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
[ 34, 63, 31, 64 ]
64
[ "34+63=97", "64-31=33", "97-33=64" ]
Current State: 64:[34, 63, 31, 64], Operations: [] Exploring Operation: 34+63=97, Resulting Numbers: [31, 64, 97] Generated Node #2: [31, 64, 97] from Operation: 34+63=97 Current State: 64:[31, 64, 97], Operations: ['34+63=97'] Exploring Operation: 64-31=33, Resulting Numbers: [97, 33] Generated Node #3: [97, 33] from Operation: 64-31=33 Current State: 64:[97, 33], Operations: ['34+63=97', '64-31=33'] Exploring Operation: 97-33=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[34, 63, 31, 64], Operations: [] Exploring Operation: 34-31=3, Resulting Numbers: [63, 64, 3] Generated Node #0,0: 64:[63, 64, 3] Operation: 34-31=3 Exploring Operation: 63-31=32, Resulting Numbers: [34, 64, 32] Generated Node #0,1: 64:[34, 64, 32] Operation: 63-31=32 Exploring Operation: 34+31=65, Resulting Numbers: [63, 64, 65] Generated Node #0,2: 64:[63, 64, 65] Operation: 34+31=65 Moving to Node #0,0 Current State: 64:[63, 64, 3], Operations: ['34-31=3'] Exploring Operation: 64-63=1, Resulting Numbers: [3, 1] Generated Node #0,0,0: 64:[3, 1] Operation: 64-63=1 Exploring Operation: 63+3=66, Resulting Numbers: [64, 66] Generated Node #0,0,1: 64:[64, 66] Operation: 63+3=66 Exploring Operation: 63-3=60, Resulting Numbers: [64, 60] Generated Node #0,0,2: 64:[64, 60] Operation: 63-3=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[3, 1], Operations: ['34-31=3', '64-63=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,64 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[64, 66], Operations: ['34-31=3', '63+3=66'] Exploring Operation: 64*66=4224, Resulting Numbers: [4224] 4224,64 unequal: No Solution Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 64+66=130, Resulting Numbers: [130] 130,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 64:[64, 60], Operations: ['34-31=3', '63-3=60'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 64*60=3840, Resulting Numbers: [3840] 3840,64 unequal: No Solution Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 64:[34, 64, 32], Operations: ['63-31=32'] Exploring Operation: 64-34=30, Resulting Numbers: [32, 30] Generated Node #0,1,0: 64:[32, 30] Operation: 64-34=30 Exploring Operation: 34+32=66, Resulting Numbers: [64, 66] Generated Node #0,1,1: 64:[64, 66] Operation: 34+32=66 Exploring Operation: 34-32=2, Resulting Numbers: [64, 2] Generated Node #0,1,2: 64:[64, 2] Operation: 34-32=2 Moving to Node #0,2 Current State: 64:[63, 64, 65], Operations: ['34+31=65'] Exploring Operation: 65-63=2, Resulting Numbers: [64, 2] Generated Node #0,2,0: 64:[64, 2] Operation: 65-63=2 Exploring Operation: 64-63=1, Resulting Numbers: [65, 1] Generated Node #0,2,1: 64:[65, 1] Operation: 64-63=1 Exploring Operation: 65-64=1, Resulting Numbers: [63, 1] Generated Node #0,2,2: 64:[63, 1] Operation: 65-64=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[64, 2], Operations: ['34+31=65', '65-63=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,64 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[65, 1], Operations: ['34+31=65', '64-63=1'] 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:[34, 63, 31, 64], Operations: [] Exploring Operation: 34+31=65, Resulting Numbers: [63, 64, 65] Generated Node #0,2: 64:[63, 64, 65] Operation: 34+31=65 Moving to Node #0,2 Current State: 64:[63, 64, 65], Operations: ['34+31=65'] Exploring Operation: 64-63=1, Resulting Numbers: [65, 1] Generated Node #0,2,1: 64:[65, 1] Operation: 64-63=1 Moving to Node #0,2,1 Current State: 64:[65, 1], Operations: ['34+31=65', '64-63=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_3
sum_heuristic
[ 49, 63, 92, 15 ]
35
[ "49+63=112", "92-15=77", "112-77=35" ]
Current State: 35:[49, 63, 92, 15], Operations: [] Exploring Operation: 49+63=112, Resulting Numbers: [92, 15, 112] Generated Node #2: [92, 15, 112] from Operation: 49+63=112 Current State: 35:[92, 15, 112], Operations: ['49+63=112'] Exploring Operation: 92-15=77, Resulting Numbers: [112, 77] Generated Node #3: [112, 77] from Operation: 92-15=77 Current State: 35:[112, 77], Operations: ['49+63=112', '92-15=77'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[49, 63, 92, 15], Operations: [] Exploring Operation: 92-49=43, Resulting Numbers: [63, 15, 43] Generated Node #0,0: 35:[63, 15, 43] Operation: 92-49=43 Exploring Operation: 92-63=29, Resulting Numbers: [49, 15, 29] Generated Node #0,1: 35:[49, 15, 29] Operation: 92-63=29 Exploring Operation: 92-15=77, Resulting Numbers: [49, 63, 77] Generated Node #0,2: 35:[49, 63, 77] Operation: 92-15=77 Exploring Operation: 63-15=48, Resulting Numbers: [49, 92, 48] Generated Node #0,3: 35:[49, 92, 48] Operation: 63-15=48 Exploring Operation: 63-49=14, Resulting Numbers: [92, 15, 14] Generated Node #0,4: 35:[92, 15, 14] Operation: 63-49=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[49, 15, 29], Operations: ['92-63=29'] Exploring Operation: 49-15=34, Resulting Numbers: [29, 34] Generated Node #0,1,0: 35:[29, 34] Operation: 49-15=34 Exploring Operation: 49-29=20, Resulting Numbers: [15, 20] Generated Node #0,1,1: 35:[15, 20] Operation: 49-29=20 Exploring Operation: 49+15=64, Resulting Numbers: [29, 64] Generated Node #0,1,2: 35:[29, 64] Operation: 49+15=64 Exploring Operation: 15+29=44, Resulting Numbers: [49, 44] Generated Node #0,1,3: 35:[49, 44] Operation: 15+29=44 Exploring Operation: 29-15=14, Resulting Numbers: [49, 14] Generated Node #0,1,4: 35:[49, 14] Operation: 29-15=14 Moving to Node #0,1,0 Current State: 35:[29, 34], Operations: ['92-63=29', '49-15=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,35 unequal: No Solution Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,35 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,1,4 Current State: 35:[49, 14], Operations: ['92-63=29', '29-15=14'] Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,35 unequal: No Solution Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,35 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[49, 63, 92, 15], Operations: [] Exploring Operation: 92-63=29, Resulting Numbers: [49, 15, 29] Generated Node #0,1: 35:[49, 15, 29] Operation: 92-63=29 Moving to Node #0,1 Current State: 35:[49, 15, 29], Operations: ['92-63=29'] Exploring Operation: 29-15=14, Resulting Numbers: [49, 14] Generated Node #0,1,4: 35:[49, 14] Operation: 29-15=14 Moving to Node #0,1,4 Current State: 35:[49, 14], Operations: ['92-63=29', '29-15=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 44, 26, 83, 3 ]
89
[ "44-26=18", "18/3=6", "83+6=89" ]
Current State: 89:[44, 26, 83, 3], Operations: [] Exploring Operation: 44-26=18, Resulting Numbers: [83, 3, 18] Generated Node #2: [83, 3, 18] from Operation: 44-26=18 Current State: 89:[83, 3, 18], Operations: ['44-26=18'] Exploring Operation: 18/3=6, Resulting Numbers: [83, 6] Generated Node #3: [83, 6] from Operation: 18/3=6 Current State: 89:[83, 6], Operations: ['44-26=18', '18/3=6'] Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[44, 26, 83, 3], Operations: [] Exploring Operation: 26+3=29, Resulting Numbers: [44, 83, 29] Generated Node #0,0: 89:[44, 83, 29] Operation: 26+3=29 Exploring Operation: 44+3=47, Resulting Numbers: [26, 83, 47] Generated Node #0,1: 89:[26, 83, 47] Operation: 44+3=47 Exploring Operation: 44+26=70, Resulting Numbers: [83, 3, 70] Generated Node #0,2: 89:[83, 3, 70] Operation: 44+26=70 Exploring Operation: 26*3=78, Resulting Numbers: [44, 83, 78] Generated Node #0,3: 89:[44, 83, 78] Operation: 26*3=78 Moving to Node #0,3 Current State: 89:[44, 83, 78], Operations: ['26*3=78'] Exploring Operation: 78-44=34, Resulting Numbers: [83, 34] Generated Node #0,3,0: 89:[83, 34] Operation: 78-44=34 Exploring Operation: 44+78=122, Resulting Numbers: [83, 122] Generated Node #0,3,1: 89:[83, 122] Operation: 44+78=122 Exploring Operation: 44+83=127, Resulting Numbers: [78, 127] Generated Node #0,3,2: 89:[78, 127] Operation: 44+83=127 Exploring Operation: 83-44=39, Resulting Numbers: [78, 39] Generated Node #0,3,3: 89:[78, 39] Operation: 83-44=39 Moving to Node #0,1 Current State: 89:[26, 83, 47], Operations: ['44+3=47'] Exploring Operation: 47-26=21, Resulting Numbers: [83, 21] Generated Node #0,1,0: 89:[83, 21] Operation: 47-26=21 Exploring Operation: 83-26=57, Resulting Numbers: [47, 57] Generated Node #0,1,1: 89:[47, 57] Operation: 83-26=57 Exploring Operation: 26+83=109, Resulting Numbers: [47, 109] Generated Node #0,1,2: 89:[47, 109] Operation: 26+83=109 Exploring Operation: 26+47=73, Resulting Numbers: [83, 73] Generated Node #0,1,3: 89:[83, 73] Operation: 26+47=73 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[83, 73], Operations: ['44+3=47', '26+47=73'] Exploring Operation: 83+73=156, Resulting Numbers: [156] 156,89 unequal: No Solution Exploring Operation: 83*73=6059, Resulting Numbers: [6059] 6059,89 unequal: No Solution Exploring Operation: 83-73=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[47, 109], Operations: ['44+3=47', '26+83=109'] Exploring Operation: 47*109=5123, Resulting Numbers: [5123] 5123,89 unequal: No Solution Exploring Operation: 109-47=62, Resulting Numbers: [62] 62,89 unequal: No Solution Exploring Operation: 47+109=156, Resulting Numbers: [156] 156,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[83, 21], Operations: ['44+3=47', '47-26=21'] Exploring Operation: 83*21=1743, Resulting Numbers: [1743] 1743,89 unequal: No Solution Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,89 unequal: No Solution Exploring Operation: 83+21=104, Resulting Numbers: [104] 104,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[47, 57], Operations: ['44+3=47', '83-26=57'] Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,89 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,89 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: 89:[44, 83, 29], Operations: ['26+3=29'] Exploring Operation: 44-29=15, Resulting Numbers: [83, 15] Generated Node #0,0,0: 89:[83, 15] Operation: 44-29=15 Exploring Operation: 83-29=54, Resulting Numbers: [44, 54] Generated Node #0,0,1: 89:[44, 54] Operation: 83-29=54 Exploring Operation: 44+29=73, Resulting Numbers: [83, 73] Generated Node #0,0,2: 89:[83, 73] Operation: 44+29=73 Exploring Operation: 83+29=112, Resulting Numbers: [44, 112] Generated Node #0,0,3: 89:[44, 112] Operation: 83+29=112 Moving to Node #0,2 Current State: 89:[83, 3, 70], Operations: ['44+26=70'] Exploring Operation: 3+70=73, Resulting Numbers: [83, 73] Generated Node #0,2,0: 89:[83, 73] Operation: 3+70=73 Exploring Operation: 83-3=80, Resulting Numbers: [70, 80] Generated Node #0,2,1: 89:[70, 80] Operation: 83-3=80 Exploring Operation: 70-3=67, Resulting Numbers: [83, 67] Generated Node #0,2,2: 89:[83, 67] Operation: 70-3=67 Exploring Operation: 83+3=86, Resulting Numbers: [70, 86] Generated Node #0,2,3: 89:[70, 86] Operation: 83+3=86 Moving to Node #0,0,2 Current State: 89:[83, 73], Operations: ['26+3=29', '44+29=73'] Exploring Operation: 83-73=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 83*73=6059, Resulting Numbers: [6059] 6059,89 unequal: No Solution Exploring Operation: 83+73=156, Resulting Numbers: [156] 156,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[83, 73], Operations: ['44+26=70', '3+70=73'] Exploring Operation: 83-73=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 83+73=156, Resulting Numbers: [156] 156,89 unequal: No Solution Exploring Operation: 83*73=6059, Resulting Numbers: [6059] 6059,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[70, 86], Operations: ['44+26=70', '83+3=86'] Exploring Operation: 70*86=6020, Resulting Numbers: [6020] 6020,89 unequal: No Solution Exploring Operation: 70+86=156, Resulting Numbers: [156] 156,89 unequal: No Solution Exploring Operation: 86-70=16, Resulting Numbers: [16] 16,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[83, 67], Operations: ['44+26=70', '70-3=67'] Exploring Operation: 83+67=150, Resulting Numbers: [150] 150,89 unequal: No Solution Exploring Operation: 83-67=16, Resulting Numbers: [16] 16,89 unequal: No Solution Exploring Operation: 83*67=5561, Resulting Numbers: [5561] 5561,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[70, 80], Operations: ['44+26=70', '83-3=80'] Exploring Operation: 70*80=5600, Resulting Numbers: [5600] 5600,89 unequal: No Solution Exploring Operation: 80-70=10, Resulting Numbers: [10] 10,89 unequal: No Solution Exploring Operation: 70+80=150, Resulting Numbers: [150] 150,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[83, 122], Operations: ['26*3=78', '44+78=122'] Exploring Operation: 83*122=10126, Resulting Numbers: [10126] 10126,89 unequal: No Solution Exploring Operation: 122-83=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 83+122=205, Resulting Numbers: [205] 205,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[78, 127], Operations: ['26*3=78', '44+83=127'] Exploring Operation: 78*127=9906, Resulting Numbers: [9906] 9906,89 unequal: No Solution Exploring Operation: 127-78=49, Resulting Numbers: [49] 49,89 unequal: No Solution Exploring Operation: 78+127=205, Resulting Numbers: [205] 205,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[83, 34], Operations: ['26*3=78', '78-44=34'] Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,89 unequal: No Solution Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[78, 39], Operations: ['26*3=78', '83-44=39'] Exploring Operation: 78+39=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 78/39=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 78*39=3042, Resulting Numbers: [3042] 3042,89 unequal: No Solution Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[44, 112], Operations: ['26+3=29', '83+29=112'] Exploring Operation: 112-44=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 44+112=156, Resulting Numbers: [156] 156,89 unequal: No Solution Exploring Operation: 44*112=4928, Resulting Numbers: [4928] 4928,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[83, 15], Operations: ['26+3=29', '44-29=15'] Exploring Operation: 83*15=1245, Resulting Numbers: [1245] 1245,89 unequal: No Solution Exploring Operation: 83-15=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 83+15=98, Resulting Numbers: [98] 98,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[44, 54], Operations: ['26+3=29', '83-29=54'] Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,89 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,89 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,89 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 34, 93, 5, 52 ]
25
[ "34*5=170", "93+52=145", "170-145=25" ]
Current State: 25:[34, 93, 5, 52], Operations: [] Exploring Operation: 34*5=170, Resulting Numbers: [93, 52, 170] Generated Node #2: [93, 52, 170] from Operation: 34*5=170 Current State: 25:[93, 52, 170], Operations: ['34*5=170'] Exploring Operation: 93+52=145, Resulting Numbers: [170, 145] Generated Node #3: [170, 145] from Operation: 93+52=145 Current State: 25:[170, 145], Operations: ['34*5=170', '93+52=145'] Exploring Operation: 170-145=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[34, 93, 5, 52], Operations: [] Exploring Operation: 93-52=41, Resulting Numbers: [34, 5, 41] Generated Node #0,0: 25:[34, 5, 41] Operation: 93-52=41 Moving to Node #0,0 Current State: 25:[34, 5, 41], Operations: ['93-52=41'] Exploring Operation: 41-34=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 25:[5, 7] Operation: 41-34=7 Moving to Node #0,0,0 Current State: 25:[5, 7], Operations: ['93-52=41', '41-34=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,25 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 59, 86, 66, 41 ]
80
[ "86-59=27", "66+41=107", "107-27=80" ]
Current State: 80:[59, 86, 66, 41], Operations: [] Exploring Operation: 86-59=27, Resulting Numbers: [66, 41, 27] Generated Node #2: [66, 41, 27] from Operation: 86-59=27 Current State: 80:[66, 41, 27], Operations: ['86-59=27'] Exploring Operation: 66+41=107, Resulting Numbers: [27, 107] Generated Node #3: [27, 107] from Operation: 66+41=107 Current State: 80:[27, 107], Operations: ['86-59=27', '66+41=107'] Exploring Operation: 107-27=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[59, 86, 66, 41], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [59, 41, 20] Generated Node #0,0: 80:[59, 41, 20] Operation: 86-66=20 Exploring Operation: 86-59=27, Resulting Numbers: [66, 41, 27] Generated Node #0,1: 80:[66, 41, 27] Operation: 86-59=27 Exploring Operation: 66-41=25, Resulting Numbers: [59, 86, 25] Generated Node #0,2: 80:[59, 86, 25] Operation: 66-41=25 Exploring Operation: 59-41=18, Resulting Numbers: [86, 66, 18] Generated Node #0,3: 80:[86, 66, 18] Operation: 59-41=18 Exploring Operation: 66-59=7, Resulting Numbers: [86, 41, 7] Generated Node #0,4: 80:[86, 41, 7] Operation: 66-59=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 80:[86, 41, 7], Operations: ['66-59=7'] Exploring Operation: 86-41=45, Resulting Numbers: [7, 45] Generated Node #0,4,0: 80:[7, 45] Operation: 86-41=45 Exploring Operation: 41-7=34, Resulting Numbers: [86, 34] Generated Node #0,4,1: 80:[86, 34] Operation: 41-7=34 Exploring Operation: 41+7=48, Resulting Numbers: [86, 48] Generated Node #0,4,2: 80:[86, 48] Operation: 41+7=48 Exploring Operation: 86+7=93, Resulting Numbers: [41, 93] Generated Node #0,4,3: 80:[41, 93] Operation: 86+7=93 Exploring Operation: 86-7=79, Resulting Numbers: [41, 79] Generated Node #0,4,4: 80:[41, 79] Operation: 86-7=79 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 80:[41, 79], Operations: ['66-59=7', '86-7=79'] Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 41+79=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 41*79=3239, Resulting Numbers: [3239] 3239,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 80:[7, 45], Operations: ['66-59=7', '86-41=45'] Exploring Operation: 7*45=315, Resulting Numbers: [315] 315,80 unequal: No Solution Exploring Operation: 7+45=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 80:[86, 34], Operations: ['66-59=7', '41-7=34'] Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 86+34=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 86*34=2924, Resulting Numbers: [2924] 2924,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 80:[86, 48], Operations: ['66-59=7', '41+7=48'] Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 86*48=4128, Resulting Numbers: [4128] 4128,80 unequal: No Solution Exploring Operation: 86+48=134, Resulting Numbers: [134] 134,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 80:[41, 93], Operations: ['66-59=7', '86+7=93'] Exploring Operation: 41*93=3813, Resulting Numbers: [3813] 3813,80 unequal: No Solution Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 41+93=134, Resulting Numbers: [134] 134,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[59, 41, 20], Operations: ['86-66=20'] Exploring Operation: 59+41=100, Resulting Numbers: [20, 100] Generated Node #0,0,0: 80:[20, 100] Operation: 59+41=100 Exploring Operation: 41-20=21, Resulting Numbers: [59, 21] Generated Node #0,0,1: 80:[59, 21] Operation: 41-20=21 Exploring Operation: 59-20=39, Resulting Numbers: [41, 39] Generated Node #0,0,2: 80:[41, 39] Operation: 59-20=39 Exploring Operation: 59+20=79, Resulting Numbers: [41, 79] Generated Node #0,0,3: 80:[41, 79] Operation: 59+20=79 Exploring Operation: 59-41=18, Resulting Numbers: [20, 18] Generated Node #0,0,4: 80:[20, 18] Operation: 59-41=18 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 80:[41, 39], Operations: ['86-66=20', '59-20=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,80 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[59, 86, 66, 41], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [59, 41, 20] Generated Node #0,0: 80:[59, 41, 20] Operation: 86-66=20 Moving to Node #0,0 Current State: 80:[59, 41, 20], Operations: ['86-66=20'] Exploring Operation: 59-20=39, Resulting Numbers: [41, 39] Generated Node #0,0,2: 80:[41, 39] Operation: 59-20=39 Moving to Node #0,0,2 Current State: 80:[41, 39], Operations: ['86-66=20', '59-20=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 91, 45, 4, 94 ]
89
[ "94-4=90", "90/45=2", "91-2=89" ]
Current State: 89:[91, 45, 4, 94], Operations: [] Exploring Operation: 94-4=90, Resulting Numbers: [91, 45, 90] Generated Node #2: [91, 45, 90] from Operation: 94-4=90 Current State: 89:[91, 45, 90], Operations: ['94-4=90'] Exploring Operation: 90/45=2, Resulting Numbers: [91, 2] Generated Node #3: [91, 2] from Operation: 90/45=2 Current State: 89:[91, 2], Operations: ['94-4=90', '90/45=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[91, 45, 4, 94], Operations: [] Exploring Operation: 45+4=49, Resulting Numbers: [91, 94, 49] Generated Node #0,0: 89:[91, 94, 49] Operation: 45+4=49 Exploring Operation: 94-4=90, Resulting Numbers: [91, 45, 90] Generated Node #0,1: 89:[91, 45, 90] Operation: 94-4=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[91, 94, 49], Operations: ['45+4=49'] Exploring Operation: 91-49=42, Resulting Numbers: [94, 42] Generated Node #0,0,0: 89:[94, 42] Operation: 91-49=42 Exploring Operation: 94-49=45, Resulting Numbers: [91, 45] Generated Node #0,0,1: 89:[91, 45] Operation: 94-49=45 Moving to Node #0,0,1 Current State: 89:[91, 45], Operations: ['45+4=49', '94-49=45'] Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[94, 42], Operations: ['45+4=49', '91-49=42'] Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,89 unequal: No Solution Exploring Operation: 94+42=136, Resulting Numbers: [136] 136,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[91, 45, 90], Operations: ['94-4=90'] Exploring Operation: 91-45=46, Resulting Numbers: [90, 46] Generated Node #0,1,0: 89:[90, 46] Operation: 91-45=46 Exploring Operation: 90-45=45, Resulting Numbers: [91, 45] Generated Node #0,1,1: 89:[91, 45] Operation: 90-45=45 Moving to Node #0,1,0 Current State: 89:[90, 46], Operations: ['94-4=90', '91-45=46'] Exploring Operation: 90+46=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 90-46=44, Resulting Numbers: [44] 44,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[91, 45], Operations: ['94-4=90', '90-45=45'] Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,89 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 41, 72, 46, 96 ]
19
[ "72-41=31", "96-46=50", "50-31=19" ]
Current State: 19:[41, 72, 46, 96], Operations: [] Exploring Operation: 72-41=31, Resulting Numbers: [46, 96, 31] Generated Node #2: [46, 96, 31] from Operation: 72-41=31 Current State: 19:[46, 96, 31], Operations: ['72-41=31'] Exploring Operation: 96-46=50, Resulting Numbers: [31, 50] Generated Node #3: [31, 50] from Operation: 96-46=50 Current State: 19:[31, 50], Operations: ['72-41=31', '96-46=50'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[41, 72, 46, 96], Operations: [] Exploring Operation: 96-72=24, Resulting Numbers: [41, 46, 24] Generated Node #0,0: 19:[41, 46, 24] Operation: 96-72=24 Moving to Node #0,0 Current State: 19:[41, 46, 24], Operations: ['96-72=24'] Exploring Operation: 46-41=5, Resulting Numbers: [24, 5] Generated Node #0,0,0: 19:[24, 5] Operation: 46-41=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[24, 5], Operations: ['96-72=24', '46-41=5'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[41, 72, 46, 96], Operations: [] Exploring Operation: 96-72=24, Resulting Numbers: [41, 46, 24] Generated Node #0,0: 19:[41, 46, 24] Operation: 96-72=24 Moving to Node #0,0 Current State: 19:[41, 46, 24], Operations: ['96-72=24'] Exploring Operation: 46-41=5, Resulting Numbers: [24, 5] Generated Node #0,0,0: 19:[24, 5] Operation: 46-41=5 Moving to Node #0,0,0 Current State: 19:[24, 5], Operations: ['96-72=24', '46-41=5'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 84, 25, 8, 4 ]
97
[ "84+25=109", "8+4=12", "109-12=97" ]
Current State: 97:[84, 25, 8, 4], Operations: [] Exploring Operation: 84+25=109, Resulting Numbers: [8, 4, 109] Generated Node #2: [8, 4, 109] from Operation: 84+25=109 Current State: 97:[8, 4, 109], Operations: ['84+25=109'] Exploring Operation: 8+4=12, Resulting Numbers: [109, 12] Generated Node #3: [109, 12] from Operation: 8+4=12 Current State: 97:[109, 12], Operations: ['84+25=109', '8+4=12'] Exploring Operation: 109-12=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[84, 25, 8, 4], Operations: [] Exploring Operation: 25+8=33, Resulting Numbers: [84, 4, 33] Generated Node #0,0: 97:[84, 4, 33] Operation: 25+8=33 Exploring Operation: 84+8=92, Resulting Numbers: [25, 4, 92] Generated Node #0,1: 97:[25, 4, 92] Operation: 84+8=92 Exploring Operation: 84+4=88, Resulting Numbers: [25, 8, 88] Generated Node #0,2: 97:[25, 8, 88] Operation: 84+4=88 Exploring Operation: 8*4=32, Resulting Numbers: [84, 25, 32] Generated Node #0,3: 97:[84, 25, 32] Operation: 8*4=32 Exploring Operation: 25*4=100, Resulting Numbers: [84, 8, 100] Generated Node #0,4: 97:[84, 8, 100] Operation: 25*4=100 Moving to Node #0,4 Current State: 97:[84, 8, 100], Operations: ['25*4=100'] Exploring Operation: 100-84=16, Resulting Numbers: [8, 16] Generated Node #0,4,0: 97:[8, 16] Operation: 100-84=16 Exploring Operation: 84+8=92, Resulting Numbers: [100, 92] Generated Node #0,4,1: 97:[100, 92] Operation: 84+8=92 Exploring Operation: 100-8=92, Resulting Numbers: [84, 92] Generated Node #0,4,2: 97:[84, 92] Operation: 100-8=92 Exploring Operation: 84-8=76, Resulting Numbers: [100, 76] Generated Node #0,4,3: 97:[100, 76] Operation: 84-8=76 Exploring Operation: 8+100=108, Resulting Numbers: [84, 108] Generated Node #0,4,4: 97:[84, 108] Operation: 8+100=108 Moving to Node #0,3 Current State: 97:[84, 25, 32], Operations: ['8*4=32'] Exploring Operation: 84+32=116, Resulting Numbers: [25, 116] Generated Node #0,3,0: 97:[25, 116] Operation: 84+32=116 Exploring Operation: 25+32=57, Resulting Numbers: [84, 57] Generated Node #0,3,1: 97:[84, 57] Operation: 25+32=57 Exploring Operation: 32-25=7, Resulting Numbers: [84, 7] Generated Node #0,3,2: 97:[84, 7] Operation: 32-25=7 Exploring Operation: 84-25=59, Resulting Numbers: [32, 59] Generated Node #0,3,3: 97:[32, 59] Operation: 84-25=59 Exploring Operation: 84+25=109, Resulting Numbers: [32, 109] Generated Node #0,3,4: 97:[32, 109] Operation: 84+25=109 Moving to Node #0,0 Current State: 97:[84, 4, 33], Operations: ['25+8=33'] Exploring Operation: 4+33=37, Resulting Numbers: [84, 37] Generated Node #0,0,0: 97:[84, 37] Operation: 4+33=37 Exploring Operation: 33-4=29, Resulting Numbers: [84, 29] Generated Node #0,0,1: 97:[84, 29] Operation: 33-4=29 Exploring Operation: 84-4=80, Resulting Numbers: [33, 80] Generated Node #0,0,2: 97:[33, 80] Operation: 84-4=80 Exploring Operation: 84+4=88, Resulting Numbers: [33, 88] Generated Node #0,0,3: 97:[33, 88] Operation: 84+4=88 Exploring Operation: 4*33=132, Resulting Numbers: [84, 132] Generated Node #0,0,4: 97:[84, 132] Operation: 4*33=132 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 97:[84, 132], Operations: ['25+8=33', '4*33=132'] Exploring Operation: 132-84=48, Resulting Numbers: [48] 48,97 unequal: No Solution Exploring Operation: 84+132=216, Resulting Numbers: [216] 216,97 unequal: No Solution Exploring Operation: 84*132=11088, Resulting Numbers: [11088] 11088,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[84, 37], Operations: ['25+8=33', '4+33=37'] Exploring Operation: 84*37=3108, Resulting Numbers: [3108] 3108,97 unequal: No Solution Exploring Operation: 84+37=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 97:[33, 88], Operations: ['25+8=33', '84+4=88'] Exploring Operation: 33*88=2904, Resulting Numbers: [2904] 2904,97 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 33+88=121, Resulting Numbers: [121] 121,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[84, 29], Operations: ['25+8=33', '33-4=29'] Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 84*29=2436, Resulting Numbers: [2436] 2436,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[33, 80], Operations: ['25+8=33', '84-4=80'] Exploring Operation: 33+80=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 33*80=2640, Resulting Numbers: [2640] 2640,97 unequal: No Solution Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,97 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: 97:[25, 4, 92], Operations: ['84+8=92'] Exploring Operation: 25*4=100, Resulting Numbers: [92, 100] Generated Node #0,1,0: 97:[92, 100] Operation: 25*4=100 Exploring Operation: 25+4=29, Resulting Numbers: [92, 29] Generated Node #0,1,1: 97:[92, 29] Operation: 25+4=29 Exploring Operation: 4+92=96, Resulting Numbers: [25, 96] Generated Node #0,1,2: 97:[25, 96] Operation: 4+92=96 Exploring Operation: 25-4=21, Resulting Numbers: [92, 21] Generated Node #0,1,3: 97:[92, 21] Operation: 25-4=21 Exploring Operation: 92-4=88, Resulting Numbers: [25, 88] Generated Node #0,1,4: 97:[25, 88] Operation: 92-4=88 Moving to Node #0,2 Current State: 97:[25, 8, 88], Operations: ['84+4=88'] Exploring Operation: 25+8=33, Resulting Numbers: [88, 33] Generated Node #0,2,0: 97:[88, 33] Operation: 25+8=33 Exploring Operation: 88-8=80, Resulting Numbers: [25, 80] Generated Node #0,2,1: 97:[25, 80] Operation: 88-8=80 Exploring Operation: 8+88=96, Resulting Numbers: [25, 96] Generated Node #0,2,2: 97:[25, 96] Operation: 8+88=96 Exploring Operation: 25+88=113, Resulting Numbers: [8, 113] Generated Node #0,2,3: 97:[8, 113] Operation: 25+88=113 Exploring Operation: 25-8=17, Resulting Numbers: [88, 17] Generated Node #0,2,4: 97:[88, 17] Operation: 25-8=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[88, 33], Operations: ['84+4=88', '25+8=33'] Exploring Operation: 88+33=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 88*33=2904, Resulting Numbers: [2904] 2904,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[25, 96], Operations: ['84+4=88', '8+88=96'] Exploring Operation: 25*96=2400, Resulting Numbers: [2400] 2400,97 unequal: No Solution Exploring Operation: 25+96=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 96-25=71, Resulting Numbers: [71] 71,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[25, 80], Operations: ['84+4=88', '88-8=80'] Exploring Operation: 25+80=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 25*80=2000, Resulting Numbers: [2000] 2000,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 97:[88, 17], Operations: ['84+4=88', '25-8=17'] Exploring Operation: 88+17=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 88*17=1496, Resulting Numbers: [1496] 1496,97 unequal: No Solution Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[8, 113], Operations: ['84+4=88', '25+88=113'] Exploring Operation: 8+113=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 8*113=904, Resulting Numbers: [904] 904,97 unequal: No Solution Exploring Operation: 113-8=105, Resulting Numbers: [105] 105,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 97:[100, 92], Operations: ['25*4=100', '84+8=92'] Exploring Operation: 100+92=192, Resulting Numbers: [192] 192,97 unequal: No Solution Exploring Operation: 100*92=9200, Resulting Numbers: [9200] 9200,97 unequal: No Solution Exploring Operation: 100-92=8, Resulting Numbers: [8] 8,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[92, 100], Operations: ['84+8=92', '25*4=100'] Exploring Operation: 92+100=192, Resulting Numbers: [192] 192,97 unequal: No Solution Exploring Operation: 92*100=9200, Resulting Numbers: [9200] 9200,97 unequal: No Solution Exploring Operation: 100-92=8, Resulting Numbers: [8] 8,97 unequal: No Solution Moving to Node #0,4,2 Current State: 97:[84, 92], Operations: ['25*4=100', '100-8=92'] Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 84+92=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 84*92=7728, Resulting Numbers: [7728] 7728,97 unequal: No Solution Moving to Node #0,4,3 Current State: 97:[100, 76], Operations: ['25*4=100', '84-8=76'] Exploring Operation: 100-76=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 100*76=7600, Resulting Numbers: [7600] 7600,97 unequal: No Solution Exploring Operation: 100+76=176, Resulting Numbers: [176] 176,97 unequal: No Solution Moving to Node #0,4,4 Current State: 97:[84, 108], Operations: ['25*4=100', '8+100=108'] Exploring Operation: 108-84=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 84*108=9072, Resulting Numbers: [9072] 9072,97 unequal: No Solution Exploring Operation: 84+108=192, Resulting Numbers: [192] 192,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[84, 57], Operations: ['8*4=32', '25+32=57'] Exploring Operation: 84*57=4788, Resulting Numbers: [4788] 4788,97 unequal: No Solution Exploring Operation: 84+57=141, Resulting Numbers: [141] 141,97 unequal: No Solution Exploring Operation: 84-57=27, Resulting Numbers: [27] 27,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[92, 29], Operations: ['84+8=92', '25+4=29'] Exploring Operation: 92+29=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 92*29=2668, Resulting Numbers: [2668] 2668,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[25, 96], Operations: ['84+8=92', '4+92=96'] Exploring Operation: 25+96=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 25*96=2400, Resulting Numbers: [2400] 2400,97 unequal: No Solution Exploring Operation: 96-25=71, Resulting Numbers: [71] 71,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[32, 109], Operations: ['8*4=32', '84+25=109'] Exploring Operation: 109-32=77, Resulting Numbers: [77] 77,97 unequal: No Solution Exploring Operation: 32*109=3488, Resulting Numbers: [3488] 3488,97 unequal: No Solution Exploring Operation: 32+109=141, Resulting Numbers: [141] 141,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[25, 88], Operations: ['84+8=92', '92-4=88'] Exploring Operation: 25*88=2200, Resulting Numbers: [2200] 2200,97 unequal: No Solution Exploring Operation: 25+88=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[92, 21], Operations: ['84+8=92', '25-4=21'] Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 92+21=113, Resulting Numbers: [113] 113,97 unequal: No Solution Exploring Operation: 92*21=1932, Resulting Numbers: [1932] 1932,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[25, 116], Operations: ['8*4=32', '84+32=116'] Exploring Operation: 116-25=91, Resulting Numbers: [91] 91,97 unequal: No Solution Exploring Operation: 25+116=141, Resulting Numbers: [141] 141,97 unequal: No Solution Exploring Operation: 25*116=2900, Resulting Numbers: [2900] 2900,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[32, 59], Operations: ['8*4=32', '84-25=59'] Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,97 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[84, 7], Operations: ['8*4=32', '32-25=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,97 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,97 unequal: No Solution Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,97 unequal: No Solution Exploring Operation: 84*7=588, Resulting Numbers: [588] 588,97 unequal: No Solution Moving to Node #0,4,0 Current State: 97:[8, 16], Operations: ['25*4=100', '100-84=16'] Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,97 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 98, 12, 62, 51 ]
75
[ "98-12=86", "62-51=11", "86-11=75" ]
Current State: 75:[98, 12, 62, 51], Operations: [] Exploring Operation: 98-12=86, Resulting Numbers: [62, 51, 86] Generated Node #2: [62, 51, 86] from Operation: 98-12=86 Current State: 75:[62, 51, 86], Operations: ['98-12=86'] Exploring Operation: 62-51=11, Resulting Numbers: [86, 11] Generated Node #3: [86, 11] from Operation: 62-51=11 Current State: 75:[86, 11], Operations: ['98-12=86', '62-51=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[98, 12, 62, 51], Operations: [] Exploring Operation: 98-12=86, Resulting Numbers: [62, 51, 86] Generated Node #0,0: 75:[62, 51, 86] Operation: 98-12=86 Exploring Operation: 98-51=47, Resulting Numbers: [12, 62, 47] Generated Node #0,1: 75:[12, 62, 47] Operation: 98-51=47 Exploring Operation: 62-51=11, Resulting Numbers: [98, 12, 11] Generated Node #0,2: 75:[98, 12, 11] Operation: 62-51=11 Exploring Operation: 98-62=36, Resulting Numbers: [12, 51, 36] Generated Node #0,3: 75:[12, 51, 36] Operation: 98-62=36 Moving to Node #0,2 Current State: 75:[98, 12, 11], Operations: ['62-51=11'] Exploring Operation: 12-11=1, Resulting Numbers: [98, 1] Generated Node #0,2,0: 75:[98, 1] Operation: 12-11=1 Exploring Operation: 12+11=23, Resulting Numbers: [98, 23] Generated Node #0,2,1: 75:[98, 23] Operation: 12+11=23 Exploring Operation: 98-11=87, Resulting Numbers: [12, 87] Generated Node #0,2,2: 75:[12, 87] Operation: 98-11=87 Exploring Operation: 98-12=86, Resulting Numbers: [11, 86] Generated Node #0,2,3: 75:[11, 86] Operation: 98-12=86 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[12, 87], Operations: ['62-51=11', '98-11=87'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[98, 12, 62, 51], Operations: [] Exploring Operation: 62-51=11, Resulting Numbers: [98, 12, 11] Generated Node #0,2: 75:[98, 12, 11] Operation: 62-51=11 Moving to Node #0,2 Current State: 75:[98, 12, 11], Operations: ['62-51=11'] Exploring Operation: 98-11=87, Resulting Numbers: [12, 87] Generated Node #0,2,2: 75:[12, 87] Operation: 98-11=87 Moving to Node #0,2,2 Current State: 75:[12, 87], Operations: ['62-51=11', '98-11=87'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 30, 45, 13, 9 ]
38
[ "30+13=43", "45/9=5", "43-5=38" ]
Current State: 38:[30, 45, 13, 9], Operations: [] Exploring Operation: 30+13=43, Resulting Numbers: [45, 9, 43] Generated Node #2: [45, 9, 43] from Operation: 30+13=43 Current State: 38:[45, 9, 43], Operations: ['30+13=43'] Exploring Operation: 45/9=5, Resulting Numbers: [43, 5] Generated Node #3: [43, 5] from Operation: 45/9=5 Current State: 38:[43, 5], Operations: ['30+13=43', '45/9=5'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[30, 45, 13, 9], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [45, 13, 21] Generated Node #0,0: 38:[45, 13, 21] Operation: 30-9=21 Exploring Operation: 30-13=17, Resulting Numbers: [45, 9, 17] Generated Node #0,1: 38:[45, 9, 17] Operation: 30-13=17 Exploring Operation: 30+9=39, Resulting Numbers: [45, 13, 39] Generated Node #0,2: 38:[45, 13, 39] Operation: 30+9=39 Moving to Node #0,2 Current State: 38:[45, 13, 39], Operations: ['30+9=39'] Exploring Operation: 45-39=6, Resulting Numbers: [13, 6] Generated Node #0,2,0: 38:[13, 6] Operation: 45-39=6 Exploring Operation: 39/13=3, Resulting Numbers: [45, 3] Generated Node #0,2,1: 38:[45, 3] Operation: 39/13=3 Exploring Operation: 45-13=32, Resulting Numbers: [39, 32] Generated Node #0,2,2: 38:[39, 32] Operation: 45-13=32 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 38:[39, 32], Operations: ['30+9=39', '45-13=32'] Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,38 unequal: No Solution Exploring Operation: 39*32=1248, Resulting Numbers: [1248] 1248,38 unequal: No Solution No 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: 38:[45, 3], Operations: ['30+9=39', '39/13=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,38 unequal: No Solution No 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: 38:[13, 6], Operations: ['30+9=39', '45-39=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,38 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,38 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: 38:[45, 13, 21], Operations: ['30-9=21'] Exploring Operation: 13+21=34, Resulting Numbers: [45, 34] Generated Node #0,0,0: 38:[45, 34] Operation: 13+21=34 Exploring Operation: 45-13=32, Resulting Numbers: [21, 32] Generated Node #0,0,1: 38:[21, 32] Operation: 45-13=32 Exploring Operation: 45-21=24, Resulting Numbers: [13, 24] Generated Node #0,0,2: 38:[13, 24] Operation: 45-21=24 Moving to Node #0,1 Current State: 38:[45, 9, 17], Operations: ['30-13=17'] Exploring Operation: 45/9=5, Resulting Numbers: [17, 5] Generated Node #0,1,0: 38:[17, 5] Operation: 45/9=5 Exploring Operation: 45-9=36, Resulting Numbers: [17, 36] Generated Node #0,1,1: 38:[17, 36] Operation: 45-9=36 Exploring Operation: 17-9=8, Resulting Numbers: [45, 8] Generated Node #0,1,2: 38:[45, 8] Operation: 17-9=8 Moving to Node #0,1,1 Current State: 38:[17, 36], Operations: ['30-13=17', '45-9=36'] Exploring Operation: 17*36=612, Resulting Numbers: [612] 612,38 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[17, 5], Operations: ['30-13=17', '45/9=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,38 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[21, 32], Operations: ['30-9=21', '45-13=32'] Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,38 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[13, 24], Operations: ['30-9=21', '45-21=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,38 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[45, 34], Operations: ['30-9=21', '13+21=34'] Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,38 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,38 unequal: No Solution Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[45, 8], Operations: ['30-13=17', '17-9=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,38 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,38 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,38 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 10, 76, 17, 69 ]
53
[ "76-69=7", "10*7=70", "70-17=53" ]
Current State: 53:[10, 76, 17, 69], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [10, 17, 7] Generated Node #2: [10, 17, 7] from Operation: 76-69=7 Current State: 53:[10, 17, 7], Operations: ['76-69=7'] Exploring Operation: 10*7=70, Resulting Numbers: [17, 70] Generated Node #3: [17, 70] from Operation: 10*7=70 Current State: 53:[17, 70], Operations: ['76-69=7', '10*7=70'] Exploring Operation: 70-17=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[10, 76, 17, 69], Operations: [] Exploring Operation: 10+17=27, Resulting Numbers: [76, 69, 27] Generated Node #0,0: 53:[76, 69, 27] Operation: 10+17=27 Exploring Operation: 76-10=66, Resulting Numbers: [17, 69, 66] Generated Node #0,1: 53:[17, 69, 66] Operation: 76-10=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[76, 69, 27], Operations: ['10+17=27'] Exploring Operation: 69-27=42, Resulting Numbers: [76, 42] Generated Node #0,0,0: 53:[76, 42] Operation: 69-27=42 Exploring Operation: 76-27=49, Resulting Numbers: [69, 49] Generated Node #0,0,1: 53:[69, 49] Operation: 76-27=49 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[69, 49], Operations: ['10+17=27', '76-27=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[76, 42], Operations: ['10+17=27', '69-27=42'] Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 76+42=118, Resulting Numbers: [118] 118,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[17, 69, 66], Operations: ['76-10=66'] Exploring Operation: 69-17=52, Resulting Numbers: [66, 52] Generated Node #0,1,0: 53:[66, 52] Operation: 69-17=52 Exploring Operation: 66-17=49, Resulting Numbers: [69, 49] Generated Node #0,1,1: 53:[69, 49] Operation: 66-17=49 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[66, 52], Operations: ['76-10=66', '69-17=52'] Exploring Operation: 66+52=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[69, 49], Operations: ['76-10=66', '66-17=49'] Exploring Operation: 69+49=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 69-49=20, Resulting Numbers: [20] 20,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 30, 87, 4, 99 ]
18
[ "99-87=12", "4*12=48", "48-30=18" ]
Current State: 18:[30, 87, 4, 99], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [30, 4, 12] Generated Node #2: [30, 4, 12] from Operation: 99-87=12 Current State: 18:[30, 4, 12], Operations: ['99-87=12'] Exploring Operation: 4*12=48, Resulting Numbers: [30, 48] Generated Node #3: [30, 48] from Operation: 4*12=48 Current State: 18:[30, 48], Operations: ['99-87=12', '4*12=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[30, 87, 4, 99], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [30, 4, 12] Generated Node #0,0: 18:[30, 4, 12] Operation: 99-87=12 Exploring Operation: 87-30=57, Resulting Numbers: [4, 99, 57] Generated Node #0,1: 18:[4, 99, 57] Operation: 87-30=57 Moving to Node #0,0 Current State: 18:[30, 4, 12], Operations: ['99-87=12'] Exploring Operation: 30-12=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 18:[4, 18] Operation: 30-12=18 Exploring Operation: 30-4=26, Resulting Numbers: [12, 26] Generated Node #0,0,1: 18:[12, 26] Operation: 30-4=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[4, 18], Operations: ['99-87=12', '30-12=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[12, 26], Operations: ['99-87=12', '30-4=26'] Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[4, 99, 57], Operations: ['87-30=57'] Exploring Operation: 99-57=42, Resulting Numbers: [4, 42] Generated Node #0,1,0: 18:[4, 42] Operation: 99-57=42 Exploring Operation: 99-4=95, Resulting Numbers: [57, 95] Generated Node #0,1,1: 18:[57, 95] Operation: 99-4=95 Moving to Node #0,1,0 Current State: 18:[4, 42], Operations: ['87-30=57', '99-57=42'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[57, 95], Operations: ['87-30=57', '99-4=95'] Exploring Operation: 57+95=152, Resulting Numbers: [152] 152,18 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,18 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 94, 30, 25, 35 ]
54
[ "94-30=64", "35-25=10", "64-10=54" ]
Current State: 54:[94, 30, 25, 35], Operations: [] Exploring Operation: 94-30=64, Resulting Numbers: [25, 35, 64] Generated Node #2: [25, 35, 64] from Operation: 94-30=64 Current State: 54:[25, 35, 64], Operations: ['94-30=64'] Exploring Operation: 35-25=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 35-25=10 Current State: 54:[64, 10], Operations: ['94-30=64', '35-25=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[94, 30, 25, 35], Operations: [] Exploring Operation: 94-35=59, Resulting Numbers: [30, 25, 59] Generated Node #0,0: 54:[30, 25, 59] Operation: 94-35=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[30, 25, 59], Operations: ['94-35=59'] Exploring Operation: 59-30=29, Resulting Numbers: [25, 29] Generated Node #0,0,0: 54:[25, 29] Operation: 59-30=29 Moving to Node #0,0,0 Current State: 54:[25, 29], Operations: ['94-35=59', '59-30=29'] Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[94, 30, 25, 35], Operations: [] Exploring Operation: 94-35=59, Resulting Numbers: [30, 25, 59] Generated Node #0,0: 54:[30, 25, 59] Operation: 94-35=59 Moving to Node #0,0 Current State: 54:[30, 25, 59], Operations: ['94-35=59'] Exploring Operation: 59-30=29, Resulting Numbers: [25, 29] Generated Node #0,0,0: 54:[25, 29] Operation: 59-30=29 Moving to Node #0,0,0 Current State: 54:[25, 29], Operations: ['94-35=59', '59-30=29'] Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 90, 55, 22, 26 ]
50
[ "55*22=1210", "90+1210=1300", "1300/26=50" ]
Current State: 50:[90, 55, 22, 26], Operations: [] Exploring Operation: 55*22=1210, Resulting Numbers: [90, 26, 1210] Generated Node #2: [90, 26, 1210] from Operation: 55*22=1210 Current State: 50:[90, 26, 1210], Operations: ['55*22=1210'] Exploring Operation: 90+1210=1300, Resulting Numbers: [26, 1300] Generated Node #3: [26, 1300] from Operation: 90+1210=1300 Current State: 50:[26, 1300], Operations: ['55*22=1210', '90+1210=1300'] Exploring Operation: 1300/26=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[90, 55, 22, 26], Operations: [] Exploring Operation: 90-26=64, Resulting Numbers: [55, 22, 64] Generated Node #0,0: 50:[55, 22, 64] Operation: 90-26=64 Exploring Operation: 90-55=35, Resulting Numbers: [22, 26, 35] Generated Node #0,1: 50:[22, 26, 35] Operation: 90-55=35 Moving to Node #0,1 Current State: 50:[22, 26, 35], Operations: ['90-55=35'] Exploring Operation: 35-26=9, Resulting Numbers: [22, 9] Generated Node #0,1,0: 50:[22, 9] Operation: 35-26=9 Exploring Operation: 35-22=13, Resulting Numbers: [26, 13] Generated Node #0,1,1: 50:[26, 13] Operation: 35-22=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[22, 9], Operations: ['90-55=35', '35-26=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,50 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[26, 13], Operations: ['90-55=35', '35-22=13'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,50 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,50 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: 50:[55, 22, 64], Operations: ['90-26=64'] Exploring Operation: 64-55=9, Resulting Numbers: [22, 9] Generated Node #0,0,0: 50:[22, 9] Operation: 64-55=9 Exploring Operation: 64-22=42, Resulting Numbers: [55, 42] Generated Node #0,0,1: 50:[55, 42] Operation: 64-22=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[22, 9], Operations: ['90-26=64', '64-55=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,50 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 50:[55, 42], Operations: ['90-26=64', '64-22=42'] Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,50 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,50 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
[ 14, 89, 40, 14 ]
89
[ "14-14=0", "40*0=0", "89+0=89" ]
Current State: 89:[14, 89, 40, 14], Operations: [] Exploring Operation: 14-14=0, Resulting Numbers: [89, 40, 0] Generated Node #2: [89, 40, 0] from Operation: 14-14=0 Current State: 89:[89, 40, 0], Operations: ['14-14=0'] Exploring Operation: 40*0=0, Resulting Numbers: [89, 0] Generated Node #3: [89, 0] from Operation: 40*0=0 Current State: 89:[89, 0], Operations: ['14-14=0', '40*0=0'] Exploring Operation: 89+0=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[14, 89, 40, 14], Operations: [] Exploring Operation: 40+14=54, Resulting Numbers: [14, 89, 54] Generated Node #0,0: 89:[14, 89, 54] Operation: 40+14=54 Exploring Operation: 14+40=54, Resulting Numbers: [89, 14, 54] Generated Node #0,1: 89:[89, 14, 54] Operation: 14+40=54 Exploring Operation: 14+14=28, Resulting Numbers: [89, 40, 28] Generated Node #0,2: 89:[89, 40, 28] Operation: 14+14=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[14, 89, 54], Operations: ['40+14=54'] Exploring Operation: 14+89=103, Resulting Numbers: [54, 103] Generated Node #0,0,0: 89:[54, 103] Operation: 14+89=103 Exploring Operation: 89-14=75, Resulting Numbers: [54, 75] Generated Node #0,0,1: 89:[54, 75] Operation: 89-14=75 Exploring Operation: 14+54=68, Resulting Numbers: [89, 68] Generated Node #0,0,2: 89:[89, 68] Operation: 14+54=68 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[89, 68], Operations: ['40+14=54', '14+54=68'] Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 89+68=157, Resulting Numbers: [157] 157,89 unequal: No Solution Exploring Operation: 89*68=6052, Resulting Numbers: [6052] 6052,89 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:[54, 103], Operations: ['40+14=54', '14+89=103'] Exploring Operation: 54*103=5562, Resulting Numbers: [5562] 5562,89 unequal: No Solution Exploring Operation: 54+103=157, Resulting Numbers: [157] 157,89 unequal: No Solution Exploring Operation: 103-54=49, Resulting Numbers: [49] 49,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[54, 75], Operations: ['40+14=54', '89-14=75'] Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,89 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:[89, 14, 54], Operations: ['14+40=54'] Exploring Operation: 14+54=68, Resulting Numbers: [89, 68] Generated Node #0,1,0: 89:[89, 68] Operation: 14+54=68 Exploring Operation: 89-14=75, Resulting Numbers: [54, 75] Generated Node #0,1,1: 89:[54, 75] Operation: 89-14=75 Exploring Operation: 89+14=103, Resulting Numbers: [54, 103] Generated Node #0,1,2: 89:[54, 103] Operation: 89+14=103 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[89, 68], Operations: ['14+40=54', '14+54=68'] Exploring Operation: 89*68=6052, Resulting Numbers: [6052] 6052,89 unequal: No Solution Exploring Operation: 89+68=157, Resulting Numbers: [157] 157,89 unequal: No Solution Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,89 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:[54, 75], Operations: ['14+40=54', '89-14=75'] Exploring Operation: 75-54=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 54+75=129, Resulting Numbers: [129] 129,89 unequal: No Solution Exploring Operation: 54*75=4050, Resulting Numbers: [4050] 4050,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[54, 103], Operations: ['14+40=54', '89+14=103'] Exploring Operation: 103-54=49, Resulting Numbers: [49] 49,89 unequal: No Solution Exploring Operation: 54*103=5562, Resulting Numbers: [5562] 5562,89 unequal: No Solution Exploring Operation: 54+103=157, Resulting Numbers: [157] 157,89 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 #0,2 Current State: 89:[89, 40, 28], Operations: ['14+14=28'] Exploring Operation: 40+28=68, Resulting Numbers: [89, 68] Generated Node #0,2,0: 89:[89, 68] Operation: 40+28=68 Exploring Operation: 89+28=117, Resulting Numbers: [40, 117] Generated Node #0,2,1: 89:[40, 117] Operation: 89+28=117 Exploring Operation: 89-28=61, Resulting Numbers: [40, 61] Generated Node #0,2,2: 89:[40, 61] Operation: 89-28=61 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[89, 68], Operations: ['14+14=28', '40+28=68'] Exploring Operation: 89+68=157, Resulting Numbers: [157] 157,89 unequal: No Solution Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 89*68=6052, Resulting Numbers: [6052] 6052,89 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 #0,2,1 Current State: 89:[40, 117], Operations: ['14+14=28', '89+28=117'] Exploring Operation: 40*117=4680, Resulting Numbers: [4680] 4680,89 unequal: No Solution Exploring Operation: 117-40=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 40+117=157, Resulting Numbers: [157] 157,89 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 #0,2,2 Current State: 89:[40, 61], Operations: ['14+14=28', '89-28=61'] Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,89 unequal: No Solution Exploring Operation: 40*61=2440, Resulting Numbers: [2440] 2440,89 unequal: No Solution Exploring Operation: 40+61=101, Resulting Numbers: [101] 101,89 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_3
sum_heuristic
[ 7, 45, 71, 10 ]
86
[ "10-7=3", "45/3=15", "71+15=86" ]
Current State: 86:[7, 45, 71, 10], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [45, 71, 3] Generated Node #2: [45, 71, 3] from Operation: 10-7=3 Current State: 86:[45, 71, 3], Operations: ['10-7=3'] Exploring Operation: 45/3=15, Resulting Numbers: [71, 15] Generated Node #3: [71, 15] from Operation: 45/3=15 Current State: 86:[71, 15], Operations: ['10-7=3', '45/3=15'] Exploring Operation: 71+15=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[7, 45, 71, 10], Operations: [] Exploring Operation: 71+10=81, Resulting Numbers: [7, 45, 81] Generated Node #0,0: 86:[7, 45, 81] Operation: 71+10=81 Moving to Node #0,0 Current State: 86:[7, 45, 81], Operations: ['71+10=81'] Exploring Operation: 7+81=88, Resulting Numbers: [45, 88] Generated Node #0,0,0: 86:[45, 88] Operation: 7+81=88 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[45, 88], Operations: ['71+10=81', '7+81=88'] Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,86 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
[ 7, 25, 4, 89 ]
38
[ "7-4=3", "25+89=114", "114/3=38" ]
Current State: 38:[7, 25, 4, 89], Operations: [] Exploring Operation: 7-4=3, Resulting Numbers: [25, 89, 3] Generated Node #2: [25, 89, 3] from Operation: 7-4=3 Current State: 38:[25, 89, 3], Operations: ['7-4=3'] Exploring Operation: 25+89=114, Resulting Numbers: [3, 114] Generated Node #3: [3, 114] from Operation: 25+89=114 Current State: 38:[3, 114], Operations: ['7-4=3', '25+89=114'] Exploring Operation: 114/3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[7, 25, 4, 89], Operations: [] Exploring Operation: 89-25=64, Resulting Numbers: [7, 4, 64] Generated Node #0,0: 38:[7, 4, 64] Operation: 89-25=64 Exploring Operation: 89-7=82, Resulting Numbers: [25, 4, 82] Generated Node #0,1: 38:[25, 4, 82] Operation: 89-7=82 Moving to Node #0,0 Current State: 38:[7, 4, 64], Operations: ['89-25=64'] Exploring Operation: 64/4=16, Resulting Numbers: [7, 16] Generated Node #0,0,0: 38:[7, 16] Operation: 64/4=16 Exploring Operation: 64-7=57, Resulting Numbers: [4, 57] Generated Node #0,0,1: 38:[4, 57] Operation: 64-7=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[7, 16], Operations: ['89-25=64', '64/4=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,38 unequal: No Solution No 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: 38:[4, 57], Operations: ['89-25=64', '64-7=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,38 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: 38:[25, 4, 82], Operations: ['89-7=82'] Exploring Operation: 82-25=57, Resulting Numbers: [4, 57] Generated Node #0,1,0: 38:[4, 57] Operation: 82-25=57 Exploring Operation: 25-4=21, Resulting Numbers: [82, 21] Generated Node #0,1,1: 38:[82, 21] Operation: 25-4=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[4, 57], Operations: ['89-7=82', '82-25=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,38 unequal: No Solution No 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: 38:[82, 21], Operations: ['89-7=82', '25-4=21'] Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,38 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
[ 80, 55, 40, 43 ]
75
[ "80-55=25", "43-40=3", "25*3=75" ]
Current State: 75:[80, 55, 40, 43], Operations: [] Exploring Operation: 80-55=25, Resulting Numbers: [40, 43, 25] Generated Node #2: [40, 43, 25] from Operation: 80-55=25 Current State: 75:[40, 43, 25], Operations: ['80-55=25'] Exploring Operation: 43-40=3, Resulting Numbers: [25, 3] Generated Node #3: [25, 3] from Operation: 43-40=3 Current State: 75:[25, 3], Operations: ['80-55=25', '43-40=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[80, 55, 40, 43], Operations: [] Exploring Operation: 40+43=83, Resulting Numbers: [80, 55, 83] Generated Node #0,0: 75:[80, 55, 83] Operation: 40+43=83 Exploring Operation: 55-43=12, Resulting Numbers: [80, 40, 12] Generated Node #0,1: 75:[80, 40, 12] Operation: 55-43=12 Exploring Operation: 55-40=15, Resulting Numbers: [80, 43, 15] Generated Node #0,2: 75:[80, 43, 15] Operation: 55-40=15 Exploring Operation: 43-40=3, Resulting Numbers: [80, 55, 3] Generated Node #0,3: 75:[80, 55, 3] Operation: 43-40=3 Exploring Operation: 80-55=25, Resulting Numbers: [40, 43, 25] Generated Node #0,4: 75:[40, 43, 25] Operation: 80-55=25 Moving to Node #0,1 Current State: 75:[80, 40, 12], Operations: ['55-43=12'] Exploring Operation: 40+12=52, Resulting Numbers: [80, 52] Generated Node #0,1,0: 75:[80, 52] Operation: 40+12=52 Exploring Operation: 80/40=2, Resulting Numbers: [12, 2] Generated Node #0,1,1: 75:[12, 2] Operation: 80/40=2 Exploring Operation: 80-40=40, Resulting Numbers: [12, 40] Generated Node #0,1,2: 75:[12, 40] Operation: 80-40=40 Exploring Operation: 40-12=28, Resulting Numbers: [80, 28] Generated Node #0,1,3: 75:[80, 28] Operation: 40-12=28 Exploring Operation: 80-12=68, Resulting Numbers: [40, 68] Generated Node #0,1,4: 75:[40, 68] Operation: 80-12=68 Moving to Node #0,2 Current State: 75:[80, 43, 15], Operations: ['55-40=15'] Exploring Operation: 80-15=65, Resulting Numbers: [43, 65] Generated Node #0,2,0: 75:[43, 65] Operation: 80-15=65 Exploring Operation: 80+15=95, Resulting Numbers: [43, 95] Generated Node #0,2,1: 75:[43, 95] Operation: 80+15=95 Exploring Operation: 43-15=28, Resulting Numbers: [80, 28] Generated Node #0,2,2: 75:[80, 28] Operation: 43-15=28 Exploring Operation: 80-43=37, Resulting Numbers: [15, 37] Generated Node #0,2,3: 75:[15, 37] Operation: 80-43=37 Exploring Operation: 43+15=58, Resulting Numbers: [80, 58] Generated Node #0,2,4: 75:[80, 58] Operation: 43+15=58 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[80, 28], Operations: ['55-40=15', '43-15=28'] Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,75 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,75 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 #0,2,3 Current State: 75:[15, 37], Operations: ['55-40=15', '80-43=37'] Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,75 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,75 unequal: No Solution Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,75 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 #0,2,4 Current State: 75:[80, 58], Operations: ['55-40=15', '43+15=58'] Exploring Operation: 80+58=138, Resulting Numbers: [138] 138,75 unequal: No Solution Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,75 unequal: No Solution Exploring Operation: 80*58=4640, Resulting Numbers: [4640] 4640,75 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 #0,2,0 Current State: 75:[43, 65], Operations: ['55-40=15', '80-15=65'] Exploring Operation: 43+65=108, Resulting Numbers: [108] 108,75 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,75 unequal: No Solution Exploring Operation: 43*65=2795, Resulting Numbers: [2795] 2795,75 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 #0,2,1 Current State: 75:[43, 95], Operations: ['55-40=15', '80+15=95'] Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,75 unequal: No Solution Exploring Operation: 43*95=4085, Resulting Numbers: [4085] 4085,75 unequal: No Solution Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 75:[80, 55, 3], Operations: ['43-40=3'] Exploring Operation: 80-3=77, Resulting Numbers: [55, 77] Generated Node #0,3,0: 75:[55, 77] Operation: 80-3=77 Exploring Operation: 80+3=83, Resulting Numbers: [55, 83] Generated Node #0,3,1: 75:[55, 83] Operation: 80+3=83 Exploring Operation: 55-3=52, Resulting Numbers: [80, 52] Generated Node #0,3,2: 75:[80, 52] Operation: 55-3=52 Exploring Operation: 80-55=25, Resulting Numbers: [3, 25] Generated Node #0,3,3: 75:[3, 25] Operation: 80-55=25 Exploring Operation: 55+3=58, Resulting Numbers: [80, 58] Generated Node #0,3,4: 75:[80, 58] Operation: 55+3=58 Moving to Node #0,0 Current State: 75:[80, 55, 83], Operations: ['40+43=83'] Exploring Operation: 80-55=25, Resulting Numbers: [83, 25] Generated Node #0,0,0: 75:[83, 25] Operation: 80-55=25 Exploring Operation: 83-55=28, Resulting Numbers: [80, 28] Generated Node #0,0,1: 75:[80, 28] Operation: 83-55=28 Exploring Operation: 83-80=3, Resulting Numbers: [55, 3] Generated Node #0,0,2: 75:[55, 3] Operation: 83-80=3 Exploring Operation: 80+55=135, Resulting Numbers: [83, 135] Generated Node #0,0,3: 75:[83, 135] Operation: 80+55=135 Exploring Operation: 55+83=138, Resulting Numbers: [80, 138] Generated Node #0,0,4: 75:[80, 138] Operation: 55+83=138 Moving to Node #0,4 Current State: 75:[40, 43, 25], Operations: ['80-55=25'] Exploring Operation: 43-40=3, Resulting Numbers: [25, 3] Generated Node #0,4,0: 75:[25, 3] Operation: 43-40=3 Exploring Operation: 43-25=18, Resulting Numbers: [40, 18] Generated Node #0,4,1: 75:[40, 18] Operation: 43-25=18 Exploring Operation: 43+25=68, Resulting Numbers: [40, 68] Generated Node #0,4,2: 75:[40, 68] Operation: 43+25=68 Exploring Operation: 40-25=15, Resulting Numbers: [43, 15] Generated Node #0,4,3: 75:[43, 15] Operation: 40-25=15 Exploring Operation: 40+43=83, Resulting Numbers: [25, 83] Generated Node #0,4,4: 75:[25, 83] Operation: 40+43=83 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 75:[25, 3], Operations: ['80-55=25', '43-40=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[80, 55, 40, 43], Operations: [] Exploring Operation: 80-55=25, Resulting Numbers: [40, 43, 25] Generated Node #0,4: 75:[40, 43, 25] Operation: 80-55=25 Moving to Node #0,4 Current State: 75:[40, 43, 25], Operations: ['80-55=25'] Exploring Operation: 43-40=3, Resulting Numbers: [25, 3] Generated Node #0,4,0: 75:[25, 3] Operation: 43-40=3 Moving to Node #0,4,0 Current State: 75:[25, 3], Operations: ['80-55=25', '43-40=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_5
sum_heuristic
[ 15, 6, 44, 73 ]
17
[ "44-15=29", "73+29=102", "102/6=17" ]
Current State: 17:[15, 6, 44, 73], Operations: [] Exploring Operation: 44-15=29, Resulting Numbers: [6, 73, 29] Generated Node #2: [6, 73, 29] from Operation: 44-15=29 Current State: 17:[6, 73, 29], Operations: ['44-15=29'] Exploring Operation: 73+29=102, Resulting Numbers: [6, 102] Generated Node #3: [6, 102] from Operation: 73+29=102 Current State: 17:[6, 102], Operations: ['44-15=29', '73+29=102'] Exploring Operation: 102/6=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[15, 6, 44, 73], Operations: [] Exploring Operation: 73-44=29, Resulting Numbers: [15, 6, 29] Generated Node #0,0: 17:[15, 6, 29] Operation: 73-44=29 Exploring Operation: 44-15=29, Resulting Numbers: [6, 73, 29] Generated Node #0,1: 17:[6, 73, 29] Operation: 44-15=29 Exploring Operation: 73-15=58, Resulting Numbers: [6, 44, 58] Generated Node #0,2: 17:[6, 44, 58] Operation: 73-15=58 Moving to Node #0,0 Current State: 17:[15, 6, 29], Operations: ['73-44=29'] Exploring Operation: 29-6=23, Resulting Numbers: [15, 23] Generated Node #0,0,0: 17:[15, 23] Operation: 29-6=23 Exploring Operation: 15+6=21, Resulting Numbers: [29, 21] Generated Node #0,0,1: 17:[29, 21] Operation: 15+6=21 Exploring Operation: 29-15=14, Resulting Numbers: [6, 14] Generated Node #0,0,2: 17:[6, 14] Operation: 29-15=14 Moving to Node #0,1 Current State: 17:[6, 73, 29], Operations: ['44-15=29'] Exploring Operation: 29-6=23, Resulting Numbers: [73, 23] Generated Node #0,1,0: 17:[73, 23] Operation: 29-6=23 Exploring Operation: 73-6=67, Resulting Numbers: [29, 67] Generated Node #0,1,1: 17:[29, 67] Operation: 73-6=67 Exploring Operation: 73-29=44, Resulting Numbers: [6, 44] Generated Node #0,1,2: 17:[6, 44] Operation: 73-29=44 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 17:[6, 44], Operations: ['44-15=29', '73-29=44'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[73, 23], Operations: ['44-15=29', '29-6=23'] Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 73*23=1679, Resulting Numbers: [1679] 1679,17 unequal: No Solution Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[29, 67], Operations: ['44-15=29', '73-6=67'] Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 29*67=1943, Resulting Numbers: [1943] 1943,17 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: 17:[6, 44, 58], Operations: ['73-15=58'] Exploring Operation: 58-44=14, Resulting Numbers: [6, 14] Generated Node #0,2,0: 17:[6, 14] Operation: 58-44=14 Exploring Operation: 44-6=38, Resulting Numbers: [58, 38] Generated Node #0,2,1: 17:[58, 38] Operation: 44-6=38 Exploring Operation: 58-6=52, Resulting Numbers: [44, 52] Generated Node #0,2,2: 17:[44, 52] Operation: 58-6=52 Moving to Node #0,0,0 Current State: 17:[15, 23], Operations: ['73-44=29', '29-6=23'] Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 15*23=345, Resulting Numbers: [345] 345,17 unequal: No Solution Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[6, 14], Operations: ['73-44=29', '29-15=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,17 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[6, 14], Operations: ['73-15=58', '58-44=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[29, 21], Operations: ['73-44=29', '15+6=21'] Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,17 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[44, 52], Operations: ['73-15=58', '58-6=52'] Exploring Operation: 44*52=2288, Resulting Numbers: [2288] 2288,17 unequal: No Solution Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 44+52=96, Resulting Numbers: [96] 96,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[58, 38], Operations: ['73-15=58', '44-6=38'] Exploring Operation: 58*38=2204, Resulting Numbers: [2204] 2204,17 unequal: No Solution Exploring Operation: 58+38=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,17 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 92, 33, 81, 12 ]
99
[ "92-81=11", "12*11=132", "132-33=99" ]
Current State: 99:[92, 33, 81, 12], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [33, 12, 11] Generated Node #2: [33, 12, 11] from Operation: 92-81=11 Current State: 99:[33, 12, 11], Operations: ['92-81=11'] Exploring Operation: 12*11=132, Resulting Numbers: [33, 132] Generated Node #3: [33, 132] from Operation: 12*11=132 Current State: 99:[33, 132], Operations: ['92-81=11', '12*11=132'] Exploring Operation: 132-33=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[92, 33, 81, 12], Operations: [] Exploring Operation: 81-33=48, Resulting Numbers: [92, 12, 48] Generated Node #0,0: 99:[92, 12, 48] Operation: 81-33=48 Exploring Operation: 92-81=11, Resulting Numbers: [33, 12, 11] Generated Node #0,1: 99:[33, 12, 11] Operation: 92-81=11 Exploring Operation: 81+12=93, Resulting Numbers: [92, 33, 93] Generated Node #0,2: 99:[92, 33, 93] Operation: 81+12=93 Exploring Operation: 92+12=104, Resulting Numbers: [33, 81, 104] Generated Node #0,3: 99:[33, 81, 104] Operation: 92+12=104 Exploring Operation: 33+81=114, Resulting Numbers: [92, 12, 114] Generated Node #0,4: 99:[92, 12, 114] Operation: 33+81=114 Moving to Node #0,1 Current State: 99:[33, 12, 11], Operations: ['92-81=11'] Exploring Operation: 33+12=45, Resulting Numbers: [11, 45] Generated Node #0,1,0: 99:[11, 45] Operation: 33+12=45 Exploring Operation: 33-12=21, Resulting Numbers: [11, 21] Generated Node #0,1,1: 99:[11, 21] Operation: 33-12=21 Exploring Operation: 12-11=1, Resulting Numbers: [33, 1] Generated Node #0,1,2: 99:[33, 1] Operation: 12-11=1 Exploring Operation: 33/11=3, Resulting Numbers: [12, 3] Generated Node #0,1,3: 99:[12, 3] Operation: 33/11=3 Exploring Operation: 12+11=23, Resulting Numbers: [33, 23] Generated Node #0,1,4: 99:[33, 23] Operation: 12+11=23 Moving to Node #0,2 Current State: 99:[92, 33, 93], Operations: ['81+12=93'] Exploring Operation: 33+93=126, Resulting Numbers: [92, 126] Generated Node #0,2,0: 99:[92, 126] Operation: 33+93=126 Exploring Operation: 92+33=125, Resulting Numbers: [93, 125] Generated Node #0,2,1: 99:[93, 125] Operation: 92+33=125 Exploring Operation: 93-92=1, Resulting Numbers: [33, 1] Generated Node #0,2,2: 99:[33, 1] Operation: 93-92=1 Exploring Operation: 93-33=60, Resulting Numbers: [92, 60] Generated Node #0,2,3: 99:[92, 60] Operation: 93-33=60 Exploring Operation: 92-33=59, Resulting Numbers: [93, 59] Generated Node #0,2,4: 99:[93, 59] Operation: 92-33=59 Moving to Node #0,0 Current State: 99:[92, 12, 48], Operations: ['81-33=48'] Exploring Operation: 92-12=80, Resulting Numbers: [48, 80] Generated Node #0,0,0: 99:[48, 80] Operation: 92-12=80 Exploring Operation: 92-48=44, Resulting Numbers: [12, 44] Generated Node #0,0,1: 99:[12, 44] Operation: 92-48=44 Exploring Operation: 92+12=104, Resulting Numbers: [48, 104] Generated Node #0,0,2: 99:[48, 104] Operation: 92+12=104 Exploring Operation: 48/12=4, Resulting Numbers: [92, 4] Generated Node #0,0,3: 99:[92, 4] Operation: 48/12=4 Exploring Operation: 48-12=36, Resulting Numbers: [92, 36] Generated Node #0,0,4: 99:[92, 36] Operation: 48-12=36 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 99:[92, 4], Operations: ['81-33=48', '48/12=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,99 unequal: No Solution Exploring Operation: 92*4=368, Resulting Numbers: [368] 368,99 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,99 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 #0,0,4 Current State: 99:[92, 36], Operations: ['81-33=48', '48-12=36'] Exploring Operation: 92*36=3312, Resulting Numbers: [3312] 3312,99 unequal: No Solution Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,99 unequal: No Solution Exploring Operation: 92+36=128, Resulting Numbers: [128] 128,99 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 #0,0,1 Current State: 99:[12, 44], Operations: ['81-33=48', '92-48=44'] Exploring Operation: 12*44=528, Resulting Numbers: [528] 528,99 unequal: No Solution Exploring Operation: 12+44=56, Resulting Numbers: [56] 56,99 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[48, 104], Operations: ['81-33=48', '92+12=104'] Exploring Operation: 48+104=152, Resulting Numbers: [152] 152,99 unequal: No Solution Exploring Operation: 48*104=4992, Resulting Numbers: [4992] 4992,99 unequal: No Solution Exploring Operation: 104-48=56, Resulting Numbers: [56] 56,99 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 #0,0,0 Current State: 99:[48, 80], Operations: ['81-33=48', '92-12=80'] Exploring Operation: 48*80=3840, Resulting Numbers: [3840] 3840,99 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 48+80=128, Resulting Numbers: [128] 128,99 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: 99:[33, 81, 104], Operations: ['92+12=104'] Exploring Operation: 33+81=114, Resulting Numbers: [104, 114] Generated Node #0,3,0: 99:[104, 114] Operation: 33+81=114 Exploring Operation: 81-33=48, Resulting Numbers: [104, 48] Generated Node #0,3,1: 99:[104, 48] Operation: 81-33=48 Exploring Operation: 33+104=137, Resulting Numbers: [81, 137] Generated Node #0,3,2: 99:[81, 137] Operation: 33+104=137 Exploring Operation: 104-81=23, Resulting Numbers: [33, 23] Generated Node #0,3,3: 99:[33, 23] Operation: 104-81=23 Exploring Operation: 104-33=71, Resulting Numbers: [81, 71] Generated Node #0,3,4: 99:[81, 71] Operation: 104-33=71 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 99:[33, 23], Operations: ['92+12=104', '104-81=23'] Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 33*23=759, Resulting Numbers: [759] 759,99 unequal: No Solution Exploring Operation: 33+23=56, Resulting Numbers: [56] 56,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 99:[104, 114], Operations: ['92+12=104', '33+81=114'] Exploring Operation: 104+114=218, Resulting Numbers: [218] 218,99 unequal: No Solution Exploring Operation: 104*114=11856, Resulting Numbers: [11856] 11856,99 unequal: No Solution Exploring Operation: 114-104=10, Resulting Numbers: [10] 10,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 99:[104, 48], Operations: ['92+12=104', '81-33=48'] Exploring Operation: 104*48=4992, Resulting Numbers: [4992] 4992,99 unequal: No Solution Exploring Operation: 104+48=152, Resulting Numbers: [152] 152,99 unequal: No Solution Exploring Operation: 104-48=56, Resulting Numbers: [56] 56,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 99:[81, 71], Operations: ['92+12=104', '104-33=71'] Exploring Operation: 81+71=152, Resulting Numbers: [152] 152,99 unequal: No Solution Exploring Operation: 81-71=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 81*71=5751, Resulting Numbers: [5751] 5751,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[81, 137], Operations: ['92+12=104', '33+104=137'] Exploring Operation: 81*137=11097, Resulting Numbers: [11097] 11097,99 unequal: No Solution Exploring Operation: 81+137=218, Resulting Numbers: [218] 218,99 unequal: No Solution Exploring Operation: 137-81=56, Resulting Numbers: [56] 56,99 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: 99:[92, 12, 114], Operations: ['33+81=114'] Exploring Operation: 12+114=126, Resulting Numbers: [92, 126] Generated Node #0,4,0: 99:[92, 126] Operation: 12+114=126 Exploring Operation: 92-12=80, Resulting Numbers: [114, 80] Generated Node #0,4,1: 99:[114, 80] Operation: 92-12=80 Exploring Operation: 92+12=104, Resulting Numbers: [114, 104] Generated Node #0,4,2: 99:[114, 104] Operation: 92+12=104 Exploring Operation: 114-92=22, Resulting Numbers: [12, 22] Generated Node #0,4,3: 99:[12, 22] Operation: 114-92=22 Exploring Operation: 114-12=102, Resulting Numbers: [92, 102] Generated Node #0,4,4: 99:[92, 102] Operation: 114-12=102 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 99:[92, 102], Operations: ['33+81=114', '114-12=102'] Exploring Operation: 92+102=194, Resulting Numbers: [194] 194,99 unequal: No Solution Exploring Operation: 92*102=9384, Resulting Numbers: [9384] 9384,99 unequal: No Solution Exploring Operation: 102-92=10, Resulting Numbers: [10] 10,99 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 #0,4,3 Current State: 99:[12, 22], Operations: ['33+81=114', '114-92=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,99 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,99 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 #0,4,2 Current State: 99:[114, 104], Operations: ['33+81=114', '92+12=104'] Exploring Operation: 114*104=11856, Resulting Numbers: [11856] 11856,99 unequal: No Solution Exploring Operation: 114+104=218, Resulting Numbers: [218] 218,99 unequal: No Solution Exploring Operation: 114-104=10, Resulting Numbers: [10] 10,99 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 #0,4,0 Current State: 99:[92, 126], Operations: ['33+81=114', '12+114=126'] Exploring Operation: 92+126=218, Resulting Numbers: [218] 218,99 unequal: No Solution Exploring Operation: 126-92=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 92*126=11592, Resulting Numbers: [11592] 11592,99 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 #0,4,1 Current State: 99:[114, 80], Operations: ['33+81=114', '92-12=80'] Exploring Operation: 114-80=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 114*80=9120, Resulting Numbers: [9120] 9120,99 unequal: No Solution Exploring Operation: 114+80=194, Resulting Numbers: [194] 194,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 99:[12, 3], Operations: ['92-81=11', '33/11=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,99 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[33, 1], Operations: ['81+12=93', '93-92=1'] Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[33, 1], Operations: ['92-81=11', '12-11=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[11, 21], Operations: ['92-81=11', '33-12=21'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,99 unequal: No Solution Moving to Node #0,1,4 Current State: 99:[33, 23], Operations: ['92-81=11', '12+11=23'] Exploring Operation: 33*23=759, Resulting Numbers: [759] 759,99 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,99 unequal: No Solution Exploring Operation: 33+23=56, Resulting Numbers: [56] 56,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[11, 45], Operations: ['92-81=11', '33+12=45'] Exploring Operation: 11+45=56, Resulting Numbers: [56] 56,99 unequal: No Solution Exploring Operation: 11*45=495, Resulting Numbers: [495] 495,99 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[93, 125], Operations: ['81+12=93', '92+33=125'] Exploring Operation: 93*125=11625, Resulting Numbers: [11625] 11625,99 unequal: No Solution Exploring Operation: 125-93=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 93+125=218, Resulting Numbers: [218] 218,99 unequal: No Solution Moving to Node #0,2,4 Current State: 99:[93, 59], Operations: ['81+12=93', '92-33=59'] Exploring Operation: 93-59=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 93+59=152, Resulting Numbers: [152] 152,99 unequal: No Solution Exploring Operation: 93*59=5487, Resulting Numbers: [5487] 5487,99 unequal: No Solution Moving to Node #0,2,3 Current State: 99:[92, 60], Operations: ['81+12=93', '93-33=60'] Exploring Operation: 92-60=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 92+60=152, Resulting Numbers: [152] 152,99 unequal: No Solution Exploring Operation: 92*60=5520, Resulting Numbers: [5520] 5520,99 unequal: No Solution Moving to Node #0,2,0 Current State: 99:[92, 126], Operations: ['81+12=93', '33+93=126'] Exploring Operation: 126-92=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 92+126=218, Resulting Numbers: [218] 218,99 unequal: No Solution Exploring Operation: 92*126=11592, Resulting Numbers: [11592] 11592,99 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 20, 43, 2, 50 ]
75
[ "43-20=23", "2+50=52", "23+52=75" ]
Current State: 75:[20, 43, 2, 50], Operations: [] Exploring Operation: 43-20=23, Resulting Numbers: [2, 50, 23] Generated Node #2: [2, 50, 23] from Operation: 43-20=23 Current State: 75:[2, 50, 23], Operations: ['43-20=23'] Exploring Operation: 2+50=52, Resulting Numbers: [23, 52] Generated Node #3: [23, 52] from Operation: 2+50=52 Current State: 75:[23, 52], Operations: ['43-20=23', '2+50=52'] Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[20, 43, 2, 50], Operations: [] Exploring Operation: 50-43=7, Resulting Numbers: [20, 2, 7] Generated Node #0,0: 75:[20, 2, 7] Operation: 50-43=7 Exploring Operation: 50/2=25, Resulting Numbers: [20, 43, 25] Generated Node #0,1: 75:[20, 43, 25] Operation: 50/2=25 Moving to Node #0,0 Current State: 75:[20, 2, 7], Operations: ['50-43=7'] Exploring Operation: 20-7=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 75:[2, 13] Operation: 20-7=13 Exploring Operation: 20+7=27, Resulting Numbers: [2, 27] Generated Node #0,0,1: 75:[2, 27] Operation: 20+7=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[2, 13], Operations: ['50-43=7', '20-7=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 2*13=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 #0,0,1 Current State: 75:[2, 27], Operations: ['50-43=7', '20+7=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 75:[20, 43, 25], Operations: ['50/2=25'] Exploring Operation: 43-20=23, Resulting Numbers: [25, 23] Generated Node #0,1,0: 75:[25, 23] Operation: 43-20=23 Exploring Operation: 43-25=18, Resulting Numbers: [20, 18] Generated Node #0,1,1: 75:[20, 18] Operation: 43-25=18 Moving to Node #0,1,0 Current State: 75:[25, 23], Operations: ['50/2=25', '43-20=23'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[20, 18], Operations: ['50/2=25', '43-25=18'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,75 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 66, 2, 26, 52 ]
38
[ "66-2=64", "52-26=26", "64-26=38" ]
Current State: 38:[66, 2, 26, 52], Operations: [] Exploring Operation: 66-2=64, Resulting Numbers: [26, 52, 64] Generated Node #2: [26, 52, 64] from Operation: 66-2=64 Current State: 38:[26, 52, 64], Operations: ['66-2=64'] Exploring Operation: 52-26=26, Resulting Numbers: [64, 26] Generated Node #3: [64, 26] from Operation: 52-26=26 Current State: 38:[64, 26], Operations: ['66-2=64', '52-26=26'] Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[66, 2, 26, 52], Operations: [] Exploring Operation: 66-52=14, Resulting Numbers: [2, 26, 14] Generated Node #0,0: 38:[2, 26, 14] Operation: 66-52=14 Moving to Node #0,0 Current State: 38:[2, 26, 14], Operations: ['66-52=14'] Exploring Operation: 26+14=40, Resulting Numbers: [2, 40] Generated Node #0,0,0: 38:[2, 40] Operation: 26+14=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[2, 40], Operations: ['66-52=14', '26+14=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[66, 2, 26, 52], Operations: [] Exploring Operation: 66-52=14, Resulting Numbers: [2, 26, 14] Generated Node #0,0: 38:[2, 26, 14] Operation: 66-52=14 Moving to Node #0,0 Current State: 38:[2, 26, 14], Operations: ['66-52=14'] Exploring Operation: 26+14=40, Resulting Numbers: [2, 40] Generated Node #0,0,0: 38:[2, 40] Operation: 26+14=40 Moving to Node #0,0,0 Current State: 38:[2, 40], Operations: ['66-52=14', '26+14=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 64, 60, 18, 59 ]
73
[ "64-60=4", "18+59=77", "77-4=73" ]
Current State: 73:[64, 60, 18, 59], Operations: [] Exploring Operation: 64-60=4, Resulting Numbers: [18, 59, 4] Generated Node #2: [18, 59, 4] from Operation: 64-60=4 Current State: 73:[18, 59, 4], Operations: ['64-60=4'] Exploring Operation: 18+59=77, Resulting Numbers: [4, 77] Generated Node #3: [4, 77] from Operation: 18+59=77 Current State: 73:[4, 77], Operations: ['64-60=4', '18+59=77'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[64, 60, 18, 59], Operations: [] Exploring Operation: 18+59=77, Resulting Numbers: [64, 60, 77] Generated Node #0,0: 73:[64, 60, 77] Operation: 18+59=77 Exploring Operation: 60+18=78, Resulting Numbers: [64, 59, 78] Generated Node #0,1: 73:[64, 59, 78] Operation: 60+18=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[64, 60, 77], Operations: ['18+59=77'] Exploring Operation: 77-60=17, Resulting Numbers: [64, 17] Generated Node #0,0,0: 73:[64, 17] Operation: 77-60=17 Exploring Operation: 64+60=124, Resulting Numbers: [77, 124] Generated Node #0,0,1: 73:[77, 124] Operation: 64+60=124 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[77, 124], Operations: ['18+59=77', '64+60=124'] Exploring Operation: 77+124=201, Resulting Numbers: [201] 201,73 unequal: No Solution Exploring Operation: 124-77=47, Resulting Numbers: [47] 47,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[64, 17], Operations: ['18+59=77', '77-60=17'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,73 unequal: No Solution Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[64, 59, 78], Operations: ['60+18=78'] Exploring Operation: 78-59=19, Resulting Numbers: [64, 19] Generated Node #0,1,0: 73:[64, 19] Operation: 78-59=19 Exploring Operation: 64+59=123, Resulting Numbers: [78, 123] Generated Node #0,1,1: 73:[78, 123] Operation: 64+59=123 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[78, 123], Operations: ['60+18=78', '64+59=123'] Exploring Operation: 78+123=201, Resulting Numbers: [201] 201,73 unequal: No Solution Exploring Operation: 123-78=45, Resulting Numbers: [45] 45,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[64, 19], Operations: ['60+18=78', '78-59=19'] Exploring Operation: 64+19=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 64-19=45, Resulting Numbers: [45] 45,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 63, 45, 42, 5 ]
35
[ "63*5=315", "315/45=7", "42-7=35" ]
Current State: 35:[63, 45, 42, 5], Operations: [] Exploring Operation: 63*5=315, Resulting Numbers: [45, 42, 315] Generated Node #2: [45, 42, 315] from Operation: 63*5=315 Current State: 35:[45, 42, 315], Operations: ['63*5=315'] Exploring Operation: 315/45=7, Resulting Numbers: [42, 7] Generated Node #3: [42, 7] from Operation: 315/45=7 Current State: 35:[42, 7], Operations: ['63*5=315', '315/45=7'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[63, 45, 42, 5], Operations: [] Exploring Operation: 63-45=18, Resulting Numbers: [42, 5, 18] Generated Node #0,0: 35:[42, 5, 18] Operation: 63-45=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[42, 5, 18], Operations: ['63-45=18'] Exploring Operation: 42-18=24, Resulting Numbers: [5, 24] Generated Node #0,0,0: 35:[5, 24] Operation: 42-18=24 Moving to Node #0,0,0 Current State: 35:[5, 24], Operations: ['63-45=18', '42-18=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 16, 25, 39, 50 ]
94
[ "50/25=2", "39*2=78", "16+78=94" ]
Current State: 94:[16, 25, 39, 50], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [16, 39, 2] Generated Node #2: [16, 39, 2] from Operation: 50/25=2 Current State: 94:[16, 39, 2], Operations: ['50/25=2'] Exploring Operation: 39*2=78, Resulting Numbers: [16, 78] Generated Node #3: [16, 78] from Operation: 39*2=78 Current State: 94:[16, 78], Operations: ['50/25=2', '39*2=78'] Exploring Operation: 16+78=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[16, 25, 39, 50], Operations: [] Exploring Operation: 16+25=41, Resulting Numbers: [39, 50, 41] Generated Node #0,0: 94:[39, 50, 41] Operation: 16+25=41 Exploring Operation: 16+39=55, Resulting Numbers: [25, 50, 55] Generated Node #0,1: 94:[25, 50, 55] Operation: 16+39=55 Exploring Operation: 25-16=9, Resulting Numbers: [39, 50, 9] Generated Node #0,2: 94:[39, 50, 9] Operation: 25-16=9 Exploring Operation: 50/25=2, Resulting Numbers: [16, 39, 2] Generated Node #0,3: 94:[16, 39, 2] Operation: 50/25=2 Exploring Operation: 39-25=14, Resulting Numbers: [16, 50, 14] Generated Node #0,4: 94:[16, 50, 14] Operation: 39-25=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[39, 50, 41], Operations: ['16+25=41'] Exploring Operation: 50+41=91, Resulting Numbers: [39, 91] Generated Node #0,0,0: 94:[39, 91] Operation: 50+41=91 Exploring Operation: 50-39=11, Resulting Numbers: [41, 11] Generated Node #0,0,1: 94:[41, 11] Operation: 50-39=11 Exploring Operation: 39+50=89, Resulting Numbers: [41, 89] Generated Node #0,0,2: 94:[41, 89] Operation: 39+50=89 Exploring Operation: 50-41=9, Resulting Numbers: [39, 9] Generated Node #0,0,3: 94:[39, 9] Operation: 50-41=9 Exploring Operation: 41-39=2, Resulting Numbers: [50, 2] Generated Node #0,0,4: 94:[50, 2] Operation: 41-39=2 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 94:[50, 2], Operations: ['16+25=41', '41-39=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,94 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,94 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:[39, 91], Operations: ['16+25=41', '50+41=91'] Exploring Operation: 39*91=3549, Resulting Numbers: [3549] 3549,94 unequal: No Solution Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 39+91=130, Resulting Numbers: [130] 130,94 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:[41, 89], Operations: ['16+25=41', '39+50=89'] Exploring Operation: 41+89=130, Resulting Numbers: [130] 130,94 unequal: No Solution Exploring Operation: 89-41=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 41*89=3649, Resulting Numbers: [3649] 3649,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[41, 11], Operations: ['16+25=41', '50-39=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,94 unequal: No Solution Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 94:[39, 9], Operations: ['16+25=41', '50-41=9'] Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,94 unequal: No Solution Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,94 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:[39, 50, 9], Operations: ['25-16=9'] Exploring Operation: 50-39=11, Resulting Numbers: [9, 11] Generated Node #0,2,0: 94:[9, 11] Operation: 50-39=11 Exploring Operation: 39+9=48, Resulting Numbers: [50, 48] Generated Node #0,2,1: 94:[50, 48] Operation: 39+9=48 Exploring Operation: 39+50=89, Resulting Numbers: [9, 89] Generated Node #0,2,2: 94:[9, 89] Operation: 39+50=89 Exploring Operation: 50-9=41, Resulting Numbers: [39, 41] Generated Node #0,2,3: 94:[39, 41] Operation: 50-9=41 Exploring Operation: 39-9=30, Resulting Numbers: [50, 30] Generated Node #0,2,4: 94:[50, 30] Operation: 39-9=30 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[50, 48], Operations: ['25-16=9', '39+9=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,94 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,94 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:[9, 89], Operations: ['25-16=9', '39+50=89'] Exploring Operation: 9+89=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 9*89=801, Resulting Numbers: [801] 801,94 unequal: No Solution Exploring Operation: 89-9=80, Resulting Numbers: [80] 80,94 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 #0,2,3 Current State: 94:[39, 41], Operations: ['25-16=9', '50-9=41'] Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 39*41=1599, Resulting Numbers: [1599] 1599,94 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:[9, 11], Operations: ['25-16=9', '50-39=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 94:[50, 30], Operations: ['25-16=9', '39-9=30'] Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[16, 39, 2], Operations: ['50/25=2'] Exploring Operation: 39-16=23, Resulting Numbers: [2, 23] Generated Node #0,3,0: 94:[2, 23] Operation: 39-16=23 Exploring Operation: 16+39=55, Resulting Numbers: [2, 55] Generated Node #0,3,1: 94:[2, 55] Operation: 16+39=55 Exploring Operation: 16-2=14, Resulting Numbers: [39, 14] Generated Node #0,3,2: 94:[39, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [39, 8] Generated Node #0,3,3: 94:[39, 8] Operation: 16/2=8 Exploring Operation: 39+2=41, Resulting Numbers: [16, 41] Generated Node #0,3,4: 94:[16, 41] Operation: 39+2=41 Moving to Node #0,3,1 Current State: 94:[2, 55], Operations: ['50/25=2', '16+39=55'] Exploring Operation: 2*55=110, Resulting Numbers: [110] 110,94 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 2+55=57, Resulting Numbers: [57] 57,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[39, 8], Operations: ['50/25=2', '16/2=8'] Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,94 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,94 unequal: No Solution Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[39, 14], Operations: ['50/25=2', '16-2=14'] Exploring Operation: 39*14=546, Resulting Numbers: [546] 546,94 unequal: No Solution Exploring Operation: 39+14=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,94 unequal: No Solution Moving to Node #0,3,4 Current State: 94:[16, 41], Operations: ['50/25=2', '39+2=41'] Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,94 unequal: No Solution Exploring Operation: 16*41=656, Resulting Numbers: [656] 656,94 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[2, 23], Operations: ['50/25=2', '39-16=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,94 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,94 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 #0,4 Current State: 94:[16, 50, 14], Operations: ['39-25=14'] Exploring Operation: 16+14=30, Resulting Numbers: [50, 30] Generated Node #0,4,0: 94:[50, 30] Operation: 16+14=30 Exploring Operation: 16+50=66, Resulting Numbers: [14, 66] Generated Node #0,4,1: 94:[14, 66] Operation: 16+50=66 Exploring Operation: 50-16=34, Resulting Numbers: [14, 34] Generated Node #0,4,2: 94:[14, 34] Operation: 50-16=34 Exploring Operation: 50-14=36, Resulting Numbers: [16, 36] Generated Node #0,4,3: 94:[16, 36] Operation: 50-14=36 Exploring Operation: 16-14=2, Resulting Numbers: [50, 2] Generated Node #0,4,4: 94:[50, 2] Operation: 16-14=2 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 94:[50, 2], Operations: ['39-25=14', '16-14=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,94 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,94 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 94:[50, 30], Operations: ['39-25=14', '16+14=30'] Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,94 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 94:[14, 34], Operations: ['39-25=14', '50-16=34'] Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,94 unequal: No Solution Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 94:[16, 36], Operations: ['39-25=14', '50-14=36'] Exploring Operation: 16+36=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 16*36=576, Resulting Numbers: [576] 576,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 94:[14, 66], Operations: ['39-25=14', '16+50=66'] Exploring Operation: 14*66=924, Resulting Numbers: [924] 924,94 unequal: No Solution Exploring Operation: 14+66=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[25, 50, 55], Operations: ['16+39=55'] Exploring Operation: 25+55=80, Resulting Numbers: [50, 80] Generated Node #0,1,0: 94:[50, 80] Operation: 25+55=80 Exploring Operation: 55-50=5, Resulting Numbers: [25, 5] Generated Node #0,1,1: 94:[25, 5] Operation: 55-50=5 Exploring Operation: 25+50=75, Resulting Numbers: [55, 75] Generated Node #0,1,2: 94:[55, 75] Operation: 25+50=75 Exploring Operation: 50/25=2, Resulting Numbers: [55, 2] Generated Node #0,1,3: 94:[55, 2] Operation: 50/25=2 Exploring Operation: 55-25=30, Resulting Numbers: [50, 30] Generated Node #0,1,4: 94:[50, 30] Operation: 55-25=30 Moving to Node #0,1,3 Current State: 94:[55, 2], Operations: ['16+39=55', '50/25=2'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[50, 80], Operations: ['16+39=55', '25+55=80'] Exploring Operation: 50+80=130, Resulting Numbers: [130] 130,94 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,94 unequal: No Solution Exploring Operation: 50*80=4000, Resulting Numbers: [4000] 4000,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[50, 30], Operations: ['16+39=55', '55-25=30'] Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,94 unequal: No Solution Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[25, 5], Operations: ['16+39=55', '55-50=5'] Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,94 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,94 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[55, 75], Operations: ['16+39=55', '25+50=75'] Exploring Operation: 55*75=4125, Resulting Numbers: [4125] 4125,94 unequal: No Solution Exploring Operation: 75-55=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 55+75=130, Resulting Numbers: [130] 130,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 58, 93, 55, 3 ]
17
[ "93-58=35", "55-3=52", "52-35=17" ]
Current State: 17:[58, 93, 55, 3], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [55, 3, 35] Generated Node #2: [55, 3, 35] from Operation: 93-58=35 Current State: 17:[55, 3, 35], Operations: ['93-58=35'] Exploring Operation: 55-3=52, Resulting Numbers: [35, 52] Generated Node #3: [35, 52] from Operation: 55-3=52 Current State: 17:[35, 52], Operations: ['93-58=35', '55-3=52'] Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[58, 93, 55, 3], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [55, 3, 35] Generated Node #0,0: 17:[55, 3, 35] Operation: 93-58=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[55, 3, 35], Operations: ['93-58=35'] Exploring Operation: 55-35=20, Resulting Numbers: [3, 20] Generated Node #0,0,0: 17:[3, 20] Operation: 55-35=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[3, 20], Operations: ['93-58=35', '55-35=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[58, 93, 55, 3], Operations: [] Exploring Operation: 93-58=35, Resulting Numbers: [55, 3, 35] Generated Node #0,0: 17:[55, 3, 35] Operation: 93-58=35 Moving to Node #0,0 Current State: 17:[55, 3, 35], Operations: ['93-58=35'] Exploring Operation: 55-35=20, Resulting Numbers: [3, 20] Generated Node #0,0,0: 17:[3, 20] Operation: 55-35=20 Moving to Node #0,0,0 Current State: 17:[3, 20], Operations: ['93-58=35', '55-35=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 59, 23, 40 ]
27
[ "59-15=44", "40-23=17", "44-17=27" ]
Current State: 27:[15, 59, 23, 40], Operations: [] Exploring Operation: 59-15=44, Resulting Numbers: [23, 40, 44] Generated Node #2: [23, 40, 44] from Operation: 59-15=44 Current State: 27:[23, 40, 44], Operations: ['59-15=44'] Exploring Operation: 40-23=17, Resulting Numbers: [44, 17] Generated Node #3: [44, 17] from Operation: 40-23=17 Current State: 27:[44, 17], Operations: ['59-15=44', '40-23=17'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[15, 59, 23, 40], Operations: [] Exploring Operation: 59-15=44, Resulting Numbers: [23, 40, 44] Generated Node #0,0: 27:[23, 40, 44] Operation: 59-15=44 Exploring Operation: 59-23=36, Resulting Numbers: [15, 40, 36] Generated Node #0,1: 27:[15, 40, 36] Operation: 59-23=36 Exploring Operation: 59-40=19, Resulting Numbers: [15, 23, 19] Generated Node #0,2: 27:[15, 23, 19] Operation: 59-40=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[15, 23, 19], Operations: ['59-40=19'] Exploring Operation: 19-15=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 27:[23, 4] Operation: 19-15=4 Exploring Operation: 23-19=4, Resulting Numbers: [15, 4] Generated Node #0,2,1: 27:[15, 4] Operation: 23-19=4 Exploring Operation: 23-15=8, Resulting Numbers: [19, 8] Generated Node #0,2,2: 27:[19, 8] Operation: 23-15=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 27:[23, 4], Operations: ['59-40=19', '19-15=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,27 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[15, 59, 23, 40], Operations: [] Exploring Operation: 59-40=19, Resulting Numbers: [15, 23, 19] Generated Node #0,2: 27:[15, 23, 19] Operation: 59-40=19 Moving to Node #0,2 Current State: 27:[15, 23, 19], Operations: ['59-40=19'] Exploring Operation: 19-15=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 27:[23, 4] Operation: 19-15=4 Moving to Node #0,2,0 Current State: 27:[23, 4], Operations: ['59-40=19', '19-15=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 80, 39, 58, 65 ]
34
[ "80-39=41", "65-58=7", "41-7=34" ]
Current State: 34:[80, 39, 58, 65], Operations: [] Exploring Operation: 80-39=41, Resulting Numbers: [58, 65, 41] Generated Node #2: [58, 65, 41] from Operation: 80-39=41 Current State: 34:[58, 65, 41], Operations: ['80-39=41'] Exploring Operation: 65-58=7, Resulting Numbers: [41, 7] Generated Node #3: [41, 7] from Operation: 65-58=7 Current State: 34:[41, 7], Operations: ['80-39=41', '65-58=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[80, 39, 58, 65], Operations: [] Exploring Operation: 65-58=7, Resulting Numbers: [80, 39, 7] Generated Node #0,0: 34:[80, 39, 7] Operation: 65-58=7 Exploring Operation: 80-65=15, Resulting Numbers: [39, 58, 15] Generated Node #0,1: 34:[39, 58, 15] Operation: 80-65=15 Exploring Operation: 80-39=41, Resulting Numbers: [58, 65, 41] Generated Node #0,2: 34:[58, 65, 41] Operation: 80-39=41 Exploring Operation: 80-58=22, Resulting Numbers: [39, 65, 22] Generated Node #0,3: 34:[39, 65, 22] Operation: 80-58=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[39, 58, 15], Operations: ['80-65=15'] Exploring Operation: 39+15=54, Resulting Numbers: [58, 54] Generated Node #0,1,0: 34:[58, 54] Operation: 39+15=54 Exploring Operation: 58-15=43, Resulting Numbers: [39, 43] Generated Node #0,1,1: 34:[39, 43] Operation: 58-15=43 Exploring Operation: 39-15=24, Resulting Numbers: [58, 24] Generated Node #0,1,2: 34:[58, 24] Operation: 39-15=24 Exploring Operation: 58-39=19, Resulting Numbers: [15, 19] Generated Node #0,1,3: 34:[15, 19] Operation: 58-39=19 Moving to Node #0,1,3 Current State: 34:[15, 19], Operations: ['80-65=15', '58-39=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[80, 39, 58, 65], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [39, 58, 15] Generated Node #0,1: 34:[39, 58, 15] Operation: 80-65=15 Moving to Node #0,1 Current State: 34:[39, 58, 15], Operations: ['80-65=15'] Exploring Operation: 58-39=19, Resulting Numbers: [15, 19] Generated Node #0,1,3: 34:[15, 19] Operation: 58-39=19 Moving to Node #0,1,3 Current State: 34:[15, 19], Operations: ['80-65=15', '58-39=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 29, 25, 30, 88 ]
52
[ "29-25=4", "88/4=22", "30+22=52" ]
Current State: 52:[29, 25, 30, 88], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [30, 88, 4] Generated Node #2: [30, 88, 4] from Operation: 29-25=4 Current State: 52:[30, 88, 4], Operations: ['29-25=4'] Exploring Operation: 88/4=22, Resulting Numbers: [30, 22] Generated Node #3: [30, 22] from Operation: 88/4=22 Current State: 52:[30, 22], Operations: ['29-25=4', '88/4=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[29, 25, 30, 88], Operations: [] Exploring Operation: 88-29=59, Resulting Numbers: [25, 30, 59] Generated Node #0,0: 52:[25, 30, 59] Operation: 88-29=59 Exploring Operation: 88-30=58, Resulting Numbers: [29, 25, 58] Generated Node #0,1: 52:[29, 25, 58] Operation: 88-30=58 Moving to Node #0,1 Current State: 52:[29, 25, 58], Operations: ['88-30=58'] Exploring Operation: 58/29=2, Resulting Numbers: [25, 2] Generated Node #0,1,0: 52:[25, 2] Operation: 58/29=2 Exploring Operation: 58-29=29, Resulting Numbers: [25, 29] Generated Node #0,1,1: 52:[25, 29] Operation: 58-29=29 Moving to Node #0,0 Current State: 52:[25, 30, 59], Operations: ['88-29=59'] Exploring Operation: 30-25=5, Resulting Numbers: [59, 5] Generated Node #0,0,0: 52:[59, 5] Operation: 30-25=5 Exploring Operation: 59-30=29, Resulting Numbers: [25, 29] Generated Node #0,0,1: 52:[25, 29] Operation: 59-30=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[25, 29], Operations: ['88-29=59', '59-30=29'] Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[59, 5], Operations: ['88-29=59', '30-25=5'] Exploring Operation: 59+5=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,52 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: 52:[25, 2], Operations: ['88-30=58', '58/29=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[25, 29], Operations: ['88-30=58', '58-29=29'] Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,52 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 57, 93, 42, 29 ]
23
[ "93-57=36", "42-29=13", "36-13=23" ]
Current State: 23:[57, 93, 42, 29], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [42, 29, 36] Generated Node #2: [42, 29, 36] from Operation: 93-57=36 Current State: 23:[42, 29, 36], Operations: ['93-57=36'] Exploring Operation: 42-29=13, Resulting Numbers: [36, 13] Generated Node #3: [36, 13] from Operation: 42-29=13 Current State: 23:[36, 13], Operations: ['93-57=36', '42-29=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[57, 93, 42, 29], Operations: [] Exploring Operation: 93-42=51, Resulting Numbers: [57, 29, 51] Generated Node #0,0: 23:[57, 29, 51] Operation: 93-42=51 Exploring Operation: 93-57=36, Resulting Numbers: [42, 29, 36] Generated Node #0,1: 23:[42, 29, 36] Operation: 93-57=36 Moving to Node #0,1 Current State: 23:[42, 29, 36], Operations: ['93-57=36'] Exploring Operation: 42-29=13, Resulting Numbers: [36, 13] Generated Node #0,1,0: 23:[36, 13] Operation: 42-29=13 Exploring Operation: 42-36=6, Resulting Numbers: [29, 6] Generated Node #0,1,1: 23:[29, 6] Operation: 42-36=6 Moving to Node #0,0 Current State: 23:[57, 29, 51], Operations: ['93-42=51'] Exploring Operation: 57-29=28, Resulting Numbers: [51, 28] Generated Node #0,0,0: 23:[51, 28] Operation: 57-29=28 Exploring Operation: 57-51=6, Resulting Numbers: [29, 6] Generated Node #0,0,1: 23:[29, 6] Operation: 57-51=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 23:[29, 6], Operations: ['93-42=51', '57-51=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[57, 93, 42, 29], Operations: [] Exploring Operation: 93-42=51, Resulting Numbers: [57, 29, 51] Generated Node #0,0: 23:[57, 29, 51] Operation: 93-42=51 Moving to Node #0,0 Current State: 23:[57, 29, 51], Operations: ['93-42=51'] Exploring Operation: 57-51=6, Resulting Numbers: [29, 6] Generated Node #0,0,1: 23:[29, 6] Operation: 57-51=6 Moving to Node #0,0,1 Current State: 23:[29, 6], Operations: ['93-42=51', '57-51=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 76, 84, 24, 84 ]
69
[ "84+84=168", "168/24=7", "76-7=69" ]
Current State: 69:[76, 84, 24, 84], Operations: [] Exploring Operation: 84+84=168, Resulting Numbers: [76, 24, 168] Generated Node #2: [76, 24, 168] from Operation: 84+84=168 Current State: 69:[76, 24, 168], Operations: ['84+84=168'] Exploring Operation: 168/24=7, Resulting Numbers: [76, 7] Generated Node #3: [76, 7] from Operation: 168/24=7 Current State: 69:[76, 7], Operations: ['84+84=168', '168/24=7'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[76, 84, 24, 84], Operations: [] Exploring Operation: 84/84=1, Resulting Numbers: [76, 24, 1] Generated Node #0,0: 69:[76, 24, 1] Operation: 84/84=1 Exploring Operation: 84-84=0, Resulting Numbers: [76, 24, 0] Generated Node #0,1: 69:[76, 24, 0] Operation: 84-84=0 Exploring Operation: 84-76=8, Resulting Numbers: [24, 84, 8] Generated Node #0,2: 69:[24, 84, 8] Operation: 84-76=8 Exploring Operation: 84-76=8, Resulting Numbers: [84, 24, 8] Generated Node #0,3: 69:[84, 24, 8] Operation: 84-76=8 Exploring Operation: 84-24=60, Resulting Numbers: [76, 84, 60] Generated Node #0,4: 69:[76, 84, 60] Operation: 84-24=60 Moving to Node #0,0 Current State: 69:[76, 24, 1], Operations: ['84/84=1'] Exploring Operation: 24*1=24, Resulting Numbers: [76, 24] Generated Node #0,0,0: 69:[76, 24] Operation: 24*1=24 Exploring Operation: 76*1=76, Resulting Numbers: [24, 76] Generated Node #0,0,1: 69:[24, 76] Operation: 76*1=76 Exploring Operation: 76/1=76, Resulting Numbers: [24, 76] Generated Node #0,0,2: 69:[24, 76] Operation: 76/1=76 Exploring Operation: 76-1=75, Resulting Numbers: [24, 75] Generated Node #0,0,3: 69:[24, 75] Operation: 76-1=75 Exploring Operation: 24-1=23, Resulting Numbers: [76, 23] Generated Node #0,0,4: 69:[76, 23] Operation: 24-1=23 Moving to Node #0,1 Current State: 69:[76, 24, 0], Operations: ['84-84=0'] Exploring Operation: 24-0=24, Resulting Numbers: [76, 24] Generated Node #0,1,0: 69:[76, 24] Operation: 24-0=24 Exploring Operation: 24+0=24, Resulting Numbers: [76, 24] Generated Node #0,1,1: 69:[76, 24] Operation: 24+0=24 Exploring Operation: 76*0=0, Resulting Numbers: [24, 0] Generated Node #0,1,2: 69:[24, 0] Operation: 76*0=0 Exploring Operation: 76-0=76, Resulting Numbers: [24, 76] Generated Node #0,1,3: 69:[24, 76] Operation: 76-0=76 Exploring Operation: 76+0=76, Resulting Numbers: [24, 76] Generated Node #0,1,4: 69:[24, 76] Operation: 76+0=76 Moving to Node #0,2 Current State: 69:[24, 84, 8], Operations: ['84-76=8'] Exploring Operation: 84-8=76, Resulting Numbers: [24, 76] Generated Node #0,2,0: 69:[24, 76] Operation: 84-8=76 Exploring Operation: 24+8=32, Resulting Numbers: [84, 32] Generated Node #0,2,1: 69:[84, 32] Operation: 24+8=32 Exploring Operation: 24-8=16, Resulting Numbers: [84, 16] Generated Node #0,2,2: 69:[84, 16] Operation: 24-8=16 Exploring Operation: 84-24=60, Resulting Numbers: [8, 60] Generated Node #0,2,3: 69:[8, 60] Operation: 84-24=60 Exploring Operation: 24/8=3, Resulting Numbers: [84, 3] Generated Node #0,2,4: 69:[84, 3] Operation: 24/8=3 Moving to Node #0,3 Current State: 69:[84, 24, 8], Operations: ['84-76=8'] Exploring Operation: 84+8=92, Resulting Numbers: [24, 92] Generated Node #0,3,0: 69:[24, 92] Operation: 84+8=92 Exploring Operation: 24-8=16, Resulting Numbers: [84, 16] Generated Node #0,3,1: 69:[84, 16] Operation: 24-8=16 Exploring Operation: 84-24=60, Resulting Numbers: [8, 60] Generated Node #0,3,2: 69:[8, 60] Operation: 84-24=60 Exploring Operation: 24/8=3, Resulting Numbers: [84, 3] Generated Node #0,3,3: 69:[84, 3] Operation: 24/8=3 Exploring Operation: 84-8=76, Resulting Numbers: [24, 76] Generated Node #0,3,4: 69:[24, 76] Operation: 84-8=76 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 69:[24, 76], Operations: ['84-76=8', '84-8=76'] Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 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 #0,3,2 Current State: 69:[8, 60], Operations: ['84-76=8', '84-24=60'] Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,69 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,69 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 #0,3,3 Current State: 69:[84, 3], Operations: ['84-76=8', '24/8=3'] Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,69 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,69 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 #0,3,1 Current State: 69:[84, 16], Operations: ['84-76=8', '24-8=16'] Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,69 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[24, 92], Operations: ['84-76=8', '84+8=92'] Exploring Operation: 24*92=2208, Resulting Numbers: [2208] 2208,69 unequal: No Solution Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 24+92=116, Resulting Numbers: [116] 116,69 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: 69:[76, 84, 60], Operations: ['84-24=60'] Exploring Operation: 84-60=24, Resulting Numbers: [76, 24] Generated Node #0,4,0: 69:[76, 24] Operation: 84-60=24 Exploring Operation: 76-60=16, Resulting Numbers: [84, 16] Generated Node #0,4,1: 69:[84, 16] Operation: 76-60=16 Exploring Operation: 84-76=8, Resulting Numbers: [60, 8] Generated Node #0,4,2: 69:[60, 8] Operation: 84-76=8 Exploring Operation: 84+60=144, Resulting Numbers: [76, 144] Generated Node #0,4,3: 69:[76, 144] Operation: 84+60=144 Exploring Operation: 76+60=136, Resulting Numbers: [84, 136] Generated Node #0,4,4: 69:[84, 136] Operation: 76+60=136 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 69:[76, 24], Operations: ['84-24=60', '84-60=24'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 69:[60, 8], Operations: ['84-24=60', '84-76=8'] Exploring Operation: 60*8=480, Resulting Numbers: [480] 480,69 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,69 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 #0,4,1 Current State: 69:[84, 16], Operations: ['84-24=60', '76-60=16'] Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,69 unequal: No Solution Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 69:[76, 144], Operations: ['84-24=60', '84+60=144'] Exploring Operation: 144-76=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 76+144=220, Resulting Numbers: [220] 220,69 unequal: No Solution Exploring Operation: 76*144=10944, Resulting Numbers: [10944] 10944,69 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 #0,4,4 Current State: 69:[84, 136], Operations: ['84-24=60', '76+60=136'] Exploring Operation: 136-84=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 84+136=220, Resulting Numbers: [220] 220,69 unequal: No Solution Exploring Operation: 84*136=11424, Resulting Numbers: [11424] 11424,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 69:[24, 0], Operations: ['84-84=0', '76*0=0'] Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,69 unequal: No Solution Moving to Node #0,0,3 Current State: 69:[24, 75], Operations: ['84/84=1', '76-1=75'] Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,69 unequal: No Solution Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,69 unequal: No Solution Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,69 unequal: No Solution Moving to Node #0,0,4 Current State: 69:[76, 23], Operations: ['84/84=1', '24-1=23'] Exploring Operation: 76*23=1748, Resulting Numbers: [1748] 1748,69 unequal: No Solution Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,69 unequal: No Solution Exploring Operation: 76+23=99, Resulting Numbers: [99] 99,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[76, 24], Operations: ['84-84=0', '24-0=24'] Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[76, 24], Operations: ['84/84=1', '24*1=24'] Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[24, 76], Operations: ['84/84=1', '76/1=76'] Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[24, 76], Operations: ['84-76=8', '84-8=76'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Moving to Node #0,1,4 Current State: 69:[24, 76], Operations: ['84-84=0', '76+0=76'] Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[24, 76], Operations: ['84/84=1', '76*1=76'] Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[76, 24], Operations: ['84-84=0', '24+0=24'] Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[24, 76], Operations: ['84-84=0', '76-0=76'] Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 24*76=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[8, 60], Operations: ['84-76=8', '84-24=60'] Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,69 unequal: No Solution Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,69 unequal: No Solution Moving to Node #0,2,4 Current State: 69:[84, 3], Operations: ['84-76=8', '24/8=3'] Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,69 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,69 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[84, 16], Operations: ['84-76=8', '24-8=16'] Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,69 unequal: No Solution Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[84, 32], Operations: ['84-76=8', '24+8=32'] Exploring Operation: 84-32=52, Resulting Numbers: [52] 52,69 unequal: No Solution Exploring Operation: 84+32=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 84*32=2688, Resulting Numbers: [2688] 2688,69 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 36, 2, 8, 47 ]
97
[ "36/2=18", "8*18=144", "144-47=97" ]
Current State: 97:[36, 2, 8, 47], Operations: [] Exploring Operation: 36/2=18, Resulting Numbers: [8, 47, 18] Generated Node #2: [8, 47, 18] from Operation: 36/2=18 Current State: 97:[8, 47, 18], Operations: ['36/2=18'] Exploring Operation: 8*18=144, Resulting Numbers: [47, 144] Generated Node #3: [47, 144] from Operation: 8*18=144 Current State: 97:[47, 144], Operations: ['36/2=18', '8*18=144'] Exploring Operation: 144-47=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[36, 2, 8, 47], Operations: [] Exploring Operation: 36*2=72, Resulting Numbers: [8, 47, 72] Generated Node #0,0: 97:[8, 47, 72] Operation: 36*2=72 Exploring Operation: 2*47=94, Resulting Numbers: [36, 8, 94] Generated Node #0,1: 97:[36, 8, 94] Operation: 2*47=94 Exploring Operation: 2*8=16, Resulting Numbers: [36, 47, 16] Generated Node #0,2: 97:[36, 47, 16] Operation: 2*8=16 Moving to Node #0,1 Current State: 97:[36, 8, 94], Operations: ['2*47=94'] Exploring Operation: 8+94=102, Resulting Numbers: [36, 102] Generated Node #0,1,0: 97:[36, 102] Operation: 8+94=102 Exploring Operation: 36-8=28, Resulting Numbers: [94, 28] Generated Node #0,1,1: 97:[94, 28] Operation: 36-8=28 Exploring Operation: 36+8=44, Resulting Numbers: [94, 44] Generated Node #0,1,2: 97:[94, 44] Operation: 36+8=44 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[94, 44], Operations: ['2*47=94', '36+8=44'] Exploring Operation: 94*44=4136, Resulting Numbers: [4136] 4136,97 unequal: No Solution Exploring Operation: 94-44=50, Resulting Numbers: [50] 50,97 unequal: No Solution Exploring Operation: 94+44=138, Resulting Numbers: [138] 138,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[36, 102], Operations: ['2*47=94', '8+94=102'] Exploring Operation: 102-36=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 36+102=138, Resulting Numbers: [138] 138,97 unequal: No Solution Exploring Operation: 36*102=3672, Resulting Numbers: [3672] 3672,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[94, 28], Operations: ['2*47=94', '36-8=28'] Exploring Operation: 94+28=122, Resulting Numbers: [122] 122,97 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 94*28=2632, Resulting Numbers: [2632] 2632,97 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: 97:[8, 47, 72], Operations: ['36*2=72'] Exploring Operation: 47-8=39, Resulting Numbers: [72, 39] Generated Node #0,0,0: 97:[72, 39] Operation: 47-8=39 Exploring Operation: 8+72=80, Resulting Numbers: [47, 80] Generated Node #0,0,1: 97:[47, 80] Operation: 8+72=80 Exploring Operation: 8+47=55, Resulting Numbers: [72, 55] Generated Node #0,0,2: 97:[72, 55] Operation: 8+47=55 Moving to Node #0,2 Current State: 97:[36, 47, 16], Operations: ['2*8=16'] Exploring Operation: 36+47=83, Resulting Numbers: [16, 83] Generated Node #0,2,0: 97:[16, 83] Operation: 36+47=83 Exploring Operation: 47+16=63, Resulting Numbers: [36, 63] Generated Node #0,2,1: 97:[36, 63] Operation: 47+16=63 Exploring Operation: 36+16=52, Resulting Numbers: [47, 52] Generated Node #0,2,2: 97:[47, 52] Operation: 36+16=52 Moving to Node #0,0,1 Current State: 97:[47, 80], Operations: ['36*2=72', '8+72=80'] Exploring Operation: 47+80=127, Resulting Numbers: [127] 127,97 unequal: No Solution Exploring Operation: 80-47=33, Resulting Numbers: [33] 33,97 unequal: No Solution Exploring Operation: 47*80=3760, Resulting Numbers: [3760] 3760,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[72, 55], Operations: ['36*2=72', '8+47=55'] Exploring Operation: 72-55=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 72+55=127, Resulting Numbers: [127] 127,97 unequal: No Solution Exploring Operation: 72*55=3960, Resulting Numbers: [3960] 3960,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[72, 39], Operations: ['36*2=72', '47-8=39'] Exploring Operation: 72-39=33, Resulting Numbers: [33] 33,97 unequal: No Solution Exploring Operation: 72*39=2808, Resulting Numbers: [2808] 2808,97 unequal: No Solution Exploring Operation: 72+39=111, Resulting Numbers: [111] 111,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[47, 52], Operations: ['2*8=16', '36+16=52'] Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,97 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,97 unequal: No Solution Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[36, 63], Operations: ['2*8=16', '47+16=63'] Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,97 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[16, 83], Operations: ['2*8=16', '36+47=83'] Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,97 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,97 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,97 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 25, 39, 7, 89 ]
87
[ "39-25=14", "14/7=2", "89-2=87" ]
Current State: 87:[25, 39, 7, 89], Operations: [] Exploring Operation: 39-25=14, Resulting Numbers: [7, 89, 14] Generated Node #2: [7, 89, 14] from Operation: 39-25=14 Current State: 87:[7, 89, 14], Operations: ['39-25=14'] Exploring Operation: 14/7=2, Resulting Numbers: [89, 2] Generated Node #3: [89, 2] from Operation: 14/7=2 Current State: 87:[89, 2], Operations: ['39-25=14', '14/7=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[25, 39, 7, 89], Operations: [] Exploring Operation: 39-7=32, Resulting Numbers: [25, 89, 32] Generated Node #0,0: 87:[25, 89, 32] Operation: 39-7=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[25, 89, 32], Operations: ['39-7=32'] Exploring Operation: 32-25=7, Resulting Numbers: [89, 7] Generated Node #0,0,0: 87:[89, 7] Operation: 32-25=7 Moving to Node #0,0,0 Current State: 87:[89, 7], Operations: ['39-7=32', '32-25=7'] Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 97, 14, 53, 99 ]
81
[ "99-97=2", "14*2=28", "53+28=81" ]
Current State: 81:[97, 14, 53, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [14, 53, 2] Generated Node #2: [14, 53, 2] from Operation: 99-97=2 Current State: 81:[14, 53, 2], Operations: ['99-97=2'] Exploring Operation: 14*2=28, Resulting Numbers: [53, 28] Generated Node #3: [53, 28] from Operation: 14*2=28 Current State: 81:[53, 28], Operations: ['99-97=2', '14*2=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[97, 14, 53, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [14, 53, 2] Generated Node #0,0: 81:[14, 53, 2] Operation: 99-97=2 Exploring Operation: 99-53=46, Resulting Numbers: [97, 14, 46] Generated Node #0,1: 81:[97, 14, 46] Operation: 99-53=46 Exploring Operation: 97-14=83, Resulting Numbers: [53, 99, 83] Generated Node #0,2: 81:[53, 99, 83] Operation: 97-14=83 Exploring Operation: 97-53=44, Resulting Numbers: [14, 99, 44] Generated Node #0,3: 81:[14, 99, 44] Operation: 97-53=44 Exploring Operation: 53-14=39, Resulting Numbers: [97, 99, 39] Generated Node #0,4: 81:[97, 99, 39] Operation: 53-14=39 Moving to Node #0,0 Current State: 81:[14, 53, 2], Operations: ['99-97=2'] Exploring Operation: 14+53=67, Resulting Numbers: [2, 67] Generated Node #0,0,0: 81:[2, 67] Operation: 14+53=67 Exploring Operation: 14-2=12, Resulting Numbers: [53, 12] Generated Node #0,0,1: 81:[53, 12] Operation: 14-2=12 Exploring Operation: 14/2=7, Resulting Numbers: [53, 7] Generated Node #0,0,2: 81:[53, 7] Operation: 14/2=7 Exploring Operation: 53-14=39, Resulting Numbers: [2, 39] Generated Node #0,0,3: 81:[2, 39] Operation: 53-14=39 Exploring Operation: 14*2=28, Resulting Numbers: [53, 28] Generated Node #0,0,4: 81:[53, 28] Operation: 14*2=28 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 81:[2, 39], Operations: ['99-97=2', '53-14=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[2, 67], Operations: ['99-97=2', '14+53=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,81 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 81:[53, 28], Operations: ['99-97=2', '14*2=28'] Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,81 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[97, 14, 53, 99], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [14, 53, 2] Generated Node #0,0: 81:[14, 53, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 81:[14, 53, 2], Operations: ['99-97=2'] Exploring Operation: 14*2=28, Resulting Numbers: [53, 28] Generated Node #0,0,4: 81:[53, 28] Operation: 14*2=28 Moving to Node #0,0,4 Current State: 81:[53, 28], Operations: ['99-97=2', '14*2=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 1, 49, 29, 69 ]
50
[ "49-1=48", "29+69=98", "98-48=50" ]
Current State: 50:[1, 49, 29, 69], Operations: [] Exploring Operation: 49-1=48, Resulting Numbers: [29, 69, 48] Generated Node #2: [29, 69, 48] from Operation: 49-1=48 Current State: 50:[29, 69, 48], Operations: ['49-1=48'] Exploring Operation: 29+69=98, Resulting Numbers: [48, 98] Generated Node #3: [48, 98] from Operation: 29+69=98 Current State: 50:[48, 98], Operations: ['49-1=48', '29+69=98'] Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[1, 49, 29, 69], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [1, 29, 20] Generated Node #0,0: 50:[1, 29, 20] Operation: 69-49=20 Exploring Operation: 69-29=40, Resulting Numbers: [1, 49, 40] Generated Node #0,1: 50:[1, 49, 40] Operation: 69-29=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[1, 29, 20], Operations: ['69-49=20'] Exploring Operation: 29+20=49, Resulting Numbers: [1, 49] Generated Node #0,0,0: 50:[1, 49] Operation: 29+20=49 Exploring Operation: 29-20=9, Resulting Numbers: [1, 9] Generated Node #0,0,1: 50:[1, 9] Operation: 29-20=9 Moving to Node #0,0,0 Current State: 50:[1, 49], Operations: ['69-49=20', '29+20=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[1, 49, 29, 69], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [1, 29, 20] Generated Node #0,0: 50:[1, 29, 20] Operation: 69-49=20 Moving to Node #0,0 Current State: 50:[1, 29, 20], Operations: ['69-49=20'] Exploring Operation: 29+20=49, Resulting Numbers: [1, 49] Generated Node #0,0,0: 50:[1, 49] Operation: 29+20=49 Moving to Node #0,0,0 Current State: 50:[1, 49], Operations: ['69-49=20', '29+20=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 21, 58, 62, 55 ]
86
[ "21+58=79", "62-55=7", "79+7=86" ]
Current State: 86:[21, 58, 62, 55], Operations: [] Exploring Operation: 21+58=79, Resulting Numbers: [62, 55, 79] Generated Node #2: [62, 55, 79] from Operation: 21+58=79 Current State: 86:[62, 55, 79], Operations: ['21+58=79'] Exploring Operation: 62-55=7, Resulting Numbers: [79, 7] Generated Node #3: [79, 7] from Operation: 62-55=7 Current State: 86:[79, 7], Operations: ['21+58=79', '62-55=7'] Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[21, 58, 62, 55], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [58, 55, 41] Generated Node #0,0: 86:[58, 55, 41] Operation: 62-21=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[58, 55, 41], Operations: ['62-21=41'] Exploring Operation: 58-55=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 86:[41, 3] Operation: 58-55=3 Moving to Node #0,0,0 Current State: 86:[41, 3], Operations: ['62-21=41', '58-55=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,86 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
[ 54, 19, 3, 46 ]
45
[ "54/3=18", "46-19=27", "18+27=45" ]
Current State: 45:[54, 19, 3, 46], Operations: [] Exploring Operation: 54/3=18, Resulting Numbers: [19, 46, 18] Generated Node #2: [19, 46, 18] from Operation: 54/3=18 Current State: 45:[19, 46, 18], Operations: ['54/3=18'] Exploring Operation: 46-19=27, Resulting Numbers: [18, 27] Generated Node #3: [18, 27] from Operation: 46-19=27 Current State: 45:[18, 27], Operations: ['54/3=18', '46-19=27'] Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[54, 19, 3, 46], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [19, 3, 8] Generated Node #0,0: 45:[19, 3, 8] Operation: 54-46=8 Exploring Operation: 54/3=18, Resulting Numbers: [19, 46, 18] Generated Node #0,1: 45:[19, 46, 18] Operation: 54/3=18 Exploring Operation: 54-3=51, Resulting Numbers: [19, 46, 51] Generated Node #0,2: 45:[19, 46, 51] Operation: 54-3=51 Exploring Operation: 54-19=35, Resulting Numbers: [3, 46, 35] Generated Node #0,3: 45:[3, 46, 35] Operation: 54-19=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[19, 3, 8], Operations: ['54-46=8'] Exploring Operation: 3+8=11, Resulting Numbers: [19, 11] Generated Node #0,0,0: 45:[19, 11] Operation: 3+8=11 Exploring Operation: 8-3=5, Resulting Numbers: [19, 5] Generated Node #0,0,1: 45:[19, 5] Operation: 8-3=5 Exploring Operation: 19-3=16, Resulting Numbers: [8, 16] Generated Node #0,0,2: 45:[8, 16] Operation: 19-3=16 Exploring Operation: 19-8=11, Resulting Numbers: [3, 11] Generated Node #0,0,3: 45:[3, 11] Operation: 19-8=11 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[8, 16], Operations: ['54-46=8', '19-3=16'] Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,45 unequal: No Solution No 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: 45:[3, 11], Operations: ['54-46=8', '19-8=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,45 unequal: No Solution No 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: 45:[19, 5], Operations: ['54-46=8', '8-3=5'] Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,45 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,45 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,45 unequal: No Solution No 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: 45:[19, 11], Operations: ['54-46=8', '3+8=11'] Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[19, 46, 18], Operations: ['54/3=18'] Exploring Operation: 19-18=1, Resulting Numbers: [46, 1] Generated Node #0,1,0: 45:[46, 1] Operation: 19-18=1 Exploring Operation: 19+18=37, Resulting Numbers: [46, 37] Generated Node #0,1,1: 45:[46, 37] Operation: 19+18=37 Exploring Operation: 46-19=27, Resulting Numbers: [18, 27] Generated Node #0,1,2: 45:[18, 27] Operation: 46-19=27 Exploring Operation: 46-18=28, Resulting Numbers: [19, 28] Generated Node #0,1,3: 45:[19, 28] Operation: 46-18=28 Moving to Node #0,1,0 Current State: 45:[46, 1], Operations: ['54/3=18', '19-18=1'] Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,45 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[54, 19, 3, 46], Operations: [] Exploring Operation: 54/3=18, Resulting Numbers: [19, 46, 18] Generated Node #0,1: 45:[19, 46, 18] Operation: 54/3=18 Moving to Node #0,1 Current State: 45:[19, 46, 18], Operations: ['54/3=18'] Exploring Operation: 19-18=1, Resulting Numbers: [46, 1] Generated Node #0,1,0: 45:[46, 1] Operation: 19-18=1 Moving to Node #0,1,0 Current State: 45:[46, 1], Operations: ['54/3=18', '19-18=1'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 2, 10, 4, 42 ]
89
[ "4*42=168", "10+168=178", "178/2=89" ]
Current State: 89:[2, 10, 4, 42], Operations: [] Exploring Operation: 4*42=168, Resulting Numbers: [2, 10, 168] Generated Node #2: [2, 10, 168] from Operation: 4*42=168 Current State: 89:[2, 10, 168], Operations: ['4*42=168'] Exploring Operation: 10+168=178, Resulting Numbers: [2, 178] Generated Node #3: [2, 178] from Operation: 10+168=178 Current State: 89:[2, 178], Operations: ['4*42=168', '10+168=178'] Exploring Operation: 178/2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[2, 10, 4, 42], Operations: [] Exploring Operation: 2*4=8, Resulting Numbers: [10, 42, 8] Generated Node #0,0: 89:[10, 42, 8] Operation: 2*4=8 Exploring Operation: 2*42=84, Resulting Numbers: [10, 4, 84] Generated Node #0,1: 89:[10, 4, 84] Operation: 2*42=84 Exploring Operation: 2+10=12, Resulting Numbers: [4, 42, 12] Generated Node #0,2: 89:[4, 42, 12] Operation: 2+10=12 Exploring Operation: 2*10=20, Resulting Numbers: [4, 42, 20] Generated Node #0,3: 89:[4, 42, 20] Operation: 2*10=20 Exploring Operation: 10*4=40, Resulting Numbers: [2, 42, 40] Generated Node #0,4: 89:[2, 42, 40] Operation: 10*4=40 Moving to Node #0,1 Current State: 89:[10, 4, 84], Operations: ['2*42=84'] Exploring Operation: 10-4=6, Resulting Numbers: [84, 6] Generated Node #0,1,0: 89:[84, 6] Operation: 10-4=6 Exploring Operation: 10+4=14, Resulting Numbers: [84, 14] Generated Node #0,1,1: 89:[84, 14] Operation: 10+4=14 Exploring Operation: 10*4=40, Resulting Numbers: [84, 40] Generated Node #0,1,2: 89:[84, 40] Operation: 10*4=40 Exploring Operation: 4+84=88, Resulting Numbers: [10, 88] Generated Node #0,1,3: 89:[10, 88] Operation: 4+84=88 Exploring Operation: 84-4=80, Resulting Numbers: [10, 80] Generated Node #0,1,4: 89:[10, 80] Operation: 84-4=80 Moving to Node #0,4 Current State: 89:[2, 42, 40], Operations: ['10*4=40'] Exploring Operation: 2+42=44, Resulting Numbers: [40, 44] Generated Node #0,4,0: 89:[40, 44] Operation: 2+42=44 Exploring Operation: 2+40=42, Resulting Numbers: [42, 42] Generated Node #0,4,1: 89:[42, 42] Operation: 2+40=42 Exploring Operation: 42+40=82, Resulting Numbers: [2, 82] Generated Node #0,4,2: 89:[2, 82] Operation: 42+40=82 Exploring Operation: 2*42=84, Resulting Numbers: [40, 84] Generated Node #0,4,3: 89:[40, 84] Operation: 2*42=84 Exploring Operation: 2*40=80, Resulting Numbers: [42, 80] Generated Node #0,4,4: 89:[42, 80] Operation: 2*40=80 Moving to Node #0,3 Current State: 89:[4, 42, 20], Operations: ['2*10=20'] Exploring Operation: 4+20=24, Resulting Numbers: [42, 24] Generated Node #0,3,0: 89:[42, 24] Operation: 4+20=24 Exploring Operation: 4+42=46, Resulting Numbers: [20, 46] Generated Node #0,3,1: 89:[20, 46] Operation: 4+42=46 Exploring Operation: 4*20=80, Resulting Numbers: [42, 80] Generated Node #0,3,2: 89:[42, 80] Operation: 4*20=80 Exploring Operation: 42-4=38, Resulting Numbers: [20, 38] Generated Node #0,3,3: 89:[20, 38] Operation: 42-4=38 Exploring Operation: 42+20=62, Resulting Numbers: [4, 62] Generated Node #0,3,4: 89:[4, 62] Operation: 42+20=62 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 89:[42, 80], Operations: ['2*10=20', '4*20=80'] Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 89:[42, 24], Operations: ['2*10=20', '4+20=24'] Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,89 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 89:[20, 46], Operations: ['2*10=20', '4+42=46'] Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 20*46=920, Resulting Numbers: [920] 920,89 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 89:[4, 62], Operations: ['2*10=20', '42+20=62'] Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,89 unequal: No Solution Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[20, 38], Operations: ['2*10=20', '42-4=38'] Exploring Operation: 20*38=760, Resulting Numbers: [760] 760,89 unequal: No Solution Exploring Operation: 20+38=58, Resulting Numbers: [58] 58,89 unequal: No Solution Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,89 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: 89:[10, 42, 8], Operations: ['2*4=8'] Exploring Operation: 10*8=80, Resulting Numbers: [42, 80] Generated Node #0,0,0: 89:[42, 80] Operation: 10*8=80 Exploring Operation: 10+8=18, Resulting Numbers: [42, 18] Generated Node #0,0,1: 89:[42, 18] Operation: 10+8=18 Exploring Operation: 42+8=50, Resulting Numbers: [10, 50] Generated Node #0,0,2: 89:[10, 50] Operation: 42+8=50 Exploring Operation: 10+42=52, Resulting Numbers: [8, 52] Generated Node #0,0,3: 89:[8, 52] Operation: 10+42=52 Exploring Operation: 10-8=2, Resulting Numbers: [42, 2] Generated Node #0,0,4: 89:[42, 2] Operation: 10-8=2 Moving to Node #0,2 Current State: 89:[4, 42, 12], Operations: ['2+10=12'] Exploring Operation: 42+12=54, Resulting Numbers: [4, 54] Generated Node #0,2,0: 89:[4, 54] Operation: 42+12=54 Exploring Operation: 42-4=38, Resulting Numbers: [12, 38] Generated Node #0,2,1: 89:[12, 38] Operation: 42-4=38 Exploring Operation: 4*12=48, Resulting Numbers: [42, 48] Generated Node #0,2,2: 89:[42, 48] Operation: 4*12=48 Exploring Operation: 4+12=16, Resulting Numbers: [42, 16] Generated Node #0,2,3: 89:[42, 16] Operation: 4+12=16 Exploring Operation: 4+42=46, Resulting Numbers: [12, 46] Generated Node #0,2,4: 89:[12, 46] Operation: 4+42=46 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[42, 48], Operations: ['2+10=12', '4*12=48'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,89 unequal: No Solution Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[4, 54], Operations: ['2+10=12', '42+12=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,89 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[42, 16], Operations: ['2+10=12', '4+12=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,89 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,89 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 89:[12, 46], Operations: ['2+10=12', '4+42=46'] Exploring Operation: 12*46=552, Resulting Numbers: [552] 552,89 unequal: No Solution Exploring Operation: 12+46=58, Resulting Numbers: [58] 58,89 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[12, 38], Operations: ['2+10=12', '42-4=38'] Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,89 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,89 unequal: No Solution Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 89:[84, 40], Operations: ['2*42=84', '10*4=40'] Exploring Operation: 84*40=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution Exploring Operation: 84+40=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[40, 84], Operations: ['10*4=40', '2*42=84'] Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,89 unequal: No Solution Exploring Operation: 40*84=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[42, 80], Operations: ['10*4=40', '2*40=80'] Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[42, 80], Operations: ['2*4=8', '10*8=80'] Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,89 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[10, 88], Operations: ['2*42=84', '4+84=88'] Exploring Operation: 10*88=880, Resulting Numbers: [880] 880,89 unequal: No Solution Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,89 unequal: No Solution Exploring Operation: 10+88=98, Resulting Numbers: [98] 98,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[84, 14], Operations: ['2*42=84', '10+4=14'] Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,89 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 84*14=1176, Resulting Numbers: [1176] 1176,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[10, 80], Operations: ['2*42=84', '84-4=80'] Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 10*80=800, Resulting Numbers: [800] 800,89 unequal: No Solution Exploring Operation: 10+80=90, Resulting Numbers: [90] 90,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[84, 6], Operations: ['2*42=84', '10-4=6'] Exploring Operation: 84*6=504, Resulting Numbers: [504] 504,89 unequal: No Solution Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,89 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[2, 82], Operations: ['10*4=40', '42+40=82'] Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,89 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,89 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[42, 42], Operations: ['10*4=40', '2+40=42'] Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,89 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 42*42=1764, Resulting Numbers: [1764] 1764,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[40, 44], Operations: ['10*4=40', '2+42=44'] Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,89 unequal: No Solution Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[8, 52], Operations: ['2*4=8', '10+42=52'] Exploring Operation: 8*52=416, Resulting Numbers: [416] 416,89 unequal: No Solution Exploring Operation: 8+52=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[42, 18], Operations: ['2*4=8', '10+8=18'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,89 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[10, 50], Operations: ['2*4=8', '42+8=50'] Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 10*50=500, Resulting Numbers: [500] 500,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[42, 2], Operations: ['2*4=8', '10-8=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,89 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,89 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,89 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 89, 84, 45, 13 ]
86
[ "84-45=39", "39/13=3", "89-3=86" ]
Current State: 86:[89, 84, 45, 13], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [89, 13, 39] Generated Node #2: [89, 13, 39] from Operation: 84-45=39 Current State: 86:[89, 13, 39], Operations: ['84-45=39'] Exploring Operation: 39/13=3, Resulting Numbers: [89, 3] Generated Node #3: [89, 3] from Operation: 39/13=3 Current State: 86:[89, 3], Operations: ['84-45=39', '39/13=3'] Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[89, 84, 45, 13], Operations: [] Exploring Operation: 84+13=97, Resulting Numbers: [89, 45, 97] Generated Node #0,0: 86:[89, 45, 97] Operation: 84+13=97 Exploring Operation: 89-13=76, Resulting Numbers: [84, 45, 76] Generated Node #0,1: 86:[84, 45, 76] Operation: 89-13=76 Exploring Operation: 89-84=5, Resulting Numbers: [45, 13, 5] Generated Node #0,2: 86:[45, 13, 5] Operation: 89-84=5 Exploring Operation: 89-45=44, Resulting Numbers: [84, 13, 44] Generated Node #0,3: 86:[84, 13, 44] Operation: 89-45=44 Moving to Node #0,1 Current State: 86:[84, 45, 76], Operations: ['89-13=76'] Exploring Operation: 84-45=39, Resulting Numbers: [76, 39] Generated Node #0,1,0: 86:[76, 39] Operation: 84-45=39 Exploring Operation: 84-76=8, Resulting Numbers: [45, 8] Generated Node #0,1,1: 86:[45, 8] Operation: 84-76=8 Exploring Operation: 76-45=31, Resulting Numbers: [84, 31] Generated Node #0,1,2: 86:[84, 31] Operation: 76-45=31 Exploring Operation: 45+76=121, Resulting Numbers: [84, 121] Generated Node #0,1,3: 86:[84, 121] Operation: 45+76=121 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[45, 8], Operations: ['89-13=76', '84-76=8'] Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[76, 39], Operations: ['89-13=76', '84-45=39'] Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 76+39=115, Resulting Numbers: [115] 115,86 unequal: No Solution Exploring Operation: 76*39=2964, Resulting Numbers: [2964] 2964,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[84, 31], Operations: ['89-13=76', '76-45=31'] Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 84+31=115, Resulting Numbers: [115] 115,86 unequal: No Solution Exploring Operation: 84*31=2604, Resulting Numbers: [2604] 2604,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[84, 121], Operations: ['89-13=76', '45+76=121'] Exploring Operation: 84*121=10164, Resulting Numbers: [10164] 10164,86 unequal: No Solution Exploring Operation: 121-84=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 84+121=205, Resulting Numbers: [205] 205,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 86:[84, 13, 44], Operations: ['89-45=44'] Exploring Operation: 44-13=31, Resulting Numbers: [84, 31] Generated Node #0,3,0: 86:[84, 31] Operation: 44-13=31 Exploring Operation: 84-44=40, Resulting Numbers: [13, 40] Generated Node #0,3,1: 86:[13, 40] Operation: 84-44=40 Exploring Operation: 84+13=97, Resulting Numbers: [44, 97] Generated Node #0,3,2: 86:[44, 97] Operation: 84+13=97 Exploring Operation: 84-13=71, Resulting Numbers: [44, 71] Generated Node #0,3,3: 86:[44, 71] Operation: 84-13=71 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 86:[44, 97], Operations: ['89-45=44', '84+13=97'] Exploring Operation: 97-44=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 44*97=4268, Resulting Numbers: [4268] 4268,86 unequal: No Solution Exploring Operation: 44+97=141, Resulting Numbers: [141] 141,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 86:[84, 31], Operations: ['89-45=44', '44-13=31'] Exploring Operation: 84+31=115, Resulting Numbers: [115] 115,86 unequal: No Solution Exploring Operation: 84-31=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 84*31=2604, Resulting Numbers: [2604] 2604,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 86:[13, 40], Operations: ['89-45=44', '84-44=40'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,86 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 86:[44, 71], Operations: ['89-45=44', '84-13=71'] Exploring Operation: 44+71=115, Resulting Numbers: [115] 115,86 unequal: No Solution Exploring Operation: 44*71=3124, Resulting Numbers: [3124] 3124,86 unequal: No Solution Exploring Operation: 71-44=27, Resulting Numbers: [27] 27,86 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: 86:[45, 13, 5], Operations: ['89-84=5'] Exploring Operation: 45+13=58, Resulting Numbers: [5, 58] Generated Node #0,2,0: 86:[5, 58] Operation: 45+13=58 Exploring Operation: 45-13=32, Resulting Numbers: [5, 32] Generated Node #0,2,1: 86:[5, 32] Operation: 45-13=32 Exploring Operation: 45-5=40, Resulting Numbers: [13, 40] Generated Node #0,2,2: 86:[13, 40] Operation: 45-5=40 Exploring Operation: 13-5=8, Resulting Numbers: [45, 8] Generated Node #0,2,3: 86:[45, 8] Operation: 13-5=8 Moving to Node #0,0 Current State: 86:[89, 45, 97], Operations: ['84+13=97'] Exploring Operation: 97-89=8, Resulting Numbers: [45, 8] Generated Node #0,0,0: 86:[45, 8] Operation: 97-89=8 Exploring Operation: 89+45=134, Resulting Numbers: [97, 134] Generated Node #0,0,1: 86:[97, 134] Operation: 89+45=134 Exploring Operation: 97-45=52, Resulting Numbers: [89, 52] Generated Node #0,0,2: 86:[89, 52] Operation: 97-45=52 Exploring Operation: 89-45=44, Resulting Numbers: [97, 44] Generated Node #0,0,3: 86:[97, 44] Operation: 89-45=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[45, 8], Operations: ['84+13=97', '97-89=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,86 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[89, 52], Operations: ['84+13=97', '97-45=52'] Exploring Operation: 89+52=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 89*52=4628, Resulting Numbers: [4628] 4628,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 86:[97, 44], Operations: ['84+13=97', '89-45=44'] Exploring Operation: 97+44=141, Resulting Numbers: [141] 141,86 unequal: No Solution Exploring Operation: 97-44=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 97*44=4268, Resulting Numbers: [4268] 4268,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[97, 134], Operations: ['84+13=97', '89+45=134'] Exploring Operation: 134-97=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 97+134=231, Resulting Numbers: [231] 231,86 unequal: No Solution Exploring Operation: 97*134=12998, Resulting Numbers: [12998] 12998,86 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: 86:[45, 8], Operations: ['89-84=5', '13-5=8'] Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,86 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[13, 40], Operations: ['89-84=5', '45-5=40'] Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,86 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,86 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[5, 32], Operations: ['89-84=5', '45-13=32'] Exploring Operation: 5+32=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 5*32=160, Resulting Numbers: [160] 160,86 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[5, 58], Operations: ['89-84=5', '45+13=58'] Exploring Operation: 5*58=290, Resulting Numbers: [290] 290,86 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,86 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,86 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 35, 80, 74, 92 ]
51
[ "35+80=115", "74+92=166", "166-115=51" ]
Current State: 51:[35, 80, 74, 92], Operations: [] Exploring Operation: 35+80=115, Resulting Numbers: [74, 92, 115] Generated Node #2: [74, 92, 115] from Operation: 35+80=115 Current State: 51:[74, 92, 115], Operations: ['35+80=115'] Exploring Operation: 74+92=166, Resulting Numbers: [115, 166] Generated Node #3: [115, 166] from Operation: 74+92=166 Current State: 51:[115, 166], Operations: ['35+80=115', '74+92=166'] Exploring Operation: 166-115=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[35, 80, 74, 92], Operations: [] Exploring Operation: 80-74=6, Resulting Numbers: [35, 92, 6] Generated Node #0,0: 51:[35, 92, 6] Operation: 80-74=6 Exploring Operation: 92-80=12, Resulting Numbers: [35, 74, 12] Generated Node #0,1: 51:[35, 74, 12] Operation: 92-80=12 Exploring Operation: 92-74=18, Resulting Numbers: [35, 80, 18] Generated Node #0,2: 51:[35, 80, 18] Operation: 92-74=18 Exploring Operation: 80-35=45, Resulting Numbers: [74, 92, 45] Generated Node #0,3: 51:[74, 92, 45] Operation: 80-35=45 Exploring Operation: 92-35=57, Resulting Numbers: [80, 74, 57] Generated Node #0,4: 51:[80, 74, 57] Operation: 92-35=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[35, 74, 12], Operations: ['92-80=12'] Exploring Operation: 74-35=39, Resulting Numbers: [12, 39] Generated Node #0,1,0: 51:[12, 39] Operation: 74-35=39 Exploring Operation: 35-12=23, Resulting Numbers: [74, 23] Generated Node #0,1,1: 51:[74, 23] Operation: 35-12=23 Exploring Operation: 35+12=47, Resulting Numbers: [74, 47] Generated Node #0,1,2: 51:[74, 47] Operation: 35+12=47 Exploring Operation: 74+12=86, Resulting Numbers: [35, 86] Generated Node #0,1,3: 51:[35, 86] Operation: 74+12=86 Exploring Operation: 74-12=62, Resulting Numbers: [35, 62] Generated Node #0,1,4: 51:[35, 62] Operation: 74-12=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[12, 39], Operations: ['92-80=12', '74-35=39'] Exploring Operation: 12*39=468, Resulting Numbers: [468] 468,51 unequal: No Solution Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 12+39=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[35, 80, 74, 92], Operations: [] Exploring Operation: 92-80=12, Resulting Numbers: [35, 74, 12] Generated Node #0,1: 51:[35, 74, 12] Operation: 92-80=12 Moving to Node #0,1 Current State: 51:[35, 74, 12], Operations: ['92-80=12'] Exploring Operation: 74-35=39, Resulting Numbers: [12, 39] Generated Node #0,1,0: 51:[12, 39] Operation: 74-35=39 Moving to Node #0,1,0 Current State: 51:[12, 39], Operations: ['92-80=12', '74-35=39'] Exploring Operation: 12+39=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 53, 6, 66, 9 ]
73
[ "53+9=62", "66/6=11", "62+11=73" ]
Current State: 73:[53, 6, 66, 9], Operations: [] Exploring Operation: 53+9=62, Resulting Numbers: [6, 66, 62] Generated Node #2: [6, 66, 62] from Operation: 53+9=62 Current State: 73:[6, 66, 62], Operations: ['53+9=62'] Exploring Operation: 66/6=11, Resulting Numbers: [62, 11] Generated Node #3: [62, 11] from Operation: 66/6=11 Current State: 73:[62, 11], Operations: ['53+9=62', '66/6=11'] Exploring Operation: 62+11=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[53, 6, 66, 9], Operations: [] Exploring Operation: 6*9=54, Resulting Numbers: [53, 66, 54] Generated Node #0,0: 73:[53, 66, 54] Operation: 6*9=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[53, 66, 54], Operations: ['6*9=54'] Exploring Operation: 53+54=107, Resulting Numbers: [66, 107] Generated Node #0,0,0: 73:[66, 107] Operation: 53+54=107 Moving to Node #0,0,0 Current State: 73:[66, 107], Operations: ['6*9=54', '53+54=107'] Exploring Operation: 107-66=41, Resulting Numbers: [41] 41,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 82, 35, 29, 36 ]
87
[ "36-29=7", "35/7=5", "82+5=87" ]
Current State: 87:[82, 35, 29, 36], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [82, 35, 7] Generated Node #2: [82, 35, 7] from Operation: 36-29=7 Current State: 87:[82, 35, 7], Operations: ['36-29=7'] Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 35/7=5 Current State: 87:[82, 5], Operations: ['36-29=7', '35/7=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[82, 35, 29, 36], Operations: [] Exploring Operation: 35+36=71, Resulting Numbers: [82, 29, 71] Generated Node #0,0: 87:[82, 29, 71] Operation: 35+36=71 Exploring Operation: 35-29=6, Resulting Numbers: [82, 36, 6] Generated Node #0,1: 87:[82, 36, 6] Operation: 35-29=6 Exploring Operation: 82-36=46, Resulting Numbers: [35, 29, 46] Generated Node #0,2: 87:[35, 29, 46] Operation: 82-36=46 Exploring Operation: 36-29=7, Resulting Numbers: [82, 35, 7] Generated Node #0,3: 87:[82, 35, 7] Operation: 36-29=7 Exploring Operation: 36-35=1, Resulting Numbers: [82, 29, 1] Generated Node #0,4: 87:[82, 29, 1] Operation: 36-35=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 87:[82, 29, 1], Operations: ['36-35=1'] Exploring Operation: 29*1=29, Resulting Numbers: [82, 29] Generated Node #0,4,0: 87:[82, 29] Operation: 29*1=29 Exploring Operation: 82/1=82, Resulting Numbers: [29, 82] Generated Node #0,4,1: 87:[29, 82] Operation: 82/1=82 Exploring Operation: 82+1=83, Resulting Numbers: [29, 83] Generated Node #0,4,2: 87:[29, 83] Operation: 82+1=83 Exploring Operation: 82*1=82, Resulting Numbers: [29, 82] Generated Node #0,4,3: 87:[29, 82] Operation: 82*1=82 Exploring Operation: 29/1=29, Resulting Numbers: [82, 29] Generated Node #0,4,4: 87:[82, 29] Operation: 29/1=29 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 87:[29, 83], Operations: ['36-35=1', '82+1=83'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 29+83=112, Resulting Numbers: [112] 112,87 unequal: No Solution Exploring Operation: 29*83=2407, Resulting Numbers: [2407] 2407,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 87:[82, 29], Operations: ['36-35=1', '29*1=29'] Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,87 unequal: No Solution Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,87 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 87:[29, 82], Operations: ['36-35=1', '82/1=82'] Exploring Operation: 29+82=111, Resulting Numbers: [111] 111,87 unequal: No Solution Exploring Operation: 29*82=2378, Resulting Numbers: [2378] 2378,87 unequal: No Solution Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 87:[29, 82], Operations: ['36-35=1', '82*1=82'] Exploring Operation: 29+82=111, Resulting Numbers: [111] 111,87 unequal: No Solution Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,87 unequal: No Solution Exploring Operation: 29*82=2378, Resulting Numbers: [2378] 2378,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 87:[82, 29], Operations: ['36-35=1', '29/1=29'] Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,87 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,87 unequal: No Solution Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[82, 36, 6], Operations: ['35-29=6'] Exploring Operation: 82+6=88, Resulting Numbers: [36, 88] Generated Node #0,1,0: 87:[36, 88] Operation: 82+6=88 Exploring Operation: 36-6=30, Resulting Numbers: [82, 30] Generated Node #0,1,1: 87:[82, 30] Operation: 36-6=30 Exploring Operation: 36+6=42, Resulting Numbers: [82, 42] Generated Node #0,1,2: 87:[82, 42] Operation: 36+6=42 Exploring Operation: 82-6=76, Resulting Numbers: [36, 76] Generated Node #0,1,3: 87:[36, 76] Operation: 82-6=76 Exploring Operation: 36/6=6, Resulting Numbers: [82, 6] Generated Node #0,1,4: 87:[82, 6] Operation: 36/6=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[82, 30], Operations: ['35-29=6', '36-6=30'] Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,87 unequal: No Solution Exploring Operation: 82*30=2460, Resulting Numbers: [2460] 2460,87 unequal: No Solution Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[36, 88], Operations: ['35-29=6', '82+6=88'] Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,87 unequal: No Solution Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,87 unequal: No Solution Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 87:[82, 6], Operations: ['35-29=6', '36/6=6'] Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 82+6=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 82*6=492, Resulting Numbers: [492] 492,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[82, 42], Operations: ['35-29=6', '36+6=42'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,87 unequal: No Solution Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 87:[36, 76], Operations: ['35-29=6', '82-6=76'] Exploring Operation: 36*76=2736, Resulting Numbers: [2736] 2736,87 unequal: No Solution Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,87 unequal: No Solution Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[82, 35, 7], Operations: ['36-29=7'] Exploring Operation: 35+7=42, Resulting Numbers: [82, 42] Generated Node #0,3,0: 87:[82, 42] Operation: 35+7=42 Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #0,3,1: 87:[82, 5] Operation: 35/7=5 Exploring Operation: 82+7=89, Resulting Numbers: [35, 89] Generated Node #0,3,2: 87:[35, 89] Operation: 82+7=89 Exploring Operation: 82-7=75, Resulting Numbers: [35, 75] Generated Node #0,3,3: 87:[35, 75] Operation: 82-7=75 Exploring Operation: 35-7=28, Resulting Numbers: [82, 28] Generated Node #0,3,4: 87:[82, 28] Operation: 35-7=28 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 87:[82, 28], Operations: ['36-29=7', '35-7=28'] Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,87 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[82, 5], Operations: ['36-29=7', '35/7=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[82, 35, 29, 36], Operations: [] Exploring Operation: 36-29=7, Resulting Numbers: [82, 35, 7] Generated Node #0,3: 87:[82, 35, 7] Operation: 36-29=7 Moving to Node #0,3 Current State: 87:[82, 35, 7], Operations: ['36-29=7'] Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #0,3,1: 87:[82, 5] Operation: 35/7=5 Moving to Node #0,3,1 Current State: 87:[82, 5], Operations: ['36-29=7', '35/7=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.948785
hs_5
sum_heuristic
[ 45, 99, 1, 91 ]
37
[ "99-45=54", "1*91=91", "91-54=37" ]
Current State: 37:[45, 99, 1, 91], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [1, 91, 54] Generated Node #2: [1, 91, 54] from Operation: 99-45=54 Current State: 37:[1, 91, 54], Operations: ['99-45=54'] Exploring Operation: 1*91=91, Resulting Numbers: [54, 91] Generated Node #3: [54, 91] from Operation: 1*91=91 Current State: 37:[54, 91], Operations: ['99-45=54', '1*91=91'] Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[45, 99, 1, 91], Operations: [] Exploring Operation: 99-45=54, Resulting Numbers: [1, 91, 54] Generated Node #0,0: 37:[1, 91, 54] Operation: 99-45=54 Exploring Operation: 99-91=8, Resulting Numbers: [45, 1, 8] Generated Node #0,1: 37:[45, 1, 8] Operation: 99-91=8 Moving to Node #0,1 Current State: 37:[45, 1, 8], Operations: ['99-91=8'] Exploring Operation: 45-8=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 37:[1, 37] Operation: 45-8=37 Exploring Operation: 45-1=44, Resulting Numbers: [8, 44] Generated Node #0,1,1: 37:[8, 44] Operation: 45-1=44 Moving to Node #0,0 Current State: 37:[1, 91, 54], Operations: ['99-45=54'] Exploring Operation: 91-1=90, Resulting Numbers: [54, 90] Generated Node #0,0,0: 37:[54, 90] Operation: 91-1=90 Exploring Operation: 91-54=37, Resulting Numbers: [1, 37] Generated Node #0,0,1: 37:[1, 37] Operation: 91-54=37 Moving to Node #0,1,0 Current State: 37:[1, 37], Operations: ['99-91=8', '45-8=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[45, 99, 1, 91], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [45, 1, 8] Generated Node #0,1: 37:[45, 1, 8] Operation: 99-91=8 Moving to Node #0,1 Current State: 37:[45, 1, 8], Operations: ['99-91=8'] Exploring Operation: 45-8=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 37:[1, 37] Operation: 45-8=37 Moving to Node #0,1,0 Current State: 37:[1, 37], Operations: ['99-91=8', '45-8=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 32, 21, 69, 17 ]
36
[ "69*17=1173", "1173-21=1152", "1152/32=36" ]
Current State: 36:[32, 21, 69, 17], Operations: [] Exploring Operation: 69*17=1173, Resulting Numbers: [32, 21, 1173] Generated Node #2: [32, 21, 1173] from Operation: 69*17=1173 Current State: 36:[32, 21, 1173], Operations: ['69*17=1173'] Exploring Operation: 1173-21=1152, Resulting Numbers: [32, 1152] Generated Node #3: [32, 1152] from Operation: 1173-21=1152 Current State: 36:[32, 1152], Operations: ['69*17=1173', '1173-21=1152'] Exploring Operation: 1152/32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[32, 21, 69, 17], Operations: [] Exploring Operation: 69-32=37, Resulting Numbers: [21, 17, 37] Generated Node #0,0: 36:[21, 17, 37] Operation: 69-32=37 Moving to Node #0,0 Current State: 36:[21, 17, 37], Operations: ['69-32=37'] Exploring Operation: 21-17=4, Resulting Numbers: [37, 4] Generated Node #0,0,0: 36:[37, 4] Operation: 21-17=4 Moving to Node #0,0,0 Current State: 36:[37, 4], Operations: ['69-32=37', '21-17=4'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,36 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 61, 44, 47, 54 ]
42
[ "61+47=108", "108/54=2", "44-2=42" ]
Current State: 42:[61, 44, 47, 54], Operations: [] Exploring Operation: 61+47=108, Resulting Numbers: [44, 54, 108] Generated Node #2: [44, 54, 108] from Operation: 61+47=108 Current State: 42:[44, 54, 108], Operations: ['61+47=108'] Exploring Operation: 108/54=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 108/54=2 Current State: 42:[44, 2], Operations: ['61+47=108', '108/54=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[61, 44, 47, 54], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [61, 44, 7] Generated Node #0,0: 42:[61, 44, 7] Operation: 54-47=7 Exploring Operation: 61-47=14, Resulting Numbers: [44, 54, 14] Generated Node #0,1: 42:[44, 54, 14] Operation: 61-47=14 Exploring Operation: 61-44=17, Resulting Numbers: [47, 54, 17] Generated Node #0,2: 42:[47, 54, 17] Operation: 61-44=17 Exploring Operation: 54-44=10, Resulting Numbers: [61, 47, 10] Generated Node #0,3: 42:[61, 47, 10] Operation: 54-44=10 Exploring Operation: 61-54=7, Resulting Numbers: [44, 47, 7] Generated Node #0,4: 42:[44, 47, 7] Operation: 61-54=7 Moving to Node #0,4 Current State: 42:[44, 47, 7], Operations: ['61-54=7'] Exploring Operation: 47-44=3, Resulting Numbers: [7, 3] Generated Node #0,4,0: 42:[7, 3] Operation: 47-44=3 Exploring Operation: 44-7=37, Resulting Numbers: [47, 37] Generated Node #0,4,1: 42:[47, 37] Operation: 44-7=37 Exploring Operation: 44+7=51, Resulting Numbers: [47, 51] Generated Node #0,4,2: 42:[47, 51] Operation: 44+7=51 Exploring Operation: 47-7=40, Resulting Numbers: [44, 40] Generated Node #0,4,3: 42:[44, 40] Operation: 47-7=40 Exploring Operation: 47+7=54, Resulting Numbers: [44, 54] Generated Node #0,4,4: 42:[44, 54] Operation: 47+7=54 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 42:[7, 3], Operations: ['61-54=7', '47-44=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 42:[44, 40], Operations: ['61-54=7', '47-7=40'] Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,42 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 42:[47, 37], Operations: ['61-54=7', '44-7=37'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 42:[47, 51], Operations: ['61-54=7', '44+7=51'] Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,42 unequal: No Solution Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,42 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 42:[44, 54], Operations: ['61-54=7', '47+7=54'] Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,42 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,42 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,42 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: 42:[44, 54, 14], Operations: ['61-47=14'] Exploring Operation: 54+14=68, Resulting Numbers: [44, 68] Generated Node #0,1,0: 42:[44, 68] Operation: 54+14=68 Exploring Operation: 44+14=58, Resulting Numbers: [54, 58] Generated Node #0,1,1: 42:[54, 58] Operation: 44+14=58 Exploring Operation: 54-14=40, Resulting Numbers: [44, 40] Generated Node #0,1,2: 42:[44, 40] Operation: 54-14=40 Exploring Operation: 44-14=30, Resulting Numbers: [54, 30] Generated Node #0,1,3: 42:[54, 30] Operation: 44-14=30 Exploring Operation: 54-44=10, Resulting Numbers: [14, 10] Generated Node #0,1,4: 42:[14, 10] Operation: 54-44=10 Moving to Node #0,2 Current State: 42:[47, 54, 17], Operations: ['61-44=17'] Exploring Operation: 54-17=37, Resulting Numbers: [47, 37] Generated Node #0,2,0: 42:[47, 37] Operation: 54-17=37 Exploring Operation: 47-17=30, Resulting Numbers: [54, 30] Generated Node #0,2,1: 42:[54, 30] Operation: 47-17=30 Exploring Operation: 54+17=71, Resulting Numbers: [47, 71] Generated Node #0,2,2: 42:[47, 71] Operation: 54+17=71 Exploring Operation: 54-47=7, Resulting Numbers: [17, 7] Generated Node #0,2,3: 42:[17, 7] Operation: 54-47=7 Exploring Operation: 47+17=64, Resulting Numbers: [54, 64] Generated Node #0,2,4: 42:[54, 64] Operation: 47+17=64 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 42:[17, 7], Operations: ['61-44=17', '54-47=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,42 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[47, 37], Operations: ['61-44=17', '54-17=37'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,42 unequal: No Solution Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[54, 30], Operations: ['61-44=17', '47-17=30'] Exploring Operation: 54+30=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 54*30=1620, Resulting Numbers: [1620] 1620,42 unequal: No Solution Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[47, 71], Operations: ['61-44=17', '54+17=71'] Exploring Operation: 71-47=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 47+71=118, Resulting Numbers: [118] 118,42 unequal: No Solution Exploring Operation: 47*71=3337, Resulting Numbers: [3337] 3337,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 42:[54, 64], Operations: ['61-44=17', '47+17=64'] Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,42 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,42 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: 42:[61, 44, 7], Operations: ['54-47=7'] Exploring Operation: 44+7=51, Resulting Numbers: [61, 51] Generated Node #0,0,0: 42:[61, 51] Operation: 44+7=51 Exploring Operation: 61-7=54, Resulting Numbers: [44, 54] Generated Node #0,0,1: 42:[44, 54] Operation: 61-7=54 Exploring Operation: 61-44=17, Resulting Numbers: [7, 17] Generated Node #0,0,2: 42:[7, 17] Operation: 61-44=17 Exploring Operation: 61+7=68, Resulting Numbers: [44, 68] Generated Node #0,0,3: 42:[44, 68] Operation: 61+7=68 Exploring Operation: 44-7=37, Resulting Numbers: [61, 37] Generated Node #0,0,4: 42:[61, 37] Operation: 44-7=37 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[7, 17], Operations: ['54-47=7', '61-44=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,42 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[44, 54], Operations: ['54-47=7', '61-7=54'] Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,42 unequal: No Solution Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 42:[61, 37], Operations: ['54-47=7', '44-7=37'] Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,42 unequal: No Solution Exploring Operation: 61*37=2257, Resulting Numbers: [2257] 2257,42 unequal: No Solution Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[61, 51], Operations: ['54-47=7', '44+7=51'] Exploring Operation: 61+51=112, Resulting Numbers: [112] 112,42 unequal: No Solution Exploring Operation: 61*51=3111, Resulting Numbers: [3111] 3111,42 unequal: No Solution Exploring Operation: 61-51=10, Resulting Numbers: [10] 10,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 42:[44, 68], Operations: ['54-47=7', '61+7=68'] Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 44+68=112, Resulting Numbers: [112] 112,42 unequal: No Solution Exploring Operation: 44*68=2992, Resulting Numbers: [2992] 2992,42 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: 42:[61, 47, 10], Operations: ['54-44=10'] Exploring Operation: 61-10=51, Resulting Numbers: [47, 51] Generated Node #0,3,0: 42:[47, 51] Operation: 61-10=51 Exploring Operation: 47-10=37, Resulting Numbers: [61, 37] Generated Node #0,3,1: 42:[61, 37] Operation: 47-10=37 Exploring Operation: 61+10=71, Resulting Numbers: [47, 71] Generated Node #0,3,2: 42:[47, 71] Operation: 61+10=71 Exploring Operation: 47+10=57, Resulting Numbers: [61, 57] Generated Node #0,3,3: 42:[61, 57] Operation: 47+10=57 Exploring Operation: 61-47=14, Resulting Numbers: [10, 14] Generated Node #0,3,4: 42:[10, 14] Operation: 61-47=14 Moving to Node #0,1,4 Current State: 42:[14, 10], Operations: ['61-47=14', '54-44=10'] Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 14*10=140, Resulting Numbers: [140] 140,42 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,3,4 Current State: 42:[10, 14], Operations: ['54-44=10', '61-47=14'] Exploring Operation: 10*14=140, Resulting Numbers: [140] 140,42 unequal: No Solution Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[44, 40], Operations: ['61-47=14', '54-14=40'] Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,42 unequal: No Solution Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,42 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[47, 51], Operations: ['54-44=10', '61-10=51'] Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,42 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[54, 30], Operations: ['61-47=14', '44-14=30'] Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 54*30=1620, Resulting Numbers: [1620] 1620,42 unequal: No Solution Exploring Operation: 54+30=84, Resulting Numbers: [84] 84,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[61, 37], Operations: ['54-44=10', '47-10=37'] Exploring Operation: 61*37=2257, Resulting Numbers: [2257] 2257,42 unequal: No Solution Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[54, 58], Operations: ['61-47=14', '44+14=58'] Exploring Operation: 54+58=112, Resulting Numbers: [112] 112,42 unequal: No Solution Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 54*58=3132, Resulting Numbers: [3132] 3132,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[44, 68], Operations: ['61-47=14', '54+14=68'] Exploring Operation: 44+68=112, Resulting Numbers: [112] 112,42 unequal: No Solution Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 44*68=2992, Resulting Numbers: [2992] 2992,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[61, 57], Operations: ['54-44=10', '47+10=57'] Exploring Operation: 61*57=3477, Resulting Numbers: [3477] 3477,42 unequal: No Solution Exploring Operation: 61+57=118, Resulting Numbers: [118] 118,42 unequal: No Solution Exploring Operation: 61-57=4, Resulting Numbers: [4] 4,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[47, 71], Operations: ['54-44=10', '61+10=71'] Exploring Operation: 47*71=3337, Resulting Numbers: [3337] 3337,42 unequal: No Solution Exploring Operation: 71-47=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 47+71=118, Resulting Numbers: [118] 118,42 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 87, 89, 47, 69 ]
44
[ "89-87=2", "69-47=22", "2*22=44" ]
Current State: 44:[87, 89, 47, 69], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [47, 69, 2] Generated Node #2: [47, 69, 2] from Operation: 89-87=2 Current State: 44:[47, 69, 2], Operations: ['89-87=2'] Exploring Operation: 69-47=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 69-47=22 Current State: 44:[2, 22], Operations: ['89-87=2', '69-47=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[87, 89, 47, 69], Operations: [] Exploring Operation: 89-69=20, Resulting Numbers: [87, 47, 20] Generated Node #0,0: 44:[87, 47, 20] Operation: 89-69=20 Exploring Operation: 87-69=18, Resulting Numbers: [89, 47, 18] Generated Node #0,1: 44:[89, 47, 18] Operation: 87-69=18 Exploring Operation: 89-87=2, Resulting Numbers: [47, 69, 2] Generated Node #0,2: 44:[47, 69, 2] Operation: 89-87=2 Moving to Node #0,2 Current State: 44:[47, 69, 2], Operations: ['89-87=2'] Exploring Operation: 47-2=45, Resulting Numbers: [69, 45] Generated Node #0,2,0: 44:[69, 45] Operation: 47-2=45 Exploring Operation: 69-2=67, Resulting Numbers: [47, 67] Generated Node #0,2,1: 44:[47, 67] Operation: 69-2=67 Exploring Operation: 69-47=22, Resulting Numbers: [2, 22] Generated Node #0,2,2: 44:[2, 22] Operation: 69-47=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[2, 22], Operations: ['89-87=2', '69-47=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[87, 89, 47, 69], Operations: [] Exploring Operation: 89-87=2, Resulting Numbers: [47, 69, 2] Generated Node #0,2: 44:[47, 69, 2] Operation: 89-87=2 Moving to Node #0,2 Current State: 44:[47, 69, 2], Operations: ['89-87=2'] Exploring Operation: 69-47=22, Resulting Numbers: [2, 22] Generated Node #0,2,2: 44:[2, 22] Operation: 69-47=22 Moving to Node #0,2,2 Current State: 44:[2, 22], Operations: ['89-87=2', '69-47=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 59, 49, 57, 33 ]
18
[ "59+49=108", "57+33=90", "108-90=18" ]
Current State: 18:[59, 49, 57, 33], Operations: [] Exploring Operation: 59+49=108, Resulting Numbers: [57, 33, 108] Generated Node #2: [57, 33, 108] from Operation: 59+49=108 Current State: 18:[57, 33, 108], Operations: ['59+49=108'] Exploring Operation: 57+33=90, Resulting Numbers: [108, 90] Generated Node #3: [108, 90] from Operation: 57+33=90 Current State: 18:[108, 90], Operations: ['59+49=108', '57+33=90'] Exploring Operation: 108-90=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[59, 49, 57, 33], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [49, 33, 2] Generated Node #0,0: 18:[49, 33, 2] Operation: 59-57=2 Exploring Operation: 57-49=8, Resulting Numbers: [59, 33, 8] Generated Node #0,1: 18:[59, 33, 8] Operation: 57-49=8 Exploring Operation: 59-49=10, Resulting Numbers: [57, 33, 10] Generated Node #0,2: 18:[57, 33, 10] Operation: 59-49=10 Exploring Operation: 57-33=24, Resulting Numbers: [59, 49, 24] Generated Node #0,3: 18:[59, 49, 24] Operation: 57-33=24 Exploring Operation: 59-33=26, Resulting Numbers: [49, 57, 26] Generated Node #0,4: 18:[49, 57, 26] Operation: 59-33=26 Moving to Node #0,0 Current State: 18:[49, 33, 2], Operations: ['59-57=2'] Exploring Operation: 49-33=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 18:[2, 16] Operation: 49-33=16 Exploring Operation: 49-2=47, Resulting Numbers: [33, 47] Generated Node #0,0,1: 18:[33, 47] Operation: 49-2=47 Exploring Operation: 33+2=35, Resulting Numbers: [49, 35] Generated Node #0,0,2: 18:[49, 35] Operation: 33+2=35 Exploring Operation: 49+2=51, Resulting Numbers: [33, 51] Generated Node #0,0,3: 18:[33, 51] Operation: 49+2=51 Exploring Operation: 33-2=31, Resulting Numbers: [49, 31] Generated Node #0,0,4: 18:[49, 31] Operation: 33-2=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[2, 16], Operations: ['59-57=2', '49-33=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[59, 49, 57, 33], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [49, 33, 2] Generated Node #0,0: 18:[49, 33, 2] Operation: 59-57=2 Moving to Node #0,0 Current State: 18:[49, 33, 2], Operations: ['59-57=2'] Exploring Operation: 49-33=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 18:[2, 16] Operation: 49-33=16 Moving to Node #0,0,0 Current State: 18:[2, 16], Operations: ['59-57=2', '49-33=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 18, 77, 4, 90 ]
76
[ "90/18=5", "77+4=81", "81-5=76" ]
Current State: 76:[18, 77, 4, 90], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [77, 4, 5] Generated Node #2: [77, 4, 5] from Operation: 90/18=5 Current State: 76:[77, 4, 5], Operations: ['90/18=5'] Exploring Operation: 77+4=81, Resulting Numbers: [5, 81] Generated Node #3: [5, 81] from Operation: 77+4=81 Current State: 76:[5, 81], Operations: ['90/18=5', '77+4=81'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[18, 77, 4, 90], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [77, 4, 5] Generated Node #0,0: 76:[77, 4, 5] Operation: 90/18=5 Exploring Operation: 90-77=13, Resulting Numbers: [18, 4, 13] Generated Node #0,1: 76:[18, 4, 13] Operation: 90-77=13 Exploring Operation: 90-18=72, Resulting Numbers: [77, 4, 72] Generated Node #0,2: 76:[77, 4, 72] Operation: 90-18=72 Moving to Node #0,0 Current State: 76:[77, 4, 5], Operations: ['90/18=5'] Exploring Operation: 77-4=73, Resulting Numbers: [5, 73] Generated Node #0,0,0: 76:[5, 73] Operation: 77-4=73 Exploring Operation: 4*5=20, Resulting Numbers: [77, 20] Generated Node #0,0,1: 76:[77, 20] Operation: 4*5=20 Exploring Operation: 5-4=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 76:[77, 1] Operation: 5-4=1 Moving to Node #0,2 Current State: 76:[77, 4, 72], Operations: ['90-18=72'] Exploring Operation: 72/4=18, Resulting Numbers: [77, 18] Generated Node #0,2,0: 76:[77, 18] Operation: 72/4=18 Exploring Operation: 77-72=5, Resulting Numbers: [4, 5] Generated Node #0,2,1: 76:[4, 5] Operation: 77-72=5 Exploring Operation: 4+72=76, Resulting Numbers: [77, 76] Generated Node #0,2,2: 76:[77, 76] Operation: 4+72=76 Moving to Node #0,1 Current State: 76:[18, 4, 13], Operations: ['90-77=13'] Exploring Operation: 4+13=17, Resulting Numbers: [18, 17] Generated Node #0,1,0: 76:[18, 17] Operation: 4+13=17 Exploring Operation: 18-13=5, Resulting Numbers: [4, 5] Generated Node #0,1,1: 76:[4, 5] Operation: 18-13=5 Exploring Operation: 13-4=9, Resulting Numbers: [18, 9] Generated Node #0,1,2: 76:[18, 9] Operation: 13-4=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[4, 5], Operations: ['90-77=13', '18-13=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[18, 17], Operations: ['90-77=13', '4+13=17'] Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 18*17=306, Resulting Numbers: [306] 306,76 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[18, 9], Operations: ['90-77=13', '13-4=9'] Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 76:[4, 5], Operations: ['90-18=72', '77-72=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[77, 76], Operations: ['90-18=72', '4+72=76'] Exploring Operation: 77+76=153, Resulting Numbers: [153] 153,76 unequal: No Solution Exploring Operation: 77*76=5852, Resulting Numbers: [5852] 5852,76 unequal: No Solution Exploring Operation: 77-76=1, Resulting Numbers: [1] 1,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[77, 18], Operations: ['90-18=72', '72/4=18'] Exploring Operation: 77*18=1386, Resulting Numbers: [1386] 1386,76 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 77+18=95, Resulting Numbers: [95] 95,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[77, 20], Operations: ['90/18=5', '4*5=20'] Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,76 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,76 unequal: No Solution Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[77, 1], Operations: ['90/18=5', '5-4=1'] Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[18, 77, 4, 90], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [77, 4, 5] Generated Node #0,0: 76:[77, 4, 5] Operation: 90/18=5 Moving to Node #0,0 Current State: 76:[77, 4, 5], Operations: ['90/18=5'] Exploring Operation: 5-4=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 76:[77, 1] Operation: 5-4=1 Moving to Node #0,0,2 Current State: 76:[77, 1], Operations: ['90/18=5', '5-4=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.965278
hs_3
mult_heuristic
[ 27, 4, 13, 80 ]
15
[ "27*4=108", "13+80=93", "108-93=15" ]
Current State: 15:[27, 4, 13, 80], Operations: [] Exploring Operation: 27*4=108, Resulting Numbers: [13, 80, 108] Generated Node #2: [13, 80, 108] from Operation: 27*4=108 Current State: 15:[13, 80, 108], Operations: ['27*4=108'] Exploring Operation: 13+80=93, Resulting Numbers: [108, 93] Generated Node #3: [108, 93] from Operation: 13+80=93 Current State: 15:[108, 93], Operations: ['27*4=108', '13+80=93'] Exploring Operation: 108-93=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[27, 4, 13, 80], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [27, 13, 20] Generated Node #0,0: 15:[27, 13, 20] Operation: 80/4=20 Exploring Operation: 80-27=53, Resulting Numbers: [4, 13, 53] Generated Node #0,1: 15:[4, 13, 53] Operation: 80-27=53 Moving to Node #0,0 Current State: 15:[27, 13, 20], Operations: ['80/4=20'] Exploring Operation: 27-20=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 15:[13, 7] Operation: 27-20=7 Exploring Operation: 27-13=14, Resulting Numbers: [20, 14] Generated Node #0,0,1: 15:[20, 14] Operation: 27-13=14 Moving to Node #0,1 Current State: 15:[4, 13, 53], Operations: ['80-27=53'] Exploring Operation: 53-4=49, Resulting Numbers: [13, 49] Generated Node #0,1,0: 15:[13, 49] Operation: 53-4=49 Exploring Operation: 53-13=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 15:[4, 40] Operation: 53-13=40 Moving to Node #0,0,0 Current State: 15:[13, 7], Operations: ['80/4=20', '27-20=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[20, 14], Operations: ['80/4=20', '27-13=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,15 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[4, 40], Operations: ['80-27=53', '53-13=40'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[13, 49], Operations: ['80-27=53', '53-4=49'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,15 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 48, 51, 54, 61 ]
39
[ "61-48=13", "54-51=3", "13*3=39" ]
Current State: 39:[48, 51, 54, 61], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [51, 54, 13] Generated Node #2: [51, 54, 13] from Operation: 61-48=13 Current State: 39:[51, 54, 13], Operations: ['61-48=13'] Exploring Operation: 54-51=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 54-51=3 Current State: 39:[13, 3], Operations: ['61-48=13', '54-51=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[48, 51, 54, 61], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [51, 54, 13] Generated Node #0,0: 39:[51, 54, 13] Operation: 61-48=13 Exploring Operation: 61-54=7, Resulting Numbers: [48, 51, 7] Generated Node #0,1: 39:[48, 51, 7] Operation: 61-54=7 Exploring Operation: 61-51=10, Resulting Numbers: [48, 54, 10] Generated Node #0,2: 39:[48, 54, 10] Operation: 61-51=10 Moving to Node #0,1 Current State: 39:[48, 51, 7], Operations: ['61-54=7'] Exploring Operation: 51-48=3, Resulting Numbers: [7, 3] Generated Node #0,1,0: 39:[7, 3] Operation: 51-48=3 Exploring Operation: 48-7=41, Resulting Numbers: [51, 41] Generated Node #0,1,1: 39:[51, 41] Operation: 48-7=41 Exploring Operation: 51-7=44, Resulting Numbers: [48, 44] Generated Node #0,1,2: 39:[48, 44] Operation: 51-7=44 Moving to Node #0,0 Current State: 39:[51, 54, 13], Operations: ['61-48=13'] Exploring Operation: 54-13=41, Resulting Numbers: [51, 41] Generated Node #0,0,0: 39:[51, 41] Operation: 54-13=41 Exploring Operation: 51-13=38, Resulting Numbers: [54, 38] Generated Node #0,0,1: 39:[54, 38] Operation: 51-13=38 Exploring Operation: 54-51=3, Resulting Numbers: [13, 3] Generated Node #0,0,2: 39:[13, 3] Operation: 54-51=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[13, 3], Operations: ['61-48=13', '54-51=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[48, 51, 54, 61], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [51, 54, 13] Generated Node #0,0: 39:[51, 54, 13] Operation: 61-48=13 Moving to Node #0,0 Current State: 39:[51, 54, 13], Operations: ['61-48=13'] Exploring Operation: 54-51=3, Resulting Numbers: [13, 3] Generated Node #0,0,2: 39:[13, 3] Operation: 54-51=3 Moving to Node #0,0,2 Current State: 39:[13, 3], Operations: ['61-48=13', '54-51=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 82, 36, 80, 38 ]
39
[ "38-36=2", "82/2=41", "80-41=39" ]
Current State: 39:[82, 36, 80, 38], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [82, 80, 2] Generated Node #2: [82, 80, 2] from Operation: 38-36=2 Current State: 39:[82, 80, 2], Operations: ['38-36=2'] Exploring Operation: 82/2=41, Resulting Numbers: [80, 41] Generated Node #3: [80, 41] from Operation: 82/2=41 Current State: 39:[80, 41], Operations: ['38-36=2', '82/2=41'] Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[82, 36, 80, 38], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [80, 38, 46] Generated Node #0,0: 39:[80, 38, 46] Operation: 82-36=46 Exploring Operation: 80-36=44, Resulting Numbers: [82, 38, 44] Generated Node #0,1: 39:[82, 38, 44] Operation: 80-36=44 Exploring Operation: 82-38=44, Resulting Numbers: [36, 80, 44] Generated Node #0,2: 39:[36, 80, 44] Operation: 82-38=44 Exploring Operation: 82-80=2, Resulting Numbers: [36, 38, 2] Generated Node #0,3: 39:[36, 38, 2] Operation: 82-80=2 Moving to Node #0,3 Current State: 39:[36, 38, 2], Operations: ['82-80=2'] Exploring Operation: 38+2=40, Resulting Numbers: [36, 40] Generated Node #0,3,0: 39:[36, 40] Operation: 38+2=40 Exploring Operation: 36+2=38, Resulting Numbers: [38, 38] Generated Node #0,3,1: 39:[38, 38] Operation: 36+2=38 Exploring Operation: 36-2=34, Resulting Numbers: [38, 34] Generated Node #0,3,2: 39:[38, 34] Operation: 36-2=34 Exploring Operation: 38-36=2, Resulting Numbers: [2, 2] Generated Node #0,3,3: 39:[2, 2] Operation: 38-36=2 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[38, 38], Operations: ['82-80=2', '36+2=38'] Exploring Operation: 38*38=1444, Resulting Numbers: [1444] 1444,39 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,39 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 #0,3,3 Current State: 39:[2, 2], Operations: ['82-80=2', '38-36=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,39 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 #0,3,0 Current State: 39:[36, 40], Operations: ['82-80=2', '38+2=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,39 unequal: No Solution Exploring Operation: 36*40=1440, Resulting Numbers: [1440] 1440,39 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 #0,3,2 Current State: 39:[38, 34], Operations: ['82-80=2', '36-2=34'] Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,39 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,39 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:[82, 38, 44], Operations: ['80-36=44'] Exploring Operation: 44-38=6, Resulting Numbers: [82, 6] Generated Node #0,1,0: 39:[82, 6] Operation: 44-38=6 Exploring Operation: 82-44=38, Resulting Numbers: [38, 38] Generated Node #0,1,1: 39:[38, 38] Operation: 82-44=38 Exploring Operation: 82+38=120, Resulting Numbers: [44, 120] Generated Node #0,1,2: 39:[44, 120] Operation: 82+38=120 Exploring Operation: 82-38=44, Resulting Numbers: [44, 44] Generated Node #0,1,3: 39:[44, 44] Operation: 82-38=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[38, 38], Operations: ['80-36=44', '82-44=38'] Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,39 unequal: No Solution Exploring Operation: 38*38=1444, Resulting Numbers: [1444] 1444,39 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 #0,1,3 Current State: 39:[44, 44], Operations: ['80-36=44', '82-38=44'] Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,39 unequal: No Solution Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,39 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 #0,1,0 Current State: 39:[82, 6], Operations: ['80-36=44', '44-38=6'] Exploring Operation: 82+6=88, Resulting Numbers: [88] 88,39 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,39 unequal: No Solution Exploring Operation: 82*6=492, Resulting Numbers: [492] 492,39 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 #0,1,2 Current State: 39:[44, 120], Operations: ['80-36=44', '82+38=120'] Exploring Operation: 120-44=76, Resulting Numbers: [76] 76,39 unequal: No Solution Exploring Operation: 44+120=164, Resulting Numbers: [164] 164,39 unequal: No Solution Exploring Operation: 44*120=5280, Resulting Numbers: [5280] 5280,39 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: 39:[80, 38, 46], Operations: ['82-36=46'] Exploring Operation: 46-38=8, Resulting Numbers: [80, 8] Generated Node #0,0,0: 39:[80, 8] Operation: 46-38=8 Exploring Operation: 80-38=42, Resulting Numbers: [46, 42] Generated Node #0,0,1: 39:[46, 42] Operation: 80-38=42 Exploring Operation: 80+38=118, Resulting Numbers: [46, 118] Generated Node #0,0,2: 39:[46, 118] Operation: 80+38=118 Exploring Operation: 80-46=34, Resulting Numbers: [38, 34] Generated Node #0,0,3: 39:[38, 34] Operation: 80-46=34 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 39:[38, 34], Operations: ['82-36=46', '80-46=34'] Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,39 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,39 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:[46, 42], Operations: ['82-36=46', '80-38=42'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,39 unequal: No Solution Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,39 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 #0,0,0 Current State: 39:[80, 8], Operations: ['82-36=46', '46-38=8'] Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,39 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,39 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 #0,0,2 Current State: 39:[46, 118], Operations: ['82-36=46', '80+38=118'] Exploring Operation: 46*118=5428, Resulting Numbers: [5428] 5428,39 unequal: No Solution Exploring Operation: 46+118=164, Resulting Numbers: [164] 164,39 unequal: No Solution Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,39 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: 39:[36, 80, 44], Operations: ['82-38=44'] Exploring Operation: 44-36=8, Resulting Numbers: [80, 8] Generated Node #0,2,0: 39:[80, 8] Operation: 44-36=8 Exploring Operation: 36+80=116, Resulting Numbers: [44, 116] Generated Node #0,2,1: 39:[44, 116] Operation: 36+80=116 Exploring Operation: 80-36=44, Resulting Numbers: [44, 44] Generated Node #0,2,2: 39:[44, 44] Operation: 80-36=44 Exploring Operation: 80-44=36, Resulting Numbers: [36, 36] Generated Node #0,2,3: 39:[36, 36] Operation: 80-44=36 Moving to Node #0,2,3 Current State: 39:[36, 36], Operations: ['82-38=44', '80-44=36'] Exploring Operation: 36/36=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 36+36=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 36-36=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 36*36=1296, Resulting Numbers: [1296] 1296,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[44, 44], Operations: ['82-38=44', '80-36=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,39 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,39 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,39 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[80, 8], Operations: ['82-38=44', '44-36=8'] Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,39 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,39 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[44, 116], Operations: ['82-38=44', '36+80=116'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,39 unequal: No Solution Exploring Operation: 44+116=160, Resulting Numbers: [160] 160,39 unequal: No Solution Exploring Operation: 44*116=5104, Resulting Numbers: [5104] 5104,39 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 38, 52, 57, 75 ]
53
[ "57-52=5", "75/5=15", "38+15=53" ]
Current State: 53:[38, 52, 57, 75], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [38, 75, 5] Generated Node #2: [38, 75, 5] from Operation: 57-52=5 Current State: 53:[38, 75, 5], Operations: ['57-52=5'] Exploring Operation: 75/5=15, Resulting Numbers: [38, 15] Generated Node #3: [38, 15] from Operation: 75/5=15 Current State: 53:[38, 15], Operations: ['57-52=5', '75/5=15'] Exploring Operation: 38+15=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[38, 52, 57, 75], Operations: [] Exploring Operation: 75-38=37, Resulting Numbers: [52, 57, 37] Generated Node #0,0: 53:[52, 57, 37] Operation: 75-38=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[52, 57, 37], Operations: ['75-38=37'] Exploring Operation: 57-37=20, Resulting Numbers: [52, 20] Generated Node #0,0,0: 53:[52, 20] Operation: 57-37=20 Moving to Node #0,0,0 Current State: 53:[52, 20], Operations: ['75-38=37', '57-37=20'] Exploring Operation: 52+20=72, Resulting Numbers: [72] 72,53 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
[ 53, 45, 37, 30 ]
31
[ "53+45=98", "37+30=67", "98-67=31" ]
Current State: 31:[53, 45, 37, 30], Operations: [] Exploring Operation: 53+45=98, Resulting Numbers: [37, 30, 98] Generated Node #2: [37, 30, 98] from Operation: 53+45=98 Current State: 31:[37, 30, 98], Operations: ['53+45=98'] Exploring Operation: 37+30=67, Resulting Numbers: [98, 67] Generated Node #3: [98, 67] from Operation: 37+30=67 Current State: 31:[98, 67], Operations: ['53+45=98', '37+30=67'] Exploring Operation: 98-67=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[53, 45, 37, 30], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [37, 30, 8] Generated Node #0,0: 31:[37, 30, 8] Operation: 53-45=8 Exploring Operation: 53-30=23, Resulting Numbers: [45, 37, 23] Generated Node #0,1: 31:[45, 37, 23] Operation: 53-30=23 Exploring Operation: 45-30=15, Resulting Numbers: [53, 37, 15] Generated Node #0,2: 31:[53, 37, 15] Operation: 45-30=15 Exploring Operation: 53-37=16, Resulting Numbers: [45, 30, 16] Generated Node #0,3: 31:[45, 30, 16] Operation: 53-37=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[45, 37, 23], Operations: ['53-30=23'] Exploring Operation: 45-37=8, Resulting Numbers: [23, 8] Generated Node #0,1,0: 31:[23, 8] Operation: 45-37=8 Exploring Operation: 37-23=14, Resulting Numbers: [45, 14] Generated Node #0,1,1: 31:[45, 14] Operation: 37-23=14 Exploring Operation: 45+23=68, Resulting Numbers: [37, 68] Generated Node #0,1,2: 31:[37, 68] Operation: 45+23=68 Exploring Operation: 45-23=22, Resulting Numbers: [37, 22] Generated Node #0,1,3: 31:[37, 22] Operation: 45-23=22 Moving to Node #0,1,3 Current State: 31:[37, 22], Operations: ['53-30=23', '45-23=22'] Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,31 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 37*22=814, Resulting Numbers: [814] 814,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[45, 14], Operations: ['53-30=23', '37-23=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[53, 45, 37, 30], Operations: [] Exploring Operation: 53-30=23, Resulting Numbers: [45, 37, 23] Generated Node #0,1: 31:[45, 37, 23] Operation: 53-30=23 Moving to Node #0,1 Current State: 31:[45, 37, 23], Operations: ['53-30=23'] Exploring Operation: 37-23=14, Resulting Numbers: [45, 14] Generated Node #0,1,1: 31:[45, 14] Operation: 37-23=14 Moving to Node #0,1,1 Current State: 31:[45, 14], Operations: ['53-30=23', '37-23=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 66, 5, 17, 42 ]
23
[ "66+42=108", "5*17=85", "108-85=23" ]
Current State: 23:[66, 5, 17, 42], Operations: [] Exploring Operation: 66+42=108, Resulting Numbers: [5, 17, 108] Generated Node #2: [5, 17, 108] from Operation: 66+42=108 Current State: 23:[5, 17, 108], Operations: ['66+42=108'] Exploring Operation: 5*17=85, Resulting Numbers: [108, 85] Generated Node #3: [108, 85] from Operation: 5*17=85 Current State: 23:[108, 85], Operations: ['66+42=108', '5*17=85'] Exploring Operation: 108-85=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[66, 5, 17, 42], Operations: [] Exploring Operation: 66-5=61, Resulting Numbers: [17, 42, 61] Generated Node #0,0: 23:[17, 42, 61] Operation: 66-5=61 Exploring Operation: 5+17=22, Resulting Numbers: [66, 42, 22] Generated Node #0,1: 23:[66, 42, 22] Operation: 5+17=22 Exploring Operation: 42-5=37, Resulting Numbers: [66, 17, 37] Generated Node #0,2: 23:[66, 17, 37] Operation: 42-5=37 Exploring Operation: 66-42=24, Resulting Numbers: [5, 17, 24] Generated Node #0,3: 23:[5, 17, 24] Operation: 66-42=24 Exploring Operation: 66-17=49, Resulting Numbers: [5, 42, 49] Generated Node #0,4: 23:[5, 42, 49] Operation: 66-17=49 Moving to Node #0,3 Current State: 23:[5, 17, 24], Operations: ['66-42=24'] Exploring Operation: 24-17=7, Resulting Numbers: [5, 7] Generated Node #0,3,0: 23:[5, 7] Operation: 24-17=7 Exploring Operation: 5+24=29, Resulting Numbers: [17, 29] Generated Node #0,3,1: 23:[17, 29] Operation: 5+24=29 Exploring Operation: 17-5=12, Resulting Numbers: [24, 12] Generated Node #0,3,2: 23:[24, 12] Operation: 17-5=12 Exploring Operation: 24-5=19, Resulting Numbers: [17, 19] Generated Node #0,3,3: 23:[17, 19] Operation: 24-5=19 Exploring Operation: 5+17=22, Resulting Numbers: [24, 22] Generated Node #0,3,4: 23:[24, 22] Operation: 5+17=22 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 23:[24, 22], Operations: ['66-42=24', '5+17=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,23 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 23:[17, 19], Operations: ['66-42=24', '24-5=19'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 17+19=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 17*19=323, Resulting Numbers: [323] 323,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[17, 29], Operations: ['66-42=24', '5+24=29'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 17*29=493, Resulting Numbers: [493] 493,23 unequal: No Solution Exploring Operation: 17+29=46, Resulting Numbers: [46] 46,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[24, 12], Operations: ['66-42=24', '17-5=12'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 24*12=288, Resulting Numbers: [288] 288,23 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 23:[5, 7], Operations: ['66-42=24', '24-17=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,23 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: 23:[66, 42, 22], Operations: ['5+17=22'] Exploring Operation: 66+22=88, Resulting Numbers: [42, 88] Generated Node #0,1,0: 23:[42, 88] Operation: 66+22=88 Exploring Operation: 66-42=24, Resulting Numbers: [22, 24] Generated Node #0,1,1: 23:[22, 24] Operation: 66-42=24 Exploring Operation: 42-22=20, Resulting Numbers: [66, 20] Generated Node #0,1,2: 23:[66, 20] Operation: 42-22=20 Exploring Operation: 66/22=3, Resulting Numbers: [42, 3] Generated Node #0,1,3: 23:[42, 3] Operation: 66/22=3 Exploring Operation: 66-22=44, Resulting Numbers: [42, 44] Generated Node #0,1,4: 23:[42, 44] Operation: 66-22=44 Moving to Node #0,4 Current State: 23:[5, 42, 49], Operations: ['66-17=49'] Exploring Operation: 5+49=54, Resulting Numbers: [42, 54] Generated Node #0,4,0: 23:[42, 54] Operation: 5+49=54 Exploring Operation: 49-42=7, Resulting Numbers: [5, 7] Generated Node #0,4,1: 23:[5, 7] Operation: 49-42=7 Exploring Operation: 42-5=37, Resulting Numbers: [49, 37] Generated Node #0,4,2: 23:[49, 37] Operation: 42-5=37 Exploring Operation: 5+42=47, Resulting Numbers: [49, 47] Generated Node #0,4,3: 23:[49, 47] Operation: 5+42=47 Exploring Operation: 49-5=44, Resulting Numbers: [42, 44] Generated Node #0,4,4: 23:[42, 44] Operation: 49-5=44 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 23:[5, 7], Operations: ['66-17=49', '49-42=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 23:[49, 37], Operations: ['66-17=49', '42-5=37'] Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,23 unequal: No Solution Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 49*37=1813, Resulting Numbers: [1813] 1813,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 23:[42, 44], Operations: ['66-17=49', '49-5=44'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,23 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 23:[42, 54], Operations: ['66-17=49', '5+49=54'] Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,23 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 23:[49, 47], Operations: ['66-17=49', '5+42=47'] Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,23 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,23 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: 23:[17, 42, 61], Operations: ['66-5=61'] Exploring Operation: 17+61=78, Resulting Numbers: [42, 78] Generated Node #0,0,0: 23:[42, 78] Operation: 17+61=78 Exploring Operation: 42-17=25, Resulting Numbers: [61, 25] Generated Node #0,0,1: 23:[61, 25] Operation: 42-17=25 Exploring Operation: 61-42=19, Resulting Numbers: [17, 19] Generated Node #0,0,2: 23:[17, 19] Operation: 61-42=19 Exploring Operation: 17+42=59, Resulting Numbers: [61, 59] Generated Node #0,0,3: 23:[61, 59] Operation: 17+42=59 Exploring Operation: 61-17=44, Resulting Numbers: [42, 44] Generated Node #0,0,4: 23:[42, 44] Operation: 61-17=44 Moving to Node #0,2 Current State: 23:[66, 17, 37], Operations: ['42-5=37'] Exploring Operation: 66+17=83, Resulting Numbers: [37, 83] Generated Node #0,2,0: 23:[37, 83] Operation: 66+17=83 Exploring Operation: 66-17=49, Resulting Numbers: [37, 49] Generated Node #0,2,1: 23:[37, 49] Operation: 66-17=49 Exploring Operation: 17+37=54, Resulting Numbers: [66, 54] Generated Node #0,2,2: 23:[66, 54] Operation: 17+37=54 Exploring Operation: 66-37=29, Resulting Numbers: [17, 29] Generated Node #0,2,3: 23:[17, 29] Operation: 66-37=29 Exploring Operation: 37-17=20, Resulting Numbers: [66, 20] Generated Node #0,2,4: 23:[66, 20] Operation: 37-17=20 Moving to Node #0,1,1 Current State: 23:[22, 24], Operations: ['5+17=22', '66-42=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,23 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[17, 19], Operations: ['66-5=61', '61-42=19'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 17+19=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 17*19=323, Resulting Numbers: [323] 323,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[17, 29], Operations: ['42-5=37', '66-37=29'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 17+29=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 17*29=493, Resulting Numbers: [493] 493,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[42, 3], Operations: ['5+17=22', '66/22=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,23 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,23 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,23 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[61, 25], Operations: ['66-5=61', '42-17=25'] Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,23 unequal: No Solution Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[42, 44], Operations: ['5+17=22', '66-22=44'] Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,23 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,23 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[37, 49], Operations: ['42-5=37', '66-17=49'] Exploring Operation: 37*49=1813, Resulting Numbers: [1813] 1813,23 unequal: No Solution Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[42, 44], Operations: ['66-5=61', '61-17=44'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,23 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[66, 20], Operations: ['5+17=22', '42-22=20'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,23 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,23 unequal: No Solution Moving to Node #0,2,4 Current State: 23:[66, 20], Operations: ['42-5=37', '37-17=20'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,23 unequal: No Solution Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[37, 83], Operations: ['42-5=37', '66+17=83'] Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 37+83=120, Resulting Numbers: [120] 120,23 unequal: No Solution Exploring Operation: 37*83=3071, Resulting Numbers: [3071] 3071,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[66, 54], Operations: ['42-5=37', '17+37=54'] Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 66*54=3564, Resulting Numbers: [3564] 3564,23 unequal: No Solution Exploring Operation: 66+54=120, Resulting Numbers: [120] 120,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[61, 59], Operations: ['66-5=61', '17+42=59'] Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 61*59=3599, Resulting Numbers: [3599] 3599,23 unequal: No Solution Exploring Operation: 61+59=120, Resulting Numbers: [120] 120,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[42, 78], Operations: ['66-5=61', '17+61=78'] Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 42*78=3276, Resulting Numbers: [3276] 3276,23 unequal: No Solution Exploring Operation: 42+78=120, Resulting Numbers: [120] 120,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[42, 88], Operations: ['5+17=22', '66+22=88'] Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 42*88=3696, Resulting Numbers: [3696] 3696,23 unequal: No Solution Exploring Operation: 42+88=130, Resulting Numbers: [130] 130,23 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 70, 33, 33, 2 ]
69
[ "70-2=68", "33/33=1", "68+1=69" ]
Current State: 69:[70, 33, 33, 2], Operations: [] Exploring Operation: 70-2=68, Resulting Numbers: [33, 33, 68] Generated Node #2: [33, 33, 68] from Operation: 70-2=68 Current State: 69:[33, 33, 68], Operations: ['70-2=68'] Exploring Operation: 33/33=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 33/33=1 Current State: 69:[68, 1], Operations: ['70-2=68', '33/33=1'] Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[70, 33, 33, 2], Operations: [] Exploring Operation: 33/33=1, Resulting Numbers: [70, 2, 1] Generated Node #0,0: 69:[70, 2, 1] Operation: 33/33=1 Moving to Node #0,0 Current State: 69:[70, 2, 1], Operations: ['33/33=1'] Exploring Operation: 70-1=69, Resulting Numbers: [2, 69] Generated Node #0,0,0: 69:[2, 69] Operation: 70-1=69 Moving to Node #0,0,0 Current State: 69:[2, 69], Operations: ['33/33=1', '70-1=69'] Exploring Operation: 2+69=71, Resulting Numbers: [71] 71,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 61, 35, 44, 80 ]
60
[ "61+35=96", "80-44=36", "96-36=60" ]
Current State: 60:[61, 35, 44, 80], Operations: [] Exploring Operation: 61+35=96, Resulting Numbers: [44, 80, 96] Generated Node #2: [44, 80, 96] from Operation: 61+35=96 Current State: 60:[44, 80, 96], Operations: ['61+35=96'] Exploring Operation: 80-44=36, Resulting Numbers: [96, 36] Generated Node #3: [96, 36] from Operation: 80-44=36 Current State: 60:[96, 36], Operations: ['61+35=96', '80-44=36'] Exploring Operation: 96-36=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[61, 35, 44, 80], Operations: [] Exploring Operation: 80-44=36, Resulting Numbers: [61, 35, 36] Generated Node #0,0: 60:[61, 35, 36] Operation: 80-44=36 Moving to Node #0,0 Current State: 60:[61, 35, 36], Operations: ['80-44=36'] Exploring Operation: 36-35=1, Resulting Numbers: [61, 1] Generated Node #0,0,0: 60:[61, 1] Operation: 36-35=1 Moving to Node #0,0,0 Current State: 60:[61, 1], Operations: ['80-44=36', '36-35=1'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[61, 35, 44, 80], Operations: [] Exploring Operation: 80-44=36, Resulting Numbers: [61, 35, 36] Generated Node #0,0: 60:[61, 35, 36] Operation: 80-44=36 Moving to Node #0,0 Current State: 60:[61, 35, 36], Operations: ['80-44=36'] Exploring Operation: 36-35=1, Resulting Numbers: [61, 1] Generated Node #0,0,0: 60:[61, 1] Operation: 36-35=1 Moving to Node #0,0,0 Current State: 60:[61, 1], Operations: ['80-44=36', '36-35=1'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 2, 80, 88, 16 ]
91
[ "2*88=176", "176/16=11", "80+11=91" ]
Current State: 91:[2, 80, 88, 16], Operations: [] Exploring Operation: 2*88=176, Resulting Numbers: [80, 16, 176] Generated Node #2: [80, 16, 176] from Operation: 2*88=176 Current State: 91:[80, 16, 176], Operations: ['2*88=176'] Exploring Operation: 176/16=11, Resulting Numbers: [80, 11] Generated Node #3: [80, 11] from Operation: 176/16=11 Current State: 91:[80, 11], Operations: ['2*88=176', '176/16=11'] Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[2, 80, 88, 16], Operations: [] Exploring Operation: 80/16=5, Resulting Numbers: [2, 88, 5] Generated Node #0,0: 91:[2, 88, 5] Operation: 80/16=5 Exploring Operation: 2+88=90, Resulting Numbers: [80, 16, 90] Generated Node #0,1: 91:[80, 16, 90] Operation: 2+88=90 Exploring Operation: 2+80=82, Resulting Numbers: [88, 16, 82] Generated Node #0,2: 91:[88, 16, 82] Operation: 2+80=82 Exploring Operation: 88-80=8, Resulting Numbers: [2, 16, 8] Generated Node #0,3: 91:[2, 16, 8] Operation: 88-80=8 Exploring Operation: 80+16=96, Resulting Numbers: [2, 88, 96] Generated Node #0,4: 91:[2, 88, 96] Operation: 80+16=96 Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[2, 16, 8], Operations: ['88-80=8'] Exploring Operation: 16-2=14, Resulting Numbers: [8, 14] Generated Node #0,3,0: 91:[8, 14] Operation: 16-2=14 Exploring Operation: 8-2=6, Resulting Numbers: [16, 6] Generated Node #0,3,1: 91:[16, 6] Operation: 8-2=6 Exploring Operation: 2+8=10, Resulting Numbers: [16, 10] Generated Node #0,3,2: 91:[16, 10] Operation: 2+8=10 Exploring Operation: 16/2=8, Resulting Numbers: [8, 8] Generated Node #0,3,3: 91:[8, 8] Operation: 16/2=8 Exploring Operation: 2+16=18, Resulting Numbers: [8, 18] Generated Node #0,3,4: 91:[8, 18] Operation: 2+16=18 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 91:[8, 14], Operations: ['88-80=8', '16-2=14'] Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,91 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,91 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 #0,3,3 Current State: 91:[8, 8], Operations: ['88-80=8', '16/2=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,91 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,91 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,91 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 #0,3,1 Current State: 91:[16, 6], Operations: ['88-80=8', '8-2=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,91 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 #0,3,2 Current State: 91:[16, 10], Operations: ['88-80=8', '2+8=10'] Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,91 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,91 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,91 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 #0,3,4 Current State: 91:[8, 18], Operations: ['88-80=8', '2+16=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[2, 88, 5], Operations: ['80/16=5'] Exploring Operation: 2+88=90, Resulting Numbers: [5, 90] Generated Node #0,0,0: 91:[5, 90] Operation: 2+88=90 Exploring Operation: 2+5=7, Resulting Numbers: [88, 7] Generated Node #0,0,1: 91:[88, 7] Operation: 2+5=7 Exploring Operation: 88-2=86, Resulting Numbers: [5, 86] Generated Node #0,0,2: 91:[5, 86] Operation: 88-2=86 Exploring Operation: 2*5=10, Resulting Numbers: [88, 10] Generated Node #0,0,3: 91:[88, 10] Operation: 2*5=10 Exploring Operation: 5-2=3, Resulting Numbers: [88, 3] Generated Node #0,0,4: 91:[88, 3] Operation: 5-2=3 Moving to Node #0,0,0 Current State: 91:[5, 90], Operations: ['80/16=5', '2+88=90'] Exploring Operation: 5*90=450, Resulting Numbers: [450] 450,91 unequal: No Solution Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[88, 7], Operations: ['80/16=5', '2+5=7'] Exploring Operation: 88*7=616, Resulting Numbers: [616] 616,91 unequal: No Solution Exploring Operation: 88+7=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[88, 10], Operations: ['80/16=5', '2*5=10'] Exploring Operation: 88*10=880, Resulting Numbers: [880] 880,91 unequal: No Solution Exploring Operation: 88+10=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[5, 86], Operations: ['80/16=5', '88-2=86'] Exploring Operation: 5*86=430, Resulting Numbers: [430] 430,91 unequal: No Solution Exploring Operation: 5+86=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[2, 80, 88, 16], Operations: [] Exploring Operation: 80/16=5, Resulting Numbers: [2, 88, 5] Generated Node #0,0: 91:[2, 88, 5] Operation: 80/16=5 Moving to Node #0,0 Current State: 91:[2, 88, 5], Operations: ['80/16=5'] Exploring Operation: 88-2=86, Resulting Numbers: [5, 86] Generated Node #0,0,2: 91:[5, 86] Operation: 88-2=86 Moving to Node #0,0,2 Current State: 91:[5, 86], Operations: ['80/16=5', '88-2=86'] Exploring Operation: 5+86=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 41, 90, 73, 68 ]
59
[ "73-68=5", "90/5=18", "41+18=59" ]
Current State: 59:[41, 90, 73, 68], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [41, 90, 5] Generated Node #2: [41, 90, 5] from Operation: 73-68=5 Current State: 59:[41, 90, 5], Operations: ['73-68=5'] Exploring Operation: 90/5=18, Resulting Numbers: [41, 18] Generated Node #3: [41, 18] from Operation: 90/5=18 Current State: 59:[41, 18], Operations: ['73-68=5', '90/5=18'] Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[41, 90, 73, 68], Operations: [] Exploring Operation: 90-41=49, Resulting Numbers: [73, 68, 49] Generated Node #0,0: 59:[73, 68, 49] Operation: 90-41=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[73, 68, 49], Operations: ['90-41=49'] Exploring Operation: 73-49=24, Resulting Numbers: [68, 24] Generated Node #0,0,0: 59:[68, 24] Operation: 73-49=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[68, 24], Operations: ['90-41=49', '73-49=24'] Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 25, 54, 76, 33 ]
30
[ "25+54=79", "76+33=109", "109-79=30" ]
Current State: 30:[25, 54, 76, 33], Operations: [] Exploring Operation: 25+54=79, Resulting Numbers: [76, 33, 79] Generated Node #2: [76, 33, 79] from Operation: 25+54=79 Current State: 30:[76, 33, 79], Operations: ['25+54=79'] Exploring Operation: 76+33=109, Resulting Numbers: [79, 109] Generated Node #3: [79, 109] from Operation: 76+33=109 Current State: 30:[79, 109], Operations: ['25+54=79', '76+33=109'] Exploring Operation: 109-79=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[25, 54, 76, 33], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [25, 33, 22] Generated Node #0,0: 30:[25, 33, 22] Operation: 76-54=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[25, 33, 22], Operations: ['76-54=22'] Exploring Operation: 25-22=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 30:[33, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 30:[33, 3], Operations: ['76-54=22', '25-22=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[25, 54, 76, 33], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [25, 33, 22] Generated Node #0,0: 30:[25, 33, 22] Operation: 76-54=22 Moving to Node #0,0 Current State: 30:[25, 33, 22], Operations: ['76-54=22'] Exploring Operation: 25-22=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 30:[33, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 30:[33, 3], Operations: ['76-54=22', '25-22=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 21, 95, 38 ]
33
[ "21-2=19", "95/19=5", "38-5=33" ]
Current State: 33:[2, 21, 95, 38], Operations: [] Exploring Operation: 21-2=19, Resulting Numbers: [95, 38, 19] Generated Node #2: [95, 38, 19] from Operation: 21-2=19 Current State: 33:[95, 38, 19], Operations: ['21-2=19'] Exploring Operation: 95/19=5, Resulting Numbers: [38, 5] Generated Node #3: [38, 5] from Operation: 95/19=5 Current State: 33:[38, 5], Operations: ['21-2=19', '95/19=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[2, 21, 95, 38], Operations: [] Exploring Operation: 95-21=74, Resulting Numbers: [2, 38, 74] Generated Node #0,0: 33:[2, 38, 74] Operation: 95-21=74 Exploring Operation: 95-38=57, Resulting Numbers: [2, 21, 57] Generated Node #0,1: 33:[2, 21, 57] Operation: 95-38=57 Moving to Node #0,1 Current State: 33:[2, 21, 57], Operations: ['95-38=57'] Exploring Operation: 57-21=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 33:[2, 36] Operation: 57-21=36 Exploring Operation: 21-2=19, Resulting Numbers: [57, 19] Generated Node #0,1,1: 33:[57, 19] Operation: 21-2=19 Moving to Node #0,0 Current State: 33:[2, 38, 74], Operations: ['95-21=74'] Exploring Operation: 74-38=36, Resulting Numbers: [2, 36] Generated Node #0,0,0: 33:[2, 36] Operation: 74-38=36 Exploring Operation: 74/2=37, Resulting Numbers: [38, 37] Generated Node #0,0,1: 33:[38, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[2, 36], Operations: ['95-21=74', '74-38=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,33 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,33 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 #0,0,1 Current State: 33:[38, 37], Operations: ['95-21=74', '74/2=37'] Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 38+37=75, Resulting Numbers: [75] 75,33 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: 33:[2, 36], Operations: ['95-38=57', '57-21=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[57, 19], Operations: ['95-38=57', '21-2=19'] Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,33 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 52, 76, 3, 4 ]
37
[ "52*3=156", "156/4=39", "76-39=37" ]
Current State: 37:[52, 76, 3, 4], Operations: [] Exploring Operation: 52*3=156, Resulting Numbers: [76, 4, 156] Generated Node #2: [76, 4, 156] from Operation: 52*3=156 Current State: 37:[76, 4, 156], Operations: ['52*3=156'] Exploring Operation: 156/4=39, Resulting Numbers: [76, 39] Generated Node #3: [76, 39] from Operation: 156/4=39 Current State: 37:[76, 39], Operations: ['52*3=156', '156/4=39'] Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[52, 76, 3, 4], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [52, 3, 19] Generated Node #0,0: 37:[52, 3, 19] Operation: 76/4=19 Exploring Operation: 3*4=12, Resulting Numbers: [52, 76, 12] Generated Node #0,1: 37:[52, 76, 12] Operation: 3*4=12 Moving to Node #0,0 Current State: 37:[52, 3, 19], Operations: ['76/4=19'] Exploring Operation: 52-3=49, Resulting Numbers: [19, 49] Generated Node #0,0,0: 37:[19, 49] Operation: 52-3=49 Exploring Operation: 3+19=22, Resulting Numbers: [52, 22] Generated Node #0,0,1: 37:[52, 22] Operation: 3+19=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[19, 49], Operations: ['76/4=19', '52-3=49'] Exploring Operation: 49-19=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 19+49=68, Resulting Numbers: [68] 68,37 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 #0,0,1 Current State: 37:[52, 22], Operations: ['76/4=19', '3+19=22'] Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,37 unequal: No Solution Exploring Operation: 52+22=74, Resulting Numbers: [74] 74,37 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: 37:[52, 76, 12], Operations: ['3*4=12'] Exploring Operation: 52-12=40, Resulting Numbers: [76, 40] Generated Node #0,1,0: 37:[76, 40] Operation: 52-12=40 Exploring Operation: 76-52=24, Resulting Numbers: [12, 24] Generated Node #0,1,1: 37:[12, 24] Operation: 76-52=24 Moving to Node #0,1,1 Current State: 37:[12, 24], Operations: ['3*4=12', '76-52=24'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 12+24=36, Resulting Numbers: [36] 36,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[76, 40], Operations: ['3*4=12', '52-12=40'] Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,37 unequal: No Solution Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,37 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 51, 4, 68, 27 ]
48
[ "51-4=47", "68+27=95", "95-47=48" ]
Current State: 48:[51, 4, 68, 27], Operations: [] Exploring Operation: 51-4=47, Resulting Numbers: [68, 27, 47] Generated Node #2: [68, 27, 47] from Operation: 51-4=47 Current State: 48:[68, 27, 47], Operations: ['51-4=47'] Exploring Operation: 68+27=95, Resulting Numbers: [47, 95] Generated Node #3: [47, 95] from Operation: 68+27=95 Current State: 48:[47, 95], Operations: ['51-4=47', '68+27=95'] Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[51, 4, 68, 27], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [4, 68, 24] Generated Node #0,0: 48:[4, 68, 24] Operation: 51-27=24 Exploring Operation: 68-51=17, Resulting Numbers: [4, 27, 17] Generated Node #0,1: 48:[4, 27, 17] Operation: 68-51=17 Exploring Operation: 68-4=64, Resulting Numbers: [51, 27, 64] Generated Node #0,2: 48:[51, 27, 64] Operation: 68-4=64 Exploring Operation: 68-27=41, Resulting Numbers: [51, 4, 41] Generated Node #0,3: 48:[51, 4, 41] Operation: 68-27=41 Exploring Operation: 68/4=17, Resulting Numbers: [51, 27, 17] Generated Node #0,4: 48:[51, 27, 17] Operation: 68/4=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[4, 27, 17], Operations: ['68-51=17'] Exploring Operation: 27+17=44, Resulting Numbers: [4, 44] Generated Node #0,1,0: 48:[4, 44] Operation: 27+17=44 Exploring Operation: 27-17=10, Resulting Numbers: [4, 10] Generated Node #0,1,1: 48:[4, 10] Operation: 27-17=10 Exploring Operation: 27-4=23, Resulting Numbers: [17, 23] Generated Node #0,1,2: 48:[17, 23] Operation: 27-4=23 Exploring Operation: 4+17=21, Resulting Numbers: [27, 21] Generated Node #0,1,3: 48:[27, 21] Operation: 4+17=21 Exploring Operation: 17-4=13, Resulting Numbers: [27, 13] Generated Node #0,1,4: 48:[27, 13] Operation: 17-4=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[4, 10], Operations: ['68-51=17', '27-17=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,48 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 #0,1,2 Current State: 48:[17, 23], Operations: ['68-51=17', '27-4=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,48 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,48 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 #0,1,0 Current State: 48:[4, 44], Operations: ['68-51=17', '27+17=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[51, 4, 68, 27], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [4, 27, 17] Generated Node #0,1: 48:[4, 27, 17] Operation: 68-51=17 Moving to Node #0,1 Current State: 48:[4, 27, 17], Operations: ['68-51=17'] Exploring Operation: 27+17=44, Resulting Numbers: [4, 44] Generated Node #0,1,0: 48:[4, 44] Operation: 27+17=44 Moving to Node #0,1,0 Current State: 48:[4, 44], Operations: ['68-51=17', '27+17=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 48, 69, 37, 7 ]
23
[ "69-48=21", "37+7=44", "44-21=23" ]
Current State: 23:[48, 69, 37, 7], Operations: [] Exploring Operation: 69-48=21, Resulting Numbers: [37, 7, 21] Generated Node #2: [37, 7, 21] from Operation: 69-48=21 Current State: 23:[37, 7, 21], Operations: ['69-48=21'] Exploring Operation: 37+7=44, Resulting Numbers: [21, 44] Generated Node #3: [21, 44] from Operation: 37+7=44 Current State: 23:[21, 44], Operations: ['69-48=21', '37+7=44'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[48, 69, 37, 7], Operations: [] Exploring Operation: 48-37=11, Resulting Numbers: [69, 7, 11] Generated Node #0,0: 23:[69, 7, 11] Operation: 48-37=11 Exploring Operation: 69-37=32, Resulting Numbers: [48, 7, 32] Generated Node #0,1: 23:[48, 7, 32] Operation: 69-37=32 Exploring Operation: 69-48=21, Resulting Numbers: [37, 7, 21] Generated Node #0,2: 23:[37, 7, 21] Operation: 69-48=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[37, 7, 21], Operations: ['69-48=21'] Exploring Operation: 37-7=30, Resulting Numbers: [21, 30] Generated Node #0,2,0: 23:[21, 30] Operation: 37-7=30 Exploring Operation: 37+7=44, Resulting Numbers: [21, 44] Generated Node #0,2,1: 23:[21, 44] Operation: 37+7=44 Exploring Operation: 7+21=28, Resulting Numbers: [37, 28] Generated Node #0,2,2: 23:[37, 28] Operation: 7+21=28 Moving to Node #0,2,0 Current State: 23:[21, 30], Operations: ['69-48=21', '37-7=30'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[37, 28], Operations: ['69-48=21', '7+21=28'] Exploring Operation: 37-28=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 37*28=1036, Resulting Numbers: [1036] 1036,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[21, 44], Operations: ['69-48=21', '37+7=44'] Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,23 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[48, 69, 37, 7], Operations: [] Exploring Operation: 69-48=21, Resulting Numbers: [37, 7, 21] Generated Node #0,2: 23:[37, 7, 21] Operation: 69-48=21 Moving to Node #0,2 Current State: 23:[37, 7, 21], Operations: ['69-48=21'] Exploring Operation: 37+7=44, Resulting Numbers: [21, 44] Generated Node #0,2,1: 23:[21, 44] Operation: 37+7=44 Moving to Node #0,2,1 Current State: 23:[21, 44], Operations: ['69-48=21', '37+7=44'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 69, 59, 68, 43 ]
16
[ "69-68=1", "59-43=16", "1*16=16" ]
Current State: 16:[69, 59, 68, 43], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [59, 43, 1] Generated Node #2: [59, 43, 1] from Operation: 69-68=1 Current State: 16:[59, 43, 1], Operations: ['69-68=1'] Exploring Operation: 59-43=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 59-43=16 Current State: 16:[1, 16], Operations: ['69-68=1', '59-43=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[69, 59, 68, 43], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [68, 43, 10] Generated Node #0,0: 16:[68, 43, 10] Operation: 69-59=10 Exploring Operation: 68-59=9, Resulting Numbers: [69, 43, 9] Generated Node #0,1: 16:[69, 43, 9] Operation: 68-59=9 Exploring Operation: 69-43=26, Resulting Numbers: [59, 68, 26] Generated Node #0,2: 16:[59, 68, 26] Operation: 69-43=26 Exploring Operation: 69-68=1, Resulting Numbers: [59, 43, 1] Generated Node #0,3: 16:[59, 43, 1] Operation: 69-68=1 Moving to Node #0,3 Current State: 16:[59, 43, 1], Operations: ['69-68=1'] Exploring Operation: 59-43=16, Resulting Numbers: [1, 16] Generated Node #0,3,0: 16:[1, 16] Operation: 59-43=16 Exploring Operation: 43-1=42, Resulting Numbers: [59, 42] Generated Node #0,3,1: 16:[59, 42] Operation: 43-1=42 Exploring Operation: 59*1=59, Resulting Numbers: [43, 59] Generated Node #0,3,2: 16:[43, 59] Operation: 59*1=59 Exploring Operation: 59-1=58, Resulting Numbers: [43, 58] Generated Node #0,3,3: 16:[43, 58] Operation: 59-1=58 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 16:[1, 16], Operations: ['69-68=1', '59-43=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[69, 59, 68, 43], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [59, 43, 1] Generated Node #0,3: 16:[59, 43, 1] Operation: 69-68=1 Moving to Node #0,3 Current State: 16:[59, 43, 1], Operations: ['69-68=1'] Exploring Operation: 59-43=16, Resulting Numbers: [1, 16] Generated Node #0,3,0: 16:[1, 16] Operation: 59-43=16 Moving to Node #0,3,0 Current State: 16:[1, 16], Operations: ['69-68=1', '59-43=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 86, 44, 6, 84 ]
94
[ "86+84=170", "44*6=264", "264-170=94" ]
Current State: 94:[86, 44, 6, 84], Operations: [] Exploring Operation: 86+84=170, Resulting Numbers: [44, 6, 170] Generated Node #2: [44, 6, 170] from Operation: 86+84=170 Current State: 94:[44, 6, 170], Operations: ['86+84=170'] Exploring Operation: 44*6=264, Resulting Numbers: [170, 264] Generated Node #3: [170, 264] from Operation: 44*6=264 Current State: 94:[170, 264], Operations: ['86+84=170', '44*6=264'] Exploring Operation: 264-170=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[86, 44, 6, 84], Operations: [] Exploring Operation: 86+6=92, Resulting Numbers: [44, 84, 92] Generated Node #0,0: 94:[44, 84, 92] Operation: 86+6=92 Exploring Operation: 86-84=2, Resulting Numbers: [44, 6, 2] Generated Node #0,1: 94:[44, 6, 2] Operation: 86-84=2 Moving to Node #0,1 Current State: 94:[44, 6, 2], Operations: ['86-84=2'] Exploring Operation: 6/2=3, Resulting Numbers: [44, 3] Generated Node #0,1,0: 94:[44, 3] Operation: 6/2=3 Exploring Operation: 44+6=50, Resulting Numbers: [2, 50] Generated Node #0,1,1: 94:[2, 50] Operation: 44+6=50 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[2, 50], Operations: ['86-84=2', '44+6=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[44, 3], Operations: ['86-84=2', '6/2=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 44+3=47, Resulting Numbers: [47] 47,94 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: 94:[44, 84, 92], Operations: ['86+6=92'] Exploring Operation: 92-84=8, Resulting Numbers: [44, 8] Generated Node #0,0,0: 94:[44, 8] Operation: 92-84=8 Exploring Operation: 84-44=40, Resulting Numbers: [92, 40] Generated Node #0,0,1: 94:[92, 40] Operation: 84-44=40 Moving to Node #0,0,0 Current State: 94:[44, 8], Operations: ['86+6=92', '92-84=8'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,94 unequal: No Solution Exploring Operation: 44+8=52, Resulting Numbers: [52] 52,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[92, 40], Operations: ['86+6=92', '84-44=40'] Exploring Operation: 92-40=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 92+40=132, Resulting Numbers: [132] 132,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 7, 20, 83, 80 ]
94
[ "7+83=90", "80/20=4", "90+4=94" ]
Current State: 94:[7, 20, 83, 80], Operations: [] Exploring Operation: 7+83=90, Resulting Numbers: [20, 80, 90] Generated Node #2: [20, 80, 90] from Operation: 7+83=90 Current State: 94:[20, 80, 90], Operations: ['7+83=90'] Exploring Operation: 80/20=4, Resulting Numbers: [90, 4] Generated Node #3: [90, 4] from Operation: 80/20=4 Current State: 94:[90, 4], Operations: ['7+83=90', '80/20=4'] Exploring Operation: 90+4=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[7, 20, 83, 80], Operations: [] Exploring Operation: 20+80=100, Resulting Numbers: [7, 83, 100] Generated Node #0,0: 94:[7, 83, 100] Operation: 20+80=100 Exploring Operation: 80/20=4, Resulting Numbers: [7, 83, 4] Generated Node #0,1: 94:[7, 83, 4] Operation: 80/20=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[7, 83, 4], Operations: ['80/20=4'] Exploring Operation: 7-4=3, Resulting Numbers: [83, 3] Generated Node #0,1,0: 94:[83, 3] Operation: 7-4=3 Exploring Operation: 7+83=90, Resulting Numbers: [4, 90] Generated Node #0,1,1: 94:[4, 90] Operation: 7+83=90 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[4, 90], Operations: ['80/20=4', '7+83=90'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,94 unequal: No Solution Exploring Operation: 4+90=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[7, 20, 83, 80], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [7, 83, 4] Generated Node #0,1: 94:[7, 83, 4] Operation: 80/20=4 Moving to Node #0,1 Current State: 94:[7, 83, 4], Operations: ['80/20=4'] Exploring Operation: 7+83=90, Resulting Numbers: [4, 90] Generated Node #0,1,1: 94:[4, 90] Operation: 7+83=90 Moving to Node #0,1,1 Current State: 94:[4, 90], Operations: ['80/20=4', '7+83=90'] Exploring Operation: 4+90=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 63, 30, 70, 14 ]
68
[ "70-63=7", "14*7=98", "98-30=68" ]
Current State: 68:[63, 30, 70, 14], Operations: [] Exploring Operation: 70-63=7, Resulting Numbers: [30, 14, 7] Generated Node #2: [30, 14, 7] from Operation: 70-63=7 Current State: 68:[30, 14, 7], Operations: ['70-63=7'] Exploring Operation: 14*7=98, Resulting Numbers: [30, 98] Generated Node #3: [30, 98] from Operation: 14*7=98 Current State: 68:[30, 98], Operations: ['70-63=7', '14*7=98'] Exploring Operation: 98-30=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[63, 30, 70, 14], Operations: [] Exploring Operation: 63-30=33, Resulting Numbers: [70, 14, 33] Generated Node #0,0: 68:[70, 14, 33] Operation: 63-30=33 Moving to Node #0,0 Current State: 68:[70, 14, 33], Operations: ['63-30=33'] Exploring Operation: 70/14=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 68:[33, 5] Operation: 70/14=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[33, 5], Operations: ['63-30=33', '70/14=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,68 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
[ 73, 93, 2, 67 ]
49
[ "93-73=20", "2+67=69", "69-20=49" ]
Current State: 49:[73, 93, 2, 67], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [2, 67, 20] Generated Node #2: [2, 67, 20] from Operation: 93-73=20 Current State: 49:[2, 67, 20], Operations: ['93-73=20'] Exploring Operation: 2+67=69, Resulting Numbers: [20, 69] Generated Node #3: [20, 69] from Operation: 2+67=69 Current State: 49:[20, 69], Operations: ['93-73=20', '2+67=69'] Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[73, 93, 2, 67], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [93, 2, 6] Generated Node #0,0: 49:[93, 2, 6] Operation: 73-67=6 Exploring Operation: 93-67=26, Resulting Numbers: [73, 2, 26] Generated Node #0,1: 49:[73, 2, 26] Operation: 93-67=26 Exploring Operation: 93-73=20, Resulting Numbers: [2, 67, 20] Generated Node #0,2: 49:[2, 67, 20] Operation: 93-73=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[2, 67, 20], Operations: ['93-73=20'] Exploring Operation: 2*20=40, Resulting Numbers: [67, 40] Generated Node #0,2,0: 49:[67, 40] Operation: 2*20=40 Exploring Operation: 20/2=10, Resulting Numbers: [67, 10] Generated Node #0,2,1: 49:[67, 10] Operation: 20/2=10 Exploring Operation: 67-20=47, Resulting Numbers: [2, 47] Generated Node #0,2,2: 49:[2, 47] Operation: 67-20=47 Moving to Node #0,2,2 Current State: 49:[2, 47], Operations: ['93-73=20', '67-20=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[73, 93, 2, 67], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [2, 67, 20] Generated Node #0,2: 49:[2, 67, 20] Operation: 93-73=20 Moving to Node #0,2 Current State: 49:[2, 67, 20], Operations: ['93-73=20'] Exploring Operation: 67-20=47, Resulting Numbers: [2, 47] Generated Node #0,2,2: 49:[2, 47] Operation: 67-20=47 Moving to Node #0,2,2 Current State: 49:[2, 47], Operations: ['93-73=20', '67-20=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 56, 72, 8, 27 ]
18
[ "56-8=48", "27*48=1296", "1296/72=18" ]
Current State: 18:[56, 72, 8, 27], Operations: [] Exploring Operation: 56-8=48, Resulting Numbers: [72, 27, 48] Generated Node #2: [72, 27, 48] from Operation: 56-8=48 Current State: 18:[72, 27, 48], Operations: ['56-8=48'] Exploring Operation: 27*48=1296, Resulting Numbers: [72, 1296] Generated Node #3: [72, 1296] from Operation: 27*48=1296 Current State: 18:[72, 1296], Operations: ['56-8=48', '27*48=1296'] Exploring Operation: 1296/72=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[56, 72, 8, 27], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [8, 27, 16] Generated Node #0,0: 18:[8, 27, 16] Operation: 72-56=16 Exploring Operation: 72/8=9, Resulting Numbers: [56, 27, 9] Generated Node #0,1: 18:[56, 27, 9] Operation: 72/8=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[8, 27, 16], Operations: ['72-56=16'] Exploring Operation: 27-8=19, Resulting Numbers: [16, 19] Generated Node #0,0,0: 18:[16, 19] Operation: 27-8=19 Exploring Operation: 27-16=11, Resulting Numbers: [8, 11] Generated Node #0,0,1: 18:[8, 11] Operation: 27-16=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[16, 19], Operations: ['72-56=16', '27-8=19'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,18 unequal: No Solution No 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: 18:[8, 11], Operations: ['72-56=16', '27-16=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,18 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: 18:[56, 27, 9], Operations: ['72/8=9'] Exploring Operation: 56-9=47, Resulting Numbers: [27, 47] Generated Node #0,1,0: 18:[27, 47] Operation: 56-9=47 Exploring Operation: 56-27=29, Resulting Numbers: [9, 29] Generated Node #0,1,1: 18:[9, 29] Operation: 56-27=29 Moving to Node #0,1,1 Current State: 18:[9, 29], Operations: ['72/8=9', '56-27=29'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[27, 47], Operations: ['72/8=9', '56-9=47'] Exploring Operation: 27+47=74, Resulting Numbers: [74] 74,18 unequal: No Solution Exploring Operation: 47-27=20, Resulting Numbers: [20] 20,18 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
[ 75, 83, 60, 61 ]
45
[ "60*61=3660", "75+3660=3735", "3735/83=45" ]
Current State: 45:[75, 83, 60, 61], Operations: [] Exploring Operation: 60*61=3660, Resulting Numbers: [75, 83, 3660] Generated Node #2: [75, 83, 3660] from Operation: 60*61=3660 Current State: 45:[75, 83, 3660], Operations: ['60*61=3660'] Exploring Operation: 75+3660=3735, Resulting Numbers: [83, 3735] Generated Node #3: [83, 3735] from Operation: 75+3660=3735 Current State: 45:[83, 3735], Operations: ['60*61=3660', '75+3660=3735'] Exploring Operation: 3735/83=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[75, 83, 60, 61], Operations: [] Exploring Operation: 83-75=8, Resulting Numbers: [60, 61, 8] Generated Node #0,0: 45:[60, 61, 8] Operation: 83-75=8 Moving to Node #0,0 Current State: 45:[60, 61, 8], Operations: ['83-75=8'] Exploring Operation: 61-60=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 45:[8, 1] Operation: 61-60=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[8, 1], Operations: ['83-75=8', '61-60=1'] Exploring Operation: 8+1=9, Resulting Numbers: [9] 9,45 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
[ 60, 88, 49, 50 ]
58
[ "60-49=11", "88/11=8", "50+8=58" ]
Current State: 58:[60, 88, 49, 50], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [88, 50, 11] Generated Node #2: [88, 50, 11] from Operation: 60-49=11 Current State: 58:[88, 50, 11], Operations: ['60-49=11'] Exploring Operation: 88/11=8, Resulting Numbers: [50, 8] Generated Node #3: [50, 8] from Operation: 88/11=8 Current State: 58:[50, 8], Operations: ['60-49=11', '88/11=8'] Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[60, 88, 49, 50], Operations: [] Exploring Operation: 88-60=28, Resulting Numbers: [49, 50, 28] Generated Node #0,0: 58:[49, 50, 28] Operation: 88-60=28 Exploring Operation: 88-49=39, Resulting Numbers: [60, 50, 39] Generated Node #0,1: 58:[60, 50, 39] Operation: 88-49=39 Moving to Node #0,0 Current State: 58:[49, 50, 28], Operations: ['88-60=28'] Exploring Operation: 50-49=1, Resulting Numbers: [28, 1] Generated Node #0,0,0: 58:[28, 1] Operation: 50-49=1 Exploring Operation: 49-28=21, Resulting Numbers: [50, 21] Generated Node #0,0,1: 58:[50, 21] Operation: 49-28=21 Moving to Node #0,1 Current State: 58:[60, 50, 39], Operations: ['88-49=39'] Exploring Operation: 60-39=21, Resulting Numbers: [50, 21] Generated Node #0,1,0: 58:[50, 21] Operation: 60-39=21 Exploring Operation: 50-39=11, Resulting Numbers: [60, 11] Generated Node #0,1,1: 58:[60, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[60, 11], Operations: ['88-49=39', '50-39=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,58 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 58:[50, 21], Operations: ['88-49=39', '60-39=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,58 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,58 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: 58:[28, 1], Operations: ['88-60=28', '50-49=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,58 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[50, 21], Operations: ['88-60=28', '49-28=21'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,58 unequal: No Solution Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,58 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 66, 3, 18, 34 ]
62
[ "66+18=84", "84/3=28", "34+28=62" ]
Current State: 62:[66, 3, 18, 34], Operations: [] Exploring Operation: 66+18=84, Resulting Numbers: [3, 34, 84] Generated Node #2: [3, 34, 84] from Operation: 66+18=84 Current State: 62:[3, 34, 84], Operations: ['66+18=84'] Exploring Operation: 84/3=28, Resulting Numbers: [34, 28] Generated Node #3: [34, 28] from Operation: 84/3=28 Current State: 62:[34, 28], Operations: ['66+18=84', '84/3=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[66, 3, 18, 34], Operations: [] Exploring Operation: 3*18=54, Resulting Numbers: [66, 34, 54] Generated Node #0,0: 62:[66, 34, 54] Operation: 3*18=54 Exploring Operation: 18+34=52, Resulting Numbers: [66, 3, 52] Generated Node #0,1: 62:[66, 3, 52] Operation: 18+34=52 Exploring Operation: 66-34=32, Resulting Numbers: [3, 18, 32] Generated Node #0,2: 62:[3, 18, 32] Operation: 66-34=32 Exploring Operation: 18/3=6, Resulting Numbers: [66, 34, 6] Generated Node #0,3: 62:[66, 34, 6] Operation: 18/3=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[66, 34, 6], Operations: ['18/3=6'] Exploring Operation: 66-6=60, Resulting Numbers: [34, 60] Generated Node #0,3,0: 62:[34, 60] Operation: 66-6=60 Exploring Operation: 34-6=28, Resulting Numbers: [66, 28] Generated Node #0,3,1: 62:[66, 28] Operation: 34-6=28 Exploring Operation: 66/6=11, Resulting Numbers: [34, 11] Generated Node #0,3,2: 62:[34, 11] Operation: 66/6=11 Exploring Operation: 66-34=32, Resulting Numbers: [6, 32] Generated Node #0,3,3: 62:[6, 32] Operation: 66-34=32 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[34, 60], Operations: ['18/3=6', '66-6=60'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,62 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,62 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:[6, 32], Operations: ['18/3=6', '66-34=32'] Exploring Operation: 6*32=192, Resulting Numbers: [192] 192,62 unequal: No Solution Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[66, 28], Operations: ['18/3=6', '34-6=28'] Exploring Operation: 66+28=94, Resulting Numbers: [94] 94,62 unequal: No Solution Exploring Operation: 66-28=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 66*28=1848, Resulting Numbers: [1848] 1848,62 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:[34, 11], Operations: ['18/3=6', '66/6=11'] Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,62 unequal: No Solution Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,62 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 #0,0 Current State: 62:[66, 34, 54], Operations: ['3*18=54'] Exploring Operation: 66-54=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 62:[34, 12] Operation: 66-54=12 Exploring Operation: 54-34=20, Resulting Numbers: [66, 20] Generated Node #0,0,1: 62:[66, 20] Operation: 54-34=20 Exploring Operation: 34+54=88, Resulting Numbers: [66, 88] Generated Node #0,0,2: 62:[66, 88] Operation: 34+54=88 Exploring Operation: 66-34=32, Resulting Numbers: [54, 32] Generated Node #0,0,3: 62:[54, 32] Operation: 66-34=32 Moving to Node #0,0,3 Current State: 62:[54, 32], Operations: ['3*18=54', '66-34=32'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 54*32=1728, Resulting Numbers: [1728] 1728,62 unequal: No Solution Exploring Operation: 54+32=86, Resulting Numbers: [86] 86,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[34, 12], Operations: ['3*18=54', '66-54=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 34+12=46, Resulting Numbers: [46] 46,62 unequal: No Solution Exploring Operation: 34*12=408, Resulting Numbers: [408] 408,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[66, 20], Operations: ['3*18=54', '54-34=20'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,62 unequal: No Solution Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[66, 88], Operations: ['3*18=54', '34+54=88'] Exploring Operation: 88-66=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 66*88=5808, Resulting Numbers: [5808] 5808,62 unequal: No Solution Exploring Operation: 66+88=154, Resulting Numbers: [154] 154,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[66, 3, 52], Operations: ['18+34=52'] Exploring Operation: 3+52=55, Resulting Numbers: [66, 55] Generated Node #0,1,0: 62:[66, 55] Operation: 3+52=55 Exploring Operation: 66-52=14, Resulting Numbers: [3, 14] Generated Node #0,1,1: 62:[3, 14] Operation: 66-52=14 Exploring Operation: 66+3=69, Resulting Numbers: [52, 69] Generated Node #0,1,2: 62:[52, 69] Operation: 66+3=69 Exploring Operation: 66-3=63, Resulting Numbers: [52, 63] Generated Node #0,1,3: 62:[52, 63] Operation: 66-3=63 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[66, 55], Operations: ['18+34=52', '3+52=55'] Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 62:[52, 63], Operations: ['18+34=52', '66-3=63'] Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,62 unequal: No Solution Exploring Operation: 52*63=3276, Resulting Numbers: [3276] 3276,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[3, 14], Operations: ['18+34=52', '66-52=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[52, 69], Operations: ['18+34=52', '66+3=69'] Exploring Operation: 52*69=3588, Resulting Numbers: [3588] 3588,62 unequal: No Solution Exploring Operation: 52+69=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[3, 18, 32], Operations: ['66-34=32'] Exploring Operation: 18/3=6, Resulting Numbers: [32, 6] Generated Node #0,2,0: 62:[32, 6] Operation: 18/3=6 Exploring Operation: 3+18=21, Resulting Numbers: [32, 21] Generated Node #0,2,1: 62:[32, 21] Operation: 3+18=21 Exploring Operation: 18+32=50, Resulting Numbers: [3, 50] Generated Node #0,2,2: 62:[3, 50] Operation: 18+32=50 Exploring Operation: 3*18=54, Resulting Numbers: [32, 54] Generated Node #0,2,3: 62:[32, 54] Operation: 3*18=54 Moving to Node #0,2,0 Current State: 62:[32, 6], Operations: ['66-34=32', '18/3=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,62 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[32, 54], Operations: ['66-34=32', '3*18=54'] Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[32, 21], Operations: ['66-34=32', '3+18=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[3, 50], Operations: ['66-34=32', '18+32=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,62 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,62 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
[ 36, 31, 92, 36 ]
11
[ "36+31=67", "92-36=56", "67-56=11" ]
Current State: 11:[36, 31, 92, 36], Operations: [] Exploring Operation: 36+31=67, Resulting Numbers: [92, 67] Generated Node #2: [92, 67] from Operation: 36+31=67 Current State: 11:[92, 67], Operations: ['36+31=67'] Exploring Operation: 92-36=56, Resulting Numbers: [67, 56] Generated Node #3: [67, 56] from Operation: 92-36=56 Current State: 11:[67, 56], Operations: ['36+31=67', '92-36=56'] Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[36, 31, 92, 36], Operations: [] Exploring Operation: 92-36=56, Resulting Numbers: [36, 31, 56] Generated Node #0,0: 11:[36, 31, 56] Operation: 92-36=56 Exploring Operation: 92-36=56, Resulting Numbers: [31, 36, 56] Generated Node #0,1: 11:[31, 36, 56] Operation: 92-36=56 Exploring Operation: 92-31=61, Resulting Numbers: [36, 36, 61] Generated Node #0,2: 11:[36, 36, 61] Operation: 92-31=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[36, 31, 56], Operations: ['92-36=56'] Exploring Operation: 36-31=5, Resulting Numbers: [56, 5] Generated Node #0,0,0: 11:[56, 5] Operation: 36-31=5 Exploring Operation: 56-36=20, Resulting Numbers: [31, 20] Generated Node #0,0,1: 11:[31, 20] Operation: 56-36=20 Exploring Operation: 56-31=25, Resulting Numbers: [36, 25] Generated Node #0,0,2: 11:[36, 25] Operation: 56-31=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[31, 20], Operations: ['92-36=56', '56-36=20'] Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,11 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,11 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[36, 31, 92, 36], Operations: [] Exploring Operation: 92-36=56, Resulting Numbers: [36, 31, 56] Generated Node #0,0: 11:[36, 31, 56] Operation: 92-36=56 Moving to Node #0,0 Current State: 11:[36, 31, 56], Operations: ['92-36=56'] Exploring Operation: 56-36=20, Resulting Numbers: [31, 20] Generated Node #0,0,1: 11:[31, 20] Operation: 56-36=20 Moving to Node #0,0,1 Current State: 11:[31, 20], Operations: ['92-36=56', '56-36=20'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 15, 9, 49, 19 ]
10
[ "19-15=4", "49-9=40", "40/4=10" ]
Current State: 10:[15, 9, 49, 19], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [9, 49, 4] Generated Node #2: [9, 49, 4] from Operation: 19-15=4 Current State: 10:[9, 49, 4], Operations: ['19-15=4'] Exploring Operation: 49-9=40, Resulting Numbers: [4, 40] Generated Node #3: [4, 40] from Operation: 49-9=40 Current State: 10:[4, 40], Operations: ['19-15=4', '49-9=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[15, 9, 49, 19], Operations: [] Exploring Operation: 49-15=34, Resulting Numbers: [9, 19, 34] Generated Node #0,0: 10:[9, 19, 34] Operation: 49-15=34 Exploring Operation: 19-15=4, Resulting Numbers: [9, 49, 4] Generated Node #0,1: 10:[9, 49, 4] Operation: 19-15=4 Exploring Operation: 49-19=30, Resulting Numbers: [15, 9, 30] Generated Node #0,2: 10:[15, 9, 30] Operation: 49-19=30 Moving to Node #0,2 Current State: 10:[15, 9, 30], Operations: ['49-19=30'] Exploring Operation: 30-9=21, Resulting Numbers: [15, 21] Generated Node #0,2,0: 10:[15, 21] Operation: 30-9=21 Exploring Operation: 30/15=2, Resulting Numbers: [9, 2] Generated Node #0,2,1: 10:[9, 2] Operation: 30/15=2 Exploring Operation: 30-15=15, Resulting Numbers: [9, 15] Generated Node #0,2,2: 10:[9, 15] Operation: 30-15=15 Moving to Node #0,0 Current State: 10:[9, 19, 34], Operations: ['49-15=34'] Exploring Operation: 34-19=15, Resulting Numbers: [9, 15] Generated Node #0,0,0: 10:[9, 15] Operation: 34-19=15 Exploring Operation: 19-9=10, Resulting Numbers: [34, 10] Generated Node #0,0,1: 10:[34, 10] Operation: 19-9=10 Exploring Operation: 34-9=25, Resulting Numbers: [19, 25] Generated Node #0,0,2: 10:[19, 25] Operation: 34-9=25 Moving to Node #0,1 Current State: 10:[9, 49, 4], Operations: ['19-15=4'] Exploring Operation: 9-4=5, Resulting Numbers: [49, 5] Generated Node #0,1,0: 10:[49, 5] Operation: 9-4=5 Exploring Operation: 49-9=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 10:[4, 40] Operation: 49-9=40 Exploring Operation: 49-4=45, Resulting Numbers: [9, 45] Generated Node #0,1,2: 10:[9, 45] Operation: 49-4=45 Moving to Node #0,2,1 Current State: 10:[9, 2], Operations: ['49-19=30', '30/15=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[9, 15], Operations: ['49-19=30', '30-15=15'] Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,10 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,10 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[9, 15], Operations: ['49-15=34', '34-19=15'] Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,10 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,10 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,10 unequal: No Solution Moving to Node #0,2,0 Current State: 10:[15, 21], Operations: ['49-19=30', '30-9=21'] Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,10 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[19, 25], Operations: ['49-15=34', '34-9=25'] Exploring Operation: 19*25=475, Resulting Numbers: [475] 475,10 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[34, 10], Operations: ['49-15=34', '19-9=10'] Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,10 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,10 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[4, 40], Operations: ['19-15=4', '49-9=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[15, 9, 49, 19], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [9, 49, 4] Generated Node #0,1: 10:[9, 49, 4] Operation: 19-15=4 Moving to Node #0,1 Current State: 10:[9, 49, 4], Operations: ['19-15=4'] Exploring Operation: 49-9=40, Resulting Numbers: [4, 40] Generated Node #0,1,1: 10:[4, 40] Operation: 49-9=40 Moving to Node #0,1,1 Current State: 10:[4, 40], Operations: ['19-15=4', '49-9=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.969618
hs_3
sum_heuristic
[ 88, 2, 50, 33 ]
39
[ "88/2=44", "50+33=83", "83-44=39" ]
Current State: 39:[88, 2, 50, 33], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [50, 33, 44] Generated Node #2: [50, 33, 44] from Operation: 88/2=44 Current State: 39:[50, 33, 44], Operations: ['88/2=44'] Exploring Operation: 50+33=83, Resulting Numbers: [44, 83] Generated Node #3: [44, 83] from Operation: 50+33=83 Current State: 39:[44, 83], Operations: ['88/2=44', '50+33=83'] Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[88, 2, 50, 33], Operations: [] Exploring Operation: 88-50=38, Resulting Numbers: [2, 33, 38] Generated Node #0,0: 39:[2, 33, 38] Operation: 88-50=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[2, 33, 38], Operations: ['88-50=38'] Exploring Operation: 38-33=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 39:[2, 5] Operation: 38-33=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[2, 5], Operations: ['88-50=38', '38-33=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 98, 3, 28, 80 ]
30
[ "98-28=70", "80-70=10", "3*10=30" ]
Current State: 30:[98, 3, 28, 80], Operations: [] Exploring Operation: 98-28=70, Resulting Numbers: [3, 80, 70] Generated Node #2: [3, 80, 70] from Operation: 98-28=70 Current State: 30:[3, 80, 70], Operations: ['98-28=70'] Exploring Operation: 80-70=10, Resulting Numbers: [3, 10] Generated Node #3: [3, 10] from Operation: 80-70=10 Current State: 30:[3, 10], Operations: ['98-28=70', '80-70=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[98, 3, 28, 80], Operations: [] Exploring Operation: 80-3=77, Resulting Numbers: [98, 28, 77] Generated Node #0,0: 30:[98, 28, 77] Operation: 80-3=77 Exploring Operation: 98-80=18, Resulting Numbers: [3, 28, 18] Generated Node #0,1: 30:[3, 28, 18] Operation: 98-80=18 Exploring Operation: 98-3=95, Resulting Numbers: [28, 80, 95] Generated Node #0,2: 30:[28, 80, 95] Operation: 98-3=95 Exploring Operation: 98-28=70, Resulting Numbers: [3, 80, 70] Generated Node #0,3: 30:[3, 80, 70] Operation: 98-28=70 Exploring Operation: 80-28=52, Resulting Numbers: [98, 3, 52] Generated Node #0,4: 30:[98, 3, 52] Operation: 80-28=52 Moving to Node #0,1 Current State: 30:[3, 28, 18], Operations: ['98-80=18'] Exploring Operation: 18/3=6, Resulting Numbers: [28, 6] Generated Node #0,1,0: 30:[28, 6] Operation: 18/3=6 Exploring Operation: 28-18=10, Resulting Numbers: [3, 10] Generated Node #0,1,1: 30:[3, 10] Operation: 28-18=10 Exploring Operation: 3+28=31, Resulting Numbers: [18, 31] Generated Node #0,1,2: 30:[18, 31] Operation: 3+28=31 Exploring Operation: 28-3=25, Resulting Numbers: [18, 25] Generated Node #0,1,3: 30:[18, 25] Operation: 28-3=25 Exploring Operation: 18-3=15, Resulting Numbers: [28, 15] Generated Node #0,1,4: 30:[28, 15] Operation: 18-3=15 Moving to Node #0,4 Current State: 30:[98, 3, 52], Operations: ['80-28=52'] Exploring Operation: 98+3=101, Resulting Numbers: [52, 101] Generated Node #0,4,0: 30:[52, 101] Operation: 98+3=101 Exploring Operation: 98-3=95, Resulting Numbers: [52, 95] Generated Node #0,4,1: 30:[52, 95] Operation: 98-3=95 Exploring Operation: 98-52=46, Resulting Numbers: [3, 46] Generated Node #0,4,2: 30:[3, 46] Operation: 98-52=46 Exploring Operation: 3+52=55, Resulting Numbers: [98, 55] Generated Node #0,4,3: 30:[98, 55] Operation: 3+52=55 Exploring Operation: 52-3=49, Resulting Numbers: [98, 49] Generated Node #0,4,4: 30:[98, 49] Operation: 52-3=49 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 30:[3, 46], Operations: ['80-28=52', '98-52=46'] Exploring Operation: 3*46=138, Resulting Numbers: [138] 138,30 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 30:[52, 95], Operations: ['80-28=52', '98-3=95'] Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 52*95=4940, Resulting Numbers: [4940] 4940,30 unequal: No Solution Exploring Operation: 52+95=147, Resulting Numbers: [147] 147,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 30:[98, 49], Operations: ['80-28=52', '52-3=49'] Exploring Operation: 98/49=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 98*49=4802, Resulting Numbers: [4802] 4802,30 unequal: No Solution Exploring Operation: 98-49=49, Resulting Numbers: [49] 49,30 unequal: No Solution Exploring Operation: 98+49=147, Resulting Numbers: [147] 147,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 30:[52, 101], Operations: ['80-28=52', '98+3=101'] Exploring Operation: 101-52=49, Resulting Numbers: [49] 49,30 unequal: No Solution Exploring Operation: 52+101=153, Resulting Numbers: [153] 153,30 unequal: No Solution Exploring Operation: 52*101=5252, Resulting Numbers: [5252] 5252,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 30:[98, 55], Operations: ['80-28=52', '3+52=55'] Exploring Operation: 98+55=153, Resulting Numbers: [153] 153,30 unequal: No Solution Exploring Operation: 98-55=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 98*55=5390, Resulting Numbers: [5390] 5390,30 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: 30:[3, 80, 70], Operations: ['98-28=70'] Exploring Operation: 3+80=83, Resulting Numbers: [70, 83] Generated Node #0,3,0: 30:[70, 83] Operation: 3+80=83 Exploring Operation: 80-3=77, Resulting Numbers: [70, 77] Generated Node #0,3,1: 30:[70, 77] Operation: 80-3=77 Exploring Operation: 3+70=73, Resulting Numbers: [80, 73] Generated Node #0,3,2: 30:[80, 73] Operation: 3+70=73 Exploring Operation: 80-70=10, Resulting Numbers: [3, 10] Generated Node #0,3,3: 30:[3, 10] Operation: 80-70=10 Exploring Operation: 70-3=67, Resulting Numbers: [80, 67] Generated Node #0,3,4: 30:[80, 67] Operation: 70-3=67 Moving to Node #0,0 Current State: 30:[98, 28, 77], Operations: ['80-3=77'] Exploring Operation: 28+77=105, Resulting Numbers: [98, 105] Generated Node #0,0,0: 30:[98, 105] Operation: 28+77=105 Exploring Operation: 98-28=70, Resulting Numbers: [77, 70] Generated Node #0,0,1: 30:[77, 70] Operation: 98-28=70 Exploring Operation: 98-77=21, Resulting Numbers: [28, 21] Generated Node #0,0,2: 30:[28, 21] Operation: 98-77=21 Exploring Operation: 98+28=126, Resulting Numbers: [77, 126] Generated Node #0,0,3: 30:[77, 126] Operation: 98+28=126 Exploring Operation: 77-28=49, Resulting Numbers: [98, 49] Generated Node #0,0,4: 30:[98, 49] Operation: 77-28=49 Moving to Node #0,2 Current State: 30:[28, 80, 95], Operations: ['98-3=95'] Exploring Operation: 95-28=67, Resulting Numbers: [80, 67] Generated Node #0,2,0: 30:[80, 67] Operation: 95-28=67 Exploring Operation: 28+95=123, Resulting Numbers: [80, 123] Generated Node #0,2,1: 30:[80, 123] Operation: 28+95=123 Exploring Operation: 95-80=15, Resulting Numbers: [28, 15] Generated Node #0,2,2: 30:[28, 15] Operation: 95-80=15 Exploring Operation: 28+80=108, Resulting Numbers: [95, 108] Generated Node #0,2,3: 30:[95, 108] Operation: 28+80=108 Exploring Operation: 80-28=52, Resulting Numbers: [95, 52] Generated Node #0,2,4: 30:[95, 52] Operation: 80-28=52 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 30:[28, 15], Operations: ['98-3=95', '95-80=15'] Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,30 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[80, 67], Operations: ['98-3=95', '95-28=67'] Exploring Operation: 80-67=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 80+67=147, Resulting Numbers: [147] 147,30 unequal: No Solution Exploring Operation: 80*67=5360, Resulting Numbers: [5360] 5360,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 30:[95, 52], Operations: ['98-3=95', '80-28=52'] Exploring Operation: 95+52=147, Resulting Numbers: [147] 147,30 unequal: No Solution Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 95*52=4940, Resulting Numbers: [4940] 4940,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[80, 123], Operations: ['98-3=95', '28+95=123'] Exploring Operation: 80+123=203, Resulting Numbers: [203] 203,30 unequal: No Solution Exploring Operation: 123-80=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 80*123=9840, Resulting Numbers: [9840] 9840,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 30:[95, 108], Operations: ['98-3=95', '28+80=108'] Exploring Operation: 95*108=10260, Resulting Numbers: [10260] 10260,30 unequal: No Solution Exploring Operation: 108-95=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 95+108=203, Resulting Numbers: [203] 203,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 30:[3, 10], Operations: ['98-80=18', '28-18=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[98, 3, 28, 80], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [3, 28, 18] Generated Node #0,1: 30:[3, 28, 18] Operation: 98-80=18 Moving to Node #0,1 Current State: 30:[3, 28, 18], Operations: ['98-80=18'] Exploring Operation: 28-18=10, Resulting Numbers: [3, 10] Generated Node #0,1,1: 30:[3, 10] Operation: 28-18=10 Moving to Node #0,1,1 Current State: 30:[3, 10], Operations: ['98-80=18', '28-18=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.942708
hs_5
sum_heuristic
[ 43, 2, 1, 1 ]
45
[ "43+2=45", "1*1=1", "45*1=45" ]
Current State: 45:[43, 2, 1, 1], Operations: [] Exploring Operation: 43+2=45, Resulting Numbers: [1, 1, 45] Generated Node #2: [1, 1, 45] from Operation: 43+2=45 Current State: 45:[1, 1, 45], Operations: ['43+2=45'] Exploring Operation: 1*1=1, Resulting Numbers: [45, 1] Generated Node #3: [45, 1] from Operation: 1*1=1 Current State: 45:[45, 1], Operations: ['43+2=45', '1*1=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[43, 2, 1, 1], Operations: [] Exploring Operation: 43+2=45, Resulting Numbers: [1, 1, 45] Generated Node #0,0: 45:[1, 1, 45] Operation: 43+2=45 Moving to Node #0,0 Current State: 45:[1, 1, 45], Operations: ['43+2=45'] Exploring Operation: 1+1=2, Resulting Numbers: [45, 2] Generated Node #0,0,0: 45:[45, 2] Operation: 1+1=2 Moving to Node #0,0,0 Current State: 45:[45, 2], Operations: ['43+2=45', '1+1=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,45 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 91, 78, 85, 35 ]
37
[ "91-78=13", "85-35=50", "50-13=37" ]
Current State: 37:[91, 78, 85, 35], Operations: [] Exploring Operation: 91-78=13, Resulting Numbers: [85, 35, 13] Generated Node #2: [85, 35, 13] from Operation: 91-78=13 Current State: 37:[85, 35, 13], Operations: ['91-78=13'] Exploring Operation: 85-35=50, Resulting Numbers: [13, 50] Generated Node #3: [13, 50] from Operation: 85-35=50 Current State: 37:[13, 50], Operations: ['91-78=13', '85-35=50'] Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[91, 78, 85, 35], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [78, 35, 6] Generated Node #0,0: 37:[78, 35, 6] Operation: 91-85=6 Exploring Operation: 91-35=56, Resulting Numbers: [78, 85, 56] Generated Node #0,1: 37:[78, 85, 56] Operation: 91-35=56 Exploring Operation: 78-35=43, Resulting Numbers: [91, 85, 43] Generated Node #0,2: 37:[91, 85, 43] Operation: 78-35=43 Exploring Operation: 85-78=7, Resulting Numbers: [91, 35, 7] Generated Node #0,3: 37:[91, 35, 7] Operation: 85-78=7 Exploring Operation: 91-78=13, Resulting Numbers: [85, 35, 13] Generated Node #0,4: 37:[85, 35, 13] Operation: 91-78=13 Moving to Node #0,0 Current State: 37:[78, 35, 6], Operations: ['91-85=6'] Exploring Operation: 78-35=43, Resulting Numbers: [6, 43] Generated Node #0,0,0: 37:[6, 43] Operation: 78-35=43 Exploring Operation: 78+6=84, Resulting Numbers: [35, 84] Generated Node #0,0,1: 37:[35, 84] Operation: 78+6=84 Exploring Operation: 78-6=72, Resulting Numbers: [35, 72] Generated Node #0,0,2: 37:[35, 72] Operation: 78-6=72 Exploring Operation: 78/6=13, Resulting Numbers: [35, 13] Generated Node #0,0,3: 37:[35, 13] Operation: 78/6=13 Exploring Operation: 35+6=41, Resulting Numbers: [78, 41] Generated Node #0,0,4: 37:[78, 41] Operation: 35+6=41 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[35, 13], Operations: ['91-85=6', '78/6=13'] Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,37 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,37 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 #0,0,0 Current State: 37:[6, 43], Operations: ['91-85=6', '78-35=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 6*43=258, Resulting Numbers: [258] 258,37 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[91, 78, 85, 35], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [78, 35, 6] Generated Node #0,0: 37:[78, 35, 6] Operation: 91-85=6 Moving to Node #0,0 Current State: 37:[78, 35, 6], Operations: ['91-85=6'] Exploring Operation: 78-35=43, Resulting Numbers: [6, 43] Generated Node #0,0,0: 37:[6, 43] Operation: 78-35=43 Moving to Node #0,0,0 Current State: 37:[6, 43], Operations: ['91-85=6', '78-35=43'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 15, 59, 46, 43 ]
77
[ "15+59=74", "46-43=3", "74+3=77" ]
Current State: 77:[15, 59, 46, 43], Operations: [] Exploring Operation: 15+59=74, Resulting Numbers: [46, 43, 74] Generated Node #2: [46, 43, 74] from Operation: 15+59=74 Current State: 77:[46, 43, 74], Operations: ['15+59=74'] Exploring Operation: 46-43=3, Resulting Numbers: [74, 3] Generated Node #3: [74, 3] from Operation: 46-43=3 Current State: 77:[74, 3], Operations: ['15+59=74', '46-43=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[15, 59, 46, 43], Operations: [] Exploring Operation: 46+43=89, Resulting Numbers: [15, 59, 89] Generated Node #0,0: 77:[15, 59, 89] Operation: 46+43=89 Exploring Operation: 46-43=3, Resulting Numbers: [15, 59, 3] Generated Node #0,1: 77:[15, 59, 3] Operation: 46-43=3 Moving to Node #0,1 Current State: 77:[15, 59, 3], Operations: ['46-43=3'] Exploring Operation: 15+59=74, Resulting Numbers: [3, 74] Generated Node #0,1,0: 77:[3, 74] Operation: 15+59=74 Exploring Operation: 15-3=12, Resulting Numbers: [59, 12] Generated Node #0,1,1: 77:[59, 12] Operation: 15-3=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[3, 74], Operations: ['46-43=3', '15+59=74'] Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[15, 59, 46, 43], Operations: [] Exploring Operation: 46-43=3, Resulting Numbers: [15, 59, 3] Generated Node #0,1: 77:[15, 59, 3] Operation: 46-43=3 Moving to Node #0,1 Current State: 77:[15, 59, 3], Operations: ['46-43=3'] Exploring Operation: 15+59=74, Resulting Numbers: [3, 74] Generated Node #0,1,0: 77:[3, 74] Operation: 15+59=74 Moving to Node #0,1,0 Current State: 77:[3, 74], Operations: ['46-43=3', '15+59=74'] Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 27, 75, 97, 2 ]
13
[ "27+97=124", "124/2=62", "75-62=13" ]
Current State: 13:[27, 75, 97, 2], Operations: [] Exploring Operation: 27+97=124, Resulting Numbers: [75, 2, 124] Generated Node #2: [75, 2, 124] from Operation: 27+97=124 Current State: 13:[75, 2, 124], Operations: ['27+97=124'] Exploring Operation: 124/2=62, Resulting Numbers: [75, 62] Generated Node #3: [75, 62] from Operation: 124/2=62 Current State: 13:[75, 62], Operations: ['27+97=124', '124/2=62'] Exploring Operation: 75-62=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[27, 75, 97, 2], Operations: [] Exploring Operation: 75-27=48, Resulting Numbers: [97, 2, 48] Generated Node #0,0: 13:[97, 2, 48] Operation: 75-27=48 Exploring Operation: 97-75=22, Resulting Numbers: [27, 2, 22] Generated Node #0,1: 13:[27, 2, 22] Operation: 97-75=22 Exploring Operation: 97-27=70, Resulting Numbers: [75, 2, 70] Generated Node #0,2: 13:[75, 2, 70] Operation: 97-27=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[27, 2, 22], Operations: ['97-75=22'] Exploring Operation: 22/2=11, Resulting Numbers: [27, 11] Generated Node #0,1,0: 13:[27, 11] Operation: 22/2=11 Exploring Operation: 27-2=25, Resulting Numbers: [22, 25] Generated Node #0,1,1: 13:[22, 25] Operation: 27-2=25 Exploring Operation: 27-22=5, Resulting Numbers: [2, 5] Generated Node #0,1,2: 13:[2, 5] Operation: 27-22=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[27, 11], Operations: ['97-75=22', '22/2=11'] Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[2, 5], Operations: ['97-75=22', '27-22=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[22, 25], Operations: ['97-75=22', '27-2=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,13 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[97, 2, 48], Operations: ['75-27=48'] Exploring Operation: 97-48=49, Resulting Numbers: [2, 49] Generated Node #0,0,0: 13:[2, 49] Operation: 97-48=49 Exploring Operation: 48/2=24, Resulting Numbers: [97, 24] Generated Node #0,0,1: 13:[97, 24] Operation: 48/2=24 Exploring Operation: 97-2=95, Resulting Numbers: [48, 95] Generated Node #0,0,2: 13:[48, 95] Operation: 97-2=95 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[2, 49], Operations: ['75-27=48', '97-48=49'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,13 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,13 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[97, 24], Operations: ['75-27=48', '48/2=24'] Exploring Operation: 97*24=2328, Resulting Numbers: [2328] 2328,13 unequal: No Solution Exploring Operation: 97+24=121, Resulting Numbers: [121] 121,13 unequal: No Solution Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[48, 95], Operations: ['75-27=48', '97-2=95'] Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,13 unequal: No Solution Exploring Operation: 48*95=4560, Resulting Numbers: [4560] 4560,13 unequal: No Solution Exploring Operation: 48+95=143, Resulting Numbers: [143] 143,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[75, 2, 70], Operations: ['97-27=70'] Exploring Operation: 75-2=73, Resulting Numbers: [70, 73] Generated Node #0,2,0: 13:[70, 73] Operation: 75-2=73 Exploring Operation: 75-70=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 13:[2, 5] Operation: 75-70=5 Exploring Operation: 70/2=35, Resulting Numbers: [75, 35] Generated Node #0,2,2: 13:[75, 35] Operation: 70/2=35 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[2, 5], Operations: ['97-27=70', '75-70=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[75, 35], Operations: ['97-27=70', '70/2=35'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 75+35=110, Resulting Numbers: [110] 110,13 unequal: No Solution Exploring Operation: 75*35=2625, Resulting Numbers: [2625] 2625,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[70, 73], Operations: ['97-27=70', '75-2=73'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 70*73=5110, Resulting Numbers: [5110] 5110,13 unequal: No Solution Exploring Operation: 70+73=143, Resulting Numbers: [143] 143,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 65, 63, 38, 50 ]
43
[ "63-50=13", "65/13=5", "38+5=43" ]
Current State: 43:[65, 63, 38, 50], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [65, 38, 13] Generated Node #2: [65, 38, 13] from Operation: 63-50=13 Current State: 43:[65, 38, 13], Operations: ['63-50=13'] Exploring Operation: 65/13=5, Resulting Numbers: [38, 5] Generated Node #3: [38, 5] from Operation: 65/13=5 Current State: 43:[38, 5], Operations: ['63-50=13', '65/13=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[65, 63, 38, 50], Operations: [] Exploring Operation: 65-38=27, Resulting Numbers: [63, 50, 27] Generated Node #0,0: 43:[63, 50, 27] Operation: 65-38=27 Exploring Operation: 63-38=25, Resulting Numbers: [65, 50, 25] Generated Node #0,1: 43:[65, 50, 25] Operation: 63-38=25 Moving to Node #0,0 Current State: 43:[63, 50, 27], Operations: ['65-38=27'] Exploring Operation: 50-27=23, Resulting Numbers: [63, 23] Generated Node #0,0,0: 43:[63, 23] Operation: 50-27=23 Exploring Operation: 63-27=36, Resulting Numbers: [50, 36] Generated Node #0,0,1: 43:[50, 36] Operation: 63-27=36 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[50, 36], Operations: ['65-38=27', '63-27=36'] Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[63, 23], Operations: ['65-38=27', '50-27=23'] Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,43 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 43:[65, 50, 25], Operations: ['63-38=25'] Exploring Operation: 50-25=25, Resulting Numbers: [65, 25] Generated Node #0,1,0: 43:[65, 25] Operation: 50-25=25 Exploring Operation: 65-25=40, Resulting Numbers: [50, 40] Generated Node #0,1,1: 43:[50, 40] Operation: 65-25=40 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[50, 40], Operations: ['63-38=25', '65-25=40'] Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,43 unequal: No Solution Exploring Operation: 50+40=90, Resulting Numbers: [90] 90,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[65, 25], Operations: ['63-38=25', '50-25=25'] Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,43 unequal: No Solution Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,43 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
[ 59, 51, 31, 5 ]
93
[ "59-51=8", "8-5=3", "31*3=93" ]
Current State: 93:[59, 51, 31, 5], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [31, 5, 8] Generated Node #2: [31, 5, 8] from Operation: 59-51=8 Current State: 93:[31, 5, 8], Operations: ['59-51=8'] Exploring Operation: 8-5=3, Resulting Numbers: [31, 3] Generated Node #3: [31, 3] from Operation: 8-5=3 Current State: 93:[31, 3], Operations: ['59-51=8', '8-5=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[59, 51, 31, 5], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [31, 5, 8] Generated Node #0,0: 93:[31, 5, 8] Operation: 59-51=8 Moving to Node #0,0 Current State: 93:[31, 5, 8], Operations: ['59-51=8'] Exploring Operation: 8-5=3, Resulting Numbers: [31, 3] Generated Node #0,0,0: 93:[31, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[31, 3], Operations: ['59-51=8', '8-5=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[59, 51, 31, 5], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [31, 5, 8] Generated Node #0,0: 93:[31, 5, 8] Operation: 59-51=8 Moving to Node #0,0 Current State: 93:[31, 5, 8], Operations: ['59-51=8'] Exploring Operation: 8-5=3, Resulting Numbers: [31, 3] Generated Node #0,0,0: 93:[31, 3] Operation: 8-5=3 Moving to Node #0,0,0 Current State: 93:[31, 3], Operations: ['59-51=8', '8-5=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 41, 35, 80, 29 ]
69
[ "35*80=2800", "29+2800=2829", "2829/41=69" ]
Current State: 69:[41, 35, 80, 29], Operations: [] Exploring Operation: 35*80=2800, Resulting Numbers: [41, 29, 2800] Generated Node #2: [41, 29, 2800] from Operation: 35*80=2800 Current State: 69:[41, 29, 2800], Operations: ['35*80=2800'] Exploring Operation: 29+2800=2829, Resulting Numbers: [41, 2829] Generated Node #3: [41, 2829] from Operation: 29+2800=2829 Current State: 69:[41, 2829], Operations: ['35*80=2800', '29+2800=2829'] Exploring Operation: 2829/41=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[41, 35, 80, 29], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [80, 29, 6] Generated Node #0,0: 69:[80, 29, 6] Operation: 41-35=6 Moving to Node #0,0 Current State: 69:[80, 29, 6], Operations: ['41-35=6'] Exploring Operation: 80-6=74, Resulting Numbers: [29, 74] Generated Node #0,0,0: 69:[29, 74] Operation: 80-6=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[29, 74], Operations: ['41-35=6', '80-6=74'] Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,69 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
[ 7, 34, 61, 41 ]
62
[ "7+34=41", "41/41=1", "61+1=62" ]
Current State: 62:[7, 34, 61, 41], Operations: [] Exploring Operation: 7+34=41, Resulting Numbers: [61, 41, 41] Generated Node #2: [61, 41, 41] from Operation: 7+34=41 Current State: 62:[61, 41, 41], Operations: ['7+34=41'] Exploring Operation: 41/41=1, Resulting Numbers: [61, 1] Generated Node #3: [61, 1] from Operation: 41/41=1 Current State: 62:[61, 1], Operations: ['7+34=41', '41/41=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[7, 34, 61, 41], Operations: [] Exploring Operation: 34-7=27, Resulting Numbers: [61, 41, 27] Generated Node #0,0: 62:[61, 41, 27] Operation: 34-7=27 Exploring Operation: 41-7=34, Resulting Numbers: [34, 61, 34] Generated Node #0,1: 62:[34, 61, 34] Operation: 41-7=34 Exploring Operation: 41-34=7, Resulting Numbers: [7, 61, 7] Generated Node #0,2: 62:[7, 61, 7] Operation: 41-34=7 Moving to Node #0,1 Current State: 62:[34, 61, 34], Operations: ['41-7=34'] Exploring Operation: 34-34=0, Resulting Numbers: [61, 0] Generated Node #0,1,0: 62:[61, 0] Operation: 34-34=0 Exploring Operation: 61-34=27, Resulting Numbers: [34, 27] Generated Node #0,1,1: 62:[34, 27] Operation: 61-34=27 Exploring Operation: 34/34=1, Resulting Numbers: [61, 1] Generated Node #0,1,2: 62:[61, 1] Operation: 34/34=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[61, 1], Operations: ['41-7=34', '34/34=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[7, 34, 61, 41], Operations: [] Exploring Operation: 41-7=34, Resulting Numbers: [34, 61, 34] Generated Node #0,1: 62:[34, 61, 34] Operation: 41-7=34 Moving to Node #0,1 Current State: 62:[34, 61, 34], Operations: ['41-7=34'] Exploring Operation: 34/34=1, Resulting Numbers: [61, 1] Generated Node #0,1,2: 62:[61, 1] Operation: 34/34=1 Moving to Node #0,1,2 Current State: 62:[61, 1], Operations: ['41-7=34', '34/34=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 28, 41, 32, 3 ]
61
[ "28+32=60", "60/3=20", "41+20=61" ]
Current State: 61:[28, 41, 32, 3], Operations: [] Exploring Operation: 28+32=60, Resulting Numbers: [41, 3, 60] Generated Node #2: [41, 3, 60] from Operation: 28+32=60 Current State: 61:[41, 3, 60], Operations: ['28+32=60'] Exploring Operation: 60/3=20, Resulting Numbers: [41, 20] Generated Node #3: [41, 20] from Operation: 60/3=20 Current State: 61:[41, 20], Operations: ['28+32=60', '60/3=20'] Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[28, 41, 32, 3], Operations: [] Exploring Operation: 28*3=84, Resulting Numbers: [41, 32, 84] Generated Node #0,0: 61:[41, 32, 84] Operation: 28*3=84 Exploring Operation: 28+3=31, Resulting Numbers: [41, 32, 31] Generated Node #0,1: 61:[41, 32, 31] Operation: 28+3=31 Exploring Operation: 28+32=60, Resulting Numbers: [41, 3, 60] Generated Node #0,2: 61:[41, 3, 60] Operation: 28+32=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[41, 32, 84], Operations: ['28*3=84'] Exploring Operation: 41+32=73, Resulting Numbers: [84, 73] Generated Node #0,0,0: 61:[84, 73] Operation: 41+32=73 Exploring Operation: 84-32=52, Resulting Numbers: [41, 52] Generated Node #0,0,1: 61:[41, 52] Operation: 84-32=52 Exploring Operation: 84-41=43, Resulting Numbers: [32, 43] Generated Node #0,0,2: 61:[32, 43] Operation: 84-41=43 Moving to Node #0,0,1 Current State: 61:[41, 52], Operations: ['28*3=84', '84-32=52'] Exploring Operation: 41*52=2132, Resulting Numbers: [2132] 2132,61 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 41+52=93, Resulting Numbers: [93] 93,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[84, 73], Operations: ['28*3=84', '41+32=73'] Exploring Operation: 84+73=157, Resulting Numbers: [157] 157,61 unequal: No Solution Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 84*73=6132, Resulting Numbers: [6132] 6132,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[32, 43], Operations: ['28*3=84', '84-41=43'] Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,61 unequal: No Solution Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,61 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,61 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:[41, 32, 31], Operations: ['28+3=31'] Exploring Operation: 41+32=73, Resulting Numbers: [31, 73] Generated Node #0,1,0: 61:[31, 73] Operation: 41+32=73 Exploring Operation: 32+31=63, Resulting Numbers: [41, 63] Generated Node #0,1,1: 61:[41, 63] Operation: 32+31=63 Exploring Operation: 41+31=72, Resulting Numbers: [32, 72] Generated Node #0,1,2: 61:[32, 72] Operation: 41+31=72 Moving to Node #0,1,1 Current State: 61:[41, 63], Operations: ['28+3=31', '32+31=63'] Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,61 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[32, 72], Operations: ['28+3=31', '41+31=72'] Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[31, 73], Operations: ['28+3=31', '41+32=73'] Exploring Operation: 31+73=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 31*73=2263, Resulting Numbers: [2263] 2263,61 unequal: No Solution Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[41, 3, 60], Operations: ['28+32=60'] Exploring Operation: 3+60=63, Resulting Numbers: [41, 63] Generated Node #0,2,0: 61:[41, 63] Operation: 3+60=63 Exploring Operation: 41+3=44, Resulting Numbers: [60, 44] Generated Node #0,2,1: 61:[60, 44] Operation: 41+3=44 Exploring Operation: 41-3=38, Resulting Numbers: [60, 38] Generated Node #0,2,2: 61:[60, 38] Operation: 41-3=38 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[60, 44], Operations: ['28+32=60', '41+3=44'] Exploring Operation: 60*44=2640, Resulting Numbers: [2640] 2640,61 unequal: No Solution Exploring Operation: 60+44=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[41, 63], Operations: ['28+32=60', '3+60=63'] Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,61 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,61 unequal: No Solution Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[60, 38], Operations: ['28+32=60', '41-3=38'] Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,61 unequal: No Solution Exploring Operation: 60*38=2280, Resulting Numbers: [2280] 2280,61 unequal: No Solution Exploring Operation: 60+38=98, Resulting Numbers: [98] 98,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 13, 52, 7, 88 ]
49
[ "13*7=91", "52+88=140", "140-91=49" ]
Current State: 49:[13, 52, 7, 88], Operations: [] Exploring Operation: 13*7=91, Resulting Numbers: [52, 88, 91] Generated Node #2: [52, 88, 91] from Operation: 13*7=91 Current State: 49:[52, 88, 91], Operations: ['13*7=91'] Exploring Operation: 52+88=140, Resulting Numbers: [91, 140] Generated Node #3: [91, 140] from Operation: 52+88=140 Current State: 49:[91, 140], Operations: ['13*7=91', '52+88=140'] Exploring Operation: 140-91=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[13, 52, 7, 88], Operations: [] Exploring Operation: 88-52=36, Resulting Numbers: [13, 7, 36] Generated Node #0,0: 49:[13, 7, 36] Operation: 88-52=36 Exploring Operation: 88-13=75, Resulting Numbers: [52, 7, 75] Generated Node #0,1: 49:[52, 7, 75] Operation: 88-13=75 Moving to Node #0,0 Current State: 49:[13, 7, 36], Operations: ['88-52=36'] Exploring Operation: 7+36=43, Resulting Numbers: [13, 43] Generated Node #0,0,0: 49:[13, 43] Operation: 7+36=43 Exploring Operation: 13+36=49, Resulting Numbers: [7, 49] Generated Node #0,0,1: 49:[7, 49] Operation: 13+36=49 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[7, 49], Operations: ['88-52=36', '13+36=49'] Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[13, 43], Operations: ['88-52=36', '7+36=43'] Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,49 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: 49:[52, 7, 75], Operations: ['88-13=75'] Exploring Operation: 75-7=68, Resulting Numbers: [52, 68] Generated Node #0,1,0: 49:[52, 68] Operation: 75-7=68 Exploring Operation: 75-52=23, Resulting Numbers: [7, 23] Generated Node #0,1,1: 49:[7, 23] Operation: 75-52=23 Moving to Node #0,1,1 Current State: 49:[7, 23], Operations: ['88-13=75', '75-52=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[52, 68], Operations: ['88-13=75', '75-7=68'] Exploring Operation: 52+68=120, Resulting Numbers: [120] 120,49 unequal: No Solution Exploring Operation: 68-52=16, Resulting Numbers: [16] 16,49 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 85, 93, 42, 2 ]
52
[ "93-85=8", "42+2=44", "8+44=52" ]
Current State: 52:[85, 93, 42, 2], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [42, 2, 8] Generated Node #2: [42, 2, 8] from Operation: 93-85=8 Current State: 52:[42, 2, 8], Operations: ['93-85=8'] Exploring Operation: 42+2=44, Resulting Numbers: [8, 44] Generated Node #3: [8, 44] from Operation: 42+2=44 Current State: 52:[8, 44], Operations: ['93-85=8', '42+2=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[85, 93, 42, 2], Operations: [] Exploring Operation: 85-42=43, Resulting Numbers: [93, 2, 43] Generated Node #0,0: 52:[93, 2, 43] Operation: 85-42=43 Exploring Operation: 93-85=8, Resulting Numbers: [42, 2, 8] Generated Node #0,1: 52:[42, 2, 8] Operation: 93-85=8 Exploring Operation: 93-42=51, Resulting Numbers: [85, 2, 51] Generated Node #0,2: 52:[85, 2, 51] Operation: 93-42=51 Exploring Operation: 85-2=83, Resulting Numbers: [93, 42, 83] Generated Node #0,3: 52:[93, 42, 83] Operation: 85-2=83 Exploring Operation: 42/2=21, Resulting Numbers: [85, 93, 21] Generated Node #0,4: 52:[85, 93, 21] Operation: 42/2=21 Moving to Node #0,1 Current State: 52:[42, 2, 8], Operations: ['93-85=8'] Exploring Operation: 42+8=50, Resulting Numbers: [2, 50] Generated Node #0,1,0: 52:[2, 50] Operation: 42+8=50 Exploring Operation: 42-8=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 52:[2, 34] Operation: 42-8=34 Exploring Operation: 42+2=44, Resulting Numbers: [8, 44] Generated Node #0,1,2: 52:[8, 44] Operation: 42+2=44 Exploring Operation: 8/2=4, Resulting Numbers: [42, 4] Generated Node #0,1,3: 52:[42, 4] Operation: 8/2=4 Exploring Operation: 42/2=21, Resulting Numbers: [8, 21] Generated Node #0,1,4: 52:[8, 21] Operation: 42/2=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[2, 50], Operations: ['93-85=8', '42+8=50'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[85, 93, 42, 2], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [42, 2, 8] Generated Node #0,1: 52:[42, 2, 8] Operation: 93-85=8 Moving to Node #0,1 Current State: 52:[42, 2, 8], Operations: ['93-85=8'] Exploring Operation: 42+8=50, Resulting Numbers: [2, 50] Generated Node #0,1,0: 52:[2, 50] Operation: 42+8=50 Moving to Node #0,1,0 Current State: 52:[2, 50], Operations: ['93-85=8', '42+8=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 9, 74, 58, 98 ]
76
[ "58-9=49", "98/49=2", "74+2=76" ]
Current State: 76:[9, 74, 58, 98], Operations: [] Exploring Operation: 58-9=49, Resulting Numbers: [74, 98, 49] Generated Node #2: [74, 98, 49] from Operation: 58-9=49 Current State: 76:[74, 98, 49], Operations: ['58-9=49'] Exploring Operation: 98/49=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 98/49=2 Current State: 76:[74, 2], Operations: ['58-9=49', '98/49=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[9, 74, 58, 98], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [9, 58, 24] Generated Node #0,0: 76:[9, 58, 24] Operation: 98-74=24 Exploring Operation: 74-58=16, Resulting Numbers: [9, 98, 16] Generated Node #0,1: 76:[9, 98, 16] Operation: 74-58=16 Exploring Operation: 98-58=40, Resulting Numbers: [9, 74, 40] Generated Node #0,2: 76:[9, 74, 40] Operation: 98-58=40 Exploring Operation: 98-9=89, Resulting Numbers: [74, 58, 89] Generated Node #0,3: 76:[74, 58, 89] Operation: 98-9=89 Exploring Operation: 9+58=67, Resulting Numbers: [74, 98, 67] Generated Node #0,4: 76:[74, 98, 67] Operation: 9+58=67 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[9, 74, 40], Operations: ['98-58=40'] Exploring Operation: 40-9=31, Resulting Numbers: [74, 31] Generated Node #0,2,0: 76:[74, 31] Operation: 40-9=31 Exploring Operation: 9+40=49, Resulting Numbers: [74, 49] Generated Node #0,2,1: 76:[74, 49] Operation: 9+40=49 Exploring Operation: 9+74=83, Resulting Numbers: [40, 83] Generated Node #0,2,2: 76:[40, 83] Operation: 9+74=83 Exploring Operation: 74-40=34, Resulting Numbers: [9, 34] Generated Node #0,2,3: 76:[9, 34] Operation: 74-40=34 Exploring Operation: 74-9=65, Resulting Numbers: [40, 65] Generated Node #0,2,4: 76:[40, 65] Operation: 74-9=65 Moving to Node #0,2,0 Current State: 76:[74, 31], Operations: ['98-58=40', '40-9=31'] Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 74+31=105, Resulting Numbers: [105] 105,76 unequal: No Solution Exploring Operation: 74*31=2294, Resulting Numbers: [2294] 2294,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[9, 34], Operations: ['98-58=40', '74-40=34'] Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 9*34=306, Resulting Numbers: [306] 306,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[40, 83], Operations: ['98-58=40', '9+74=83'] Exploring Operation: 40+83=123, Resulting Numbers: [123] 123,76 unequal: No Solution Exploring Operation: 83-40=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 40*83=3320, Resulting Numbers: [3320] 3320,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[74, 49], Operations: ['98-58=40', '9+40=49'] Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 74+49=123, Resulting Numbers: [123] 123,76 unequal: No Solution Exploring Operation: 74*49=3626, Resulting Numbers: [3626] 3626,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[40, 65], Operations: ['98-58=40', '74-9=65'] Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 40*65=2600, Resulting Numbers: [2600] 2600,76 unequal: No Solution Exploring Operation: 40+65=105, Resulting Numbers: [105] 105,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[9, 58, 24], Operations: ['98-74=24'] Exploring Operation: 24-9=15, Resulting Numbers: [58, 15] Generated Node #0,0,0: 76:[58, 15] Operation: 24-9=15 Exploring Operation: 9+58=67, Resulting Numbers: [24, 67] Generated Node #0,0,1: 76:[24, 67] Operation: 9+58=67 Exploring Operation: 58+24=82, Resulting Numbers: [9, 82] Generated Node #0,0,2: 76:[9, 82] Operation: 58+24=82 Exploring Operation: 58-24=34, Resulting Numbers: [9, 34] Generated Node #0,0,3: 76:[9, 34] Operation: 58-24=34 Exploring Operation: 58-9=49, Resulting Numbers: [24, 49] Generated Node #0,0,4: 76:[24, 49] Operation: 58-9=49 Moving to Node #0,0,3 Current State: 76:[9, 34], Operations: ['98-74=24', '58-24=34'] Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 9*34=306, Resulting Numbers: [306] 306,76 unequal: No Solution Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[9, 82], Operations: ['98-74=24', '58+24=82'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 9+82=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 9*82=738, Resulting Numbers: [738] 738,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[24, 67], Operations: ['98-74=24', '9+58=67'] Exploring Operation: 24+67=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 24*67=1608, Resulting Numbers: [1608] 1608,76 unequal: No Solution Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,76 unequal: No Solution Moving to Node #0,0,4 Current State: 76:[24, 49], Operations: ['98-74=24', '58-9=49'] Exploring Operation: 24*49=1176, Resulting Numbers: [1176] 1176,76 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 24+49=73, Resulting Numbers: [73] 73,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[58, 15], Operations: ['98-74=24', '24-9=15'] Exploring Operation: 58*15=870, Resulting Numbers: [870] 870,76 unequal: No Solution Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 58+15=73, Resulting Numbers: [73] 73,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[9, 98, 16], Operations: ['74-58=16'] Exploring Operation: 98-16=82, Resulting Numbers: [9, 82] Generated Node #0,1,0: 76:[9, 82] Operation: 98-16=82 Exploring Operation: 9+98=107, Resulting Numbers: [16, 107] Generated Node #0,1,1: 76:[16, 107] Operation: 9+98=107 Exploring Operation: 9+16=25, Resulting Numbers: [98, 25] Generated Node #0,1,2: 76:[98, 25] Operation: 9+16=25 Exploring Operation: 16-9=7, Resulting Numbers: [98, 7] Generated Node #0,1,3: 76:[98, 7] Operation: 16-9=7 Exploring Operation: 98-9=89, Resulting Numbers: [16, 89] Generated Node #0,1,4: 76:[16, 89] Operation: 98-9=89 Moving to Node #0,1,0 Current State: 76:[9, 82], Operations: ['74-58=16', '98-16=82'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 9*82=738, Resulting Numbers: [738] 738,76 unequal: No Solution Exploring Operation: 9+82=91, Resulting Numbers: [91] 91,76 unequal: No Solution Moving to Node #0,1,4 Current State: 76:[16, 89], Operations: ['74-58=16', '98-9=89'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 16*89=1424, Resulting Numbers: [1424] 1424,76 unequal: No Solution Exploring Operation: 16+89=105, Resulting Numbers: [105] 105,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[98, 7], Operations: ['74-58=16', '16-9=7'] Exploring Operation: 98*7=686, Resulting Numbers: [686] 686,76 unequal: No Solution Exploring Operation: 98+7=105, Resulting Numbers: [105] 105,76 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[98, 25], Operations: ['74-58=16', '9+16=25'] Exploring Operation: 98+25=123, Resulting Numbers: [123] 123,76 unequal: No Solution Exploring Operation: 98*25=2450, Resulting Numbers: [2450] 2450,76 unequal: No Solution Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[16, 107], Operations: ['74-58=16', '9+98=107'] Exploring Operation: 16+107=123, Resulting Numbers: [123] 123,76 unequal: No Solution Exploring Operation: 107-16=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 16*107=1712, Resulting Numbers: [1712] 1712,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[74, 58, 89], Operations: ['98-9=89'] Exploring Operation: 74-58=16, Resulting Numbers: [89, 16] Generated Node #0,3,0: 76:[89, 16] Operation: 74-58=16 Exploring Operation: 89-58=31, Resulting Numbers: [74, 31] Generated Node #0,3,1: 76:[74, 31] Operation: 89-58=31 Exploring Operation: 89-74=15, Resulting Numbers: [58, 15] Generated Node #0,3,2: 76:[58, 15] Operation: 89-74=15 Exploring Operation: 58+89=147, Resulting Numbers: [74, 147] Generated Node #0,3,3: 76:[74, 147] Operation: 58+89=147 Exploring Operation: 74+58=132, Resulting Numbers: [89, 132] Generated Node #0,3,4: 76:[89, 132] Operation: 74+58=132 Moving to Node #0,3,1 Current State: 76:[74, 31], Operations: ['98-9=89', '89-58=31'] Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 74+31=105, Resulting Numbers: [105] 105,76 unequal: No Solution Exploring Operation: 74*31=2294, Resulting Numbers: [2294] 2294,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[89, 16], Operations: ['98-9=89', '74-58=16'] Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,76 unequal: No Solution Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[58, 15], Operations: ['98-9=89', '89-74=15'] Exploring Operation: 58*15=870, Resulting Numbers: [870] 870,76 unequal: No Solution Exploring Operation: 58+15=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,76 unequal: No Solution Moving to Node #0,3,4 Current State: 76:[89, 132], Operations: ['98-9=89', '74+58=132'] Exploring Operation: 89+132=221, Resulting Numbers: [221] 221,76 unequal: No Solution Exploring Operation: 89*132=11748, Resulting Numbers: [11748] 11748,76 unequal: No Solution Exploring Operation: 132-89=43, Resulting Numbers: [43] 43,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[74, 147], Operations: ['98-9=89', '58+89=147'] Exploring Operation: 74*147=10878, Resulting Numbers: [10878] 10878,76 unequal: No Solution Exploring Operation: 147-74=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 74+147=221, Resulting Numbers: [221] 221,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 76:[74, 98, 67], Operations: ['9+58=67'] Exploring Operation: 98-67=31, Resulting Numbers: [74, 31] Generated Node #0,4,0: 76:[74, 31] Operation: 98-67=31 Exploring Operation: 74+67=141, Resulting Numbers: [98, 141] Generated Node #0,4,1: 76:[98, 141] Operation: 74+67=141 Exploring Operation: 98-74=24, Resulting Numbers: [67, 24] Generated Node #0,4,2: 76:[67, 24] Operation: 98-74=24 Exploring Operation: 74-67=7, Resulting Numbers: [98, 7] Generated Node #0,4,3: 76:[98, 7] Operation: 74-67=7 Exploring Operation: 98+67=165, Resulting Numbers: [74, 165] Generated Node #0,4,4: 76:[74, 165] Operation: 98+67=165 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 76:[74, 31], Operations: ['9+58=67', '98-67=31'] Exploring Operation: 74*31=2294, Resulting Numbers: [2294] 2294,76 unequal: No Solution Exploring Operation: 74+31=105, Resulting Numbers: [105] 105,76 unequal: No Solution Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 76:[67, 24], Operations: ['9+58=67', '98-74=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 76:[98, 7], Operations: ['9+58=67', '74-67=7'] Exploring Operation: 98/7=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 98*7=686, Resulting Numbers: [686] 686,76 unequal: No Solution Exploring Operation: 98-7=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 98+7=105, Resulting Numbers: [105] 105,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 76:[98, 141], Operations: ['9+58=67', '74+67=141'] Exploring Operation: 141-98=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 98*141=13818, Resulting Numbers: [13818] 13818,76 unequal: No Solution Exploring Operation: 98+141=239, Resulting Numbers: [239] 239,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 76:[74, 165], Operations: ['9+58=67', '98+67=165'] Exploring Operation: 74+165=239, Resulting Numbers: [239] 239,76 unequal: No Solution Exploring Operation: 165-74=91, Resulting Numbers: [91] 91,76 unequal: No Solution Exploring Operation: 74*165=12210, Resulting Numbers: [12210] 12210,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 10, 9, 73, 59 ]
42
[ "10*9=90", "73+59=132", "132-90=42" ]
Current State: 42:[10, 9, 73, 59], Operations: [] Exploring Operation: 10*9=90, Resulting Numbers: [73, 59, 90] Generated Node #2: [73, 59, 90] from Operation: 10*9=90 Current State: 42:[73, 59, 90], Operations: ['10*9=90'] Exploring Operation: 73+59=132, Resulting Numbers: [90, 132] Generated Node #3: [90, 132] from Operation: 73+59=132 Current State: 42:[90, 132], Operations: ['10*9=90', '73+59=132'] Exploring Operation: 132-90=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[10, 9, 73, 59], Operations: [] Exploring Operation: 59-10=49, Resulting Numbers: [9, 73, 49] Generated Node #0,0: 42:[9, 73, 49] Operation: 59-10=49 Exploring Operation: 59-9=50, Resulting Numbers: [10, 73, 50] Generated Node #0,1: 42:[10, 73, 50] Operation: 59-9=50 Exploring Operation: 73-10=63, Resulting Numbers: [9, 59, 63] Generated Node #0,2: 42:[9, 59, 63] Operation: 73-10=63 Exploring Operation: 73-59=14, Resulting Numbers: [10, 9, 14] Generated Node #0,3: 42:[10, 9, 14] Operation: 73-59=14 Exploring Operation: 73-9=64, Resulting Numbers: [10, 59, 64] Generated Node #0,4: 42:[10, 59, 64] Operation: 73-9=64 Moving to Node #0,3 Current State: 42:[10, 9, 14], Operations: ['73-59=14'] Exploring Operation: 14-10=4, Resulting Numbers: [9, 4] Generated Node #0,3,0: 42:[9, 4] Operation: 14-10=4 Exploring Operation: 10+9=19, Resulting Numbers: [14, 19] Generated Node #0,3,1: 42:[14, 19] Operation: 10+9=19 Exploring Operation: 14-9=5, Resulting Numbers: [10, 5] Generated Node #0,3,2: 42:[10, 5] Operation: 14-9=5 Exploring Operation: 10-9=1, Resulting Numbers: [14, 1] Generated Node #0,3,3: 42:[14, 1] Operation: 10-9=1 Exploring Operation: 10+14=24, Resulting Numbers: [9, 24] Generated Node #0,3,4: 42:[9, 24] Operation: 10+14=24 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 42:[14, 1], Operations: ['73-59=14', '10-9=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 42:[14, 19], Operations: ['73-59=14', '10+9=19'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 14*19=266, Resulting Numbers: [266] 266,42 unequal: No Solution Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 42:[9, 4], Operations: ['73-59=14', '14-10=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 42:[10, 5], Operations: ['73-59=14', '14-9=5'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 42:[9, 24], Operations: ['73-59=14', '10+14=24'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,42 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: 42:[9, 59, 63], Operations: ['73-10=63'] Exploring Operation: 59-9=50, Resulting Numbers: [63, 50] Generated Node #0,2,0: 42:[63, 50] Operation: 59-9=50 Exploring Operation: 63-59=4, Resulting Numbers: [9, 4] Generated Node #0,2,1: 42:[9, 4] Operation: 63-59=4 Exploring Operation: 63/9=7, Resulting Numbers: [59, 7] Generated Node #0,2,2: 42:[59, 7] Operation: 63/9=7 Exploring Operation: 63-9=54, Resulting Numbers: [59, 54] Generated Node #0,2,3: 42:[59, 54] Operation: 63-9=54 Exploring Operation: 9+59=68, Resulting Numbers: [63, 68] Generated Node #0,2,4: 42:[63, 68] Operation: 9+59=68 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[9, 4], Operations: ['73-10=63', '63-59=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 42:[59, 7], Operations: ['73-10=63', '63/9=7'] Exploring Operation: 59*7=413, Resulting Numbers: [413] 413,42 unequal: No Solution Exploring Operation: 59-7=52, Resulting Numbers: [52] 52,42 unequal: No Solution Exploring Operation: 59+7=66, Resulting Numbers: [66] 66,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 42:[63, 50], Operations: ['73-10=63', '59-9=50'] Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 63+50=113, Resulting Numbers: [113] 113,42 unequal: No Solution Exploring Operation: 63*50=3150, Resulting Numbers: [3150] 3150,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 42:[59, 54], Operations: ['73-10=63', '63-9=54'] Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 59*54=3186, Resulting Numbers: [3186] 3186,42 unequal: No Solution Exploring Operation: 59+54=113, Resulting Numbers: [113] 113,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 42:[63, 68], Operations: ['73-10=63', '9+59=68'] Exploring Operation: 63*68=4284, Resulting Numbers: [4284] 4284,42 unequal: No Solution Exploring Operation: 63+68=131, Resulting Numbers: [131] 131,42 unequal: No Solution Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,42 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: 42:[9, 73, 49], Operations: ['59-10=49'] Exploring Operation: 9+73=82, Resulting Numbers: [49, 82] Generated Node #0,0,0: 42:[49, 82] Operation: 9+73=82 Exploring Operation: 49-9=40, Resulting Numbers: [73, 40] Generated Node #0,0,1: 42:[73, 40] Operation: 49-9=40 Exploring Operation: 73-9=64, Resulting Numbers: [49, 64] Generated Node #0,0,2: 42:[49, 64] Operation: 73-9=64 Exploring Operation: 73-49=24, Resulting Numbers: [9, 24] Generated Node #0,0,3: 42:[9, 24] Operation: 73-49=24 Exploring Operation: 9+49=58, Resulting Numbers: [73, 58] Generated Node #0,0,4: 42:[73, 58] Operation: 9+49=58 Moving to Node #0,1 Current State: 42:[10, 73, 50], Operations: ['59-9=50'] Exploring Operation: 50/10=5, Resulting Numbers: [73, 5] Generated Node #0,1,0: 42:[73, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [73, 40] Generated Node #0,1,1: 42:[73, 40] Operation: 50-10=40 Exploring Operation: 73-50=23, Resulting Numbers: [10, 23] Generated Node #0,1,2: 42:[10, 23] Operation: 73-50=23 Exploring Operation: 10+73=83, Resulting Numbers: [50, 83] Generated Node #0,1,3: 42:[50, 83] Operation: 10+73=83 Exploring Operation: 73-10=63, Resulting Numbers: [50, 63] Generated Node #0,1,4: 42:[50, 63] Operation: 73-10=63 Moving to Node #0,4 Current State: 42:[10, 59, 64], Operations: ['73-9=64'] Exploring Operation: 59-10=49, Resulting Numbers: [64, 49] Generated Node #0,4,0: 42:[64, 49] Operation: 59-10=49 Exploring Operation: 64-59=5, Resulting Numbers: [10, 5] Generated Node #0,4,1: 42:[10, 5] Operation: 64-59=5 Exploring Operation: 64-10=54, Resulting Numbers: [59, 54] Generated Node #0,4,2: 42:[59, 54] Operation: 64-10=54 Exploring Operation: 10+59=69, Resulting Numbers: [64, 69] Generated Node #0,4,3: 42:[64, 69] Operation: 10+59=69 Exploring Operation: 10+64=74, Resulting Numbers: [59, 74] Generated Node #0,4,4: 42:[59, 74] Operation: 10+64=74 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 42:[10, 5], Operations: ['73-9=64', '64-59=5'] Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 42:[64, 49], Operations: ['73-9=64', '59-10=49'] Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,42 unequal: No Solution Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 42:[59, 54], Operations: ['73-9=64', '64-10=54'] Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 59*54=3186, Resulting Numbers: [3186] 3186,42 unequal: No Solution Exploring Operation: 59+54=113, Resulting Numbers: [113] 113,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 42:[64, 69], Operations: ['73-9=64', '10+59=69'] Exploring Operation: 69-64=5, Resulting Numbers: [5] 5,42 unequal: No Solution Exploring Operation: 64+69=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 64*69=4416, Resulting Numbers: [4416] 4416,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 42:[59, 74], Operations: ['73-9=64', '10+64=74'] Exploring Operation: 59*74=4366, Resulting Numbers: [4366] 4366,42 unequal: No Solution Exploring Operation: 59+74=133, Resulting Numbers: [133] 133,42 unequal: No Solution Exploring Operation: 74-59=15, Resulting Numbers: [15] 15,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 42:[9, 24], Operations: ['59-10=49', '73-49=24'] Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,42 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[10, 23], Operations: ['59-9=50', '73-50=23'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,42 unequal: No Solution Moving to Node #0,1,4 Current State: 42:[50, 63], Operations: ['59-9=50', '73-10=63'] Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,42 unequal: No Solution Exploring Operation: 50*63=3150, Resulting Numbers: [3150] 3150,42 unequal: No Solution Exploring Operation: 50+63=113, Resulting Numbers: [113] 113,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[49, 64], Operations: ['59-10=49', '73-9=64'] Exploring Operation: 49+64=113, Resulting Numbers: [113] 113,42 unequal: No Solution Exploring Operation: 49*64=3136, Resulting Numbers: [3136] 3136,42 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[73, 5], Operations: ['59-9=50', '50/10=5'] Exploring Operation: 73*5=365, Resulting Numbers: [365] 365,42 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,42 unequal: No Solution Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[73, 40], Operations: ['59-10=49', '49-9=40'] Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,42 unequal: No Solution Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,42 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[73, 40], Operations: ['59-9=50', '50-10=40'] Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,42 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,42 unequal: No Solution Moving to Node #0,0,4 Current State: 42:[73, 58], Operations: ['59-10=49', '9+49=58'] Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 73*58=4234, Resulting Numbers: [4234] 4234,42 unequal: No Solution Exploring Operation: 73+58=131, Resulting Numbers: [131] 131,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[49, 82], Operations: ['59-10=49', '9+73=82'] Exploring Operation: 82-49=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 49+82=131, Resulting Numbers: [131] 131,42 unequal: No Solution Exploring Operation: 49*82=4018, Resulting Numbers: [4018] 4018,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[50, 83], Operations: ['59-9=50', '10+73=83'] Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,42 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,42 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 66, 35, 65, 26 ]
80
[ "35*26=910", "910/65=14", "66+14=80" ]
Current State: 80:[66, 35, 65, 26], Operations: [] Exploring Operation: 35*26=910, Resulting Numbers: [66, 65, 910] Generated Node #2: [66, 65, 910] from Operation: 35*26=910 Current State: 80:[66, 65, 910], Operations: ['35*26=910'] Exploring Operation: 910/65=14, Resulting Numbers: [66, 14] Generated Node #3: [66, 14] from Operation: 910/65=14 Current State: 80:[66, 14], Operations: ['35*26=910', '910/65=14'] Exploring Operation: 66+14=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[66, 35, 65, 26], Operations: [] Exploring Operation: 66-35=31, Resulting Numbers: [65, 26, 31] Generated Node #0,0: 80:[65, 26, 31] Operation: 66-35=31 Exploring Operation: 66-26=40, Resulting Numbers: [35, 65, 40] Generated Node #0,1: 80:[35, 65, 40] Operation: 66-26=40 Exploring Operation: 66-65=1, Resulting Numbers: [35, 26, 1] Generated Node #0,2: 80:[35, 26, 1] Operation: 66-65=1 Exploring Operation: 65-26=39, Resulting Numbers: [66, 35, 39] Generated Node #0,3: 80:[66, 35, 39] Operation: 65-26=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[35, 26, 1], Operations: ['66-65=1'] Exploring Operation: 26-1=25, Resulting Numbers: [35, 25] Generated Node #0,2,0: 80:[35, 25] Operation: 26-1=25 Exploring Operation: 35*1=35, Resulting Numbers: [26, 35] Generated Node #0,2,1: 80:[26, 35] Operation: 35*1=35 Exploring Operation: 35+1=36, Resulting Numbers: [26, 36] Generated Node #0,2,2: 80:[26, 36] Operation: 35+1=36 Exploring Operation: 35-26=9, Resulting Numbers: [1, 9] Generated Node #0,2,3: 80:[1, 9] Operation: 35-26=9 Moving to Node #0,2,3 Current State: 80:[1, 9], Operations: ['66-65=1', '35-26=9'] Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[26, 36], Operations: ['66-65=1', '35+1=36'] Exploring Operation: 26+36=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 36-26=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 26*36=936, Resulting Numbers: [936] 936,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[35, 25], Operations: ['66-65=1', '26-1=25'] Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,80 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[26, 35], Operations: ['66-65=1', '35*1=35'] Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,80 unequal: No Solution Exploring Operation: 26*35=910, Resulting Numbers: [910] 910,80 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[35, 65, 40], Operations: ['66-26=40'] Exploring Operation: 40-35=5, Resulting Numbers: [65, 5] Generated Node #0,1,0: 80:[65, 5] Operation: 40-35=5 Exploring Operation: 65-35=30, Resulting Numbers: [40, 30] Generated Node #0,1,1: 80:[40, 30] Operation: 65-35=30 Exploring Operation: 35+65=100, Resulting Numbers: [40, 100] Generated Node #0,1,2: 80:[40, 100] Operation: 35+65=100 Exploring Operation: 65-40=25, Resulting Numbers: [35, 25] Generated Node #0,1,3: 80:[35, 25] Operation: 65-40=25 Moving to Node #0,1,1 Current State: 80:[40, 30], Operations: ['66-26=40', '65-35=30'] Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[35, 25], Operations: ['66-26=40', '65-40=25'] Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[65, 5], Operations: ['66-26=40', '40-35=5'] Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 65+5=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 65*5=325, Resulting Numbers: [325] 325,80 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[40, 100], Operations: ['66-26=40', '35+65=100'] Exploring Operation: 40+100=140, Resulting Numbers: [140] 140,80 unequal: No Solution Exploring Operation: 100-40=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 40*100=4000, Resulting Numbers: [4000] 4000,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 80:[66, 35, 39], Operations: ['65-26=39'] Exploring Operation: 39-35=4, Resulting Numbers: [66, 4] Generated Node #0,3,0: 80:[66, 4] Operation: 39-35=4 Exploring Operation: 35+39=74, Resulting Numbers: [66, 74] Generated Node #0,3,1: 80:[66, 74] Operation: 35+39=74 Exploring Operation: 66-39=27, Resulting Numbers: [35, 27] Generated Node #0,3,2: 80:[35, 27] Operation: 66-39=27 Exploring Operation: 66-35=31, Resulting Numbers: [39, 31] Generated Node #0,3,3: 80:[39, 31] Operation: 66-35=31 Moving to Node #0,3,3 Current State: 80:[39, 31], Operations: ['65-26=39', '66-35=31'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 39+31=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 39*31=1209, Resulting Numbers: [1209] 1209,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[35, 27], Operations: ['65-26=39', '66-39=27'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[66, 4], Operations: ['65-26=39', '39-35=4'] Exploring Operation: 66+4=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 66*4=264, Resulting Numbers: [264] 264,80 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[66, 74], Operations: ['65-26=39', '35+39=74'] Exploring Operation: 66+74=140, Resulting Numbers: [140] 140,80 unequal: No Solution Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 66*74=4884, Resulting Numbers: [4884] 4884,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[65, 26, 31], Operations: ['66-35=31'] Exploring Operation: 65+26=91, Resulting Numbers: [31, 91] Generated Node #0,0,0: 80:[31, 91] Operation: 65+26=91 Exploring Operation: 65-26=39, Resulting Numbers: [31, 39] Generated Node #0,0,1: 80:[31, 39] Operation: 65-26=39 Exploring Operation: 65-31=34, Resulting Numbers: [26, 34] Generated Node #0,0,2: 80:[26, 34] Operation: 65-31=34 Exploring Operation: 31-26=5, Resulting Numbers: [65, 5] Generated Node #0,0,3: 80:[65, 5] Operation: 31-26=5 Moving to Node #0,0,1 Current State: 80:[31, 39], Operations: ['66-35=31', '65-26=39'] Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,80 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[26, 34], Operations: ['66-35=31', '65-31=34'] Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,80 unequal: No Solution Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[65, 5], Operations: ['66-35=31', '31-26=5'] Exploring Operation: 65+5=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 65*5=325, Resulting Numbers: [325] 325,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[31, 91], Operations: ['66-35=31', '65+26=91'] Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,80 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,80 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
[ 5, 19, 22, 9 ]
61
[ "5*22=110", "19*9=171", "171-110=61" ]
Current State: 61:[5, 19, 22, 9], Operations: [] Exploring Operation: 5*22=110, Resulting Numbers: [19, 9, 110] Generated Node #2: [19, 9, 110] from Operation: 5*22=110 Current State: 61:[19, 9, 110], Operations: ['5*22=110'] Exploring Operation: 19*9=171, Resulting Numbers: [110, 171] Generated Node #3: [110, 171] from Operation: 19*9=171 Current State: 61:[110, 171], Operations: ['5*22=110', '19*9=171'] Exploring Operation: 171-110=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[5, 19, 22, 9], Operations: [] Exploring Operation: 5*9=45, Resulting Numbers: [19, 22, 45] Generated Node #0,0: 61:[19, 22, 45] Operation: 5*9=45 Exploring Operation: 5*19=95, Resulting Numbers: [22, 9, 95] Generated Node #0,1: 61:[22, 9, 95] Operation: 5*19=95 Moving to Node #0,0 Current State: 61:[19, 22, 45], Operations: ['5*9=45'] Exploring Operation: 19+45=64, Resulting Numbers: [22, 64] Generated Node #0,0,0: 61:[22, 64] Operation: 19+45=64 Exploring Operation: 19+22=41, Resulting Numbers: [45, 41] Generated Node #0,0,1: 61:[45, 41] Operation: 19+22=41 Moving to Node #0,1 Current State: 61:[22, 9, 95], Operations: ['5*19=95'] Exploring Operation: 95-22=73, Resulting Numbers: [9, 73] Generated Node #0,1,0: 61:[9, 73] Operation: 95-22=73 Exploring Operation: 22+9=31, Resulting Numbers: [95, 31] Generated Node #0,1,1: 61:[95, 31] Operation: 22+9=31 Moving to Node #0,0,1 Current State: 61:[45, 41], Operations: ['5*9=45', '19+22=41'] Exploring Operation: 45+41=86, Resulting Numbers: [86] 86,61 unequal: No Solution Exploring Operation: 45-41=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[22, 64], Operations: ['5*9=45', '19+45=64'] Exploring Operation: 22+64=86, Resulting Numbers: [86] 86,61 unequal: No Solution Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[95, 31], Operations: ['5*19=95', '22+9=31'] Exploring Operation: 95-31=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 95+31=126, Resulting Numbers: [126] 126,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[9, 73], Operations: ['5*19=95', '95-22=73'] Exploring Operation: 9+73=82, Resulting Numbers: [82] 82,61 unequal: No Solution Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,61 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 47, 81, 31, 6 ]
94
[ "47+31=78", "78/6=13", "81+13=94" ]
Current State: 94:[47, 81, 31, 6], Operations: [] Exploring Operation: 47+31=78, Resulting Numbers: [81, 6, 78] Generated Node #2: [81, 6, 78] from Operation: 47+31=78 Current State: 94:[81, 6, 78], Operations: ['47+31=78'] Exploring Operation: 78/6=13, Resulting Numbers: [81, 13] Generated Node #3: [81, 13] from Operation: 78/6=13 Current State: 94:[81, 13], Operations: ['47+31=78', '78/6=13'] Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[47, 81, 31, 6], Operations: [] Exploring Operation: 31+6=37, Resulting Numbers: [47, 81, 37] Generated Node #0,0: 94:[47, 81, 37] Operation: 31+6=37 Exploring Operation: 81+6=87, Resulting Numbers: [47, 31, 87] Generated Node #0,1: 94:[47, 31, 87] Operation: 81+6=87 Exploring Operation: 81+31=112, Resulting Numbers: [47, 6, 112] Generated Node #0,2: 94:[47, 6, 112] Operation: 81+31=112 Exploring Operation: 81-31=50, Resulting Numbers: [47, 6, 50] Generated Node #0,3: 94:[47, 6, 50] Operation: 81-31=50 Moving to Node #0,3 Current State: 94:[47, 6, 50], Operations: ['81-31=50'] Exploring Operation: 47+6=53, Resulting Numbers: [50, 53] Generated Node #0,3,0: 94:[50, 53] Operation: 47+6=53 Exploring Operation: 47+50=97, Resulting Numbers: [6, 97] Generated Node #0,3,1: 94:[6, 97] Operation: 47+50=97 Exploring Operation: 50-6=44, Resulting Numbers: [47, 44] Generated Node #0,3,2: 94:[47, 44] Operation: 50-6=44 Exploring Operation: 50-47=3, Resulting Numbers: [6, 3] Generated Node #0,3,3: 94:[6, 3] Operation: 50-47=3 Moving to Node #0,2 Current State: 94:[47, 6, 112], Operations: ['81+31=112'] Exploring Operation: 112-47=65, Resulting Numbers: [6, 65] Generated Node #0,2,0: 94:[6, 65] Operation: 112-47=65 Exploring Operation: 112-6=106, Resulting Numbers: [47, 106] Generated Node #0,2,1: 94:[47, 106] Operation: 112-6=106 Exploring Operation: 47-6=41, Resulting Numbers: [112, 41] Generated Node #0,2,2: 94:[112, 41] Operation: 47-6=41 Exploring Operation: 47+6=53, Resulting Numbers: [112, 53] Generated Node #0,2,3: 94:[112, 53] Operation: 47+6=53 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 94:[47, 106], Operations: ['81+31=112', '112-6=106'] Exploring Operation: 106-47=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 47*106=4982, Resulting Numbers: [4982] 4982,94 unequal: No Solution Exploring Operation: 47+106=153, Resulting Numbers: [153] 153,94 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 #0,2,0 Current State: 94:[6, 65], Operations: ['81+31=112', '112-47=65'] Exploring Operation: 6+65=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 6*65=390, Resulting Numbers: [390] 390,94 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 #0,2,2 Current State: 94:[112, 41], Operations: ['81+31=112', '47-6=41'] Exploring Operation: 112+41=153, Resulting Numbers: [153] 153,94 unequal: No Solution Exploring Operation: 112*41=4592, Resulting Numbers: [4592] 4592,94 unequal: No Solution Exploring Operation: 112-41=71, Resulting Numbers: [71] 71,94 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 #0,2,3 Current State: 94:[112, 53], Operations: ['81+31=112', '47+6=53'] Exploring Operation: 112-53=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 112*53=5936, Resulting Numbers: [5936] 5936,94 unequal: No Solution Exploring Operation: 112+53=165, Resulting Numbers: [165] 165,94 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: 94:[47, 31, 87], Operations: ['81+6=87'] Exploring Operation: 87-47=40, Resulting Numbers: [31, 40] Generated Node #0,1,0: 94:[31, 40] Operation: 87-47=40 Exploring Operation: 47-31=16, Resulting Numbers: [87, 16] Generated Node #0,1,1: 94:[87, 16] Operation: 47-31=16 Exploring Operation: 87-31=56, Resulting Numbers: [47, 56] Generated Node #0,1,2: 94:[47, 56] Operation: 87-31=56 Exploring Operation: 47+31=78, Resulting Numbers: [87, 78] Generated Node #0,1,3: 94:[87, 78] Operation: 47+31=78 Moving to Node #0,0 Current State: 94:[47, 81, 37], Operations: ['31+6=37'] Exploring Operation: 81-37=44, Resulting Numbers: [47, 44] Generated Node #0,0,0: 94:[47, 44] Operation: 81-37=44 Exploring Operation: 47-37=10, Resulting Numbers: [81, 10] Generated Node #0,0,1: 94:[81, 10] Operation: 47-37=10 Exploring Operation: 81-47=34, Resulting Numbers: [37, 34] Generated Node #0,0,2: 94:[37, 34] Operation: 81-47=34 Exploring Operation: 47+37=84, Resulting Numbers: [81, 84] Generated Node #0,0,3: 94:[81, 84] Operation: 47+37=84 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[47, 44], Operations: ['31+6=37', '81-37=44'] Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,94 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,94 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 #0,0,1 Current State: 94:[81, 10], Operations: ['31+6=37', '47-37=10'] Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,94 unequal: No Solution Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[37, 34], Operations: ['31+6=37', '81-47=34'] Exploring Operation: 37*34=1258, Resulting Numbers: [1258] 1258,94 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,94 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 #0,0,3 Current State: 94:[81, 84], Operations: ['31+6=37', '47+37=84'] Exploring Operation: 84-81=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 81+84=165, Resulting Numbers: [165] 165,94 unequal: No Solution Exploring Operation: 81*84=6804, Resulting Numbers: [6804] 6804,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 94:[47, 44], Operations: ['81-31=50', '50-6=44'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[6, 3], Operations: ['81-31=50', '50-47=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,94 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[6, 97], Operations: ['81-31=50', '47+50=97'] Exploring Operation: 6*97=582, Resulting Numbers: [582] 582,94 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 6+97=103, Resulting Numbers: [103] 103,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[47, 56], Operations: ['81+6=87', '87-31=56'] Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,94 unequal: No Solution Exploring Operation: 47*56=2632, Resulting Numbers: [2632] 2632,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[50, 53], Operations: ['81-31=50', '47+6=53'] Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,94 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[87, 16], Operations: ['81+6=87', '47-31=16'] Exploring Operation: 87*16=1392, Resulting Numbers: [1392] 1392,94 unequal: No Solution Exploring Operation: 87+16=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 87-16=71, Resulting Numbers: [71] 71,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[31, 40], Operations: ['81+6=87', '87-47=40'] Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,94 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,94 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[87, 78], Operations: ['81+6=87', '47+31=78'] Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,94 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,94 unequal: No Solution Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,94 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 28, 28, 4, 23 ]
12
[ "28/4=7", "28-23=5", "7+5=12" ]
Current State: 12:[28, 28, 4, 23], Operations: [] Exploring Operation: 28/4=7, Resulting Numbers: [23, 7] Generated Node #2: [23, 7] from Operation: 28/4=7 Current State: 12:[23, 7], Operations: ['28/4=7'] Exploring Operation: 28-23=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 28-23=5 Current State: 12:[7, 5], Operations: ['28/4=7', '28-23=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[28, 28, 4, 23], Operations: [] Exploring Operation: 28-28=0, Resulting Numbers: [4, 23, 0] Generated Node #0,0: 12:[4, 23, 0] Operation: 28-28=0 Exploring Operation: 28/28=1, Resulting Numbers: [4, 23, 1] Generated Node #0,1: 12:[4, 23, 1] Operation: 28/28=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[4, 23, 1], Operations: ['28/28=1'] Exploring Operation: 23-4=19, Resulting Numbers: [1, 19] Generated Node #0,1,0: 12:[1, 19] Operation: 23-4=19 Exploring Operation: 23-1=22, Resulting Numbers: [4, 22] Generated Node #0,1,1: 12:[4, 22] Operation: 23-1=22 Moving to Node #0,1,0 Current State: 12:[1, 19], Operations: ['28/28=1', '23-4=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[4, 22], Operations: ['28/28=1', '23-1=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,12 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:[4, 23, 0], Operations: ['28-28=0'] Exploring Operation: 23*0=0, Resulting Numbers: [4, 0] Generated Node #0,0,0: 12:[4, 0] Operation: 23*0=0 Exploring Operation: 23-4=19, Resulting Numbers: [0, 19] Generated Node #0,0,1: 12:[0, 19] Operation: 23-4=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[4, 0], Operations: ['28-28=0', '23*0=0'] Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,12 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:[0, 19], Operations: ['28-28=0', '23-4=19'] Exploring Operation: 0*19=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 0+19=19, Resulting Numbers: [19] 19,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 3, 95, 60, 45 ]
90
[ "95-45=50", "3*50=150", "150-60=90" ]
Current State: 90:[3, 95, 60, 45], Operations: [] Exploring Operation: 95-45=50, Resulting Numbers: [3, 60, 50] Generated Node #2: [3, 60, 50] from Operation: 95-45=50 Current State: 90:[3, 60, 50], Operations: ['95-45=50'] Exploring Operation: 3*50=150, Resulting Numbers: [60, 150] Generated Node #3: [60, 150] from Operation: 3*50=150 Current State: 90:[60, 150], Operations: ['95-45=50', '3*50=150'] Exploring Operation: 150-60=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[3, 95, 60, 45], Operations: [] Exploring Operation: 95-60=35, Resulting Numbers: [3, 45, 35] Generated Node #0,0: 90:[3, 45, 35] Operation: 95-60=35 Exploring Operation: 60/3=20, Resulting Numbers: [95, 45, 20] Generated Node #0,1: 90:[95, 45, 20] Operation: 60/3=20 Exploring Operation: 60-45=15, Resulting Numbers: [3, 95, 15] Generated Node #0,2: 90:[3, 95, 15] Operation: 60-45=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[3, 45, 35], Operations: ['95-60=35'] Exploring Operation: 35-3=32, Resulting Numbers: [45, 32] Generated Node #0,0,0: 90:[45, 32] Operation: 35-3=32 Exploring Operation: 45/3=15, Resulting Numbers: [35, 15] Generated Node #0,0,1: 90:[35, 15] Operation: 45/3=15 Exploring Operation: 45-35=10, Resulting Numbers: [3, 10] Generated Node #0,0,2: 90:[3, 10] Operation: 45-35=10 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[3, 10], Operations: ['95-60=35', '45-35=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,90 unequal: No Solution No 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: 90:[45, 32], Operations: ['95-60=35', '35-3=32'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,90 unequal: No Solution Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,90 unequal: No Solution No 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: 90:[35, 15], Operations: ['95-60=35', '45/3=15'] Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,90 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[3, 95, 15], Operations: ['60-45=15'] Exploring Operation: 95-3=92, Resulting Numbers: [15, 92] Generated Node #0,2,0: 90:[15, 92] Operation: 95-3=92 Exploring Operation: 3+15=18, Resulting Numbers: [95, 18] Generated Node #0,2,1: 90:[95, 18] Operation: 3+15=18 Exploring Operation: 3*15=45, Resulting Numbers: [95, 45] Generated Node #0,2,2: 90:[95, 45] Operation: 3*15=45 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[15, 92], Operations: ['60-45=15', '95-3=92'] Exploring Operation: 15*92=1380, Resulting Numbers: [1380] 1380,90 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,90 unequal: No Solution Exploring Operation: 15+92=107, Resulting Numbers: [107] 107,90 unequal: No Solution No 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: 90:[95, 18], Operations: ['60-45=15', '3+15=18'] Exploring Operation: 95+18=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 95*18=1710, Resulting Numbers: [1710] 1710,90 unequal: No Solution Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,90 unequal: No Solution No 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: 90:[95, 45], Operations: ['60-45=15', '3*15=45'] Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,90 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,90 unequal: No Solution Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[95, 45, 20], Operations: ['60/3=20'] Exploring Operation: 45-20=25, Resulting Numbers: [95, 25] Generated Node #0,1,0: 90:[95, 25] Operation: 45-20=25 Exploring Operation: 95-20=75, Resulting Numbers: [45, 75] Generated Node #0,1,1: 90:[45, 75] Operation: 95-20=75 Exploring Operation: 95-45=50, Resulting Numbers: [20, 50] Generated Node #0,1,2: 90:[20, 50] Operation: 95-45=50 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[20, 50], Operations: ['60/3=20', '95-45=50'] Exploring Operation: 20*50=1000, Resulting Numbers: [1000] 1000,90 unequal: No Solution Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 20+50=70, Resulting Numbers: [70] 70,90 unequal: No Solution No 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: 90:[95, 25], Operations: ['60/3=20', '45-20=25'] Exploring Operation: 95-25=70, Resulting Numbers: [70] 70,90 unequal: No Solution Exploring Operation: 95+25=120, Resulting Numbers: [120] 120,90 unequal: No Solution Exploring Operation: 95*25=2375, Resulting Numbers: [2375] 2375,90 unequal: No Solution No 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: 90:[45, 75], Operations: ['60/3=20', '95-20=75'] Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,90 unequal: No Solution Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 49, 87, 87, 84 ]
35
[ "49+87=136", "87+84=171", "171-136=35" ]
Current State: 35:[49, 87, 87, 84], Operations: [] Exploring Operation: 49+87=136, Resulting Numbers: [84, 136] Generated Node #2: [84, 136] from Operation: 49+87=136 Current State: 35:[84, 136], Operations: ['49+87=136'] Exploring Operation: 87+84=171, Resulting Numbers: [136, 171] Generated Node #3: [136, 171] from Operation: 87+84=171 Current State: 35:[136, 171], Operations: ['49+87=136', '87+84=171'] Exploring Operation: 171-136=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[49, 87, 87, 84], Operations: [] Exploring Operation: 87/87=1, Resulting Numbers: [49, 84, 1] Generated Node #0,0: 35:[49, 84, 1] Operation: 87/87=1 Moving to Node #0,0 Current State: 35:[49, 84, 1], Operations: ['87/87=1'] Exploring Operation: 84-49=35, Resulting Numbers: [1, 35] Generated Node #0,0,0: 35:[1, 35] Operation: 84-49=35 Moving to Node #0,0,0 Current State: 35:[1, 35], Operations: ['87/87=1', '84-49=35'] Exploring Operation: 1*35=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[49, 87, 87, 84], Operations: [] Exploring Operation: 87/87=1, Resulting Numbers: [49, 84, 1] Generated Node #0,0: 35:[49, 84, 1] Operation: 87/87=1 Moving to Node #0,0 Current State: 35:[49, 84, 1], Operations: ['87/87=1'] Exploring Operation: 84-49=35, Resulting Numbers: [1, 35] Generated Node #0,0,0: 35:[1, 35] Operation: 84-49=35 Moving to Node #0,0,0 Current State: 35:[1, 35], Operations: ['87/87=1', '84-49=35'] Exploring Operation: 1*35=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 91, 91, 70, 26 ]
26
[ "91-91=0", "70*0=0", "26+0=26" ]
Current State: 26:[91, 91, 70, 26], Operations: [] Exploring Operation: 91-91=0, Resulting Numbers: [70, 26, 0] Generated Node #2: [70, 26, 0] from Operation: 91-91=0 Current State: 26:[70, 26, 0], Operations: ['91-91=0'] Exploring Operation: 70*0=0, Resulting Numbers: [26, 0] Generated Node #3: [26, 0] from Operation: 70*0=0 Current State: 26:[26, 0], Operations: ['91-91=0', '70*0=0'] Exploring Operation: 26+0=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[91, 91, 70, 26], Operations: [] Exploring Operation: 91-26=65, Resulting Numbers: [91, 70, 65] Generated Node #0,0: 26:[91, 70, 65] Operation: 91-26=65 Exploring Operation: 91-91=0, Resulting Numbers: [70, 26, 0] Generated Node #0,1: 26:[70, 26, 0] Operation: 91-91=0 Exploring Operation: 91/91=1, Resulting Numbers: [70, 26, 1] Generated Node #0,2: 26:[70, 26, 1] Operation: 91/91=1 Exploring Operation: 91-70=21, Resulting Numbers: [91, 26, 21] Generated Node #0,3: 26:[91, 26, 21] Operation: 91-70=21 Exploring Operation: 91-70=21, Resulting Numbers: [91, 26, 21] Generated Node #0,4: 26:[91, 26, 21] Operation: 91-70=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[70, 26, 1], Operations: ['91/91=1'] Exploring Operation: 70-1=69, Resulting Numbers: [26, 69] Generated Node #0,2,0: 26:[26, 69] Operation: 70-1=69 Exploring Operation: 26*1=26, Resulting Numbers: [70, 26] Generated Node #0,2,1: 26:[70, 26] Operation: 26*1=26 Exploring Operation: 70-26=44, Resulting Numbers: [1, 44] Generated Node #0,2,2: 26:[1, 44] Operation: 70-26=44 Exploring Operation: 70/1=70, Resulting Numbers: [26, 70] Generated Node #0,2,3: 26:[26, 70] Operation: 70/1=70 Exploring Operation: 70*1=70, Resulting Numbers: [26, 70] Generated Node #0,2,4: 26:[26, 70] Operation: 70*1=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 26:[1, 44], Operations: ['91/91=1', '70-26=44'] Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,26 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,26 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 26:[26, 69], Operations: ['91/91=1', '70-1=69'] Exploring Operation: 26*69=1794, Resulting Numbers: [1794] 1794,26 unequal: No Solution Exploring Operation: 26+69=95, Resulting Numbers: [95] 95,26 unequal: No Solution Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 26:[70, 26], Operations: ['91/91=1', '26*1=26'] Exploring Operation: 70+26=96, Resulting Numbers: [96] 96,26 unequal: No Solution Exploring Operation: 70*26=1820, Resulting Numbers: [1820] 1820,26 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 26:[26, 70], Operations: ['91/91=1', '70/1=70'] Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,26 unequal: No Solution Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,26 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 26:[26, 70], Operations: ['91/91=1', '70*1=70'] Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,26 unequal: No Solution Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,26 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[70, 26, 0], Operations: ['91-91=0'] Exploring Operation: 70*0=0, Resulting Numbers: [26, 0] Generated Node #0,1,0: 26:[26, 0] Operation: 70*0=0 Exploring Operation: 70-0=70, Resulting Numbers: [26, 70] Generated Node #0,1,1: 26:[26, 70] Operation: 70-0=70 Exploring Operation: 70+0=70, Resulting Numbers: [26, 70] Generated Node #0,1,2: 26:[26, 70] Operation: 70+0=70 Exploring Operation: 26+0=26, Resulting Numbers: [70, 26] Generated Node #0,1,3: 26:[70, 26] Operation: 26+0=26 Exploring Operation: 70-26=44, Resulting Numbers: [0, 44] Generated Node #0,1,4: 26:[0, 44] Operation: 70-26=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 26:[26, 0], Operations: ['91-91=0', '70*0=0'] Exploring Operation: 26*0=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 26+0=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[91, 91, 70, 26], Operations: [] Exploring Operation: 91-91=0, Resulting Numbers: [70, 26, 0] Generated Node #0,1: 26:[70, 26, 0] Operation: 91-91=0 Moving to Node #0,1 Current State: 26:[70, 26, 0], Operations: ['91-91=0'] Exploring Operation: 70*0=0, Resulting Numbers: [26, 0] Generated Node #0,1,0: 26:[26, 0] Operation: 70*0=0 Moving to Node #0,1,0 Current State: 26:[26, 0], Operations: ['91-91=0', '70*0=0'] Exploring Operation: 26+0=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 84, 3, 77, 9 ]
21
[ "84-77=7", "9/3=3", "7*3=21" ]
Current State: 21:[84, 3, 77, 9], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [3, 9, 7] Generated Node #2: [3, 9, 7] from Operation: 84-77=7 Current State: 21:[3, 9, 7], Operations: ['84-77=7'] Exploring Operation: 9/3=3, Resulting Numbers: [7, 3] Generated Node #3: [7, 3] from Operation: 9/3=3 Current State: 21:[7, 3], Operations: ['84-77=7', '9/3=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[84, 3, 77, 9], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [3, 9, 7] Generated Node #0,0: 21:[3, 9, 7] Operation: 84-77=7 Exploring Operation: 77-9=68, Resulting Numbers: [84, 3, 68] Generated Node #0,1: 21:[84, 3, 68] Operation: 77-9=68 Exploring Operation: 84/3=28, Resulting Numbers: [77, 9, 28] Generated Node #0,2: 21:[77, 9, 28] Operation: 84/3=28 Exploring Operation: 84-9=75, Resulting Numbers: [3, 77, 75] Generated Node #0,3: 21:[3, 77, 75] Operation: 84-9=75 Moving to Node #0,0 Current State: 21:[3, 9, 7], Operations: ['84-77=7'] Exploring Operation: 3*7=21, Resulting Numbers: [9, 21] Generated Node #0,0,0: 21:[9, 21] Operation: 3*7=21 Exploring Operation: 9/3=3, Resulting Numbers: [7, 3] Generated Node #0,0,1: 21:[7, 3] Operation: 9/3=3 Exploring Operation: 9-3=6, Resulting Numbers: [7, 6] Generated Node #0,0,2: 21:[7, 6] Operation: 9-3=6 Exploring Operation: 9-7=2, Resulting Numbers: [3, 2] Generated Node #0,0,3: 21:[3, 2] Operation: 9-7=2 Moving to Node #0,2 Current State: 21:[77, 9, 28], Operations: ['84/3=28'] Exploring Operation: 77-9=68, Resulting Numbers: [28, 68] Generated Node #0,2,0: 21:[28, 68] Operation: 77-9=68 Exploring Operation: 28-9=19, Resulting Numbers: [77, 19] Generated Node #0,2,1: 21:[77, 19] Operation: 28-9=19 Exploring Operation: 77-28=49, Resulting Numbers: [9, 49] Generated Node #0,2,2: 21:[9, 49] Operation: 77-28=49 Exploring Operation: 77+9=86, Resulting Numbers: [28, 86] Generated Node #0,2,3: 21:[28, 86] Operation: 77+9=86 Moving to Node #0,3 Current State: 21:[3, 77, 75], Operations: ['84-9=75'] Exploring Operation: 77-75=2, Resulting Numbers: [3, 2] Generated Node #0,3,0: 21:[3, 2] Operation: 77-75=2 Exploring Operation: 75-3=72, Resulting Numbers: [77, 72] Generated Node #0,3,1: 21:[77, 72] Operation: 75-3=72 Exploring Operation: 77-3=74, Resulting Numbers: [75, 74] Generated Node #0,3,2: 21:[75, 74] Operation: 77-3=74 Exploring Operation: 75/3=25, Resulting Numbers: [77, 25] Generated Node #0,3,3: 21:[77, 25] Operation: 75/3=25 Moving to Node #0,1 Current State: 21:[84, 3, 68], Operations: ['77-9=68'] Exploring Operation: 84/3=28, Resulting Numbers: [68, 28] Generated Node #0,1,0: 21:[68, 28] Operation: 84/3=28 Exploring Operation: 68-3=65, Resulting Numbers: [84, 65] Generated Node #0,1,1: 21:[84, 65] Operation: 68-3=65 Exploring Operation: 84-3=81, Resulting Numbers: [68, 81] Generated Node #0,1,2: 21:[68, 81] Operation: 84-3=81 Exploring Operation: 84-68=16, Resulting Numbers: [3, 16] Generated Node #0,1,3: 21:[3, 16] Operation: 84-68=16 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 21:[3, 16], Operations: ['77-9=68', '84-68=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[68, 28], Operations: ['77-9=68', '84/3=28'] Exploring Operation: 68*28=1904, Resulting Numbers: [1904] 1904,21 unequal: No Solution Exploring Operation: 68+28=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,21 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:[84, 65], Operations: ['77-9=68', '68-3=65'] Exploring Operation: 84-65=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 84*65=5460, Resulting Numbers: [5460] 5460,21 unequal: No Solution Exploring Operation: 84+65=149, Resulting Numbers: [149] 149,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[68, 81], Operations: ['77-9=68', '84-3=81'] Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,21 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,21 unequal: No Solution Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,21 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: 21:[7, 3], Operations: ['84-77=7', '9/3=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[84, 3, 77, 9], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [3, 9, 7] Generated Node #0,0: 21:[3, 9, 7] Operation: 84-77=7 Moving to Node #0,0 Current State: 21:[3, 9, 7], Operations: ['84-77=7'] Exploring Operation: 9/3=3, Resulting Numbers: [7, 3] Generated Node #0,0,1: 21:[7, 3] Operation: 9/3=3 Moving to Node #0,0,1 Current State: 21:[7, 3], Operations: ['84-77=7', '9/3=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 54, 38, 51, 58 ]
52
[ "58-54=4", "51-38=13", "4*13=52" ]
Current State: 52:[54, 38, 51, 58], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [38, 51, 4] Generated Node #2: [38, 51, 4] from Operation: 58-54=4 Current State: 52:[38, 51, 4], Operations: ['58-54=4'] Exploring Operation: 51-38=13, Resulting Numbers: [4, 13] Generated Node #3: [4, 13] from Operation: 51-38=13 Current State: 52:[4, 13], Operations: ['58-54=4', '51-38=13'] Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[54, 38, 51, 58], Operations: [] Exploring Operation: 54-38=16, Resulting Numbers: [51, 58, 16] Generated Node #0,0: 52:[51, 58, 16] Operation: 54-38=16 Exploring Operation: 58-54=4, Resulting Numbers: [38, 51, 4] Generated Node #0,1: 52:[38, 51, 4] Operation: 58-54=4 Exploring Operation: 51-38=13, Resulting Numbers: [54, 58, 13] Generated Node #0,2: 52:[54, 58, 13] Operation: 51-38=13 Exploring Operation: 58-38=20, Resulting Numbers: [54, 51, 20] Generated Node #0,3: 52:[54, 51, 20] Operation: 58-38=20 Moving to Node #0,2 Current State: 52:[54, 58, 13], Operations: ['51-38=13'] Exploring Operation: 58-54=4, Resulting Numbers: [13, 4] Generated Node #0,2,0: 52:[13, 4] Operation: 58-54=4 Exploring Operation: 54-13=41, Resulting Numbers: [58, 41] Generated Node #0,2,1: 52:[58, 41] Operation: 54-13=41 Exploring Operation: 54+13=67, Resulting Numbers: [58, 67] Generated Node #0,2,2: 52:[58, 67] Operation: 54+13=67 Exploring Operation: 58-13=45, Resulting Numbers: [54, 45] Generated Node #0,2,3: 52:[54, 45] Operation: 58-13=45 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[13, 4], Operations: ['51-38=13', '58-54=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[54, 38, 51, 58], Operations: [] Exploring Operation: 51-38=13, Resulting Numbers: [54, 58, 13] Generated Node #0,2: 52:[54, 58, 13] Operation: 51-38=13 Moving to Node #0,2 Current State: 52:[54, 58, 13], Operations: ['51-38=13'] Exploring Operation: 58-54=4, Resulting Numbers: [13, 4] Generated Node #0,2,0: 52:[13, 4] Operation: 58-54=4 Moving to Node #0,2,0 Current State: 52:[13, 4], Operations: ['51-38=13', '58-54=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 45, 85, 31, 60 ]
51
[ "85-45=40", "31+60=91", "91-40=51" ]
Current State: 51:[45, 85, 31, 60], Operations: [] Exploring Operation: 85-45=40, Resulting Numbers: [31, 60, 40] Generated Node #2: [31, 60, 40] from Operation: 85-45=40 Current State: 51:[31, 60, 40], Operations: ['85-45=40'] Exploring Operation: 31+60=91, Resulting Numbers: [40, 91] Generated Node #3: [40, 91] from Operation: 31+60=91 Current State: 51:[40, 91], Operations: ['85-45=40', '31+60=91'] Exploring Operation: 91-40=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[45, 85, 31, 60], Operations: [] Exploring Operation: 85-60=25, Resulting Numbers: [45, 31, 25] Generated Node #0,0: 51:[45, 31, 25] Operation: 85-60=25 Exploring Operation: 85-31=54, Resulting Numbers: [45, 60, 54] Generated Node #0,1: 51:[45, 60, 54] Operation: 85-31=54 Exploring Operation: 45-31=14, Resulting Numbers: [85, 60, 14] Generated Node #0,2: 51:[85, 60, 14] Operation: 45-31=14 Exploring Operation: 85-45=40, Resulting Numbers: [31, 60, 40] Generated Node #0,3: 51:[31, 60, 40] Operation: 85-45=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[45, 60, 54], Operations: ['85-31=54'] Exploring Operation: 54-45=9, Resulting Numbers: [60, 9] Generated Node #0,1,0: 51:[60, 9] Operation: 54-45=9 Exploring Operation: 60-45=15, Resulting Numbers: [54, 15] Generated Node #0,1,1: 51:[54, 15] Operation: 60-45=15 Exploring Operation: 45+60=105, Resulting Numbers: [54, 105] Generated Node #0,1,2: 51:[54, 105] Operation: 45+60=105 Exploring Operation: 60-54=6, Resulting Numbers: [45, 6] Generated Node #0,1,3: 51:[45, 6] Operation: 60-54=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[54, 15], Operations: ['85-31=54', '60-45=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,51 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,51 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 #0,1,3 Current State: 51:[45, 6], Operations: ['85-31=54', '60-54=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,51 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[45, 85, 31, 60], Operations: [] Exploring Operation: 85-31=54, Resulting Numbers: [45, 60, 54] Generated Node #0,1: 51:[45, 60, 54] Operation: 85-31=54 Moving to Node #0,1 Current State: 51:[45, 60, 54], Operations: ['85-31=54'] Exploring Operation: 60-54=6, Resulting Numbers: [45, 6] Generated Node #0,1,3: 51:[45, 6] Operation: 60-54=6 Moving to Node #0,1,3 Current State: 51:[45, 6], Operations: ['85-31=54', '60-54=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 70, 9, 54, 90 ]
72
[ "54-9=45", "90/45=2", "70+2=72" ]
Current State: 72:[70, 9, 54, 90], Operations: [] Exploring Operation: 54-9=45, Resulting Numbers: [70, 90, 45] Generated Node #2: [70, 90, 45] from Operation: 54-9=45 Current State: 72:[70, 90, 45], Operations: ['54-9=45'] Exploring Operation: 90/45=2, Resulting Numbers: [70, 2] Generated Node #3: [70, 2] from Operation: 90/45=2 Current State: 72:[70, 2], Operations: ['54-9=45', '90/45=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[70, 9, 54, 90], Operations: [] Exploring Operation: 70-54=16, Resulting Numbers: [9, 90, 16] Generated Node #0,0: 72:[9, 90, 16] Operation: 70-54=16 Exploring Operation: 90-54=36, Resulting Numbers: [70, 9, 36] Generated Node #0,1: 72:[70, 9, 36] Operation: 90-54=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[70, 9, 36], Operations: ['90-54=36'] Exploring Operation: 36/9=4, Resulting Numbers: [70, 4] Generated Node #0,1,0: 72:[70, 4] Operation: 36/9=4 Exploring Operation: 70-36=34, Resulting Numbers: [9, 34] Generated Node #0,1,1: 72:[9, 34] Operation: 70-36=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[70, 4], Operations: ['90-54=36', '36/9=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,72 unequal: No Solution No 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: 72:[9, 34], Operations: ['90-54=36', '70-36=34'] Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,72 unequal: No Solution Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,72 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: 72:[9, 90, 16], Operations: ['70-54=16'] Exploring Operation: 90-16=74, Resulting Numbers: [9, 74] Generated Node #0,0,0: 72:[9, 74] Operation: 90-16=74 Exploring Operation: 90/9=10, Resulting Numbers: [16, 10] Generated Node #0,0,1: 72:[16, 10] Operation: 90/9=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[9, 74], Operations: ['70-54=16', '90-16=74'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,72 unequal: No Solution Exploring Operation: 9+74=83, Resulting Numbers: [83] 83,72 unequal: No Solution No 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: 72:[16, 10], Operations: ['70-54=16', '90/9=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic