['45-24=21', '95-21=74'] Exploring Operation: 1+74=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 29, 19, 29, 89 ]
71
[ "29/29=1", "89-19=70", "1+70=71" ]
Current State: 71:[29, 19, 29, 89], Operations: [] Exploring Operation: 29/29=1, Resulting Numbers: [19, 89, 1] Generated Node #2: [19, 89, 1] from Operation: 29/29=1 Current State: 71:[19, 89, 1], Operations: ['29/29=1'] Exploring Operation: 89-19=70, Resulting Numbers: [1, 70] Generated Node #3: [1, 70] from Operation: 89-19=70 Current State: 71:[1, 70], Operations: ['29/29=1', '89-19=70'] Exploring Operation: 1+70=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[29, 19, 29, 89], Operations: [] Exploring Operation: 29+29=58, Resulting Numbers: [19, 89, 58] Generated Node #0,0: 71:[19, 89, 58] Operation: 29+29=58 Exploring Operation: 19+29=48, Resulting Numbers: [29, 89, 48] Generated Node #0,1: 71:[29, 89, 48] Operation: 19+29=48 Exploring Operation: 29+19=48, Resulting Numbers: [29, 89, 48] Generated Node #0,2: 71:[29, 89, 48] Operation: 29+19=48 Exploring Operation: 89-19=70, Resulting Numbers: [29, 29, 70] Generated Node #0,3: 71:[29, 29, 70] Operation: 89-19=70 Exploring Operation: 89-29=60, Resulting Numbers: [19, 29, 60] Generated Node #0,4: 71:[19, 29, 60] Operation: 89-29=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[19, 89, 58], Operations: ['29+29=58'] Exploring Operation: 19+58=77, Resulting Numbers: [89, 77] Generated Node #0,0,0: 71:[89, 77] Operation: 19+58=77 Exploring Operation: 58-19=39, Resulting Numbers: [89, 39] Generated Node #0,0,1: 71:[89, 39] Operation: 58-19=39 Exploring Operation: 89-58=31, Resulting Numbers: [19, 31] Generated Node #0,0,2: 71:[19, 31] Operation: 89-58=31 Exploring Operation: 19+89=108, Resulting Numbers: [58, 108] Generated Node #0,0,3: 71:[58, 108] Operation: 19+89=108 Exploring Operation: 89-19=70, Resulting Numbers: [58, 70] Generated Node #0,0,4: 71:[58, 70] Operation: 89-19=70 Moving to Node #0,0,4 Current State: 71:[58, 70], Operations: ['29+29=58', '89-19=70'] Exploring Operation: 58+70=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 58*70=4060, Resulting Numbers: [4060] 4060,71 unequal: No Solution Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[89, 77], Operations: ['29+29=58', '19+58=77'] Exploring Operation: 89*77=6853, Resulting Numbers: [6853] 6853,71 unequal: No Solution Exploring Operation: 89+77=166, Resulting Numbers: [166] 166,71 unequal: No Solution Exploring Operation: 89-77=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[89, 39], Operations: ['29+29=58', '58-19=39'] Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 89+39=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 89*39=3471, Resulting Numbers: [3471] 3471,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[58, 108], Operations: ['29+29=58', '19+89=108'] Exploring Operation: 58+108=166, Resulting Numbers: [166] 166,71 unequal: No Solution Exploring Operation: 58*108=6264, Resulting Numbers: [6264] 6264,71 unequal: No Solution Exploring Operation: 108-58=50, Resulting Numbers: [50] 50,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[19, 31], Operations: ['29+29=58', '89-58=31'] Exploring Operation: 19+31=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 19*31=589, Resulting Numbers: [589] 589,71 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 Current State: 71:[29, 89, 48], Operations: ['19+29=48'] Exploring Operation: 29+48=77, Resulting Numbers: [89, 77] Generated Node #0,1,0: 71:[89, 77] Operation: 29+48=77 Exploring Operation: 89-29=60, Resulting Numbers: [48, 60] Generated Node #0,1,1: 71:[48, 60] Operation: 89-29=60 Exploring Operation: 29+89=118, Resulting Numbers: [48, 118] Generated Node #0,1,2: 71:[48, 118] Operation: 29+89=118 Exploring Operation: 89-48=41, Resulting Numbers: [29, 41] Generated Node #0,1,3: 71:[29, 41] Operation: 89-48=41 Exploring Operation: 48-29=19, Resulting Numbers: [89, 19] Generated Node #0,1,4: 71:[89, 19] Operation: 48-29=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[89, 77], Operations: ['19+29=48', '29+48=77'] Exploring Operation: 89+77=166, Resulting Numbers: [166] 166,71 unequal: No Solution Exploring Operation: 89-77=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 89*77=6853, Resulting Numbers: [6853] 6853,71 unequal: No Solution No 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: 71:[48, 60], Operations: ['19+29=48', '89-29=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,71 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,71 unequal: No Solution No 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: 71:[48, 118], Operations: ['19+29=48', '29+89=118'] Exploring Operation: 118-48=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 48*118=5664, Resulting Numbers: [5664] 5664,71 unequal: No Solution Exploring Operation: 48+118=166, Resulting Numbers: [166] 166,71 unequal: No Solution No 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: 71:[89, 19], Operations: ['19+29=48', '48-29=19'] Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 89+19=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 89*19=1691, Resulting Numbers: [1691] 1691,71 unequal: No Solution No 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: 71:[29, 41], Operations: ['19+29=48', '89-48=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,71 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,71 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: 71:[29, 89, 48], Operations: ['29+19=48'] Exploring Operation: 48-29=19, Resulting Numbers: [89, 19] Generated Node #0,2,0: 71:[89, 19] Operation: 48-29=19 Exploring Operation: 29+89=118, Resulting Numbers: [48, 118] Generated Node #0,2,1: 71:[48, 118] Operation: 29+89=118 Exploring Operation: 89-48=41, Resulting Numbers: [29, 41] Generated Node #0,2,2: 71:[29, 41] Operation: 89-48=41 Exploring Operation: 89-29=60, Resulting Numbers: [48, 60] Generated Node #0,2,3: 71:[48, 60] Operation: 89-29=60 Exploring Operation: 29+48=77, Resulting Numbers: [89, 77] Generated Node #0,2,4: 71:[89, 77] Operation: 29+48=77 Moving to Node #0,2,4 Current State: 71:[89, 77], Operations: ['29+19=48', '29+48=77'] Exploring Operation: 89-77=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 89+77=166, Resulting Numbers: [166] 166,71 unequal: No Solution Exploring Operation: 89*77=6853, Resulting Numbers: [6853] 6853,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[48, 60], Operations: ['29+19=48', '89-29=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[89, 19], Operations: ['29+19=48', '48-29=19'] Exploring Operation: 89+19=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 89*19=1691, Resulting Numbers: [1691] 1691,71 unequal: No Solution Exploring Operation: 89-19=70, Resulting Numbers: [70] 70,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[48, 118], Operations: ['29+19=48', '29+89=118'] Exploring Operation: 48+118=166, Resulting Numbers: [166] 166,71 unequal: No Solution Exploring Operation: 48*118=5664, Resulting Numbers: [5664] 5664,71 unequal: No Solution Exploring Operation: 118-48=70, Resulting Numbers: [70] 70,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[29, 41], Operations: ['29+19=48', '89-48=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,71 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,71 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 #0,3 Current State: 71:[29, 29, 70], Operations: ['89-19=70'] Exploring Operation: 29-29=0, Resulting Numbers: [70, 0] Generated Node #0,3,0: 71:[70, 0] Operation: 29-29=0 Exploring Operation: 29+70=99, Resulting Numbers: [29, 99] Generated Node #0,3,1: 71:[29, 99] Operation: 29+70=99 Exploring Operation: 29/29=1, Resulting Numbers: [70, 1] Generated Node #0,3,2: 71:[70, 1] Operation: 29/29=1 Exploring Operation: 29+29=58, Resulting Numbers: [70, 58] Generated Node #0,3,3: 71:[70, 58] Operation: 29+29=58 Exploring Operation: 29+70=99, Resulting Numbers: [29, 99] Generated Node #0,3,4: 71:[29, 99] Operation: 29+70=99 Moving to Node #0,3,3 Current State: 71:[70, 58], Operations: ['89-19=70', '29+29=58'] Exploring Operation: 70*58=4060, Resulting Numbers: [4060] 4060,71 unequal: No Solution Exploring Operation: 70-58=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 70+58=128, Resulting Numbers: [128] 128,71 unequal: No Solution Moving to Node #0,3,4 Current State: 71:[29, 99], Operations: ['89-19=70', '29+70=99'] Exploring Operation: 29+99=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 29*99=2871, Resulting Numbers: [2871] 2871,71 unequal: No Solution Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[29, 99], Operations: ['89-19=70', '29+70=99'] Exploring Operation: 29*99=2871, Resulting Numbers: [2871] 2871,71 unequal: No Solution Exploring Operation: 29+99=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[70, 1], Operations: ['89-19=70', '29/29=1'] Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,71 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,71 unequal: No Solution Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[29, 19, 29, 89], Operations: [] Exploring Operation: 89-19=70, Resulting Numbers: [29, 29, 70] Generated Node #0,3: 71:[29, 29, 70] Operation: 89-19=70 Moving to Node #0,3 Current State: 71:[29, 29, 70], Operations: ['89-19=70'] Exploring Operation: 29/29=1, Resulting Numbers: [70, 1] Generated Node #0,3,2: 71:[70, 1] Operation: 29/29=1 Moving to Node #0,3,2 Current State: 71:[70, 1], Operations: ['89-19=70', '29/29=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.924479
hs_5
mult_heuristic
[ 46, 92, 63, 41 ]
11
[ "92/46=2", "63-41=22", "22/2=11" ]
Current State: 11:[46, 92, 63, 41], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [63, 41, 2] Generated Node #2: [63, 41, 2] from Operation: 92/46=2 Current State: 11:[63, 41, 2], Operations: ['92/46=2'] Exploring Operation: 63-41=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 63-41=22 Current State: 11:[2, 22], Operations: ['92/46=2', '63-41=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[46, 92, 63, 41], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [63, 41, 46] Generated Node #0,0: 11:[63, 41, 46] Operation: 92-46=46 Exploring Operation: 92-63=29, Resulting Numbers: [46, 41, 29] Generated Node #0,1: 11:[46, 41, 29] Operation: 92-63=29 Exploring Operation: 92/46=2, Resulting Numbers: [63, 41, 2] Generated Node #0,2: 11:[63, 41, 2] Operation: 92/46=2 Exploring Operation: 63-46=17, Resulting Numbers: [92, 41, 17] Generated Node #0,3: 11:[92, 41, 17] Operation: 63-46=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[46, 41, 29], Operations: ['92-63=29'] Exploring Operation: 46-29=17, Resulting Numbers: [41, 17] Generated Node #0,1,0: 11:[41, 17] Operation: 46-29=17 Exploring Operation: 46+41=87, Resulting Numbers: [29, 87] Generated Node #0,1,1: 11:[29, 87] Operation: 46+41=87 Exploring Operation: 41-29=12, Resulting Numbers: [46, 12] Generated Node #0,1,2: 11:[46, 12] Operation: 41-29=12 Exploring Operation: 46-41=5, Resulting Numbers: [29, 5] Generated Node #0,1,3: 11:[29, 5] Operation: 46-41=5 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 11:[29, 5], Operations: ['92-63=29', '46-41=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,11 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,11 unequal: No Solution No 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: 11:[41, 17], Operations: ['92-63=29', '46-29=17'] Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 41+17=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 41*17=697, Resulting Numbers: [697] 697,11 unequal: No Solution No 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: 11:[46, 12], Operations: ['92-63=29', '41-29=12'] Exploring Operation: 46+12=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 46*12=552, Resulting Numbers: [552] 552,11 unequal: No Solution No 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: 11:[29, 87], Operations: ['92-63=29', '46+41=87'] Exploring Operation: 87/29=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 29*87=2523, Resulting Numbers: [2523] 2523,11 unequal: No Solution Exploring Operation: 29+87=116, Resulting Numbers: [116] 116,11 unequal: No Solution Exploring Operation: 87-29=58, Resulting Numbers: [58] 58,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 11:[63, 41, 2], Operations: ['92/46=2'] Exploring Operation: 63-2=61, Resulting Numbers: [41, 61] Generated Node #0,2,0: 11:[41, 61] Operation: 63-2=61 Exploring Operation: 63-41=22, Resulting Numbers: [2, 22] Generated Node #0,2,1: 11:[2, 22] Operation: 63-41=22 Exploring Operation: 63+2=65, Resulting Numbers: [41, 65] Generated Node #0,2,2: 11:[41, 65] Operation: 63+2=65 Exploring Operation: 41-2=39, Resulting Numbers: [63, 39] Generated Node #0,2,3: 11:[63, 39] Operation: 41-2=39 Moving to Node #0,2,1 Current State: 11:[2, 22], Operations: ['92/46=2', '63-41=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[46, 92, 63, 41], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [63, 41, 2] Generated Node #0,2: 11:[63, 41, 2] Operation: 92/46=2 Moving to Node #0,2 Current State: 11:[63, 41, 2], Operations: ['92/46=2'] Exploring Operation: 63-41=22, Resulting Numbers: [2, 22] Generated Node #0,2,1: 11:[2, 22] Operation: 63-41=22 Moving to Node #0,2,1 Current State: 11:[2, 22], Operations: ['92/46=2', '63-41=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 2, 44, 62, 60 ]
70
[ "60-44=16", "16/2=8", "62+8=70" ]
Current State: 70:[2, 44, 62, 60], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [2, 62, 16] Generated Node #2: [2, 62, 16] from Operation: 60-44=16 Current State: 70:[2, 62, 16], Operations: ['60-44=16'] Exploring Operation: 16/2=8, Resulting Numbers: [62, 8] Generated Node #3: [62, 8] from Operation: 16/2=8 Current State: 70:[62, 8], Operations: ['60-44=16', '16/2=8'] Exploring Operation: 62+8=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[2, 44, 62, 60], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [2, 62, 16] Generated Node #0,0: 70:[2, 62, 16] Operation: 60-44=16 Exploring Operation: 62-60=2, Resulting Numbers: [2, 44, 2] Generated Node #0,1: 70:[2, 44, 2] Operation: 62-60=2 Exploring Operation: 62-44=18, Resulting Numbers: [2, 60, 18] Generated Node #0,2: 70:[2, 60, 18] Operation: 62-44=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[2, 44, 2], Operations: ['62-60=2'] Exploring Operation: 44/2=22, Resulting Numbers: [2, 22] Generated Node #0,1,0: 70:[2, 22] Operation: 44/2=22 Exploring Operation: 44-2=42, Resulting Numbers: [2, 42] Generated Node #0,1,1: 70:[2, 42] Operation: 44-2=42 Exploring Operation: 44-2=42, Resulting Numbers: [2, 42] Generated Node #0,1,2: 70:[2, 42] Operation: 44-2=42 Moving to Node #0,1,1 Current State: 70:[2, 42], Operations: ['62-60=2', '44-2=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[2, 42], Operations: ['62-60=2', '44-2=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[2, 22], Operations: ['62-60=2', '44/2=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,70 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[2, 62, 16], Operations: ['60-44=16'] Exploring Operation: 2+62=64, Resulting Numbers: [16, 64] Generated Node #0,0,0: 70:[16, 64] Operation: 2+62=64 Exploring Operation: 62/2=31, Resulting Numbers: [16, 31] Generated Node #0,0,1: 70:[16, 31] Operation: 62/2=31 Exploring Operation: 16-2=14, Resulting Numbers: [62, 14] Generated Node #0,0,2: 70:[62, 14] Operation: 16-2=14 Moving to Node #0,0,1 Current State: 70:[16, 31], Operations: ['60-44=16', '62/2=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,70 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 16*31=496, Resulting Numbers: [496] 496,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[16, 64], Operations: ['60-44=16', '2+62=64'] Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 16+64=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[62, 14], Operations: ['60-44=16', '16-2=14'] Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,70 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,70 unequal: No Solution Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[2, 60, 18], Operations: ['62-44=18'] Exploring Operation: 60/2=30, Resulting Numbers: [18, 30] Generated Node #0,2,0: 70:[18, 30] Operation: 60/2=30 Exploring Operation: 60-18=42, Resulting Numbers: [2, 42] Generated Node #0,2,1: 70:[2, 42] Operation: 60-18=42 Exploring Operation: 60+18=78, Resulting Numbers: [2, 78] Generated Node #0,2,2: 70:[2, 78] Operation: 60+18=78 Moving to Node #0,2,1 Current State: 70:[2, 42], Operations: ['62-44=18', '60-18=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[2, 78], Operations: ['62-44=18', '60+18=78'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,70 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[18, 30], Operations: ['62-44=18', '60/2=30'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,70 unequal: No Solution Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,70 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
[ 63, 14, 76, 69 ]
35
[ "76-69=7", "14*7=98", "98-63=35" ]
Current State: 35:[63, 14, 76, 69], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [63, 14, 7] Generated Node #2: [63, 14, 7] from Operation: 76-69=7 Current State: 35:[63, 14, 7], Operations: ['76-69=7'] Exploring Operation: 14*7=98, Resulting Numbers: [63, 98] Generated Node #3: [63, 98] from Operation: 14*7=98 Current State: 35:[63, 98], Operations: ['76-69=7', '14*7=98'] Exploring Operation: 98-63=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[63, 14, 76, 69], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [63, 14, 7] Generated Node #0,0: 35:[63, 14, 7] Operation: 76-69=7 Exploring Operation: 76-63=13, Resulting Numbers: [14, 69, 13] Generated Node #0,1: 35:[14, 69, 13] Operation: 76-63=13 Exploring Operation: 69-63=6, Resulting Numbers: [14, 76, 6] Generated Node #0,2: 35:[14, 76, 6] Operation: 69-63=6 Moving to Node #0,0 Current State: 35:[63, 14, 7], Operations: ['76-69=7'] Exploring Operation: 63/7=9, Resulting Numbers: [14, 9] Generated Node #0,0,0: 35:[14, 9] Operation: 63/7=9 Exploring Operation: 63-14=49, Resulting Numbers: [7, 49] Generated Node #0,0,1: 35:[7, 49] Operation: 63-14=49 Exploring Operation: 63-7=56, Resulting Numbers: [14, 56] Generated Node #0,0,2: 35:[14, 56] Operation: 63-7=56 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[14, 9], Operations: ['76-69=7', '63/7=9'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 14+9=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 14*9=126, Resulting Numbers: [126] 126,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[7, 49], Operations: ['76-69=7', '63-14=49'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[14, 56], Operations: ['76-69=7', '63-7=56'] Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,35 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: 35:[14, 69, 13], Operations: ['76-63=13'] Exploring Operation: 69-14=55, Resulting Numbers: [13, 55] Generated Node #0,1,0: 35:[13, 55] Operation: 69-14=55 Exploring Operation: 14-13=1, Resulting Numbers: [69, 1] Generated Node #0,1,1: 35:[69, 1] Operation: 14-13=1 Exploring Operation: 69-13=56, Resulting Numbers: [14, 56] Generated Node #0,1,2: 35:[14, 56] Operation: 69-13=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[13, 55], Operations: ['76-63=13', '69-14=55'] Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 13+55=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 13*55=715, Resulting Numbers: [715] 715,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[14, 56], Operations: ['76-63=13', '69-13=56'] Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,35 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[69, 1], Operations: ['76-63=13', '14-13=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,35 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 35:[14, 76, 6], Operations: ['69-63=6'] Exploring Operation: 14-6=8, Resulting Numbers: [76, 8] Generated Node #0,2,0: 35:[76, 8] Operation: 14-6=8 Exploring Operation: 76-14=62, Resulting Numbers: [6, 62] Generated Node #0,2,1: 35:[6, 62] Operation: 76-14=62 Exploring Operation: 76-6=70, Resulting Numbers: [14, 70] Generated Node #0,2,2: 35:[14, 70] Operation: 76-6=70 Moving to Node #0,2,1 Current State: 35:[6, 62], Operations: ['69-63=6', '76-14=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[76, 8], Operations: ['69-63=6', '14-6=8'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[14, 70], Operations: ['69-63=6', '76-6=70'] Exploring Operation: 14+70=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,35 unequal: No Solution Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,35 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 37, 35, 84, 35 ]
15
[ "37*35=1295", "1295-35=1260", "1260/84=15" ]
Current State: 15:[37, 35, 84, 35], Operations: [] Exploring Operation: 37*35=1295, Resulting Numbers: [84, 1295] Generated Node #2: [84, 1295] from Operation: 37*35=1295 Current State: 15:[84, 1295], Operations: ['37*35=1295'] Exploring Operation: 1295-35=1260, Resulting Numbers: [84, 1260] Generated Node #3: [84, 1260] from Operation: 1295-35=1260 Current State: 15:[84, 1260], Operations: ['37*35=1295', '1295-35=1260'] Exploring Operation: 1260/84=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[37, 35, 84, 35], Operations: [] Exploring Operation: 84-35=49, Resulting Numbers: [37, 35, 49] Generated Node #0,0: 15:[37, 35, 49] Operation: 84-35=49 Exploring Operation: 84-35=49, Resulting Numbers: [37, 35, 49] Generated Node #0,1: 15:[37, 35, 49] Operation: 84-35=49 Exploring Operation: 84-37=47, Resulting Numbers: [35, 35, 47] Generated Node #0,2: 15:[35, 35, 47] Operation: 84-37=47 Exploring Operation: 37-35=2, Resulting Numbers: [84, 35, 2] Generated Node #0,3: 15:[84, 35, 2] Operation: 37-35=2 Moving to Node #0,2 Current State: 15:[35, 35, 47], Operations: ['84-37=47'] Exploring Operation: 35/35=1, Resulting Numbers: [47, 1] Generated Node #0,2,0: 15:[47, 1] Operation: 35/35=1 Exploring Operation: 47-35=12, Resulting Numbers: [35, 12] Generated Node #0,2,1: 15:[35, 12] Operation: 47-35=12 Exploring Operation: 47-35=12, Resulting Numbers: [35, 12] Generated Node #0,2,2: 15:[35, 12] Operation: 47-35=12 Exploring Operation: 35-35=0, Resulting Numbers: [47, 0] Generated Node #0,2,3: 15:[47, 0] Operation: 35-35=0 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[35, 12], Operations: ['84-37=47', '47-35=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,15 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,15 unequal: No Solution No 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: 15:[35, 12], Operations: ['84-37=47', '47-35=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,15 unequal: No Solution No 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: 15:[47, 1], Operations: ['84-37=47', '35/35=1'] Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,15 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,15 unequal: No Solution No 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: 15:[47, 0], Operations: ['84-37=47', '35-35=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 47*0=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 47-0=47, Resulting Numbers: [47] 47,15 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: 15:[37, 35, 49], Operations: ['84-35=49'] Exploring Operation: 37-35=2, Resulting Numbers: [49, 2] Generated Node #0,1,0: 15:[49, 2] Operation: 37-35=2 Exploring Operation: 49-35=14, Resulting Numbers: [37, 14] Generated Node #0,1,1: 15:[37, 14] Operation: 49-35=14 Exploring Operation: 37+35=72, Resulting Numbers: [49, 72] Generated Node #0,1,2: 15:[49, 72] Operation: 37+35=72 Exploring Operation: 49-37=12, Resulting Numbers: [35, 12] Generated Node #0,1,3: 15:[35, 12] Operation: 49-37=12 Moving to Node #0,0 Current State: 15:[37, 35, 49], Operations: ['84-35=49'] Exploring Operation: 49-35=14, Resulting Numbers: [37, 14] Generated Node #0,0,0: 15:[37, 14] Operation: 49-35=14 Exploring Operation: 37-35=2, Resulting Numbers: [49, 2] Generated Node #0,0,1: 15:[49, 2] Operation: 37-35=2 Exploring Operation: 49-37=12, Resulting Numbers: [35, 12] Generated Node #0,0,2: 15:[35, 12] Operation: 49-37=12 Exploring Operation: 37+35=72, Resulting Numbers: [49, 72] Generated Node #0,0,3: 15:[49, 72] Operation: 37+35=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[37, 14], Operations: ['84-35=49', '49-35=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,15 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,15 unequal: No Solution No 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: 15:[35, 12], Operations: ['84-35=49', '49-37=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,15 unequal: No Solution No 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: 15:[49, 2], Operations: ['84-35=49', '37-35=2'] Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,15 unequal: No Solution No 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: 15:[49, 72], Operations: ['84-35=49', '37+35=72'] Exploring Operation: 49+72=121, Resulting Numbers: [121] 121,15 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 49*72=3528, Resulting Numbers: [3528] 3528,15 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: 15:[84, 35, 2], Operations: ['37-35=2'] Exploring Operation: 35-2=33, Resulting Numbers: [84, 33] Generated Node #0,3,0: 15:[84, 33] Operation: 35-2=33 Exploring Operation: 84/2=42, Resulting Numbers: [35, 42] Generated Node #0,3,1: 15:[35, 42] Operation: 84/2=42 Exploring Operation: 84-2=82, Resulting Numbers: [35, 82] Generated Node #0,3,2: 15:[35, 82] Operation: 84-2=82 Exploring Operation: 84-35=49, Resulting Numbers: [2, 49] Generated Node #0,3,3: 15:[2, 49] Operation: 84-35=49 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 15:[2, 49], Operations: ['37-35=2', '84-35=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,15 unequal: No Solution No 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: 15:[35, 42], Operations: ['37-35=2', '84/2=42'] Exploring Operation: 35*42=1470, Resulting Numbers: [1470] 1470,15 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 35+42=77, Resulting Numbers: [77] 77,15 unequal: No Solution No 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: 15:[84, 33], Operations: ['37-35=2', '35-2=33'] Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 84*33=2772, Resulting Numbers: [2772] 2772,15 unequal: No Solution Exploring Operation: 84+33=117, Resulting Numbers: [117] 117,15 unequal: No Solution No 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: 15:[35, 82], Operations: ['37-35=2', '84-2=82'] Exploring Operation: 82-35=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 35+82=117, Resulting Numbers: [117] 117,15 unequal: No Solution Exploring Operation: 35*82=2870, Resulting Numbers: [2870] 2870,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 15:[37, 14], Operations: ['84-35=49', '49-35=14'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,15 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[35, 12], Operations: ['84-35=49', '49-37=12'] Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,15 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[49, 2], Operations: ['84-35=49', '37-35=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,15 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[49, 72], Operations: ['84-35=49', '37+35=72'] Exploring Operation: 49+72=121, Resulting Numbers: [121] 121,15 unequal: No Solution Exploring Operation: 72-49=23, Resulting Numbers: [23] 23,15 unequal: No Solution Exploring Operation: 49*72=3528, Resulting Numbers: [3528] 3528,15 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 78, 38, 91, 45 ]
86
[ "78-38=40", "91-45=46", "40+46=86" ]
Current State: 86:[78, 38, 91, 45], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [91, 45, 40] Generated Node #2: [91, 45, 40] from Operation: 78-38=40 Current State: 86:[91, 45, 40], Operations: ['78-38=40'] Exploring Operation: 91-45=46, Resulting Numbers: [40, 46] Generated Node #3: [40, 46] from Operation: 91-45=46 Current State: 86:[40, 46], Operations: ['78-38=40', '91-45=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[78, 38, 91, 45], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [91, 45, 40] Generated Node #0,0: 86:[91, 45, 40] Operation: 78-38=40 Exploring Operation: 91-78=13, Resulting Numbers: [38, 45, 13] Generated Node #0,1: 86:[38, 45, 13] Operation: 91-78=13 Exploring Operation: 91-45=46, Resulting Numbers: [78, 38, 46] Generated Node #0,2: 86:[78, 38, 46] Operation: 91-45=46 Exploring Operation: 45-38=7, Resulting Numbers: [78, 91, 7] Generated Node #0,3: 86:[78, 91, 7] Operation: 45-38=7 Exploring Operation: 38+45=83, Resulting Numbers: [78, 91, 83] Generated Node #0,4: 86:[78, 91, 83] Operation: 38+45=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[91, 45, 40], Operations: ['78-38=40'] Exploring Operation: 91+40=131, Resulting Numbers: [45, 131] Generated Node #0,0,0: 86:[45, 131] Operation: 91+40=131 Exploring Operation: 91-40=51, Resulting Numbers: [45, 51] Generated Node #0,0,1: 86:[45, 51] Operation: 91-40=51 Exploring Operation: 45-40=5, Resulting Numbers: [91, 5] Generated Node #0,0,2: 86:[91, 5] Operation: 45-40=5 Exploring Operation: 91-45=46, Resulting Numbers: [40, 46] Generated Node #0,0,3: 86:[40, 46] Operation: 91-45=46 Exploring Operation: 45+40=85, Resulting Numbers: [91, 85] Generated Node #0,0,4: 86:[91, 85] Operation: 45+40=85 Moving to Node #0,0,3 Current State: 86:[40, 46], Operations: ['78-38=40', '91-45=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[78, 38, 91, 45], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [91, 45, 40] Generated Node #0,0: 86:[91, 45, 40] Operation: 78-38=40 Moving to Node #0,0 Current State: 86:[91, 45, 40], Operations: ['78-38=40'] Exploring Operation: 91-45=46, Resulting Numbers: [40, 46] Generated Node #0,0,3: 86:[40, 46] Operation: 91-45=46 Moving to Node #0,0,3 Current State: 86:[40, 46], Operations: ['78-38=40', '91-45=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 95, 30, 8, 94 ]
51
[ "95+94=189", "30*8=240", "240-189=51" ]
Current State: 51:[95, 30, 8, 94], Operations: [] Exploring Operation: 95+94=189, Resulting Numbers: [30, 8, 189] Generated Node #2: [30, 8, 189] from Operation: 95+94=189 Current State: 51:[30, 8, 189], Operations: ['95+94=189'] Exploring Operation: 30*8=240, Resulting Numbers: [189, 240] Generated Node #3: [189, 240] from Operation: 30*8=240 Current State: 51:[189, 240], Operations: ['95+94=189', '30*8=240'] Exploring Operation: 240-189=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[95, 30, 8, 94], Operations: [] Exploring Operation: 95-30=65, Resulting Numbers: [8, 94, 65] Generated Node #0,0: 51:[8, 94, 65] Operation: 95-30=65 Exploring Operation: 94-30=64, Resulting Numbers: [95, 8, 64] Generated Node #0,1: 51:[95, 8, 64] Operation: 94-30=64 Exploring Operation: 95-94=1, Resulting Numbers: [30, 8, 1] Generated Node #0,2: 51:[30, 8, 1] Operation: 95-94=1 Exploring Operation: 95-8=87, Resulting Numbers: [30, 94, 87] Generated Node #0,3: 51:[30, 94, 87] Operation: 95-8=87 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[30, 8, 1], Operations: ['95-94=1'] Exploring Operation: 8-1=7, Resulting Numbers: [30, 7] Generated Node #0,2,0: 51:[30, 7] Operation: 8-1=7 Exploring Operation: 30+8=38, Resulting Numbers: [1, 38] Generated Node #0,2,1: 51:[1, 38] Operation: 30+8=38 Exploring Operation: 30-8=22, Resulting Numbers: [1, 22] Generated Node #0,2,2: 51:[1, 22] Operation: 30-8=22 Exploring Operation: 30-1=29, Resulting Numbers: [8, 29] Generated Node #0,2,3: 51:[8, 29] Operation: 30-1=29 Moving to Node #0,2,2 Current State: 51:[1, 22], Operations: ['95-94=1', '30-8=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[1, 38], Operations: ['95-94=1', '30+8=38'] Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,51 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[8, 29], Operations: ['95-94=1', '30-1=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[30, 7], Operations: ['95-94=1', '8-1=7'] Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[8, 94, 65], Operations: ['95-30=65'] Exploring Operation: 94-8=86, Resulting Numbers: [65, 86] Generated Node #0,0,0: 51:[65, 86] Operation: 94-8=86 Exploring Operation: 65-8=57, Resulting Numbers: [94, 57] Generated Node #0,0,1: 51:[94, 57] Operation: 65-8=57 Exploring Operation: 8+94=102, Resulting Numbers: [65, 102] Generated Node #0,0,2: 51:[65, 102] Operation: 8+94=102 Exploring Operation: 94-65=29, Resulting Numbers: [8, 29] Generated Node #0,0,3: 51:[8, 29] Operation: 94-65=29 Moving to Node #0,0,3 Current State: 51:[8, 29], Operations: ['95-30=65', '94-65=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[94, 57], Operations: ['95-30=65', '65-8=57'] Exploring Operation: 94*57=5358, Resulting Numbers: [5358] 5358,51 unequal: No Solution Exploring Operation: 94+57=151, Resulting Numbers: [151] 151,51 unequal: No Solution Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[65, 86], Operations: ['95-30=65', '94-8=86'] Exploring Operation: 65+86=151, Resulting Numbers: [151] 151,51 unequal: No Solution Exploring Operation: 65*86=5590, Resulting Numbers: [5590] 5590,51 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[65, 102], Operations: ['95-30=65', '8+94=102'] Exploring Operation: 65*102=6630, Resulting Numbers: [6630] 6630,51 unequal: No Solution Exploring Operation: 65+102=167, Resulting Numbers: [167] 167,51 unequal: No Solution Exploring Operation: 102-65=37, Resulting Numbers: [37] 37,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[95, 8, 64], Operations: ['94-30=64'] Exploring Operation: 64-8=56, Resulting Numbers: [95, 56] Generated Node #0,1,0: 51:[95, 56] Operation: 64-8=56 Exploring Operation: 95-8=87, Resulting Numbers: [64, 87] Generated Node #0,1,1: 51:[64, 87] Operation: 95-8=87 Exploring Operation: 64/8=8, Resulting Numbers: [95, 8] Generated Node #0,1,2: 51:[95, 8] Operation: 64/8=8 Exploring Operation: 95-64=31, Resulting Numbers: [8, 31] Generated Node #0,1,3: 51:[8, 31] Operation: 95-64=31 Moving to Node #0,1,3 Current State: 51:[8, 31], Operations: ['94-30=64', '95-64=31'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[64, 87], Operations: ['94-30=64', '95-8=87'] Exploring Operation: 87-64=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 64*87=5568, Resulting Numbers: [5568] 5568,51 unequal: No Solution Exploring Operation: 64+87=151, Resulting Numbers: [151] 151,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[95, 56], Operations: ['94-30=64', '64-8=56'] Exploring Operation: 95+56=151, Resulting Numbers: [151] 151,51 unequal: No Solution Exploring Operation: 95*56=5320, Resulting Numbers: [5320] 5320,51 unequal: No Solution Exploring Operation: 95-56=39, Resulting Numbers: [39] 39,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[95, 8], Operations: ['94-30=64', '64/8=8'] Exploring Operation: 95*8=760, Resulting Numbers: [760] 760,51 unequal: No Solution Exploring Operation: 95+8=103, Resulting Numbers: [103] 103,51 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[30, 94, 87], Operations: ['95-8=87'] Exploring Operation: 94-87=7, Resulting Numbers: [30, 7] Generated Node #0,3,0: 51:[30, 7] Operation: 94-87=7 Exploring Operation: 94-30=64, Resulting Numbers: [87, 64] Generated Node #0,3,1: 51:[87, 64] Operation: 94-30=64 Exploring Operation: 30+94=124, Resulting Numbers: [87, 124] Generated Node #0,3,2: 51:[87, 124] Operation: 30+94=124 Exploring Operation: 87-30=57, Resulting Numbers: [94, 57] Generated Node #0,3,3: 51:[94, 57] Operation: 87-30=57 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[30, 7], Operations: ['95-8=87', '94-87=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[87, 64], Operations: ['95-8=87', '94-30=64'] Exploring Operation: 87-64=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 87+64=151, Resulting Numbers: [151] 151,51 unequal: No Solution Exploring Operation: 87*64=5568, Resulting Numbers: [5568] 5568,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[94, 57], Operations: ['95-8=87', '87-30=57'] Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 94*57=5358, Resulting Numbers: [5358] 5358,51 unequal: No Solution Exploring Operation: 94+57=151, Resulting Numbers: [151] 151,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 51:[87, 124], Operations: ['95-8=87', '30+94=124'] Exploring Operation: 87+124=211, Resulting Numbers: [211] 211,51 unequal: No Solution Exploring Operation: 87*124=10788, Resulting Numbers: [10788] 10788,51 unequal: No Solution Exploring Operation: 124-87=37, Resulting Numbers: [37] 37,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 5, 23, 3, 48 ]
56
[ "5*3=15", "23+48=71", "71-15=56" ]
Current State: 56:[5, 23, 3, 48], Operations: [] Exploring Operation: 5*3=15, Resulting Numbers: [23, 48, 15] Generated Node #2: [23, 48, 15] from Operation: 5*3=15 Current State: 56:[23, 48, 15], Operations: ['5*3=15'] Exploring Operation: 23+48=71, Resulting Numbers: [15, 71] Generated Node #3: [15, 71] from Operation: 23+48=71 Current State: 56:[15, 71], Operations: ['5*3=15', '23+48=71'] Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[5, 23, 3, 48], Operations: [] Exploring Operation: 48/3=16, Resulting Numbers: [5, 23, 16] Generated Node #0,0: 56:[5, 23, 16] Operation: 48/3=16 Exploring Operation: 5+23=28, Resulting Numbers: [3, 48, 28] Generated Node #0,1: 56:[3, 48, 28] Operation: 5+23=28 Exploring Operation: 48-23=25, Resulting Numbers: [5, 3, 25] Generated Node #0,2: 56:[5, 3, 25] Operation: 48-23=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[5, 3, 25], Operations: ['48-23=25'] Exploring Operation: 25/5=5, Resulting Numbers: [3, 5] Generated Node #0,2,0: 56:[3, 5] Operation: 25/5=5 Exploring Operation: 3+25=28, Resulting Numbers: [5, 28] Generated Node #0,2,1: 56:[5, 28] Operation: 3+25=28 Exploring Operation: 5+3=8, Resulting Numbers: [25, 8] Generated Node #0,2,2: 56:[25, 8] Operation: 5+3=8 Moving to Node #0,2,1 Current State: 56:[5, 28], Operations: ['48-23=25', '3+25=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,56 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[3, 5], Operations: ['48-23=25', '25/5=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[25, 8], Operations: ['48-23=25', '5+3=8'] Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,56 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,56 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 #0,0 Current State: 56:[5, 23, 16], Operations: ['48/3=16'] Exploring Operation: 23-5=18, Resulting Numbers: [16, 18] Generated Node #0,0,0: 56:[16, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [16, 28] Generated Node #0,0,1: 56:[16, 28] Operation: 5+23=28 Exploring Operation: 23-16=7, Resulting Numbers: [5, 7] Generated Node #0,0,2: 56:[5, 7] Operation: 23-16=7 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 56:[5, 7], Operations: ['48/3=16', '23-16=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,56 unequal: No Solution No 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: 56:[16, 28], Operations: ['48/3=16', '5+23=28'] Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,56 unequal: No Solution Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,56 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,56 unequal: No Solution No 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: 56:[16, 18], Operations: ['48/3=16', '23-5=18'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,56 unequal: No Solution Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,56 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: 56:[3, 48, 28], Operations: ['5+23=28'] Exploring Operation: 3+48=51, Resulting Numbers: [28, 51] Generated Node #0,1,0: 56:[28, 51] Operation: 3+48=51 Exploring Operation: 48-28=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 56:[3, 20] Operation: 48-28=20 Exploring Operation: 48/3=16, Resulting Numbers: [28, 16] Generated Node #0,1,2: 56:[28, 16] Operation: 48/3=16 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 56:[28, 16], Operations: ['5+23=28', '48/3=16'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,56 unequal: No Solution Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,56 unequal: No Solution No 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: 56:[28, 51], Operations: ['5+23=28', '3+48=51'] Exploring Operation: 28+51=79, Resulting Numbers: [79] 79,56 unequal: No Solution Exploring Operation: 28*51=1428, Resulting Numbers: [1428] 1428,56 unequal: No Solution Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,56 unequal: No Solution No 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: 56:[3, 20], Operations: ['5+23=28', '48-28=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,56 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 2, 53, 8, 79 ]
33
[ "8/2=4", "53+79=132", "132/4=33" ]
Current State: 33:[2, 53, 8, 79], Operations: [] Exploring Operation: 8/2=4, Resulting Numbers: [53, 79, 4] Generated Node #2: [53, 79, 4] from Operation: 8/2=4 Current State: 33:[53, 79, 4], Operations: ['8/2=4'] Exploring Operation: 53+79=132, Resulting Numbers: [4, 132] Generated Node #3: [4, 132] from Operation: 53+79=132 Current State: 33:[4, 132], Operations: ['8/2=4', '53+79=132'] Exploring Operation: 132/4=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[2, 53, 8, 79], Operations: [] Exploring Operation: 53-2=51, Resulting Numbers: [8, 79, 51] Generated Node #0,0: 33:[8, 79, 51] Operation: 53-2=51 Exploring Operation: 79-8=71, Resulting Numbers: [2, 53, 71] Generated Node #0,1: 33:[2, 53, 71] Operation: 79-8=71 Exploring Operation: 79-53=26, Resulting Numbers: [2, 8, 26] Generated Node #0,2: 33:[2, 8, 26] Operation: 79-53=26 Exploring Operation: 53-8=45, Resulting Numbers: [2, 79, 45] Generated Node #0,3: 33:[2, 79, 45] Operation: 53-8=45 Moving to Node #0,2 Current State: 33:[2, 8, 26], Operations: ['79-53=26'] Exploring Operation: 8+26=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 33:[2, 34] Operation: 8+26=34 Exploring Operation: 2+8=10, Resulting Numbers: [26, 10] Generated Node #0,2,1: 33:[26, 10] Operation: 2+8=10 Exploring Operation: 26/2=13, Resulting Numbers: [8, 13] Generated Node #0,2,2: 33:[8, 13] Operation: 26/2=13 Exploring Operation: 8/2=4, Resulting Numbers: [26, 4] Generated Node #0,2,3: 33:[26, 4] Operation: 8/2=4 Moving to Node #0,3 Current State: 33:[2, 79, 45], Operations: ['53-8=45'] Exploring Operation: 2+79=81, Resulting Numbers: [45, 81] Generated Node #0,3,0: 33:[45, 81] Operation: 2+79=81 Exploring Operation: 79-45=34, Resulting Numbers: [2, 34] Generated Node #0,3,1: 33:[2, 34] Operation: 79-45=34 Exploring Operation: 79-2=77, Resulting Numbers: [45, 77] Generated Node #0,3,2: 33:[45, 77] Operation: 79-2=77 Exploring Operation: 45-2=43, Resulting Numbers: [79, 43] Generated Node #0,3,3: 33:[79, 43] Operation: 45-2=43 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 33:[2, 34], Operations: ['53-8=45', '79-45=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,33 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,33 unequal: No Solution No 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: 33:[45, 77], Operations: ['53-8=45', '79-2=77'] Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 45*77=3465, Resulting Numbers: [3465] 3465,33 unequal: No Solution Exploring Operation: 45+77=122, Resulting Numbers: [122] 122,33 unequal: No Solution No 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: 33:[79, 43], Operations: ['53-8=45', '45-2=43'] Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,33 unequal: No Solution Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,33 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,33 unequal: No Solution No 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: 33:[45, 81], Operations: ['53-8=45', '2+79=81'] Exploring Operation: 45*81=3645, Resulting Numbers: [3645] 3645,33 unequal: No Solution Exploring Operation: 81-45=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 45+81=126, Resulting Numbers: [126] 126,33 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: 33:[2, 53, 71], Operations: ['79-8=71'] Exploring Operation: 53-2=51, Resulting Numbers: [71, 51] Generated Node #0,1,0: 33:[71, 51] Operation: 53-2=51 Exploring Operation: 71-2=69, Resulting Numbers: [53, 69] Generated Node #0,1,1: 33:[53, 69] Operation: 71-2=69 Exploring Operation: 2+53=55, Resulting Numbers: [71, 55] Generated Node #0,1,2: 33:[71, 55] Operation: 2+53=55 Exploring Operation: 71-53=18, Resulting Numbers: [2, 18] Generated Node #0,1,3: 33:[2, 18] Operation: 71-53=18 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[2, 18], Operations: ['79-8=71', '71-53=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,33 unequal: No Solution No 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: 33:[71, 51], Operations: ['79-8=71', '53-2=51'] Exploring Operation: 71*51=3621, Resulting Numbers: [3621] 3621,33 unequal: No Solution Exploring Operation: 71+51=122, Resulting Numbers: [122] 122,33 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,33 unequal: No Solution No 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: 33:[53, 69], Operations: ['79-8=71', '71-2=69'] Exploring Operation: 53+69=122, Resulting Numbers: [122] 122,33 unequal: No Solution Exploring Operation: 53*69=3657, Resulting Numbers: [3657] 3657,33 unequal: No Solution Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,33 unequal: No Solution No 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: 33:[71, 55], Operations: ['79-8=71', '2+53=55'] Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 71*55=3905, Resulting Numbers: [3905] 3905,33 unequal: No Solution Exploring Operation: 71+55=126, Resulting Numbers: [126] 126,33 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: 33:[8, 79, 51], Operations: ['53-2=51'] Exploring Operation: 51-8=43, Resulting Numbers: [79, 43] Generated Node #0,0,0: 33:[79, 43] Operation: 51-8=43 Exploring Operation: 8+79=87, Resulting Numbers: [51, 87] Generated Node #0,0,1: 33:[51, 87] Operation: 8+79=87 Exploring Operation: 79-51=28, Resulting Numbers: [8, 28] Generated Node #0,0,2: 33:[8, 28] Operation: 79-51=28 Exploring Operation: 79-8=71, Resulting Numbers: [51, 71] Generated Node #0,0,3: 33:[51, 71] Operation: 79-8=71 Moving to Node #0,2,0 Current State: 33:[2, 34], Operations: ['79-53=26', '8+26=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,33 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[8, 13], Operations: ['79-53=26', '26/2=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,33 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[26, 10], Operations: ['79-53=26', '2+8=10'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,33 unequal: No Solution Moving to Node #0,0,2 Current State: 33:[8, 28], Operations: ['53-2=51', '79-51=28'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 8+28=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 8*28=224, Resulting Numbers: [224] 224,33 unequal: No Solution Moving to Node #0,2,3 Current State: 33:[26, 4], Operations: ['79-53=26', '8/2=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,33 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,33 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[79, 43], Operations: ['53-2=51', '51-8=43'] Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,33 unequal: No Solution Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,33 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,33 unequal: No Solution Moving to Node #0,0,3 Current State: 33:[51, 71], Operations: ['53-2=51', '79-8=71'] Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,33 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[51, 87], Operations: ['53-2=51', '8+79=87'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,33 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,33 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 8, 40, 48, 3 ]
32
[ "8+40=48", "48/3=16", "48-16=32" ]
Current State: 32:[8, 40, 48, 3], Operations: [] Exploring Operation: 8+40=48, Resulting Numbers: [48, 3, 48] Generated Node #2: [48, 3, 48] from Operation: 8+40=48 Current State: 32:[48, 3, 48], Operations: ['8+40=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,32 equal: Goal Reached Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[8, 40, 48, 3], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [8, 3, 8] Generated Node #0,0: 32:[8, 3, 8] Operation: 48-40=8 Exploring Operation: 48/3=16, Resulting Numbers: [8, 40, 16] Generated Node #0,1: 32:[8, 40, 16] Operation: 48/3=16 Moving to Node #0,0 Current State: 32:[8, 3, 8], Operations: ['48-40=8'] Exploring Operation: 8-3=5, Resulting Numbers: [8, 5] Generated Node #0,0,0: 32:[8, 5] Operation: 8-3=5 Exploring Operation: 8+8=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 32:[3, 16] Operation: 8+8=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[8, 5], Operations: ['48-40=8', '8-3=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[3, 16], Operations: ['48-40=8', '8+8=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,32 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: 32:[8, 40, 16], Operations: ['48/3=16'] Exploring Operation: 40-8=32, Resulting Numbers: [16, 32] Generated Node #0,1,0: 32:[16, 32] Operation: 40-8=32 Exploring Operation: 40/8=5, Resulting Numbers: [16, 5] Generated Node #0,1,1: 32:[16, 5] Operation: 40/8=5 Moving to Node #0,1,0 Current State: 32:[16, 32], Operations: ['48/3=16', '40-8=32'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[16, 5], Operations: ['48/3=16', '40/8=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,32 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 60, 38, 21, 20 ]
56
[ "60/20=3", "38+21=59", "59-3=56" ]
Current State: 56:[60, 38, 21, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [38, 21, 3] Generated Node #2: [38, 21, 3] from Operation: 60/20=3 Current State: 56:[38, 21, 3], Operations: ['60/20=3'] Exploring Operation: 38+21=59, Resulting Numbers: [3, 59] Generated Node #3: [3, 59] from Operation: 38+21=59 Current State: 56:[3, 59], Operations: ['60/20=3', '38+21=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[60, 38, 21, 20], Operations: [] Exploring Operation: 38-21=17, Resulting Numbers: [60, 20, 17] Generated Node #0,0: 56:[60, 20, 17] Operation: 38-21=17 Exploring Operation: 38+21=59, Resulting Numbers: [60, 20, 59] Generated Node #0,1: 56:[60, 20, 59] Operation: 38+21=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[60, 20, 17], Operations: ['38-21=17'] Exploring Operation: 60/20=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 56:[17, 3] Operation: 60/20=3 Exploring Operation: 20-17=3, Resulting Numbers: [60, 3] Generated Node #0,0,1: 56:[60, 3] Operation: 20-17=3 Moving to Node #0,0,0 Current State: 56:[17, 3], Operations: ['38-21=17', '60/20=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[60, 3], Operations: ['38-21=17', '20-17=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[60, 20, 59], Operations: ['38+21=59'] Exploring Operation: 60/20=3, Resulting Numbers: [59, 3] Generated Node #0,1,0: 56:[59, 3] Operation: 60/20=3 Exploring Operation: 60-59=1, Resulting Numbers: [20, 1] Generated Node #0,1,1: 56:[20, 1] Operation: 60-59=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[59, 3], Operations: ['38+21=59', '60/20=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[60, 38, 21, 20], Operations: [] Exploring Operation: 38+21=59, Resulting Numbers: [60, 20, 59] Generated Node #0,1: 56:[60, 20, 59] Operation: 38+21=59 Moving to Node #0,1 Current State: 56:[60, 20, 59], Operations: ['38+21=59'] Exploring Operation: 60/20=3, Resulting Numbers: [59, 3] Generated Node #0,1,0: 56:[59, 3] Operation: 60/20=3 Moving to Node #0,1,0 Current State: 56:[59, 3], Operations: ['38+21=59', '60/20=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 71, 60, 32, 8 ]
51
[ "71-60=11", "32+8=40", "11+40=51" ]
Current State: 51:[71, 60, 32, 8], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [32, 8, 11] Generated Node #2: [32, 8, 11] from Operation: 71-60=11 Current State: 51:[32, 8, 11], Operations: ['71-60=11'] Exploring Operation: 32+8=40, Resulting Numbers: [11, 40] Generated Node #3: [11, 40] from Operation: 32+8=40 Current State: 51:[11, 40], Operations: ['71-60=11', '32+8=40'] Exploring Operation: 11+40=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[71, 60, 32, 8], Operations: [] Exploring Operation: 71-32=39, Resulting Numbers: [60, 8, 39] Generated Node #0,0: 51:[60, 8, 39] Operation: 71-32=39 Exploring Operation: 71-60=11, Resulting Numbers: [32, 8, 11] Generated Node #0,1: 51:[32, 8, 11] Operation: 71-60=11 Exploring Operation: 32/8=4, Resulting Numbers: [71, 60, 4] Generated Node #0,2: 51:[71, 60, 4] Operation: 32/8=4 Exploring Operation: 71-8=63, Resulting Numbers: [60, 32, 63] Generated Node #0,3: 51:[60, 32, 63] Operation: 71-8=63 Moving to Node #0,0 Current State: 51:[60, 8, 39], Operations: ['71-32=39'] Exploring Operation: 60-8=52, Resulting Numbers: [39, 52] Generated Node #0,0,0: 51:[39, 52] Operation: 60-8=52 Exploring Operation: 60-39=21, Resulting Numbers: [8, 21] Generated Node #0,0,1: 51:[8, 21] Operation: 60-39=21 Exploring Operation: 39-8=31, Resulting Numbers: [60, 31] Generated Node #0,0,2: 51:[60, 31] Operation: 39-8=31 Exploring Operation: 8+39=47, Resulting Numbers: [60, 47] Generated Node #0,0,3: 51:[60, 47] Operation: 8+39=47 Moving to Node #0,1 Current State: 51:[32, 8, 11], Operations: ['71-60=11'] Exploring Operation: 32-8=24, Resulting Numbers: [11, 24] Generated Node #0,1,0: 51:[11, 24] Operation: 32-8=24 Exploring Operation: 32-11=21, Resulting Numbers: [8, 21] Generated Node #0,1,1: 51:[8, 21] Operation: 32-11=21 Exploring Operation: 32/8=4, Resulting Numbers: [11, 4] Generated Node #0,1,2: 51:[11, 4] Operation: 32/8=4 Exploring Operation: 32+11=43, Resulting Numbers: [8, 43] Generated Node #0,1,3: 51:[8, 43] Operation: 32+11=43 Moving to Node #0,2 Current State: 51:[71, 60, 4], Operations: ['32/8=4'] Exploring Operation: 60/4=15, Resulting Numbers: [71, 15] Generated Node #0,2,0: 51:[71, 15] Operation: 60/4=15 Exploring Operation: 71-60=11, Resulting Numbers: [4, 11] Generated Node #0,2,1: 51:[4, 11] Operation: 71-60=11 Exploring Operation: 71-4=67, Resulting Numbers: [60, 67] Generated Node #0,2,2: 51:[60, 67] Operation: 71-4=67 Exploring Operation: 60-4=56, Resulting Numbers: [71, 56] Generated Node #0,2,3: 51:[71, 56] Operation: 60-4=56 Moving to Node #0,3 Current State: 51:[60, 32, 63], Operations: ['71-8=63'] Exploring Operation: 60+32=92, Resulting Numbers: [63, 92] Generated Node #0,3,0: 51:[63, 92] Operation: 60+32=92 Exploring Operation: 60-32=28, Resulting Numbers: [63, 28] Generated Node #0,3,1: 51:[63, 28] Operation: 60-32=28 Exploring Operation: 63-60=3, Resulting Numbers: [32, 3] Generated Node #0,3,2: 51:[32, 3] Operation: 63-60=3 Exploring Operation: 63-32=31, Resulting Numbers: [60, 31] Generated Node #0,3,3: 51:[60, 31] Operation: 63-32=31 Moving to Node #0,1,2 Current State: 51:[11, 4], Operations: ['71-60=11', '32/8=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,51 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[4, 11], Operations: ['32/8=4', '71-60=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,51 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[8, 21], Operations: ['71-60=11', '32-11=21'] Exploring Operation: 8*21=168, Resulting Numbers: [168] 168,51 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[8, 21], Operations: ['71-32=39', '60-39=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 8*21=168, Resulting Numbers: [168] 168,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[11, 24], Operations: ['71-60=11', '32-8=24'] Exploring Operation: 11*24=264, Resulting Numbers: [264] 264,51 unequal: No Solution Exploring Operation: 11+24=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[60, 47], Operations: ['71-32=39', '8+39=47'] Exploring Operation: 60-47=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 60+47=107, Resulting Numbers: [107] 107,51 unequal: No Solution Exploring Operation: 60*47=2820, Resulting Numbers: [2820] 2820,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[39, 52], Operations: ['71-32=39', '60-8=52'] Exploring Operation: 39+52=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 39*52=2028, Resulting Numbers: [2028] 2028,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[8, 43], Operations: ['71-60=11', '32+11=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[71, 60, 32, 8], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [32, 8, 11] Generated Node #0,1: 51:[32, 8, 11] Operation: 71-60=11 Moving to Node #0,1 Current State: 51:[32, 8, 11], Operations: ['71-60=11'] Exploring Operation: 32+11=43, Resulting Numbers: [8, 43] Generated Node #0,1,3: 51:[8, 43] Operation: 32+11=43 Moving to Node #0,1,3 Current State: 51:[8, 43], Operations: ['71-60=11', '32+11=43'] Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
0.960069
hs_4
mult_heuristic
[ 17, 25, 89, 17 ]
30
[ "17+25=42", "89-17=72", "72-42=30" ]
Current State: 30:[17, 25, 89, 17], Operations: [] Exploring Operation: 17+25=42, Resulting Numbers: [89, 42] Generated Node #2: [89, 42] from Operation: 17+25=42 Current State: 30:[89, 42], Operations: ['17+25=42'] Exploring Operation: 89-17=72, Resulting Numbers: [42, 72] Generated Node #3: [42, 72] from Operation: 89-17=72 Current State: 30:[42, 72], Operations: ['17+25=42', '89-17=72'] Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[17, 25, 89, 17], Operations: [] Exploring Operation: 25-17=8, Resulting Numbers: [89, 17, 8] Generated Node #0,0: 30:[89, 17, 8] Operation: 25-17=8 Exploring Operation: 89-17=72, Resulting Numbers: [17, 25, 72] Generated Node #0,1: 30:[17, 25, 72] Operation: 89-17=72 Exploring Operation: 89-25=64, Resulting Numbers: [17, 17, 64] Generated Node #0,2: 30:[17, 17, 64] Operation: 89-25=64 Exploring Operation: 89-17=72, Resulting Numbers: [25, 17, 72] Generated Node #0,3: 30:[25, 17, 72] Operation: 89-17=72 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[17, 17, 64], Operations: ['89-25=64'] Exploring Operation: 64-17=47, Resulting Numbers: [17, 47] Generated Node #0,2,0: 30:[17, 47] Operation: 64-17=47 Exploring Operation: 64-17=47, Resulting Numbers: [17, 47] Generated Node #0,2,1: 30:[17, 47] Operation: 64-17=47 Exploring Operation: 17/17=1, Resulting Numbers: [64, 1] Generated Node #0,2,2: 30:[64, 1] Operation: 17/17=1 Exploring Operation: 17-17=0, Resulting Numbers: [64, 0] Generated Node #0,2,3: 30:[64, 0] Operation: 17-17=0 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[17, 47], Operations: ['89-25=64', '64-17=47'] Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,30 unequal: No Solution Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,30 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[17, 25, 89, 17], Operations: [] Exploring Operation: 89-25=64, Resulting Numbers: [17, 17, 64] Generated Node #0,2: 30:[17, 17, 64] Operation: 89-25=64 Moving to Node #0,2 Current State: 30:[17, 17, 64], Operations: ['89-25=64'] Exploring Operation: 64-17=47, Resulting Numbers: [17, 47] Generated Node #0,2,0: 30:[17, 47] Operation: 64-17=47 Moving to Node #0,2,0 Current State: 30:[17, 47], Operations: ['89-25=64', '64-17=47'] Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 24, 68, 32, 35 ]
89
[ "24+68=92", "35-32=3", "92-3=89" ]
Current State: 89:[24, 68, 32, 35], Operations: [] Exploring Operation: 24+68=92, Resulting Numbers: [32, 35, 92] Generated Node #2: [32, 35, 92] from Operation: 24+68=92 Current State: 89:[32, 35, 92], Operations: ['24+68=92'] Exploring Operation: 35-32=3, Resulting Numbers: [92, 3] Generated Node #3: [92, 3] from Operation: 35-32=3 Current State: 89:[92, 3], Operations: ['24+68=92', '35-32=3'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[24, 68, 32, 35], Operations: [] Exploring Operation: 24+35=59, Resulting Numbers: [68, 32, 59] Generated Node #0,0: 89:[68, 32, 59] Operation: 24+35=59 Exploring Operation: 24+32=56, Resulting Numbers: [68, 35, 56] Generated Node #0,1: 89:[68, 35, 56] Operation: 24+32=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[68, 32, 59], Operations: ['24+35=59'] Exploring Operation: 68+32=100, Resulting Numbers: [59, 100] Generated Node #0,0,0: 89:[59, 100] Operation: 68+32=100 Exploring Operation: 32+59=91, Resulting Numbers: [68, 91] Generated Node #0,0,1: 89:[68, 91] Operation: 32+59=91 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[68, 91], Operations: ['24+35=59', '32+59=91'] Exploring Operation: 68+91=159, Resulting Numbers: [159] 159,89 unequal: No Solution Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,89 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:[59, 100], Operations: ['24+35=59', '68+32=100'] Exploring Operation: 100-59=41, Resulting Numbers: [41] 41,89 unequal: No Solution Exploring Operation: 59+100=159, Resulting Numbers: [159] 159,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[68, 35, 56], Operations: ['24+32=56'] Exploring Operation: 35+56=91, Resulting Numbers: [68, 91] Generated Node #0,1,0: 89:[68, 91] Operation: 35+56=91 Exploring Operation: 68+35=103, Resulting Numbers: [56, 103] Generated Node #0,1,1: 89:[56, 103] Operation: 68+35=103 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[68, 91], Operations: ['24+32=56', '35+56=91'] Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,89 unequal: No Solution Exploring Operation: 68+91=159, Resulting Numbers: [159] 159,89 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:[56, 103], Operations: ['24+32=56', '68+35=103'] Exploring Operation: 56+103=159, Resulting Numbers: [159] 159,89 unequal: No Solution Exploring Operation: 103-56=47, Resulting Numbers: [47] 47,89 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
mult_heuristic
[ 2, 49, 28, 77 ]
11
[ "2*28=56", "56-49=7", "77/7=11" ]
Current State: 11:[2, 49, 28, 77], Operations: [] Exploring Operation: 2*28=56, Resulting Numbers: [49, 77, 56] Generated Node #2: [49, 77, 56] from Operation: 2*28=56 Current State: 11:[49, 77, 56], Operations: ['2*28=56'] Exploring Operation: 56-49=7, Resulting Numbers: [77, 7] Generated Node #3: [77, 7] from Operation: 56-49=7 Current State: 11:[77, 7], Operations: ['2*28=56', '56-49=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[2, 49, 28, 77], Operations: [] Exploring Operation: 77-28=49, Resulting Numbers: [2, 49, 49] Generated Node #0,0: 11:[2, 49, 49] Operation: 77-28=49 Exploring Operation: 49-28=21, Resulting Numbers: [2, 77, 21] Generated Node #0,1: 11:[2, 77, 21] Operation: 49-28=21 Exploring Operation: 77-49=28, Resulting Numbers: [2, 28, 28] Generated Node #0,2: 11:[2, 28, 28] Operation: 77-49=28 Exploring Operation: 28/2=14, Resulting Numbers: [49, 77, 14] Generated Node #0,3: 11:[49, 77, 14] Operation: 28/2=14 Moving to Node #0,2 Current State: 11:[2, 28, 28], Operations: ['77-49=28'] Exploring Operation: 28/2=14, Resulting Numbers: [28, 14] Generated Node #0,2,0: 11:[28, 14] Operation: 28/2=14 Exploring Operation: 28/2=14, Resulting Numbers: [28, 14] Generated Node #0,2,1: 11:[28, 14] Operation: 28/2=14 Exploring Operation: 28/28=1, Resulting Numbers: [2, 1] Generated Node #0,2,2: 11:[2, 1] Operation: 28/28=1 Exploring Operation: 28-28=0, Resulting Numbers: [2, 0] Generated Node #0,2,3: 11:[2, 0] Operation: 28-28=0 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[2, 1], Operations: ['77-49=28', '28/28=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[28, 14], Operations: ['77-49=28', '28/2=14'] Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,11 unequal: No Solution Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[28, 14], Operations: ['77-49=28', '28/2=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,11 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[2, 0], Operations: ['77-49=28', '28-28=0'] Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,11 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 11:[2, 77, 21], Operations: ['49-28=21'] Exploring Operation: 77-2=75, Resulting Numbers: [21, 75] Generated Node #0,1,0: 11:[21, 75] Operation: 77-2=75 Exploring Operation: 2+77=79, Resulting Numbers: [21, 79] Generated Node #0,1,1: 11:[21, 79] Operation: 2+77=79 Exploring Operation: 77-21=56, Resulting Numbers: [2, 56] Generated Node #0,1,2: 11:[2, 56] Operation: 77-21=56 Exploring Operation: 21-2=19, Resulting Numbers: [77, 19] Generated Node #0,1,3: 11:[77, 19] Operation: 21-2=19 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[2, 56], Operations: ['49-28=21', '77-21=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,11 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[21, 75], Operations: ['49-28=21', '77-2=75'] Exploring Operation: 21+75=96, Resulting Numbers: [96] 96,11 unequal: No Solution Exploring Operation: 75-21=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 21*75=1575, Resulting Numbers: [1575] 1575,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 11:[77, 19], Operations: ['49-28=21', '21-2=19'] Exploring Operation: 77+19=96, Resulting Numbers: [96] 96,11 unequal: No Solution Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 77*19=1463, Resulting Numbers: [1463] 1463,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[21, 79], Operations: ['49-28=21', '2+77=79'] Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,11 unequal: No Solution Exploring Operation: 21*79=1659, Resulting Numbers: [1659] 1659,11 unequal: No Solution Exploring Operation: 21+79=100, Resulting Numbers: [100] 100,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 11:[2, 49, 49], Operations: ['77-28=49'] Exploring Operation: 49/49=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 11:[2, 1] Operation: 49/49=1 Exploring Operation: 49-49=0, Resulting Numbers: [2, 0] Generated Node #0,0,1: 11:[2, 0] Operation: 49-49=0 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,0,2: 11:[49, 47] Operation: 49-2=47 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,0,3: 11:[49, 47] Operation: 49-2=47 Moving to Node #0,3 Current State: 11:[49, 77, 14], Operations: ['28/2=14'] Exploring Operation: 77-14=63, Resulting Numbers: [49, 63] Generated Node #0,3,0: 11:[49, 63] Operation: 77-14=63 Exploring Operation: 49+77=126, Resulting Numbers: [14, 126] Generated Node #0,3,1: 11:[14, 126] Operation: 49+77=126 Exploring Operation: 77-49=28, Resulting Numbers: [14, 28] Generated Node #0,3,2: 11:[14, 28] Operation: 77-49=28 Exploring Operation: 49-14=35, Resulting Numbers: [77, 35] Generated Node #0,3,3: 11:[77, 35] Operation: 49-14=35 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[14, 28], Operations: ['28/2=14', '77-49=28'] Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,11 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[49, 63], Operations: ['28/2=14', '77-14=63'] Exploring Operation: 49*63=3087, Resulting Numbers: [3087] 3087,11 unequal: No Solution Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[77, 35], Operations: ['28/2=14', '49-14=35'] Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,11 unequal: No Solution Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[14, 126], Operations: ['28/2=14', '49+77=126'] Exploring Operation: 14*126=1764, Resulting Numbers: [1764] 1764,11 unequal: No Solution Exploring Operation: 126-14=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 14+126=140, Resulting Numbers: [140] 140,11 unequal: No Solution Exploring Operation: 126/14=9, Resulting Numbers: [9] 9,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 11:[2, 1], Operations: ['77-28=49', '49/49=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[2, 0], Operations: ['77-28=49', '49-49=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[49, 47], Operations: ['77-28=49', '49-2=47'] Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,11 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[49, 47], Operations: ['77-28=49', '49-2=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,11 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,11 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 27, 1, 68, 24 ]
64
[ "27+1=28", "68+24=92", "92-28=64" ]
Current State: 64:[27, 1, 68, 24], Operations: [] Exploring Operation: 27+1=28, Resulting Numbers: [68, 24, 28] Generated Node #2: [68, 24, 28] from Operation: 27+1=28 Current State: 64:[68, 24, 28], Operations: ['27+1=28'] Exploring Operation: 68+24=92, Resulting Numbers: [28, 92] Generated Node #3: [28, 92] from Operation: 68+24=92 Current State: 64:[28, 92], Operations: ['27+1=28', '68+24=92'] Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[27, 1, 68, 24], Operations: [] Exploring Operation: 27+1=28, Resulting Numbers: [68, 24, 28] Generated Node #0,0: 64:[68, 24, 28] Operation: 27+1=28 Exploring Operation: 68-1=67, Resulting Numbers: [27, 24, 67] Generated Node #0,1: 64:[27, 24, 67] Operation: 68-1=67 Exploring Operation: 27-24=3, Resulting Numbers: [1, 68, 3] Generated Node #0,2: 64:[1, 68, 3] Operation: 27-24=3 Moving to Node #0,2 Current State: 64:[1, 68, 3], Operations: ['27-24=3'] Exploring Operation: 68-3=65, Resulting Numbers: [1, 65] Generated Node #0,2,0: 64:[1, 65] Operation: 68-3=65 Exploring Operation: 68-1=67, Resulting Numbers: [3, 67] Generated Node #0,2,1: 64:[3, 67] Operation: 68-1=67 Exploring Operation: 1+3=4, Resulting Numbers: [68, 4] Generated Node #0,2,2: 64:[68, 4] Operation: 1+3=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[1, 65], Operations: ['27-24=3', '68-3=65'] Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[27, 1, 68, 24], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [1, 68, 3] Generated Node #0,2: 64:[1, 68, 3] Operation: 27-24=3 Moving to Node #0,2 Current State: 64:[1, 68, 3], Operations: ['27-24=3'] Exploring Operation: 68-3=65, Resulting Numbers: [1, 65] Generated Node #0,2,0: 64:[1, 65] Operation: 68-3=65 Moving to Node #0,2,0 Current State: 64:[1, 65], Operations: ['27-24=3', '68-3=65'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 36, 45, 21, 84 ]
56
[ "36+84=120", "21*120=2520", "2520/45=56" ]
Current State: 56:[36, 45, 21, 84], Operations: [] Exploring Operation: 36+84=120, Resulting Numbers: [45, 21, 120] Generated Node #2: [45, 21, 120] from Operation: 36+84=120 Current State: 56:[45, 21, 120], Operations: ['36+84=120'] Exploring Operation: 21*120=2520, Resulting Numbers: [45, 2520] Generated Node #3: [45, 2520] from Operation: 21*120=2520 Current State: 56:[45, 2520], Operations: ['36+84=120', '21*120=2520'] Exploring Operation: 2520/45=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[36, 45, 21, 84], Operations: [] Exploring Operation: 84/21=4, Resulting Numbers: [36, 45, 4] Generated Node #0,0: 56:[36, 45, 4] Operation: 84/21=4 Moving to Node #0,0 Current State: 56:[36, 45, 4], Operations: ['84/21=4'] Exploring Operation: 45-36=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 56:[4, 9] Operation: 45-36=9 Moving to Node #0,0,0 Current State: 56:[4, 9], Operations: ['84/21=4', '45-36=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,56 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 8, 6, 14, 4 ]
54
[ "8-6=2", "14*4=56", "56-2=54" ]
Current State: 54:[8, 6, 14, 4], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [14, 4, 2] Generated Node #2: [14, 4, 2] from Operation: 8-6=2 Current State: 54:[14, 4, 2], Operations: ['8-6=2'] Exploring Operation: 14*4=56, Resulting Numbers: [2, 56] Generated Node #3: [2, 56] from Operation: 14*4=56 Current State: 54:[2, 56], Operations: ['8-6=2', '14*4=56'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[8, 6, 14, 4], Operations: [] Exploring Operation: 14+4=18, Resulting Numbers: [8, 6, 18] Generated Node #0,0: 54:[8, 6, 18] Operation: 14+4=18 Exploring Operation: 14-6=8, Resulting Numbers: [8, 4, 8] Generated Node #0,1: 54:[8, 4, 8] Operation: 14-6=8 Exploring Operation: 14-4=10, Resulting Numbers: [8, 6, 10] Generated Node #0,2: 54:[8, 6, 10] Operation: 14-4=10 Exploring Operation: 14*4=56, Resulting Numbers: [8, 6, 56] Generated Node #0,3: 54:[8, 6, 56] Operation: 14*4=56 Exploring Operation: 14-8=6, Resulting Numbers: [6, 4, 6] Generated Node #0,4: 54:[6, 4, 6] Operation: 14-8=6 Moving to Node #0,0 Current State: 54:[8, 6, 18], Operations: ['14+4=18'] Exploring Operation: 8-6=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 54:[18, 2] Operation: 8-6=2 Exploring Operation: 8+18=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 54:[6, 26] Operation: 8+18=26 Exploring Operation: 8+6=14, Resulting Numbers: [18, 14] Generated Node #0,0,2: 54:[18, 14] Operation: 8+6=14 Exploring Operation: 18-8=10, Resulting Numbers: [6, 10] Generated Node #0,0,3: 54:[6, 10] Operation: 18-8=10 Exploring Operation: 18/6=3, Resulting Numbers: [8, 3] Generated Node #0,0,4: 54:[8, 3] Operation: 18/6=3 Moving to Node #0,4 Current State: 54:[6, 4, 6], Operations: ['14-8=6'] Exploring Operation: 6-4=2, Resulting Numbers: [6, 2] Generated Node #0,4,0: 54:[6, 2] Operation: 6-4=2 Exploring Operation: 6/6=1, Resulting Numbers: [4, 1] Generated Node #0,4,1: 54:[4, 1] Operation: 6/6=1 Exploring Operation: 4+6=10, Resulting Numbers: [6, 10] Generated Node #0,4,2: 54:[6, 10] Operation: 4+6=10 Exploring Operation: 6+4=10, Resulting Numbers: [6, 10] Generated Node #0,4,3: 54:[6, 10] Operation: 6+4=10 Exploring Operation: 6-4=2, Resulting Numbers: [6, 2] Generated Node #0,4,4: 54:[6, 2] Operation: 6-4=2 Moving to Node #0,2 Current State: 54:[8, 6, 10], Operations: ['14-4=10'] Exploring Operation: 6+10=16, Resulting Numbers: [8, 16] Generated Node #0,2,0: 54:[8, 16] Operation: 6+10=16 Exploring Operation: 10-8=2, Resulting Numbers: [6, 2] Generated Node #0,2,1: 54:[6, 2] Operation: 10-8=2 Exploring Operation: 10-6=4, Resulting Numbers: [8, 4] Generated Node #0,2,2: 54:[8, 4] Operation: 10-6=4 Exploring Operation: 8+10=18, Resulting Numbers: [6, 18] Generated Node #0,2,3: 54:[6, 18] Operation: 8+10=18 Exploring Operation: 8-6=2, Resulting Numbers: [10, 2] Generated Node #0,2,4: 54:[10, 2] Operation: 8-6=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[6, 2], Operations: ['14-4=10', '10-8=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 54:[6, 18], Operations: ['14-4=10', '8+10=18'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,54 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,54 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 54:[10, 2], Operations: ['14-4=10', '8-6=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[8, 4], Operations: ['14-4=10', '10-6=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[8, 16], Operations: ['14-4=10', '6+10=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,54 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,54 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 54:[8, 4, 8], Operations: ['14-6=8'] Exploring Operation: 8/8=1, Resulting Numbers: [4, 1] Generated Node #0,1,0: 54:[4, 1] Operation: 8/8=1 Exploring Operation: 8-4=4, Resulting Numbers: [8, 4] Generated Node #0,1,1: 54:[8, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [8, 2] Generated Node #0,1,2: 54:[8, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [8, 4] Generated Node #0,1,3: 54:[8, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [8, 2] Generated Node #0,1,4: 54:[8, 2] Operation: 8/4=2 Moving to Node #0,3 Current State: 54:[8, 6, 56], Operations: ['14*4=56'] Exploring Operation: 56/8=7, Resulting Numbers: [6, 7] Generated Node #0,3,0: 54:[6, 7] Operation: 56/8=7 Exploring Operation: 8-6=2, Resulting Numbers: [56, 2] Generated Node #0,3,1: 54:[56, 2] Operation: 8-6=2 Exploring Operation: 8+6=14, Resulting Numbers: [56, 14] Generated Node #0,3,2: 54:[56, 14] Operation: 8+6=14 Exploring Operation: 56-8=48, Resulting Numbers: [6, 48] Generated Node #0,3,3: 54:[6, 48] Operation: 56-8=48 Exploring Operation: 56-6=50, Resulting Numbers: [8, 50] Generated Node #0,3,4: 54:[8, 50] Operation: 56-6=50 Moving to Node #0,0,0 Current State: 54:[18, 2], Operations: ['14+4=18', '8-6=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,54 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,54 unequal: No Solution Moving to Node #0,4,0 Current State: 54:[6, 2], Operations: ['14-8=6', '6-4=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Moving to Node #0,4,4 Current State: 54:[6, 2], Operations: ['14-8=6', '6-4=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[6, 10], Operations: ['14+4=18', '18-8=10'] Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[8, 2], Operations: ['14-6=8', '8/4=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[6, 26], Operations: ['14+4=18', '8+18=26'] Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,54 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[8, 2], Operations: ['14-6=8', '8/4=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[6, 7], Operations: ['14*4=56', '56/8=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,54 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,54 unequal: No Solution Moving to Node #0,0,4 Current State: 54:[8, 3], Operations: ['14+4=18', '18/6=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,54 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,54 unequal: No Solution Moving to Node #0,4,3 Current State: 54:[6, 10], Operations: ['14-8=6', '6+4=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,54 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[6, 10], Operations: ['14-8=6', '4+6=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,54 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[8, 4], Operations: ['14-6=8', '8-4=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[8, 4], Operations: ['14-6=8', '8-4=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[4, 1], Operations: ['14-6=8', '8/8=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,4,1 Current State: 54:[4, 1], Operations: ['14-8=6', '6/6=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[56, 2], Operations: ['14*4=56', '8-6=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,54 unequal: No Solution Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,54 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[8, 6, 14, 4], Operations: [] Exploring Operation: 14*4=56, Resulting Numbers: [8, 6, 56] Generated Node #0,3: 54:[8, 6, 56] Operation: 14*4=56 Moving to Node #0,3 Current State: 54:[8, 6, 56], Operations: ['14*4=56'] Exploring Operation: 8-6=2, Resulting Numbers: [56, 2] Generated Node #0,3,1: 54:[56, 2] Operation: 8-6=2 Moving to Node #0,3,1 Current State: 54:[56, 2], Operations: ['14*4=56', '8-6=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.902778
hs_5
mult_heuristic
[ 83, 45, 42, 56 ]
96
[ "83+45=128", "42*128=5376", "5376/56=96" ]
Current State: 96:[83, 45, 42, 56], Operations: [] Exploring Operation: 83+45=128, Resulting Numbers: [42, 56, 128] Generated Node #2: [42, 56, 128] from Operation: 83+45=128 Current State: 96:[42, 56, 128], Operations: ['83+45=128'] Exploring Operation: 42*128=5376, Resulting Numbers: [56, 5376] Generated Node #3: [56, 5376] from Operation: 42*128=5376 Current State: 96:[56, 5376], Operations: ['83+45=128', '42*128=5376'] Exploring Operation: 5376/56=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[83, 45, 42, 56], Operations: [] Exploring Operation: 83-42=41, Resulting Numbers: [45, 56, 41] Generated Node #0,0: 96:[45, 56, 41] Operation: 83-42=41 Exploring Operation: 42+56=98, Resulting Numbers: [83, 45, 98] Generated Node #0,1: 96:[83, 45, 98] Operation: 42+56=98 Exploring Operation: 83-56=27, Resulting Numbers: [45, 42, 27] Generated Node #0,2: 96:[45, 42, 27] Operation: 83-56=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[45, 42, 27], Operations: ['83-56=27'] Exploring Operation: 45-27=18, Resulting Numbers: [42, 18] Generated Node #0,2,0: 96:[42, 18] Operation: 45-27=18 Exploring Operation: 45-42=3, Resulting Numbers: [27, 3] Generated Node #0,2,1: 96:[27, 3] Operation: 45-42=3 Exploring Operation: 42-27=15, Resulting Numbers: [45, 15] Generated Node #0,2,2: 96:[45, 15] Operation: 42-27=15 Moving to Node #0,2,1 Current State: 96:[27, 3], Operations: ['83-56=27', '45-42=3'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[45, 15], Operations: ['83-56=27', '42-27=15'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[42, 18], Operations: ['83-56=27', '45-27=18'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[45, 56, 41], Operations: ['83-42=41'] Exploring Operation: 56-45=11, Resulting Numbers: [41, 11] Generated Node #0,0,0: 96:[41, 11] Operation: 56-45=11 Exploring Operation: 56-41=15, Resulting Numbers: [45, 15] Generated Node #0,0,1: 96:[45, 15] Operation: 56-41=15 Exploring Operation: 56+41=97, Resulting Numbers: [45, 97] Generated Node #0,0,2: 96:[45, 97] Operation: 56+41=97 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[45, 15], Operations: ['83-42=41', '56-41=15'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[45, 97], Operations: ['83-42=41', '56+41=97'] Exploring Operation: 45*97=4365, Resulting Numbers: [4365] 4365,96 unequal: No Solution Exploring Operation: 97-45=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 45+97=142, Resulting Numbers: [142] 142,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[41, 11], Operations: ['83-42=41', '56-45=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,96 unequal: No Solution Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[83, 45, 98], Operations: ['42+56=98'] Exploring Operation: 98-45=53, Resulting Numbers: [83, 53] Generated Node #0,1,0: 96:[83, 53] Operation: 98-45=53 Exploring Operation: 83-45=38, Resulting Numbers: [98, 38] Generated Node #0,1,1: 96:[98, 38] Operation: 83-45=38 Exploring Operation: 98-83=15, Resulting Numbers: [45, 15] Generated Node #0,1,2: 96:[45, 15] Operation: 98-83=15 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[45, 15], Operations: ['42+56=98', '98-83=15'] Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[98, 38], Operations: ['42+56=98', '83-45=38'] Exploring Operation: 98-38=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 98*38=3724, Resulting Numbers: [3724] 3724,96 unequal: No Solution Exploring Operation: 98+38=136, Resulting Numbers: [136] 136,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[83, 53], Operations: ['42+56=98', '98-45=53'] Exploring Operation: 83+53=136, Resulting Numbers: [136] 136,96 unequal: No Solution Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 83*53=4399, Resulting Numbers: [4399] 4399,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 17, 4, 10, 10 ]
66
[ "17-10=7", "10*7=70", "70-4=66" ]
Current State: 66:[17, 4, 10, 10], Operations: [] Exploring Operation: 17-10=7, Resulting Numbers: [4, 7] Generated Node #2: [4, 7] from Operation: 17-10=7 Current State: 66:[4, 7], Operations: ['17-10=7'] Exploring Operation: 10*7=70, Resulting Numbers: [4, 70] Generated Node #3: [4, 70] from Operation: 10*7=70 Current State: 66:[4, 70], Operations: ['17-10=7', '10*7=70'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[17, 4, 10, 10], Operations: [] Exploring Operation: 17+4=21, Resulting Numbers: [10, 10, 21] Generated Node #0,0: 66:[10, 10, 21] Operation: 17+4=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[10, 10, 21], Operations: ['17+4=21'] Exploring Operation: 21-10=11, Resulting Numbers: [10, 11] Generated Node #0,0,0: 66:[10, 11] Operation: 21-10=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[10, 11], Operations: ['17+4=21', '21-10=11'] Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 7, 38, 59, 9 ]
71
[ "7*59=413", "38*9=342", "413-342=71" ]
Current State: 71:[7, 38, 59, 9], Operations: [] Exploring Operation: 7*59=413, Resulting Numbers: [38, 9, 413] Generated Node #2: [38, 9, 413] from Operation: 7*59=413 Current State: 71:[38, 9, 413], Operations: ['7*59=413'] Exploring Operation: 38*9=342, Resulting Numbers: [413, 342] Generated Node #3: [413, 342] from Operation: 38*9=342 Current State: 71:[413, 342], Operations: ['7*59=413', '38*9=342'] Exploring Operation: 413-342=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[7, 38, 59, 9], Operations: [] Exploring Operation: 7*9=63, Resulting Numbers: [38, 59, 63] Generated Node #0,0: 71:[38, 59, 63] Operation: 7*9=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[38, 59, 63], Operations: ['7*9=63'] Exploring Operation: 38+59=97, Resulting Numbers: [63, 97] Generated Node #0,0,0: 71:[63, 97] Operation: 38+59=97 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[63, 97], Operations: ['7*9=63', '38+59=97'] Exploring Operation: 97-63=34, Resulting Numbers: [34] 34,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 75, 88, 49, 20 ]
94
[ "75+88=163", "49+20=69", "163-69=94" ]
Current State: 94:[75, 88, 49, 20], Operations: [] Exploring Operation: 75+88=163, Resulting Numbers: [49, 20, 163] Generated Node #2: [49, 20, 163] from Operation: 75+88=163 Current State: 94:[49, 20, 163], Operations: ['75+88=163'] Exploring Operation: 49+20=69, Resulting Numbers: [163, 69] Generated Node #3: [163, 69] from Operation: 49+20=69 Current State: 94:[163, 69], Operations: ['75+88=163', '49+20=69'] Exploring Operation: 163-69=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[75, 88, 49, 20], Operations: [] Exploring Operation: 75-20=55, Resulting Numbers: [88, 49, 55] Generated Node #0,0: 94:[88, 49, 55] Operation: 75-20=55 Exploring Operation: 75+20=95, Resulting Numbers: [88, 49, 95] Generated Node #0,1: 94:[88, 49, 95] Operation: 75+20=95 Moving to Node #0,1 Current State: 94:[88, 49, 95], Operations: ['75+20=95'] Exploring Operation: 95-49=46, Resulting Numbers: [88, 46] Generated Node #0,1,0: 94:[88, 46] Operation: 95-49=46 Exploring Operation: 95-88=7, Resulting Numbers: [49, 7] Generated Node #0,1,1: 94:[49, 7] Operation: 95-88=7 Moving to Node #0,0 Current State: 94:[88, 49, 55], Operations: ['75-20=55'] Exploring Operation: 88-49=39, Resulting Numbers: [55, 39] Generated Node #0,0,0: 94:[55, 39] Operation: 88-49=39 Exploring Operation: 55-49=6, Resulting Numbers: [88, 6] Generated Node #0,0,1: 94:[88, 6] Operation: 55-49=6 Moving to Node #0,1,0 Current State: 94:[88, 46], Operations: ['75+20=95', '95-49=46'] Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 88+46=134, Resulting Numbers: [134] 134,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[49, 7], Operations: ['75+20=95', '95-88=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[88, 6], Operations: ['75-20=55', '55-49=6'] Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,94 unequal: No Solution Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[75, 88, 49, 20], Operations: [] Exploring Operation: 75-20=55, Resulting Numbers: [88, 49, 55] Generated Node #0,0: 94:[88, 49, 55] Operation: 75-20=55 Moving to Node #0,0 Current State: 94:[88, 49, 55], Operations: ['75-20=55'] Exploring Operation: 55-49=6, Resulting Numbers: [88, 6] Generated Node #0,0,1: 94:[88, 6] Operation: 55-49=6 Moving to Node #0,0,1 Current State: 94:[88, 6], Operations: ['75-20=55', '55-49=6'] Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 21, 32, 77, 14 ]
21
[ "32-21=11", "77/11=7", "14+7=21" ]
Current State: 21:[21, 32, 77, 14], Operations: [] Exploring Operation: 32-21=11, Resulting Numbers: [77, 14, 11] Generated Node #2: [77, 14, 11] from Operation: 32-21=11 Current State: 21:[77, 14, 11], Operations: ['32-21=11'] Exploring Operation: 77/11=7, Resulting Numbers: [14, 7] Generated Node #3: [14, 7] from Operation: 77/11=7 Current State: 21:[14, 7], Operations: ['32-21=11', '77/11=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[21, 32, 77, 14], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [21, 14, 45] Generated Node #0,0: 21:[21, 14, 45] Operation: 77-32=45 Exploring Operation: 77-21=56, Resulting Numbers: [32, 14, 56] Generated Node #0,1: 21:[32, 14, 56] Operation: 77-21=56 Moving to Node #0,0 Current State: 21:[21, 14, 45], Operations: ['77-32=45'] Exploring Operation: 45-21=24, Resulting Numbers: [14, 24] Generated Node #0,0,0: 21:[14, 24] Operation: 45-21=24 Exploring Operation: 45-14=31, Resulting Numbers: [21, 31] Generated Node #0,0,1: 21:[21, 31] Operation: 45-14=31 Moving to Node #0,1 Current State: 21:[32, 14, 56], Operations: ['77-21=56'] Exploring Operation: 56-32=24, Resulting Numbers: [14, 24] Generated Node #0,1,0: 21:[14, 24] Operation: 56-32=24 Exploring Operation: 56/14=4, Resulting Numbers: [32, 4] Generated Node #0,1,1: 21:[32, 4] Operation: 56/14=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[14, 24], Operations: ['77-21=56', '56-32=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[32, 4], Operations: ['77-21=56', '56/14=4'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,21 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: 21:[14, 24], Operations: ['77-32=45', '45-21=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[21, 31], Operations: ['77-32=45', '45-14=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,21 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 45, 93, 39, 41 ]
50
[ "93-45=48", "41-39=2", "48+2=50" ]
Current State: 50:[45, 93, 39, 41], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [39, 41, 48] Generated Node #2: [39, 41, 48] from Operation: 93-45=48 Current State: 50:[39, 41, 48], Operations: ['93-45=48'] Exploring Operation: 41-39=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 41-39=2 Current State: 50:[48, 2], Operations: ['93-45=48', '41-39=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[45, 93, 39, 41], Operations: [] Exploring Operation: 93-39=54, Resulting Numbers: [45, 41, 54] Generated Node #0,0: 50:[45, 41, 54] Operation: 93-39=54 Exploring Operation: 93-45=48, Resulting Numbers: [39, 41, 48] Generated Node #0,1: 50:[39, 41, 48] Operation: 93-45=48 Exploring Operation: 41-39=2, Resulting Numbers: [45, 93, 2] Generated Node #0,2: 50:[45, 93, 2] Operation: 41-39=2 Exploring Operation: 93-41=52, Resulting Numbers: [45, 39, 52] Generated Node #0,3: 50:[45, 39, 52] Operation: 93-41=52 Moving to Node #0,0 Current State: 50:[45, 41, 54], Operations: ['93-39=54'] Exploring Operation: 45-41=4, Resulting Numbers: [54, 4] Generated Node #0,0,0: 50:[54, 4] Operation: 45-41=4 Exploring Operation: 54-41=13, Resulting Numbers: [45, 13] Generated Node #0,0,1: 50:[45, 13] Operation: 54-41=13 Exploring Operation: 45+41=86, Resulting Numbers: [54, 86] Generated Node #0,0,2: 50:[54, 86] Operation: 45+41=86 Exploring Operation: 54-45=9, Resulting Numbers: [41, 9] Generated Node #0,0,3: 50:[41, 9] Operation: 54-45=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[54, 4], Operations: ['93-39=54', '45-41=4'] Exploring Operation: 54+4=58, Resulting Numbers: [58] 58,50 unequal: No Solution Exploring Operation: 54*4=216, Resulting Numbers: [216] 216,50 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[45, 93, 39, 41], Operations: [] Exploring Operation: 93-39=54, Resulting Numbers: [45, 41, 54] Generated Node #0,0: 50:[45, 41, 54] Operation: 93-39=54 Moving to Node #0,0 Current State: 50:[45, 41, 54], Operations: ['93-39=54'] Exploring Operation: 45-41=4, Resulting Numbers: [54, 4] Generated Node #0,0,0: 50:[54, 4] Operation: 45-41=4 Moving to Node #0,0,0 Current State: 50:[54, 4], Operations: ['93-39=54', '45-41=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 56, 44, 61, 16 ]
12
[ "61-56=5", "44+16=60", "60/5=12" ]
Current State: 12:[56, 44, 61, 16], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [44, 16, 5] Generated Node #2: [44, 16, 5] from Operation: 61-56=5 Current State: 12:[44, 16, 5], Operations: ['61-56=5'] Exploring Operation: 44+16=60, Resulting Numbers: [5, 60] Generated Node #3: [5, 60] from Operation: 44+16=60 Current State: 12:[5, 60], Operations: ['61-56=5', '44+16=60'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[56, 44, 61, 16], Operations: [] Exploring Operation: 56-44=12, Resulting Numbers: [61, 16, 12] Generated Node #0,0: 12:[61, 16, 12] Operation: 56-44=12 Exploring Operation: 61-56=5, Resulting Numbers: [44, 16, 5] Generated Node #0,1: 12:[44, 16, 5] Operation: 61-56=5 Exploring Operation: 56-16=40, Resulting Numbers: [44, 61, 40] Generated Node #0,2: 12:[44, 61, 40] Operation: 56-16=40 Exploring Operation: 61-44=17, Resulting Numbers: [56, 16, 17] Generated Node #0,3: 12:[56, 16, 17] Operation: 61-44=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[44, 16, 5], Operations: ['61-56=5'] Exploring Operation: 44+5=49, Resulting Numbers: [16, 49] Generated Node #0,1,0: 12:[16, 49] Operation: 44+5=49 Exploring Operation: 44-16=28, Resulting Numbers: [5, 28] Generated Node #0,1,1: 12:[5, 28] Operation: 44-16=28 Exploring Operation: 16-5=11, Resulting Numbers: [44, 11] Generated Node #0,1,2: 12:[44, 11] Operation: 16-5=11 Exploring Operation: 44-5=39, Resulting Numbers: [16, 39] Generated Node #0,1,3: 12:[16, 39] Operation: 44-5=39 Moving to Node #0,1,1 Current State: 12:[5, 28], Operations: ['61-56=5', '44-16=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,12 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[16, 39], Operations: ['61-56=5', '44-5=39'] Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,12 unequal: No Solution Exploring Operation: 16*39=624, Resulting Numbers: [624] 624,12 unequal: No Solution Exploring Operation: 16+39=55, Resulting Numbers: [55] 55,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[44, 11], Operations: ['61-56=5', '16-5=11'] Exploring Operation: 44*11=484, Resulting Numbers: [484] 484,12 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[16, 49], Operations: ['61-56=5', '44+5=49'] Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,12 unequal: No Solution Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[61, 16, 12], Operations: ['56-44=12'] Exploring Operation: 61-12=49, Resulting Numbers: [16, 49] Generated Node #0,0,0: 12:[16, 49] Operation: 61-12=49 Exploring Operation: 61+16=77, Resulting Numbers: [12, 77] Generated Node #0,0,1: 12:[12, 77] Operation: 61+16=77 Exploring Operation: 16-12=4, Resulting Numbers: [61, 4] Generated Node #0,0,2: 12:[61, 4] Operation: 16-12=4 Exploring Operation: 61-16=45, Resulting Numbers: [12, 45] Generated Node #0,0,3: 12:[12, 45] Operation: 61-16=45 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 12:[12, 45], Operations: ['56-44=12', '61-16=45'] Exploring Operation: 12*45=540, Resulting Numbers: [540] 540,12 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[16, 49], Operations: ['56-44=12', '61-12=49'] Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,12 unequal: No Solution Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[61, 4], Operations: ['56-44=12', '16-12=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 61*4=244, Resulting Numbers: [244] 244,12 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[12, 77], Operations: ['56-44=12', '61+16=77'] Exploring Operation: 12+77=89, Resulting Numbers: [89] 89,12 unequal: No Solution Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 12*77=924, Resulting Numbers: [924] 924,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[56, 16, 17], Operations: ['61-44=17'] Exploring Operation: 56+16=72, Resulting Numbers: [17, 72] Generated Node #0,3,0: 12:[17, 72] Operation: 56+16=72 Exploring Operation: 17-16=1, Resulting Numbers: [56, 1] Generated Node #0,3,1: 12:[56, 1] Operation: 17-16=1 Exploring Operation: 56-16=40, Resulting Numbers: [17, 40] Generated Node #0,3,2: 12:[17, 40] Operation: 56-16=40 Exploring Operation: 56-17=39, Resulting Numbers: [16, 39] Generated Node #0,3,3: 12:[16, 39] Operation: 56-17=39 Moving to Node #0,3,3 Current State: 12:[16, 39], Operations: ['61-44=17', '56-17=39'] Exploring Operation: 16+39=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,12 unequal: No Solution Exploring Operation: 16*39=624, Resulting Numbers: [624] 624,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[17, 40], Operations: ['61-44=17', '56-16=40'] Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,12 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[56, 1], Operations: ['61-44=17', '17-16=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,12 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[17, 72], Operations: ['61-44=17', '56+16=72'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 17+72=89, Resulting Numbers: [89] 89,12 unequal: No Solution Exploring Operation: 17*72=1224, Resulting Numbers: [1224] 1224,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[44, 61, 40], Operations: ['56-16=40'] Exploring Operation: 44+61=105, Resulting Numbers: [40, 105] Generated Node #0,2,0: 12:[40, 105] Operation: 44+61=105 Exploring Operation: 61-44=17, Resulting Numbers: [40, 17] Generated Node #0,2,1: 12:[40, 17] Operation: 61-44=17 Exploring Operation: 61-40=21, Resulting Numbers: [44, 21] Generated Node #0,2,2: 12:[44, 21] Operation: 61-40=21 Exploring Operation: 44-40=4, Resulting Numbers: [61, 4] Generated Node #0,2,3: 12:[61, 4] Operation: 44-40=4 Moving to Node #0,2,1 Current State: 12:[40, 17], Operations: ['56-16=40', '61-44=17'] Exploring Operation: 40*17=680, Resulting Numbers: [680] 680,12 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,12 unequal: No Solution Exploring Operation: 40+17=57, Resulting Numbers: [57] 57,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[44, 21], Operations: ['56-16=40', '61-40=21'] Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,12 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[61, 4], Operations: ['56-16=40', '44-40=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 61*4=244, Resulting Numbers: [244] 244,12 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[40, 105], Operations: ['56-16=40', '44+61=105'] Exploring Operation: 40+105=145, Resulting Numbers: [145] 145,12 unequal: No Solution Exploring Operation: 40*105=4200, Resulting Numbers: [4200] 4200,12 unequal: No Solution Exploring Operation: 105-40=65, Resulting Numbers: [65] 65,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 34, 58, 43, 17 ]
84
[ "58-34=24", "43+17=60", "24+60=84" ]
Current State: 84:[34, 58, 43, 17], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [43, 17, 24] Generated Node #2: [43, 17, 24] from Operation: 58-34=24 Current State: 84:[43, 17, 24], Operations: ['58-34=24'] Exploring Operation: 43+17=60, Resulting Numbers: [24, 60] Generated Node #3: [24, 60] from Operation: 43+17=60 Current State: 84:[24, 60], Operations: ['58-34=24', '43+17=60'] Exploring Operation: 24+60=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[34, 58, 43, 17], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [43, 17, 24] Generated Node #0,0: 84:[43, 17, 24] Operation: 58-34=24 Exploring Operation: 58-17=41, Resulting Numbers: [34, 43, 41] Generated Node #0,1: 84:[34, 43, 41] Operation: 58-17=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[43, 17, 24], Operations: ['58-34=24'] Exploring Operation: 24-17=7, Resulting Numbers: [43, 7] Generated Node #0,0,0: 84:[43, 7] Operation: 24-17=7 Exploring Operation: 17+24=41, Resulting Numbers: [43, 41] Generated Node #0,0,1: 84:[43, 41] Operation: 17+24=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[43, 7], Operations: ['58-34=24', '24-17=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[43, 41], Operations: ['58-34=24', '17+24=41'] Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[34, 58, 43, 17], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [43, 17, 24] Generated Node #0,0: 84:[43, 17, 24] Operation: 58-34=24 Moving to Node #0,0 Current State: 84:[43, 17, 24], Operations: ['58-34=24'] Exploring Operation: 17+24=41, Resulting Numbers: [43, 41] Generated Node #0,0,1: 84:[43, 41] Operation: 17+24=41 Moving to Node #0,0,1 Current State: 84:[43, 41], Operations: ['58-34=24', '17+24=41'] Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 97, 48, 54, 31 ]
11
[ "97-31=66", "54-48=6", "66/6=11" ]
Current State: 11:[97, 48, 54, 31], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [48, 54, 66] Generated Node #2: [48, 54, 66] from Operation: 97-31=66 Current State: 11:[48, 54, 66], Operations: ['97-31=66'] Exploring Operation: 54-48=6, Resulting Numbers: [66, 6] Generated Node #3: [66, 6] from Operation: 54-48=6 Current State: 11:[66, 6], Operations: ['97-31=66', '54-48=6'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[97, 48, 54, 31], Operations: [] Exploring Operation: 97-54=43, Resulting Numbers: [48, 31, 43] Generated Node #0,0: 11:[48, 31, 43] Operation: 97-54=43 Exploring Operation: 97-48=49, Resulting Numbers: [54, 31, 49] Generated Node #0,1: 11:[54, 31, 49] Operation: 97-48=49 Exploring Operation: 97-31=66, Resulting Numbers: [48, 54, 66] Generated Node #0,2: 11:[48, 54, 66] Operation: 97-31=66 Exploring Operation: 48-31=17, Resulting Numbers: [97, 54, 17] Generated Node #0,3: 11:[97, 54, 17] Operation: 48-31=17 Exploring Operation: 54-48=6, Resulting Numbers: [97, 31, 6] Generated Node #0,4: 11:[97, 31, 6] Operation: 54-48=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[48, 31, 43], Operations: ['97-54=43'] Exploring Operation: 43-31=12, Resulting Numbers: [48, 12] Generated Node #0,0,0: 11:[48, 12] Operation: 43-31=12 Exploring Operation: 48+31=79, Resulting Numbers: [43, 79] Generated Node #0,0,1: 11:[43, 79] Operation: 48+31=79 Exploring Operation: 48-31=17, Resulting Numbers: [43, 17] Generated Node #0,0,2: 11:[43, 17] Operation: 48-31=17 Exploring Operation: 48-43=5, Resulting Numbers: [31, 5] Generated Node #0,0,3: 11:[31, 5] Operation: 48-43=5 Exploring Operation: 48+43=91, Resulting Numbers: [31, 91] Generated Node #0,0,4: 11:[31, 91] Operation: 48+43=91 Moving to Node #0,0,3 Current State: 11:[31, 5], Operations: ['97-54=43', '48-43=5'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,11 unequal: No Solution Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[43, 17], Operations: ['97-54=43', '48-31=17'] Exploring Operation: 43*17=731, Resulting Numbers: [731] 731,11 unequal: No Solution Exploring Operation: 43+17=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[48, 12], Operations: ['97-54=43', '43-31=12'] Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 48*12=576, Resulting Numbers: [576] 576,11 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[43, 79], Operations: ['97-54=43', '48+31=79'] Exploring Operation: 43*79=3397, Resulting Numbers: [3397] 3397,11 unequal: No Solution Exploring Operation: 43+79=122, Resulting Numbers: [122] 122,11 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[31, 91], Operations: ['97-54=43', '48+43=91'] Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,11 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[54, 31, 49], Operations: ['97-48=49'] Exploring Operation: 54+49=103, Resulting Numbers: [31, 103] Generated Node #0,1,0: 11:[31, 103] Operation: 54+49=103 Exploring Operation: 54+31=85, Resulting Numbers: [49, 85] Generated Node #0,1,1: 11:[49, 85] Operation: 54+31=85 Exploring Operation: 54-31=23, Resulting Numbers: [49, 23] Generated Node #0,1,2: 11:[49, 23] Operation: 54-31=23 Exploring Operation: 54-49=5, Resulting Numbers: [31, 5] Generated Node #0,1,3: 11:[31, 5] Operation: 54-49=5 Exploring Operation: 49-31=18, Resulting Numbers: [54, 18] Generated Node #0,1,4: 11:[54, 18] Operation: 49-31=18 Moving to Node #0,1,3 Current State: 11:[31, 5], Operations: ['97-48=49', '54-49=5'] Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,11 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[54, 18], Operations: ['97-48=49', '49-31=18'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 54*18=972, Resulting Numbers: [972] 972,11 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[49, 23], Operations: ['97-48=49', '54-31=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[31, 103], Operations: ['97-48=49', '54+49=103'] Exploring Operation: 31+103=134, Resulting Numbers: [134] 134,11 unequal: No Solution Exploring Operation: 103-31=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 31*103=3193, Resulting Numbers: [3193] 3193,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[49, 85], Operations: ['97-48=49', '54+31=85'] Exploring Operation: 85-49=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 49*85=4165, Resulting Numbers: [4165] 4165,11 unequal: No Solution Exploring Operation: 49+85=134, Resulting Numbers: [134] 134,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 11:[97, 31, 6], Operations: ['54-48=6'] Exploring Operation: 97+6=103, Resulting Numbers: [31, 103] Generated Node #0,4,0: 11:[31, 103] Operation: 97+6=103 Exploring Operation: 97-6=91, Resulting Numbers: [31, 91] Generated Node #0,4,1: 11:[31, 91] Operation: 97-6=91 Exploring Operation: 97-31=66, Resulting Numbers: [6, 66] Generated Node #0,4,2: 11:[6, 66] Operation: 97-31=66 Exploring Operation: 31+6=37, Resulting Numbers: [97, 37] Generated Node #0,4,3: 11:[97, 37] Operation: 31+6=37 Exploring Operation: 31-6=25, Resulting Numbers: [97, 25] Generated Node #0,4,4: 11:[97, 25] Operation: 31-6=25 Moving to Node #0,4,2 Current State: 11:[6, 66], Operations: ['54-48=6', '97-31=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[97, 48, 54, 31], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [97, 31, 6] Generated Node #0,4: 11:[97, 31, 6] Operation: 54-48=6 Moving to Node #0,4 Current State: 11:[97, 31, 6], Operations: ['54-48=6'] Exploring Operation: 97-31=66, Resulting Numbers: [6, 66] Generated Node #0,4,2: 11:[6, 66] Operation: 97-31=66 Moving to Node #0,4,2 Current State: 11:[6, 66], Operations: ['54-48=6', '97-31=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 44, 54, 56, 59 ]
37
[ "56-54=2", "44/2=22", "59-22=37" ]
Current State: 37:[44, 54, 56, 59], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [44, 59, 2] Generated Node #2: [44, 59, 2] from Operation: 56-54=2 Current State: 37:[44, 59, 2], Operations: ['56-54=2'] Exploring Operation: 44/2=22, Resulting Numbers: [59, 22] Generated Node #3: [59, 22] from Operation: 44/2=22 Current State: 37:[59, 22], Operations: ['56-54=2', '44/2=22'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[44, 54, 56, 59], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [44, 56, 5] Generated Node #0,0: 37:[44, 56, 5] Operation: 59-54=5 Exploring Operation: 59-56=3, Resulting Numbers: [44, 54, 3] Generated Node #0,1: 37:[44, 54, 3] Operation: 59-56=3 Exploring Operation: 59-44=15, Resulting Numbers: [54, 56, 15] Generated Node #0,2: 37:[54, 56, 15] Operation: 59-44=15 Exploring Operation: 56-54=2, Resulting Numbers: [44, 59, 2] Generated Node #0,3: 37:[44, 59, 2] Operation: 56-54=2 Exploring Operation: 56-44=12, Resulting Numbers: [54, 59, 12] Generated Node #0,4: 37:[54, 59, 12] Operation: 56-44=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[44, 56, 5], Operations: ['59-54=5'] Exploring Operation: 56-5=51, Resulting Numbers: [44, 51] Generated Node #0,0,0: 37:[44, 51] Operation: 56-5=51 Exploring Operation: 56+5=61, Resulting Numbers: [44, 61] Generated Node #0,0,1: 37:[44, 61] Operation: 56+5=61 Exploring Operation: 44-5=39, Resulting Numbers: [56, 39] Generated Node #0,0,2: 37:[56, 39] Operation: 44-5=39 Exploring Operation: 56-44=12, Resulting Numbers: [5, 12] Generated Node #0,0,3: 37:[5, 12] Operation: 56-44=12 Exploring Operation: 44+5=49, Resulting Numbers: [56, 49] Generated Node #0,0,4: 37:[56, 49] Operation: 44+5=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[44, 51], Operations: ['59-54=5', '56-5=51'] Exploring Operation: 44+51=95, Resulting Numbers: [95] 95,37 unequal: No Solution Exploring Operation: 44*51=2244, Resulting Numbers: [2244] 2244,37 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,37 unequal: No Solution No 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: 37:[56, 39], Operations: ['59-54=5', '44-5=39'] Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,37 unequal: No Solution Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,37 unequal: No Solution No 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: 37:[44, 61], Operations: ['59-54=5', '56+5=61'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 44*61=2684, Resulting Numbers: [2684] 2684,37 unequal: No Solution Exploring Operation: 44+61=105, Resulting Numbers: [105] 105,37 unequal: No Solution No 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: 37:[56, 49], Operations: ['59-54=5', '44+5=49'] Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,37 unequal: No Solution No 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: 37:[5, 12], Operations: ['59-54=5', '56-44=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,37 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,37 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[44, 54, 3], Operations: ['59-56=3'] Exploring Operation: 44-3=41, Resulting Numbers: [54, 41] Generated Node #0,1,0: 37:[54, 41] Operation: 44-3=41 Exploring Operation: 54-3=51, Resulting Numbers: [44, 51] Generated Node #0,1,1: 37:[44, 51] Operation: 54-3=51 Exploring Operation: 44+3=47, Resulting Numbers: [54, 47] Generated Node #0,1,2: 37:[54, 47] Operation: 44+3=47 Exploring Operation: 54/3=18, Resulting Numbers: [44, 18] Generated Node #0,1,3: 37:[44, 18] Operation: 54/3=18 Exploring Operation: 54+3=57, Resulting Numbers: [44, 57] Generated Node #0,1,4: 37:[44, 57] Operation: 54+3=57 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[54, 41], Operations: ['59-56=3', '44-3=41'] Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,37 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 54*41=2214, Resulting Numbers: [2214] 2214,37 unequal: No Solution No 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: 37:[44, 51], Operations: ['59-56=3', '54-3=51'] Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 44*51=2244, Resulting Numbers: [2244] 2244,37 unequal: No Solution Exploring Operation: 44+51=95, Resulting Numbers: [95] 95,37 unequal: No Solution No 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: 37:[44, 18], Operations: ['59-56=3', '54/3=18'] Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,37 unequal: No Solution Exploring Operation: 44+18=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 44*18=792, Resulting Numbers: [792] 792,37 unequal: No Solution No 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: 37:[54, 47], Operations: ['59-56=3', '44+3=47'] Exploring Operation: 54*47=2538, Resulting Numbers: [2538] 2538,37 unequal: No Solution Exploring Operation: 54+47=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,37 unequal: No Solution No 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: 37:[44, 57], Operations: ['59-56=3', '54+3=57'] Exploring Operation: 44+57=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 44*57=2508, Resulting Numbers: [2508] 2508,37 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[54, 56, 15], Operations: ['59-44=15'] Exploring Operation: 54-15=39, Resulting Numbers: [56, 39] Generated Node #0,2,0: 37:[56, 39] Operation: 54-15=39 Exploring Operation: 56-15=41, Resulting Numbers: [54, 41] Generated Node #0,2,1: 37:[54, 41] Operation: 56-15=41 Exploring Operation: 54+15=69, Resulting Numbers: [56, 69] Generated Node #0,2,2: 37:[56, 69] Operation: 54+15=69 Exploring Operation: 56+15=71, Resulting Numbers: [54, 71] Generated Node #0,2,3: 37:[54, 71] Operation: 56+15=71 Exploring Operation: 56-54=2, Resulting Numbers: [15, 2] Generated Node #0,2,4: 37:[15, 2] Operation: 56-54=2 Moving to Node #0,2,0 Current State: 37:[56, 39], Operations: ['59-44=15', '54-15=39'] Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,37 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[54, 41], Operations: ['59-44=15', '56-15=41'] Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 54*41=2214, Resulting Numbers: [2214] 2214,37 unequal: No Solution Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[56, 69], Operations: ['59-44=15', '54+15=69'] Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 56+69=125, Resulting Numbers: [125] 125,37 unequal: No Solution Exploring Operation: 56*69=3864, Resulting Numbers: [3864] 3864,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[54, 71], Operations: ['59-44=15', '56+15=71'] Exploring Operation: 54+71=125, Resulting Numbers: [125] 125,37 unequal: No Solution Exploring Operation: 54*71=3834, Resulting Numbers: [3834] 3834,37 unequal: No Solution Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,2,4 Current State: 37:[15, 2], Operations: ['59-44=15', '56-54=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[44, 59, 2], Operations: ['56-54=2'] Exploring Operation: 59+2=61, Resulting Numbers: [44, 61] Generated Node #0,3,0: 37:[44, 61] Operation: 59+2=61 Exploring Operation: 44-2=42, Resulting Numbers: [59, 42] Generated Node #0,3,1: 37:[59, 42] Operation: 44-2=42 Exploring Operation: 44/2=22, Resulting Numbers: [59, 22] Generated Node #0,3,2: 37:[59, 22] Operation: 44/2=22 Exploring Operation: 59-2=57, Resulting Numbers: [44, 57] Generated Node #0,3,3: 37:[44, 57] Operation: 59-2=57 Exploring Operation: 44+2=46, Resulting Numbers: [59, 46] Generated Node #0,3,4: 37:[59, 46] Operation: 44+2=46 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 37:[59, 42], Operations: ['56-54=2', '44-2=42'] Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,37 unequal: No Solution No 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: 37:[44, 57], Operations: ['56-54=2', '59-2=57'] Exploring Operation: 44*57=2508, Resulting Numbers: [2508] 2508,37 unequal: No Solution Exploring Operation: 44+57=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,37 unequal: No Solution No 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: 37:[44, 61], Operations: ['56-54=2', '59+2=61'] Exploring Operation: 44*61=2684, Resulting Numbers: [2684] 2684,37 unequal: No Solution Exploring Operation: 44+61=105, Resulting Numbers: [105] 105,37 unequal: No Solution Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,37 unequal: No Solution No 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: 37:[59, 46], Operations: ['56-54=2', '44+2=46'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,37 unequal: No Solution Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,37 unequal: No Solution No 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: 37:[59, 22], Operations: ['56-54=2', '44/2=22'] Exploring Operation: 59*22=1298, Resulting Numbers: [1298] 1298,37 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[44, 54, 56, 59], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [44, 59, 2] Generated Node #0,3: 37:[44, 59, 2] Operation: 56-54=2 Moving to Node #0,3 Current State: 37:[44, 59, 2], Operations: ['56-54=2'] Exploring Operation: 44/2=22, Resulting Numbers: [59, 22] Generated Node #0,3,2: 37:[59, 22] Operation: 44/2=22 Moving to Node #0,3,2 Current State: 37:[59, 22], Operations: ['56-54=2', '44/2=22'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.923611
hs_5
sum_heuristic
[ 94, 1, 92, 87 ]
84
[ "94+1=95", "92+87=179", "179-95=84" ]
Current State: 84:[94, 1, 92, 87], Operations: [] Exploring Operation: 94+1=95, Resulting Numbers: [92, 87, 95] Generated Node #2: [92, 87, 95] from Operation: 94+1=95 Current State: 84:[92, 87, 95], Operations: ['94+1=95'] Exploring Operation: 92+87=179, Resulting Numbers: [95, 179] Generated Node #3: [95, 179] from Operation: 92+87=179 Current State: 84:[95, 179], Operations: ['94+1=95', '92+87=179'] Exploring Operation: 179-95=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[94, 1, 92, 87], Operations: [] Exploring Operation: 94-1=93, Resulting Numbers: [92, 87, 93] Generated Node #0,0: 84:[92, 87, 93] Operation: 94-1=93 Exploring Operation: 94-87=7, Resulting Numbers: [1, 92, 7] Generated Node #0,1: 84:[1, 92, 7] Operation: 94-87=7 Exploring Operation: 92-87=5, Resulting Numbers: [94, 1, 5] Generated Node #0,2: 84:[94, 1, 5] Operation: 92-87=5 Exploring Operation: 94-92=2, Resulting Numbers: [1, 87, 2] Generated Node #0,3: 84:[1, 87, 2] Operation: 94-92=2 Exploring Operation: 92-1=91, Resulting Numbers: [94, 87, 91] Generated Node #0,4: 84:[94, 87, 91] Operation: 92-1=91 Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[1, 87, 2], Operations: ['94-92=2'] Exploring Operation: 87/1=87, Resulting Numbers: [2, 87] Generated Node #0,3,0: 84:[2, 87] Operation: 87/1=87 Exploring Operation: 87-2=85, Resulting Numbers: [1, 85] Generated Node #0,3,1: 84:[1, 85] Operation: 87-2=85 Exploring Operation: 1*87=87, Resulting Numbers: [2, 87] Generated Node #0,3,2: 84:[2, 87] Operation: 1*87=87 Exploring Operation: 1+2=3, Resulting Numbers: [87, 3] Generated Node #0,3,3: 84:[87, 3] Operation: 1+2=3 Exploring Operation: 87-1=86, Resulting Numbers: [2, 86] Generated Node #0,3,4: 84:[2, 86] Operation: 87-1=86 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 84:[1, 85], Operations: ['94-92=2', '87-2=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 1+85=86, Resulting Numbers: [86] 86,84 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[94, 1, 92, 87], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [1, 87, 2] Generated Node #0,3: 84:[1, 87, 2] Operation: 94-92=2 Moving to Node #0,3 Current State: 84:[1, 87, 2], Operations: ['94-92=2'] Exploring Operation: 87-2=85, Resulting Numbers: [1, 85] Generated Node #0,3,1: 84:[1, 85] Operation: 87-2=85 Moving to Node #0,3,1 Current State: 84:[1, 85], Operations: ['94-92=2', '87-2=85'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 9, 12, 39, 3 ]
78
[ "39-9=30", "3*30=90", "90-12=78" ]
Current State: 78:[9, 12, 39, 3], Operations: [] Exploring Operation: 39-9=30, Resulting Numbers: [12, 3, 30] Generated Node #2: [12, 3, 30] from Operation: 39-9=30 Current State: 78:[12, 3, 30], Operations: ['39-9=30'] Exploring Operation: 3*30=90, Resulting Numbers: [12, 90] Generated Node #3: [12, 90] from Operation: 3*30=90 Current State: 78:[12, 90], Operations: ['39-9=30', '3*30=90'] Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[9, 12, 39, 3], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [12, 39, 3] Generated Node #0,0: 78:[12, 39, 3] Operation: 9/3=3 Exploring Operation: 9*3=27, Resulting Numbers: [12, 39, 27] Generated Node #0,1: 78:[12, 39, 27] Operation: 9*3=27 Exploring Operation: 9+3=12, Resulting Numbers: [12, 39, 12] Generated Node #0,2: 78:[12, 39, 12] Operation: 9+3=12 Exploring Operation: 12-9=3, Resulting Numbers: [39, 3, 3] Generated Node #0,3: 78:[39, 3, 3] Operation: 12-9=3 Exploring Operation: 9-3=6, Resulting Numbers: [12, 39, 6] Generated Node #0,4: 78:[12, 39, 6] Operation: 9-3=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[39, 3, 3], Operations: ['12-9=3'] Exploring Operation: 39/3=13, Resulting Numbers: [3, 13] Generated Node #0,3,0: 78:[3, 13] Operation: 39/3=13 Exploring Operation: 3/3=1, Resulting Numbers: [39, 1] Generated Node #0,3,1: 78:[39, 1] Operation: 3/3=1 Exploring Operation: 39/3=13, Resulting Numbers: [3, 13] Generated Node #0,3,2: 78:[3, 13] Operation: 39/3=13 Exploring Operation: 3-3=0, Resulting Numbers: [39, 0] Generated Node #0,3,3: 78:[39, 0] Operation: 3-3=0 Exploring Operation: 3+3=6, Resulting Numbers: [39, 6] Generated Node #0,3,4: 78:[39, 6] Operation: 3+3=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 78:[3, 13], Operations: ['12-9=3', '39/3=13'] Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,78 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 #0,3,2 Current State: 78:[3, 13], Operations: ['12-9=3', '39/3=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,78 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 #0,3,4 Current State: 78:[39, 6], Operations: ['12-9=3', '3+3=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 39*6=234, Resulting Numbers: [234] 234,78 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 #0,3,1 Current State: 78:[39, 1], Operations: ['12-9=3', '3/3=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,78 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,78 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 #0,3,3 Current State: 78:[39, 0], Operations: ['12-9=3', '3-3=0'] Exploring Operation: 39*0=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 39+0=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 39-0=39, Resulting Numbers: [39] 39,78 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 #0,0 Current State: 78:[12, 39, 3], Operations: ['9/3=3'] Exploring Operation: 12/3=4, Resulting Numbers: [39, 4] Generated Node #0,0,0: 78:[39, 4] Operation: 12/3=4 Exploring Operation: 39-12=27, Resulting Numbers: [3, 27] Generated Node #0,0,1: 78:[3, 27] Operation: 39-12=27 Exploring Operation: 39/3=13, Resulting Numbers: [12, 13] Generated Node #0,0,2: 78:[12, 13] Operation: 39/3=13 Exploring Operation: 12+3=15, Resulting Numbers: [39, 15] Generated Node #0,0,3: 78:[39, 15] Operation: 12+3=15 Exploring Operation: 12*3=36, Resulting Numbers: [39, 36] Generated Node #0,0,4: 78:[39, 36] Operation: 12*3=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[39, 4], Operations: ['9/3=3', '12/3=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,78 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 #0,0,1 Current State: 78:[3, 27], Operations: ['9/3=3', '39-12=27'] Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,78 unequal: No Solution Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,78 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,78 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 #0,0,2 Current State: 78:[12, 13], Operations: ['9/3=3', '39/3=13'] Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,78 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,78 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 #0,0,3 Current State: 78:[39, 15], Operations: ['9/3=3', '12+3=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,78 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,78 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,78 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 #0,0,4 Current State: 78:[39, 36], Operations: ['9/3=3', '12*3=36'] Exploring Operation: 39+36=75, Resulting Numbers: [75] 75,78 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,78 unequal: No Solution Exploring Operation: 39*36=1404, Resulting Numbers: [1404] 1404,78 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 #0,4 Current State: 78:[12, 39, 6], Operations: ['9-3=6'] Exploring Operation: 12*6=72, Resulting Numbers: [39, 72] Generated Node #0,4,0: 78:[39, 72] Operation: 12*6=72 Exploring Operation: 12-6=6, Resulting Numbers: [39, 6] Generated Node #0,4,1: 78:[39, 6] Operation: 12-6=6 Exploring Operation: 39-12=27, Resulting Numbers: [6, 27] Generated Node #0,4,2: 78:[6, 27] Operation: 39-12=27 Exploring Operation: 12/6=2, Resulting Numbers: [39, 2] Generated Node #0,4,3: 78:[39, 2] Operation: 12/6=2 Exploring Operation: 12+6=18, Resulting Numbers: [39, 18] Generated Node #0,4,4: 78:[39, 18] Operation: 12+6=18 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 78:[39, 6], Operations: ['9-3=6', '12-6=6'] Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 39*6=234, Resulting Numbers: [234] 234,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 78:[39, 2], Operations: ['9-3=6', '12/6=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[9, 12, 39, 3], Operations: [] Exploring Operation: 9-3=6, Resulting Numbers: [12, 39, 6] Generated Node #0,4: 78:[12, 39, 6] Operation: 9-3=6 Moving to Node #0,4 Current State: 78:[12, 39, 6], Operations: ['9-3=6'] Exploring Operation: 12/6=2, Resulting Numbers: [39, 2] Generated Node #0,4,3: 78:[39, 2] Operation: 12/6=2 Moving to Node #0,4,3 Current State: 78:[39, 2], Operations: ['9-3=6', '12/6=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947049
hs_5
mult_heuristic
[ 14, 83, 87, 68 ]
88
[ "83-14=69", "87-68=19", "69+19=88" ]
Current State: 88:[14, 83, 87, 68], Operations: [] Exploring Operation: 83-14=69, Resulting Numbers: [87, 68, 69] Generated Node #2: [87, 68, 69] from Operation: 83-14=69 Current State: 88:[87, 68, 69], Operations: ['83-14=69'] Exploring Operation: 87-68=19, Resulting Numbers: [69, 19] Generated Node #3: [69, 19] from Operation: 87-68=19 Current State: 88:[69, 19], Operations: ['83-14=69', '87-68=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[14, 83, 87, 68], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [14, 87, 15] Generated Node #0,0: 88:[14, 87, 15] Operation: 83-68=15 Exploring Operation: 87-68=19, Resulting Numbers: [14, 83, 19] Generated Node #0,1: 88:[14, 83, 19] Operation: 87-68=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[14, 87, 15], Operations: ['83-68=15'] Exploring Operation: 15-14=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 88:[87, 1] Operation: 15-14=1 Exploring Operation: 14+15=29, Resulting Numbers: [87, 29] Generated Node #0,0,1: 88:[87, 29] Operation: 14+15=29 Moving to Node #0,0,0 Current State: 88:[87, 1], Operations: ['83-68=15', '15-14=1'] Exploring Operation: 87*1=87, Resulting Numbers: [87] 87,88 unequal: No Solution Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[14, 83, 87, 68], Operations: [] Exploring Operation: 83-68=15, Resulting Numbers: [14, 87, 15] Generated Node #0,0: 88:[14, 87, 15] Operation: 83-68=15 Moving to Node #0,0 Current State: 88:[14, 87, 15], Operations: ['83-68=15'] Exploring Operation: 15-14=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 88:[87, 1] Operation: 15-14=1 Moving to Node #0,0,0 Current State: 88:[87, 1], Operations: ['83-68=15', '15-14=1'] Exploring Operation: 87+1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 6, 92, 10, 32 ]
94
[ "6+10=16", "32/16=2", "92+2=94" ]
Current State: 94:[6, 92, 10, 32], Operations: [] Exploring Operation: 6+10=16, Resulting Numbers: [92, 32, 16] Generated Node #2: [92, 32, 16] from Operation: 6+10=16 Current State: 94:[92, 32, 16], Operations: ['6+10=16'] Exploring Operation: 32/16=2, Resulting Numbers: [92, 2] Generated Node #3: [92, 2] from Operation: 32/16=2 Current State: 94:[92, 2], Operations: ['6+10=16', '32/16=2'] Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[6, 92, 10, 32], Operations: [] Exploring Operation: 10-6=4, Resulting Numbers: [92, 32, 4] Generated Node #0,0: 94:[92, 32, 4] Operation: 10-6=4 Exploring Operation: 10+32=42, Resulting Numbers: [6, 92, 42] Generated Node #0,1: 94:[6, 92, 42] Operation: 10+32=42 Exploring Operation: 6+32=38, Resulting Numbers: [92, 10, 38] Generated Node #0,2: 94:[92, 10, 38] Operation: 6+32=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[6, 92, 42], Operations: ['10+32=42'] Exploring Operation: 6+42=48, Resulting Numbers: [92, 48] Generated Node #0,1,0: 94:[92, 48] Operation: 6+42=48 Exploring Operation: 92-42=50, Resulting Numbers: [6, 50] Generated Node #0,1,1: 94:[6, 50] Operation: 92-42=50 Exploring Operation: 42/6=7, Resulting Numbers: [92, 7] Generated Node #0,1,2: 94:[92, 7] Operation: 42/6=7 Moving to Node #0,1,0 Current State: 94:[92, 48], Operations: ['10+32=42', '6+42=48'] Exploring Operation: 92+48=140, Resulting Numbers: [140] 140,94 unequal: No Solution Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 92*48=4416, Resulting Numbers: [4416] 4416,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[6, 50], Operations: ['10+32=42', '92-42=50'] Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 6*50=300, Resulting Numbers: [300] 300,94 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[92, 7], Operations: ['10+32=42', '42/6=7'] Exploring Operation: 92+7=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 92*7=644, Resulting Numbers: [644] 644,94 unequal: No Solution Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[92, 32, 4], Operations: ['10-6=4'] Exploring Operation: 92-32=60, Resulting Numbers: [4, 60] Generated Node #0,0,0: 94:[4, 60] Operation: 92-32=60 Exploring Operation: 32+4=36, Resulting Numbers: [92, 36] Generated Node #0,0,1: 94:[92, 36] Operation: 32+4=36 Exploring Operation: 32/4=8, Resulting Numbers: [92, 8] Generated Node #0,0,2: 94:[92, 8] Operation: 32/4=8 Moving to Node #0,0,2 Current State: 94:[92, 8], Operations: ['10-6=4', '32/4=8'] Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 92*8=736, Resulting Numbers: [736] 736,94 unequal: No Solution Exploring Operation: 92+8=100, Resulting Numbers: [100] 100,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[92, 36], Operations: ['10-6=4', '32+4=36'] Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 92*36=3312, Resulting Numbers: [3312] 3312,94 unequal: No Solution Exploring Operation: 92+36=128, Resulting Numbers: [128] 128,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[4, 60], Operations: ['10-6=4', '92-32=60'] Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,94 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,94 unequal: No Solution Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[92, 10, 38], Operations: ['6+32=38'] Exploring Operation: 92-38=54, Resulting Numbers: [10, 54] Generated Node #0,2,0: 94:[10, 54] Operation: 92-38=54 Exploring Operation: 10+38=48, Resulting Numbers: [92, 48] Generated Node #0,2,1: 94:[92, 48] Operation: 10+38=48 Exploring Operation: 92+10=102, Resulting Numbers: [38, 102] Generated Node #0,2,2: 94:[38, 102] Operation: 92+10=102 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[92, 48], Operations: ['6+32=38', '10+38=48'] Exploring Operation: 92*48=4416, Resulting Numbers: [4416] 4416,94 unequal: No Solution Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 92+48=140, Resulting Numbers: [140] 140,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[10, 54], Operations: ['6+32=38', '92-38=54'] Exploring Operation: 10*54=540, Resulting Numbers: [540] 540,94 unequal: No Solution Exploring Operation: 54-10=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 10+54=64, Resulting Numbers: [64] 64,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[38, 102], Operations: ['6+32=38', '92+10=102'] Exploring Operation: 38+102=140, Resulting Numbers: [140] 140,94 unequal: No Solution Exploring Operation: 102-38=64, Resulting Numbers: [64] 64,94 unequal: No Solution Exploring Operation: 38*102=3876, Resulting Numbers: [3876] 3876,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 81, 16, 67, 96 ]
48
[ "81-16=65", "67-65=2", "96/2=48" ]
Current State: 48:[81, 16, 67, 96], Operations: [] Exploring Operation: 81-16=65, Resulting Numbers: [67, 96, 65] Generated Node #2: [67, 96, 65] from Operation: 81-16=65 Current State: 48:[67, 96, 65], Operations: ['81-16=65'] Exploring Operation: 67-65=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 67-65=2 Current State: 48:[96, 2], Operations: ['81-16=65', '67-65=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[81, 16, 67, 96], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [81, 16, 29] Generated Node #0,0: 48:[81, 16, 29] Operation: 96-67=29 Exploring Operation: 96-81=15, Resulting Numbers: [16, 67, 15] Generated Node #0,1: 48:[16, 67, 15] Operation: 96-81=15 Moving to Node #0,1 Current State: 48:[16, 67, 15], Operations: ['96-81=15'] Exploring Operation: 67-16=51, Resulting Numbers: [15, 51] Generated Node #0,1,0: 48:[15, 51] Operation: 67-16=51 Exploring Operation: 67-15=52, Resulting Numbers: [16, 52] Generated Node #0,1,1: 48:[16, 52] Operation: 67-15=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[15, 51], Operations: ['96-81=15', '67-16=51'] Exploring Operation: 15+51=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,48 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 #0,1,1 Current State: 48:[16, 52], Operations: ['96-81=15', '67-15=52'] Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,48 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: 48:[81, 16, 29], Operations: ['96-67=29'] Exploring Operation: 81-16=65, Resulting Numbers: [29, 65] Generated Node #0,0,0: 48:[29, 65] Operation: 81-16=65 Exploring Operation: 81-29=52, Resulting Numbers: [16, 52] Generated Node #0,0,1: 48:[16, 52] Operation: 81-29=52 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[16, 52], Operations: ['96-67=29', '81-29=52'] Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[29, 65], Operations: ['96-67=29', '81-16=65'] Exploring Operation: 29+65=94, Resulting Numbers: [94] 94,48 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,48 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
[ 9, 64, 7, 48 ]
47
[ "9*7=63", "64-48=16", "63-16=47" ]
Current State: 47:[9, 64, 7, 48], Operations: [] Exploring Operation: 9*7=63, Resulting Numbers: [64, 48, 63] Generated Node #2: [64, 48, 63] from Operation: 9*7=63 Current State: 47:[64, 48, 63], Operations: ['9*7=63'] Exploring Operation: 64-48=16, Resulting Numbers: [63, 16] Generated Node #3: [63, 16] from Operation: 64-48=16 Current State: 47:[63, 16], Operations: ['9*7=63', '64-48=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[9, 64, 7, 48], Operations: [] Exploring Operation: 64-9=55, Resulting Numbers: [7, 48, 55] Generated Node #0,0: 47:[7, 48, 55] Operation: 64-9=55 Exploring Operation: 9*7=63, Resulting Numbers: [64, 48, 63] Generated Node #0,1: 47:[64, 48, 63] Operation: 9*7=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[64, 48, 63], Operations: ['9*7=63'] Exploring Operation: 64-63=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 47:[48, 1] Operation: 64-63=1 Exploring Operation: 64-48=16, Resulting Numbers: [63, 16] Generated Node #0,1,1: 47:[63, 16] Operation: 64-48=16 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[48, 1], Operations: ['9*7=63', '64-63=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[9, 64, 7, 48], Operations: [] Exploring Operation: 9*7=63, Resulting Numbers: [64, 48, 63] Generated Node #0,1: 47:[64, 48, 63] Operation: 9*7=63 Moving to Node #0,1 Current State: 47:[64, 48, 63], Operations: ['9*7=63'] Exploring Operation: 64-63=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 47:[48, 1] Operation: 64-63=1 Moving to Node #0,1,0 Current State: 47:[48, 1], Operations: ['9*7=63', '64-63=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 7, 90, 33, 6 ]
55
[ "7+33=40", "90/6=15", "40+15=55" ]
Current State: 55:[7, 90, 33, 6], Operations: [] Exploring Operation: 7+33=40, Resulting Numbers: [90, 6, 40] Generated Node #2: [90, 6, 40] from Operation: 7+33=40 Current State: 55:[90, 6, 40], Operations: ['7+33=40'] Exploring Operation: 90/6=15, Resulting Numbers: [40, 15] Generated Node #3: [40, 15] from Operation: 90/6=15 Current State: 55:[40, 15], Operations: ['7+33=40', '90/6=15'] Exploring Operation: 40+15=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[7, 90, 33, 6], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [7, 33, 15] Generated Node #0,0: 55:[7, 33, 15] Operation: 90/6=15 Exploring Operation: 7+33=40, Resulting Numbers: [90, 6, 40] Generated Node #0,1: 55:[90, 6, 40] Operation: 7+33=40 Exploring Operation: 90-7=83, Resulting Numbers: [33, 6, 83] Generated Node #0,2: 55:[33, 6, 83] Operation: 90-7=83 Exploring Operation: 33-7=26, Resulting Numbers: [90, 6, 26] Generated Node #0,3: 55:[90, 6, 26] Operation: 33-7=26 Exploring Operation: 90-33=57, Resulting Numbers: [7, 6, 57] Generated Node #0,4: 55:[7, 6, 57] Operation: 90-33=57 Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[7, 6, 57], Operations: ['90-33=57'] Exploring Operation: 57-7=50, Resulting Numbers: [6, 50] Generated Node #0,4,0: 55:[6, 50] Operation: 57-7=50 Exploring Operation: 7+57=64, Resulting Numbers: [6, 64] Generated Node #0,4,1: 55:[6, 64] Operation: 7+57=64 Exploring Operation: 7+6=13, Resulting Numbers: [57, 13] Generated Node #0,4,2: 55:[57, 13] Operation: 7+6=13 Exploring Operation: 7-6=1, Resulting Numbers: [57, 1] Generated Node #0,4,3: 55:[57, 1] Operation: 7-6=1 Exploring Operation: 57-6=51, Resulting Numbers: [7, 51] Generated Node #0,4,4: 55:[7, 51] Operation: 57-6=51 Moving to Node #0,4,2 Current State: 55:[57, 13], Operations: ['90-33=57', '7+6=13'] Exploring Operation: 57-13=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 57+13=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 57*13=741, Resulting Numbers: [741] 741,55 unequal: No Solution Moving to Node #0,4,3 Current State: 55:[57, 1], Operations: ['90-33=57', '7-6=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,55 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,55 unequal: No Solution Moving to Node #0,4,0 Current State: 55:[6, 50], Operations: ['90-33=57', '57-7=50'] Exploring Operation: 6*50=300, Resulting Numbers: [300] 300,55 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,55 unequal: No Solution Moving to Node #0,4,4 Current State: 55:[7, 51], Operations: ['90-33=57', '57-6=51'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 7*51=357, Resulting Numbers: [357] 357,55 unequal: No Solution Exploring Operation: 7+51=58, Resulting Numbers: [58] 58,55 unequal: No Solution Moving to Node #0,4,1 Current State: 55:[6, 64], Operations: ['90-33=57', '7+57=64'] Exploring Operation: 6*64=384, Resulting Numbers: [384] 384,55 unequal: No Solution Exploring Operation: 6+64=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,55 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 #0,0 Current State: 55:[7, 33, 15], Operations: ['90/6=15'] Exploring Operation: 33+15=48, Resulting Numbers: [7, 48] Generated Node #0,0,0: 55:[7, 48] Operation: 33+15=48 Exploring Operation: 33-7=26, Resulting Numbers: [15, 26] Generated Node #0,0,1: 55:[15, 26] Operation: 33-7=26 Exploring Operation: 15-7=8, Resulting Numbers: [33, 8] Generated Node #0,0,2: 55:[33, 8] Operation: 15-7=8 Exploring Operation: 33-15=18, Resulting Numbers: [7, 18] Generated Node #0,0,3: 55:[7, 18] Operation: 33-15=18 Exploring Operation: 7+33=40, Resulting Numbers: [15, 40] Generated Node #0,0,4: 55:[15, 40] Operation: 7+33=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[7, 48], Operations: ['90/6=15', '33+15=48'] Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,55 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[7, 90, 33, 6], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [7, 33, 15] Generated Node #0,0: 55:[7, 33, 15] Operation: 90/6=15 Moving to Node #0,0 Current State: 55:[7, 33, 15], Operations: ['90/6=15'] Exploring Operation: 33+15=48, Resulting Numbers: [7, 48] Generated Node #0,0,0: 55:[7, 48] Operation: 33+15=48 Moving to Node #0,0,0 Current State: 55:[7, 48], Operations: ['90/6=15', '33+15=48'] Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 35, 17, 51, 4 ]
85
[ "35*51=1785", "17+4=21", "1785/21=85" ]
Current State: 85:[35, 17, 51, 4], Operations: [] Exploring Operation: 35*51=1785, Resulting Numbers: [17, 4, 1785] Generated Node #2: [17, 4, 1785] from Operation: 35*51=1785 Current State: 85:[17, 4, 1785], Operations: ['35*51=1785'] Exploring Operation: 17+4=21, Resulting Numbers: [1785, 21] Generated Node #3: [1785, 21] from Operation: 17+4=21 Current State: 85:[1785, 21], Operations: ['35*51=1785', '17+4=21'] Exploring Operation: 1785/21=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[35, 17, 51, 4], Operations: [] Exploring Operation: 35+51=86, Resulting Numbers: [17, 4, 86] Generated Node #0,0: 85:[17, 4, 86] Operation: 35+51=86 Exploring Operation: 51-35=16, Resulting Numbers: [17, 4, 16] Generated Node #0,1: 85:[17, 4, 16] Operation: 51-35=16 Exploring Operation: 51/17=3, Resulting Numbers: [35, 4, 3] Generated Node #0,2: 85:[35, 4, 3] Operation: 51/17=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[17, 4, 86], Operations: ['35+51=86'] Exploring Operation: 17-4=13, Resulting Numbers: [86, 13] Generated Node #0,0,0: 85:[86, 13] Operation: 17-4=13 Exploring Operation: 17+4=21, Resulting Numbers: [86, 21] Generated Node #0,0,1: 85:[86, 21] Operation: 17+4=21 Exploring Operation: 86-4=82, Resulting Numbers: [17, 82] Generated Node #0,0,2: 85:[17, 82] Operation: 86-4=82 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[17, 82], Operations: ['35+51=86', '86-4=82'] Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,85 unequal: No Solution Exploring Operation: 17+82=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 17*82=1394, Resulting Numbers: [1394] 1394,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[86, 13], Operations: ['35+51=86', '17-4=13'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,85 unequal: No Solution Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,85 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[86, 21], Operations: ['35+51=86', '17+4=21'] Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,85 unequal: No Solution Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,85 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[17, 4, 16], Operations: ['51-35=16'] Exploring Operation: 4+16=20, Resulting Numbers: [17, 20] Generated Node #0,1,0: 85:[17, 20] Operation: 4+16=20 Exploring Operation: 16/4=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 85:[17, 4] Operation: 16/4=4 Exploring Operation: 17+4=21, Resulting Numbers: [16, 21] Generated Node #0,1,2: 85:[16, 21] Operation: 17+4=21 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[17, 4], Operations: ['51-35=16', '16/4=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[17, 20], Operations: ['51-35=16', '4+16=20'] Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,85 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 85:[16, 21], Operations: ['51-35=16', '17+4=21'] Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,85 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[35, 4, 3], Operations: ['51/17=3'] Exploring Operation: 35-3=32, Resulting Numbers: [4, 32] Generated Node #0,2,0: 85:[4, 32] Operation: 35-3=32 Exploring Operation: 35-4=31, Resulting Numbers: [3, 31] Generated Node #0,2,1: 85:[3, 31] Operation: 35-4=31 Exploring Operation: 4+3=7, Resulting Numbers: [35, 7] Generated Node #0,2,2: 85:[35, 7] Operation: 4+3=7 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 85:[4, 32], Operations: ['51/17=3', '35-3=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,85 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[3, 31], Operations: ['51/17=3', '35-4=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,85 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 85:[35, 7], Operations: ['51/17=3', '4+3=7'] Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 32, 76, 54, 44 ]
74
[ "54-32=22", "44/22=2", "76-2=74" ]
Current State: 74:[32, 76, 54, 44], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [76, 44, 22] Generated Node #2: [76, 44, 22] from Operation: 54-32=22 Current State: 74:[76, 44, 22], Operations: ['54-32=22'] Exploring Operation: 44/22=2, Resulting Numbers: [76, 2] Generated Node #3: [76, 2] from Operation: 44/22=2 Current State: 74:[76, 2], Operations: ['54-32=22', '44/22=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[32, 76, 54, 44], Operations: [] Exploring Operation: 54-44=10, Resulting Numbers: [32, 76, 10] Generated Node #0,0: 74:[32, 76, 10] Operation: 54-44=10 Moving to Node #0,0 Current State: 74:[32, 76, 10], Operations: ['54-44=10'] Exploring Operation: 32+10=42, Resulting Numbers: [76, 42] Generated Node #0,0,0: 74:[76, 42] Operation: 32+10=42 Moving to Node #0,0,0 Current State: 74:[76, 42], Operations: ['54-44=10', '32+10=42'] Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,74 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 96, 77, 89, 67 ]
56
[ "96-89=7", "77/7=11", "67-11=56" ]
Current State: 56:[96, 77, 89, 67], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [77, 67, 7] Generated Node #2: [77, 67, 7] from Operation: 96-89=7 Current State: 56:[77, 67, 7], Operations: ['96-89=7'] Exploring Operation: 77/7=11, Resulting Numbers: [67, 11] Generated Node #3: [67, 11] from Operation: 77/7=11 Current State: 56:[67, 11], Operations: ['96-89=7', '77/7=11'] Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[96, 77, 89, 67], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [77, 67, 7] Generated Node #0,0: 56:[77, 67, 7] Operation: 96-89=7 Exploring Operation: 89-77=12, Resulting Numbers: [96, 67, 12] Generated Node #0,1: 56:[96, 67, 12] Operation: 89-77=12 Exploring Operation: 89-67=22, Resulting Numbers: [96, 77, 22] Generated Node #0,2: 56:[96, 77, 22] Operation: 89-67=22 Exploring Operation: 96-67=29, Resulting Numbers: [77, 89, 29] Generated Node #0,3: 56:[77, 89, 29] Operation: 96-67=29 Exploring Operation: 96-77=19, Resulting Numbers: [89, 67, 19] Generated Node #0,4: 56:[89, 67, 19] Operation: 96-77=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[77, 67, 7], Operations: ['96-89=7'] Exploring Operation: 77/7=11, Resulting Numbers: [67, 11] Generated Node #0,0,0: 56:[67, 11] Operation: 77/7=11 Exploring Operation: 67-7=60, Resulting Numbers: [77, 60] Generated Node #0,0,1: 56:[77, 60] Operation: 67-7=60 Exploring Operation: 77+7=84, Resulting Numbers: [67, 84] Generated Node #0,0,2: 56:[67, 84] Operation: 77+7=84 Exploring Operation: 77-67=10, Resulting Numbers: [7, 10] Generated Node #0,0,3: 56:[7, 10] Operation: 77-67=10 Exploring Operation: 77-7=70, Resulting Numbers: [67, 70] Generated Node #0,0,4: 56:[67, 70] Operation: 77-7=70 Moving to Node #0,0,3 Current State: 56:[7, 10], Operations: ['96-89=7', '77-67=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[67, 11], Operations: ['96-89=7', '77/7=11'] Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[96, 77, 89, 67], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [77, 67, 7] Generated Node #0,0: 56:[77, 67, 7] Operation: 96-89=7 Moving to Node #0,0 Current State: 56:[77, 67, 7], Operations: ['96-89=7'] Exploring Operation: 77/7=11, Resulting Numbers: [67, 11] Generated Node #0,0,0: 56:[67, 11] Operation: 77/7=11 Moving to Node #0,0,0 Current State: 56:[67, 11], Operations: ['96-89=7', '77/7=11'] Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 87, 45, 95, 90 ]
37
[ "87-45=42", "95-90=5", "42-5=37" ]
Current State: 37:[87, 45, 95, 90], Operations: [] Exploring Operation: 87-45=42, Resulting Numbers: [95, 90, 42] Generated Node #2: [95, 90, 42] from Operation: 87-45=42 Current State: 37:[95, 90, 42], Operations: ['87-45=42'] Exploring Operation: 95-90=5, Resulting Numbers: [42, 5] Generated Node #3: [42, 5] from Operation: 95-90=5 Current State: 37:[42, 5], Operations: ['87-45=42', '95-90=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[87, 45, 95, 90], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [45, 90, 8] Generated Node #0,0: 37:[45, 90, 8] Operation: 95-87=8 Exploring Operation: 87-45=42, Resulting Numbers: [95, 90, 42] Generated Node #0,1: 37:[95, 90, 42] Operation: 87-45=42 Exploring Operation: 95-90=5, Resulting Numbers: [87, 45, 5] Generated Node #0,2: 37:[87, 45, 5] Operation: 95-90=5 Exploring Operation: 90-87=3, Resulting Numbers: [45, 95, 3] Generated Node #0,3: 37:[45, 95, 3] Operation: 90-87=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[45, 90, 8], Operations: ['95-87=8'] Exploring Operation: 90/45=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 37:[8, 2] Operation: 90/45=2 Exploring Operation: 90-8=82, Resulting Numbers: [45, 82] Generated Node #0,0,1: 37:[45, 82] Operation: 90-8=82 Exploring Operation: 90-45=45, Resulting Numbers: [8, 45] Generated Node #0,0,2: 37:[8, 45] Operation: 90-45=45 Exploring Operation: 45-8=37, Resulting Numbers: [90, 37] Generated Node #0,0,3: 37:[90, 37] Operation: 45-8=37 Moving to Node #0,0,2 Current State: 37:[8, 45], Operations: ['95-87=8', '90-45=45'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[87, 45, 95, 90], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [45, 90, 8] Generated Node #0,0: 37:[45, 90, 8] Operation: 95-87=8 Moving to Node #0,0 Current State: 37:[45, 90, 8], Operations: ['95-87=8'] Exploring Operation: 90-45=45, Resulting Numbers: [8, 45] Generated Node #0,0,2: 37:[8, 45] Operation: 90-45=45 Moving to Node #0,0,2 Current State: 37:[8, 45], Operations: ['95-87=8', '90-45=45'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 72, 79, 85, 45 ]
21
[ "72+79=151", "85+45=130", "151-130=21" ]
Current State: 21:[72, 79, 85, 45], Operations: [] Exploring Operation: 72+79=151, Resulting Numbers: [85, 45, 151] Generated Node #2: [85, 45, 151] from Operation: 72+79=151 Current State: 21:[85, 45, 151], Operations: ['72+79=151'] Exploring Operation: 85+45=130, Resulting Numbers: [151, 130] Generated Node #3: [151, 130] from Operation: 85+45=130 Current State: 21:[151, 130], Operations: ['72+79=151', '85+45=130'] Exploring Operation: 151-130=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[72, 79, 85, 45], Operations: [] Exploring Operation: 79-72=7, Resulting Numbers: [85, 45, 7] Generated Node #0,0: 21:[85, 45, 7] Operation: 79-72=7 Exploring Operation: 85-79=6, Resulting Numbers: [72, 45, 6] Generated Node #0,1: 21:[72, 45, 6] Operation: 85-79=6 Moving to Node #0,1 Current State: 21:[72, 45, 6], Operations: ['85-79=6'] Exploring Operation: 72-45=27, Resulting Numbers: [6, 27] Generated Node #0,1,0: 21:[6, 27] Operation: 72-45=27 Exploring Operation: 72/6=12, Resulting Numbers: [45, 12] Generated Node #0,1,1: 21:[45, 12] Operation: 72/6=12 Moving to Node #0,0 Current State: 21:[85, 45, 7], Operations: ['79-72=7'] Exploring Operation: 85-45=40, Resulting Numbers: [7, 40] Generated Node #0,0,0: 21:[7, 40] Operation: 85-45=40 Exploring Operation: 85-7=78, Resulting Numbers: [45, 78] Generated Node #0,0,1: 21:[45, 78] Operation: 85-7=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[7, 40], Operations: ['79-72=7', '85-45=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[45, 78], Operations: ['79-72=7', '85-7=78'] Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 45+78=123, Resulting Numbers: [123] 123,21 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: 21:[6, 27], Operations: ['85-79=6', '72-45=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[72, 79, 85, 45], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [72, 45, 6] Generated Node #0,1: 21:[72, 45, 6] Operation: 85-79=6 Moving to Node #0,1 Current State: 21:[72, 45, 6], Operations: ['85-79=6'] Exploring Operation: 72-45=27, Resulting Numbers: [6, 27] Generated Node #0,1,0: 21:[6, 27] Operation: 72-45=27 Moving to Node #0,1,0 Current State: 21:[6, 27], Operations: ['85-79=6', '72-45=27'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 5, 96, 66, 21 ]
14
[ "5+96=101", "66+21=87", "101-87=14" ]
Current State: 14:[5, 96, 66, 21], Operations: [] Exploring Operation: 5+96=101, Resulting Numbers: [66, 21, 101] Generated Node #2: [66, 21, 101] from Operation: 5+96=101 Current State: 14:[66, 21, 101], Operations: ['5+96=101'] Exploring Operation: 66+21=87, Resulting Numbers: [101, 87] Generated Node #3: [101, 87] from Operation: 66+21=87 Current State: 14:[101, 87], Operations: ['5+96=101', '66+21=87'] Exploring Operation: 101-87=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[5, 96, 66, 21], Operations: [] Exploring Operation: 96-66=30, Resulting Numbers: [5, 21, 30] Generated Node #0,0: 14:[5, 21, 30] Operation: 96-66=30 Moving to Node #0,0 Current State: 14:[5, 21, 30], Operations: ['96-66=30'] Exploring Operation: 30-21=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 14:[5, 9] Operation: 30-21=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[5, 9], Operations: ['96-66=30', '30-21=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[5, 96, 66, 21], Operations: [] Exploring Operation: 96-66=30, Resulting Numbers: [5, 21, 30] Generated Node #0,0: 14:[5, 21, 30] Operation: 96-66=30 Moving to Node #0,0 Current State: 14:[5, 21, 30], Operations: ['96-66=30'] Exploring Operation: 30-21=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 14:[5, 9] Operation: 30-21=9 Moving to Node #0,0,0 Current State: 14:[5, 9], Operations: ['96-66=30', '30-21=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 13, 2, 20, 71 ]
52
[ "13+20=33", "71+33=104", "104/2=52" ]
Current State: 52:[13, 2, 20, 71], Operations: [] Exploring Operation: 13+20=33, Resulting Numbers: [2, 71, 33] Generated Node #2: [2, 71, 33] from Operation: 13+20=33 Current State: 52:[2, 71, 33], Operations: ['13+20=33'] Exploring Operation: 71+33=104, Resulting Numbers: [2, 104] Generated Node #3: [2, 104] from Operation: 71+33=104 Current State: 52:[2, 104], Operations: ['13+20=33', '71+33=104'] Exploring Operation: 104/2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 2, 20, 71], Operations: [] Exploring Operation: 71-20=51, Resulting Numbers: [13, 2, 51] Generated Node #0,0: 52:[13, 2, 51] Operation: 71-20=51 Moving to Node #0,0 Current State: 52:[13, 2, 51], Operations: ['71-20=51'] Exploring Operation: 13*2=26, Resulting Numbers: [51, 26] Generated Node #0,0,0: 52:[51, 26] Operation: 13*2=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[51, 26], Operations: ['71-20=51', '13*2=26'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,52 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
[ 10, 74, 5, 78 ]
41
[ "10/5=2", "74/2=37", "78-37=41" ]
Current State: 41:[10, 74, 5, 78], Operations: [] Exploring Operation: 10/5=2, Resulting Numbers: [74, 78, 2] Generated Node #2: [74, 78, 2] from Operation: 10/5=2 Current State: 41:[74, 78, 2], Operations: ['10/5=2'] Exploring Operation: 74/2=37, Resulting Numbers: [78, 37] Generated Node #3: [78, 37] from Operation: 74/2=37 Current State: 41:[78, 37], Operations: ['10/5=2', '74/2=37'] Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[10, 74, 5, 78], Operations: [] Exploring Operation: 10*5=50, Resulting Numbers: [74, 78, 50] Generated Node #0,0: 41:[74, 78, 50] Operation: 10*5=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[74, 78, 50], Operations: ['10*5=50'] Exploring Operation: 78-74=4, Resulting Numbers: [50, 4] Generated Node #0,0,0: 41:[50, 4] Operation: 78-74=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[50, 4], Operations: ['10*5=50', '78-74=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 54, 32, 80, 96 ]
38
[ "54-32=22", "96-80=16", "22+16=38" ]
Current State: 38:[54, 32, 80, 96], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [80, 96, 22] Generated Node #2: [80, 96, 22] from Operation: 54-32=22 Current State: 38:[80, 96, 22], Operations: ['54-32=22'] Exploring Operation: 96-80=16, Resulting Numbers: [22, 16] Generated Node #3: [22, 16] from Operation: 96-80=16 Current State: 38:[22, 16], Operations: ['54-32=22', '96-80=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[54, 32, 80, 96], Operations: [] Exploring Operation: 96-80=16, Resulting Numbers: [54, 32, 16] Generated Node #0,0: 38:[54, 32, 16] Operation: 96-80=16 Exploring Operation: 96-54=42, Resulting Numbers: [32, 80, 42] Generated Node #0,1: 38:[32, 80, 42] Operation: 96-54=42 Exploring Operation: 96/32=3, Resulting Numbers: [54, 80, 3] Generated Node #0,2: 38:[54, 80, 3] Operation: 96/32=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[54, 32, 16], Operations: ['96-80=16'] Exploring Operation: 54-32=22, Resulting Numbers: [16, 22] Generated Node #0,0,0: 38:[16, 22] Operation: 54-32=22 Exploring Operation: 32/16=2, Resulting Numbers: [54, 2] Generated Node #0,0,1: 38:[54, 2] Operation: 32/16=2 Exploring Operation: 54-16=38, Resulting Numbers: [32, 38] Generated Node #0,0,2: 38:[32, 38] Operation: 54-16=38 Moving to Node #0,0,0 Current State: 38:[16, 22], Operations: ['96-80=16', '54-32=22'] Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,38 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[54, 32, 80, 96], Operations: [] Exploring Operation: 96-80=16, Resulting Numbers: [54, 32, 16] Generated Node #0,0: 38:[54, 32, 16] Operation: 96-80=16 Moving to Node #0,0 Current State: 38:[54, 32, 16], Operations: ['96-80=16'] Exploring Operation: 54-32=22, Resulting Numbers: [16, 22] Generated Node #0,0,0: 38:[16, 22] Operation: 54-32=22 Moving to Node #0,0,0 Current State: 38:[16, 22], Operations: ['96-80=16', '54-32=22'] Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 71, 77, 8, 83 ]
81
[ "77-71=6", "83-8=75", "6+75=81" ]
Current State: 81:[71, 77, 8, 83], Operations: [] Exploring Operation: 77-71=6, Resulting Numbers: [8, 83, 6] Generated Node #2: [8, 83, 6] from Operation: 77-71=6 Current State: 81:[8, 83, 6], Operations: ['77-71=6'] Exploring Operation: 83-8=75, Resulting Numbers: [6, 75] Generated Node #3: [6, 75] from Operation: 83-8=75 Current State: 81:[6, 75], Operations: ['77-71=6', '83-8=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[71, 77, 8, 83], Operations: [] Exploring Operation: 83-77=6, Resulting Numbers: [71, 8, 6] Generated Node #0,0: 81:[71, 8, 6] Operation: 83-77=6 Exploring Operation: 77+8=85, Resulting Numbers: [71, 83, 85] Generated Node #0,1: 81:[71, 83, 85] Operation: 77+8=85 Exploring Operation: 83-71=12, Resulting Numbers: [77, 8, 12] Generated Node #0,2: 81:[77, 8, 12] Operation: 83-71=12 Exploring Operation: 71+8=79, Resulting Numbers: [77, 83, 79] Generated Node #0,3: 81:[77, 83, 79] Operation: 71+8=79 Exploring Operation: 77-71=6, Resulting Numbers: [8, 83, 6] Generated Node #0,4: 81:[8, 83, 6] Operation: 77-71=6 Moving to Node #0,4 Current State: 81:[8, 83, 6], Operations: ['77-71=6'] Exploring Operation: 8+6=14, Resulting Numbers: [83, 14] Generated Node #0,4,0: 81:[83, 14] Operation: 8+6=14 Exploring Operation: 8-6=2, Resulting Numbers: [83, 2] Generated Node #0,4,1: 81:[83, 2] Operation: 8-6=2 Exploring Operation: 83+6=89, Resulting Numbers: [8, 89] Generated Node #0,4,2: 81:[8, 89] Operation: 83+6=89 Exploring Operation: 83-6=77, Resulting Numbers: [8, 77] Generated Node #0,4,3: 81:[8, 77] Operation: 83-6=77 Exploring Operation: 83-8=75, Resulting Numbers: [6, 75] Generated Node #0,4,4: 81:[6, 75] Operation: 83-8=75 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 81:[83, 2], Operations: ['77-71=6', '8-6=2'] Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[71, 77, 8, 83], Operations: [] Exploring Operation: 77-71=6, Resulting Numbers: [8, 83, 6] Generated Node #0,4: 81:[8, 83, 6] Operation: 77-71=6 Moving to Node #0,4 Current State: 81:[8, 83, 6], Operations: ['77-71=6'] Exploring Operation: 8-6=2, Resulting Numbers: [83, 2] Generated Node #0,4,1: 81:[83, 2] Operation: 8-6=2 Moving to Node #0,4,1 Current State: 81:[83, 2], Operations: ['77-71=6', '8-6=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 75, 91, 36, 98 ]
78
[ "91-75=16", "98-36=62", "16+62=78" ]
Current State: 78:[75, 91, 36, 98], Operations: [] Exploring Operation: 91-75=16, Resulting Numbers: [36, 98, 16] Generated Node #2: [36, 98, 16] from Operation: 91-75=16 Current State: 78:[36, 98, 16], Operations: ['91-75=16'] Exploring Operation: 98-36=62, Resulting Numbers: [16, 62] Generated Node #3: [16, 62] from Operation: 98-36=62 Current State: 78:[16, 62], Operations: ['91-75=16', '98-36=62'] Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[75, 91, 36, 98], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [75, 36, 7] Generated Node #0,0: 78:[75, 36, 7] Operation: 98-91=7 Exploring Operation: 98-75=23, Resulting Numbers: [91, 36, 23] Generated Node #0,1: 78:[91, 36, 23] Operation: 98-75=23 Exploring Operation: 75-36=39, Resulting Numbers: [91, 98, 39] Generated Node #0,2: 78:[91, 98, 39] Operation: 75-36=39 Exploring Operation: 98-36=62, Resulting Numbers: [75, 91, 62] Generated Node #0,3: 78:[75, 91, 62] Operation: 98-36=62 Exploring Operation: 91-75=16, Resulting Numbers: [36, 98, 16] Generated Node #0,4: 78:[36, 98, 16] Operation: 91-75=16 Moving to Node #0,0 Current State: 78:[75, 36, 7], Operations: ['98-91=7'] Exploring Operation: 36+7=43, Resulting Numbers: [75, 43] Generated Node #0,0,0: 78:[75, 43] Operation: 36+7=43 Exploring Operation: 75-7=68, Resulting Numbers: [36, 68] Generated Node #0,0,1: 78:[36, 68] Operation: 75-7=68 Exploring Operation: 75+7=82, Resulting Numbers: [36, 82] Generated Node #0,0,2: 78:[36, 82] Operation: 75+7=82 Exploring Operation: 75-36=39, Resulting Numbers: [7, 39] Generated Node #0,0,3: 78:[7, 39] Operation: 75-36=39 Exploring Operation: 36-7=29, Resulting Numbers: [75, 29] Generated Node #0,0,4: 78:[75, 29] Operation: 36-7=29 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[7, 39], Operations: ['98-91=7', '75-36=39'] Exploring Operation: 7*39=273, Resulting Numbers: [273] 273,78 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,78 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 #0,0,4 Current State: 78:[75, 29], Operations: ['98-91=7', '36-7=29'] Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,78 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,78 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 #0,0,0 Current State: 78:[75, 43], Operations: ['98-91=7', '36+7=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,78 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,78 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[36, 82], Operations: ['98-91=7', '75+7=82'] Exploring Operation: 36+82=118, Resulting Numbers: [118] 118,78 unequal: No Solution Exploring Operation: 36*82=2952, Resulting Numbers: [2952] 2952,78 unequal: No Solution Exploring Operation: 82-36=46, Resulting Numbers: [46] 46,78 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 #0,0,1 Current State: 78:[36, 68], Operations: ['98-91=7', '75-7=68'] Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,78 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: 78:[91, 36, 23], Operations: ['98-75=23'] Exploring Operation: 91-23=68, Resulting Numbers: [36, 68] Generated Node #0,1,0: 78:[36, 68] Operation: 91-23=68 Exploring Operation: 91-36=55, Resulting Numbers: [23, 55] Generated Node #0,1,1: 78:[23, 55] Operation: 91-36=55 Exploring Operation: 91+23=114, Resulting Numbers: [36, 114] Generated Node #0,1,2: 78:[36, 114] Operation: 91+23=114 Exploring Operation: 36+23=59, Resulting Numbers: [91, 59] Generated Node #0,1,3: 78:[91, 59] Operation: 36+23=59 Exploring Operation: 36-23=13, Resulting Numbers: [91, 13] Generated Node #0,1,4: 78:[91, 13] Operation: 36-23=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[36, 68], Operations: ['98-75=23', '91-23=68'] Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 36+68=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 36*68=2448, Resulting Numbers: [2448] 2448,78 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 #0,1,4 Current State: 78:[91, 13], Operations: ['98-75=23', '36-23=13'] Exploring Operation: 91*13=1183, Resulting Numbers: [1183] 1183,78 unequal: No Solution Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 91+13=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[75, 91, 36, 98], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [91, 36, 23] Generated Node #0,1: 78:[91, 36, 23] Operation: 98-75=23 Moving to Node #0,1 Current State: 78:[91, 36, 23], Operations: ['98-75=23'] Exploring Operation: 36-23=13, Resulting Numbers: [91, 13] Generated Node #0,1,4: 78:[91, 13] Operation: 36-23=13 Moving to Node #0,1,4 Current State: 78:[91, 13], Operations: ['98-75=23', '36-23=13'] Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 78, 18, 67, 56 ]
71
[ "78-18=60", "67-56=11", "60+11=71" ]
Current State: 71:[78, 18, 67, 56], Operations: [] Exploring Operation: 78-18=60, Resulting Numbers: [67, 56, 60] Generated Node #2: [67, 56, 60] from Operation: 78-18=60 Current State: 71:[67, 56, 60], Operations: ['78-18=60'] Exploring Operation: 67-56=11, Resulting Numbers: [60, 11] Generated Node #3: [60, 11] from Operation: 67-56=11 Current State: 71:[60, 11], Operations: ['78-18=60', '67-56=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[78, 18, 67, 56], Operations: [] Exploring Operation: 18+56=74, Resulting Numbers: [78, 67, 74] Generated Node #0,0: 71:[78, 67, 74] Operation: 18+56=74 Exploring Operation: 18+67=85, Resulting Numbers: [78, 56, 85] Generated Node #0,1: 71:[78, 56, 85] Operation: 18+67=85 Exploring Operation: 78-18=60, Resulting Numbers: [67, 56, 60] Generated Node #0,2: 71:[67, 56, 60] Operation: 78-18=60 Moving to Node #0,0 Current State: 71:[78, 67, 74], Operations: ['18+56=74'] Exploring Operation: 78-74=4, Resulting Numbers: [67, 4] Generated Node #0,0,0: 71:[67, 4] Operation: 78-74=4 Exploring Operation: 74-67=7, Resulting Numbers: [78, 7] Generated Node #0,0,1: 71:[78, 7] Operation: 74-67=7 Exploring Operation: 78-67=11, Resulting Numbers: [74, 11] Generated Node #0,0,2: 71:[74, 11] Operation: 78-67=11 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[74, 11], Operations: ['18+56=74', '78-67=11'] Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 74*11=814, Resulting Numbers: [814] 814,71 unequal: No Solution Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,71 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 #0,0,0 Current State: 71:[67, 4], Operations: ['18+56=74', '78-74=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[78, 18, 67, 56], Operations: [] Exploring Operation: 18+56=74, Resulting Numbers: [78, 67, 74] Generated Node #0,0: 71:[78, 67, 74] Operation: 18+56=74 Moving to Node #0,0 Current State: 71:[78, 67, 74], Operations: ['18+56=74'] Exploring Operation: 78-74=4, Resulting Numbers: [67, 4] Generated Node #0,0,0: 71:[67, 4] Operation: 78-74=4 Moving to Node #0,0,0 Current State: 71:[67, 4], Operations: ['18+56=74', '78-74=4'] Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 38, 28, 64, 42 ]
32
[ "38-28=10", "64-42=22", "10+22=32" ]
Current State: 32:[38, 28, 64, 42], Operations: [] Exploring Operation: 38-28=10, Resulting Numbers: [64, 42, 10] Generated Node #2: [64, 42, 10] from Operation: 38-28=10 Current State: 32:[64, 42, 10], Operations: ['38-28=10'] Exploring Operation: 64-42=22, Resulting Numbers: [10, 22] Generated Node #3: [10, 22] from Operation: 64-42=22 Current State: 32:[10, 22], Operations: ['38-28=10', '64-42=22'] Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[38, 28, 64, 42], Operations: [] Exploring Operation: 64-42=22, Resulting Numbers: [38, 28, 22] Generated Node #0,0: 32:[38, 28, 22] Operation: 64-42=22 Moving to Node #0,0 Current State: 32:[38, 28, 22], Operations: ['64-42=22'] Exploring Operation: 38-22=16, Resulting Numbers: [28, 16] Generated Node #0,0,0: 32:[28, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[28, 16], Operations: ['64-42=22', '38-22=16'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 19, 55, 82, 56 ]
10
[ "55-19=36", "82-56=26", "36-26=10" ]
Current State: 10:[19, 55, 82, 56], Operations: [] Exploring Operation: 55-19=36, Resulting Numbers: [82, 56, 36] Generated Node #2: [82, 56, 36] from Operation: 55-19=36 Current State: 10:[82, 56, 36], Operations: ['55-19=36'] Exploring Operation: 82-56=26, Resulting Numbers: [36, 26] Generated Node #3: [36, 26] from Operation: 82-56=26 Current State: 10:[36, 26], Operations: ['55-19=36', '82-56=26'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[19, 55, 82, 56], Operations: [] Exploring Operation: 82-56=26, Resulting Numbers: [19, 55, 26] Generated Node #0,0: 10:[19, 55, 26] Operation: 82-56=26 Moving to Node #0,0 Current State: 10:[19, 55, 26], Operations: ['82-56=26'] Exploring Operation: 55-26=29, Resulting Numbers: [19, 29] Generated Node #0,0,0: 10:[19, 29] Operation: 55-26=29 Moving to Node #0,0,0 Current State: 10:[19, 29], Operations: ['82-56=26', '55-26=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[19, 55, 82, 56], Operations: [] Exploring Operation: 82-56=26, Resulting Numbers: [19, 55, 26] Generated Node #0,0: 10:[19, 55, 26] Operation: 82-56=26 Moving to Node #0,0 Current State: 10:[19, 55, 26], Operations: ['82-56=26'] Exploring Operation: 55-26=29, Resulting Numbers: [19, 29] Generated Node #0,0,0: 10:[19, 29] Operation: 55-26=29 Moving to Node #0,0,0 Current State: 10:[19, 29], Operations: ['82-56=26', '55-26=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 69, 93, 58, 57 ]
91
[ "93-69=24", "58+57=115", "115-24=91" ]
Current State: 91:[69, 93, 58, 57], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [58, 57, 24] Generated Node #2: [58, 57, 24] from Operation: 93-69=24 Current State: 91:[58, 57, 24], Operations: ['93-69=24'] Exploring Operation: 58+57=115, Resulting Numbers: [24, 115] Generated Node #3: [24, 115] from Operation: 58+57=115 Current State: 91:[24, 115], Operations: ['93-69=24', '58+57=115'] Exploring Operation: 115-24=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[69, 93, 58, 57], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [93, 58, 12] Generated Node #0,0: 91:[93, 58, 12] Operation: 69-57=12 Exploring Operation: 58-57=1, Resulting Numbers: [69, 93, 1] Generated Node #0,1: 91:[69, 93, 1] Operation: 58-57=1 Exploring Operation: 69-58=11, Resulting Numbers: [93, 57, 11] Generated Node #0,2: 91:[93, 57, 11] Operation: 69-58=11 Exploring Operation: 58+57=115, Resulting Numbers: [69, 93, 115] Generated Node #0,3: 91:[69, 93, 115] Operation: 58+57=115 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[69, 93, 1], Operations: ['58-57=1'] Exploring Operation: 69+1=70, Resulting Numbers: [93, 70] Generated Node #0,1,0: 91:[93, 70] Operation: 69+1=70 Exploring Operation: 69*1=69, Resulting Numbers: [93, 69] Generated Node #0,1,1: 91:[93, 69] Operation: 69*1=69 Exploring Operation: 93-69=24, Resulting Numbers: [1, 24] Generated Node #0,1,2: 91:[1, 24] Operation: 93-69=24 Exploring Operation: 93-1=92, Resulting Numbers: [69, 92] Generated Node #0,1,3: 91:[69, 92] Operation: 93-1=92 Moving to Node #0,1,2 Current State: 91:[1, 24], Operations: ['58-57=1', '93-69=24'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,91 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,91 unequal: No Solution Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[69, 92], Operations: ['58-57=1', '93-1=92'] Exploring Operation: 69*92=6348, Resulting Numbers: [6348] 6348,91 unequal: No Solution Exploring Operation: 92-69=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 69+92=161, Resulting Numbers: [161] 161,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[93, 70], Operations: ['58-57=1', '69+1=70'] Exploring Operation: 93*70=6510, Resulting Numbers: [6510] 6510,91 unequal: No Solution Exploring Operation: 93+70=163, Resulting Numbers: [163] 163,91 unequal: No Solution Exploring Operation: 93-70=23, Resulting Numbers: [23] 23,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[93, 69], Operations: ['58-57=1', '69*1=69'] Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,91 unequal: No Solution Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,91 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[93, 58, 12], Operations: ['69-57=12'] Exploring Operation: 93-12=81, Resulting Numbers: [58, 81] Generated Node #0,0,0: 91:[58, 81] Operation: 93-12=81 Exploring Operation: 93-58=35, Resulting Numbers: [12, 35] Generated Node #0,0,1: 91:[12, 35] Operation: 93-58=35 Exploring Operation: 58-12=46, Resulting Numbers: [93, 46] Generated Node #0,0,2: 91:[93, 46] Operation: 58-12=46 Exploring Operation: 58+12=70, Resulting Numbers: [93, 70] Generated Node #0,0,3: 91:[93, 70] Operation: 58+12=70 Moving to Node #0,0,1 Current State: 91:[12, 35], Operations: ['69-57=12', '93-58=35'] Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,91 unequal: No Solution Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[93, 70], Operations: ['69-57=12', '58+12=70'] Exploring Operation: 93+70=163, Resulting Numbers: [163] 163,91 unequal: No Solution Exploring Operation: 93*70=6510, Resulting Numbers: [6510] 6510,91 unequal: No Solution Exploring Operation: 93-70=23, Resulting Numbers: [23] 23,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[93, 46], Operations: ['69-57=12', '58-12=46'] Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 93*46=4278, Resulting Numbers: [4278] 4278,91 unequal: No Solution Exploring Operation: 93+46=139, Resulting Numbers: [139] 139,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[58, 81], Operations: ['69-57=12', '93-12=81'] Exploring Operation: 58*81=4698, Resulting Numbers: [4698] 4698,91 unequal: No Solution Exploring Operation: 58+81=139, Resulting Numbers: [139] 139,91 unequal: No Solution Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[93, 57, 11], Operations: ['69-58=11'] Exploring Operation: 57+11=68, Resulting Numbers: [93, 68] Generated Node #0,2,0: 91:[93, 68] Operation: 57+11=68 Exploring Operation: 93-57=36, Resulting Numbers: [11, 36] Generated Node #0,2,1: 91:[11, 36] Operation: 93-57=36 Exploring Operation: 93-11=82, Resulting Numbers: [57, 82] Generated Node #0,2,2: 91:[57, 82] Operation: 93-11=82 Exploring Operation: 57-11=46, Resulting Numbers: [93, 46] Generated Node #0,2,3: 91:[93, 46] Operation: 57-11=46 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[93, 68], Operations: ['69-58=11', '57+11=68'] Exploring Operation: 93+68=161, Resulting Numbers: [161] 161,91 unequal: No Solution Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,91 unequal: No Solution Exploring Operation: 93*68=6324, Resulting Numbers: [6324] 6324,91 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:[11, 36], Operations: ['69-58=11', '93-57=36'] Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,91 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 91:[93, 46], Operations: ['69-58=11', '57-11=46'] Exploring Operation: 93*46=4278, Resulting Numbers: [4278] 4278,91 unequal: No Solution Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 93+46=139, Resulting Numbers: [139] 139,91 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:[57, 82], Operations: ['69-58=11', '93-11=82'] Exploring Operation: 57+82=139, Resulting Numbers: [139] 139,91 unequal: No Solution Exploring Operation: 57*82=4674, Resulting Numbers: [4674] 4674,91 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[69, 93, 115], Operations: ['58+57=115'] Exploring Operation: 115-69=46, Resulting Numbers: [93, 46] Generated Node #0,3,0: 91:[93, 46] Operation: 115-69=46 Exploring Operation: 115-93=22, Resulting Numbers: [69, 22] Generated Node #0,3,1: 91:[69, 22] Operation: 115-93=22 Exploring Operation: 69+93=162, Resulting Numbers: [115, 162] Generated Node #0,3,2: 91:[115, 162] Operation: 69+93=162 Exploring Operation: 93-69=24, Resulting Numbers: [115, 24] Generated Node #0,3,3: 91:[115, 24] Operation: 93-69=24 Moving to Node #0,3,1 Current State: 91:[69, 22], Operations: ['58+57=115', '115-93=22'] Exploring Operation: 69+22=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[69, 93, 58, 57], Operations: [] Exploring Operation: 58+57=115, Resulting Numbers: [69, 93, 115] Generated Node #0,3: 91:[69, 93, 115] Operation: 58+57=115 Moving to Node #0,3 Current State: 91:[69, 93, 115], Operations: ['58+57=115'] Exploring Operation: 115-93=22, Resulting Numbers: [69, 22] Generated Node #0,3,1: 91:[69, 22] Operation: 115-93=22 Moving to Node #0,3,1 Current State: 91:[69, 22], Operations: ['58+57=115', '115-93=22'] Exploring Operation: 69+22=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_4
mult_heuristic
[ 78, 54, 69, 43 ]
51
[ "69-43=26", "78/26=3", "54-3=51" ]
Current State: 51:[78, 54, 69, 43], Operations: [] Exploring Operation: 69-43=26, Resulting Numbers: [78, 54, 26] Generated Node #2: [78, 54, 26] from Operation: 69-43=26 Current State: 51:[78, 54, 26], Operations: ['69-43=26'] Exploring Operation: 78/26=3, Resulting Numbers: [54, 3] Generated Node #3: [54, 3] from Operation: 78/26=3 Current State: 51:[54, 3], Operations: ['69-43=26', '78/26=3'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[78, 54, 69, 43], Operations: [] Exploring Operation: 78-43=35, Resulting Numbers: [54, 69, 35] Generated Node #0,0: 51:[54, 69, 35] Operation: 78-43=35 Exploring Operation: 78-54=24, Resulting Numbers: [69, 43, 24] Generated Node #0,1: 51:[69, 43, 24] Operation: 78-54=24 Exploring Operation: 78-69=9, Resulting Numbers: [54, 43, 9] Generated Node #0,2: 51:[54, 43, 9] Operation: 78-69=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[54, 43, 9], Operations: ['78-69=9'] Exploring Operation: 54/9=6, Resulting Numbers: [43, 6] Generated Node #0,2,0: 51:[43, 6] Operation: 54/9=6 Exploring Operation: 43+9=52, Resulting Numbers: [54, 52] Generated Node #0,2,1: 51:[54, 52] Operation: 43+9=52 Exploring Operation: 54-43=11, Resulting Numbers: [9, 11] Generated Node #0,2,2: 51:[9, 11] Operation: 54-43=11 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 51:[54, 52], Operations: ['78-69=9', '43+9=52'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 51:[43, 6], Operations: ['78-69=9', '54/9=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,51 unequal: No Solution Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[9, 11], Operations: ['78-69=9', '54-43=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[69, 43, 24], Operations: ['78-54=24'] Exploring Operation: 69-24=45, Resulting Numbers: [43, 45] Generated Node #0,1,0: 51:[43, 45] Operation: 69-24=45 Exploring Operation: 69-43=26, Resulting Numbers: [24, 26] Generated Node #0,1,1: 51:[24, 26] Operation: 69-43=26 Exploring Operation: 43-24=19, Resulting Numbers: [69, 19] Generated Node #0,1,2: 51:[69, 19] Operation: 43-24=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[43, 45], Operations: ['78-54=24', '69-24=45'] Exploring Operation: 43*45=1935, Resulting Numbers: [1935] 1935,51 unequal: No Solution Exploring Operation: 43+45=88, Resulting Numbers: [88] 88,51 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[24, 26], Operations: ['78-54=24', '69-43=26'] Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 51:[69, 19], Operations: ['78-54=24', '43-24=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,51 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[54, 69, 35], Operations: ['78-43=35'] Exploring Operation: 69-54=15, Resulting Numbers: [35, 15] Generated Node #0,0,0: 51:[35, 15] Operation: 69-54=15 Exploring Operation: 54-35=19, Resulting Numbers: [69, 19] Generated Node #0,0,1: 51:[69, 19] Operation: 54-35=19 Exploring Operation: 69-35=34, Resulting Numbers: [54, 34] Generated Node #0,0,2: 51:[54, 34] Operation: 69-35=34 Moving to Node #0,0,0 Current State: 51:[35, 15], Operations: ['78-43=35', '69-54=15'] Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,51 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[69, 19], Operations: ['78-43=35', '54-35=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,51 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,51 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[54, 34], Operations: ['78-43=35', '69-35=34'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 54*34=1836, Resulting Numbers: [1836] 1836,51 unequal: No Solution Exploring Operation: 54+34=88, Resulting Numbers: [88] 88,51 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
[ 6, 67, 75, 62 ]
11
[ "75-62=13", "6*13=78", "78-67=11" ]
Current State: 11:[6, 67, 75, 62], Operations: [] Exploring Operation: 75-62=13, Resulting Numbers: [6, 67, 13] Generated Node #2: [6, 67, 13] from Operation: 75-62=13 Current State: 11:[6, 67, 13], Operations: ['75-62=13'] Exploring Operation: 6*13=78, Resulting Numbers: [67, 78] Generated Node #3: [67, 78] from Operation: 6*13=78 Current State: 11:[67, 78], Operations: ['75-62=13', '6*13=78'] Exploring Operation: 78-67=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[6, 67, 75, 62], Operations: [] Exploring Operation: 75-62=13, Resulting Numbers: [6, 67, 13] Generated Node #0,0: 11:[6, 67, 13] Operation: 75-62=13 Exploring Operation: 75-67=8, Resulting Numbers: [6, 62, 8] Generated Node #0,1: 11:[6, 62, 8] Operation: 75-67=8 Exploring Operation: 67-62=5, Resulting Numbers: [6, 75, 5] Generated Node #0,2: 11:[6, 75, 5] Operation: 67-62=5 Moving to Node #0,1 Current State: 11:[6, 62, 8], Operations: ['75-67=8'] Exploring Operation: 62-8=54, Resulting Numbers: [6, 54] Generated Node #0,1,0: 11:[6, 54] Operation: 62-8=54 Exploring Operation: 6+8=14, Resulting Numbers: [62, 14] Generated Node #0,1,1: 11:[62, 14] Operation: 6+8=14 Exploring Operation: 62-6=56, Resulting Numbers: [8, 56] Generated Node #0,1,2: 11:[8, 56] Operation: 62-6=56 Moving to Node #0,0 Current State: 11:[6, 67, 13], Operations: ['75-62=13'] Exploring Operation: 67-13=54, Resulting Numbers: [6, 54] Generated Node #0,0,0: 11:[6, 54] Operation: 67-13=54 Exploring Operation: 67-6=61, Resulting Numbers: [13, 61] Generated Node #0,0,1: 11:[13, 61] Operation: 67-6=61 Exploring Operation: 13-6=7, Resulting Numbers: [67, 7] Generated Node #0,0,2: 11:[67, 7] Operation: 13-6=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[6, 54], Operations: ['75-62=13', '67-13=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[13, 61], Operations: ['75-62=13', '67-6=61'] Exploring Operation: 13+61=74, Resulting Numbers: [74] 74,11 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 13*61=793, Resulting Numbers: [793] 793,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[67, 7], Operations: ['75-62=13', '13-6=7'] Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 67*7=469, Resulting Numbers: [469] 469,11 unequal: No Solution Exploring Operation: 67+7=74, Resulting Numbers: [74] 74,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 11:[6, 75, 5], Operations: ['67-62=5'] Exploring Operation: 6+5=11, Resulting Numbers: [75, 11] Generated Node #0,2,0: 11:[75, 11] Operation: 6+5=11 Exploring Operation: 75/5=15, Resulting Numbers: [6, 15] Generated Node #0,2,1: 11:[6, 15] Operation: 75/5=15 Exploring Operation: 75-6=69, Resulting Numbers: [5, 69] Generated Node #0,2,2: 11:[5, 69] Operation: 75-6=69 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[6, 15], Operations: ['67-62=5', '75/5=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[75, 11], Operations: ['67-62=5', '6+5=11'] Exploring Operation: 75+11=86, Resulting Numbers: [86] 86,11 unequal: No Solution Exploring Operation: 75-11=64, Resulting Numbers: [64] 64,11 unequal: No Solution Exploring Operation: 75*11=825, Resulting Numbers: [825] 825,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[5, 69], Operations: ['67-62=5', '75-6=69'] Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,11 unequal: No Solution Exploring Operation: 5+69=74, Resulting Numbers: [74] 74,11 unequal: No Solution Exploring Operation: 5*69=345, Resulting Numbers: [345] 345,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 11:[6, 54], Operations: ['75-67=8', '62-8=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[8, 56], Operations: ['75-67=8', '62-6=56'] Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,11 unequal: No Solution Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[62, 14], Operations: ['75-67=8', '6+8=14'] Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,11 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,11 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 21, 74, 4, 52 ]
10
[ "74+52=126", "126/21=6", "4+6=10" ]
Current State: 10:[21, 74, 4, 52], Operations: [] Exploring Operation: 74+52=126, Resulting Numbers: [21, 4, 126] Generated Node #2: [21, 4, 126] from Operation: 74+52=126 Current State: 10:[21, 4, 126], Operations: ['74+52=126'] Exploring Operation: 126/21=6, Resulting Numbers: [4, 6] Generated Node #3: [4, 6] from Operation: 126/21=6 Current State: 10:[4, 6], Operations: ['74+52=126', '126/21=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[21, 74, 4, 52], Operations: [] Exploring Operation: 21-4=17, Resulting Numbers: [74, 52, 17] Generated Node #0,0: 10:[74, 52, 17] Operation: 21-4=17 Exploring Operation: 74-52=22, Resulting Numbers: [21, 4, 22] Generated Node #0,1: 10:[21, 4, 22] Operation: 74-52=22 Exploring Operation: 74-21=53, Resulting Numbers: [4, 52, 53] Generated Node #0,2: 10:[4, 52, 53] Operation: 74-21=53 Exploring Operation: 52/4=13, Resulting Numbers: [21, 74, 13] Generated Node #0,3: 10:[21, 74, 13] Operation: 52/4=13 Exploring Operation: 52-21=31, Resulting Numbers: [74, 4, 31] Generated Node #0,4: 10:[74, 4, 31] Operation: 52-21=31 Moving to Node #0,1 Current State: 10:[21, 4, 22], Operations: ['74-52=22'] Exploring Operation: 21+4=25, Resulting Numbers: [22, 25] Generated Node #0,1,0: 10:[22, 25] Operation: 21+4=25 Exploring Operation: 21-4=17, Resulting Numbers: [22, 17] Generated Node #0,1,1: 10:[22, 17] Operation: 21-4=17 Exploring Operation: 22-21=1, Resulting Numbers: [4, 1] Generated Node #0,1,2: 10:[4, 1] Operation: 22-21=1 Exploring Operation: 22-4=18, Resulting Numbers: [21, 18] Generated Node #0,1,3: 10:[21, 18] Operation: 22-4=18 Exploring Operation: 4+22=26, Resulting Numbers: [21, 26] Generated Node #0,1,4: 10:[21, 26] Operation: 4+22=26 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[4, 1], Operations: ['74-52=22', '22-21=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,10 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:[22, 17], Operations: ['74-52=22', '21-4=17'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,10 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 #0,1,3 Current State: 10:[21, 18], Operations: ['74-52=22', '22-4=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,10 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,10 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 #0,1,0 Current State: 10:[22, 25], Operations: ['74-52=22', '21+4=25'] Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,10 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,10 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 #0,1,4 Current State: 10:[21, 26], Operations: ['74-52=22', '4+22=26'] Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,10 unequal: No Solution Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,10 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: 10:[21, 74, 13], Operations: ['52/4=13'] Exploring Operation: 74-13=61, Resulting Numbers: [21, 61] Generated Node #0,3,0: 10:[21, 61] Operation: 74-13=61 Exploring Operation: 21+13=34, Resulting Numbers: [74, 34] Generated Node #0,3,1: 10:[74, 34] Operation: 21+13=34 Exploring Operation: 21+74=95, Resulting Numbers: [13, 95] Generated Node #0,3,2: 10:[13, 95] Operation: 21+74=95 Exploring Operation: 74-21=53, Resulting Numbers: [13, 53] Generated Node #0,3,3: 10:[13, 53] Operation: 74-21=53 Exploring Operation: 21-13=8, Resulting Numbers: [74, 8] Generated Node #0,3,4: 10:[74, 8] Operation: 21-13=8 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 10:[13, 53], Operations: ['52/4=13', '74-21=53'] Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,10 unequal: No Solution Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,10 unequal: No Solution Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,10 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 #0,3,0 Current State: 10:[21, 61], Operations: ['52/4=13', '74-13=61'] Exploring Operation: 21+61=82, Resulting Numbers: [82] 82,10 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,10 unequal: No Solution Exploring Operation: 21*61=1281, Resulting Numbers: [1281] 1281,10 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 #0,3,4 Current State: 10:[74, 8], Operations: ['52/4=13', '21-13=8'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,10 unequal: No Solution Exploring Operation: 74*8=592, Resulting Numbers: [592] 592,10 unequal: No Solution Exploring Operation: 74+8=82, Resulting Numbers: [82] 82,10 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 #0,3,1 Current State: 10:[74, 34], Operations: ['52/4=13', '21+13=34'] Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,10 unequal: No Solution Exploring Operation: 74*34=2516, Resulting Numbers: [2516] 2516,10 unequal: No Solution Exploring Operation: 74+34=108, Resulting Numbers: [108] 108,10 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 #0,3,2 Current State: 10:[13, 95], Operations: ['52/4=13', '21+74=95'] Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,10 unequal: No Solution Exploring Operation: 13+95=108, Resulting Numbers: [108] 108,10 unequal: No Solution Exploring Operation: 13*95=1235, Resulting Numbers: [1235] 1235,10 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:[4, 52, 53], Operations: ['74-21=53'] Exploring Operation: 52/4=13, Resulting Numbers: [53, 13] Generated Node #0,2,0: 10:[53, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [53, 48] Generated Node #0,2,1: 10:[53, 48] Operation: 52-4=48 Exploring Operation: 53-4=49, Resulting Numbers: [52, 49] Generated Node #0,2,2: 10:[52, 49] Operation: 53-4=49 Exploring Operation: 53-52=1, Resulting Numbers: [4, 1] Generated Node #0,2,3: 10:[4, 1] Operation: 53-52=1 Exploring Operation: 4+52=56, Resulting Numbers: [53, 56] Generated Node #0,2,4: 10:[53, 56] Operation: 4+52=56 Moving to Node #0,4 Current State: 10:[74, 4, 31], Operations: ['52-21=31'] Exploring Operation: 4+31=35, Resulting Numbers: [74, 35] Generated Node #0,4,0: 10:[74, 35] Operation: 4+31=35 Exploring Operation: 74-4=70, Resulting Numbers: [31, 70] Generated Node #0,4,1: 10:[31, 70] Operation: 74-4=70 Exploring Operation: 74+4=78, Resulting Numbers: [31, 78] Generated Node #0,4,2: 10:[31, 78] Operation: 74+4=78 Exploring Operation: 74-31=43, Resulting Numbers: [4, 43] Generated Node #0,4,3: 10:[4, 43] Operation: 74-31=43 Exploring Operation: 31-4=27, Resulting Numbers: [74, 27] Generated Node #0,4,4: 10:[74, 27] Operation: 31-4=27 Moving to Node #0,0 Current State: 10:[74, 52, 17], Operations: ['21-4=17'] Exploring Operation: 74+17=91, Resulting Numbers: [52, 91] Generated Node #0,0,0: 10:[52, 91] Operation: 74+17=91 Exploring Operation: 74-17=57, Resulting Numbers: [52, 57] Generated Node #0,0,1: 10:[52, 57] Operation: 74-17=57 Exploring Operation: 74+52=126, Resulting Numbers: [17, 126] Generated Node #0,0,2: 10:[17, 126] Operation: 74+52=126 Exploring Operation: 52-17=35, Resulting Numbers: [74, 35] Generated Node #0,0,3: 10:[74, 35] Operation: 52-17=35 Exploring Operation: 74-52=22, Resulting Numbers: [17, 22] Generated Node #0,0,4: 10:[17, 22] Operation: 74-52=22 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 10:[17, 22], Operations: ['21-4=17', '74-52=22'] Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,10 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,10 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 #0,0,1 Current State: 10:[52, 57], Operations: ['21-4=17', '74-17=57'] Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 52+57=109, Resulting Numbers: [109] 109,10 unequal: No Solution Exploring Operation: 52*57=2964, Resulting Numbers: [2964] 2964,10 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 #0,0,3 Current State: 10:[74, 35], Operations: ['21-4=17', '52-17=35'] Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,10 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,10 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,10 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:[52, 91], Operations: ['21-4=17', '74+17=91'] Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,10 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,10 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,10 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:[17, 126], Operations: ['21-4=17', '74+52=126'] Exploring Operation: 17*126=2142, Resulting Numbers: [2142] 2142,10 unequal: No Solution Exploring Operation: 17+126=143, Resulting Numbers: [143] 143,10 unequal: No Solution Exploring Operation: 126-17=109, Resulting Numbers: [109] 109,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 10:[4, 1], Operations: ['74-21=53', '53-52=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,10 unequal: No Solution Moving to Node #0,4,3 Current State: 10:[4, 43], Operations: ['52-21=31', '74-31=43'] Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,10 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,10 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,10 unequal: No Solution Moving to Node #0,2,0 Current State: 10:[53, 13], Operations: ['74-21=53', '52/4=13'] Exploring Operation: 53+13=66, Resulting Numbers: [66] 66,10 unequal: No Solution Exploring Operation: 53*13=689, Resulting Numbers: [689] 689,10 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,10 unequal: No Solution Moving to Node #0,4,1 Current State: 10:[31, 70], Operations: ['52-21=31', '74-4=70'] Exploring Operation: 31*70=2170, Resulting Numbers: [2170] 2170,10 unequal: No Solution Exploring Operation: 70-31=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 31+70=101, Resulting Numbers: [101] 101,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[53, 48], Operations: ['74-21=53', '52-4=48'] Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,10 unequal: No Solution Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,10 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[52, 49], Operations: ['74-21=53', '53-4=49'] Exploring Operation: 52*49=2548, Resulting Numbers: [2548] 2548,10 unequal: No Solution Exploring Operation: 52+49=101, Resulting Numbers: [101] 101,10 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,10 unequal: No Solution Moving to Node #0,4,4 Current State: 10:[74, 27], Operations: ['52-21=31', '31-4=27'] Exploring Operation: 74*27=1998, Resulting Numbers: [1998] 1998,10 unequal: No Solution Exploring Operation: 74+27=101, Resulting Numbers: [101] 101,10 unequal: No Solution Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,10 unequal: No Solution Moving to Node #0,4,0 Current State: 10:[74, 35], Operations: ['52-21=31', '4+31=35'] Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,10 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,10 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,10 unequal: No Solution Moving to Node #0,4,2 Current State: 10:[31, 78], Operations: ['52-21=31', '74+4=78'] Exploring Operation: 31*78=2418, Resulting Numbers: [2418] 2418,10 unequal: No Solution Exploring Operation: 31+78=109, Resulting Numbers: [109] 109,10 unequal: No Solution Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,10 unequal: No Solution Moving to Node #0,2,4 Current State: 10:[53, 56], Operations: ['74-21=53', '4+52=56'] Exploring Operation: 53+56=109, Resulting Numbers: [109] 109,10 unequal: No Solution Exploring Operation: 53*56=2968, Resulting Numbers: [2968] 2968,10 unequal: No Solution Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,10 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 59, 90, 3, 72 ]
100
[ "90-59=31", "72-3=69", "31+69=100" ]
Current State: 100:[59, 90, 3, 72], Operations: [] Exploring Operation: 90-59=31, Resulting Numbers: [3, 72, 31] Generated Node #2: [3, 72, 31] from Operation: 90-59=31 Current State: 100:[3, 72, 31], Operations: ['90-59=31'] Exploring Operation: 72-3=69, Resulting Numbers: [31, 69] Generated Node #3: [31, 69] from Operation: 72-3=69 Current State: 100:[31, 69], Operations: ['90-59=31', '72-3=69'] Exploring Operation: 31+69=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[59, 90, 3, 72], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [90, 3, 13] Generated Node #0,0: 100:[90, 3, 13] Operation: 72-59=13 Exploring Operation: 90-72=18, Resulting Numbers: [59, 3, 18] Generated Node #0,1: 100:[59, 3, 18] Operation: 90-72=18 Moving to Node #0,1 Current State: 100:[59, 3, 18], Operations: ['90-72=18'] Exploring Operation: 59-3=56, Resulting Numbers: [18, 56] Generated Node #0,1,0: 100:[18, 56] Operation: 59-3=56 Exploring Operation: 59-18=41, Resulting Numbers: [3, 41] Generated Node #0,1,1: 100:[3, 41] Operation: 59-18=41 Moving to Node #0,0 Current State: 100:[90, 3, 13], Operations: ['72-59=13'] Exploring Operation: 90+13=103, Resulting Numbers: [3, 103] Generated Node #0,0,0: 100:[3, 103] Operation: 90+13=103 Exploring Operation: 90/3=30, Resulting Numbers: [13, 30] Generated Node #0,0,1: 100:[13, 30] Operation: 90/3=30 Moving to Node #0,0,0 Current State: 100:[3, 103], Operations: ['72-59=13', '90+13=103'] Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[59, 90, 3, 72], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [90, 3, 13] Generated Node #0,0: 100:[90, 3, 13] Operation: 72-59=13 Moving to Node #0,0 Current State: 100:[90, 3, 13], Operations: ['72-59=13'] Exploring Operation: 90+13=103, Resulting Numbers: [3, 103] Generated Node #0,0,0: 100:[3, 103] Operation: 90+13=103 Moving to Node #0,0,0 Current State: 100:[3, 103], Operations: ['72-59=13', '90+13=103'] Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 58, 11, 94, 37 ]
84
[ "58-11=47", "94+37=131", "131-47=84" ]
Current State: 84:[58, 11, 94, 37], Operations: [] Exploring Operation: 58-11=47, Resulting Numbers: [94, 37, 47] Generated Node #2: [94, 37, 47] from Operation: 58-11=47 Current State: 84:[94, 37, 47], Operations: ['58-11=47'] Exploring Operation: 94+37=131, Resulting Numbers: [47, 131] Generated Node #3: [47, 131] from Operation: 94+37=131 Current State: 84:[47, 131], Operations: ['58-11=47', '94+37=131'] Exploring Operation: 131-47=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[58, 11, 94, 37], Operations: [] Exploring Operation: 58+37=95, Resulting Numbers: [11, 94, 95] Generated Node #0,0: 84:[11, 94, 95] Operation: 58+37=95 Exploring Operation: 58-11=47, Resulting Numbers: [94, 37, 47] Generated Node #0,1: 84:[94, 37, 47] Operation: 58-11=47 Exploring Operation: 58-37=21, Resulting Numbers: [11, 94, 21] Generated Node #0,2: 84:[11, 94, 21] Operation: 58-37=21 Exploring Operation: 94-58=36, Resulting Numbers: [11, 37, 36] Generated Node #0,3: 84:[11, 37, 36] Operation: 94-58=36 Moving to Node #0,2 Current State: 84:[11, 94, 21], Operations: ['58-37=21'] Exploring Operation: 11+21=32, Resulting Numbers: [94, 32] Generated Node #0,2,0: 84:[94, 32] Operation: 11+21=32 Exploring Operation: 94-11=83, Resulting Numbers: [21, 83] Generated Node #0,2,1: 84:[21, 83] Operation: 94-11=83 Exploring Operation: 94-21=73, Resulting Numbers: [11, 73] Generated Node #0,2,2: 84:[11, 73] Operation: 94-21=73 Exploring Operation: 21-11=10, Resulting Numbers: [94, 10] Generated Node #0,2,3: 84:[94, 10] Operation: 21-11=10 Moving to Node #0,3 Current State: 84:[11, 37, 36], Operations: ['94-58=36'] Exploring Operation: 36-11=25, Resulting Numbers: [37, 25] Generated Node #0,3,0: 84:[37, 25] Operation: 36-11=25 Exploring Operation: 11+36=47, Resulting Numbers: [37, 47] Generated Node #0,3,1: 84:[37, 47] Operation: 11+36=47 Exploring Operation: 37-11=26, Resulting Numbers: [36, 26] Generated Node #0,3,2: 84:[36, 26] Operation: 37-11=26 Exploring Operation: 37-36=1, Resulting Numbers: [11, 1] Generated Node #0,3,3: 84:[11, 1] Operation: 37-36=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[11, 1], Operations: ['94-58=36', '37-36=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,84 unequal: No Solution No 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: 84:[37, 25], Operations: ['94-58=36', '36-11=25'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,84 unequal: No Solution Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,84 unequal: No Solution No 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: 84:[36, 26], Operations: ['94-58=36', '37-11=26'] Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 36+26=62, Resulting Numbers: [62] 62,84 unequal: No Solution Exploring Operation: 36*26=936, Resulting Numbers: [936] 936,84 unequal: No Solution No 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: 84:[37, 47], Operations: ['94-58=36', '11+36=47'] Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,84 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[58, 11, 94, 37], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [11, 37, 36] Generated Node #0,3: 84:[11, 37, 36] Operation: 94-58=36 Moving to Node #0,3 Current State: 84:[11, 37, 36], Operations: ['94-58=36'] Exploring Operation: 11+36=47, Resulting Numbers: [37, 47] Generated Node #0,3,1: 84:[37, 47] Operation: 11+36=47 Moving to Node #0,3,1 Current State: 84:[37, 47], Operations: ['94-58=36', '11+36=47'] Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_4
sum_heuristic
[ 76, 33, 79, 74 ]
48
[ "76-33=43", "79-74=5", "43+5=48" ]
Current State: 48:[76, 33, 79, 74], Operations: [] Exploring Operation: 76-33=43, Resulting Numbers: [79, 74, 43] Generated Node #2: [79, 74, 43] from Operation: 76-33=43 Current State: 48:[79, 74, 43], Operations: ['76-33=43'] Exploring Operation: 79-74=5, Resulting Numbers: [43, 5] Generated Node #3: [43, 5] from Operation: 79-74=5 Current State: 48:[43, 5], Operations: ['76-33=43', '79-74=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[76, 33, 79, 74], Operations: [] Exploring Operation: 79-76=3, Resulting Numbers: [33, 74, 3] Generated Node #0,0: 48:[33, 74, 3] Operation: 79-76=3 Exploring Operation: 79-74=5, Resulting Numbers: [76, 33, 5] Generated Node #0,1: 48:[76, 33, 5] Operation: 79-74=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[33, 74, 3], Operations: ['79-76=3'] Exploring Operation: 74-33=41, Resulting Numbers: [3, 41] Generated Node #0,0,0: 48:[3, 41] Operation: 74-33=41 Exploring Operation: 33/3=11, Resulting Numbers: [74, 11] Generated Node #0,0,1: 48:[74, 11] Operation: 33/3=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[3, 41], Operations: ['79-76=3', '74-33=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,48 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[74, 11], Operations: ['79-76=3', '33/3=11'] Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,48 unequal: No Solution Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[76, 33, 5], Operations: ['79-74=5'] Exploring Operation: 76-33=43, Resulting Numbers: [5, 43] Generated Node #0,1,0: 48:[5, 43] Operation: 76-33=43 Exploring Operation: 76-5=71, Resulting Numbers: [33, 71] Generated Node #0,1,1: 48:[33, 71] Operation: 76-5=71 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[5, 43], Operations: ['79-74=5', '76-33=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[76, 33, 79, 74], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [76, 33, 5] Generated Node #0,1: 48:[76, 33, 5] Operation: 79-74=5 Moving to Node #0,1 Current State: 48:[76, 33, 5], Operations: ['79-74=5'] Exploring Operation: 76-33=43, Resulting Numbers: [5, 43] Generated Node #0,1,0: 48:[5, 43] Operation: 76-33=43 Moving to Node #0,1,0 Current State: 48:[5, 43], Operations: ['79-74=5', '76-33=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 6, 88, 8, 13 ]
67
[ "6*13=78", "88/8=11", "78-11=67" ]
Current State: 67:[6, 88, 8, 13], Operations: [] Exploring Operation: 6*13=78, Resulting Numbers: [88, 8, 78] Generated Node #2: [88, 8, 78] from Operation: 6*13=78 Current State: 67:[88, 8, 78], Operations: ['6*13=78'] Exploring Operation: 88/8=11, Resulting Numbers: [78, 11] Generated Node #3: [78, 11] from Operation: 88/8=11 Current State: 67:[78, 11], Operations: ['6*13=78', '88/8=11'] Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[6, 88, 8, 13], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [88, 13, 48] Generated Node #0,0: 67:[88, 13, 48] Operation: 6*8=48 Exploring Operation: 6+8=14, Resulting Numbers: [88, 13, 14] Generated Node #0,1: 67:[88, 13, 14] Operation: 6+8=14 Exploring Operation: 88-6=82, Resulting Numbers: [8, 13, 82] Generated Node #0,2: 67:[8, 13, 82] Operation: 88-6=82 Exploring Operation: 6*13=78, Resulting Numbers: [88, 8, 78] Generated Node #0,3: 67:[88, 8, 78] Operation: 6*13=78 Exploring Operation: 8*13=104, Resulting Numbers: [6, 88, 104] Generated Node #0,4: 67:[6, 88, 104] Operation: 8*13=104 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[88, 8, 78], Operations: ['6*13=78'] Exploring Operation: 78-8=70, Resulting Numbers: [88, 70] Generated Node #0,3,0: 67:[88, 70] Operation: 78-8=70 Exploring Operation: 8+78=86, Resulting Numbers: [88, 86] Generated Node #0,3,1: 67:[88, 86] Operation: 8+78=86 Exploring Operation: 88/8=11, Resulting Numbers: [78, 11] Generated Node #0,3,2: 67:[78, 11] Operation: 88/8=11 Exploring Operation: 88+8=96, Resulting Numbers: [78, 96] Generated Node #0,3,3: 67:[78, 96] Operation: 88+8=96 Exploring Operation: 88-8=80, Resulting Numbers: [78, 80] Generated Node #0,3,4: 67:[78, 80] Operation: 88-8=80 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 67:[88, 70], Operations: ['6*13=78', '78-8=70'] Exploring Operation: 88-70=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 88*70=6160, Resulting Numbers: [6160] 6160,67 unequal: No Solution Exploring Operation: 88+70=158, Resulting Numbers: [158] 158,67 unequal: No Solution No 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: 67:[78, 80], Operations: ['6*13=78', '88-8=80'] Exploring Operation: 78*80=6240, Resulting Numbers: [6240] 6240,67 unequal: No Solution Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 78+80=158, Resulting Numbers: [158] 158,67 unequal: No Solution No 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: 67:[88, 86], Operations: ['6*13=78', '8+78=86'] Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 88+86=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 88*86=7568, Resulting Numbers: [7568] 7568,67 unequal: No Solution No 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: 67:[78, 96], Operations: ['6*13=78', '88+8=96'] Exploring Operation: 78+96=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 96-78=18, Resulting Numbers: [18] 18,67 unequal: No Solution Exploring Operation: 78*96=7488, Resulting Numbers: [7488] 7488,67 unequal: No Solution No 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: 67:[78, 11], Operations: ['6*13=78', '88/8=11'] Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,67 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[6, 88, 8, 13], Operations: [] Exploring Operation: 6*13=78, Resulting Numbers: [88, 8, 78] Generated Node #0,3: 67:[88, 8, 78] Operation: 6*13=78 Moving to Node #0,3 Current State: 67:[88, 8, 78], Operations: ['6*13=78'] Exploring Operation: 88/8=11, Resulting Numbers: [78, 11] Generated Node #0,3,2: 67:[78, 11] Operation: 88/8=11 Moving to Node #0,3,2 Current State: 67:[78, 11], Operations: ['6*13=78', '88/8=11'] Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 80, 67, 8, 85 ]
28
[ "80/8=10", "85-67=18", "10+18=28" ]
Current State: 28:[80, 67, 8, 85], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [67, 85, 10] Generated Node #2: [67, 85, 10] from Operation: 80/8=10 Current State: 28:[67, 85, 10], Operations: ['80/8=10'] Exploring Operation: 85-67=18, Resulting Numbers: [10, 18] Generated Node #3: [10, 18] from Operation: 85-67=18 Current State: 28:[10, 18], Operations: ['80/8=10', '85-67=18'] Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[80, 67, 8, 85], Operations: [] Exploring Operation: 85-80=5, Resulting Numbers: [67, 8, 5] Generated Node #0,0: 28:[67, 8, 5] Operation: 85-80=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[67, 8, 5], Operations: ['85-80=5'] Exploring Operation: 67-8=59, Resulting Numbers: [5, 59] Generated Node #0,0,0: 28:[5, 59] Operation: 67-8=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[5, 59], Operations: ['85-80=5', '67-8=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 40, 56, 75, 65 ]
44
[ "40+56=96", "75+65=140", "140-96=44" ]
Current State: 44:[40, 56, 75, 65], Operations: [] Exploring Operation: 40+56=96, Resulting Numbers: [75, 65, 96] Generated Node #2: [75, 65, 96] from Operation: 40+56=96 Current State: 44:[75, 65, 96], Operations: ['40+56=96'] Exploring Operation: 75+65=140, Resulting Numbers: [96, 140] Generated Node #3: [96, 140] from Operation: 75+65=140 Current State: 44:[96, 140], Operations: ['40+56=96', '75+65=140'] Exploring Operation: 140-96=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[40, 56, 75, 65], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [40, 65, 19] Generated Node #0,0: 44:[40, 65, 19] Operation: 75-56=19 Exploring Operation: 75-65=10, Resulting Numbers: [40, 56, 10] Generated Node #0,1: 44:[40, 56, 10] Operation: 75-65=10 Moving to Node #0,1 Current State: 44:[40, 56, 10], Operations: ['75-65=10'] Exploring Operation: 56-10=46, Resulting Numbers: [40, 46] Generated Node #0,1,0: 44:[40, 46] Operation: 56-10=46 Exploring Operation: 56-40=16, Resulting Numbers: [10, 16] Generated Node #0,1,1: 44:[10, 16] Operation: 56-40=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[40, 46], Operations: ['75-65=10', '56-10=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[10, 16], Operations: ['75-65=10', '56-40=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,44 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: 44:[40, 65, 19], Operations: ['75-56=19'] Exploring Operation: 65-40=25, Resulting Numbers: [19, 25] Generated Node #0,0,0: 44:[19, 25] Operation: 65-40=25 Exploring Operation: 65-19=46, Resulting Numbers: [40, 46] Generated Node #0,0,1: 44:[40, 46] Operation: 65-19=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[19, 25], Operations: ['75-56=19', '65-40=25'] Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[40, 56, 75, 65], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [40, 65, 19] Generated Node #0,0: 44:[40, 65, 19] Operation: 75-56=19 Moving to Node #0,0 Current State: 44:[40, 65, 19], Operations: ['75-56=19'] Exploring Operation: 65-40=25, Resulting Numbers: [19, 25] Generated Node #0,0,0: 44:[19, 25] Operation: 65-40=25 Moving to Node #0,0,0 Current State: 44:[19, 25], Operations: ['75-56=19', '65-40=25'] Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 51, 43, 54, 81 ]
77
[ "51*54=2754", "2754/81=34", "43+34=77" ]
Current State: 77:[51, 43, 54, 81], Operations: [] Exploring Operation: 51*54=2754, Resulting Numbers: [43, 81, 2754] Generated Node #2: [43, 81, 2754] from Operation: 51*54=2754 Current State: 77:[43, 81, 2754], Operations: ['51*54=2754'] Exploring Operation: 2754/81=34, Resulting Numbers: [43, 34] Generated Node #3: [43, 34] from Operation: 2754/81=34 Current State: 77:[43, 34], Operations: ['51*54=2754', '2754/81=34'] Exploring Operation: 43+34=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[51, 43, 54, 81], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [43, 81, 3] Generated Node #0,0: 77:[43, 81, 3] Operation: 54-51=3 Exploring Operation: 54-43=11, Resulting Numbers: [51, 81, 11] Generated Node #0,1: 77:[51, 81, 11] Operation: 54-43=11 Exploring Operation: 51+43=94, Resulting Numbers: [54, 81, 94] Generated Node #0,2: 77:[54, 81, 94] Operation: 51+43=94 Exploring Operation: 51-43=8, Resulting Numbers: [54, 81, 8] Generated Node #0,3: 77:[54, 81, 8] Operation: 51-43=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[54, 81, 8], Operations: ['51-43=8'] Exploring Operation: 81-8=73, Resulting Numbers: [54, 73] Generated Node #0,3,0: 77:[54, 73] Operation: 81-8=73 Exploring Operation: 54+8=62, Resulting Numbers: [81, 62] Generated Node #0,3,1: 77:[81, 62] Operation: 54+8=62 Exploring Operation: 54-8=46, Resulting Numbers: [81, 46] Generated Node #0,3,2: 77:[81, 46] Operation: 54-8=46 Exploring Operation: 81-54=27, Resulting Numbers: [8, 27] Generated Node #0,3,3: 77:[8, 27] Operation: 81-54=27 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 77:[8, 27], Operations: ['51-43=8', '81-54=27'] Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,77 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 77:[81, 62], Operations: ['51-43=8', '54+8=62'] Exploring Operation: 81+62=143, Resulting Numbers: [143] 143,77 unequal: No Solution Exploring Operation: 81*62=5022, Resulting Numbers: [5022] 5022,77 unequal: No Solution Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 77:[54, 73], Operations: ['51-43=8', '81-8=73'] Exploring Operation: 54*73=3942, Resulting Numbers: [3942] 3942,77 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 77:[81, 46], Operations: ['51-43=8', '54-8=46'] Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 81+46=127, Resulting Numbers: [127] 127,77 unequal: No Solution Exploring Operation: 81*46=3726, Resulting Numbers: [3726] 3726,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[51, 81, 11], Operations: ['54-43=11'] Exploring Operation: 81-11=70, Resulting Numbers: [51, 70] Generated Node #0,1,0: 77:[51, 70] Operation: 81-11=70 Exploring Operation: 51-11=40, Resulting Numbers: [81, 40] Generated Node #0,1,1: 77:[81, 40] Operation: 51-11=40 Exploring Operation: 81-51=30, Resulting Numbers: [11, 30] Generated Node #0,1,2: 77:[11, 30] Operation: 81-51=30 Exploring Operation: 51+11=62, Resulting Numbers: [81, 62] Generated Node #0,1,3: 77:[81, 62] Operation: 51+11=62 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 77:[11, 30], Operations: ['54-43=11', '81-51=30'] Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 77:[81, 62], Operations: ['54-43=11', '51+11=62'] Exploring Operation: 81*62=5022, Resulting Numbers: [5022] 5022,77 unequal: No Solution Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 81+62=143, Resulting Numbers: [143] 143,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[51, 70], Operations: ['54-43=11', '81-11=70'] Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,77 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[81, 40], Operations: ['54-43=11', '51-11=40'] Exploring Operation: 81+40=121, Resulting Numbers: [121] 121,77 unequal: No Solution Exploring Operation: 81*40=3240, Resulting Numbers: [3240] 3240,77 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[43, 81, 3], Operations: ['54-51=3'] Exploring Operation: 43-3=40, Resulting Numbers: [81, 40] Generated Node #0,0,0: 77:[81, 40] Operation: 43-3=40 Exploring Operation: 43+3=46, Resulting Numbers: [81, 46] Generated Node #0,0,1: 77:[81, 46] Operation: 43+3=46 Exploring Operation: 81-3=78, Resulting Numbers: [43, 78] Generated Node #0,0,2: 77:[43, 78] Operation: 81-3=78 Exploring Operation: 81-43=38, Resulting Numbers: [3, 38] Generated Node #0,0,3: 77:[3, 38] Operation: 81-43=38 Moving to Node #0,0,3 Current State: 77:[3, 38], Operations: ['54-51=3', '81-43=38'] Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,77 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[43, 78], Operations: ['54-51=3', '81-3=78'] Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,77 unequal: No Solution Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,77 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[81, 40], Operations: ['54-51=3', '43-3=40'] Exploring Operation: 81*40=3240, Resulting Numbers: [3240] 3240,77 unequal: No Solution Exploring Operation: 81+40=121, Resulting Numbers: [121] 121,77 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[81, 46], Operations: ['54-51=3', '43+3=46'] Exploring Operation: 81*46=3726, Resulting Numbers: [3726] 3726,77 unequal: No Solution Exploring Operation: 81+46=127, Resulting Numbers: [127] 127,77 unequal: No Solution Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[54, 81, 94], Operations: ['51+43=94'] Exploring Operation: 54+81=135, Resulting Numbers: [94, 135] Generated Node #0,2,0: 77:[94, 135] Operation: 54+81=135 Exploring Operation: 94-54=40, Resulting Numbers: [81, 40] Generated Node #0,2,1: 77:[81, 40] Operation: 94-54=40 Exploring Operation: 81-54=27, Resulting Numbers: [94, 27] Generated Node #0,2,2: 77:[94, 27] Operation: 81-54=27 Exploring Operation: 94-81=13, Resulting Numbers: [54, 13] Generated Node #0,2,3: 77:[54, 13] Operation: 94-81=13 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 77:[54, 13], Operations: ['51+43=94', '94-81=13'] Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,77 unequal: No Solution Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[81, 40], Operations: ['51+43=94', '94-54=40'] Exploring Operation: 81*40=3240, Resulting Numbers: [3240] 3240,77 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 81+40=121, Resulting Numbers: [121] 121,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[94, 27], Operations: ['51+43=94', '81-54=27'] Exploring Operation: 94+27=121, Resulting Numbers: [121] 121,77 unequal: No Solution Exploring Operation: 94-27=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 94*27=2538, Resulting Numbers: [2538] 2538,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[94, 135], Operations: ['51+43=94', '54+81=135'] Exploring Operation: 94*135=12690, Resulting Numbers: [12690] 12690,77 unequal: No Solution Exploring Operation: 135-94=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 94+135=229, Resulting Numbers: [229] 229,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 2, 85, 99, 94 ]
33
[ "94/2=47", "99-85=14", "47-14=33" ]
Current State: 33:[2, 85, 99, 94], Operations: [] Exploring Operation: 94/2=47, Resulting Numbers: [85, 99, 47] Generated Node #2: [85, 99, 47] from Operation: 94/2=47 Current State: 33:[85, 99, 47], Operations: ['94/2=47'] Exploring Operation: 99-85=14, Resulting Numbers: [47, 14] Generated Node #3: [47, 14] from Operation: 99-85=14 Current State: 33:[47, 14], Operations: ['94/2=47', '99-85=14'] Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[2, 85, 99, 94], Operations: [] Exploring Operation: 85-2=83, Resulting Numbers: [99, 94, 83] Generated Node #0,0: 33:[99, 94, 83] Operation: 85-2=83 Exploring Operation: 99-85=14, Resulting Numbers: [2, 94, 14] Generated Node #0,1: 33:[2, 94, 14] Operation: 99-85=14 Exploring Operation: 99-94=5, Resulting Numbers: [2, 85, 5] Generated Node #0,2: 33:[2, 85, 5] Operation: 99-94=5 Exploring Operation: 94/2=47, Resulting Numbers: [85, 99, 47] Generated Node #0,3: 33:[85, 99, 47] Operation: 94/2=47 Exploring Operation: 94-85=9, Resulting Numbers: [2, 99, 9] Generated Node #0,4: 33:[2, 99, 9] Operation: 94-85=9 Moving to Node #0,2 Current State: 33:[2, 85, 5], Operations: ['99-94=5'] Exploring Operation: 85/5=17, Resulting Numbers: [2, 17] Generated Node #0,2,0: 33:[2, 17] Operation: 85/5=17 Exploring Operation: 2*5=10, Resulting Numbers: [85, 10] Generated Node #0,2,1: 33:[85, 10] Operation: 2*5=10 Exploring Operation: 85-2=83, Resulting Numbers: [5, 83] Generated Node #0,2,2: 33:[5, 83] Operation: 85-2=83 Exploring Operation: 85-5=80, Resulting Numbers: [2, 80] Generated Node #0,2,3: 33:[2, 80] Operation: 85-5=80 Exploring Operation: 5-2=3, Resulting Numbers: [85, 3] Generated Node #0,2,4: 33:[85, 3] Operation: 5-2=3 Moving to Node #0,1 Current State: 33:[2, 94, 14], Operations: ['99-85=14'] Exploring Operation: 94/2=47, Resulting Numbers: [14, 47] Generated Node #0,1,0: 33:[14, 47] Operation: 94/2=47 Exploring Operation: 14/2=7, Resulting Numbers: [94, 7] Generated Node #0,1,1: 33:[94, 7] Operation: 14/2=7 Exploring Operation: 94-2=92, Resulting Numbers: [14, 92] Generated Node #0,1,2: 33:[14, 92] Operation: 94-2=92 Exploring Operation: 94-14=80, Resulting Numbers: [2, 80] Generated Node #0,1,3: 33:[2, 80] Operation: 94-14=80 Exploring Operation: 14-2=12, Resulting Numbers: [94, 12] Generated Node #0,1,4: 33:[94, 12] Operation: 14-2=12 Moving to Node #0,4 Current State: 33:[2, 99, 9], Operations: ['94-85=9'] Exploring Operation: 2+99=101, Resulting Numbers: [9, 101] Generated Node #0,4,0: 33:[9, 101] Operation: 2+99=101 Exploring Operation: 2+9=11, Resulting Numbers: [99, 11] Generated Node #0,4,1: 33:[99, 11] Operation: 2+9=11 Exploring Operation: 99-2=97, Resulting Numbers: [9, 97] Generated Node #0,4,2: 33:[9, 97] Operation: 99-2=97 Exploring Operation: 99-9=90, Resulting Numbers: [2, 90] Generated Node #0,4,3: 33:[2, 90] Operation: 99-9=90 Exploring Operation: 99/9=11, Resulting Numbers: [2, 11] Generated Node #0,4,4: 33:[2, 11] Operation: 99/9=11 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 33:[2, 11], Operations: ['94-85=9', '99/9=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,33 unequal: No Solution No 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: 33:[2, 90], Operations: ['94-85=9', '99-9=90'] Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,33 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,33 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,33 unequal: No Solution No 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: 33:[99, 11], Operations: ['94-85=9', '2+9=11'] Exploring Operation: 99-11=88, Resulting Numbers: [88] 88,33 unequal: No Solution Exploring Operation: 99+11=110, Resulting Numbers: [110] 110,33 unequal: No Solution Exploring Operation: 99/11=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 99*11=1089, Resulting Numbers: [1089] 1089,33 unequal: No Solution No 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: 33:[9, 97], Operations: ['94-85=9', '99-2=97'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,33 unequal: No Solution Exploring Operation: 9*97=873, Resulting Numbers: [873] 873,33 unequal: No Solution Exploring Operation: 9+97=106, Resulting Numbers: [106] 106,33 unequal: No Solution No 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: 33:[9, 101], Operations: ['94-85=9', '2+99=101'] Exploring Operation: 9+101=110, Resulting Numbers: [110] 110,33 unequal: No Solution Exploring Operation: 9*101=909, Resulting Numbers: [909] 909,33 unequal: No Solution Exploring Operation: 101-9=92, Resulting Numbers: [92] 92,33 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: 33:[85, 99, 47], Operations: ['94/2=47'] Exploring Operation: 99-85=14, Resulting Numbers: [47, 14] Generated Node #0,3,0: 33:[47, 14] Operation: 99-85=14 Exploring Operation: 99-47=52, Resulting Numbers: [85, 52] Generated Node #0,3,1: 33:[85, 52] Operation: 99-47=52 Exploring Operation: 85+99=184, Resulting Numbers: [47, 184] Generated Node #0,3,2: 33:[47, 184] Operation: 85+99=184 Exploring Operation: 85+47=132, Resulting Numbers: [99, 132] Generated Node #0,3,3: 33:[99, 132] Operation: 85+47=132 Exploring Operation: 85-47=38, Resulting Numbers: [99, 38] Generated Node #0,3,4: 33:[99, 38] Operation: 85-47=38 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 33:[47, 14], Operations: ['94/2=47', '99-85=14'] Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,33 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[2, 85, 99, 94], Operations: [] Exploring Operation: 94/2=47, Resulting Numbers: [85, 99, 47] Generated Node #0,3: 33:[85, 99, 47] Operation: 94/2=47 Moving to Node #0,3 Current State: 33:[85, 99, 47], Operations: ['94/2=47'] Exploring Operation: 99-85=14, Resulting Numbers: [47, 14] Generated Node #0,3,0: 33:[47, 14] Operation: 99-85=14 Moving to Node #0,3,0 Current State: 33:[47, 14], Operations: ['94/2=47', '99-85=14'] Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_5
sum_heuristic
[ 95, 53, 84, 28 ]
98
[ "95-53=42", "84-28=56", "42+56=98" ]
Current State: 98:[95, 53, 84, 28], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [84, 28, 42] Generated Node #2: [84, 28, 42] from Operation: 95-53=42 Current State: 98:[84, 28, 42], Operations: ['95-53=42'] Exploring Operation: 84-28=56, Resulting Numbers: [42, 56] Generated Node #3: [42, 56] from Operation: 84-28=56 Current State: 98:[42, 56], Operations: ['95-53=42', '84-28=56'] Exploring Operation: 42+56=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[95, 53, 84, 28], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [95, 53, 3] Generated Node #0,0: 98:[95, 53, 3] Operation: 84/28=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[95, 53, 3], Operations: ['84/28=3'] Exploring Operation: 95+3=98, Resulting Numbers: [53, 98] Generated Node #0,0,0: 98:[53, 98] Operation: 95+3=98 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[53, 98], Operations: ['84/28=3', '95+3=98'] Exploring Operation: 98-53=45, Resulting Numbers: [45] 45,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 19, 19, 74, 7 ]
80
[ "19/19=1", "74+7=81", "81-1=80" ]
Current State: 80:[19, 19, 74, 7], Operations: [] Exploring Operation: 19/19=1, Resulting Numbers: [74, 7, 1] Generated Node #2: [74, 7, 1] from Operation: 19/19=1 Current State: 80:[74, 7, 1], Operations: ['19/19=1'] Exploring Operation: 74+7=81, Resulting Numbers: [1, 81] Generated Node #3: [1, 81] from Operation: 74+7=81 Current State: 80:[1, 81], Operations: ['19/19=1', '74+7=81'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[19, 19, 74, 7], Operations: [] Exploring Operation: 19/19=1, Resulting Numbers: [74, 7, 1] Generated Node #0,0: 80:[74, 7, 1] Operation: 19/19=1 Exploring Operation: 19+19=38, Resulting Numbers: [74, 7, 38] Generated Node #0,1: 80:[74, 7, 38] Operation: 19+19=38 Exploring Operation: 74+7=81, Resulting Numbers: [19, 19, 81] Generated Node #0,2: 80:[19, 19, 81] Operation: 74+7=81 Exploring Operation: 19-19=0, Resulting Numbers: [74, 7, 0] Generated Node #0,3: 80:[74, 7, 0] Operation: 19-19=0 Exploring Operation: 19-7=12, Resulting Numbers: [19, 74, 12] Generated Node #0,4: 80:[19, 74, 12] Operation: 19-7=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[19, 19, 81], Operations: ['74+7=81'] Exploring Operation: 19+19=38, Resulting Numbers: [81, 38] Generated Node #0,2,0: 80:[81, 38] Operation: 19+19=38 Exploring Operation: 81-19=62, Resulting Numbers: [19, 62] Generated Node #0,2,1: 80:[19, 62] Operation: 81-19=62 Exploring Operation: 19/19=1, Resulting Numbers: [81, 1] Generated Node #0,2,2: 80:[81, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [81, 0] Generated Node #0,2,3: 80:[81, 0] Operation: 19-19=0 Exploring Operation: 81-19=62, Resulting Numbers: [19, 62] Generated Node #0,2,4: 80:[19, 62] Operation: 81-19=62 Moving to Node #0,2,2 Current State: 80:[81, 1], Operations: ['74+7=81', '19/19=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[19, 19, 74, 7], Operations: [] Exploring Operation: 74+7=81, Resulting Numbers: [19, 19, 81] Generated Node #0,2: 80:[19, 19, 81] Operation: 74+7=81 Moving to Node #0,2 Current State: 80:[19, 19, 81], Operations: ['74+7=81'] Exploring Operation: 19/19=1, Resulting Numbers: [81, 1] Generated Node #0,2,2: 80:[81, 1] Operation: 19/19=1 Moving to Node #0,2,2 Current State: 80:[81, 1], Operations: ['74+7=81', '19/19=1'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 92, 14, 2, 8 ]
91
[ "92-8=84", "14/2=7", "84+7=91" ]
Current State: 91:[92, 14, 2, 8], Operations: [] Exploring Operation: 92-8=84, Resulting Numbers: [14, 2, 84] Generated Node #2: [14, 2, 84] from Operation: 92-8=84 Current State: 91:[14, 2, 84], Operations: ['92-8=84'] Exploring Operation: 14/2=7, Resulting Numbers: [84, 7] Generated Node #3: [84, 7] from Operation: 14/2=7 Current State: 91:[84, 7], Operations: ['92-8=84', '14/2=7'] Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[92, 14, 2, 8], Operations: [] Exploring Operation: 14/2=7, Resulting Numbers: [92, 8, 7] Generated Node #0,0: 91:[92, 8, 7] Operation: 14/2=7 Exploring Operation: 92-2=90, Resulting Numbers: [14, 8, 90] Generated Node #0,1: 91:[14, 8, 90] Operation: 92-2=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[92, 8, 7], Operations: ['14/2=7'] Exploring Operation: 8+7=15, Resulting Numbers: [92, 15] Generated Node #0,0,0: 91:[92, 15] Operation: 8+7=15 Exploring Operation: 92-8=84, Resulting Numbers: [7, 84] Generated Node #0,0,1: 91:[7, 84] Operation: 92-8=84 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[92, 15], Operations: ['14/2=7', '8+7=15'] Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,91 unequal: No Solution Exploring Operation: 92+15=107, Resulting Numbers: [107] 107,91 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 #0,0,1 Current State: 91:[7, 84], Operations: ['14/2=7', '92-8=84'] Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[92, 14, 2, 8], Operations: [] Exploring Operation: 14/2=7, Resulting Numbers: [92, 8, 7] Generated Node #0,0: 91:[92, 8, 7] Operation: 14/2=7 Moving to Node #0,0 Current State: 91:[92, 8, 7], Operations: ['14/2=7'] Exploring Operation: 92-8=84, Resulting Numbers: [7, 84] Generated Node #0,0,1: 91:[7, 84] Operation: 92-8=84 Moving to Node #0,0,1 Current State: 91:[7, 84], Operations: ['14/2=7', '92-8=84'] Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 2, 88, 10, 26 ]
56
[ "26-10=16", "2*16=32", "88-32=56" ]
Current State: 56:[2, 88, 10, 26], Operations: [] Exploring Operation: 26-10=16, Resulting Numbers: [2, 88, 16] Generated Node #2: [2, 88, 16] from Operation: 26-10=16 Current State: 56:[2, 88, 16], Operations: ['26-10=16'] Exploring Operation: 2*16=32, Resulting Numbers: [88, 32] Generated Node #3: [88, 32] from Operation: 2*16=32 Current State: 56:[88, 32], Operations: ['26-10=16', '2*16=32'] Exploring Operation: 88-32=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[2, 88, 10, 26], Operations: [] Exploring Operation: 88-26=62, Resulting Numbers: [2, 10, 62] Generated Node #0,0: 56:[2, 10, 62] Operation: 88-26=62 Moving to Node #0,0 Current State: 56:[2, 10, 62], Operations: ['88-26=62'] Exploring Operation: 62-10=52, Resulting Numbers: [2, 52] Generated Node #0,0,0: 56:[2, 52] Operation: 62-10=52 Moving to Node #0,0,0 Current State: 56:[2, 52], Operations: ['88-26=62', '62-10=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,56 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 49, 2, 47, 16 ]
20
[ "49+2=51", "47-16=31", "51-31=20" ]
Current State: 20:[49, 2, 47, 16], Operations: [] Exploring Operation: 49+2=51, Resulting Numbers: [47, 16, 51] Generated Node #2: [47, 16, 51] from Operation: 49+2=51 Current State: 20:[47, 16, 51], Operations: ['49+2=51'] Exploring Operation: 47-16=31, Resulting Numbers: [51, 31] Generated Node #3: [51, 31] from Operation: 47-16=31 Current State: 20:[51, 31], Operations: ['49+2=51', '47-16=31'] Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[49, 2, 47, 16], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [2, 16, 2] Generated Node #0,0: 20:[2, 16, 2] Operation: 49-47=2 Exploring Operation: 49-16=33, Resulting Numbers: [2, 47, 33] Generated Node #0,1: 20:[2, 47, 33] Operation: 49-16=33 Moving to Node #0,0 Current State: 20:[2, 16, 2], Operations: ['49-47=2'] Exploring Operation: 2+16=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 20:[2, 18] Operation: 2+16=18 Exploring Operation: 16/2=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 20:[2, 8] Operation: 16/2=8 Moving to Node #0,1 Current State: 20:[2, 47, 33], Operations: ['49-16=33'] Exploring Operation: 47-33=14, Resulting Numbers: [2, 14] Generated Node #0,1,0: 20:[2, 14] Operation: 47-33=14 Exploring Operation: 47-2=45, Resulting Numbers: [33, 45] Generated Node #0,1,1: 20:[33, 45] Operation: 47-2=45 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[2, 14], Operations: ['49-16=33', '47-33=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,20 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,20 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 #0,1,1 Current State: 20:[33, 45], Operations: ['49-16=33', '47-2=45'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 33+45=78, Resulting Numbers: [78] 78,20 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: 20:[2, 18], Operations: ['49-47=2', '2+16=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[49, 2, 47, 16], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [2, 16, 2] Generated Node #0,0: 20:[2, 16, 2] Operation: 49-47=2 Moving to Node #0,0 Current State: 20:[2, 16, 2], Operations: ['49-47=2'] Exploring Operation: 2+16=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 20:[2, 18] Operation: 2+16=18 Moving to Node #0,0,0 Current State: 20:[2, 18], Operations: ['49-47=2', '2+16=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 48, 4, 74, 11 ]
73
[ "48/4=12", "74+11=85", "85-12=73" ]
Current State: 73:[48, 4, 74, 11], Operations: [] Exploring Operation: 48/4=12, Resulting Numbers: [74, 11, 12] Generated Node #2: [74, 11, 12] from Operation: 48/4=12 Current State: 73:[74, 11, 12], Operations: ['48/4=12'] Exploring Operation: 74+11=85, Resulting Numbers: [12, 85] Generated Node #3: [12, 85] from Operation: 74+11=85 Current State: 73:[12, 85], Operations: ['48/4=12', '74+11=85'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[48, 4, 74, 11], Operations: [] Exploring Operation: 4*11=44, Resulting Numbers: [48, 74, 44] Generated Node #0,0: 73:[48, 74, 44] Operation: 4*11=44 Exploring Operation: 48+4=52, Resulting Numbers: [74, 11, 52] Generated Node #0,1: 73:[74, 11, 52] Operation: 48+4=52 Moving to Node #0,0 Current State: 73:[48, 74, 44], Operations: ['4*11=44'] Exploring Operation: 74-44=30, Resulting Numbers: [48, 30] Generated Node #0,0,0: 73:[48, 30] Operation: 74-44=30 Exploring Operation: 48+44=92, Resulting Numbers: [74, 92] Generated Node #0,0,1: 73:[74, 92] Operation: 48+44=92 Moving to Node #0,1 Current State: 73:[74, 11, 52], Operations: ['48+4=52'] Exploring Operation: 11+52=63, Resulting Numbers: [74, 63] Generated Node #0,1,0: 73:[74, 63] Operation: 11+52=63 Exploring Operation: 74-11=63, Resulting Numbers: [52, 63] Generated Node #0,1,1: 73:[52, 63] Operation: 74-11=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[74, 63], Operations: ['48+4=52', '11+52=63'] Exploring Operation: 74-63=11, Resulting Numbers: [11] 11,73 unequal: No Solution Exploring Operation: 74+63=137, Resulting Numbers: [137] 137,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[52, 63], Operations: ['48+4=52', '74-11=63'] Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,73 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,73 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: 73:[74, 92], Operations: ['4*11=44', '48+44=92'] Exploring Operation: 74+92=166, Resulting Numbers: [166] 166,73 unequal: No Solution Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[48, 30], Operations: ['4*11=44', '74-44=30'] Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,73 unequal: No Solution Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,73 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 23, 58, 62, 80 ]
61
[ "23+58=81", "62+80=142", "142-81=61" ]
Current State: 61:[23, 58, 62, 80], Operations: [] Exploring Operation: 23+58=81, Resulting Numbers: [62, 80, 81] Generated Node #2: [62, 80, 81] from Operation: 23+58=81 Current State: 61:[62, 80, 81], Operations: ['23+58=81'] Exploring Operation: 62+80=142, Resulting Numbers: [81, 142] Generated Node #3: [81, 142] from Operation: 62+80=142 Current State: 61:[81, 142], Operations: ['23+58=81', '62+80=142'] Exploring Operation: 142-81=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[23, 58, 62, 80], Operations: [] Exploring Operation: 62-23=39, Resulting Numbers: [58, 80, 39] Generated Node #0,0: 61:[58, 80, 39] Operation: 62-23=39 Exploring Operation: 58-23=35, Resulting Numbers: [62, 80, 35] Generated Node #0,1: 61:[62, 80, 35] Operation: 58-23=35 Exploring Operation: 23+58=81, Resulting Numbers: [62, 80, 81] Generated Node #0,2: 61:[62, 80, 81] Operation: 23+58=81 Exploring Operation: 80-23=57, Resulting Numbers: [58, 62, 57] Generated Node #0,3: 61:[58, 62, 57] Operation: 80-23=57 Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[58, 62, 57], Operations: ['80-23=57'] Exploring Operation: 62-58=4, Resulting Numbers: [57, 4] Generated Node #0,3,0: 61:[57, 4] Operation: 62-58=4 Exploring Operation: 58-57=1, Resulting Numbers: [62, 1] Generated Node #0,3,1: 61:[62, 1] Operation: 58-57=1 Exploring Operation: 58+57=115, Resulting Numbers: [62, 115] Generated Node #0,3,2: 61:[62, 115] Operation: 58+57=115 Exploring Operation: 62-57=5, Resulting Numbers: [58, 5] Generated Node #0,3,3: 61:[58, 5] Operation: 62-57=5 Moving to Node #0,3,2 Current State: 61:[62, 115], Operations: ['80-23=57', '58+57=115'] Exploring Operation: 62+115=177, Resulting Numbers: [177] 177,61 unequal: No Solution Exploring Operation: 62*115=7130, Resulting Numbers: [7130] 7130,61 unequal: No Solution Exploring Operation: 115-62=53, Resulting Numbers: [53] 53,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[58, 5], Operations: ['80-23=57', '62-57=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[62, 1], Operations: ['80-23=57', '58-57=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[23, 58, 62, 80], Operations: [] Exploring Operation: 80-23=57, Resulting Numbers: [58, 62, 57] Generated Node #0,3: 61:[58, 62, 57] Operation: 80-23=57 Moving to Node #0,3 Current State: 61:[58, 62, 57], Operations: ['80-23=57'] Exploring Operation: 58-57=1, Resulting Numbers: [62, 1] Generated Node #0,3,1: 61:[62, 1] Operation: 58-57=1 Moving to Node #0,3,1 Current State: 61:[62, 1], Operations: ['80-23=57', '58-57=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 43, 84, 18, 11 ]
81
[ "43+11=54", "54/18=3", "84-3=81" ]
Current State: 81:[43, 84, 18, 11], Operations: [] Exploring Operation: 43+11=54, Resulting Numbers: [84, 18, 54] Generated Node #2: [84, 18, 54] from Operation: 43+11=54 Current State: 81:[84, 18, 54], Operations: ['43+11=54'] Exploring Operation: 54/18=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 54/18=3 Current State: 81:[84, 3], Operations: ['43+11=54', '54/18=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[43, 84, 18, 11], Operations: [] Exploring Operation: 43-18=25, Resulting Numbers: [84, 11, 25] Generated Node #0,0: 81:[84, 11, 25] Operation: 43-18=25 Exploring Operation: 43-11=32, Resulting Numbers: [84, 18, 32] Generated Node #0,1: 81:[84, 18, 32] Operation: 43-11=32 Exploring Operation: 18+11=29, Resulting Numbers: [43, 84, 29] Generated Node #0,2: 81:[43, 84, 29] Operation: 18+11=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[84, 11, 25], Operations: ['43-18=25'] Exploring Operation: 11+25=36, Resulting Numbers: [84, 36] Generated Node #0,0,0: 81:[84, 36] Operation: 11+25=36 Exploring Operation: 25-11=14, Resulting Numbers: [84, 14] Generated Node #0,0,1: 81:[84, 14] Operation: 25-11=14 Exploring Operation: 84-11=73, Resulting Numbers: [25, 73] Generated Node #0,0,2: 81:[25, 73] Operation: 84-11=73 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[84, 14], Operations: ['43-18=25', '25-11=14'] Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,81 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 #0,0,2 Current State: 81:[25, 73], Operations: ['43-18=25', '84-11=73'] Exploring Operation: 25*73=1825, Resulting Numbers: [1825] 1825,81 unequal: No Solution Exploring Operation: 73-25=48, Resulting Numbers: [48] 48,81 unequal: No Solution Exploring Operation: 25+73=98, Resulting Numbers: [98] 98,81 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:[84, 36], Operations: ['43-18=25', '11+25=36'] Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,81 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,81 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,81 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 #0,1 Current State: 81:[84, 18, 32], Operations: ['43-11=32'] Exploring Operation: 32-18=14, Resulting Numbers: [84, 14] Generated Node #0,1,0: 81:[84, 14] Operation: 32-18=14 Exploring Operation: 84-18=66, Resulting Numbers: [32, 66] Generated Node #0,1,1: 81:[32, 66] Operation: 84-18=66 Exploring Operation: 84+18=102, Resulting Numbers: [32, 102] Generated Node #0,1,2: 81:[32, 102] Operation: 84+18=102 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[84, 14], Operations: ['43-11=32', '32-18=14'] Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[32, 66], Operations: ['43-11=32', '84-18=66'] Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 32*66=2112, Resulting Numbers: [2112] 2112,81 unequal: No Solution Exploring Operation: 32+66=98, Resulting Numbers: [98] 98,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 81:[32, 102], Operations: ['43-11=32', '84+18=102'] Exploring Operation: 102-32=70, Resulting Numbers: [70] 70,81 unequal: No Solution Exploring Operation: 32+102=134, Resulting Numbers: [134] 134,81 unequal: No Solution Exploring Operation: 32*102=3264, Resulting Numbers: [3264] 3264,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[43, 84, 29], Operations: ['18+11=29'] Exploring Operation: 84-43=41, Resulting Numbers: [29, 41] Generated Node #0,2,0: 81:[29, 41] Operation: 84-43=41 Exploring Operation: 43-29=14, Resulting Numbers: [84, 14] Generated Node #0,2,1: 81:[84, 14] Operation: 43-29=14 Exploring Operation: 43+29=72, Resulting Numbers: [84, 72] Generated Node #0,2,2: 81:[84, 72] Operation: 43+29=72 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 81:[84, 14], Operations: ['18+11=29', '43-29=14'] Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,81 unequal: No Solution Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,81 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:[84, 72], Operations: ['18+11=29', '43+29=72'] Exploring Operation: 84-72=12, Resulting Numbers: [12] 12,81 unequal: No Solution Exploring Operation: 84*72=6048, Resulting Numbers: [6048] 6048,81 unequal: No Solution Exploring Operation: 84+72=156, Resulting Numbers: [156] 156,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[29, 41], Operations: ['18+11=29', '84-43=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,81 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,81 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 1, 46, 60, 63 ]
15
[ "46-1=45", "63-60=3", "45/3=15" ]
Current State: 15:[1, 46, 60, 63], Operations: [] Exploring Operation: 46-1=45, Resulting Numbers: [60, 63, 45] Generated Node #2: [60, 63, 45] from Operation: 46-1=45 Current State: 15:[60, 63, 45], Operations: ['46-1=45'] Exploring Operation: 63-60=3, Resulting Numbers: [45, 3] Generated Node #3: [45, 3] from Operation: 63-60=3 Current State: 15:[45, 3], Operations: ['46-1=45', '63-60=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[1, 46, 60, 63], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [1, 46, 3] Generated Node #0,0: 15:[1, 46, 3] Operation: 63-60=3 Exploring Operation: 63-46=17, Resulting Numbers: [1, 60, 17] Generated Node #0,1: 15:[1, 60, 17] Operation: 63-46=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[1, 46, 3], Operations: ['63-60=3'] Exploring Operation: 46-3=43, Resulting Numbers: [1, 43] Generated Node #0,0,0: 15:[1, 43] Operation: 46-3=43 Exploring Operation: 46-1=45, Resulting Numbers: [3, 45] Generated Node #0,0,1: 15:[3, 45] Operation: 46-1=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[1, 43], Operations: ['63-60=3', '46-3=43'] Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,15 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,15 unequal: No Solution No 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: 15:[3, 45], Operations: ['63-60=3', '46-1=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[1, 46, 60, 63], Operations: [] Exploring Operation: 63-60=3, Resulting Numbers: [1, 46, 3] Generated Node #0,0: 15:[1, 46, 3] Operation: 63-60=3 Moving to Node #0,0 Current State: 15:[1, 46, 3], Operations: ['63-60=3'] Exploring Operation: 46-1=45, Resulting Numbers: [3, 45] Generated Node #0,0,1: 15:[3, 45] Operation: 46-1=45 Moving to Node #0,0,1 Current State: 15:[3, 45], Operations: ['63-60=3', '46-1=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 4, 94, 8, 4 ]
94
[ "4+94=98", "8-4=4", "98-4=94" ]
Current State: 94:[4, 94, 8, 4], Operations: [] Exploring Operation: 4+94=98, Resulting Numbers: [8, 98] Generated Node #2: [8, 98] from Operation: 4+94=98 Current State: 94:[8, 98], Operations: ['4+94=98'] Exploring Operation: 8-4=4, Resulting Numbers: [98, 4] Generated Node #3: [98, 4] from Operation: 8-4=4 Current State: 94:[98, 4], Operations: ['4+94=98', '8-4=4'] Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[4, 94, 8, 4], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [4, 94, 2] Generated Node #0,0: 94:[4, 94, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [94, 4, 4] Generated Node #0,1: 94:[94, 4, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [94, 4, 2] Generated Node #0,2: 94:[94, 4, 2] Operation: 8/4=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[4, 94, 2], Operations: ['8/4=2'] Exploring Operation: 94/2=47, Resulting Numbers: [4, 47] Generated Node #0,0,0: 94:[4, 47] Operation: 94/2=47 Exploring Operation: 4-2=2, Resulting Numbers: [94, 2] Generated Node #0,0,1: 94:[94, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [94, 2] Generated Node #0,0,2: 94:[94, 2] Operation: 4/2=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[94, 2], Operations: ['8/4=2', '4-2=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[94, 2], Operations: ['8/4=2', '4/2=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[4, 47], Operations: ['8/4=2', '94/2=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,94 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,94 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[94, 4, 2], Operations: ['8/4=2'] Exploring Operation: 94/2=47, Resulting Numbers: [4, 47] Generated Node #0,2,0: 94:[4, 47] Operation: 94/2=47 Exploring Operation: 4-2=2, Resulting Numbers: [94, 2] Generated Node #0,2,1: 94:[94, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [94, 2] Generated Node #0,2,2: 94:[94, 2] Operation: 4/2=2 Moving to Node #0,2,1 Current State: 94:[94, 2], Operations: ['8/4=2', '4-2=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[94, 2], Operations: ['8/4=2', '4/2=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[4, 47], Operations: ['8/4=2', '94/2=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,94 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[94, 4, 4], Operations: ['8-4=4'] Exploring Operation: 4/4=1, Resulting Numbers: [94, 1] Generated Node #0,1,0: 94:[94, 1] Operation: 4/4=1 Exploring Operation: 94+4=98, Resulting Numbers: [4, 98] Generated Node #0,1,1: 94:[4, 98] Operation: 94+4=98 Exploring Operation: 4-4=0, Resulting Numbers: [94, 0] Generated Node #0,1,2: 94:[94, 0] Operation: 4-4=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[94, 1], Operations: ['8-4=4', '4/4=1'] Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[4, 94, 8, 4], Operations: [] Exploring Operation: 8-4=4, Resulting Numbers: [94, 4, 4] Generated Node #0,1: 94:[94, 4, 4] Operation: 8-4=4 Moving to Node #0,1 Current State: 94:[94, 4, 4], Operations: ['8-4=4'] Exploring Operation: 4/4=1, Resulting Numbers: [94, 1] Generated Node #0,1,0: 94:[94, 1] Operation: 4/4=1 Moving to Node #0,1,0 Current State: 94:[94, 1], Operations: ['8-4=4', '4/4=1'] Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_3
mult_heuristic
[ 4, 93, 2, 37 ]
48
[ "4*2=8", "93-37=56", "56-8=48" ]
Current State: 48:[4, 93, 2, 37], Operations: [] Exploring Operation: 4*2=8, Resulting Numbers: [93, 37, 8] Generated Node #2: [93, 37, 8] from Operation: 4*2=8 Current State: 48:[93, 37, 8], Operations: ['4*2=8'] Exploring Operation: 93-37=56, Resulting Numbers: [8, 56] Generated Node #3: [8, 56] from Operation: 93-37=56 Current State: 48:[8, 56], Operations: ['4*2=8', '93-37=56'] Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[4, 93, 2, 37], Operations: [] Exploring Operation: 93-37=56, Resulting Numbers: [4, 2, 56] Generated Node #0,0: 48:[4, 2, 56] Operation: 93-37=56 Moving to Node #0,0 Current State: 48:[4, 2, 56], Operations: ['93-37=56'] Exploring Operation: 56/4=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 48:[2, 14] Operation: 56/4=14 Moving to Node #0,0,0 Current State: 48:[2, 14], Operations: ['93-37=56', '56/4=14'] Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,48 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 26, 10, 27, 10 ]
20
[ "27-26=1", "10+10=20", "1*20=20" ]
Current State: 20:[26, 10, 27, 10], Operations: [] Exploring Operation: 27-26=1, Resulting Numbers: [10, 10, 1] Generated Node #2: [10, 10, 1] from Operation: 27-26=1 Current State: 20:[10, 10, 1], Operations: ['27-26=1'] Exploring Operation: 10+10=20, Resulting Numbers: [1, 20] Generated Node #3: [1, 20] from Operation: 10+10=20 Current State: 20:[1, 20], Operations: ['27-26=1', '10+10=20'] Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[26, 10, 27, 10], Operations: [] Exploring Operation: 27-10=17, Resulting Numbers: [26, 10, 17] Generated Node #0,0: 20:[26, 10, 17] Operation: 27-10=17 Exploring Operation: 26-10=16, Resulting Numbers: [27, 10, 16] Generated Node #0,1: 20:[27, 10, 16] Operation: 26-10=16 Exploring Operation: 27-26=1, Resulting Numbers: [10, 10, 1] Generated Node #0,2: 20:[10, 10, 1] Operation: 27-26=1 Exploring Operation: 27-10=17, Resulting Numbers: [26, 10, 17] Generated Node #0,3: 20:[26, 10, 17] Operation: 27-10=17 Moving to Node #0,2 Current State: 20:[10, 10, 1], Operations: ['27-26=1'] Exploring Operation: 10/1=10, Resulting Numbers: [10, 10] Generated Node #0,2,0: 20:[10, 10] Operation: 10/1=10 Exploring Operation: 10/1=10, Resulting Numbers: [10, 10] Generated Node #0,2,1: 20:[10, 10] Operation: 10/1=10 Exploring Operation: 10*1=10, Resulting Numbers: [10, 10] Generated Node #0,2,2: 20:[10, 10] Operation: 10*1=10 Exploring Operation: 10*1=10, Resulting Numbers: [10, 10] Generated Node #0,2,3: 20:[10, 10] Operation: 10*1=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[10, 10], Operations: ['27-26=1', '10/1=10'] Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,20 unequal: No Solution Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[26, 10, 27, 10], Operations: [] Exploring Operation: 27-26=1, Resulting Numbers: [10, 10, 1] Generated Node #0,2: 20:[10, 10, 1] Operation: 27-26=1 Moving to Node #0,2 Current State: 20:[10, 10, 1], Operations: ['27-26=1'] Exploring Operation: 10/1=10, Resulting Numbers: [10, 10] Generated Node #0,2,0: 20:[10, 10] Operation: 10/1=10 Moving to Node #0,2,0 Current State: 20:[10, 10], Operations: ['27-26=1', '10/1=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 48, 10, 10, 28 ]
21
[ "48-28=20", "10/10=1", "20+1=21" ]
Current State: 21:[48, 10, 10, 28], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [10, 10, 20] Generated Node #2: [10, 10, 20] from Operation: 48-28=20 Current State: 21:[10, 10, 20], Operations: ['48-28=20'] Exploring Operation: 10/10=1, Resulting Numbers: [20, 1] Generated Node #3: [20, 1] from Operation: 10/10=1 Current State: 21:[20, 1], Operations: ['48-28=20', '10/10=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[48, 10, 10, 28], Operations: [] Exploring Operation: 48-10=38, Resulting Numbers: [10, 28, 38] Generated Node #0,0: 21:[10, 28, 38] Operation: 48-10=38 Exploring Operation: 48-28=20, Resulting Numbers: [10, 10, 20] Generated Node #0,1: 21:[10, 10, 20] Operation: 48-28=20 Exploring Operation: 48-10=38, Resulting Numbers: [10, 28, 38] Generated Node #0,2: 21:[10, 28, 38] Operation: 48-10=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[10, 10, 20], Operations: ['48-28=20'] Exploring Operation: 10-10=0, Resulting Numbers: [20, 0] Generated Node #0,1,0: 21:[20, 0] Operation: 10-10=0 Exploring Operation: 10+10=20, Resulting Numbers: [20, 20] Generated Node #0,1,1: 21:[20, 20] Operation: 10+10=20 Exploring Operation: 10/10=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 21:[20, 1] Operation: 10/10=1 Moving to Node #0,1,1 Current State: 21:[20, 20], Operations: ['48-28=20', '10+10=20'] Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,21 unequal: No Solution Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,21 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[20, 1], Operations: ['48-28=20', '10/10=1'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[48, 10, 10, 28], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [10, 10, 20] Generated Node #0,1: 21:[10, 10, 20] Operation: 48-28=20 Moving to Node #0,1 Current State: 21:[10, 10, 20], Operations: ['48-28=20'] Exploring Operation: 10/10=1, Resulting Numbers: [20, 1] Generated Node #0,1,2: 21:[20, 1] Operation: 10/10=1 Moving to Node #0,1,2 Current State: 21:[20, 1], Operations: ['48-28=20', '10/10=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 19, 51, 11, 96 ]
39
[ "19-11=8", "96/8=12", "51-12=39" ]
Current State: 39:[19, 51, 11, 96], Operations: [] Exploring Operation: 19-11=8, Resulting Numbers: [51, 96, 8] Generated Node #2: [51, 96, 8] from Operation: 19-11=8 Current State: 39:[51, 96, 8], Operations: ['19-11=8'] Exploring Operation: 96/8=12, Resulting Numbers: [51, 12] Generated Node #3: [51, 12] from Operation: 96/8=12 Current State: 39:[51, 12], Operations: ['19-11=8', '96/8=12'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[19, 51, 11, 96], Operations: [] Exploring Operation: 96-51=45, Resulting Numbers: [19, 11, 45] Generated Node #0,0: 39:[19, 11, 45] Operation: 96-51=45 Exploring Operation: 96-19=77, Resulting Numbers: [51, 11, 77] Generated Node #0,1: 39:[51, 11, 77] Operation: 96-19=77 Moving to Node #0,0 Current State: 39:[19, 11, 45], Operations: ['96-51=45'] Exploring Operation: 19-11=8, Resulting Numbers: [45, 8] Generated Node #0,0,0: 39:[45, 8] Operation: 19-11=8 Exploring Operation: 45-11=34, Resulting Numbers: [19, 34] Generated Node #0,0,1: 39:[19, 34] Operation: 45-11=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[45, 8], Operations: ['96-51=45', '19-11=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[19, 34], Operations: ['96-51=45', '45-11=34'] Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,39 unequal: No Solution Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 39:[51, 11, 77], Operations: ['96-19=77'] Exploring Operation: 77-51=26, Resulting Numbers: [11, 26] Generated Node #0,1,0: 39:[11, 26] Operation: 77-51=26 Exploring Operation: 77/11=7, Resulting Numbers: [51, 7] Generated Node #0,1,1: 39:[51, 7] Operation: 77/11=7 Moving to Node #0,1,0 Current State: 39:[11, 26], Operations: ['96-19=77', '77-51=26'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[51, 7], Operations: ['96-19=77', '77/11=7'] Exploring Operation: 51+7=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,39 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 31, 51, 69, 13 ]
62
[ "51-31=20", "69+13=82", "82-20=62" ]
Current State: 62:[31, 51, 69, 13], Operations: [] Exploring Operation: 51-31=20, Resulting Numbers: [69, 13, 20] Generated Node #2: [69, 13, 20] from Operation: 51-31=20 Current State: 62:[69, 13, 20], Operations: ['51-31=20'] Exploring Operation: 69+13=82, Resulting Numbers: [20, 82] Generated Node #3: [20, 82] from Operation: 69+13=82 Current State: 62:[20, 82], Operations: ['51-31=20', '69+13=82'] Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[31, 51, 69, 13], Operations: [] Exploring Operation: 69-51=18, Resulting Numbers: [31, 13, 18] Generated Node #0,0: 62:[31, 13, 18] Operation: 69-51=18 Exploring Operation: 51-13=38, Resulting Numbers: [31, 69, 38] Generated Node #0,1: 62:[31, 69, 38] Operation: 51-13=38 Exploring Operation: 51-31=20, Resulting Numbers: [69, 13, 20] Generated Node #0,2: 62:[69, 13, 20] Operation: 51-31=20 Exploring Operation: 51+13=64, Resulting Numbers: [31, 69, 64] Generated Node #0,3: 62:[31, 69, 64] Operation: 51+13=64 Exploring Operation: 69-13=56, Resulting Numbers: [31, 51, 56] Generated Node #0,4: 62:[31, 51, 56] Operation: 69-13=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[31, 69, 64], Operations: ['51+13=64'] Exploring Operation: 64-31=33, Resulting Numbers: [69, 33] Generated Node #0,3,0: 62:[69, 33] Operation: 64-31=33 Exploring Operation: 69-64=5, Resulting Numbers: [31, 5] Generated Node #0,3,1: 62:[31, 5] Operation: 69-64=5 Exploring Operation: 69-31=38, Resulting Numbers: [64, 38] Generated Node #0,3,2: 62:[64, 38] Operation: 69-31=38 Exploring Operation: 31+64=95, Resulting Numbers: [69, 95] Generated Node #0,3,3: 62:[69, 95] Operation: 31+64=95 Exploring Operation: 31+69=100, Resulting Numbers: [64, 100] Generated Node #0,3,4: 62:[64, 100] Operation: 31+69=100 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[31, 5], Operations: ['51+13=64', '69-64=5'] Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[69, 33], Operations: ['51+13=64', '64-31=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,62 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 62:[64, 38], Operations: ['51+13=64', '69-31=38'] Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 64+38=102, Resulting Numbers: [102] 102,62 unequal: No Solution Exploring Operation: 64*38=2432, Resulting Numbers: [2432] 2432,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 62:[69, 95], Operations: ['51+13=64', '31+64=95'] Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 69+95=164, Resulting Numbers: [164] 164,62 unequal: No Solution Exploring Operation: 69*95=6555, Resulting Numbers: [6555] 6555,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 62:[64, 100], Operations: ['51+13=64', '31+69=100'] Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 64*100=6400, Resulting Numbers: [6400] 6400,62 unequal: No Solution Exploring Operation: 64+100=164, Resulting Numbers: [164] 164,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[31, 69, 38], Operations: ['51-13=38'] Exploring Operation: 31+69=100, Resulting Numbers: [38, 100] Generated Node #0,1,0: 62:[38, 100] Operation: 31+69=100 Exploring Operation: 69-38=31, Resulting Numbers: [31, 31] Generated Node #0,1,1: 62:[31, 31] Operation: 69-38=31 Exploring Operation: 69-31=38, Resulting Numbers: [38, 38] Generated Node #0,1,2: 62:[38, 38] Operation: 69-31=38 Exploring Operation: 31+38=69, Resulting Numbers: [69, 69] Generated Node #0,1,3: 62:[69, 69] Operation: 31+38=69 Exploring Operation: 38-31=7, Resulting Numbers: [69, 7] Generated Node #0,1,4: 62:[69, 7] Operation: 38-31=7 Moving to Node #0,1,1 Current State: 62:[31, 31], Operations: ['51-13=38', '69-38=31'] Exploring Operation: 31-31=0, Resulting Numbers: [0] 0,62 unequal: No Solution Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[31, 51, 69, 13], Operations: [] Exploring Operation: 51-13=38, Resulting Numbers: [31, 69, 38] Generated Node #0,1: 62:[31, 69, 38] Operation: 51-13=38 Moving to Node #0,1 Current State: 62:[31, 69, 38], Operations: ['51-13=38'] Exploring Operation: 69-38=31, Resulting Numbers: [31, 31] Generated Node #0,1,1: 62:[31, 31] Operation: 69-38=31 Moving to Node #0,1,1 Current State: 62:[31, 31], Operations: ['51-13=38', '69-38=31'] Exploring Operation: 31+31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 54, 56, 78, 16 ]
16
[ "54+56=110", "78+16=94", "110-94=16" ]
Current State: 16:[54, 56, 78, 16], Operations: [] Exploring Operation: 54+56=110, Resulting Numbers: [78, 16, 110] Generated Node #2: [78, 16, 110] from Operation: 54+56=110 Current State: 16:[78, 16, 110], Operations: ['54+56=110'] Exploring Operation: 78+16=94, Resulting Numbers: [110, 94] Generated Node #3: [110, 94] from Operation: 78+16=94 Current State: 16:[110, 94], Operations: ['54+56=110', '78+16=94'] Exploring Operation: 110-94=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[54, 56, 78, 16], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [78, 16, 2] Generated Node #0,0: 16:[78, 16, 2] Operation: 56-54=2 Exploring Operation: 78-54=24, Resulting Numbers: [56, 16, 24] Generated Node #0,1: 16:[56, 16, 24] Operation: 78-54=24 Exploring Operation: 78-56=22, Resulting Numbers: [54, 16, 22] Generated Node #0,2: 16:[54, 16, 22] Operation: 78-56=22 Moving to Node #0,2 Current State: 16:[54, 16, 22], Operations: ['78-56=22'] Exploring Operation: 22-16=6, Resulting Numbers: [54, 6] Generated Node #0,2,0: 16:[54, 6] Operation: 22-16=6 Exploring Operation: 54-22=32, Resulting Numbers: [16, 32] Generated Node #0,2,1: 16:[16, 32] Operation: 54-22=32 Exploring Operation: 54-16=38, Resulting Numbers: [22, 38] Generated Node #0,2,2: 16:[22, 38] Operation: 54-16=38 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[16, 32], Operations: ['78-56=22', '54-22=32'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[54, 56, 78, 16], Operations: [] Exploring Operation: 78-56=22, Resulting Numbers: [54, 16, 22] Generated Node #0,2: 16:[54, 16, 22] Operation: 78-56=22 Moving to Node #0,2 Current State: 16:[54, 16, 22], Operations: ['78-56=22'] Exploring Operation: 54-22=32, Resulting Numbers: [16, 32] Generated Node #0,2,1: 16:[16, 32] Operation: 54-22=32 Moving to Node #0,2,1 Current State: 16:[16, 32], Operations: ['78-56=22', '54-22=32'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 1, 17, 64, 17 ]
99
[ "1+17=18", "64+17=81", "18+81=99" ]
Current State: 99:[1, 17, 64, 17], Operations: [] Exploring Operation: 1+17=18, Resulting Numbers: [64, 18] Generated Node #2: [64, 18] from Operation: 1+17=18 Current State: 99:[64, 18], Operations: ['1+17=18'] Exploring Operation: 64+17=81, Resulting Numbers: [18, 81] Generated Node #3: [18, 81] from Operation: 64+17=81 Current State: 99:[18, 81], Operations: ['1+17=18', '64+17=81'] Exploring Operation: 18+81=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[1, 17, 64, 17], Operations: [] Exploring Operation: 64-17=47, Resulting Numbers: [1, 17, 47] Generated Node #0,0: 99:[1, 17, 47] Operation: 64-17=47 Exploring Operation: 64-17=47, Resulting Numbers: [1, 17, 47] Generated Node #0,1: 99:[1, 17, 47] Operation: 64-17=47 Exploring Operation: 17+64=81, Resulting Numbers: [1, 17, 81] Generated Node #0,2: 99:[1, 17, 81] Operation: 17+64=81 Exploring Operation: 64+17=81, Resulting Numbers: [1, 17, 81] Generated Node #0,3: 99:[1, 17, 81] Operation: 64+17=81 Exploring Operation: 17+17=34, Resulting Numbers: [1, 64, 34] Generated Node #0,4: 99:[1, 64, 34] Operation: 17+17=34 Moving to Node #0,0 Current State: 99:[1, 17, 47], Operations: ['64-17=47'] Exploring Operation: 17/1=17, Resulting Numbers: [47, 17] Generated Node #0,0,0: 99:[47, 17] Operation: 17/1=17 Exploring Operation: 47-17=30, Resulting Numbers: [1, 30] Generated Node #0,0,1: 99:[1, 30] Operation: 47-17=30 Exploring Operation: 17-1=16, Resulting Numbers: [47, 16] Generated Node #0,0,2: 99:[47, 16] Operation: 17-1=16 Exploring Operation: 47-1=46, Resulting Numbers: [17, 46] Generated Node #0,0,3: 99:[17, 46] Operation: 47-1=46 Exploring Operation: 1*17=17, Resulting Numbers: [47, 17] Generated Node #0,0,4: 99:[47, 17] Operation: 1*17=17 Moving to Node #0,1 Current State: 99:[1, 17, 47], Operations: ['64-17=47'] Exploring Operation: 47-17=30, Resulting Numbers: [1, 30] Generated Node #0,1,0: 99:[1, 30] Operation: 47-17=30 Exploring Operation: 17-1=16, Resulting Numbers: [47, 16] Generated Node #0,1,1: 99:[47, 16] Operation: 17-1=16 Exploring Operation: 1*17=17, Resulting Numbers: [47, 17] Generated Node #0,1,2: 99:[47, 17] Operation: 1*17=17 Exploring Operation: 47-1=46, Resulting Numbers: [17, 46] Generated Node #0,1,3: 99:[17, 46] Operation: 47-1=46 Exploring Operation: 17/1=17, Resulting Numbers: [47, 17] Generated Node #0,1,4: 99:[47, 17] Operation: 17/1=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[1, 30], Operations: ['64-17=47', '47-17=30'] Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[47, 16], Operations: ['64-17=47', '17-1=16'] Exploring Operation: 47*16=752, Resulting Numbers: [752] 752,99 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[17, 46], Operations: ['64-17=47', '47-1=46'] Exploring Operation: 17*46=782, Resulting Numbers: [782] 782,99 unequal: No Solution Exploring Operation: 17+46=63, Resulting Numbers: [63] 63,99 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[47, 17], Operations: ['64-17=47', '1*17=17'] Exploring Operation: 47*17=799, Resulting Numbers: [799] 799,99 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 99:[47, 17], Operations: ['64-17=47', '17/1=17'] Exploring Operation: 47*17=799, Resulting Numbers: [799] 799,99 unequal: No Solution Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,99 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,99 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: 99:[1, 17, 81], Operations: ['17+64=81'] Exploring Operation: 17-1=16, Resulting Numbers: [81, 16] Generated Node #0,2,0: 99:[81, 16] Operation: 17-1=16 Exploring Operation: 17/1=17, Resulting Numbers: [81, 17] Generated Node #0,2,1: 99:[81, 17] Operation: 17/1=17 Exploring Operation: 17+81=98, Resulting Numbers: [1, 98] Generated Node #0,2,2: 99:[1, 98] Operation: 17+81=98 Exploring Operation: 1+81=82, Resulting Numbers: [17, 82] Generated Node #0,2,3: 99:[17, 82] Operation: 1+81=82 Exploring Operation: 1*17=17, Resulting Numbers: [81, 17] Generated Node #0,2,4: 99:[81, 17] Operation: 1*17=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[1, 98], Operations: ['17+64=81', '17+81=98'] Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,99 unequal: No Solution Exploring Operation: 1*98=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 1+98=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[1, 17, 64, 17], Operations: [] Exploring Operation: 17+64=81, Resulting Numbers: [1, 17, 81] Generated Node #0,2: 99:[1, 17, 81] Operation: 17+64=81 Moving to Node #0,2 Current State: 99:[1, 17, 81], Operations: ['17+64=81'] Exploring Operation: 17+81=98, Resulting Numbers: [1, 98] Generated Node #0,2,2: 99:[1, 98] Operation: 17+81=98 Moving to Node #0,2,2 Current State: 99:[1, 98], Operations: ['17+64=81', '17+81=98'] Exploring Operation: 1+98=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 68, 35, 10, 67 ]
44
[ "68-35=33", "10+67=77", "77-33=44" ]
Current State: 44:[68, 35, 10, 67], Operations: [] Exploring Operation: 68-35=33, Resulting Numbers: [10, 67, 33] Generated Node #2: [10, 67, 33] from Operation: 68-35=33 Current State: 44:[10, 67, 33], Operations: ['68-35=33'] Exploring Operation: 10+67=77, Resulting Numbers: [33, 77] Generated Node #3: [33, 77] from Operation: 10+67=77 Current State: 44:[33, 77], Operations: ['68-35=33', '10+67=77'] Exploring Operation: 77-33=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[68, 35, 10, 67], Operations: [] Exploring Operation: 68-35=33, Resulting Numbers: [10, 67, 33] Generated Node #0,0: 44:[10, 67, 33] Operation: 68-35=33 Exploring Operation: 68-67=1, Resulting Numbers: [35, 10, 1] Generated Node #0,1: 44:[35, 10, 1] Operation: 68-67=1 Exploring Operation: 67-35=32, Resulting Numbers: [68, 10, 32] Generated Node #0,2: 44:[68, 10, 32] Operation: 67-35=32 Exploring Operation: 68-10=58, Resulting Numbers: [35, 67, 58] Generated Node #0,3: 44:[35, 67, 58] Operation: 68-10=58 Moving to Node #0,1 Current State: 44:[35, 10, 1], Operations: ['68-67=1'] Exploring Operation: 10+1=11, Resulting Numbers: [35, 11] Generated Node #0,1,0: 44:[35, 11] Operation: 10+1=11 Exploring Operation: 35-10=25, Resulting Numbers: [1, 25] Generated Node #0,1,1: 44:[1, 25] Operation: 35-10=25 Exploring Operation: 35+1=36, Resulting Numbers: [10, 36] Generated Node #0,1,2: 44:[10, 36] Operation: 35+1=36 Exploring Operation: 35+10=45, Resulting Numbers: [1, 45] Generated Node #0,1,3: 44:[1, 45] Operation: 35+10=45 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 44:[1, 45], Operations: ['68-67=1', '35+10=45'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[68, 35, 10, 67], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [35, 10, 1] Generated Node #0,1: 44:[35, 10, 1] Operation: 68-67=1 Moving to Node #0,1 Current State: 44:[35, 10, 1], Operations: ['68-67=1'] Exploring Operation: 35+10=45, Resulting Numbers: [1, 45] Generated Node #0,1,3: 44:[1, 45] Operation: 35+10=45 Moving to Node #0,1,3 Current State: 44:[1, 45], Operations: ['68-67=1', '35+10=45'] Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 50, 42, 32, 34 ]
58
[ "50-42=8", "32+34=66", "66-8=58" ]
Current State: 58:[50, 42, 32, 34], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [32, 34, 8] Generated Node #2: [32, 34, 8] from Operation: 50-42=8 Current State: 58:[32, 34, 8], Operations: ['50-42=8'] Exploring Operation: 32+34=66, Resulting Numbers: [8, 66] Generated Node #3: [8, 66] from Operation: 32+34=66 Current State: 58:[8, 66], Operations: ['50-42=8', '32+34=66'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[50, 42, 32, 34], Operations: [] Exploring Operation: 42-34=8, Resulting Numbers: [50, 32, 8] Generated Node #0,0: 58:[50, 32, 8] Operation: 42-34=8 Exploring Operation: 50-42=8, Resulting Numbers: [32, 34, 8] Generated Node #0,1: 58:[32, 34, 8] Operation: 50-42=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[32, 34, 8], Operations: ['50-42=8'] Exploring Operation: 34-32=2, Resulting Numbers: [8, 2] Generated Node #0,1,0: 58:[8, 2] Operation: 34-32=2 Exploring Operation: 34-8=26, Resulting Numbers: [32, 26] Generated Node #0,1,1: 58:[32, 26] Operation: 34-8=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[8, 2], Operations: ['50-42=8', '34-32=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,58 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[32, 26], Operations: ['50-42=8', '34-8=26'] Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[50, 42, 32, 34], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [32, 34, 8] Generated Node #0,1: 58:[32, 34, 8] Operation: 50-42=8 Moving to Node #0,1 Current State: 58:[32, 34, 8], Operations: ['50-42=8'] Exploring Operation: 34-8=26, Resulting Numbers: [32, 26] Generated Node #0,1,1: 58:[32, 26] Operation: 34-8=26 Moving to Node #0,1,1 Current State: 58:[32, 26], Operations: ['50-42=8', '34-8=26'] Exploring Operation: 32+26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 23, 33, 22, 19 ]
13
[ "33-23=10", "22-19=3", "10+3=13" ]
Current State: 13:[23, 33, 22, 19], Operations: [] Exploring Operation: 33-23=10, Resulting Numbers: [22, 19, 10] Generated Node #2: [22, 19, 10] from Operation: 33-23=10 Current State: 13:[22, 19, 10], Operations: ['33-23=10'] Exploring Operation: 22-19=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 22-19=3 Current State: 13:[10, 3], Operations: ['33-23=10', '22-19=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[23, 33, 22, 19], Operations: [] Exploring Operation: 33-23=10, Resulting Numbers: [22, 19, 10] Generated Node #0,0: 13:[22, 19, 10] Operation: 33-23=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[22, 19, 10], Operations: ['33-23=10'] Exploring Operation: 22-10=12, Resulting Numbers: [19, 12] Generated Node #0,0,0: 13:[19, 12] Operation: 22-10=12 Moving to Node #0,0,0 Current State: 13:[19, 12], Operations: ['33-23=10', '22-10=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,13 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
[ 3, 8, 74, 28 ]
51
[ "8-3=5", "74-28=46", "5+46=51" ]
Current State: 51:[3, 8, 74, 28], Operations: [] Exploring Operation: 8-3=5, Resulting Numbers: [74, 28, 5] Generated Node #2: [74, 28, 5] from Operation: 8-3=5 Current State: 51:[74, 28, 5], Operations: ['8-3=5'] Exploring Operation: 74-28=46, Resulting Numbers: [5, 46] Generated Node #3: [5, 46] from Operation: 74-28=46 Current State: 51:[5, 46], Operations: ['8-3=5', '74-28=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[3, 8, 74, 28], Operations: [] Exploring Operation: 74-28=46, Resulting Numbers: [3, 8, 46] Generated Node #0,0: 51:[3, 8, 46] Operation: 74-28=46 Exploring Operation: 74-3=71, Resulting Numbers: [8, 28, 71] Generated Node #0,1: 51:[8, 28, 71] Operation: 74-3=71 Exploring Operation: 74-8=66, Resulting Numbers: [3, 28, 66] Generated Node #0,2: 51:[3, 28, 66] Operation: 74-8=66 Exploring Operation: 28-8=20, Resulting Numbers: [3, 74, 20] Generated Node #0,3: 51:[3, 74, 20] Operation: 28-8=20 Exploring Operation: 8-3=5, Resulting Numbers: [74, 28, 5] Generated Node #0,4: 51:[74, 28, 5] Operation: 8-3=5 Moving to Node #0,0 Current State: 51:[3, 8, 46], Operations: ['74-28=46'] Exploring Operation: 3+46=49, Resulting Numbers: [8, 49] Generated Node #0,0,0: 51:[8, 49] Operation: 3+46=49 Exploring Operation: 3+8=11, Resulting Numbers: [46, 11] Generated Node #0,0,1: 51:[46, 11] Operation: 3+8=11 Exploring Operation: 3*8=24, Resulting Numbers: [46, 24] Generated Node #0,0,2: 51:[46, 24] Operation: 3*8=24 Exploring Operation: 8+46=54, Resulting Numbers: [3, 54] Generated Node #0,0,3: 51:[3, 54] Operation: 8+46=54 Exploring Operation: 8-3=5, Resulting Numbers: [46, 5] Generated Node #0,0,4: 51:[46, 5] Operation: 8-3=5 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 51:[3, 54], Operations: ['74-28=46', '8+46=54'] Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,51 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[3, 8, 74, 28], Operations: [] Exploring Operation: 74-28=46, Resulting Numbers: [3, 8, 46] Generated Node #0,0: 51:[3, 8, 46] Operation: 74-28=46 Moving to Node #0,0 Current State: 51:[3, 8, 46], Operations: ['74-28=46'] Exploring Operation: 8+46=54, Resulting Numbers: [3, 54] Generated Node #0,0,3: 51:[3, 54] Operation: 8+46=54 Moving to Node #0,0,3 Current State: 51:[3, 54], Operations: ['74-28=46', '8+46=54'] Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 89, 44, 94, 45 ]
35
[ "94-89=5", "45/5=9", "44-9=35" ]
Current State: 35:[89, 44, 94, 45], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [44, 45, 5] Generated Node #2: [44, 45, 5] from Operation: 94-89=5 Current State: 35:[44, 45, 5], Operations: ['94-89=5'] Exploring Operation: 45/5=9, Resulting Numbers: [44, 9] Generated Node #3: [44, 9] from Operation: 45/5=9 Current State: 35:[44, 9], Operations: ['94-89=5', '45/5=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[89, 44, 94, 45], Operations: [] Exploring Operation: 94-45=49, Resulting Numbers: [89, 44, 49] Generated Node #0,0: 35:[89, 44, 49] Operation: 94-45=49 Exploring Operation: 94-89=5, Resulting Numbers: [44, 45, 5] Generated Node #0,1: 35:[44, 45, 5] Operation: 94-89=5 Exploring Operation: 89-45=44, Resulting Numbers: [44, 94, 44] Generated Node #0,2: 35:[44, 94, 44] Operation: 89-45=44 Exploring Operation: 89-44=45, Resulting Numbers: [94, 45, 45] Generated Node #0,3: 35:[94, 45, 45] Operation: 89-44=45 Exploring Operation: 94-44=50, Resulting Numbers: [89, 45, 50] Generated Node #0,4: 35:[89, 45, 50] Operation: 94-44=50 Moving to Node #0,1 Current State: 35:[44, 45, 5], Operations: ['94-89=5'] Exploring Operation: 45-44=1, Resulting Numbers: [5, 1] Generated Node #0,1,0: 35:[5, 1] Operation: 45-44=1 Exploring Operation: 44-5=39, Resulting Numbers: [45, 39] Generated Node #0,1,1: 35:[45, 39] Operation: 44-5=39 Exploring Operation: 44+5=49, Resulting Numbers: [45, 49] Generated Node #0,1,2: 35:[45, 49] Operation: 44+5=49 Exploring Operation: 45-5=40, Resulting Numbers: [44, 40] Generated Node #0,1,3: 35:[44, 40] Operation: 45-5=40 Exploring Operation: 45/5=9, Resulting Numbers: [44, 9] Generated Node #0,1,4: 35:[44, 9] Operation: 45/5=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[5, 1], Operations: ['94-89=5', '45-44=1'] Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 35:[44, 9], Operations: ['94-89=5', '45/5=9'] Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 44*9=396, Resulting Numbers: [396] 396,35 unequal: No Solution Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[89, 44, 94, 45], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [44, 45, 5] Generated Node #0,1: 35:[44, 45, 5] Operation: 94-89=5 Moving to Node #0,1 Current State: 35:[44, 45, 5], Operations: ['94-89=5'] Exploring Operation: 45/5=9, Resulting Numbers: [44, 9] Generated Node #0,1,4: 35:[44, 9] Operation: 45/5=9 Moving to Node #0,1,4 Current State: 35:[44, 9], Operations: ['94-89=5', '45/5=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 8, 80, 63, 57 ]
94
[ "8+80=88", "63-57=6", "88+6=94" ]
Current State: 94:[8, 80, 63, 57], Operations: [] Exploring Operation: 8+80=88, Resulting Numbers: [63, 57, 88] Generated Node #2: [63, 57, 88] from Operation: 8+80=88 Current State: 94:[63, 57, 88], Operations: ['8+80=88'] Exploring Operation: 63-57=6, Resulting Numbers: [88, 6] Generated Node #3: [88, 6] from Operation: 63-57=6 Current State: 94:[88, 6], Operations: ['8+80=88', '63-57=6'] Exploring Operation: 88+6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[8, 80, 63, 57], Operations: [] Exploring Operation: 57-8=49, Resulting Numbers: [80, 63, 49] Generated Node #0,0: 94:[80, 63, 49] Operation: 57-8=49 Exploring Operation: 8+80=88, Resulting Numbers: [63, 57, 88] Generated Node #0,1: 94:[63, 57, 88] Operation: 8+80=88 Exploring Operation: 63-57=6, Resulting Numbers: [8, 80, 6] Generated Node #0,2: 94:[8, 80, 6] Operation: 63-57=6 Exploring Operation: 63-8=55, Resulting Numbers: [80, 57, 55] Generated Node #0,3: 94:[80, 57, 55] Operation: 63-8=55 Exploring Operation: 80-63=17, Resulting Numbers: [8, 57, 17] Generated Node #0,4: 94:[8, 57, 17] Operation: 80-63=17 Moving to Node #0,2 Current State: 94:[8, 80, 6], Operations: ['63-57=6'] Exploring Operation: 8+80=88, Resulting Numbers: [6, 88] Generated Node #0,2,0: 94:[6, 88] Operation: 8+80=88 Exploring Operation: 80+6=86, Resulting Numbers: [8, 86] Generated Node #0,2,1: 94:[8, 86] Operation: 80+6=86 Exploring Operation: 80/8=10, Resulting Numbers: [6, 10] Generated Node #0,2,2: 94:[6, 10] Operation: 80/8=10 Exploring Operation: 8-6=2, Resulting Numbers: [80, 2] Generated Node #0,2,3: 94:[80, 2] Operation: 8-6=2 Exploring Operation: 8*6=48, Resulting Numbers: [80, 48] Generated Node #0,2,4: 94:[80, 48] Operation: 8*6=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[6, 88], Operations: ['63-57=6', '8+80=88'] Exploring Operation: 6*88=528, Resulting Numbers: [528] 528,94 unequal: No Solution Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[8, 80, 63, 57], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [8, 80, 6] Generated Node #0,2: 94:[8, 80, 6] Operation: 63-57=6 Moving to Node #0,2 Current State: 94:[8, 80, 6], Operations: ['63-57=6'] Exploring Operation: 8+80=88, Resulting Numbers: [6, 88] Generated Node #0,2,0: 94:[6, 88] Operation: 8+80=88 Moving to Node #0,2,0 Current State: 94:[6, 88], Operations: ['63-57=6', '8+80=88'] Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 27, 89, 60, 41 ]
43
[ "89-27=62", "60-41=19", "62-19=43" ]
Current State: 43:[27, 89, 60, 41], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [60, 41, 62] Generated Node #2: [60, 41, 62] from Operation: 89-27=62 Current State: 43:[60, 41, 62], Operations: ['89-27=62'] Exploring Operation: 60-41=19, Resulting Numbers: [62, 19] Generated Node #3: [62, 19] from Operation: 60-41=19 Current State: 43:[62, 19], Operations: ['89-27=62', '60-41=19'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[27, 89, 60, 41], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [60, 41, 62] Generated Node #0,0: 43:[60, 41, 62] Operation: 89-27=62 Exploring Operation: 89-60=29, Resulting Numbers: [27, 41, 29] Generated Node #0,1: 43:[27, 41, 29] Operation: 89-60=29 Moving to Node #0,1 Current State: 43:[27, 41, 29], Operations: ['89-60=29'] Exploring Operation: 27+41=68, Resulting Numbers: [29, 68] Generated Node #0,1,0: 43:[29, 68] Operation: 27+41=68 Exploring Operation: 27+29=56, Resulting Numbers: [41, 56] Generated Node #0,1,1: 43:[41, 56] Operation: 27+29=56 Moving to Node #0,0 Current State: 43:[60, 41, 62], Operations: ['89-27=62'] Exploring Operation: 60-41=19, Resulting Numbers: [62, 19] Generated Node #0,0,0: 43:[62, 19] Operation: 60-41=19 Exploring Operation: 62-41=21, Resulting Numbers: [60, 21] Generated Node #0,0,1: 43:[60, 21] Operation: 62-41=21 Moving to Node #0,1,1 Current State: 43:[41, 56], Operations: ['89-60=29', '27+29=56'] Exploring Operation: 41+56=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[60, 21], Operations: ['89-27=62', '62-41=21'] Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[29, 68], Operations: ['89-60=29', '27+41=68'] Exploring Operation: 29+68=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[62, 19], Operations: ['89-27=62', '60-41=19'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[27, 89, 60, 41], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [60, 41, 62] Generated Node #0,0: 43:[60, 41, 62] Operation: 89-27=62 Moving to Node #0,0 Current State: 43:[60, 41, 62], Operations: ['89-27=62'] Exploring Operation: 60-41=19, Resulting Numbers: [62, 19] Generated Node #0,0,0: 43:[62, 19] Operation: 60-41=19 Moving to Node #0,0,0 Current State: 43:[62, 19], Operations: ['89-27=62', '60-41=19'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 38, 85, 14, 32 ]
93
[ "85-38=47", "14+32=46", "47+46=93" ]
Current State: 93:[38, 85, 14, 32], Operations: [] Exploring Operation: 85-38=47, Resulting Numbers: [14, 32, 47] Generated Node #2: [14, 32, 47] from Operation: 85-38=47 Current State: 93:[14, 32, 47], Operations: ['85-38=47'] Exploring Operation: 14+32=46, Resulting Numbers: [47, 46] Generated Node #3: [47, 46] from Operation: 14+32=46 Current State: 93:[47, 46], Operations: ['85-38=47', '14+32=46'] Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[38, 85, 14, 32], Operations: [] Exploring Operation: 85+14=99, Resulting Numbers: [38, 32, 99] Generated Node #0,0: 93:[38, 32, 99] Operation: 85+14=99 Moving to Node #0,0 Current State: 93:[38, 32, 99], Operations: ['85+14=99'] 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: ['85+14=99', '38-32=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[38, 85, 14, 32], Operations: [] Exploring Operation: 85+14=99, Resulting Numbers: [38, 32, 99] Generated Node #0,0: 93:[38, 32, 99] Operation: 85+14=99 Moving to Node #0,0 Current State: 93:[38, 32, 99], Operations: ['85+14=99'] 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: ['85+14=99', '38-32=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 49, 84, 28, 23 ]
24
[ "49+23=72", "84/28=3", "72/3=24" ]
Current State: 24:[49, 84, 28, 23], Operations: [] Exploring Operation: 49+23=72, Resulting Numbers: [84, 28, 72] Generated Node #2: [84, 28, 72] from Operation: 49+23=72 Current State: 24:[84, 28, 72], Operations: ['49+23=72'] Exploring Operation: 84/28=3, Resulting Numbers: [72, 3] Generated Node #3: [72, 3] from Operation: 84/28=3 Current State: 24:[72, 3], Operations: ['49+23=72', '84/28=3'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[49, 84, 28, 23], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [49, 23, 3] Generated Node #0,0: 24:[49, 23, 3] Operation: 84/28=3 Exploring Operation: 84-49=35, Resulting Numbers: [28, 23, 35] Generated Node #0,1: 24:[28, 23, 35] Operation: 84-49=35 Moving to Node #0,1 Current State: 24:[28, 23, 35], Operations: ['84-49=35'] Exploring Operation: 35-28=7, Resulting Numbers: [23, 7] Generated Node #0,1,0: 24:[23, 7] Operation: 35-28=7 Exploring Operation: 35-23=12, Resulting Numbers: [28, 12] Generated Node #0,1,1: 24:[28, 12] Operation: 35-23=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[23, 7], Operations: ['84-49=35', '35-28=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[28, 12], Operations: ['84-49=35', '35-23=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,24 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,24 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: 24:[49, 23, 3], Operations: ['84/28=3'] Exploring Operation: 49-3=46, Resulting Numbers: [23, 46] Generated Node #0,0,0: 24:[23, 46] Operation: 49-3=46 Exploring Operation: 49-23=26, Resulting Numbers: [3, 26] Generated Node #0,0,1: 24:[3, 26] Operation: 49-23=26 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[3, 26], Operations: ['84/28=3', '49-23=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[23, 46], Operations: ['84/28=3', '49-3=46'] Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 98, 35, 58, 97 ]
92
[ "98-35=63", "58+97=155", "155-63=92" ]
Current State: 92:[98, 35, 58, 97], Operations: [] Exploring Operation: 98-35=63, Resulting Numbers: [58, 97, 63] Generated Node #2: [58, 97, 63] from Operation: 98-35=63 Current State: 92:[58, 97, 63], Operations: ['98-35=63'] Exploring Operation: 58+97=155, Resulting Numbers: [63, 155] Generated Node #3: [63, 155] from Operation: 58+97=155 Current State: 92:[63, 155], Operations: ['98-35=63', '58+97=155'] Exploring Operation: 155-63=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[98, 35, 58, 97], Operations: [] Exploring Operation: 58-35=23, Resulting Numbers: [98, 97, 23] Generated Node #0,0: 92:[98, 97, 23] Operation: 58-35=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[98, 97, 23], Operations: ['58-35=23'] Exploring Operation: 98-97=1, Resulting Numbers: [23, 1] Generated Node #0,0,0: 92:[23, 1] Operation: 98-97=1 Moving to Node #0,0,0 Current State: 92:[23, 1], Operations: ['58-35=23', '98-97=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 26, 28, 95, 93 ]
91
[ "28-26=2", "93*2=186", "186-95=91" ]
Current State: 91:[26, 28, 95, 93], Operations: [] Exploring Operation: 28-26=2, Resulting Numbers: [95, 93, 2] Generated Node #2: [95, 93, 2] from Operation: 28-26=2 Current State: 91:[95, 93, 2], Operations: ['28-26=2'] Exploring Operation: 93*2=186, Resulting Numbers: [95, 186] Generated Node #3: [95, 186] from Operation: 93*2=186 Current State: 91:[95, 186], Operations: ['28-26=2', '93*2=186'] Exploring Operation: 186-95=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[26, 28, 95, 93], Operations: [] Exploring Operation: 28-26=2, Resulting Numbers: [95, 93, 2] Generated Node #0,0: 91:[95, 93, 2] Operation: 28-26=2 Exploring Operation: 95-93=2, Resulting Numbers: [26, 28, 2] Generated Node #0,1: 91:[26, 28, 2] Operation: 95-93=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[95, 93, 2], Operations: ['28-26=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93, 93] Generated Node #0,0,0: 91:[93, 93] Operation: 95-2=93 Exploring Operation: 93-2=91, Resulting Numbers: [95, 91] Generated Node #0,0,1: 91:[95, 91] Operation: 93-2=91 Moving to Node #0,0,0 Current State: 91:[93, 93], Operations: ['28-26=2', '95-2=93'] Exploring Operation: 93/93=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 93-93=0, Resulting Numbers: [0] 0,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[95, 91], Operations: ['28-26=2', '93-2=91'] Exploring Operation: 95-91=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 95+91=186, Resulting Numbers: [186] 186,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[26, 28, 2], Operations: ['95-93=2'] Exploring Operation: 28-26=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 91:[2, 2] Operation: 28-26=2 Exploring Operation: 28/2=14, Resulting Numbers: [26, 14] Generated Node #0,1,1: 91:[26, 14] Operation: 28/2=14 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[2, 2], Operations: ['95-93=2', '28-26=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[26, 14], Operations: ['95-93=2', '28/2=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 69, 3, 1, 2 ]
37
[ "69+3=72", "72/2=36", "1+36=37" ]
Current State: 37:[69, 3, 1, 2], Operations: [] Exploring Operation: 69+3=72, Resulting Numbers: [1, 2, 72] Generated Node #2: [1, 2, 72] from Operation: 69+3=72 Current State: 37:[1, 2, 72], Operations: ['69+3=72'] Exploring Operation: 72/2=36, Resulting Numbers: [1, 36] Generated Node #3: [1, 36] from Operation: 72/2=36 Current State: 37:[1, 36], Operations: ['69+3=72', '72/2=36'] Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[69, 3, 1, 2], Operations: [] Exploring Operation: 69/3=23, Resulting Numbers: [1, 2, 23] Generated Node #0,0: 37:[1, 2, 23] Operation: 69/3=23 Exploring Operation: 3*2=6, Resulting Numbers: [69, 1, 6] Generated Node #0,1: 37:[69, 1, 6] Operation: 3*2=6 Moving to Node #0,0 Current State: 37:[1, 2, 23], Operations: ['69/3=23'] Exploring Operation: 1+2=3, Resulting Numbers: [23, 3] Generated Node #0,0,0: 37:[23, 3] Operation: 1+2=3 Exploring Operation: 2*23=46, Resulting Numbers: [1, 46] Generated Node #0,0,1: 37:[1, 46] Operation: 2*23=46 Moving to Node #0,1 Current State: 37:[69, 1, 6], Operations: ['3*2=6'] Exploring Operation: 69-1=68, Resulting Numbers: [6, 68] Generated Node #0,1,0: 37:[6, 68] Operation: 69-1=68 Exploring Operation: 69-6=63, Resulting Numbers: [1, 63] Generated Node #0,1,1: 37:[1, 63] Operation: 69-6=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[6, 68], Operations: ['3*2=6', '69-1=68'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,37 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[1, 63], Operations: ['3*2=6', '69-6=63'] Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,37 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: 37:[1, 46], Operations: ['69/3=23', '2*23=46'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,37 unequal: No Solution Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[23, 3], Operations: ['69/3=23', '1+2=3'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,37 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,37 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 61, 18, 5, 8 ]
83
[ "61-18=43", "5*8=40", "43+40=83" ]
Current State: 83:[61, 18, 5, 8], Operations: [] Exploring Operation: 61-18=43, Resulting Numbers: [5, 8, 43] Generated Node #2: [5, 8, 43] from Operation: 61-18=43 Current State: 83:[5, 8, 43], Operations: ['61-18=43'] Exploring Operation: 5*8=40, Resulting Numbers: [43, 40] Generated Node #3: [43, 40] from Operation: 5*8=40 Current State: 83:[43, 40], Operations: ['61-18=43', '5*8=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[61, 18, 5, 8], Operations: [] Exploring Operation: 5*8=40, Resulting Numbers: [61, 18, 40] Generated Node #0,0: 83:[61, 18, 40] Operation: 5*8=40 Exploring Operation: 18*5=90, Resulting Numbers: [61, 8, 90] Generated Node #0,1: 83:[61, 8, 90] Operation: 18*5=90 Moving to Node #0,1 Current State: 83:[61, 8, 90], Operations: ['18*5=90'] Exploring Operation: 90-8=82, Resulting Numbers: [61, 82] Generated Node #0,1,0: 83:[61, 82] Operation: 90-8=82 Exploring Operation: 61+8=69, Resulting Numbers: [90, 69] Generated Node #0,1,1: 83:[90, 69] Operation: 61+8=69 Moving to Node #0,0 Current State: 83:[61, 18, 40], Operations: ['5*8=40'] Exploring Operation: 18+40=58, Resulting Numbers: [61, 58] Generated Node #0,0,0: 83:[61, 58] Operation: 18+40=58 Exploring Operation: 61+18=79, Resulting Numbers: [40, 79] Generated Node #0,0,1: 83:[40, 79] Operation: 61+18=79 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[61, 58], Operations: ['5*8=40', '18+40=58'] Exploring Operation: 61+58=119, Resulting Numbers: [119] 119,83 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,83 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:[40, 79], Operations: ['5*8=40', '61+18=79'] Exploring Operation: 40+79=119, Resulting Numbers: [119] 119,83 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 83:[90, 69], Operations: ['18*5=90', '61+8=69'] Exploring Operation: 90-69=21, Resulting Numbers: [21] 21,83 unequal: No Solution Exploring Operation: 90+69=159, Resulting Numbers: [159] 159,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[61, 82], Operations: ['18*5=90', '90-8=82'] Exploring Operation: 61+82=143, Resulting Numbers: [143] 143,83 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,83 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 40, 49, 2, 6 ]
12
[ "49-40=9", "6/2=3", "9+3=12" ]
Current State: 12:[40, 49, 2, 6], Operations: [] Exploring Operation: 49-40=9, Resulting Numbers: [2, 6, 9] Generated Node #2: [2, 6, 9] from Operation: 49-40=9 Current State: 12:[2, 6, 9], Operations: ['49-40=9'] Exploring Operation: 6/2=3, Resulting Numbers: [9, 3] Generated Node #3: [9, 3] from Operation: 6/2=3 Current State: 12:[9, 3], Operations: ['49-40=9', '6/2=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[40, 49, 2, 6], Operations: [] Exploring Operation: 40-2=38, Resulting Numbers: [49, 6, 38] Generated Node #0,0: 12:[49, 6, 38] Operation: 40-2=38 Exploring Operation: 40/2=20, Resulting Numbers: [49, 6, 20] Generated Node #0,1: 12:[49, 6, 20] Operation: 40/2=20 Exploring Operation: 40-6=34, Resulting Numbers: [49, 2, 34] Generated Node #0,2: 12:[49, 2, 34] Operation: 40-6=34 Exploring Operation: 49-6=43, Resulting Numbers: [40, 2, 43] Generated Node #0,3: 12:[40, 2, 43] Operation: 49-6=43 Exploring Operation: 49-40=9, Resulting Numbers: [2, 6, 9] Generated Node #0,4: 12:[2, 6, 9] Operation: 49-40=9 Moving to Node #0,4 Current State: 12:[2, 6, 9], Operations: ['49-40=9'] Exploring Operation: 9-6=3, Resulting Numbers: [2, 3] Generated Node #0,4,0: 12:[2, 3] Operation: 9-6=3 Exploring Operation: 2*6=12, Resulting Numbers: [9, 12] Generated Node #0,4,1: 12:[9, 12] Operation: 2*6=12 Exploring Operation: 6-2=4, Resulting Numbers: [9, 4] Generated Node #0,4,2: 12:[9, 4] Operation: 6-2=4 Exploring Operation: 9-2=7, Resulting Numbers: [6, 7] Generated Node #0,4,3: 12:[6, 7] Operation: 9-2=7 Exploring Operation: 2+9=11, Resulting Numbers: [6, 11] Generated Node #0,4,4: 12:[6, 11] Operation: 2+9=11 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 12:[2, 3], Operations: ['49-40=9', '9-6=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 12:[6, 7], Operations: ['49-40=9', '9-2=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 12:[6, 11], Operations: ['49-40=9', '2+9=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 12:[9, 12], Operations: ['49-40=9', '2*6=12'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,12 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 12:[9, 4], Operations: ['49-40=9', '6-2=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,12 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,12 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: 12:[49, 6, 20], Operations: ['40/2=20'] Exploring Operation: 49+6=55, Resulting Numbers: [20, 55] Generated Node #0,1,0: 12:[20, 55] Operation: 49+6=55 Exploring Operation: 6+20=26, Resulting Numbers: [49, 26] Generated Node #0,1,1: 12:[49, 26] Operation: 6+20=26 Exploring Operation: 49-20=29, Resulting Numbers: [6, 29] Generated Node #0,1,2: 12:[6, 29] Operation: 49-20=29 Exploring Operation: 20-6=14, Resulting Numbers: [49, 14] Generated Node #0,1,3: 12:[49, 14] Operation: 20-6=14 Exploring Operation: 49-6=43, Resulting Numbers: [20, 43] Generated Node #0,1,4: 12:[20, 43] Operation: 49-6=43 Moving to Node #0,2 Current State: 12:[49, 2, 34], Operations: ['40-6=34'] Exploring Operation: 34/2=17, Resulting Numbers: [49, 17] Generated Node #0,2,0: 12:[49, 17] Operation: 34/2=17 Exploring Operation: 49+2=51, Resulting Numbers: [34, 51] Generated Node #0,2,1: 12:[34, 51] Operation: 49+2=51 Exploring Operation: 49-34=15, Resulting Numbers: [2, 15] Generated Node #0,2,2: 12:[2, 15] Operation: 49-34=15 Exploring Operation: 34-2=32, Resulting Numbers: [49, 32] Generated Node #0,2,3: 12:[49, 32] Operation: 34-2=32 Exploring Operation: 49-2=47, Resulting Numbers: [34, 47] Generated Node #0,2,4: 12:[34, 47] Operation: 49-2=47 Moving to Node #0,3 Current State: 12:[40, 2, 43], Operations: ['49-6=43'] Exploring Operation: 40-2=38, Resulting Numbers: [43, 38] Generated Node #0,3,0: 12:[43, 38] Operation: 40-2=38 Exploring Operation: 43-40=3, Resulting Numbers: [2, 3] Generated Node #0,3,1: 12:[2, 3] Operation: 43-40=3 Exploring Operation: 40+2=42, Resulting Numbers: [43, 42] Generated Node #0,3,2: 12:[43, 42] Operation: 40+2=42 Exploring Operation: 40/2=20, Resulting Numbers: [43, 20] Generated Node #0,3,3: 12:[43, 20] Operation: 40/2=20 Exploring Operation: 43-2=41, Resulting Numbers: [40, 41] Generated Node #0,3,4: 12:[40, 41] Operation: 43-2=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 12:[2, 3], Operations: ['49-6=43', '43-40=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 12:[43, 20], Operations: ['49-6=43', '40/2=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,12 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,12 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[43, 38], Operations: ['49-6=43', '40-2=38'] Exploring Operation: 43+38=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 43*38=1634, Resulting Numbers: [1634] 1634,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 12:[40, 41], Operations: ['49-6=43', '43-2=41'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,12 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 12:[43, 42], Operations: ['49-6=43', '40+2=42'] Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,12 unequal: No Solution Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,12 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: 12:[49, 6, 38], Operations: ['40-2=38'] Exploring Operation: 49-6=43, Resulting Numbers: [38, 43] Generated Node #0,0,0: 12:[38, 43] Operation: 49-6=43 Exploring Operation: 6+38=44, Resulting Numbers: [49, 44] Generated Node #0,0,1: 12:[49, 44] Operation: 6+38=44 Exploring Operation: 49-38=11, Resulting Numbers: [6, 11] Generated Node #0,0,2: 12:[6, 11] Operation: 49-38=11 Exploring Operation: 49+6=55, Resulting Numbers: [38, 55] Generated Node #0,0,3: 12:[38, 55] Operation: 49+6=55 Exploring Operation: 38-6=32, Resulting Numbers: [49, 32] Generated Node #0,0,4: 12:[49, 32] Operation: 38-6=32 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[6, 11], Operations: ['40-2=38', '49-38=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,12 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[38, 43], Operations: ['40-2=38', '49-6=43'] Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 38+43=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 38*43=1634, Resulting Numbers: [1634] 1634,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 12:[49, 32], Operations: ['40-2=38', '38-6=32'] Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[49, 44], Operations: ['40-2=38', '6+38=44'] Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,12 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 12:[38, 55], Operations: ['40-2=38', '49+6=55'] Exploring Operation: 38*55=2090, Resulting Numbers: [2090] 2090,12 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 38+55=93, Resulting Numbers: [93] 93,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 12:[2, 15], Operations: ['40-6=34', '49-34=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[6, 29], Operations: ['40/2=20', '49-20=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,12 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,12 unequal: No Solution Moving to Node #0,1,4 Current State: 12:[20, 43], Operations: ['40/2=20', '49-6=43'] Exploring Operation: 20*43=860, Resulting Numbers: [860] 860,12 unequal: No Solution Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,12 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[49, 14], Operations: ['40/2=20', '20-6=14'] Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,12 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[49, 17], Operations: ['40-6=34', '34/2=17'] Exploring Operation: 49+17=66, Resulting Numbers: [66] 66,12 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,12 unequal: No Solution Exploring Operation: 49*17=833, Resulting Numbers: [833] 833,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[49, 26], Operations: ['40/2=20', '6+20=26'] Exploring Operation: 49*26=1274, Resulting Numbers: [1274] 1274,12 unequal: No Solution Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,12 unequal: No Solution Exploring Operation: 49+26=75, Resulting Numbers: [75] 75,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[20, 55], Operations: ['40/2=20', '49+6=55'] Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,12 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,12 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[34, 47], Operations: ['40-6=34', '49-2=47'] Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,12 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[49, 32], Operations: ['40-6=34', '34-2=32'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[34, 51], Operations: ['40-6=34', '49+2=51'] Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,12 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,12 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 95, 93, 31, 65 ]
99
[ "95-93=2", "65*2=130", "130-31=99" ]
Current State: 99:[95, 93, 31, 65], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [31, 65, 2] Generated Node #2: [31, 65, 2] from Operation: 95-93=2 Current State: 99:[31, 65, 2], Operations: ['95-93=2'] Exploring Operation: 65*2=130, Resulting Numbers: [31, 130] Generated Node #3: [31, 130] from Operation: 65*2=130 Current State: 99:[31, 130], Operations: ['95-93=2', '65*2=130'] Exploring Operation: 130-31=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[95, 93, 31, 65], Operations: [] Exploring Operation: 93-65=28, Resulting Numbers: [95, 31, 28] Generated Node #0,0: 99:[95, 31, 28] Operation: 93-65=28 Exploring Operation: 95-65=30, Resulting Numbers: [93, 31, 30] Generated Node #0,1: 99:[93, 31, 30] Operation: 95-65=30 Exploring Operation: 65-31=34, Resulting Numbers: [95, 93, 34] Generated Node #0,2: 99:[95, 93, 34] Operation: 65-31=34 Moving to Node #0,0 Current State: 99:[95, 31, 28], Operations: ['93-65=28'] Exploring Operation: 31+28=59, Resulting Numbers: [95, 59] Generated Node #0,0,0: 99:[95, 59] Operation: 31+28=59 Exploring Operation: 31-28=3, Resulting Numbers: [95, 3] Generated Node #0,0,1: 99:[95, 3] Operation: 31-28=3 Exploring Operation: 95+28=123, Resulting Numbers: [31, 123] Generated Node #0,0,2: 99:[31, 123] Operation: 95+28=123 Moving to Node #0,1 Current State: 99:[93, 31, 30], Operations: ['95-65=30'] Exploring Operation: 93+30=123, Resulting Numbers: [31, 123] Generated Node #0,1,0: 99:[31, 123] Operation: 93+30=123 Exploring Operation: 93/31=3, Resulting Numbers: [30, 3] Generated Node #0,1,1: 99:[30, 3] Operation: 93/31=3 Exploring Operation: 31-30=1, Resulting Numbers: [93, 1] Generated Node #0,1,2: 99:[93, 1] Operation: 31-30=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[30, 3], Operations: ['95-65=30', '93/31=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[93, 1], Operations: ['95-65=30', '31-30=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,99 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,99 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[31, 123], Operations: ['95-65=30', '93+30=123'] Exploring Operation: 123-31=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 31*123=3813, Resulting Numbers: [3813] 3813,99 unequal: No Solution Exploring Operation: 31+123=154, Resulting Numbers: [154] 154,99 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: 99:[95, 93, 34], Operations: ['65-31=34'] Exploring Operation: 93-34=59, Resulting Numbers: [95, 59] Generated Node #0,2,0: 99:[95, 59] Operation: 93-34=59 Exploring Operation: 95-93=2, Resulting Numbers: [34, 2] Generated Node #0,2,1: 99:[34, 2] Operation: 95-93=2 Exploring Operation: 93+34=127, Resulting Numbers: [95, 127] Generated Node #0,2,2: 99:[95, 127] Operation: 93+34=127 Moving to Node #0,2,1 Current State: 99:[34, 2], Operations: ['65-31=34', '95-93=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[95, 3], Operations: ['93-65=28', '31-28=3'] Exploring Operation: 95*3=285, Resulting Numbers: [285] 285,99 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[31, 123], Operations: ['93-65=28', '95+28=123'] Exploring Operation: 123-31=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 31*123=3813, Resulting Numbers: [3813] 3813,99 unequal: No Solution Exploring Operation: 31+123=154, Resulting Numbers: [154] 154,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[95, 59], Operations: ['93-65=28', '31+28=59'] Exploring Operation: 95+59=154, Resulting Numbers: [154] 154,99 unequal: No Solution Exploring Operation: 95*59=5605, Resulting Numbers: [5605] 5605,99 unequal: No Solution Exploring Operation: 95-59=36, Resulting Numbers: [36] 36,99 unequal: No Solution Moving to Node #0,2,0 Current State: 99:[95, 59], Operations: ['65-31=34', '93-34=59'] Exploring Operation: 95*59=5605, Resulting Numbers: [5605] 5605,99 unequal: No Solution Exploring Operation: 95-59=36, Resulting Numbers: [36] 36,99 unequal: No Solution Exploring Operation: 95+59=154, Resulting Numbers: [154] 154,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[95, 127], Operations: ['65-31=34', '93+34=127'] Exploring Operation: 95+127=222, Resulting Numbers: [222] 222,99 unequal: No Solution Exploring Operation: 127-95=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 95*127=12065, Resulting Numbers: [12065] 12065,99 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 85, 24, 14, 10 ]
65
[ "85-24=61", "14-10=4", "61+4=65" ]
Current State: 65:[85, 24, 14, 10], Operations: [] Exploring Operation: 85-24=61, Resulting Numbers: [14, 10, 61] Generated Node #2: [14, 10, 61] from Operation: 85-24=61 Current State: 65:[14, 10, 61], Operations: ['85-24=61'] Exploring Operation: 14-10=4, Resulting Numbers: [61, 4] Generated Node #3: [61, 4] from Operation: 14-10=4 Current State: 65:[61, 4], Operations: ['85-24=61', '14-10=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[85, 24, 14, 10], Operations: [] Exploring Operation: 85-14=71, Resulting Numbers: [24, 10, 71] Generated Node #0,0: 65:[24, 10, 71] Operation: 85-14=71 Exploring Operation: 85-10=75, Resulting Numbers: [24, 14, 75] Generated Node #0,1: 65:[24, 14, 75] Operation: 85-10=75 Exploring Operation: 85-24=61, Resulting Numbers: [14, 10, 61] Generated Node #0,2: 65:[14, 10, 61] Operation: 85-24=61 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[14, 10, 61], Operations: ['85-24=61'] Exploring Operation: 14+61=75, Resulting Numbers: [10, 75] Generated Node #0,2,0: 65:[10, 75] Operation: 14+61=75 Exploring Operation: 10+61=71, Resulting Numbers: [14, 71] Generated Node #0,2,1: 65:[14, 71] Operation: 10+61=71 Exploring Operation: 14-10=4, Resulting Numbers: [61, 4] Generated Node #0,2,2: 65:[61, 4] Operation: 14-10=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 65:[61, 4], Operations: ['85-24=61', '14-10=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[85, 24, 14, 10], Operations: [] Exploring Operation: 85-24=61, Resulting Numbers: [14, 10, 61] Generated Node #0,2: 65:[14, 10, 61] Operation: 85-24=61 Moving to Node #0,2 Current State: 65:[14, 10, 61], Operations: ['85-24=61'] Exploring Operation: 14-10=4, Resulting Numbers: [61, 4] Generated Node #0,2,2: 65:[61, 4] Operation: 14-10=4 Moving to Node #0,2,2 Current State: 65:[61, 4], Operations: ['85-24=61', '14-10=4'] Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 36, 18, 18, 78 ]
69
[ "36/18=2", "18/2=9", "78-9=69" ]
Current State: 69:[36, 18, 18, 78], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [78, 2] Generated Node #2: [78, 2] from Operation: 36/18=2 Current State: 69:[78, 2], Operations: ['36/18=2'] Exploring Operation: 18/2=9, Resulting Numbers: [78, 9] Generated Node #3: [78, 9] from Operation: 18/2=9 Current State: 69:[78, 9], Operations: ['36/18=2', '18/2=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[36, 18, 18, 78], Operations: [] Exploring Operation: 36-18=18, Resulting Numbers: [18, 78, 18] Generated Node #0,0: 69:[18, 78, 18] Operation: 36-18=18 Exploring Operation: 36/18=2, Resulting Numbers: [18, 78, 2] Generated Node #0,1: 69:[18, 78, 2] Operation: 36/18=2 Exploring Operation: 36/18=2, Resulting Numbers: [18, 78, 2] Generated Node #0,2: 69:[18, 78, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [18, 78, 18] Generated Node #0,3: 69:[18, 78, 18] Operation: 36-18=18 Moving to Node #0,1 Current State: 69:[18, 78, 2], Operations: ['36/18=2'] Exploring Operation: 78-18=60, Resulting Numbers: [2, 60] Generated Node #0,1,0: 69:[2, 60] Operation: 78-18=60 Exploring Operation: 18+2=20, Resulting Numbers: [78, 20] Generated Node #0,1,1: 69:[78, 20] Operation: 18+2=20 Exploring Operation: 78-2=76, Resulting Numbers: [18, 76] Generated Node #0,1,2: 69:[18, 76] Operation: 78-2=76 Exploring Operation: 18/2=9, Resulting Numbers: [78, 9] Generated Node #0,1,3: 69:[78, 9] Operation: 18/2=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[2, 60], Operations: ['36/18=2', '78-18=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,69 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[78, 20], Operations: ['36/18=2', '18+2=20'] Exploring Operation: 78*20=1560, Resulting Numbers: [1560] 1560,69 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 78+20=98, Resulting Numbers: [98] 98,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[18, 76], Operations: ['36/18=2', '78-2=76'] Exploring Operation: 18*76=1368, Resulting Numbers: [1368] 1368,69 unequal: No Solution Exploring Operation: 18+76=94, Resulting Numbers: [94] 94,69 unequal: No Solution Exploring Operation: 76-18=58, Resulting Numbers: [58] 58,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[78, 9], Operations: ['36/18=2', '18/2=9'] Exploring Operation: 78+9=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[36, 18, 18, 78], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [18, 78, 2] Generated Node #0,1: 69:[18, 78, 2] Operation: 36/18=2 Moving to Node #0,1 Current State: 69:[18, 78, 2], Operations: ['36/18=2'] Exploring Operation: 18/2=9, Resulting Numbers: [78, 9] Generated Node #0,1,3: 69:[78, 9] Operation: 18/2=9 Moving to Node #0,1,3 Current State: 69:[78, 9], Operations: ['36/18=2', '18/2=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 17, 73, 13, 16 ]
61
[ "17+73=90", "13+16=29", "90-29=61" ]
Current State: 61:[17, 73, 13, 16], Operations: [] Exploring Operation: 17+73=90, Resulting Numbers: [13, 16, 90] Generated Node #2: [13, 16, 90] from Operation: 17+73=90 Current State: 61:[13, 16, 90], Operations: ['17+73=90'] Exploring Operation: 13+16=29, Resulting Numbers: [90, 29] Generated Node #3: [90, 29] from Operation: 13+16=29 Current State: 61:[90, 29], Operations: ['17+73=90', '13+16=29'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[17, 73, 13, 16], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [73, 16, 30] Generated Node #0,0: 61:[73, 16, 30] Operation: 17+13=30 Exploring Operation: 13+16=29, Resulting Numbers: [17, 73, 29] Generated Node #0,1: 61:[17, 73, 29] Operation: 13+16=29 Exploring Operation: 73-16=57, Resulting Numbers: [17, 13, 57] Generated Node #0,2: 61:[17, 13, 57] Operation: 73-16=57 Exploring Operation: 17+16=33, Resulting Numbers: [73, 13, 33] Generated Node #0,3: 61:[73, 13, 33] Operation: 17+16=33 Exploring Operation: 73-13=60, Resulting Numbers: [17, 16, 60] Generated Node #0,4: 61:[17, 16, 60] Operation: 73-13=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[73, 16, 30], Operations: ['17+13=30'] Exploring Operation: 73+16=89, Resulting Numbers: [30, 89] Generated Node #0,0,0: 61:[30, 89] Operation: 73+16=89 Exploring Operation: 73-30=43, Resulting Numbers: [16, 43] Generated Node #0,0,1: 61:[16, 43] Operation: 73-30=43 Exploring Operation: 30-16=14, Resulting Numbers: [73, 14] Generated Node #0,0,2: 61:[73, 14] Operation: 30-16=14 Exploring Operation: 16+30=46, Resulting Numbers: [73, 46] Generated Node #0,0,3: 61:[73, 46] Operation: 16+30=46 Exploring Operation: 73-16=57, Resulting Numbers: [30, 57] Generated Node #0,0,4: 61:[30, 57] Operation: 73-16=57 Moving to Node #0,0,3 Current State: 61:[73, 46], Operations: ['17+13=30', '16+30=46'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,61 unequal: No Solution Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[30, 57], Operations: ['17+13=30', '73-16=57'] Exploring Operation: 30*57=1710, Resulting Numbers: [1710] 1710,61 unequal: No Solution Exploring Operation: 30+57=87, Resulting Numbers: [87] 87,61 unequal: No Solution Exploring Operation: 57-30=27, Resulting Numbers: [27] 27,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[30, 89], Operations: ['17+13=30', '73+16=89'] Exploring Operation: 30+89=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 30*89=2670, Resulting Numbers: [2670] 2670,61 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[73, 14], Operations: ['17+13=30', '30-16=14'] Exploring Operation: 73+14=87, Resulting Numbers: [87] 87,61 unequal: No Solution Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,61 unequal: No Solution Exploring Operation: 73*14=1022, Resulting Numbers: [1022] 1022,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[16, 43], Operations: ['17+13=30', '73-30=43'] Exploring Operation: 16+43=59, Resulting Numbers: [59] 59,61 unequal: No Solution Exploring Operation: 16*43=688, Resulting Numbers: [688] 688,61 unequal: No Solution Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[17, 73, 29], Operations: ['13+16=29'] Exploring Operation: 73-17=56, Resulting Numbers: [29, 56] Generated Node #0,1,0: 61:[29, 56] Operation: 73-17=56 Exploring Operation: 17+29=46, Resulting Numbers: [73, 46] Generated Node #0,1,1: 61:[73, 46] Operation: 17+29=46 Exploring Operation: 17+73=90, Resulting Numbers: [29, 90] Generated Node #0,1,2: 61:[29, 90] Operation: 17+73=90 Exploring Operation: 29-17=12, Resulting Numbers: [73, 12] Generated Node #0,1,3: 61:[73, 12] Operation: 29-17=12 Exploring Operation: 73-29=44, Resulting Numbers: [17, 44] Generated Node #0,1,4: 61:[17, 44] Operation: 73-29=44 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[73, 46], Operations: ['13+16=29', '17+29=46'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,61 unequal: No Solution Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[29, 56], Operations: ['13+16=29', '73-17=56'] Exploring Operation: 29*56=1624, Resulting Numbers: [1624] 1624,61 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,61 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[29, 90], Operations: ['13+16=29', '17+73=90'] Exploring Operation: 29*90=2610, Resulting Numbers: [2610] 2610,61 unequal: No Solution Exploring Operation: 29+90=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[17, 73, 13, 16], Operations: [] Exploring Operation: 13+16=29, Resulting Numbers: [17, 73, 29] Generated Node #0,1: 61:[17, 73, 29] Operation: 13+16=29 Moving to Node #0,1 Current State: 61:[17, 73, 29], Operations: ['13+16=29'] Exploring Operation: 17+73=90, Resulting Numbers: [29, 90] Generated Node #0,1,2: 61:[29, 90] Operation: 17+73=90 Moving to Node #0,1,2 Current State: 61:[29, 90], Operations: ['13+16=29', '17+73=90'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic