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
[ 69, 69, 48, 97 ]
49
[ "69-69=0", "97-48=49", "0+49=49" ]
Current State: 49:[69, 69, 48, 97], Operations: [] Exploring Operation: 69-69=0, Resulting Numbers: [48, 97, 0] Generated Node #2: [48, 97, 0] from Operation: 69-69=0 Current State: 49:[48, 97, 0], Operations: ['69-69=0'] Exploring Operation: 97-48=49, Resulting Numbers: [0, 49] Generated Node #3: [0, 49] from Operation: 97-48=49 Current State: 49:[0, 49], Operations: ['69-69=0', '97-48=49'] Exploring Operation: 0+49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[69, 69, 48, 97], Operations: [] Exploring Operation: 97-48=49, Resulting Numbers: [69, 69, 49] Generated Node #0,0: 49:[69, 69, 49] Operation: 97-48=49 Exploring Operation: 97-69=28, Resulting Numbers: [69, 48, 28] Generated Node #0,1: 49:[69, 48, 28] Operation: 97-69=28 Exploring Operation: 69/69=1, Resulting Numbers: [48, 97, 1] Generated Node #0,2: 49:[48, 97, 1] Operation: 69/69=1 Exploring Operation: 97-69=28, Resulting Numbers: [69, 48, 28] Generated Node #0,3: 49:[69, 48, 28] Operation: 97-69=28 Exploring Operation: 69-69=0, Resulting Numbers: [48, 97, 0] Generated Node #0,4: 49:[48, 97, 0] Operation: 69-69=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[69, 69, 49], Operations: ['97-48=49'] Exploring Operation: 69+69=138, Resulting Numbers: [49, 138] Generated Node #0,0,0: 49:[49, 138] Operation: 69+69=138 Exploring Operation: 69-49=20, Resulting Numbers: [69, 20] Generated Node #0,0,1: 49:[69, 20] Operation: 69-49=20 Exploring Operation: 69/69=1, Resulting Numbers: [49, 1] Generated Node #0,0,2: 49:[49, 1] Operation: 69/69=1 Exploring Operation: 69-49=20, Resulting Numbers: [69, 20] Generated Node #0,0,3: 49:[69, 20] Operation: 69-49=20 Exploring Operation: 69-69=0, Resulting Numbers: [49, 0] Generated Node #0,0,4: 49:[49, 0] Operation: 69-69=0 Moving to Node #0,0,2 Current State: 49:[49, 1], Operations: ['97-48=49', '69/69=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[69, 69, 48, 97], Operations: [] Exploring Operation: 97-48=49, Resulting Numbers: [69, 69, 49] Generated Node #0,0: 49:[69, 69, 49] Operation: 97-48=49 Moving to Node #0,0 Current State: 49:[69, 69, 49], Operations: ['97-48=49'] Exploring Operation: 69/69=1, Resulting Numbers: [49, 1] Generated Node #0,0,2: 49:[49, 1] Operation: 69/69=1 Moving to Node #0,0,2 Current State: 49:[49, 1], Operations: ['97-48=49', '69/69=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 43, 43, 2, 77 ]
11
[ "43+43=86", "77-2=75", "86-75=11" ]
Current State: 11:[43, 43, 2, 77], Operations: [] Exploring Operation: 43+43=86, Resulting Numbers: [2, 77, 86] Generated Node #2: [2, 77, 86] from Operation: 43+43=86 Current State: 11:[2, 77, 86], Operations: ['43+43=86'] Exploring Operation: 77-2=75, Resulting Numbers: [86, 75] Generated Node #3: [86, 75] from Operation: 77-2=75 Current State: 11:[86, 75], Operations: ['43+43=86', '77-2=75'] Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[43, 43, 2, 77], Operations: [] Exploring Operation: 43/43=1, Resulting Numbers: [2, 77, 1] Generated Node #0,0: 11:[2, 77, 1] Operation: 43/43=1 Exploring Operation: 77-43=34, Resulting Numbers: [43, 2, 34] Generated Node #0,1: 11:[43, 2, 34] Operation: 77-43=34 Exploring Operation: 77-43=34, Resulting Numbers: [43, 2, 34] Generated Node #0,2: 11:[43, 2, 34] Operation: 77-43=34 Moving to Node #0,1 Current State: 11:[43, 2, 34], Operations: ['77-43=34'] Exploring Operation: 43-2=41, Resulting Numbers: [34, 41] Generated Node #0,1,0: 11:[34, 41] Operation: 43-2=41 Exploring Operation: 34/2=17, Resulting Numbers: [43, 17] Generated Node #0,1,1: 11:[43, 17] Operation: 34/2=17 Exploring Operation: 43-34=9, Resulting Numbers: [2, 9] Generated Node #0,1,2: 11:[2, 9] Operation: 43-34=9 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[2, 9], Operations: ['77-43=34', '43-34=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[43, 43, 2, 77], Operations: [] Exploring Operation: 77-43=34, Resulting Numbers: [43, 2, 34] Generated Node #0,1: 11:[43, 2, 34] Operation: 77-43=34 Moving to Node #0,1 Current State: 11:[43, 2, 34], Operations: ['77-43=34'] Exploring Operation: 43-34=9, Resulting Numbers: [2, 9] Generated Node #0,1,2: 11:[2, 9] Operation: 43-34=9 Moving to Node #0,1,2 Current State: 11:[2, 9], Operations: ['77-43=34', '43-34=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 14, 26, 28, 31 ]
88
[ "28/14=2", "31*2=62", "26+62=88" ]
Current State: 88:[14, 26, 28, 31], Operations: [] Exploring Operation: 28/14=2, Resulting Numbers: [26, 31, 2] Generated Node #2: [26, 31, 2] from Operation: 28/14=2 Current State: 88:[26, 31, 2], Operations: ['28/14=2'] Exploring Operation: 31*2=62, Resulting Numbers: [26, 62] Generated Node #3: [26, 62] from Operation: 31*2=62 Current State: 88:[26, 62], Operations: ['28/14=2', '31*2=62'] Exploring Operation: 26+62=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[14, 26, 28, 31], Operations: [] Exploring Operation: 14+31=45, Resulting Numbers: [26, 28, 45] Generated Node #0,0: 88:[26, 28, 45] Operation: 14+31=45 Exploring Operation: 28-26=2, Resulting Numbers: [14, 31, 2] Generated Node #0,1: 88:[14, 31, 2] Operation: 28-26=2 Exploring Operation: 31-28=3, Resulting Numbers: [14, 26, 3] Generated Node #0,2: 88:[14, 26, 3] Operation: 31-28=3 Exploring Operation: 31-26=5, Resulting Numbers: [14, 28, 5] Generated Node #0,3: 88:[14, 28, 5] Operation: 31-26=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[14, 26, 3], Operations: ['31-28=3'] Exploring Operation: 14+26=40, Resulting Numbers: [3, 40] Generated Node #0,2,0: 88:[3, 40] Operation: 14+26=40 Exploring Operation: 26-3=23, Resulting Numbers: [14, 23] Generated Node #0,2,1: 88:[14, 23] Operation: 26-3=23 Exploring Operation: 14-3=11, Resulting Numbers: [26, 11] Generated Node #0,2,2: 88:[26, 11] Operation: 14-3=11 Exploring Operation: 26-14=12, Resulting Numbers: [3, 12] Generated Node #0,2,3: 88:[3, 12] Operation: 26-14=12 Moving to Node #0,2,3 Current State: 88:[3, 12], Operations: ['31-28=3', '26-14=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,88 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[26, 11], Operations: ['31-28=3', '14-3=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,88 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[14, 23], Operations: ['31-28=3', '26-3=23'] Exploring Operation: 14*23=322, Resulting Numbers: [322] 322,88 unequal: No Solution Exploring Operation: 14+23=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[3, 40], Operations: ['31-28=3', '14+26=40'] Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[14, 28, 5], Operations: ['31-26=5'] Exploring Operation: 28-5=23, Resulting Numbers: [14, 23] Generated Node #0,3,0: 88:[14, 23] Operation: 28-5=23 Exploring Operation: 14+28=42, Resulting Numbers: [5, 42] Generated Node #0,3,1: 88:[5, 42] Operation: 14+28=42 Exploring Operation: 28-14=14, Resulting Numbers: [5, 14] Generated Node #0,3,2: 88:[5, 14] Operation: 28-14=14 Exploring Operation: 28/14=2, Resulting Numbers: [5, 2] Generated Node #0,3,3: 88:[5, 2] Operation: 28/14=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[5, 2], Operations: ['31-26=5', '28/14=2'] Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[5, 42], Operations: ['31-26=5', '14+28=42'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 5*42=210, Resulting Numbers: [210] 210,88 unequal: No Solution Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[14, 23], Operations: ['31-26=5', '28-5=23'] Exploring Operation: 14*23=322, Resulting Numbers: [322] 322,88 unequal: No Solution Exploring Operation: 14+23=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[5, 14], Operations: ['31-26=5', '28-14=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,88 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[26, 28, 45], Operations: ['14+31=45'] Exploring Operation: 45-26=19, Resulting Numbers: [28, 19] Generated Node #0,0,0: 88:[28, 19] Operation: 45-26=19 Exploring Operation: 26+28=54, Resulting Numbers: [45, 54] Generated Node #0,0,1: 88:[45, 54] Operation: 26+28=54 Exploring Operation: 45-28=17, Resulting Numbers: [26, 17] Generated Node #0,0,2: 88:[26, 17] Operation: 45-28=17 Exploring Operation: 28-26=2, Resulting Numbers: [45, 2] Generated Node #0,0,3: 88:[45, 2] Operation: 28-26=2 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[45, 2], Operations: ['14+31=45', '28-26=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[28, 19], Operations: ['14+31=45', '45-26=19'] Exploring Operation: 28*19=532, Resulting Numbers: [532] 532,88 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 28+19=47, Resulting Numbers: [47] 47,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[26, 17], Operations: ['14+31=45', '45-28=17'] Exploring Operation: 26+17=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 26*17=442, Resulting Numbers: [442] 442,88 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[45, 54], Operations: ['14+31=45', '26+28=54'] Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,88 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[14, 31, 2], Operations: ['28-26=2'] Exploring Operation: 14-2=12, Resulting Numbers: [31, 12] Generated Node #0,1,0: 88:[31, 12] Operation: 14-2=12 Exploring Operation: 31-14=17, Resulting Numbers: [2, 17] Generated Node #0,1,1: 88:[2, 17] Operation: 31-14=17 Exploring Operation: 14+31=45, Resulting Numbers: [2, 45] Generated Node #0,1,2: 88:[2, 45] Operation: 14+31=45 Exploring Operation: 14/2=7, Resulting Numbers: [31, 7] Generated Node #0,1,3: 88:[31, 7] Operation: 14/2=7 Moving to Node #0,1,2 Current State: 88:[2, 45], Operations: ['28-26=2', '14+31=45'] Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[2, 17], Operations: ['28-26=2', '31-14=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[31, 7], Operations: ['28-26=2', '14/2=7'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[31, 12], Operations: ['28-26=2', '14-2=12'] Exploring Operation: 31*12=372, Resulting Numbers: [372] 372,88 unequal: No Solution Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,88 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
[ 48, 28, 32, 56 ]
98
[ "48*28=1344", "1344/32=42", "56+42=98" ]
Current State: 98:[48, 28, 32, 56], Operations: [] Exploring Operation: 48*28=1344, Resulting Numbers: [32, 56, 1344] Generated Node #2: [32, 56, 1344] from Operation: 48*28=1344 Current State: 98:[32, 56, 1344], Operations: ['48*28=1344'] Exploring Operation: 1344/32=42, Resulting Numbers: [56, 42] Generated Node #3: [56, 42] from Operation: 1344/32=42 Current State: 98:[56, 42], Operations: ['48*28=1344', '1344/32=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[48, 28, 32, 56], Operations: [] Exploring Operation: 32-28=4, Resulting Numbers: [48, 56, 4] Generated Node #0,0: 98:[48, 56, 4] Operation: 32-28=4 Exploring Operation: 56/28=2, Resulting Numbers: [48, 32, 2] Generated Node #0,1: 98:[48, 32, 2] Operation: 56/28=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[48, 56, 4], Operations: ['32-28=4'] Exploring Operation: 56/4=14, Resulting Numbers: [48, 14] Generated Node #0,0,0: 98:[48, 14] Operation: 56/4=14 Exploring Operation: 56-48=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 98:[4, 8] Operation: 56-48=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[48, 14], Operations: ['32-28=4', '56/4=14'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,98 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[4, 8], Operations: ['32-28=4', '56-48=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,98 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[48, 32, 2], Operations: ['56/28=2'] Exploring Operation: 32/2=16, Resulting Numbers: [48, 16] Generated Node #0,1,0: 98:[48, 16] Operation: 32/2=16 Exploring Operation: 48-32=16, Resulting Numbers: [2, 16] Generated Node #0,1,1: 98:[2, 16] Operation: 48-32=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[2, 16], Operations: ['56/28=2', '48-32=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[48, 16], Operations: ['56/28=2', '32/2=16'] Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 48+16=64, Resulting Numbers: [64] 64,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 20, 2, 50, 39 ]
49
[ "20*2=40", "50+39=89", "89-40=49" ]
Current State: 49:[20, 2, 50, 39], Operations: [] Exploring Operation: 20*2=40, Resulting Numbers: [50, 39, 40] Generated Node #2: [50, 39, 40] from Operation: 20*2=40 Current State: 49:[50, 39, 40], Operations: ['20*2=40'] Exploring Operation: 50+39=89, Resulting Numbers: [40, 89] Generated Node #3: [40, 89] from Operation: 50+39=89 Current State: 49:[40, 89], Operations: ['20*2=40', '50+39=89'] Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[20, 2, 50, 39], Operations: [] Exploring Operation: 20/2=10, Resulting Numbers: [50, 39, 10] Generated Node #0,0: 49:[50, 39, 10] Operation: 20/2=10 Exploring Operation: 20+39=59, Resulting Numbers: [2, 50, 59] Generated Node #0,1: 49:[2, 50, 59] Operation: 20+39=59 Exploring Operation: 39-20=19, Resulting Numbers: [2, 50, 19] Generated Node #0,2: 49:[2, 50, 19] Operation: 39-20=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[50, 39, 10], Operations: ['20/2=10'] Exploring Operation: 39+10=49, Resulting Numbers: [50, 49] Generated Node #0,0,0: 49:[50, 49] Operation: 39+10=49 Exploring Operation: 50-39=11, Resulting Numbers: [10, 11] Generated Node #0,0,1: 49:[10, 11] Operation: 50-39=11 Exploring Operation: 50/10=5, Resulting Numbers: [39, 5] Generated Node #0,0,2: 49:[39, 5] Operation: 50/10=5 Moving to Node #0,0,0 Current State: 49:[50, 49], Operations: ['20/2=10', '39+10=49'] Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 50+49=99, Resulting Numbers: [99] 99,49 unequal: No Solution Exploring Operation: 50*49=2450, Resulting Numbers: [2450] 2450,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[10, 11], Operations: ['20/2=10', '50-39=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,49 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[39, 5], Operations: ['20/2=10', '50/10=5'] Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,49 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,49 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[2, 50, 59], Operations: ['20+39=59'] Exploring Operation: 59-2=57, Resulting Numbers: [50, 57] Generated Node #0,1,0: 49:[50, 57] Operation: 59-2=57 Exploring Operation: 59-50=9, Resulting Numbers: [2, 9] Generated Node #0,1,1: 49:[2, 9] Operation: 59-50=9 Exploring Operation: 50-2=48, Resulting Numbers: [59, 48] Generated Node #0,1,2: 49:[59, 48] Operation: 50-2=48 Moving to Node #0,1,1 Current State: 49:[2, 9], Operations: ['20+39=59', '59-50=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[50, 57], Operations: ['20+39=59', '59-2=57'] Exploring Operation: 50+57=107, Resulting Numbers: [107] 107,49 unequal: No Solution Exploring Operation: 57-50=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 50*57=2850, Resulting Numbers: [2850] 2850,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[59, 48], Operations: ['20+39=59', '50-2=48'] Exploring Operation: 59-48=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 59*48=2832, Resulting Numbers: [2832] 2832,49 unequal: No Solution Exploring Operation: 59+48=107, Resulting Numbers: [107] 107,49 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 #0,2 Current State: 49:[2, 50, 19], Operations: ['39-20=19'] Exploring Operation: 2*19=38, Resulting Numbers: [50, 38] Generated Node #0,2,0: 49:[50, 38] Operation: 2*19=38 Exploring Operation: 50-2=48, Resulting Numbers: [19, 48] Generated Node #0,2,1: 49:[19, 48] Operation: 50-2=48 Exploring Operation: 19-2=17, Resulting Numbers: [50, 17] Generated Node #0,2,2: 49:[50, 17] Operation: 19-2=17 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 49:[50, 17], Operations: ['39-20=19', '19-2=17'] Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,49 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,49 unequal: No Solution No 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: 49:[50, 38], Operations: ['39-20=19', '2*19=38'] Exploring Operation: 50*38=1900, Resulting Numbers: [1900] 1900,49 unequal: No Solution Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,49 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,49 unequal: No Solution No 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: 49:[19, 48], Operations: ['39-20=19', '50-2=48'] Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 19*48=912, Resulting Numbers: [912] 912,49 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 51, 44, 62, 61 ]
96
[ "51+44=95", "62-61=1", "95+1=96" ]
Current State: 96:[51, 44, 62, 61], Operations: [] Exploring Operation: 51+44=95, Resulting Numbers: [62, 61, 95] Generated Node #2: [62, 61, 95] from Operation: 51+44=95 Current State: 96:[62, 61, 95], Operations: ['51+44=95'] Exploring Operation: 62-61=1, Resulting Numbers: [95, 1] Generated Node #3: [95, 1] from Operation: 62-61=1 Current State: 96:[95, 1], Operations: ['51+44=95', '62-61=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[51, 44, 62, 61], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [51, 44, 1] Generated Node #0,0: 96:[51, 44, 1] Operation: 62-61=1 Exploring Operation: 62-51=11, Resulting Numbers: [44, 61, 11] Generated Node #0,1: 96:[44, 61, 11] Operation: 62-51=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[51, 44, 1], Operations: ['62-61=1'] Exploring Operation: 51+44=95, Resulting Numbers: [1, 95] Generated Node #0,0,0: 96:[1, 95] Operation: 51+44=95 Exploring Operation: 51-44=7, Resulting Numbers: [1, 7] Generated Node #0,0,1: 96:[1, 7] Operation: 51-44=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[1, 95], Operations: ['62-61=1', '51+44=95'] Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[51, 44, 62, 61], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [51, 44, 1] Generated Node #0,0: 96:[51, 44, 1] Operation: 62-61=1 Moving to Node #0,0 Current State: 96:[51, 44, 1], Operations: ['62-61=1'] Exploring Operation: 51+44=95, Resulting Numbers: [1, 95] Generated Node #0,0,0: 96:[1, 95] Operation: 51+44=95 Moving to Node #0,0,0 Current State: 96:[1, 95], Operations: ['62-61=1', '51+44=95'] Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 98, 3, 77, 67 ]
85
[ "98-3=95", "77-67=10", "95-10=85" ]
Current State: 85:[98, 3, 77, 67], Operations: [] Exploring Operation: 98-3=95, Resulting Numbers: [77, 67, 95] Generated Node #2: [77, 67, 95] from Operation: 98-3=95 Current State: 85:[77, 67, 95], Operations: ['98-3=95'] Exploring Operation: 77-67=10, Resulting Numbers: [95, 10] Generated Node #3: [95, 10] from Operation: 77-67=10 Current State: 85:[95, 10], Operations: ['98-3=95', '77-67=10'] Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[98, 3, 77, 67], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [98, 3, 10] Generated Node #0,0: 85:[98, 3, 10] Operation: 77-67=10 Moving to Node #0,0 Current State: 85:[98, 3, 10], Operations: ['77-67=10'] Exploring Operation: 98-10=88, Resulting Numbers: [3, 88] Generated Node #0,0,0: 85:[3, 88] Operation: 98-10=88 Moving to Node #0,0,0 Current State: 85:[3, 88], Operations: ['77-67=10', '98-10=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[98, 3, 77, 67], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [98, 3, 10] Generated Node #0,0: 85:[98, 3, 10] Operation: 77-67=10 Moving to Node #0,0 Current State: 85:[98, 3, 10], Operations: ['77-67=10'] Exploring Operation: 98-10=88, Resulting Numbers: [3, 88] Generated Node #0,0,0: 85:[3, 88] Operation: 98-10=88 Moving to Node #0,0,0 Current State: 85:[3, 88], Operations: ['77-67=10', '98-10=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 90, 18, 67, 6 ]
67
[ "90/18=5", "6-5=1", "67*1=67" ]
Current State: 67:[90, 18, 67, 6], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [67, 6, 5] Generated Node #2: [67, 6, 5] from Operation: 90/18=5 Current State: 67:[67, 6, 5], Operations: ['90/18=5'] Exploring Operation: 6-5=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 6-5=1 Current State: 67:[67, 1], Operations: ['90/18=5', '6-5=1'] Exploring Operation: 67*1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[90, 18, 67, 6], Operations: [] Exploring Operation: 18*6=108, Resulting Numbers: [90, 67, 108] Generated Node #0,0: 67:[90, 67, 108] Operation: 18*6=108 Exploring Operation: 90-18=72, Resulting Numbers: [67, 6, 72] Generated Node #0,1: 67:[67, 6, 72] Operation: 90-18=72 Moving to Node #0,0 Current State: 67:[90, 67, 108], Operations: ['18*6=108'] Exploring Operation: 108-67=41, Resulting Numbers: [90, 41] Generated Node #0,0,0: 67:[90, 41] Operation: 108-67=41 Exploring Operation: 108-90=18, Resulting Numbers: [67, 18] Generated Node #0,0,1: 67:[67, 18] Operation: 108-90=18 Moving to Node #0,1 Current State: 67:[67, 6, 72], Operations: ['90-18=72'] Exploring Operation: 72-6=66, Resulting Numbers: [67, 66] Generated Node #0,1,0: 67:[67, 66] Operation: 72-6=66 Exploring Operation: 67+6=73, Resulting Numbers: [72, 73] Generated Node #0,1,1: 67:[72, 73] Operation: 67+6=73 Moving to Node #0,1,0 Current State: 67:[67, 66], Operations: ['90-18=72', '72-6=66'] Exploring Operation: 67-66=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 67+66=133, Resulting Numbers: [133] 133,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[72, 73], Operations: ['90-18=72', '67+6=73'] Exploring Operation: 73-72=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 72+73=145, Resulting Numbers: [145] 145,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[67, 18], Operations: ['18*6=108', '108-90=18'] Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,67 unequal: No Solution Exploring Operation: 67+18=85, Resulting Numbers: [85] 85,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[90, 41], Operations: ['18*6=108', '108-67=41'] Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,67 unequal: No Solution Exploring Operation: 90+41=131, Resulting Numbers: [131] 131,67 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 22, 36, 47, 28 ]
89
[ "36-22=14", "47+28=75", "14+75=89" ]
Current State: 89:[22, 36, 47, 28], Operations: [] Exploring Operation: 36-22=14, Resulting Numbers: [47, 28, 14] Generated Node #2: [47, 28, 14] from Operation: 36-22=14 Current State: 89:[47, 28, 14], Operations: ['36-22=14'] Exploring Operation: 47+28=75, Resulting Numbers: [14, 75] Generated Node #3: [14, 75] from Operation: 47+28=75 Current State: 89:[14, 75], Operations: ['36-22=14', '47+28=75'] Exploring Operation: 14+75=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[22, 36, 47, 28], Operations: [] Exploring Operation: 22+28=50, Resulting Numbers: [36, 47, 50] Generated Node #0,0: 89:[36, 47, 50] Operation: 22+28=50 Exploring Operation: 22+47=69, Resulting Numbers: [36, 28, 69] Generated Node #0,1: 89:[36, 28, 69] Operation: 22+47=69 Exploring Operation: 22+36=58, Resulting Numbers: [47, 28, 58] Generated Node #0,2: 89:[47, 28, 58] Operation: 22+36=58 Exploring Operation: 36+47=83, Resulting Numbers: [22, 28, 83] Generated Node #0,3: 89:[22, 28, 83] Operation: 36+47=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[36, 47, 50], Operations: ['22+28=50'] Exploring Operation: 36+47=83, Resulting Numbers: [50, 83] Generated Node #0,0,0: 89:[50, 83] Operation: 36+47=83 Exploring Operation: 36+50=86, Resulting Numbers: [47, 86] Generated Node #0,0,1: 89:[47, 86] Operation: 36+50=86 Exploring Operation: 47-36=11, Resulting Numbers: [50, 11] Generated Node #0,0,2: 89:[50, 11] Operation: 47-36=11 Exploring Operation: 47+50=97, Resulting Numbers: [36, 97] Generated Node #0,0,3: 89:[36, 97] Operation: 47+50=97 Moving to Node #0,0,0 Current State: 89:[50, 83], Operations: ['22+28=50', '36+47=83'] Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,89 unequal: No Solution Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[47, 86], Operations: ['22+28=50', '36+50=86'] Exploring Operation: 47*86=4042, Resulting Numbers: [4042] 4042,89 unequal: No Solution Exploring Operation: 47+86=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[36, 97], Operations: ['22+28=50', '47+50=97'] Exploring Operation: 36*97=3492, Resulting Numbers: [3492] 3492,89 unequal: No Solution Exploring Operation: 36+97=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[50, 11], Operations: ['22+28=50', '47-36=11'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 50*11=550, Resulting Numbers: [550] 550,89 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:[36, 28, 69], Operations: ['22+47=69'] Exploring Operation: 36-28=8, Resulting Numbers: [69, 8] Generated Node #0,1,0: 89:[69, 8] Operation: 36-28=8 Exploring Operation: 36+69=105, Resulting Numbers: [28, 105] Generated Node #0,1,1: 89:[28, 105] Operation: 36+69=105 Exploring Operation: 28+69=97, Resulting Numbers: [36, 97] Generated Node #0,1,2: 89:[36, 97] Operation: 28+69=97 Exploring Operation: 36+28=64, Resulting Numbers: [69, 64] Generated Node #0,1,3: 89:[69, 64] Operation: 36+28=64 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 89:[69, 64], Operations: ['22+47=69', '36+28=64'] Exploring Operation: 69+64=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 69*64=4416, Resulting Numbers: [4416] 4416,89 unequal: No Solution Exploring Operation: 69-64=5, Resulting Numbers: [5] 5,89 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:[36, 97], Operations: ['22+47=69', '28+69=97'] Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 36+97=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 36*97=3492, Resulting Numbers: [3492] 3492,89 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:[28, 105], Operations: ['22+47=69', '36+69=105'] Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,89 unequal: No Solution Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[69, 8], Operations: ['22+47=69', '36-28=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,89 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,89 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:[47, 28, 58], Operations: ['22+36=58'] Exploring Operation: 47+58=105, Resulting Numbers: [28, 105] Generated Node #0,2,0: 89:[28, 105] Operation: 47+58=105 Exploring Operation: 28+58=86, Resulting Numbers: [47, 86] Generated Node #0,2,1: 89:[47, 86] Operation: 28+58=86 Exploring Operation: 47-28=19, Resulting Numbers: [58, 19] Generated Node #0,2,2: 89:[58, 19] Operation: 47-28=19 Exploring Operation: 47+28=75, Resulting Numbers: [58, 75] Generated Node #0,2,3: 89:[58, 75] Operation: 47+28=75 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 89:[47, 86], Operations: ['22+36=58', '28+58=86'] Exploring Operation: 47+86=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 86-47=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 47*86=4042, Resulting Numbers: [4042] 4042,89 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 #0,2,3 Current State: 89:[58, 75], Operations: ['22+36=58', '47+28=75'] Exploring Operation: 58*75=4350, Resulting Numbers: [4350] 4350,89 unequal: No Solution Exploring Operation: 58+75=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,89 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 #0,2,0 Current State: 89:[28, 105], Operations: ['22+36=58', '47+58=105'] Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,89 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:[58, 19], Operations: ['22+36=58', '47-28=19'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,89 unequal: No Solution Exploring Operation: 58*19=1102, Resulting Numbers: [1102] 1102,89 unequal: No Solution Exploring Operation: 58+19=77, Resulting Numbers: [77] 77,89 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 #0,3 Current State: 89:[22, 28, 83], Operations: ['36+47=83'] Exploring Operation: 22+83=105, Resulting Numbers: [28, 105] Generated Node #0,3,0: 89:[28, 105] Operation: 22+83=105 Exploring Operation: 22+28=50, Resulting Numbers: [83, 50] Generated Node #0,3,1: 89:[83, 50] Operation: 22+28=50 Exploring Operation: 83-22=61, Resulting Numbers: [28, 61] Generated Node #0,3,2: 89:[28, 61] Operation: 83-22=61 Exploring Operation: 28-22=6, Resulting Numbers: [83, 6] Generated Node #0,3,3: 89:[83, 6] Operation: 28-22=6 Moving to Node #0,3,1 Current State: 89:[83, 50], Operations: ['36+47=83', '22+28=50'] Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 83+50=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 83*50=4150, Resulting Numbers: [4150] 4150,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[28, 105], Operations: ['36+47=83', '22+83=105'] Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,89 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,89 unequal: No Solution Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[83, 6], Operations: ['36+47=83', '28-22=6'] Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,89 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[22, 36, 47, 28], Operations: [] Exploring Operation: 36+47=83, Resulting Numbers: [22, 28, 83] Generated Node #0,3: 89:[22, 28, 83] Operation: 36+47=83 Moving to Node #0,3 Current State: 89:[22, 28, 83], Operations: ['36+47=83'] Exploring Operation: 28-22=6, Resulting Numbers: [83, 6] Generated Node #0,3,3: 89:[83, 6] Operation: 28-22=6 Moving to Node #0,3,3 Current State: 89:[83, 6], Operations: ['36+47=83', '28-22=6'] Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_4
sum_heuristic
[ 71, 75, 99, 41 ]
65
[ "75-71=4", "41*4=164", "164-99=65" ]
Current State: 65:[71, 75, 99, 41], Operations: [] Exploring Operation: 75-71=4, Resulting Numbers: [99, 41, 4] Generated Node #2: [99, 41, 4] from Operation: 75-71=4 Current State: 65:[99, 41, 4], Operations: ['75-71=4'] Exploring Operation: 41*4=164, Resulting Numbers: [99, 164] Generated Node #3: [99, 164] from Operation: 41*4=164 Current State: 65:[99, 164], Operations: ['75-71=4', '41*4=164'] Exploring Operation: 164-99=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[71, 75, 99, 41], Operations: [] Exploring Operation: 75-71=4, Resulting Numbers: [99, 41, 4] Generated Node #0,0: 65:[99, 41, 4] Operation: 75-71=4 Exploring Operation: 99-41=58, Resulting Numbers: [71, 75, 58] Generated Node #0,1: 65:[71, 75, 58] Operation: 99-41=58 Exploring Operation: 99-75=24, Resulting Numbers: [71, 41, 24] Generated Node #0,2: 65:[71, 41, 24] Operation: 99-75=24 Exploring Operation: 99-71=28, Resulting Numbers: [75, 41, 28] Generated Node #0,3: 65:[75, 41, 28] Operation: 99-71=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[71, 75, 58], Operations: ['99-41=58'] Exploring Operation: 75-71=4, Resulting Numbers: [58, 4] Generated Node #0,1,0: 65:[58, 4] Operation: 75-71=4 Exploring Operation: 71+58=129, Resulting Numbers: [75, 129] Generated Node #0,1,1: 65:[75, 129] Operation: 71+58=129 Exploring Operation: 71-58=13, Resulting Numbers: [75, 13] Generated Node #0,1,2: 65:[75, 13] Operation: 71-58=13 Exploring Operation: 75-58=17, Resulting Numbers: [71, 17] Generated Node #0,1,3: 65:[71, 17] Operation: 75-58=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[58, 4], Operations: ['99-41=58', '75-71=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,65 unequal: No Solution No 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: 65:[75, 13], Operations: ['99-41=58', '71-58=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,65 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,65 unequal: No Solution No 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: 65:[71, 17], Operations: ['99-41=58', '75-58=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 71*17=1207, Resulting Numbers: [1207] 1207,65 unequal: No Solution Exploring Operation: 71+17=88, Resulting Numbers: [88] 88,65 unequal: No Solution No 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: 65:[75, 129], Operations: ['99-41=58', '71+58=129'] Exploring Operation: 75*129=9675, Resulting Numbers: [9675] 9675,65 unequal: No Solution Exploring Operation: 75+129=204, Resulting Numbers: [204] 204,65 unequal: No Solution Exploring Operation: 129-75=54, Resulting Numbers: [54] 54,65 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: 65:[71, 41, 24], Operations: ['99-75=24'] Exploring Operation: 41-24=17, Resulting Numbers: [71, 17] Generated Node #0,2,0: 65:[71, 17] Operation: 41-24=17 Exploring Operation: 41+24=65, Resulting Numbers: [71, 65] Generated Node #0,2,1: 65:[71, 65] Operation: 41+24=65 Exploring Operation: 71-24=47, Resulting Numbers: [41, 47] Generated Node #0,2,2: 65:[41, 47] Operation: 71-24=47 Exploring Operation: 71-41=30, Resulting Numbers: [24, 30] Generated Node #0,2,3: 65:[24, 30] Operation: 71-41=30 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 65:[71, 65], Operations: ['99-75=24', '41+24=65'] Exploring Operation: 71-65=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 71+65=136, Resulting Numbers: [136] 136,65 unequal: No Solution Exploring Operation: 71*65=4615, Resulting Numbers: [4615] 4615,65 unequal: No Solution No 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: 65:[71, 17], Operations: ['99-75=24', '41-24=17'] Exploring Operation: 71+17=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 71*17=1207, Resulting Numbers: [1207] 1207,65 unequal: No Solution Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,65 unequal: No Solution No 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: 65:[24, 30], Operations: ['99-75=24', '71-41=30'] Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,65 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,65 unequal: No Solution No 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: 65:[41, 47], Operations: ['99-75=24', '71-24=47'] Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,65 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: 65:[75, 41, 28], Operations: ['99-71=28'] Exploring Operation: 41-28=13, Resulting Numbers: [75, 13] Generated Node #0,3,0: 65:[75, 13] Operation: 41-28=13 Exploring Operation: 75-28=47, Resulting Numbers: [41, 47] Generated Node #0,3,1: 65:[41, 47] Operation: 75-28=47 Exploring Operation: 41+28=69, Resulting Numbers: [75, 69] Generated Node #0,3,2: 65:[75, 69] Operation: 41+28=69 Exploring Operation: 75-41=34, Resulting Numbers: [28, 34] Generated Node #0,3,3: 65:[28, 34] Operation: 75-41=34 Moving to Node #0,3,0 Current State: 65:[75, 13], Operations: ['99-71=28', '41-28=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[75, 69], Operations: ['99-71=28', '41+28=69'] Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,65 unequal: No Solution Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[28, 34], Operations: ['99-71=28', '75-41=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[41, 47], Operations: ['99-71=28', '75-28=47'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,65 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[99, 41, 4], Operations: ['75-71=4'] Exploring Operation: 99-4=95, Resulting Numbers: [41, 95] Generated Node #0,0,0: 65:[41, 95] Operation: 99-4=95 Exploring Operation: 41+4=45, Resulting Numbers: [99, 45] Generated Node #0,0,1: 65:[99, 45] Operation: 41+4=45 Exploring Operation: 41-4=37, Resulting Numbers: [99, 37] Generated Node #0,0,2: 65:[99, 37] Operation: 41-4=37 Exploring Operation: 99-41=58, Resulting Numbers: [4, 58] Generated Node #0,0,3: 65:[4, 58] Operation: 99-41=58 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 65:[4, 58], Operations: ['75-71=4', '99-41=58'] Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,65 unequal: No Solution Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,65 unequal: No Solution No 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: 65:[41, 95], Operations: ['75-71=4', '99-4=95'] Exploring Operation: 41+95=136, Resulting Numbers: [136] 136,65 unequal: No Solution Exploring Operation: 95-41=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 41*95=3895, Resulting Numbers: [3895] 3895,65 unequal: No Solution No 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: 65:[99, 45], Operations: ['75-71=4', '41+4=45'] Exploring Operation: 99+45=144, Resulting Numbers: [144] 144,65 unequal: No Solution Exploring Operation: 99*45=4455, Resulting Numbers: [4455] 4455,65 unequal: No Solution Exploring Operation: 99-45=54, Resulting Numbers: [54] 54,65 unequal: No Solution No 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: 65:[99, 37], Operations: ['75-71=4', '41-4=37'] Exploring Operation: 99*37=3663, Resulting Numbers: [3663] 3663,65 unequal: No Solution Exploring Operation: 99+37=136, Resulting Numbers: [136] 136,65 unequal: No Solution Exploring Operation: 99-37=62, Resulting Numbers: [62] 62,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 8, 84, 72, 75 ]
16
[ "84-75=9", "72/9=8", "8+8=16" ]
Current State: 16:[8, 84, 72, 75], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [8, 72, 9] Generated Node #2: [8, 72, 9] from Operation: 84-75=9 Current State: 16:[8, 72, 9], Operations: ['84-75=9'] Exploring Operation: 72/9=8, Resulting Numbers: [8, 8] Generated Node #3: [8, 8] from Operation: 72/9=8 Current State: 16:[8, 8], Operations: ['84-75=9', '72/9=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[8, 84, 72, 75], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [8, 75, 12] Generated Node #0,0: 16:[8, 75, 12] Operation: 84-72=12 Exploring Operation: 84-75=9, Resulting Numbers: [8, 72, 9] Generated Node #0,1: 16:[8, 72, 9] Operation: 84-75=9 Exploring Operation: 75-72=3, Resulting Numbers: [8, 84, 3] Generated Node #0,2: 16:[8, 84, 3] Operation: 75-72=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[8, 72, 9], Operations: ['84-75=9'] Exploring Operation: 72-9=63, Resulting Numbers: [8, 63] Generated Node #0,1,0: 16:[8, 63] Operation: 72-9=63 Exploring Operation: 72/8=9, Resulting Numbers: [9, 9] Generated Node #0,1,1: 16:[9, 9] Operation: 72/8=9 Exploring Operation: 72/9=8, Resulting Numbers: [8, 8] Generated Node #0,1,2: 16:[8, 8] Operation: 72/9=8 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[8, 8], Operations: ['84-75=9', '72/9=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[8, 84, 72, 75], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [8, 72, 9] Generated Node #0,1: 16:[8, 72, 9] Operation: 84-75=9 Moving to Node #0,1 Current State: 16:[8, 72, 9], Operations: ['84-75=9'] Exploring Operation: 72/9=8, Resulting Numbers: [8, 8] Generated Node #0,1,2: 16:[8, 8] Operation: 72/9=8 Moving to Node #0,1,2 Current State: 16:[8, 8], Operations: ['84-75=9', '72/9=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 25, 26, 60, 44 ]
15
[ "26-25=1", "60-44=16", "16-1=15" ]
Current State: 15:[25, 26, 60, 44], Operations: [] Exploring Operation: 26-25=1, Resulting Numbers: [60, 44, 1] Generated Node #2: [60, 44, 1] from Operation: 26-25=1 Current State: 15:[60, 44, 1], Operations: ['26-25=1'] Exploring Operation: 60-44=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 60-44=16 Current State: 15:[1, 16], Operations: ['26-25=1', '60-44=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[25, 26, 60, 44], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [25, 26, 16] Generated Node #0,0: 15:[25, 26, 16] Operation: 60-44=16 Exploring Operation: 60-26=34, Resulting Numbers: [25, 44, 34] Generated Node #0,1: 15:[25, 44, 34] Operation: 60-26=34 Moving to Node #0,0 Current State: 15:[25, 26, 16], Operations: ['60-44=16'] Exploring Operation: 26-25=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 15:[16, 1] Operation: 26-25=1 Exploring Operation: 25-16=9, Resulting Numbers: [26, 9] Generated Node #0,0,1: 15:[26, 9] Operation: 25-16=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[16, 1], Operations: ['60-44=16', '26-25=1'] Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[25, 26, 60, 44], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [25, 26, 16] Generated Node #0,0: 15:[25, 26, 16] Operation: 60-44=16 Moving to Node #0,0 Current State: 15:[25, 26, 16], Operations: ['60-44=16'] Exploring Operation: 26-25=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 15:[16, 1] Operation: 26-25=1 Moving to Node #0,0,0 Current State: 15:[16, 1], Operations: ['60-44=16', '26-25=1'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 90, 32, 52, 56 ]
32
[ "90*32=2880", "52*56=2912", "2912-2880=32" ]
Current State: 32:[90, 32, 52, 56], Operations: [] Exploring Operation: 90*32=2880, Resulting Numbers: [52, 56, 2880] Generated Node #2: [52, 56, 2880] from Operation: 90*32=2880 Current State: 32:[52, 56, 2880], Operations: ['90*32=2880'] Exploring Operation: 52*56=2912, Resulting Numbers: [2880, 2912] Generated Node #3: [2880, 2912] from Operation: 52*56=2912 Current State: 32:[2880, 2912], Operations: ['90*32=2880', '52*56=2912'] Exploring Operation: 2912-2880=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[90, 32, 52, 56], Operations: [] Exploring Operation: 90-32=58, Resulting Numbers: [52, 56, 58] Generated Node #0,0: 32:[52, 56, 58] Operation: 90-32=58 Exploring Operation: 52-32=20, Resulting Numbers: [90, 56, 20] Generated Node #0,1: 32:[90, 56, 20] Operation: 52-32=20 Exploring Operation: 56-52=4, Resulting Numbers: [90, 32, 4] Generated Node #0,2: 32:[90, 32, 4] Operation: 56-52=4 Exploring Operation: 90-52=38, Resulting Numbers: [32, 56, 38] Generated Node #0,3: 32:[32, 56, 38] Operation: 90-52=38 Exploring Operation: 90-56=34, Resulting Numbers: [32, 52, 34] Generated Node #0,4: 32:[32, 52, 34] Operation: 90-56=34 Moving to Node #0,4 Current State: 32:[32, 52, 34], Operations: ['90-56=34'] Exploring Operation: 52-32=20, Resulting Numbers: [34, 20] Generated Node #0,4,0: 32:[34, 20] Operation: 52-32=20 Exploring Operation: 32+52=84, Resulting Numbers: [34, 84] Generated Node #0,4,1: 32:[34, 84] Operation: 32+52=84 Exploring Operation: 34-32=2, Resulting Numbers: [52, 2] Generated Node #0,4,2: 32:[52, 2] Operation: 34-32=2 Exploring Operation: 32+34=66, Resulting Numbers: [52, 66] Generated Node #0,4,3: 32:[52, 66] Operation: 32+34=66 Exploring Operation: 52-34=18, Resulting Numbers: [32, 18] Generated Node #0,4,4: 32:[32, 18] Operation: 52-34=18 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 32:[32, 18], Operations: ['90-56=34', '52-34=18'] Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,32 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 32:[34, 20], Operations: ['90-56=34', '52-32=20'] Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 34*20=680, Resulting Numbers: [680] 680,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 32:[52, 2], Operations: ['90-56=34', '34-32=2'] Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,32 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 32:[34, 84], Operations: ['90-56=34', '32+52=84'] Exploring Operation: 34+84=118, Resulting Numbers: [118] 118,32 unequal: No Solution Exploring Operation: 34*84=2856, Resulting Numbers: [2856] 2856,32 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 32:[52, 66], Operations: ['90-56=34', '32+34=66'] Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 52+66=118, Resulting Numbers: [118] 118,32 unequal: No Solution Exploring Operation: 52*66=3432, Resulting Numbers: [3432] 3432,32 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: 32:[32, 56, 38], Operations: ['90-52=38'] Exploring Operation: 56-32=24, Resulting Numbers: [38, 24] Generated Node #0,3,0: 32:[38, 24] Operation: 56-32=24 Exploring Operation: 38-32=6, Resulting Numbers: [56, 6] Generated Node #0,3,1: 32:[56, 6] Operation: 38-32=6 Exploring Operation: 32+56=88, Resulting Numbers: [38, 88] Generated Node #0,3,2: 32:[38, 88] Operation: 32+56=88 Exploring Operation: 32+38=70, Resulting Numbers: [56, 70] Generated Node #0,3,3: 32:[56, 70] Operation: 32+38=70 Exploring Operation: 56-38=18, Resulting Numbers: [32, 18] Generated Node #0,3,4: 32:[32, 18] Operation: 56-38=18 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 32:[32, 18], Operations: ['90-52=38', '56-38=18'] Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,32 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 32:[38, 24], Operations: ['90-52=38', '56-32=24'] Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 38*24=912, Resulting Numbers: [912] 912,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 32:[56, 6], Operations: ['90-52=38', '38-32=6'] Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,32 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 32:[38, 88], Operations: ['90-52=38', '32+56=88'] Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 32:[56, 70], Operations: ['90-52=38', '32+38=70'] Exploring Operation: 56+70=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 56*70=3920, Resulting Numbers: [3920] 3920,32 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: 32:[90, 32, 4], Operations: ['56-52=4'] Exploring Operation: 90+4=94, Resulting Numbers: [32, 94] Generated Node #0,2,0: 32:[32, 94] Operation: 90+4=94 Exploring Operation: 90-32=58, Resulting Numbers: [4, 58] Generated Node #0,2,1: 32:[4, 58] Operation: 90-32=58 Exploring Operation: 32/4=8, Resulting Numbers: [90, 8] Generated Node #0,2,2: 32:[90, 8] Operation: 32/4=8 Exploring Operation: 32+4=36, Resulting Numbers: [90, 36] Generated Node #0,2,3: 32:[90, 36] Operation: 32+4=36 Exploring Operation: 90-4=86, Resulting Numbers: [32, 86] Generated Node #0,2,4: 32:[32, 86] Operation: 90-4=86 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[4, 58], Operations: ['56-52=4', '90-32=58'] Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,32 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 32:[32, 86], Operations: ['56-52=4', '90-4=86'] Exploring Operation: 32*86=2752, Resulting Numbers: [2752] 2752,32 unequal: No Solution Exploring Operation: 32+86=118, Resulting Numbers: [118] 118,32 unequal: No Solution Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 32:[90, 8], Operations: ['56-52=4', '32/4=8'] Exploring Operation: 90*8=720, Resulting Numbers: [720] 720,32 unequal: No Solution Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,32 unequal: No Solution Exploring Operation: 90+8=98, Resulting Numbers: [98] 98,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[32, 94], Operations: ['56-52=4', '90+4=94'] Exploring Operation: 32+94=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 94-32=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 32*94=3008, Resulting Numbers: [3008] 3008,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 32:[90, 36], Operations: ['56-52=4', '32+4=36'] Exploring Operation: 90+36=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 90*36=3240, Resulting Numbers: [3240] 3240,32 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: 32:[52, 56, 58], Operations: ['90-32=58'] Exploring Operation: 58-52=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 32:[56, 6] Operation: 58-52=6 Exploring Operation: 56-52=4, Resulting Numbers: [58, 4] Generated Node #0,0,1: 32:[58, 4] Operation: 56-52=4 Exploring Operation: 52+56=108, Resulting Numbers: [58, 108] Generated Node #0,0,2: 32:[58, 108] Operation: 52+56=108 Exploring Operation: 52+58=110, Resulting Numbers: [56, 110] Generated Node #0,0,3: 32:[56, 110] Operation: 52+58=110 Exploring Operation: 58-56=2, Resulting Numbers: [52, 2] Generated Node #0,0,4: 32:[52, 2] Operation: 58-56=2 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 32:[52, 2], Operations: ['90-32=58', '58-56=2'] Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[56, 6], Operations: ['90-32=58', '58-52=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,32 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[58, 4], Operations: ['90-32=58', '56-52=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[58, 108], Operations: ['90-32=58', '52+56=108'] Exploring Operation: 58+108=166, Resulting Numbers: [166] 166,32 unequal: No Solution Exploring Operation: 108-58=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 58*108=6264, Resulting Numbers: [6264] 6264,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[56, 110], Operations: ['90-32=58', '52+58=110'] Exploring Operation: 56+110=166, Resulting Numbers: [166] 166,32 unequal: No Solution Exploring Operation: 56*110=6160, Resulting Numbers: [6160] 6160,32 unequal: No Solution Exploring Operation: 110-56=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 32:[90, 56, 20], Operations: ['52-32=20'] Exploring Operation: 90+20=110, Resulting Numbers: [56, 110] Generated Node #0,1,0: 32:[56, 110] Operation: 90+20=110 Exploring Operation: 56-20=36, Resulting Numbers: [90, 36] Generated Node #0,1,1: 32:[90, 36] Operation: 56-20=36 Exploring Operation: 90-56=34, Resulting Numbers: [20, 34] Generated Node #0,1,2: 32:[20, 34] Operation: 90-56=34 Exploring Operation: 56+20=76, Resulting Numbers: [90, 76] Generated Node #0,1,3: 32:[90, 76] Operation: 56+20=76 Exploring Operation: 90-20=70, Resulting Numbers: [56, 70] Generated Node #0,1,4: 32:[56, 70] Operation: 90-20=70 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[20, 34], Operations: ['52-32=20', '90-56=34'] Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,32 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[90, 36], Operations: ['52-32=20', '56-20=36'] Exploring Operation: 90*36=3240, Resulting Numbers: [3240] 3240,32 unequal: No Solution Exploring Operation: 90+36=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 32:[56, 70], Operations: ['52-32=20', '90-20=70'] Exploring Operation: 56*70=3920, Resulting Numbers: [3920] 3920,32 unequal: No Solution Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 56+70=126, Resulting Numbers: [126] 126,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[56, 110], Operations: ['52-32=20', '90+20=110'] Exploring Operation: 110-56=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 56+110=166, Resulting Numbers: [166] 166,32 unequal: No Solution Exploring Operation: 56*110=6160, Resulting Numbers: [6160] 6160,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[90, 76], Operations: ['52-32=20', '56+20=76'] Exploring Operation: 90*76=6840, Resulting Numbers: [6840] 6840,32 unequal: No Solution Exploring Operation: 90-76=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 90+76=166, Resulting Numbers: [166] 166,32 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
[ 26, 7, 7, 2 ]
33
[ "26-7=19", "7*2=14", "19+14=33" ]
Current State: 33:[26, 7, 7, 2], Operations: [] Exploring Operation: 26-7=19, Resulting Numbers: [2, 19] Generated Node #2: [2, 19] from Operation: 26-7=19 Current State: 33:[2, 19], Operations: ['26-7=19'] Exploring Operation: 7*2=14, Resulting Numbers: [19, 14] Generated Node #3: [19, 14] from Operation: 7*2=14 Current State: 33:[19, 14], Operations: ['26-7=19', '7*2=14'] Exploring Operation: 19+14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[26, 7, 7, 2], Operations: [] Exploring Operation: 26+7=33, Resulting Numbers: [7, 2, 33] Generated Node #0,0: 33:[7, 2, 33] Operation: 26+7=33 Exploring Operation: 7+7=14, Resulting Numbers: [26, 2, 14] Generated Node #0,1: 33:[26, 2, 14] Operation: 7+7=14 Exploring Operation: 7/7=1, Resulting Numbers: [26, 2, 1] Generated Node #0,2: 33:[26, 2, 1] Operation: 7/7=1 Exploring Operation: 26/2=13, Resulting Numbers: [7, 7, 13] Generated Node #0,3: 33:[7, 7, 13] Operation: 26/2=13 Exploring Operation: 26+7=33, Resulting Numbers: [7, 2, 33] Generated Node #0,4: 33:[7, 2, 33] Operation: 26+7=33 Moving to Node #0,0 Current State: 33:[7, 2, 33], Operations: ['26+7=33'] Exploring Operation: 33-2=31, Resulting Numbers: [7, 31] Generated Node #0,0,0: 33:[7, 31] Operation: 33-2=31 Exploring Operation: 2+33=35, Resulting Numbers: [7, 35] Generated Node #0,0,1: 33:[7, 35] Operation: 2+33=35 Exploring Operation: 7-2=5, Resulting Numbers: [33, 5] Generated Node #0,0,2: 33:[33, 5] Operation: 7-2=5 Exploring Operation: 7*2=14, Resulting Numbers: [33, 14] Generated Node #0,0,3: 33:[33, 14] Operation: 7*2=14 Exploring Operation: 7+2=9, Resulting Numbers: [33, 9] Generated Node #0,0,4: 33:[33, 9] Operation: 7+2=9 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[33, 5], Operations: ['26+7=33', '7-2=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,33 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,33 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 #0,0,4 Current State: 33:[33, 9], Operations: ['26+7=33', '7+2=9'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,33 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 #0,0,3 Current State: 33:[33, 14], Operations: ['26+7=33', '7*2=14'] Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,33 unequal: No Solution Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,33 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,33 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 #0,0,0 Current State: 33:[7, 31], Operations: ['26+7=33', '33-2=31'] Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,33 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 7+31=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:[7, 35], Operations: ['26+7=33', '2+33=35'] Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,33 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,33 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: 33:[7, 2, 33], Operations: ['26+7=33'] Exploring Operation: 33-2=31, Resulting Numbers: [7, 31] Generated Node #0,4,0: 33:[7, 31] Operation: 33-2=31 Exploring Operation: 7+2=9, Resulting Numbers: [33, 9] Generated Node #0,4,1: 33:[33, 9] Operation: 7+2=9 Exploring Operation: 7*2=14, Resulting Numbers: [33, 14] Generated Node #0,4,2: 33:[33, 14] Operation: 7*2=14 Exploring Operation: 2+33=35, Resulting Numbers: [7, 35] Generated Node #0,4,3: 33:[7, 35] Operation: 2+33=35 Exploring Operation: 7-2=5, Resulting Numbers: [33, 5] Generated Node #0,4,4: 33:[33, 5] Operation: 7-2=5 Moving to Node #0,2 Current State: 33:[26, 2, 1], Operations: ['7/7=1'] Exploring Operation: 26+2=28, Resulting Numbers: [1, 28] Generated Node #0,2,0: 33:[1, 28] Operation: 26+2=28 Exploring Operation: 26*1=26, Resulting Numbers: [2, 26] Generated Node #0,2,1: 33:[2, 26] Operation: 26*1=26 Exploring Operation: 26+1=27, Resulting Numbers: [2, 27] Generated Node #0,2,2: 33:[2, 27] Operation: 26+1=27 Exploring Operation: 2+1=3, Resulting Numbers: [26, 3] Generated Node #0,2,3: 33:[26, 3] Operation: 2+1=3 Exploring Operation: 26/2=13, Resulting Numbers: [1, 13] Generated Node #0,2,4: 33:[1, 13] Operation: 26/2=13 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 33:[1, 13], Operations: ['7/7=1', '26/2=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,33 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 #0,2,0 Current State: 33:[1, 28], Operations: ['7/7=1', '26+2=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,33 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 #0,2,2 Current State: 33:[2, 27], Operations: ['7/7=1', '26+1=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,33 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,33 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 #0,2,3 Current State: 33:[26, 3], Operations: ['7/7=1', '2+1=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,33 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 #0,2,1 Current State: 33:[2, 26], Operations: ['7/7=1', '26*1=26'] Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,33 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 33:[7, 7, 13], Operations: ['26/2=13'] Exploring Operation: 13-7=6, Resulting Numbers: [7, 6] Generated Node #0,3,0: 33:[7, 6] Operation: 13-7=6 Exploring Operation: 7+7=14, Resulting Numbers: [13, 14] Generated Node #0,3,1: 33:[13, 14] Operation: 7+7=14 Exploring Operation: 7/7=1, Resulting Numbers: [13, 1] Generated Node #0,3,2: 33:[13, 1] Operation: 7/7=1 Exploring Operation: 7-7=0, Resulting Numbers: [13, 0] Generated Node #0,3,3: 33:[13, 0] Operation: 7-7=0 Exploring Operation: 13-7=6, Resulting Numbers: [7, 6] Generated Node #0,3,4: 33:[7, 6] Operation: 13-7=6 Moving to Node #0,1 Current State: 33:[26, 2, 14], Operations: ['7+7=14'] Exploring Operation: 26+2=28, Resulting Numbers: [14, 28] Generated Node #0,1,0: 33:[14, 28] Operation: 26+2=28 Exploring Operation: 26+14=40, Resulting Numbers: [2, 40] Generated Node #0,1,1: 33:[2, 40] Operation: 26+14=40 Exploring Operation: 26/2=13, Resulting Numbers: [14, 13] Generated Node #0,1,2: 33:[14, 13] Operation: 26/2=13 Exploring Operation: 26-14=12, Resulting Numbers: [2, 12] Generated Node #0,1,3: 33:[2, 12] Operation: 26-14=12 Exploring Operation: 14-2=12, Resulting Numbers: [26, 12] Generated Node #0,1,4: 33:[26, 12] Operation: 14-2=12 Moving to Node #0,4,1 Current State: 33:[33, 9], Operations: ['26+7=33', '7+2=9'] Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,33 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,4,4 Current State: 33:[33, 5], Operations: ['26+7=33', '7-2=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,33 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,33 unequal: No Solution Moving to Node #0,1,3 Current State: 33:[2, 12], Operations: ['7+7=14', '26-14=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,4,2 Current State: 33:[33, 14], Operations: ['26+7=33', '7*2=14'] Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,33 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,33 unequal: No Solution Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,33 unequal: No Solution Moving to Node #0,3,2 Current State: 33:[13, 1], Operations: ['26/2=13', '7/7=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,33 unequal: No Solution Moving to Node #0,3,1 Current State: 33:[13, 14], Operations: ['26/2=13', '7+7=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[14, 13], Operations: ['7+7=14', '26/2=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[13, 0], Operations: ['26/2=13', '7-7=0'] Exploring Operation: 13+0=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 13*0=0, Resulting Numbers: [0] 0,33 unequal: No Solution Exploring Operation: 13-0=13, Resulting Numbers: [13] 13,33 unequal: No Solution Moving to Node #0,4,3 Current State: 33:[7, 35], Operations: ['26+7=33', '2+33=35'] Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,33 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,33 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,33 unequal: No Solution Moving to Node #0,4,0 Current State: 33:[7, 31], Operations: ['26+7=33', '33-2=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,33 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,33 unequal: No Solution Moving to Node #0,3,4 Current State: 33:[7, 6], Operations: ['26/2=13', '13-7=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,33 unequal: No Solution Moving to Node #0,3,0 Current State: 33:[7, 6], Operations: ['26/2=13', '13-7=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,33 unequal: No Solution Moving to Node #0,1,4 Current State: 33:[26, 12], Operations: ['7+7=14', '14-2=12'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[2, 40], Operations: ['7+7=14', '26+14=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[14, 28], Operations: ['7+7=14', '26+2=28'] Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,33 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,33 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,33 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 5, 96, 27, 50 ]
19
[ "50-27=23", "5*23=115", "115-96=19" ]
Current State: 19:[5, 96, 27, 50], Operations: [] Exploring Operation: 50-27=23, Resulting Numbers: [5, 96, 23] Generated Node #2: [5, 96, 23] from Operation: 50-27=23 Current State: 19:[5, 96, 23], Operations: ['50-27=23'] Exploring Operation: 5*23=115, Resulting Numbers: [96, 115] Generated Node #3: [96, 115] from Operation: 5*23=115 Current State: 19:[96, 115], Operations: ['50-27=23', '5*23=115'] Exploring Operation: 115-96=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[5, 96, 27, 50], Operations: [] Exploring Operation: 96-5=91, Resulting Numbers: [27, 50, 91] Generated Node #0,0: 19:[27, 50, 91] Operation: 96-5=91 Exploring Operation: 96-50=46, Resulting Numbers: [5, 27, 46] Generated Node #0,1: 19:[5, 27, 46] Operation: 96-50=46 Exploring Operation: 96-27=69, Resulting Numbers: [5, 50, 69] Generated Node #0,2: 19:[5, 50, 69] Operation: 96-27=69 Exploring Operation: 50/5=10, Resulting Numbers: [96, 27, 10] Generated Node #0,3: 19:[96, 27, 10] Operation: 50/5=10 Exploring Operation: 50-27=23, Resulting Numbers: [5, 96, 23] Generated Node #0,4: 19:[5, 96, 23] Operation: 50-27=23 Moving to Node #0,1 Current State: 19:[5, 27, 46], Operations: ['96-50=46'] Exploring Operation: 46-27=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 19:[5, 19] Operation: 46-27=19 Exploring Operation: 5+46=51, Resulting Numbers: [27, 51] Generated Node #0,1,1: 19:[27, 51] Operation: 5+46=51 Exploring Operation: 5+27=32, Resulting Numbers: [46, 32] Generated Node #0,1,2: 19:[46, 32] Operation: 5+27=32 Exploring Operation: 46-5=41, Resulting Numbers: [27, 41] Generated Node #0,1,3: 19:[27, 41] Operation: 46-5=41 Exploring Operation: 27-5=22, Resulting Numbers: [46, 22] Generated Node #0,1,4: 19:[46, 22] Operation: 27-5=22 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[5, 19], Operations: ['96-50=46', '46-27=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,19 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,19 unequal: No Solution No 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: 19:[27, 41], Operations: ['96-50=46', '46-5=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,19 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 19:[46, 22], Operations: ['96-50=46', '27-5=22'] Exploring Operation: 46+22=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 46*22=1012, Resulting Numbers: [1012] 1012,19 unequal: No Solution No 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: 19:[27, 51], Operations: ['96-50=46', '5+46=51'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,19 unequal: No Solution No 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: 19:[46, 32], Operations: ['96-50=46', '5+27=32'] Exploring Operation: 46*32=1472, Resulting Numbers: [1472] 1472,19 unequal: No Solution Exploring Operation: 46-32=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 46+32=78, Resulting Numbers: [78] 78,19 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: 19:[96, 27, 10], Operations: ['50/5=10'] Exploring Operation: 96-10=86, Resulting Numbers: [27, 86] Generated Node #0,3,0: 19:[27, 86] Operation: 96-10=86 Exploring Operation: 27+10=37, Resulting Numbers: [96, 37] Generated Node #0,3,1: 19:[96, 37] Operation: 27+10=37 Exploring Operation: 96-27=69, Resulting Numbers: [10, 69] Generated Node #0,3,2: 19:[10, 69] Operation: 96-27=69 Exploring Operation: 96+10=106, Resulting Numbers: [27, 106] Generated Node #0,3,3: 19:[27, 106] Operation: 96+10=106 Exploring Operation: 27-10=17, Resulting Numbers: [96, 17] Generated Node #0,3,4: 19:[96, 17] Operation: 27-10=17 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 19:[10, 69], Operations: ['50/5=10', '96-27=69'] Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 10*69=690, Resulting Numbers: [690] 690,19 unequal: No Solution Exploring Operation: 10+69=79, Resulting Numbers: [79] 79,19 unequal: No Solution No 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: 19:[27, 86], Operations: ['50/5=10', '96-10=86'] Exploring Operation: 27*86=2322, Resulting Numbers: [2322] 2322,19 unequal: No Solution Exploring Operation: 27+86=113, Resulting Numbers: [113] 113,19 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,19 unequal: No Solution No 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: 19:[96, 17], Operations: ['50/5=10', '27-10=17'] Exploring Operation: 96*17=1632, Resulting Numbers: [1632] 1632,19 unequal: No Solution Exploring Operation: 96+17=113, Resulting Numbers: [113] 113,19 unequal: No Solution Exploring Operation: 96-17=79, Resulting Numbers: [79] 79,19 unequal: No Solution No 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: 19:[96, 37], Operations: ['50/5=10', '27+10=37'] Exploring Operation: 96+37=133, Resulting Numbers: [133] 133,19 unequal: No Solution Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 96*37=3552, Resulting Numbers: [3552] 3552,19 unequal: No Solution No 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: 19:[27, 106], Operations: ['50/5=10', '96+10=106'] Exploring Operation: 106-27=79, Resulting Numbers: [79] 79,19 unequal: No Solution Exploring Operation: 27+106=133, Resulting Numbers: [133] 133,19 unequal: No Solution Exploring Operation: 27*106=2862, Resulting Numbers: [2862] 2862,19 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: 19:[5, 50, 69], Operations: ['96-27=69'] Exploring Operation: 50-5=45, Resulting Numbers: [69, 45] Generated Node #0,2,0: 19:[69, 45] Operation: 50-5=45 Exploring Operation: 5+50=55, Resulting Numbers: [69, 55] Generated Node #0,2,1: 19:[69, 55] Operation: 5+50=55 Exploring Operation: 69-5=64, Resulting Numbers: [50, 64] Generated Node #0,2,2: 19:[50, 64] Operation: 69-5=64 Exploring Operation: 69-50=19, Resulting Numbers: [5, 19] Generated Node #0,2,3: 19:[5, 19] Operation: 69-50=19 Exploring Operation: 50/5=10, Resulting Numbers: [69, 10] Generated Node #0,2,4: 19:[69, 10] Operation: 50/5=10 Moving to Node #0,4 Current State: 19:[5, 96, 23], Operations: ['50-27=23'] Exploring Operation: 23-5=18, Resulting Numbers: [96, 18] Generated Node #0,4,0: 19:[96, 18] Operation: 23-5=18 Exploring Operation: 96-5=91, Resulting Numbers: [23, 91] Generated Node #0,4,1: 19:[23, 91] Operation: 96-5=91 Exploring Operation: 5+96=101, Resulting Numbers: [23, 101] Generated Node #0,4,2: 19:[23, 101] Operation: 5+96=101 Exploring Operation: 96-23=73, Resulting Numbers: [5, 73] Generated Node #0,4,3: 19:[5, 73] Operation: 96-23=73 Exploring Operation: 5+23=28, Resulting Numbers: [96, 28] Generated Node #0,4,4: 19:[96, 28] Operation: 5+23=28 Moving to Node #0,0 Current State: 19:[27, 50, 91], Operations: ['96-5=91'] Exploring Operation: 50-27=23, Resulting Numbers: [91, 23] Generated Node #0,0,0: 19:[91, 23] Operation: 50-27=23 Exploring Operation: 27+91=118, Resulting Numbers: [50, 118] Generated Node #0,0,1: 19:[50, 118] Operation: 27+91=118 Exploring Operation: 91-50=41, Resulting Numbers: [27, 41] Generated Node #0,0,2: 19:[27, 41] Operation: 91-50=41 Exploring Operation: 27+50=77, Resulting Numbers: [91, 77] Generated Node #0,0,3: 19:[91, 77] Operation: 27+50=77 Exploring Operation: 91-27=64, Resulting Numbers: [50, 64] Generated Node #0,0,4: 19:[50, 64] Operation: 91-27=64 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[27, 41], Operations: ['96-5=91', '91-50=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,19 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,19 unequal: No Solution No 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: 19:[91, 23], Operations: ['96-5=91', '50-27=23'] Exploring Operation: 91*23=2093, Resulting Numbers: [2093] 2093,19 unequal: No Solution Exploring Operation: 91+23=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,19 unequal: No Solution No 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: 19:[50, 64], Operations: ['96-5=91', '91-27=64'] Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 50*64=3200, Resulting Numbers: [3200] 3200,19 unequal: No Solution Exploring Operation: 50+64=114, Resulting Numbers: [114] 114,19 unequal: No Solution No 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: 19:[50, 118], Operations: ['96-5=91', '27+91=118'] Exploring Operation: 50+118=168, Resulting Numbers: [168] 168,19 unequal: No Solution Exploring Operation: 50*118=5900, Resulting Numbers: [5900] 5900,19 unequal: No Solution Exploring Operation: 118-50=68, Resulting Numbers: [68] 68,19 unequal: No Solution No 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: 19:[91, 77], Operations: ['96-5=91', '27+50=77'] Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,19 unequal: No Solution Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,19 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: 19:[5, 19], Operations: ['96-27=69', '69-50=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,19 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,19 unequal: No Solution Moving to Node #0,2,4 Current State: 19:[69, 10], Operations: ['96-27=69', '50/5=10'] Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,19 unequal: No Solution Exploring Operation: 69+10=79, Resulting Numbers: [79] 79,19 unequal: No Solution Exploring Operation: 69*10=690, Resulting Numbers: [690] 690,19 unequal: No Solution Moving to Node #0,4,3 Current State: 19:[5, 73], Operations: ['50-27=23', '96-23=73'] Exploring Operation: 5+73=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 5*73=365, Resulting Numbers: [365] 365,19 unequal: No Solution Moving to Node #0,4,1 Current State: 19:[23, 91], Operations: ['50-27=23', '96-5=91'] Exploring Operation: 23*91=2093, Resulting Numbers: [2093] 2093,19 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 23+91=114, Resulting Numbers: [114] 114,19 unequal: No Solution Moving to Node #0,2,0 Current State: 19:[69, 45], Operations: ['96-27=69', '50-5=45'] Exploring Operation: 69+45=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 69*45=3105, Resulting Numbers: [3105] 3105,19 unequal: No Solution Moving to Node #0,2,2 Current State: 19:[50, 64], Operations: ['96-27=69', '69-5=64'] Exploring Operation: 50*64=3200, Resulting Numbers: [3200] 3200,19 unequal: No Solution Exploring Operation: 50+64=114, Resulting Numbers: [114] 114,19 unequal: No Solution Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,19 unequal: No Solution Moving to Node #0,4,0 Current State: 19:[96, 18], Operations: ['50-27=23', '23-5=18'] Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 96*18=1728, Resulting Numbers: [1728] 1728,19 unequal: No Solution Exploring Operation: 96+18=114, Resulting Numbers: [114] 114,19 unequal: No Solution Moving to Node #0,4,4 Current State: 19:[96, 28], Operations: ['50-27=23', '5+23=28'] Exploring Operation: 96-28=68, Resulting Numbers: [68] 68,19 unequal: No Solution Exploring Operation: 96+28=124, Resulting Numbers: [124] 124,19 unequal: No Solution Exploring Operation: 96*28=2688, Resulting Numbers: [2688] 2688,19 unequal: No Solution Moving to Node #0,4,2 Current State: 19:[23, 101], Operations: ['50-27=23', '5+96=101'] Exploring Operation: 101-23=78, Resulting Numbers: [78] 78,19 unequal: No Solution Exploring Operation: 23+101=124, Resulting Numbers: [124] 124,19 unequal: No Solution Exploring Operation: 23*101=2323, Resulting Numbers: [2323] 2323,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[69, 55], Operations: ['96-27=69', '5+50=55'] Exploring Operation: 69+55=124, Resulting Numbers: [124] 124,19 unequal: No Solution Exploring Operation: 69*55=3795, Resulting Numbers: [3795] 3795,19 unequal: No Solution Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,19 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 22, 84, 38, 39 ]
15
[ "84-22=62", "38+39=77", "77-62=15" ]
Current State: 15:[22, 84, 38, 39], Operations: [] Exploring Operation: 84-22=62, Resulting Numbers: [38, 39, 62] Generated Node #2: [38, 39, 62] from Operation: 84-22=62 Current State: 15:[38, 39, 62], Operations: ['84-22=62'] Exploring Operation: 38+39=77, Resulting Numbers: [62, 77] Generated Node #3: [62, 77] from Operation: 38+39=77 Current State: 15:[62, 77], Operations: ['84-22=62', '38+39=77'] Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[22, 84, 38, 39], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [22, 38, 45] Generated Node #0,0: 15:[22, 38, 45] Operation: 84-39=45 Exploring Operation: 84-38=46, Resulting Numbers: [22, 39, 46] Generated Node #0,1: 15:[22, 39, 46] Operation: 84-38=46 Moving to Node #0,0 Current State: 15:[22, 38, 45], Operations: ['84-39=45'] Exploring Operation: 45-38=7, Resulting Numbers: [22, 7] Generated Node #0,0,0: 15:[22, 7] Operation: 45-38=7 Exploring Operation: 38-22=16, Resulting Numbers: [45, 16] Generated Node #0,0,1: 15:[45, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[22, 7], Operations: ['84-39=45', '45-38=7'] Exploring Operation: 22+7=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[22, 84, 38, 39], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [22, 38, 45] Generated Node #0,0: 15:[22, 38, 45] Operation: 84-39=45 Moving to Node #0,0 Current State: 15:[22, 38, 45], Operations: ['84-39=45'] Exploring Operation: 45-38=7, Resulting Numbers: [22, 7] Generated Node #0,0,0: 15:[22, 7] Operation: 45-38=7 Moving to Node #0,0,0 Current State: 15:[22, 7], Operations: ['84-39=45', '45-38=7'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 16, 60, 2, 35 ]
73
[ "16+60=76", "76/2=38", "35+38=73" ]
Current State: 73:[16, 60, 2, 35], Operations: [] Exploring Operation: 16+60=76, Resulting Numbers: [2, 35, 76] Generated Node #2: [2, 35, 76] from Operation: 16+60=76 Current State: 73:[2, 35, 76], Operations: ['16+60=76'] Exploring Operation: 76/2=38, Resulting Numbers: [35, 38] Generated Node #3: [35, 38] from Operation: 76/2=38 Current State: 73:[35, 38], Operations: ['16+60=76', '76/2=38'] Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[16, 60, 2, 35], Operations: [] Exploring Operation: 2*35=70, Resulting Numbers: [16, 60, 70] Generated Node #0,0: 73:[16, 60, 70] Operation: 2*35=70 Exploring Operation: 16*2=32, Resulting Numbers: [60, 35, 32] Generated Node #0,1: 73:[60, 35, 32] Operation: 16*2=32 Moving to Node #0,0 Current State: 73:[16, 60, 70], Operations: ['2*35=70'] Exploring Operation: 16+60=76, Resulting Numbers: [70, 76] Generated Node #0,0,0: 73:[70, 76] Operation: 16+60=76 Exploring Operation: 16+70=86, Resulting Numbers: [60, 86] Generated Node #0,0,1: 73:[60, 86] Operation: 16+70=86 Moving to Node #0,1 Current State: 73:[60, 35, 32], Operations: ['16*2=32'] Exploring Operation: 60+32=92, Resulting Numbers: [35, 92] Generated Node #0,1,0: 73:[35, 92] Operation: 60+32=92 Exploring Operation: 35+32=67, Resulting Numbers: [60, 67] Generated Node #0,1,1: 73:[60, 67] Operation: 35+32=67 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[60, 67], Operations: ['16*2=32', '35+32=67'] Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 60+67=127, Resulting Numbers: [127] 127,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[35, 92], Operations: ['16*2=32', '60+32=92'] Exploring Operation: 92-35=57, Resulting Numbers: [57] 57,73 unequal: No Solution Exploring Operation: 35+92=127, Resulting Numbers: [127] 127,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 73:[70, 76], Operations: ['2*35=70', '16+60=76'] Exploring Operation: 76-70=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 70+76=146, Resulting Numbers: [146] 146,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[60, 86], Operations: ['2*35=70', '16+70=86'] Exploring Operation: 60+86=146, Resulting Numbers: [146] 146,73 unequal: No Solution Exploring Operation: 86-60=26, Resulting Numbers: [26] 26,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 27, 83, 71, 47 ]
86
[ "27+83=110", "71-47=24", "110-24=86" ]
Current State: 86:[27, 83, 71, 47], Operations: [] Exploring Operation: 27+83=110, Resulting Numbers: [71, 47, 110] Generated Node #2: [71, 47, 110] from Operation: 27+83=110 Current State: 86:[71, 47, 110], Operations: ['27+83=110'] Exploring Operation: 71-47=24, Resulting Numbers: [110, 24] Generated Node #3: [110, 24] from Operation: 71-47=24 Current State: 86:[110, 24], Operations: ['27+83=110', '71-47=24'] Exploring Operation: 110-24=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[27, 83, 71, 47], Operations: [] Exploring Operation: 71-27=44, Resulting Numbers: [83, 47, 44] Generated Node #0,0: 86:[83, 47, 44] Operation: 71-27=44 Exploring Operation: 27+47=74, Resulting Numbers: [83, 71, 74] Generated Node #0,1: 86:[83, 71, 74] Operation: 27+47=74 Exploring Operation: 27+71=98, Resulting Numbers: [83, 47, 98] Generated Node #0,2: 86:[83, 47, 98] Operation: 27+71=98 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[83, 47, 44], Operations: ['71-27=44'] Exploring Operation: 47-44=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 47-44=3 Exploring Operation: 83-47=36, Resulting Numbers: [44, 36] Generated Node #0,0,1: 86:[44, 36] Operation: 83-47=36 Exploring Operation: 83-44=39, Resulting Numbers: [47, 39] Generated Node #0,0,2: 86:[47, 39] Operation: 83-44=39 Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['71-27=44', '47-44=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[27, 83, 71, 47], Operations: [] Exploring Operation: 71-27=44, Resulting Numbers: [83, 47, 44] Generated Node #0,0: 86:[83, 47, 44] Operation: 71-27=44 Moving to Node #0,0 Current State: 86:[83, 47, 44], Operations: ['71-27=44'] Exploring Operation: 47-44=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 47-44=3 Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['71-27=44', '47-44=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 28, 61, 18, 94 ]
23
[ "28+61=89", "18+94=112", "112-89=23" ]
Current State: 23:[28, 61, 18, 94], Operations: [] Exploring Operation: 28+61=89, Resulting Numbers: [18, 94, 89] Generated Node #2: [18, 94, 89] from Operation: 28+61=89 Current State: 23:[18, 94, 89], Operations: ['28+61=89'] Exploring Operation: 18+94=112, Resulting Numbers: [89, 112] Generated Node #3: [89, 112] from Operation: 18+94=112 Current State: 23:[89, 112], Operations: ['28+61=89', '18+94=112'] Exploring Operation: 112-89=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[28, 61, 18, 94], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [18, 94, 33] Generated Node #0,0: 23:[18, 94, 33] Operation: 61-28=33 Exploring Operation: 94-61=33, Resulting Numbers: [28, 18, 33] Generated Node #0,1: 23:[28, 18, 33] Operation: 94-61=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[28, 18, 33], Operations: ['94-61=33'] Exploring Operation: 33-18=15, Resulting Numbers: [28, 15] Generated Node #0,1,0: 23:[28, 15] Operation: 33-18=15 Exploring Operation: 28-18=10, Resulting Numbers: [33, 10] Generated Node #0,1,1: 23:[33, 10] Operation: 28-18=10 Moving to Node #0,1,0 Current State: 23:[28, 15], Operations: ['94-61=33', '33-18=15'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[33, 10], Operations: ['94-61=33', '28-18=10'] Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[28, 61, 18, 94], Operations: [] Exploring Operation: 94-61=33, Resulting Numbers: [28, 18, 33] Generated Node #0,1: 23:[28, 18, 33] Operation: 94-61=33 Moving to Node #0,1 Current State: 23:[28, 18, 33], Operations: ['94-61=33'] Exploring Operation: 28-18=10, Resulting Numbers: [33, 10] Generated Node #0,1,1: 23:[33, 10] Operation: 28-18=10 Moving to Node #0,1,1 Current State: 23:[33, 10], Operations: ['94-61=33', '28-18=10'] Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 74, 90, 96, 48 ]
42
[ "90-74=16", "96/16=6", "48-6=42" ]
Current State: 42:[74, 90, 96, 48], Operations: [] Exploring Operation: 90-74=16, Resulting Numbers: [96, 48, 16] Generated Node #2: [96, 48, 16] from Operation: 90-74=16 Current State: 42:[96, 48, 16], Operations: ['90-74=16'] Exploring Operation: 96/16=6, Resulting Numbers: [48, 6] Generated Node #3: [48, 6] from Operation: 96/16=6 Current State: 42:[48, 6], Operations: ['90-74=16', '96/16=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[74, 90, 96, 48], Operations: [] Exploring Operation: 96-74=22, Resulting Numbers: [90, 48, 22] Generated Node #0,0: 42:[90, 48, 22] Operation: 96-74=22 Exploring Operation: 96-90=6, Resulting Numbers: [74, 48, 6] Generated Node #0,1: 42:[74, 48, 6] Operation: 96-90=6 Moving to Node #0,1 Current State: 42:[74, 48, 6], Operations: ['96-90=6'] Exploring Operation: 74-6=68, Resulting Numbers: [48, 68] Generated Node #0,1,0: 42:[48, 68] Operation: 74-6=68 Exploring Operation: 74-48=26, Resulting Numbers: [6, 26] Generated Node #0,1,1: 42:[6, 26] Operation: 74-48=26 Moving to Node #0,0 Current State: 42:[90, 48, 22], Operations: ['96-74=22'] Exploring Operation: 90-48=42, Resulting Numbers: [22, 42] Generated Node #0,0,0: 42:[22, 42] Operation: 90-48=42 Exploring Operation: 90-22=68, Resulting Numbers: [48, 68] Generated Node #0,0,1: 42:[48, 68] Operation: 90-22=68 Moving to Node #0,0,0 Current State: 42:[22, 42], Operations: ['96-74=22', '90-48=42'] Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[6, 26], Operations: ['96-90=6', '74-48=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[48, 68], Operations: ['96-90=6', '74-6=68'] Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,42 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[48, 68], Operations: ['96-74=22', '90-22=68'] Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,42 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,42 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 92, 50, 23, 79 ]
86
[ "92+50=142", "79-23=56", "142-56=86" ]
Current State: 86:[92, 50, 23, 79], Operations: [] Exploring Operation: 92+50=142, Resulting Numbers: [23, 79, 142] Generated Node #2: [23, 79, 142] from Operation: 92+50=142 Current State: 86:[23, 79, 142], Operations: ['92+50=142'] Exploring Operation: 79-23=56, Resulting Numbers: [142, 56] Generated Node #3: [142, 56] from Operation: 79-23=56 Current State: 86:[142, 56], Operations: ['92+50=142', '79-23=56'] Exploring Operation: 142-56=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[92, 50, 23, 79], Operations: [] Exploring Operation: 50+23=73, Resulting Numbers: [92, 79, 73] Generated Node #0,0: 86:[92, 79, 73] Operation: 50+23=73 Exploring Operation: 92/23=4, Resulting Numbers: [50, 79, 4] Generated Node #0,1: 86:[50, 79, 4] Operation: 92/23=4 Exploring Operation: 50-23=27, Resulting Numbers: [92, 79, 27] Generated Node #0,2: 86:[92, 79, 27] Operation: 50-23=27 Exploring Operation: 92-50=42, Resulting Numbers: [23, 79, 42] Generated Node #0,3: 86:[23, 79, 42] Operation: 92-50=42 Exploring Operation: 79-23=56, Resulting Numbers: [92, 50, 56] Generated Node #0,4: 86:[92, 50, 56] Operation: 79-23=56 Moving to Node #0,1 Current State: 86:[50, 79, 4], Operations: ['92/23=4'] Exploring Operation: 50-4=46, Resulting Numbers: [79, 46] Generated Node #0,1,0: 86:[79, 46] Operation: 50-4=46 Exploring Operation: 50+4=54, Resulting Numbers: [79, 54] Generated Node #0,1,1: 86:[79, 54] Operation: 50+4=54 Exploring Operation: 79+4=83, Resulting Numbers: [50, 83] Generated Node #0,1,2: 86:[50, 83] Operation: 79+4=83 Exploring Operation: 79-4=75, Resulting Numbers: [50, 75] Generated Node #0,1,3: 86:[50, 75] Operation: 79-4=75 Exploring Operation: 79-50=29, Resulting Numbers: [4, 29] Generated Node #0,1,4: 86:[4, 29] Operation: 79-50=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[79, 46], Operations: ['92/23=4', '50-4=46'] Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 79*46=3634, Resulting Numbers: [3634] 3634,86 unequal: No Solution Exploring Operation: 79+46=125, Resulting Numbers: [125] 125,86 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:[50, 83], Operations: ['92/23=4', '79+4=83'] Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,86 unequal: No Solution Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 86:[4, 29], Operations: ['92/23=4', '79-50=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,86 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[79, 54], Operations: ['92/23=4', '50+4=54'] Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,86 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,86 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:[50, 75], Operations: ['92/23=4', '79-4=75'] Exploring Operation: 50+75=125, Resulting Numbers: [125] 125,86 unequal: No Solution Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 50*75=3750, Resulting Numbers: [3750] 3750,86 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: 86:[92, 50, 56], Operations: ['79-23=56'] Exploring Operation: 56-50=6, Resulting Numbers: [92, 6] Generated Node #0,4,0: 86:[92, 6] Operation: 56-50=6 Exploring Operation: 92+50=142, Resulting Numbers: [56, 142] Generated Node #0,4,1: 86:[56, 142] Operation: 92+50=142 Exploring Operation: 50+56=106, Resulting Numbers: [92, 106] Generated Node #0,4,2: 86:[92, 106] Operation: 50+56=106 Exploring Operation: 92-56=36, Resulting Numbers: [50, 36] Generated Node #0,4,3: 86:[50, 36] Operation: 92-56=36 Exploring Operation: 92-50=42, Resulting Numbers: [56, 42] Generated Node #0,4,4: 86:[56, 42] Operation: 92-50=42 Moving to Node #0,0 Current State: 86:[92, 79, 73], Operations: ['50+23=73'] Exploring Operation: 79-73=6, Resulting Numbers: [92, 6] Generated Node #0,0,0: 86:[92, 6] Operation: 79-73=6 Exploring Operation: 79+73=152, Resulting Numbers: [92, 152] Generated Node #0,0,1: 86:[92, 152] Operation: 79+73=152 Exploring Operation: 92-73=19, Resulting Numbers: [79, 19] Generated Node #0,0,2: 86:[79, 19] Operation: 92-73=19 Exploring Operation: 92+73=165, Resulting Numbers: [79, 165] Generated Node #0,0,3: 86:[79, 165] Operation: 92+73=165 Exploring Operation: 92-79=13, Resulting Numbers: [73, 13] Generated Node #0,0,4: 86:[73, 13] Operation: 92-79=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[92, 6], Operations: ['50+23=73', '79-73=6'] Exploring Operation: 92*6=552, Resulting Numbers: [552] 552,86 unequal: No Solution Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[92, 50, 23, 79], Operations: [] Exploring Operation: 50+23=73, Resulting Numbers: [92, 79, 73] Generated Node #0,0: 86:[92, 79, 73] Operation: 50+23=73 Moving to Node #0,0 Current State: 86:[92, 79, 73], Operations: ['50+23=73'] Exploring Operation: 79-73=6, Resulting Numbers: [92, 6] Generated Node #0,0,0: 86:[92, 6] Operation: 79-73=6 Moving to Node #0,0,0 Current State: 86:[92, 6], Operations: ['50+23=73', '79-73=6'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 64, 52, 49, 98 ]
54
[ "64+98=162", "52-49=3", "162/3=54" ]
Current State: 54:[64, 52, 49, 98], Operations: [] Exploring Operation: 64+98=162, Resulting Numbers: [52, 49, 162] Generated Node #2: [52, 49, 162] from Operation: 64+98=162 Current State: 54:[52, 49, 162], Operations: ['64+98=162'] Exploring Operation: 52-49=3, Resulting Numbers: [162, 3] Generated Node #3: [162, 3] from Operation: 52-49=3 Current State: 54:[162, 3], Operations: ['64+98=162', '52-49=3'] Exploring Operation: 162/3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[64, 52, 49, 98], Operations: [] Exploring Operation: 98-64=34, Resulting Numbers: [52, 49, 34] Generated Node #0,0: 54:[52, 49, 34] Operation: 98-64=34 Exploring Operation: 98/49=2, Resulting Numbers: [64, 52, 2] Generated Node #0,1: 54:[64, 52, 2] Operation: 98/49=2 Exploring Operation: 98-49=49, Resulting Numbers: [64, 52, 49] Generated Node #0,2: 54:[64, 52, 49] Operation: 98-49=49 Exploring Operation: 98-52=46, Resulting Numbers: [64, 49, 46] Generated Node #0,3: 54:[64, 49, 46] Operation: 98-52=46 Moving to Node #0,1 Current State: 54:[64, 52, 2], Operations: ['98/49=2'] Exploring Operation: 64-2=62, Resulting Numbers: [52, 62] Generated Node #0,1,0: 54:[52, 62] Operation: 64-2=62 Exploring Operation: 64-52=12, Resulting Numbers: [2, 12] Generated Node #0,1,1: 54:[2, 12] Operation: 64-52=12 Exploring Operation: 64/2=32, Resulting Numbers: [52, 32] Generated Node #0,1,2: 54:[52, 32] Operation: 64/2=32 Exploring Operation: 52+2=54, Resulting Numbers: [64, 54] Generated Node #0,1,3: 54:[64, 54] Operation: 52+2=54 Moving to Node #0,0 Current State: 54:[52, 49, 34], Operations: ['98-64=34'] Exploring Operation: 49+34=83, Resulting Numbers: [52, 83] Generated Node #0,0,0: 54:[52, 83] Operation: 49+34=83 Exploring Operation: 52-34=18, Resulting Numbers: [49, 18] Generated Node #0,0,1: 54:[49, 18] Operation: 52-34=18 Exploring Operation: 49-34=15, Resulting Numbers: [52, 15] Generated Node #0,0,2: 54:[52, 15] Operation: 49-34=15 Exploring Operation: 52-49=3, Resulting Numbers: [34, 3] Generated Node #0,0,3: 54:[34, 3] Operation: 52-49=3 Moving to Node #0,2 Current State: 54:[64, 52, 49], Operations: ['98-49=49'] Exploring Operation: 52-49=3, Resulting Numbers: [64, 3] Generated Node #0,2,0: 54:[64, 3] Operation: 52-49=3 Exploring Operation: 64-52=12, Resulting Numbers: [49, 12] Generated Node #0,2,1: 54:[49, 12] Operation: 64-52=12 Exploring Operation: 52+49=101, Resulting Numbers: [64, 101] Generated Node #0,2,2: 54:[64, 101] Operation: 52+49=101 Exploring Operation: 64-49=15, Resulting Numbers: [52, 15] Generated Node #0,2,3: 54:[52, 15] Operation: 64-49=15 Moving to Node #0,3 Current State: 54:[64, 49, 46], Operations: ['98-52=46'] Exploring Operation: 49-46=3, Resulting Numbers: [64, 3] Generated Node #0,3,0: 54:[64, 3] Operation: 49-46=3 Exploring Operation: 49+46=95, Resulting Numbers: [64, 95] Generated Node #0,3,1: 54:[64, 95] Operation: 49+46=95 Exploring Operation: 64-46=18, Resulting Numbers: [49, 18] Generated Node #0,3,2: 54:[49, 18] Operation: 64-46=18 Exploring Operation: 64-49=15, Resulting Numbers: [46, 15] Generated Node #0,3,3: 54:[46, 15] Operation: 64-49=15 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 54:[49, 18], Operations: ['98-52=46', '64-46=18'] Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,54 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 54:[64, 3], Operations: ['98-52=46', '49-46=3'] Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,54 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 54:[46, 15], Operations: ['98-52=46', '64-49=15'] Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,54 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 54:[64, 95], Operations: ['98-52=46', '49+46=95'] Exploring Operation: 64*95=6080, Resulting Numbers: [6080] 6080,54 unequal: No Solution Exploring Operation: 95-64=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 64+95=159, Resulting Numbers: [159] 159,54 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: 54:[2, 12], Operations: ['98/49=2', '64-52=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,54 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[52, 15], Operations: ['98-64=34', '49-34=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,54 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[49, 18], Operations: ['98-64=34', '52-34=18'] Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,54 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[52, 15], Operations: ['98-49=49', '64-49=15'] Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,54 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[34, 3], Operations: ['98-64=34', '52-49=3'] Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,54 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[52, 32], Operations: ['98/49=2', '64/2=32'] Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,54 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,54 unequal: No Solution Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[49, 12], Operations: ['98-49=49', '64-52=12'] Exploring Operation: 49-12=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 49+12=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 49*12=588, Resulting Numbers: [588] 588,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[52, 62], Operations: ['98/49=2', '64-2=62'] Exploring Operation: 52+62=114, Resulting Numbers: [114] 114,54 unequal: No Solution Exploring Operation: 52*62=3224, Resulting Numbers: [3224] 3224,54 unequal: No Solution Exploring Operation: 62-52=10, Resulting Numbers: [10] 10,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[64, 3], Operations: ['98-49=49', '52-49=3'] Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,54 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,54 unequal: No Solution Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[64, 54], Operations: ['98/49=2', '52+2=54'] Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 64*54=3456, Resulting Numbers: [3456] 3456,54 unequal: No Solution Exploring Operation: 64+54=118, Resulting Numbers: [118] 118,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[52, 83], Operations: ['98-64=34', '49+34=83'] Exploring Operation: 83-52=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 52+83=135, Resulting Numbers: [135] 135,54 unequal: No Solution Exploring Operation: 52*83=4316, Resulting Numbers: [4316] 4316,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[64, 101], Operations: ['98-49=49', '52+49=101'] Exploring Operation: 64*101=6464, Resulting Numbers: [6464] 6464,54 unequal: No Solution Exploring Operation: 64+101=165, Resulting Numbers: [165] 165,54 unequal: No Solution Exploring Operation: 101-64=37, Resulting Numbers: [37] 37,54 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 21, 7, 14, 68 ]
65
[ "21*7=147", "14+68=82", "147-82=65" ]
Current State: 65:[21, 7, 14, 68], Operations: [] Exploring Operation: 21*7=147, Resulting Numbers: [14, 68, 147] Generated Node #2: [14, 68, 147] from Operation: 21*7=147 Current State: 65:[14, 68, 147], Operations: ['21*7=147'] Exploring Operation: 14+68=82, Resulting Numbers: [147, 82] Generated Node #3: [147, 82] from Operation: 14+68=82 Current State: 65:[147, 82], Operations: ['21*7=147', '14+68=82'] Exploring Operation: 147-82=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[21, 7, 14, 68], Operations: [] Exploring Operation: 21-7=14, Resulting Numbers: [14, 68, 14] Generated Node #0,0: 65:[14, 68, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [14, 68, 3] Generated Node #0,1: 65:[14, 68, 3] Operation: 21/7=3 Exploring Operation: 21-14=7, Resulting Numbers: [7, 68, 7] Generated Node #0,2: 65:[7, 68, 7] Operation: 21-14=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[14, 68, 14], Operations: ['21-7=14'] Exploring Operation: 14/14=1, Resulting Numbers: [68, 1] Generated Node #0,0,0: 65:[68, 1] Operation: 14/14=1 Exploring Operation: 68-14=54, Resulting Numbers: [14, 54] Generated Node #0,0,1: 65:[14, 54] Operation: 68-14=54 Exploring Operation: 14-14=0, Resulting Numbers: [68, 0] Generated Node #0,0,2: 65:[68, 0] Operation: 14-14=0 Moving to Node #0,0,0 Current State: 65:[68, 1], Operations: ['21-7=14', '14/14=1'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,65 unequal: No Solution Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,65 unequal: No Solution Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[68, 0], Operations: ['21-7=14', '14-14=0'] Exploring Operation: 68+0=68, Resulting Numbers: [68] 68,65 unequal: No Solution Exploring Operation: 68*0=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 68-0=68, Resulting Numbers: [68] 68,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[14, 54], Operations: ['21-7=14', '68-14=54'] Exploring Operation: 14*54=756, Resulting Numbers: [756] 756,65 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 14+54=68, Resulting Numbers: [68] 68,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[14, 68, 3], Operations: ['21/7=3'] Exploring Operation: 14+3=17, Resulting Numbers: [68, 17] Generated Node #0,1,0: 65:[68, 17] Operation: 14+3=17 Exploring Operation: 14-3=11, Resulting Numbers: [68, 11] Generated Node #0,1,1: 65:[68, 11] Operation: 14-3=11 Exploring Operation: 68-3=65, Resulting Numbers: [14, 65] Generated Node #0,1,2: 65:[14, 65] Operation: 68-3=65 Moving to Node #0,1,2 Current State: 65:[14, 65], Operations: ['21/7=3', '68-3=65'] Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,65 unequal: No Solution Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,65 unequal: No Solution Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[68, 11], Operations: ['21/7=3', '14-3=11'] Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,65 unequal: No Solution Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,65 unequal: No Solution Exploring Operation: 68*11=748, Resulting Numbers: [748] 748,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[68, 17], Operations: ['21/7=3', '14+3=17'] Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,65 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[7, 68, 7], Operations: ['21-14=7'] Exploring Operation: 7+7=14, Resulting Numbers: [68, 14] Generated Node #0,2,0: 65:[68, 14] Operation: 7+7=14 Exploring Operation: 68-7=61, Resulting Numbers: [7, 61] Generated Node #0,2,1: 65:[7, 61] Operation: 68-7=61 Exploring Operation: 68-7=61, Resulting Numbers: [7, 61] Generated Node #0,2,2: 65:[7, 61] Operation: 68-7=61 Moving to Node #0,2,0 Current State: 65:[68, 14], Operations: ['21-14=7', '7+7=14'] Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,65 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[7, 61], Operations: ['21-14=7', '68-7=61'] Exploring Operation: 7+61=68, Resulting Numbers: [68] 68,65 unequal: No Solution Exploring Operation: 7*61=427, Resulting Numbers: [427] 427,65 unequal: No Solution Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[7, 61], Operations: ['21-14=7', '68-7=61'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 7*61=427, Resulting Numbers: [427] 427,65 unequal: No Solution Exploring Operation: 7+61=68, Resulting Numbers: [68] 68,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 4, 38, 47, 9 ]
96
[ "4*38=152", "47+9=56", "152-56=96" ]
Current State: 96:[4, 38, 47, 9], Operations: [] Exploring Operation: 4*38=152, Resulting Numbers: [47, 9, 152] Generated Node #2: [47, 9, 152] from Operation: 4*38=152 Current State: 96:[47, 9, 152], Operations: ['4*38=152'] Exploring Operation: 47+9=56, Resulting Numbers: [152, 56] Generated Node #3: [152, 56] from Operation: 47+9=56 Current State: 96:[152, 56], Operations: ['4*38=152', '47+9=56'] Exploring Operation: 152-56=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[4, 38, 47, 9], Operations: [] Exploring Operation: 38+9=47, Resulting Numbers: [4, 47, 47] Generated Node #0,0: 96:[4, 47, 47] Operation: 38+9=47 Exploring Operation: 47-38=9, Resulting Numbers: [4, 9, 9] Generated Node #0,1: 96:[4, 9, 9] Operation: 47-38=9 Exploring Operation: 38-4=34, Resulting Numbers: [47, 9, 34] Generated Node #0,2: 96:[47, 9, 34] Operation: 38-4=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[4, 47, 47], Operations: ['38+9=47'] Exploring Operation: 47/47=1, Resulting Numbers: [4, 1] Generated Node #0,0,0: 96:[4, 1] Operation: 47/47=1 Exploring Operation: 47-47=0, Resulting Numbers: [4, 0] Generated Node #0,0,1: 96:[4, 0] Operation: 47-47=0 Exploring Operation: 47+47=94, Resulting Numbers: [4, 94] Generated Node #0,0,2: 96:[4, 94] Operation: 47+47=94 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[4, 1], Operations: ['38+9=47', '47/47=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[4, 0], Operations: ['38+9=47', '47-47=0'] Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[4, 94], Operations: ['38+9=47', '47+47=94'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 4*94=376, Resulting Numbers: [376] 376,96 unequal: No Solution Exploring Operation: 4+94=98, Resulting Numbers: [98] 98,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[4, 9, 9], Operations: ['47-38=9'] Exploring Operation: 9/9=1, Resulting Numbers: [4, 1] Generated Node #0,1,0: 96:[4, 1] Operation: 9/9=1 Exploring Operation: 4+9=13, Resulting Numbers: [9, 13] Generated Node #0,1,1: 96:[9, 13] Operation: 4+9=13 Exploring Operation: 9-4=5, Resulting Numbers: [9, 5] Generated Node #0,1,2: 96:[9, 5] Operation: 9-4=5 Moving to Node #0,1,0 Current State: 96:[4, 1], Operations: ['47-38=9', '9/9=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[9, 13], Operations: ['47-38=9', '4+9=13'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[9, 5], Operations: ['47-38=9', '9-4=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[47, 9, 34], Operations: ['38-4=34'] Exploring Operation: 47-34=13, Resulting Numbers: [9, 13] Generated Node #0,2,0: 96:[9, 13] Operation: 47-34=13 Exploring Operation: 34-9=25, Resulting Numbers: [47, 25] Generated Node #0,2,1: 96:[47, 25] Operation: 34-9=25 Exploring Operation: 9+34=43, Resulting Numbers: [47, 43] Generated Node #0,2,2: 96:[47, 43] Operation: 9+34=43 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[9, 13], Operations: ['38-4=34', '47-34=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,96 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[47, 25], Operations: ['38-4=34', '34-9=25'] Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,96 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 96:[47, 43], Operations: ['38-4=34', '9+34=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 6, 33, 97, 69 ]
91
[ "69-33=36", "36/6=6", "97-6=91" ]
Current State: 91:[6, 33, 97, 69], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [6, 97, 36] Generated Node #2: [6, 97, 36] from Operation: 69-33=36 Current State: 91:[6, 97, 36], Operations: ['69-33=36'] Exploring Operation: 36/6=6, Resulting Numbers: [97, 6] Generated Node #3: [97, 6] from Operation: 36/6=6 Current State: 91:[97, 6], Operations: ['69-33=36', '36/6=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[6, 33, 97, 69], Operations: [] Exploring Operation: 33-6=27, Resulting Numbers: [97, 69, 27] Generated Node #0,0: 91:[97, 69, 27] Operation: 33-6=27 Exploring Operation: 97-69=28, Resulting Numbers: [6, 33, 28] Generated Node #0,1: 91:[6, 33, 28] Operation: 97-69=28 Exploring Operation: 69-33=36, Resulting Numbers: [6, 97, 36] Generated Node #0,2: 91:[6, 97, 36] Operation: 69-33=36 Exploring Operation: 97-6=91, Resulting Numbers: [33, 69, 91] Generated Node #0,3: 91:[33, 69, 91] Operation: 97-6=91 Exploring Operation: 33+69=102, Resulting Numbers: [6, 97, 102] Generated Node #0,4: 91:[6, 97, 102] Operation: 33+69=102 Moving to Node #0,4 Current State: 91:[6, 97, 102], Operations: ['33+69=102'] Exploring Operation: 102/6=17, Resulting Numbers: [97, 17] Generated Node #0,4,0: 91:[97, 17] Operation: 102/6=17 Exploring Operation: 6+97=103, Resulting Numbers: [102, 103] Generated Node #0,4,1: 91:[102, 103] Operation: 6+97=103 Exploring Operation: 102-97=5, Resulting Numbers: [6, 5] Generated Node #0,4,2: 91:[6, 5] Operation: 102-97=5 Exploring Operation: 97-6=91, Resulting Numbers: [102, 91] Generated Node #0,4,3: 91:[102, 91] Operation: 97-6=91 Exploring Operation: 102-6=96, Resulting Numbers: [97, 96] Generated Node #0,4,4: 91:[97, 96] Operation: 102-6=96 Moving to Node #0,2 Current State: 91:[6, 97, 36], Operations: ['69-33=36'] Exploring Operation: 36-6=30, Resulting Numbers: [97, 30] Generated Node #0,2,0: 91:[97, 30] Operation: 36-6=30 Exploring Operation: 6+97=103, Resulting Numbers: [36, 103] Generated Node #0,2,1: 91:[36, 103] Operation: 6+97=103 Exploring Operation: 97-36=61, Resulting Numbers: [6, 61] Generated Node #0,2,2: 91:[6, 61] Operation: 97-36=61 Exploring Operation: 97-6=91, Resulting Numbers: [36, 91] Generated Node #0,2,3: 91:[36, 91] Operation: 97-6=91 Exploring Operation: 36/6=6, Resulting Numbers: [97, 6] Generated Node #0,2,4: 91:[97, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 91:[97, 6], Operations: ['69-33=36', '36/6=6'] Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[6, 33, 97, 69], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [6, 97, 36] Generated Node #0,2: 91:[6, 97, 36] Operation: 69-33=36 Moving to Node #0,2 Current State: 91:[6, 97, 36], Operations: ['69-33=36'] Exploring Operation: 36/6=6, Resulting Numbers: [97, 6] Generated Node #0,2,4: 91:[97, 6] Operation: 36/6=6 Moving to Node #0,2,4 Current State: 91:[97, 6], Operations: ['69-33=36', '36/6=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 41, 23, 1, 43 ]
47
[ "43-41=2", "23*2=46", "1+46=47" ]
Current State: 47:[41, 23, 1, 43], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [23, 1, 2] Generated Node #2: [23, 1, 2] from Operation: 43-41=2 Current State: 47:[23, 1, 2], Operations: ['43-41=2'] Exploring Operation: 23*2=46, Resulting Numbers: [1, 46] Generated Node #3: [1, 46] from Operation: 23*2=46 Current State: 47:[1, 46], Operations: ['43-41=2', '23*2=46'] Exploring Operation: 1+46=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[41, 23, 1, 43], Operations: [] Exploring Operation: 41+1=42, Resulting Numbers: [23, 43, 42] Generated Node #0,0: 47:[23, 43, 42] Operation: 41+1=42 Moving to Node #0,0 Current State: 47:[23, 43, 42], Operations: ['41+1=42'] Exploring Operation: 23+42=65, Resulting Numbers: [43, 65] Generated Node #0,0,0: 47:[43, 65] Operation: 23+42=65 Moving to Node #0,0,0 Current State: 47:[43, 65], Operations: ['41+1=42', '23+42=65'] Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,47 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 26, 48, 2, 46 ]
34
[ "48-26=22", "46+22=68", "68/2=34" ]
Current State: 34:[26, 48, 2, 46], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [2, 46, 22] Generated Node #2: [2, 46, 22] from Operation: 48-26=22 Current State: 34:[2, 46, 22], Operations: ['48-26=22'] Exploring Operation: 46+22=68, Resulting Numbers: [2, 68] Generated Node #3: [2, 68] from Operation: 46+22=68 Current State: 34:[2, 68], Operations: ['48-26=22', '46+22=68'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[26, 48, 2, 46], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [26, 2, 2] Generated Node #0,0: 34:[26, 2, 2] Operation: 48-46=2 Exploring Operation: 48-26=22, Resulting Numbers: [2, 46, 22] Generated Node #0,1: 34:[2, 46, 22] Operation: 48-26=22 Moving to Node #0,0 Current State: 34:[26, 2, 2], Operations: ['48-46=2'] Exploring Operation: 26/2=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 34:[2, 13] Operation: 26/2=13 Exploring Operation: 26/2=13, Resulting Numbers: [2, 13] Generated Node #0,0,1: 34:[2, 13] Operation: 26/2=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[2, 13], Operations: ['48-46=2', '26/2=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[2, 13], Operations: ['48-46=2', '26/2=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,34 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: 34:[2, 46, 22], Operations: ['48-26=22'] Exploring Operation: 46/2=23, Resulting Numbers: [22, 23] Generated Node #0,1,0: 34:[22, 23] Operation: 46/2=23 Exploring Operation: 46-22=24, Resulting Numbers: [2, 24] Generated Node #0,1,1: 34:[2, 24] Operation: 46-22=24 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[2, 24], Operations: ['48-26=22', '46-22=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[22, 23], Operations: ['48-26=22', '46/2=23'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,34 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
[ 22, 98, 2, 37 ]
81
[ "22+98=120", "2+37=39", "120-39=81" ]
Current State: 81:[22, 98, 2, 37], Operations: [] Exploring Operation: 22+98=120, Resulting Numbers: [2, 37, 120] Generated Node #2: [2, 37, 120] from Operation: 22+98=120 Current State: 81:[2, 37, 120], Operations: ['22+98=120'] Exploring Operation: 2+37=39, Resulting Numbers: [120, 39] Generated Node #3: [120, 39] from Operation: 2+37=39 Current State: 81:[120, 39], Operations: ['22+98=120', '2+37=39'] Exploring Operation: 120-39=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[22, 98, 2, 37], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [98, 2, 15] Generated Node #0,0: 81:[98, 2, 15] Operation: 37-22=15 Exploring Operation: 98-37=61, Resulting Numbers: [22, 2, 61] Generated Node #0,1: 81:[22, 2, 61] Operation: 98-37=61 Exploring Operation: 98-22=76, Resulting Numbers: [2, 37, 76] Generated Node #0,2: 81:[2, 37, 76] Operation: 98-22=76 Moving to Node #0,2 Current State: 81:[2, 37, 76], Operations: ['98-22=76'] Exploring Operation: 2+76=78, Resulting Numbers: [37, 78] Generated Node #0,2,0: 81:[37, 78] Operation: 2+76=78 Exploring Operation: 2*37=74, Resulting Numbers: [76, 74] Generated Node #0,2,1: 81:[76, 74] Operation: 2*37=74 Exploring Operation: 37-2=35, Resulting Numbers: [76, 35] Generated Node #0,2,2: 81:[76, 35] Operation: 37-2=35 Moving to Node #0,0 Current State: 81:[98, 2, 15], Operations: ['37-22=15'] Exploring Operation: 2*15=30, Resulting Numbers: [98, 30] Generated Node #0,0,0: 81:[98, 30] Operation: 2*15=30 Exploring Operation: 98-15=83, Resulting Numbers: [2, 83] Generated Node #0,0,1: 81:[2, 83] Operation: 98-15=83 Exploring Operation: 98-2=96, Resulting Numbers: [15, 96] Generated Node #0,0,2: 81:[15, 96] Operation: 98-2=96 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[2, 83], Operations: ['37-22=15', '98-15=83'] Exploring Operation: 2*83=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[22, 98, 2, 37], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [98, 2, 15] Generated Node #0,0: 81:[98, 2, 15] Operation: 37-22=15 Moving to Node #0,0 Current State: 81:[98, 2, 15], Operations: ['37-22=15'] Exploring Operation: 98-15=83, Resulting Numbers: [2, 83] Generated Node #0,0,1: 81:[2, 83] Operation: 98-15=83 Moving to Node #0,0,1 Current State: 81:[2, 83], Operations: ['37-22=15', '98-15=83'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 63, 23, 14, 54 ]
46
[ "63+23=86", "54-14=40", "86-40=46" ]
Current State: 46:[63, 23, 14, 54], Operations: [] Exploring Operation: 63+23=86, Resulting Numbers: [14, 54, 86] Generated Node #2: [14, 54, 86] from Operation: 63+23=86 Current State: 46:[14, 54, 86], Operations: ['63+23=86'] Exploring Operation: 54-14=40, Resulting Numbers: [86, 40] Generated Node #3: [86, 40] from Operation: 54-14=40 Current State: 46:[86, 40], Operations: ['63+23=86', '54-14=40'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[63, 23, 14, 54], Operations: [] Exploring Operation: 63-14=49, Resulting Numbers: [23, 54, 49] Generated Node #0,0: 46:[23, 54, 49] Operation: 63-14=49 Exploring Operation: 63-23=40, Resulting Numbers: [14, 54, 40] Generated Node #0,1: 46:[14, 54, 40] Operation: 63-23=40 Exploring Operation: 63-54=9, Resulting Numbers: [23, 14, 9] Generated Node #0,2: 46:[23, 14, 9] Operation: 63-54=9 Moving to Node #0,0 Current State: 46:[23, 54, 49], Operations: ['63-14=49'] Exploring Operation: 54-23=31, Resulting Numbers: [49, 31] Generated Node #0,0,0: 46:[49, 31] Operation: 54-23=31 Exploring Operation: 54-49=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 46:[23, 5] Operation: 54-49=5 Exploring Operation: 49-23=26, Resulting Numbers: [54, 26] Generated Node #0,0,2: 46:[54, 26] Operation: 49-23=26 Moving to Node #0,2 Current State: 46:[23, 14, 9], Operations: ['63-54=9'] Exploring Operation: 14-9=5, Resulting Numbers: [23, 5] Generated Node #0,2,0: 46:[23, 5] Operation: 14-9=5 Exploring Operation: 23-14=9, Resulting Numbers: [9, 9] Generated Node #0,2,1: 46:[9, 9] Operation: 23-14=9 Exploring Operation: 14+9=23, Resulting Numbers: [23, 23] Generated Node #0,2,2: 46:[23, 23] Operation: 14+9=23 Moving to Node #0,1 Current State: 46:[14, 54, 40], Operations: ['63-23=40'] Exploring Operation: 40-14=26, Resulting Numbers: [54, 26] Generated Node #0,1,0: 46:[54, 26] Operation: 40-14=26 Exploring Operation: 14+40=54, Resulting Numbers: [54, 54] Generated Node #0,1,1: 46:[54, 54] Operation: 14+40=54 Exploring Operation: 54-14=40, Resulting Numbers: [40, 40] Generated Node #0,1,2: 46:[40, 40] Operation: 54-14=40 Moving to Node #0,2,2 Current State: 46:[23, 23], Operations: ['63-54=9', '14+9=23'] Exploring Operation: 23-23=0, Resulting Numbers: [0] 0,46 unequal: No Solution Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[63, 23, 14, 54], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [23, 14, 9] Generated Node #0,2: 46:[23, 14, 9] Operation: 63-54=9 Moving to Node #0,2 Current State: 46:[23, 14, 9], Operations: ['63-54=9'] Exploring Operation: 14+9=23, Resulting Numbers: [23, 23] Generated Node #0,2,2: 46:[23, 23] Operation: 14+9=23 Moving to Node #0,2,2 Current State: 46:[23, 23], Operations: ['63-54=9', '14+9=23'] Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
0.984375
hs_3
sum_heuristic
[ 87, 3, 29, 90 ]
31
[ "87/29=3", "3+90=93", "93/3=31" ]
Current State: 31:[87, 3, 29, 90], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [3, 90, 3] Generated Node #2: [3, 90, 3] from Operation: 87/29=3 Current State: 31:[3, 90, 3], Operations: ['87/29=3'] Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,31 equal: Goal Reached Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[87, 3, 29, 90], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [3, 29, 3] Generated Node #0,0: 31:[3, 29, 3] Operation: 90-87=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[3, 29, 3], Operations: ['90-87=3'] Exploring Operation: 3*3=9, Resulting Numbers: [29, 9] Generated Node #0,0,0: 31:[29, 9] Operation: 3*3=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[29, 9], Operations: ['90-87=3', '3*3=9'] Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 76, 30, 63, 21 ]
86
[ "30*21=630", "630/63=10", "76+10=86" ]
Current State: 86:[76, 30, 63, 21], Operations: [] Exploring Operation: 30*21=630, Resulting Numbers: [76, 63, 630] Generated Node #2: [76, 63, 630] from Operation: 30*21=630 Current State: 86:[76, 63, 630], Operations: ['30*21=630'] Exploring Operation: 630/63=10, Resulting Numbers: [76, 10] Generated Node #3: [76, 10] from Operation: 630/63=10 Current State: 86:[76, 10], Operations: ['30*21=630', '630/63=10'] Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[76, 30, 63, 21], Operations: [] Exploring Operation: 63-21=42, Resulting Numbers: [76, 30, 42] Generated Node #0,0: 86:[76, 30, 42] Operation: 63-21=42 Exploring Operation: 63/21=3, Resulting Numbers: [76, 30, 3] Generated Node #0,1: 86:[76, 30, 3] Operation: 63/21=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[76, 30, 42], Operations: ['63-21=42'] Exploring Operation: 76-30=46, Resulting Numbers: [42, 46] Generated Node #0,0,0: 86:[42, 46] Operation: 76-30=46 Exploring Operation: 42-30=12, Resulting Numbers: [76, 12] Generated Node #0,0,1: 86:[76, 12] Operation: 42-30=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[42, 46], Operations: ['63-21=42', '76-30=46'] Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,86 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,86 unequal: No Solution No 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: 86:[76, 12], Operations: ['63-21=42', '42-30=12'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,86 unequal: No Solution Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,86 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: 86:[76, 30, 3], Operations: ['63/21=3'] Exploring Operation: 30*3=90, Resulting Numbers: [76, 90] Generated Node #0,1,0: 86:[76, 90] Operation: 30*3=90 Exploring Operation: 76-30=46, Resulting Numbers: [3, 46] Generated Node #0,1,1: 86:[3, 46] Operation: 76-30=46 Moving to Node #0,1,1 Current State: 86:[3, 46], Operations: ['63/21=3', '76-30=46'] Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[76, 90], Operations: ['63/21=3', '30*3=90'] Exploring Operation: 76+90=166, Resulting Numbers: [166] 166,86 unequal: No Solution Exploring Operation: 90-76=14, Resulting Numbers: [14] 14,86 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
[ 68, 20, 20, 11 ]
28
[ "68+20=88", "88/11=8", "20+8=28" ]
Current State: 28:[68, 20, 20, 11], Operations: [] Exploring Operation: 68+20=88, Resulting Numbers: [11, 88] Generated Node #2: [11, 88] from Operation: 68+20=88 Current State: 28:[11, 88], Operations: ['68+20=88'] Exploring Operation: 88/11=8, Resulting Numbers: [8] 8,28 equal: Goal Reached Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[68, 20, 20, 11], Operations: [] Exploring Operation: 20/20=1, Resulting Numbers: [68, 11, 1] Generated Node #0,0: 28:[68, 11, 1] Operation: 20/20=1 Exploring Operation: 68-20=48, Resulting Numbers: [20, 11, 48] Generated Node #0,1: 28:[20, 11, 48] Operation: 68-20=48 Exploring Operation: 68-20=48, Resulting Numbers: [20, 11, 48] Generated Node #0,2: 28:[20, 11, 48] Operation: 68-20=48 Exploring Operation: 68-11=57, Resulting Numbers: [20, 20, 57] Generated Node #0,3: 28:[20, 20, 57] Operation: 68-11=57 Moving to Node #0,1 Current State: 28:[20, 11, 48], Operations: ['68-20=48'] Exploring Operation: 48-20=28, Resulting Numbers: [11, 28] Generated Node #0,1,0: 28:[11, 28] Operation: 48-20=28 Exploring Operation: 20-11=9, Resulting Numbers: [48, 9] Generated Node #0,1,1: 28:[48, 9] Operation: 20-11=9 Exploring Operation: 48-11=37, Resulting Numbers: [20, 37] Generated Node #0,1,2: 28:[20, 37] Operation: 48-11=37 Exploring Operation: 20+11=31, Resulting Numbers: [48, 31] Generated Node #0,1,3: 28:[48, 31] Operation: 20+11=31 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[11, 28], Operations: ['68-20=48', '48-20=28'] Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,28 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[20, 37], Operations: ['68-20=48', '48-11=37'] Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,28 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[48, 9], Operations: ['68-20=48', '20-11=9'] Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,28 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 28:[48, 31], Operations: ['68-20=48', '20+11=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,28 unequal: No Solution Exploring Operation: 48*31=1488, Resulting Numbers: [1488] 1488,28 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,28 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: 28:[20, 11, 48], Operations: ['68-20=48'] Exploring Operation: 20+11=31, Resulting Numbers: [48, 31] Generated Node #0,2,0: 28:[48, 31] Operation: 20+11=31 Exploring Operation: 48-11=37, Resulting Numbers: [20, 37] Generated Node #0,2,1: 28:[20, 37] Operation: 48-11=37 Exploring Operation: 48-20=28, Resulting Numbers: [11, 28] Generated Node #0,2,2: 28:[11, 28] Operation: 48-20=28 Exploring Operation: 20-11=9, Resulting Numbers: [48, 9] Generated Node #0,2,3: 28:[48, 9] Operation: 20-11=9 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[11, 28], Operations: ['68-20=48', '48-20=28'] Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,28 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 28:[20, 37], Operations: ['68-20=48', '48-11=37'] Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,28 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 28:[48, 9], Operations: ['68-20=48', '20-11=9'] Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,28 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 28:[48, 31], Operations: ['68-20=48', '20+11=31'] Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 48*31=1488, Resulting Numbers: [1488] 1488,28 unequal: No Solution Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 28:[20, 20, 57], Operations: ['68-11=57'] Exploring Operation: 57-20=37, Resulting Numbers: [20, 37] Generated Node #0,3,0: 28:[20, 37] Operation: 57-20=37 Exploring Operation: 20-20=0, Resulting Numbers: [57, 0] Generated Node #0,3,1: 28:[57, 0] Operation: 20-20=0 Exploring Operation: 57-20=37, Resulting Numbers: [20, 37] Generated Node #0,3,2: 28:[20, 37] Operation: 57-20=37 Exploring Operation: 20/20=1, Resulting Numbers: [57, 1] Generated Node #0,3,3: 28:[57, 1] Operation: 20/20=1 Moving to Node #0,0 Current State: 28:[68, 11, 1], Operations: ['20/20=1'] Exploring Operation: 68-1=67, Resulting Numbers: [11, 67] Generated Node #0,0,0: 28:[11, 67] Operation: 68-1=67 Exploring Operation: 68*1=68, Resulting Numbers: [11, 68] Generated Node #0,0,1: 28:[11, 68] Operation: 68*1=68 Exploring Operation: 11+1=12, Resulting Numbers: [68, 12] Generated Node #0,0,2: 28:[68, 12] Operation: 11+1=12 Exploring Operation: 68-11=57, Resulting Numbers: [1, 57] Generated Node #0,0,3: 28:[1, 57] Operation: 68-11=57 Moving to Node #0,3,0 Current State: 28:[20, 37], Operations: ['68-11=57', '57-20=37'] Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,28 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,28 unequal: No Solution Moving to Node #0,3,2 Current State: 28:[20, 37], Operations: ['68-11=57', '57-20=37'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,28 unequal: No Solution Moving to Node #0,3,3 Current State: 28:[57, 1], Operations: ['68-11=57', '20/20=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[1, 57], Operations: ['20/20=1', '68-11=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,28 unequal: No Solution Moving to Node #0,3,1 Current State: 28:[57, 0], Operations: ['68-11=57', '20-20=0'] Exploring Operation: 57+0=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 57*0=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 57-0=57, Resulting Numbers: [57] 57,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[11, 67], Operations: ['20/20=1', '68-1=67'] Exploring Operation: 11+67=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 11*67=737, Resulting Numbers: [737] 737,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[68, 12], Operations: ['20/20=1', '11+1=12'] Exploring Operation: 68+12=80, Resulting Numbers: [80] 80,28 unequal: No Solution Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,28 unequal: No Solution Exploring Operation: 68*12=816, Resulting Numbers: [816] 816,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[11, 68], Operations: ['20/20=1', '68*1=68'] Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 11+68=79, Resulting Numbers: [79] 79,28 unequal: No Solution Exploring Operation: 11*68=748, Resulting Numbers: [748] 748,28 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 50, 15, 48, 33 ]
50
[ "50+15=65", "48-33=15", "65-15=50" ]
Current State: 50:[50, 15, 48, 33], Operations: [] Exploring Operation: 50+15=65, Resulting Numbers: [48, 33, 65] Generated Node #2: [48, 33, 65] from Operation: 50+15=65 Current State: 50:[48, 33, 65], Operations: ['50+15=65'] Exploring Operation: 48-33=15, Resulting Numbers: [65, 15] Generated Node #3: [65, 15] from Operation: 48-33=15 Current State: 50:[65, 15], Operations: ['50+15=65', '48-33=15'] Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[50, 15, 48, 33], Operations: [] Exploring Operation: 50-33=17, Resulting Numbers: [15, 48, 17] Generated Node #0,0: 50:[15, 48, 17] Operation: 50-33=17 Exploring Operation: 50-48=2, Resulting Numbers: [15, 33, 2] Generated Node #0,1: 50:[15, 33, 2] Operation: 50-48=2 Exploring Operation: 33-15=18, Resulting Numbers: [50, 48, 18] Generated Node #0,2: 50:[50, 48, 18] Operation: 33-15=18 Exploring Operation: 15+33=48, Resulting Numbers: [50, 48, 48] Generated Node #0,3: 50:[50, 48, 48] Operation: 15+33=48 Exploring Operation: 48-33=15, Resulting Numbers: [50, 15, 15] Generated Node #0,4: 50:[50, 15, 15] Operation: 48-33=15 Moving to Node #0,3 Current State: 50:[50, 48, 48], Operations: ['15+33=48'] Exploring Operation: 48+48=96, Resulting Numbers: [50, 96] Generated Node #0,3,0: 50:[50, 96] Operation: 48+48=96 Exploring Operation: 48/48=1, Resulting Numbers: [50, 1] Generated Node #0,3,1: 50:[50, 1] Operation: 48/48=1 Exploring Operation: 50-48=2, Resulting Numbers: [48, 2] Generated Node #0,3,2: 50:[48, 2] Operation: 50-48=2 Exploring Operation: 48-48=0, Resulting Numbers: [50, 0] Generated Node #0,3,3: 50:[50, 0] Operation: 48-48=0 Exploring Operation: 50-48=2, Resulting Numbers: [48, 2] Generated Node #0,3,4: 50:[48, 2] Operation: 50-48=2 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 50:[50, 1], Operations: ['15+33=48', '48/48=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[50, 15, 48, 33], Operations: [] Exploring Operation: 15+33=48, Resulting Numbers: [50, 48, 48] Generated Node #0,3: 50:[50, 48, 48] Operation: 15+33=48 Moving to Node #0,3 Current State: 50:[50, 48, 48], Operations: ['15+33=48'] Exploring Operation: 48/48=1, Resulting Numbers: [50, 1] Generated Node #0,3,1: 50:[50, 1] Operation: 48/48=1 Moving to Node #0,3,1 Current State: 50:[50, 1], Operations: ['15+33=48', '48/48=1'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 73, 2, 54, 7 ]
13
[ "73-54=19", "7+19=26", "26/2=13" ]
Current State: 13:[73, 2, 54, 7], Operations: [] Exploring Operation: 73-54=19, Resulting Numbers: [2, 7, 19] Generated Node #2: [2, 7, 19] from Operation: 73-54=19 Current State: 13:[2, 7, 19], Operations: ['73-54=19'] Exploring Operation: 7+19=26, Resulting Numbers: [2, 26] Generated Node #3: [2, 26] from Operation: 7+19=26 Current State: 13:[2, 26], Operations: ['73-54=19', '7+19=26'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[73, 2, 54, 7], Operations: [] Exploring Operation: 54/2=27, Resulting Numbers: [73, 7, 27] Generated Node #0,0: 13:[73, 7, 27] Operation: 54/2=27 Exploring Operation: 73-54=19, Resulting Numbers: [2, 7, 19] Generated Node #0,1: 13:[2, 7, 19] Operation: 73-54=19 Exploring Operation: 2*7=14, Resulting Numbers: [73, 54, 14] Generated Node #0,2: 13:[73, 54, 14] Operation: 2*7=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[2, 7, 19], Operations: ['73-54=19'] Exploring Operation: 2+7=9, Resulting Numbers: [19, 9] Generated Node #0,1,0: 13:[19, 9] Operation: 2+7=9 Exploring Operation: 19-2=17, Resulting Numbers: [7, 17] Generated Node #0,1,1: 13:[7, 17] Operation: 19-2=17 Exploring Operation: 2*7=14, Resulting Numbers: [19, 14] Generated Node #0,1,2: 13:[19, 14] Operation: 2*7=14 Moving to Node #0,1,2 Current State: 13:[19, 14], Operations: ['73-54=19', '2*7=14'] Exploring Operation: 19+14=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 19*14=266, Resulting Numbers: [266] 266,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[19, 9], Operations: ['73-54=19', '2+7=9'] Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,13 unequal: No Solution Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,13 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[7, 17], Operations: ['73-54=19', '19-2=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[73, 7, 27], Operations: ['54/2=27'] Exploring Operation: 27-7=20, Resulting Numbers: [73, 20] Generated Node #0,0,0: 13:[73, 20] Operation: 27-7=20 Exploring Operation: 73-7=66, Resulting Numbers: [27, 66] Generated Node #0,0,1: 13:[27, 66] Operation: 73-7=66 Exploring Operation: 73-27=46, Resulting Numbers: [7, 46] Generated Node #0,0,2: 13:[7, 46] Operation: 73-27=46 Moving to Node #0,0,2 Current State: 13:[7, 46], Operations: ['54/2=27', '73-27=46'] Exploring Operation: 7+46=53, Resulting Numbers: [53] 53,13 unequal: No Solution Exploring Operation: 7*46=322, Resulting Numbers: [322] 322,13 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[73, 20], Operations: ['54/2=27', '27-7=20'] Exploring Operation: 73*20=1460, Resulting Numbers: [1460] 1460,13 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,13 unequal: No Solution Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[27, 66], Operations: ['54/2=27', '73-7=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,13 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[73, 54, 14], Operations: ['2*7=14'] Exploring Operation: 73-54=19, Resulting Numbers: [14, 19] Generated Node #0,2,0: 13:[14, 19] Operation: 73-54=19 Exploring Operation: 73-14=59, Resulting Numbers: [54, 59] Generated Node #0,2,1: 13:[54, 59] Operation: 73-14=59 Exploring Operation: 54-14=40, Resulting Numbers: [73, 40] Generated Node #0,2,2: 13:[73, 40] Operation: 54-14=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[14, 19], Operations: ['2*7=14', '73-54=19'] Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 14*19=266, Resulting Numbers: [266] 266,13 unequal: No Solution Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[54, 59], Operations: ['2*7=14', '73-14=59'] Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,13 unequal: No Solution Exploring Operation: 54*59=3186, Resulting Numbers: [3186] 3186,13 unequal: No Solution Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,13 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:[73, 40], Operations: ['2*7=14', '54-14=40'] Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,13 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,13 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
[ 56, 6, 3, 47 ]
94
[ "56-6=50", "47-3=44", "50+44=94" ]
Current State: 94:[56, 6, 3, 47], Operations: [] Exploring Operation: 56-6=50, Resulting Numbers: [3, 47, 50] Generated Node #2: [3, 47, 50] from Operation: 56-6=50 Current State: 94:[3, 47, 50], Operations: ['56-6=50'] Exploring Operation: 47-3=44, Resulting Numbers: [50, 44] Generated Node #3: [50, 44] from Operation: 47-3=44 Current State: 94:[50, 44], Operations: ['56-6=50', '47-3=44'] Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[56, 6, 3, 47], Operations: [] Exploring Operation: 56-6=50, Resulting Numbers: [3, 47, 50] Generated Node #0,0: 94:[3, 47, 50] Operation: 56-6=50 Exploring Operation: 6-3=3, Resulting Numbers: [56, 47, 3] Generated Node #0,1: 94:[56, 47, 3] Operation: 6-3=3 Exploring Operation: 56-3=53, Resulting Numbers: [6, 47, 53] Generated Node #0,2: 94:[6, 47, 53] Operation: 56-3=53 Exploring Operation: 6/3=2, Resulting Numbers: [56, 47, 2] Generated Node #0,3: 94:[56, 47, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[3, 47, 50], Operations: ['56-6=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 94:[47, 47] Operation: 50-3=47 Exploring Operation: 3+47=50, Resulting Numbers: [50, 50] Generated Node #0,0,1: 94:[50, 50] Operation: 3+47=50 Exploring Operation: 50-47=3, Resulting Numbers: [3, 3] Generated Node #0,0,2: 94:[3, 3] Operation: 50-47=3 Exploring Operation: 47+50=97, Resulting Numbers: [3, 97] Generated Node #0,0,3: 94:[3, 97] Operation: 47+50=97 Moving to Node #0,0,0 Current State: 94:[47, 47], Operations: ['56-6=50', '50-3=47'] Exploring Operation: 47/47=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[56, 6, 3, 47], Operations: [] Exploring Operation: 56-6=50, Resulting Numbers: [3, 47, 50] Generated Node #0,0: 94:[3, 47, 50] Operation: 56-6=50 Moving to Node #0,0 Current State: 94:[3, 47, 50], Operations: ['56-6=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47, 47] Generated Node #0,0,0: 94:[47, 47] Operation: 50-3=47 Moving to Node #0,0,0 Current State: 94:[47, 47], Operations: ['56-6=50', '50-3=47'] Exploring Operation: 47+47=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 56, 53, 72, 21 ]
48
[ "56-53=3", "72-21=51", "51-3=48" ]
Current State: 48:[56, 53, 72, 21], Operations: [] Exploring Operation: 56-53=3, Resulting Numbers: [72, 21, 3] Generated Node #2: [72, 21, 3] from Operation: 56-53=3 Current State: 48:[72, 21, 3], Operations: ['56-53=3'] Exploring Operation: 72-21=51, Resulting Numbers: [3, 51] Generated Node #3: [3, 51] from Operation: 72-21=51 Current State: 48:[3, 51], Operations: ['56-53=3', '72-21=51'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[56, 53, 72, 21], Operations: [] Exploring Operation: 72-53=19, Resulting Numbers: [56, 21, 19] Generated Node #0,0: 48:[56, 21, 19] Operation: 72-53=19 Exploring Operation: 72-21=51, Resulting Numbers: [56, 53, 51] Generated Node #0,1: 48:[56, 53, 51] Operation: 72-21=51 Exploring Operation: 72-56=16, Resulting Numbers: [53, 21, 16] Generated Node #0,2: 48:[53, 21, 16] Operation: 72-56=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[53, 21, 16], Operations: ['72-56=16'] Exploring Operation: 53-16=37, Resulting Numbers: [21, 37] Generated Node #0,2,0: 48:[21, 37] Operation: 53-16=37 Exploring Operation: 21-16=5, Resulting Numbers: [53, 5] Generated Node #0,2,1: 48:[53, 5] Operation: 21-16=5 Exploring Operation: 53-21=32, Resulting Numbers: [16, 32] Generated Node #0,2,2: 48:[16, 32] Operation: 53-21=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[53, 5], Operations: ['72-56=16', '21-16=5'] Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,48 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[56, 53, 72, 21], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [53, 21, 16] Generated Node #0,2: 48:[53, 21, 16] Operation: 72-56=16 Moving to Node #0,2 Current State: 48:[53, 21, 16], Operations: ['72-56=16'] Exploring Operation: 21-16=5, Resulting Numbers: [53, 5] Generated Node #0,2,1: 48:[53, 5] Operation: 21-16=5 Moving to Node #0,2,1 Current State: 48:[53, 5], Operations: ['72-56=16', '21-16=5'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 46, 66, 38, 78 ]
72
[ "46+66=112", "78-38=40", "112-40=72" ]
Current State: 72:[46, 66, 38, 78], Operations: [] Exploring Operation: 46+66=112, Resulting Numbers: [38, 78, 112] Generated Node #2: [38, 78, 112] from Operation: 46+66=112 Current State: 72:[38, 78, 112], Operations: ['46+66=112'] Exploring Operation: 78-38=40, Resulting Numbers: [112, 40] Generated Node #3: [112, 40] from Operation: 78-38=40 Current State: 72:[112, 40], Operations: ['46+66=112', '78-38=40'] Exploring Operation: 112-40=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[46, 66, 38, 78], Operations: [] Exploring Operation: 66-46=20, Resulting Numbers: [38, 78, 20] Generated Node #0,0: 72:[38, 78, 20] Operation: 66-46=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[38, 78, 20], Operations: ['66-46=20'] Exploring Operation: 78-38=40, Resulting Numbers: [20, 40] Generated Node #0,0,0: 72:[20, 40] Operation: 78-38=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[20, 40], Operations: ['66-46=20', '78-38=40'] Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,72 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_1
mult_heuristic
[ 36, 8, 56, 97 ]
13
[ "36-8=28", "97-56=41", "41-28=13" ]
Current State: 13:[36, 8, 56, 97], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [56, 97, 28] Generated Node #2: [56, 97, 28] from Operation: 36-8=28 Current State: 13:[56, 97, 28], Operations: ['36-8=28'] Exploring Operation: 97-56=41, Resulting Numbers: [28, 41] Generated Node #3: [28, 41] from Operation: 97-56=41 Current State: 13:[28, 41], Operations: ['36-8=28', '97-56=41'] Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[36, 8, 56, 97], Operations: [] Exploring Operation: 97-36=61, Resulting Numbers: [8, 56, 61] Generated Node #0,0: 13:[8, 56, 61] Operation: 97-36=61 Exploring Operation: 56-36=20, Resulting Numbers: [8, 97, 20] Generated Node #0,1: 13:[8, 97, 20] Operation: 56-36=20 Exploring Operation: 97-56=41, Resulting Numbers: [36, 8, 41] Generated Node #0,2: 13:[36, 8, 41] Operation: 97-56=41 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[36, 8, 41], Operations: ['97-56=41'] Exploring Operation: 41-8=33, Resulting Numbers: [36, 33] Generated Node #0,2,0: 13:[36, 33] Operation: 41-8=33 Exploring Operation: 36-8=28, Resulting Numbers: [41, 28] Generated Node #0,2,1: 13:[41, 28] Operation: 36-8=28 Exploring Operation: 41-36=5, Resulting Numbers: [8, 5] Generated Node #0,2,2: 13:[8, 5] Operation: 41-36=5 Moving to Node #0,2,2 Current State: 13:[8, 5], Operations: ['97-56=41', '41-36=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[36, 8, 56, 97], Operations: [] Exploring Operation: 97-56=41, Resulting Numbers: [36, 8, 41] Generated Node #0,2: 13:[36, 8, 41] Operation: 97-56=41 Moving to Node #0,2 Current State: 13:[36, 8, 41], Operations: ['97-56=41'] Exploring Operation: 41-36=5, Resulting Numbers: [8, 5] Generated Node #0,2,2: 13:[8, 5] Operation: 41-36=5 Moving to Node #0,2,2 Current State: 13:[8, 5], Operations: ['97-56=41', '41-36=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 1, 61, 35, 68 ]
59
[ "35-1=34", "68/34=2", "61-2=59" ]
Current State: 59:[1, 61, 35, 68], Operations: [] Exploring Operation: 35-1=34, Resulting Numbers: [61, 68, 34] Generated Node #2: [61, 68, 34] from Operation: 35-1=34 Current State: 59:[61, 68, 34], Operations: ['35-1=34'] Exploring Operation: 68/34=2, Resulting Numbers: [61, 2] Generated Node #3: [61, 2] from Operation: 68/34=2 Current State: 59:[61, 2], Operations: ['35-1=34', '68/34=2'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[1, 61, 35, 68], Operations: [] Exploring Operation: 61-1=60, Resulting Numbers: [35, 68, 60] Generated Node #0,0: 59:[35, 68, 60] Operation: 61-1=60 Moving to Node #0,0 Current State: 59:[35, 68, 60], Operations: ['61-1=60'] Exploring Operation: 68-35=33, Resulting Numbers: [60, 33] Generated Node #0,0,0: 59:[60, 33] Operation: 68-35=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[60, 33], Operations: ['61-1=60', '68-35=33'] Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 60, 9, 16, 10 ]
75
[ "60+9=69", "16-10=6", "69+6=75" ]
Current State: 75:[60, 9, 16, 10], Operations: [] Exploring Operation: 60+9=69, Resulting Numbers: [16, 10, 69] Generated Node #2: [16, 10, 69] from Operation: 60+9=69 Current State: 75:[16, 10, 69], Operations: ['60+9=69'] Exploring Operation: 16-10=6, Resulting Numbers: [69, 6] Generated Node #3: [69, 6] from Operation: 16-10=6 Current State: 75:[69, 6], Operations: ['60+9=69', '16-10=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[60, 9, 16, 10], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [9, 16, 6] Generated Node #0,0: 75:[9, 16, 6] Operation: 60/10=6 Exploring Operation: 60+16=76, Resulting Numbers: [9, 10, 76] Generated Node #0,1: 75:[9, 10, 76] Operation: 60+16=76 Exploring Operation: 60+9=69, Resulting Numbers: [16, 10, 69] Generated Node #0,2: 75:[16, 10, 69] Operation: 60+9=69 Exploring Operation: 60+10=70, Resulting Numbers: [9, 16, 70] Generated Node #0,3: 75:[9, 16, 70] Operation: 60+10=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[9, 16, 6], Operations: ['60/10=6'] Exploring Operation: 16-9=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 75:[6, 7] Operation: 16-9=7 Exploring Operation: 9-6=3, Resulting Numbers: [16, 3] Generated Node #0,0,1: 75:[16, 3] Operation: 9-6=3 Exploring Operation: 9+16=25, Resulting Numbers: [6, 25] Generated Node #0,0,2: 75:[6, 25] Operation: 9+16=25 Exploring Operation: 9+6=15, Resulting Numbers: [16, 15] Generated Node #0,0,3: 75:[16, 15] Operation: 9+6=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[16, 3], Operations: ['60/10=6', '9-6=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,75 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 75:[6, 25], Operations: ['60/10=6', '9+16=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,75 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 75:[16, 15], Operations: ['60/10=6', '9+6=15'] Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 16*15=240, Resulting Numbers: [240] 240,75 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[6, 7], Operations: ['60/10=6', '16-9=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,75 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: 75:[9, 10, 76], Operations: ['60+16=76'] Exploring Operation: 9+10=19, Resulting Numbers: [76, 19] Generated Node #0,1,0: 75:[76, 19] Operation: 9+10=19 Exploring Operation: 10-9=1, Resulting Numbers: [76, 1] Generated Node #0,1,1: 75:[76, 1] Operation: 10-9=1 Exploring Operation: 76-10=66, Resulting Numbers: [9, 66] Generated Node #0,1,2: 75:[9, 66] Operation: 76-10=66 Exploring Operation: 76-9=67, Resulting Numbers: [10, 67] Generated Node #0,1,3: 75:[10, 67] Operation: 76-9=67 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[76, 1], Operations: ['60+16=76', '10-9=1'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[60, 9, 16, 10], Operations: [] Exploring Operation: 60+16=76, Resulting Numbers: [9, 10, 76] Generated Node #0,1: 75:[9, 10, 76] Operation: 60+16=76 Moving to Node #0,1 Current State: 75:[9, 10, 76], Operations: ['60+16=76'] Exploring Operation: 10-9=1, Resulting Numbers: [76, 1] Generated Node #0,1,1: 75:[76, 1] Operation: 10-9=1 Moving to Node #0,1,1 Current State: 75:[76, 1], Operations: ['60+16=76', '10-9=1'] Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 32, 9, 31, 94 ]
40
[ "32-9=23", "94-31=63", "63-23=40" ]
Current State: 40:[32, 9, 31, 94], Operations: [] Exploring Operation: 32-9=23, Resulting Numbers: [31, 94, 23] Generated Node #2: [31, 94, 23] from Operation: 32-9=23 Current State: 40:[31, 94, 23], Operations: ['32-9=23'] Exploring Operation: 94-31=63, Resulting Numbers: [23, 63] Generated Node #3: [23, 63] from Operation: 94-31=63 Current State: 40:[23, 63], Operations: ['32-9=23', '94-31=63'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[32, 9, 31, 94], Operations: [] Exploring Operation: 94-32=62, Resulting Numbers: [9, 31, 62] Generated Node #0,0: 40:[9, 31, 62] Operation: 94-32=62 Exploring Operation: 94-31=63, Resulting Numbers: [32, 9, 63] Generated Node #0,1: 40:[32, 9, 63] Operation: 94-31=63 Exploring Operation: 94-9=85, Resulting Numbers: [32, 31, 85] Generated Node #0,2: 40:[32, 31, 85] Operation: 94-9=85 Exploring Operation: 9+31=40, Resulting Numbers: [32, 94, 40] Generated Node #0,3: 40:[32, 94, 40] Operation: 9+31=40 Exploring Operation: 32-31=1, Resulting Numbers: [9, 94, 1] Generated Node #0,4: 40:[9, 94, 1] Operation: 32-31=1 Moving to Node #0,0 Current State: 40:[9, 31, 62], Operations: ['94-32=62'] Exploring Operation: 62-31=31, Resulting Numbers: [9, 31] Generated Node #0,0,0: 40:[9, 31] Operation: 62-31=31 Exploring Operation: 62-9=53, Resulting Numbers: [31, 53] Generated Node #0,0,1: 40:[31, 53] Operation: 62-9=53 Exploring Operation: 62/31=2, Resulting Numbers: [9, 2] Generated Node #0,0,2: 40:[9, 2] Operation: 62/31=2 Exploring Operation: 31-9=22, Resulting Numbers: [62, 22] Generated Node #0,0,3: 40:[62, 22] Operation: 31-9=22 Exploring Operation: 9+31=40, Resulting Numbers: [62, 40] Generated Node #0,0,4: 40:[62, 40] Operation: 9+31=40 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[9, 2], Operations: ['94-32=62', '62/31=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,40 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[9, 31], Operations: ['94-32=62', '62-31=31'] Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,40 unequal: No Solution Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[32, 9, 31, 94], Operations: [] Exploring Operation: 94-32=62, Resulting Numbers: [9, 31, 62] Generated Node #0,0: 40:[9, 31, 62] Operation: 94-32=62 Moving to Node #0,0 Current State: 40:[9, 31, 62], Operations: ['94-32=62'] Exploring Operation: 62-31=31, Resulting Numbers: [9, 31] Generated Node #0,0,0: 40:[9, 31] Operation: 62-31=31 Moving to Node #0,0,0 Current State: 40:[9, 31], Operations: ['94-32=62', '62-31=31'] Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 32, 68, 95, 76 ]
28
[ "32*95=3040", "3040/76=40", "68-40=28" ]
Current State: 28:[32, 68, 95, 76], Operations: [] Exploring Operation: 32*95=3040, Resulting Numbers: [68, 76, 3040] Generated Node #2: [68, 76, 3040] from Operation: 32*95=3040 Current State: 28:[68, 76, 3040], Operations: ['32*95=3040'] Exploring Operation: 3040/76=40, Resulting Numbers: [68, 40] Generated Node #3: [68, 40] from Operation: 3040/76=40 Current State: 28:[68, 40], Operations: ['32*95=3040', '3040/76=40'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[32, 68, 95, 76], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [32, 95, 8] Generated Node #0,0: 28:[32, 95, 8] Operation: 76-68=8 Exploring Operation: 95-76=19, Resulting Numbers: [32, 68, 19] Generated Node #0,1: 28:[32, 68, 19] Operation: 95-76=19 Exploring Operation: 95-68=27, Resulting Numbers: [32, 76, 27] Generated Node #0,2: 28:[32, 76, 27] Operation: 95-68=27 Exploring Operation: 68-32=36, Resulting Numbers: [95, 76, 36] Generated Node #0,3: 28:[95, 76, 36] Operation: 68-32=36 Moving to Node #0,1 Current State: 28:[32, 68, 19], Operations: ['95-76=19'] Exploring Operation: 68-32=36, Resulting Numbers: [19, 36] Generated Node #0,1,0: 28:[19, 36] Operation: 68-32=36 Exploring Operation: 32+19=51, Resulting Numbers: [68, 51] Generated Node #0,1,1: 28:[68, 51] Operation: 32+19=51 Exploring Operation: 68-19=49, Resulting Numbers: [32, 49] Generated Node #0,1,2: 28:[32, 49] Operation: 68-19=49 Exploring Operation: 32-19=13, Resulting Numbers: [68, 13] Generated Node #0,1,3: 28:[68, 13] Operation: 32-19=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[19, 36], Operations: ['95-76=19', '68-32=36'] Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,28 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[32, 49], Operations: ['95-76=19', '68-19=49'] Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,28 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 28:[68, 13], Operations: ['95-76=19', '32-19=13'] Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,28 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[68, 51], Operations: ['95-76=19', '32+19=51'] Exploring Operation: 68+51=119, Resulting Numbers: [119] 119,28 unequal: No Solution Exploring Operation: 68-51=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 68*51=3468, Resulting Numbers: [3468] 3468,28 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: 28:[32, 76, 27], Operations: ['95-68=27'] Exploring Operation: 76-32=44, Resulting Numbers: [27, 44] Generated Node #0,2,0: 28:[27, 44] Operation: 76-32=44 Exploring Operation: 76-27=49, Resulting Numbers: [32, 49] Generated Node #0,2,1: 28:[32, 49] Operation: 76-27=49 Exploring Operation: 32-27=5, Resulting Numbers: [76, 5] Generated Node #0,2,2: 28:[76, 5] Operation: 32-27=5 Exploring Operation: 32+27=59, Resulting Numbers: [76, 59] Generated Node #0,2,3: 28:[76, 59] Operation: 32+27=59 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 28:[27, 44], Operations: ['95-68=27', '76-32=44'] Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 27+44=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 27*44=1188, Resulting Numbers: [1188] 1188,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 28:[32, 49], Operations: ['95-68=27', '76-27=49'] Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[76, 5], Operations: ['95-68=27', '32-27=5'] Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,28 unequal: No Solution Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 28:[76, 59], Operations: ['95-68=27', '32+27=59'] Exploring Operation: 76*59=4484, Resulting Numbers: [4484] 4484,28 unequal: No Solution Exploring Operation: 76-59=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 76+59=135, Resulting Numbers: [135] 135,28 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: 28:[32, 95, 8], Operations: ['76-68=8'] Exploring Operation: 95-32=63, Resulting Numbers: [8, 63] Generated Node #0,0,0: 28:[8, 63] Operation: 95-32=63 Exploring Operation: 95-8=87, Resulting Numbers: [32, 87] Generated Node #0,0,1: 28:[32, 87] Operation: 95-8=87 Exploring Operation: 32-8=24, Resulting Numbers: [95, 24] Generated Node #0,0,2: 28:[95, 24] Operation: 32-8=24 Exploring Operation: 32/8=4, Resulting Numbers: [95, 4] Generated Node #0,0,3: 28:[95, 4] Operation: 32/8=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[8, 63], Operations: ['76-68=8', '95-32=63'] Exploring Operation: 8*63=504, Resulting Numbers: [504] 504,28 unequal: No Solution Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 28:[32, 87], Operations: ['76-68=8', '95-8=87'] Exploring Operation: 32*87=2784, Resulting Numbers: [2784] 2784,28 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 32+87=119, Resulting Numbers: [119] 119,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 28:[95, 4], Operations: ['76-68=8', '32/8=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,28 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,28 unequal: No Solution Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 28:[95, 24], Operations: ['76-68=8', '32-8=24'] Exploring Operation: 95+24=119, Resulting Numbers: [119] 119,28 unequal: No Solution Exploring Operation: 95-24=71, Resulting Numbers: [71] 71,28 unequal: No Solution Exploring Operation: 95*24=2280, Resulting Numbers: [2280] 2280,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 28:[95, 76, 36], Operations: ['68-32=36'] Exploring Operation: 95+76=171, Resulting Numbers: [36, 171] Generated Node #0,3,0: 28:[36, 171] Operation: 95+76=171 Exploring Operation: 95-36=59, Resulting Numbers: [76, 59] Generated Node #0,3,1: 28:[76, 59] Operation: 95-36=59 Exploring Operation: 95-76=19, Resulting Numbers: [36, 19] Generated Node #0,3,2: 28:[36, 19] Operation: 95-76=19 Exploring Operation: 76-36=40, Resulting Numbers: [95, 40] Generated Node #0,3,3: 28:[95, 40] Operation: 76-36=40 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 28:[36, 19], Operations: ['68-32=36', '95-76=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 28:[76, 59], Operations: ['68-32=36', '95-36=59'] Exploring Operation: 76*59=4484, Resulting Numbers: [4484] 4484,28 unequal: No Solution Exploring Operation: 76-59=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 76+59=135, Resulting Numbers: [135] 135,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 28:[95, 40], Operations: ['68-32=36', '76-36=40'] Exploring Operation: 95+40=135, Resulting Numbers: [135] 135,28 unequal: No Solution Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 95*40=3800, Resulting Numbers: [3800] 3800,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 28:[36, 171], Operations: ['68-32=36', '95+76=171'] Exploring Operation: 171-36=135, Resulting Numbers: [135] 135,28 unequal: No Solution Exploring Operation: 36*171=6156, Resulting Numbers: [6156] 6156,28 unequal: No Solution Exploring Operation: 36+171=207, Resulting Numbers: [207] 207,28 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
[ 20, 37, 36, 88 ]
68
[ "88-20=68", "37-36=1", "68*1=68" ]
Current State: 68:[20, 37, 36, 88], Operations: [] Exploring Operation: 88-20=68, Resulting Numbers: [37, 36, 68] Generated Node #2: [37, 36, 68] from Operation: 88-20=68 Current State: 68:[37, 36, 68], Operations: ['88-20=68'] Exploring Operation: 37-36=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 37-36=1 Current State: 68:[68, 1], Operations: ['88-20=68', '37-36=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[20, 37, 36, 88], Operations: [] Exploring Operation: 37-20=17, Resulting Numbers: [36, 88, 17] Generated Node #0,0: 68:[36, 88, 17] Operation: 37-20=17 Exploring Operation: 88-36=52, Resulting Numbers: [20, 37, 52] Generated Node #0,1: 68:[20, 37, 52] Operation: 88-36=52 Exploring Operation: 88-37=51, Resulting Numbers: [20, 36, 51] Generated Node #0,2: 68:[20, 36, 51] Operation: 88-37=51 Exploring Operation: 88-20=68, Resulting Numbers: [37, 36, 68] Generated Node #0,3: 68:[37, 36, 68] Operation: 88-20=68 Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[37, 36, 68], Operations: ['88-20=68'] Exploring Operation: 68-37=31, Resulting Numbers: [36, 31] Generated Node #0,3,0: 68:[36, 31] Operation: 68-37=31 Exploring Operation: 68-36=32, Resulting Numbers: [37, 32] Generated Node #0,3,1: 68:[37, 32] Operation: 68-36=32 Exploring Operation: 37-36=1, Resulting Numbers: [68, 1] Generated Node #0,3,2: 68:[68, 1] Operation: 37-36=1 Exploring Operation: 37+36=73, Resulting Numbers: [68, 73] Generated Node #0,3,3: 68:[68, 73] Operation: 37+36=73 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 68:[68, 1], Operations: ['88-20=68', '37-36=1'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[20, 37, 36, 88], Operations: [] Exploring Operation: 88-20=68, Resulting Numbers: [37, 36, 68] Generated Node #0,3: 68:[37, 36, 68] Operation: 88-20=68 Moving to Node #0,3 Current State: 68:[37, 36, 68], Operations: ['88-20=68'] Exploring Operation: 37-36=1, Resulting Numbers: [68, 1] Generated Node #0,3,2: 68:[68, 1] Operation: 37-36=1 Moving to Node #0,3,2 Current State: 68:[68, 1], Operations: ['88-20=68', '37-36=1'] Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 37, 35, 28, 17 ]
16
[ "37-17=20", "28*20=560", "560/35=16" ]
Current State: 16:[37, 35, 28, 17], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [35, 28, 20] Generated Node #2: [35, 28, 20] from Operation: 37-17=20 Current State: 16:[35, 28, 20], Operations: ['37-17=20'] Exploring Operation: 28*20=560, Resulting Numbers: [35, 560] Generated Node #3: [35, 560] from Operation: 28*20=560 Current State: 16:[35, 560], Operations: ['37-17=20', '28*20=560'] Exploring Operation: 560/35=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[37, 35, 28, 17], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [35, 28, 20] Generated Node #0,0: 16:[35, 28, 20] Operation: 37-17=20 Exploring Operation: 37-35=2, Resulting Numbers: [28, 17, 2] Generated Node #0,1: 16:[28, 17, 2] Operation: 37-35=2 Exploring Operation: 35-28=7, Resulting Numbers: [37, 17, 7] Generated Node #0,2: 16:[37, 17, 7] Operation: 35-28=7 Exploring Operation: 37-28=9, Resulting Numbers: [35, 17, 9] Generated Node #0,3: 16:[35, 17, 9] Operation: 37-28=9 Moving to Node #0,1 Current State: 16:[28, 17, 2], Operations: ['37-35=2'] Exploring Operation: 28-2=26, Resulting Numbers: [17, 26] Generated Node #0,1,0: 16:[17, 26] Operation: 28-2=26 Exploring Operation: 28-17=11, Resulting Numbers: [2, 11] Generated Node #0,1,1: 16:[2, 11] Operation: 28-17=11 Exploring Operation: 28/2=14, Resulting Numbers: [17, 14] Generated Node #0,1,2: 16:[17, 14] Operation: 28/2=14 Exploring Operation: 17-2=15, Resulting Numbers: [28, 15] Generated Node #0,1,3: 16:[28, 15] Operation: 17-2=15 Moving to Node #0,3 Current State: 16:[35, 17, 9], Operations: ['37-28=9'] Exploring Operation: 35-9=26, Resulting Numbers: [17, 26] Generated Node #0,3,0: 16:[17, 26] Operation: 35-9=26 Exploring Operation: 35+9=44, Resulting Numbers: [17, 44] Generated Node #0,3,1: 16:[17, 44] Operation: 35+9=44 Exploring Operation: 17-9=8, Resulting Numbers: [35, 8] Generated Node #0,3,2: 16:[35, 8] Operation: 17-9=8 Exploring Operation: 35-17=18, Resulting Numbers: [9, 18] Generated Node #0,3,3: 16:[9, 18] Operation: 35-17=18 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 16:[9, 18], Operations: ['37-28=9', '35-17=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,16 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,16 unequal: No Solution No 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: 16:[17, 26], Operations: ['37-28=9', '35-9=26'] Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,16 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,16 unequal: No Solution No 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: 16:[35, 8], Operations: ['37-28=9', '17-9=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,16 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,16 unequal: No Solution No 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: 16:[17, 44], Operations: ['37-28=9', '35+9=44'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 17+44=61, Resulting Numbers: [61] 61,16 unequal: No Solution Exploring Operation: 17*44=748, Resulting Numbers: [748] 748,16 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: 16:[37, 17, 7], Operations: ['35-28=7'] Exploring Operation: 37-7=30, Resulting Numbers: [17, 30] Generated Node #0,2,0: 16:[17, 30] Operation: 37-7=30 Exploring Operation: 37-17=20, Resulting Numbers: [7, 20] Generated Node #0,2,1: 16:[7, 20] Operation: 37-17=20 Exploring Operation: 17-7=10, Resulting Numbers: [37, 10] Generated Node #0,2,2: 16:[37, 10] Operation: 17-7=10 Exploring Operation: 37+7=44, Resulting Numbers: [17, 44] Generated Node #0,2,3: 16:[17, 44] Operation: 37+7=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[7, 20], Operations: ['35-28=7', '37-17=20'] Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,16 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,16 unequal: No Solution No 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: 16:[17, 30], Operations: ['35-28=7', '37-7=30'] Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,16 unequal: No Solution No 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: 16:[37, 10], Operations: ['35-28=7', '17-7=10'] Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,16 unequal: No Solution Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,16 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,16 unequal: No Solution No 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: 16:[17, 44], Operations: ['35-28=7', '37+7=44'] Exploring Operation: 17+44=61, Resulting Numbers: [61] 61,16 unequal: No Solution Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 17*44=748, Resulting Numbers: [748] 748,16 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: 16:[35, 28, 20], Operations: ['37-17=20'] Exploring Operation: 35-28=7, Resulting Numbers: [20, 7] Generated Node #0,0,0: 16:[20, 7] Operation: 35-28=7 Exploring Operation: 35+28=63, Resulting Numbers: [20, 63] Generated Node #0,0,1: 16:[20, 63] Operation: 35+28=63 Exploring Operation: 35-20=15, Resulting Numbers: [28, 15] Generated Node #0,0,2: 16:[28, 15] Operation: 35-20=15 Exploring Operation: 28-20=8, Resulting Numbers: [35, 8] Generated Node #0,0,3: 16:[35, 8] Operation: 28-20=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[20, 7], Operations: ['37-17=20', '35-28=7'] Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,16 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,16 unequal: No Solution No 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: 16:[28, 15], Operations: ['37-17=20', '35-20=15'] Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,16 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,16 unequal: No Solution No 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: 16:[35, 8], Operations: ['37-17=20', '28-20=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,16 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,16 unequal: No Solution No 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: 16:[20, 63], Operations: ['37-17=20', '35+28=63'] Exploring Operation: 20+63=83, Resulting Numbers: [83] 83,16 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,16 unequal: No Solution Exploring Operation: 20*63=1260, Resulting Numbers: [1260] 1260,16 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: 16:[2, 11], Operations: ['37-35=2', '28-17=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[17, 14], Operations: ['37-35=2', '28/2=14'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,16 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[17, 26], Operations: ['37-35=2', '28-2=26'] Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,16 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[28, 15], Operations: ['37-35=2', '17-2=15'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,16 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,16 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 14, 41, 95, 13 ]
12
[ "95-13=82", "82/41=2", "14-2=12" ]
Current State: 12:[14, 41, 95, 13], Operations: [] Exploring Operation: 95-13=82, Resulting Numbers: [14, 41, 82] Generated Node #2: [14, 41, 82] from Operation: 95-13=82 Current State: 12:[14, 41, 82], Operations: ['95-13=82'] Exploring Operation: 82/41=2, Resulting Numbers: [14, 2] Generated Node #3: [14, 2] from Operation: 82/41=2 Current State: 12:[14, 2], Operations: ['95-13=82', '82/41=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[14, 41, 95, 13], Operations: [] Exploring Operation: 41-14=27, Resulting Numbers: [95, 13, 27] Generated Node #0,0: 12:[95, 13, 27] Operation: 41-14=27 Exploring Operation: 41-13=28, Resulting Numbers: [14, 95, 28] Generated Node #0,1: 12:[14, 95, 28] Operation: 41-13=28 Exploring Operation: 95-41=54, Resulting Numbers: [14, 13, 54] Generated Node #0,2: 12:[14, 13, 54] Operation: 95-41=54 Exploring Operation: 95-14=81, Resulting Numbers: [41, 13, 81] Generated Node #0,3: 12:[41, 13, 81] Operation: 95-14=81 Exploring Operation: 95-13=82, Resulting Numbers: [14, 41, 82] Generated Node #0,4: 12:[14, 41, 82] Operation: 95-13=82 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[14, 13, 54], Operations: ['95-41=54'] Exploring Operation: 54-14=40, Resulting Numbers: [13, 40] Generated Node #0,2,0: 12:[13, 40] Operation: 54-14=40 Exploring Operation: 14+54=68, Resulting Numbers: [13, 68] Generated Node #0,2,1: 12:[13, 68] Operation: 14+54=68 Exploring Operation: 14-13=1, Resulting Numbers: [54, 1] Generated Node #0,2,2: 12:[54, 1] Operation: 14-13=1 Exploring Operation: 14+13=27, Resulting Numbers: [54, 27] Generated Node #0,2,3: 12:[54, 27] Operation: 14+13=27 Exploring Operation: 54-13=41, Resulting Numbers: [14, 41] Generated Node #0,2,4: 12:[14, 41] Operation: 54-13=41 Moving to Node #0,2,0 Current State: 12:[13, 40], Operations: ['95-41=54', '54-14=40'] Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,12 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[14, 41], Operations: ['95-41=54', '54-13=41'] Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,12 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[54, 1], Operations: ['95-41=54', '14-13=1'] Exploring Operation: 54+1=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 54*1=54, Resulting Numbers: [54] 54,12 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,12 unequal: No Solution Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[13, 68], Operations: ['95-41=54', '14+54=68'] Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,12 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[54, 27], Operations: ['95-41=54', '14+13=27'] Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 54+27=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 54*27=1458, Resulting Numbers: [1458] 1458,12 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:[95, 13, 27], Operations: ['41-14=27'] Exploring Operation: 95-13=82, Resulting Numbers: [27, 82] Generated Node #0,0,0: 12:[27, 82] Operation: 95-13=82 Exploring Operation: 95+27=122, Resulting Numbers: [13, 122] Generated Node #0,0,1: 12:[13, 122] Operation: 95+27=122 Exploring Operation: 95-27=68, Resulting Numbers: [13, 68] Generated Node #0,0,2: 12:[13, 68] Operation: 95-27=68 Exploring Operation: 27-13=14, Resulting Numbers: [95, 14] Generated Node #0,0,3: 12:[95, 14] Operation: 27-13=14 Exploring Operation: 95+13=108, Resulting Numbers: [27, 108] Generated Node #0,0,4: 12:[27, 108] Operation: 95+13=108 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 12:[13, 68], Operations: ['41-14=27', '95-27=68'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,12 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[27, 82], Operations: ['41-14=27', '95-13=82'] Exploring Operation: 27+82=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 27*82=2214, Resulting Numbers: [2214] 2214,12 unequal: No Solution Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,12 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 #0,0,3 Current State: 12:[95, 14], Operations: ['41-14=27', '27-13=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,12 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:[13, 122], Operations: ['41-14=27', '95+27=122'] Exploring Operation: 13*122=1586, Resulting Numbers: [1586] 1586,12 unequal: No Solution Exploring Operation: 122-13=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 13+122=135, Resulting Numbers: [135] 135,12 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 #0,0,4 Current State: 12:[27, 108], Operations: ['41-14=27', '95+13=108'] Exploring Operation: 108/27=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 27+108=135, Resulting Numbers: [135] 135,12 unequal: No Solution Exploring Operation: 108-27=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 27*108=2916, Resulting Numbers: [2916] 2916,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[41, 13, 81], Operations: ['95-14=81'] Exploring Operation: 41+13=54, Resulting Numbers: [81, 54] Generated Node #0,3,0: 12:[81, 54] Operation: 41+13=54 Exploring Operation: 81-41=40, Resulting Numbers: [13, 40] Generated Node #0,3,1: 12:[13, 40] Operation: 81-41=40 Exploring Operation: 41-13=28, Resulting Numbers: [81, 28] Generated Node #0,3,2: 12:[81, 28] Operation: 41-13=28 Exploring Operation: 41+81=122, Resulting Numbers: [13, 122] Generated Node #0,3,3: 12:[13, 122] Operation: 41+81=122 Exploring Operation: 81-13=68, Resulting Numbers: [41, 68] Generated Node #0,3,4: 12:[41, 68] Operation: 81-13=68 Moving to Node #0,3,1 Current State: 12:[13, 40], Operations: ['95-14=81', '81-41=40'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,12 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[41, 68], Operations: ['95-14=81', '81-13=68'] Exploring Operation: 68-41=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 41*68=2788, Resulting Numbers: [2788] 2788,12 unequal: No Solution Exploring Operation: 41+68=109, Resulting Numbers: [109] 109,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[81, 28], Operations: ['95-14=81', '41-13=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,12 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[81, 54], Operations: ['95-14=81', '41+13=54'] Exploring Operation: 81*54=4374, Resulting Numbers: [4374] 4374,12 unequal: No Solution Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 81+54=135, Resulting Numbers: [135] 135,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[13, 122], Operations: ['95-14=81', '41+81=122'] Exploring Operation: 13+122=135, Resulting Numbers: [135] 135,12 unequal: No Solution Exploring Operation: 122-13=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 13*122=1586, Resulting Numbers: [1586] 1586,12 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 #0,1 Current State: 12:[14, 95, 28], Operations: ['41-13=28'] Exploring Operation: 95-28=67, Resulting Numbers: [14, 67] Generated Node #0,1,0: 12:[14, 67] Operation: 95-28=67 Exploring Operation: 28-14=14, Resulting Numbers: [95, 14] Generated Node #0,1,1: 12:[95, 14] Operation: 28-14=14 Exploring Operation: 14+95=109, Resulting Numbers: [28, 109] Generated Node #0,1,2: 12:[28, 109] Operation: 14+95=109 Exploring Operation: 95-14=81, Resulting Numbers: [28, 81] Generated Node #0,1,3: 12:[28, 81] Operation: 95-14=81 Exploring Operation: 28/14=2, Resulting Numbers: [95, 2] Generated Node #0,1,4: 12:[95, 2] Operation: 28/14=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 12:[14, 67], Operations: ['41-13=28', '95-28=67'] Exploring Operation: 14*67=938, Resulting Numbers: [938] 938,12 unequal: No Solution Exploring Operation: 14+67=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,12 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 #0,1,4 Current State: 12:[95, 2], Operations: ['41-13=28', '28/14=2'] Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,12 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,12 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,12 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 #0,1,1 Current State: 12:[95, 14], Operations: ['41-13=28', '28-14=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,12 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,12 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 #0,1,3 Current State: 12:[28, 81], Operations: ['41-13=28', '95-14=81'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 28+81=109, Resulting Numbers: [109] 109,12 unequal: No Solution Exploring Operation: 28*81=2268, Resulting Numbers: [2268] 2268,12 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 #0,1,2 Current State: 12:[28, 109], Operations: ['41-13=28', '14+95=109'] Exploring Operation: 109-28=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 28*109=3052, Resulting Numbers: [3052] 3052,12 unequal: No Solution Exploring Operation: 28+109=137, Resulting Numbers: [137] 137,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 12:[14, 41, 82], Operations: ['95-13=82'] Exploring Operation: 82/41=2, Resulting Numbers: [14, 2] Generated Node #0,4,0: 12:[14, 2] Operation: 82/41=2 Exploring Operation: 14+41=55, Resulting Numbers: [82, 55] Generated Node #0,4,1: 12:[82, 55] Operation: 14+41=55 Exploring Operation: 41-14=27, Resulting Numbers: [82, 27] Generated Node #0,4,2: 12:[82, 27] Operation: 41-14=27 Exploring Operation: 82-14=68, Resulting Numbers: [41, 68] Generated Node #0,4,3: 12:[41, 68] Operation: 82-14=68 Exploring Operation: 82-41=41, Resulting Numbers: [14, 41] Generated Node #0,4,4: 12:[14, 41] Operation: 82-41=41 Moving to Node #0,4,0 Current State: 12:[14, 2], Operations: ['95-13=82', '82/41=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,12 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[14, 41, 95, 13], Operations: [] Exploring Operation: 95-13=82, Resulting Numbers: [14, 41, 82] Generated Node #0,4: 12:[14, 41, 82] Operation: 95-13=82 Moving to Node #0,4 Current State: 12:[14, 41, 82], Operations: ['95-13=82'] Exploring Operation: 82/41=2, Resulting Numbers: [14, 2] Generated Node #0,4,0: 12:[14, 2] Operation: 82/41=2 Moving to Node #0,4,0 Current State: 12:[14, 2], Operations: ['95-13=82', '82/41=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.913194
hs_5
sum_heuristic
[ 37, 85, 41, 35 ]
22
[ "37-35=2", "85-41=44", "44/2=22" ]
Current State: 22:[37, 85, 41, 35], Operations: [] Exploring Operation: 37-35=2, Resulting Numbers: [85, 41, 2] Generated Node #2: [85, 41, 2] from Operation: 37-35=2 Current State: 22:[85, 41, 2], Operations: ['37-35=2'] Exploring Operation: 85-41=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 85-41=44 Current State: 22:[2, 44], Operations: ['37-35=2', '85-41=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[37, 85, 41, 35], Operations: [] Exploring Operation: 85-41=44, Resulting Numbers: [37, 35, 44] Generated Node #0,0: 22:[37, 35, 44] Operation: 85-41=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[37, 35, 44], Operations: ['85-41=44'] Exploring Operation: 44-37=7, Resulting Numbers: [35, 7] Generated Node #0,0,0: 22:[35, 7] Operation: 44-37=7 Moving to Node #0,0,0 Current State: 22:[35, 7], Operations: ['85-41=44', '44-37=7'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,22 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
[ 42, 2, 50, 4 ]
31
[ "42-4=38", "38/2=19", "50-19=31" ]
Current State: 31:[42, 2, 50, 4], Operations: [] Exploring Operation: 42-4=38, Resulting Numbers: [2, 50, 38] Generated Node #2: [2, 50, 38] from Operation: 42-4=38 Current State: 31:[2, 50, 38], Operations: ['42-4=38'] Exploring Operation: 38/2=19, Resulting Numbers: [50, 19] Generated Node #3: [50, 19] from Operation: 38/2=19 Current State: 31:[50, 19], Operations: ['42-4=38', '38/2=19'] Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[42, 2, 50, 4], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [42, 4, 25] Generated Node #0,0: 31:[42, 4, 25] Operation: 50/2=25 Exploring Operation: 2*4=8, Resulting Numbers: [42, 50, 8] Generated Node #0,1: 31:[42, 50, 8] Operation: 2*4=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[42, 4, 25], Operations: ['50/2=25'] Exploring Operation: 42-4=38, Resulting Numbers: [25, 38] Generated Node #0,0,0: 31:[25, 38] Operation: 42-4=38 Exploring Operation: 4+25=29, Resulting Numbers: [42, 29] Generated Node #0,0,1: 31:[42, 29] Operation: 4+25=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[25, 38], Operations: ['50/2=25', '42-4=38'] Exploring Operation: 25+38=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,31 unequal: No Solution No 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: 31:[42, 29], Operations: ['50/2=25', '4+25=29'] Exploring Operation: 42+29=71, Resulting Numbers: [71] 71,31 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[42, 50, 8], Operations: ['2*4=8'] Exploring Operation: 42-8=34, Resulting Numbers: [50, 34] Generated Node #0,1,0: 31:[50, 34] Operation: 42-8=34 Exploring Operation: 50-8=42, Resulting Numbers: [42, 42] Generated Node #0,1,1: 31:[42, 42] Operation: 50-8=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[50, 34], Operations: ['2*4=8', '42-8=34'] Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,31 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,31 unequal: No Solution No 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: 31:[42, 42], Operations: ['2*4=8', '50-8=42'] Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,31 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 57, 2, 43, 93 ]
81
[ "57-2=55", "43+93=136", "136-55=81" ]
Current State: 81:[57, 2, 43, 93], Operations: [] Exploring Operation: 57-2=55, Resulting Numbers: [43, 93, 55] Generated Node #2: [43, 93, 55] from Operation: 57-2=55 Current State: 81:[43, 93, 55], Operations: ['57-2=55'] Exploring Operation: 43+93=136, Resulting Numbers: [55, 136] Generated Node #3: [55, 136] from Operation: 43+93=136 Current State: 81:[55, 136], Operations: ['57-2=55', '43+93=136'] Exploring Operation: 136-55=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[57, 2, 43, 93], Operations: [] Exploring Operation: 57+43=100, Resulting Numbers: [2, 93, 100] Generated Node #0,0: 81:[2, 93, 100] Operation: 57+43=100 Exploring Operation: 93-57=36, Resulting Numbers: [2, 43, 36] Generated Node #0,1: 81:[2, 43, 36] Operation: 93-57=36 Exploring Operation: 57-43=14, Resulting Numbers: [2, 93, 14] Generated Node #0,2: 81:[2, 93, 14] Operation: 57-43=14 Exploring Operation: 2*43=86, Resulting Numbers: [57, 93, 86] Generated Node #0,3: 81:[57, 93, 86] Operation: 2*43=86 Moving to Node #0,2 Current State: 81:[2, 93, 14], Operations: ['57-43=14'] Exploring Operation: 2*14=28, Resulting Numbers: [93, 28] Generated Node #0,2,0: 81:[93, 28] Operation: 2*14=28 Exploring Operation: 93-2=91, Resulting Numbers: [14, 91] Generated Node #0,2,1: 81:[14, 91] Operation: 93-2=91 Exploring Operation: 14/2=7, Resulting Numbers: [93, 7] Generated Node #0,2,2: 81:[93, 7] Operation: 14/2=7 Exploring Operation: 93-14=79, Resulting Numbers: [2, 79] Generated Node #0,2,3: 81:[2, 79] Operation: 93-14=79 Moving to Node #0,1 Current State: 81:[2, 43, 36], Operations: ['93-57=36'] Exploring Operation: 43+36=79, Resulting Numbers: [2, 79] Generated Node #0,1,0: 81:[2, 79] Operation: 43+36=79 Exploring Operation: 43-2=41, Resulting Numbers: [36, 41] Generated Node #0,1,1: 81:[36, 41] Operation: 43-2=41 Exploring Operation: 43-36=7, Resulting Numbers: [2, 7] Generated Node #0,1,2: 81:[2, 7] Operation: 43-36=7 Exploring Operation: 2*43=86, Resulting Numbers: [36, 86] Generated Node #0,1,3: 81:[36, 86] Operation: 2*43=86 Moving to Node #0,0 Current State: 81:[2, 93, 100], Operations: ['57+43=100'] Exploring Operation: 2+93=95, Resulting Numbers: [100, 95] Generated Node #0,0,0: 81:[100, 95] Operation: 2+93=95 Exploring Operation: 100-93=7, Resulting Numbers: [2, 7] Generated Node #0,0,1: 81:[2, 7] Operation: 100-93=7 Exploring Operation: 100-2=98, Resulting Numbers: [93, 98] Generated Node #0,0,2: 81:[93, 98] Operation: 100-2=98 Exploring Operation: 93-2=91, Resulting Numbers: [100, 91] Generated Node #0,0,3: 81:[100, 91] Operation: 93-2=91 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[2, 7], Operations: ['57+43=100', '100-93=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,81 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 #0,0,2 Current State: 81:[93, 98], Operations: ['57+43=100', '100-2=98'] Exploring Operation: 98-93=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 93+98=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 93*98=9114, Resulting Numbers: [9114] 9114,81 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 #0,0,3 Current State: 81:[100, 91], Operations: ['57+43=100', '93-2=91'] Exploring Operation: 100*91=9100, Resulting Numbers: [9100] 9100,81 unequal: No Solution Exploring Operation: 100+91=191, Resulting Numbers: [191] 191,81 unequal: No Solution Exploring Operation: 100-91=9, Resulting Numbers: [9] 9,81 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:[100, 95], Operations: ['57+43=100', '2+93=95'] Exploring Operation: 100*95=9500, Resulting Numbers: [9500] 9500,81 unequal: No Solution Exploring Operation: 100+95=195, Resulting Numbers: [195] 195,81 unequal: No Solution Exploring Operation: 100-95=5, Resulting Numbers: [5] 5,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 81:[57, 93, 86], Operations: ['2*43=86'] Exploring Operation: 57+93=150, Resulting Numbers: [86, 150] Generated Node #0,3,0: 81:[86, 150] Operation: 57+93=150 Exploring Operation: 86-57=29, Resulting Numbers: [93, 29] Generated Node #0,3,1: 81:[93, 29] Operation: 86-57=29 Exploring Operation: 93-86=7, Resulting Numbers: [57, 7] Generated Node #0,3,2: 81:[57, 7] Operation: 93-86=7 Exploring Operation: 93-57=36, Resulting Numbers: [86, 36] Generated Node #0,3,3: 81:[86, 36] Operation: 93-57=36 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[93, 29], Operations: ['2*43=86', '86-57=29'] Exploring Operation: 93-29=64, Resulting Numbers: [64] 64,81 unequal: No Solution Exploring Operation: 93*29=2697, Resulting Numbers: [2697] 2697,81 unequal: No Solution Exploring Operation: 93+29=122, Resulting Numbers: [122] 122,81 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 #0,3,3 Current State: 81:[86, 36], Operations: ['2*43=86', '93-57=36'] Exploring Operation: 86+36=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 86*36=3096, Resulting Numbers: [3096] 3096,81 unequal: No Solution Exploring Operation: 86-36=50, Resulting Numbers: [50] 50,81 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 #0,3,2 Current State: 81:[57, 7], Operations: ['2*43=86', '93-86=7'] Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,81 unequal: No Solution Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,81 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 #0,3,0 Current State: 81:[86, 150], Operations: ['2*43=86', '57+93=150'] Exploring Operation: 86*150=12900, Resulting Numbers: [12900] 12900,81 unequal: No Solution Exploring Operation: 150-86=64, Resulting Numbers: [64] 64,81 unequal: No Solution Exploring Operation: 86+150=236, Resulting Numbers: [236] 236,81 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: 81:[2, 79], Operations: ['57-43=14', '93-14=79'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,81 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,81 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[57, 2, 43, 93], Operations: [] Exploring Operation: 57-43=14, Resulting Numbers: [2, 93, 14] Generated Node #0,2: 81:[2, 93, 14] Operation: 57-43=14 Moving to Node #0,2 Current State: 81:[2, 93, 14], Operations: ['57-43=14'] Exploring Operation: 93-14=79, Resulting Numbers: [2, 79] Generated Node #0,2,3: 81:[2, 79] Operation: 93-14=79 Moving to Node #0,2,3 Current State: 81:[2, 79], Operations: ['57-43=14', '93-14=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 65, 12, 87, 17 ]
91
[ "65-17=48", "48/12=4", "87+4=91" ]
Current State: 91:[65, 12, 87, 17], Operations: [] Exploring Operation: 65-17=48, Resulting Numbers: [12, 87, 48] Generated Node #2: [12, 87, 48] from Operation: 65-17=48 Current State: 91:[12, 87, 48], Operations: ['65-17=48'] Exploring Operation: 48/12=4, Resulting Numbers: [87, 4] Generated Node #3: [87, 4] from Operation: 48/12=4 Current State: 91:[87, 4], Operations: ['65-17=48', '48/12=4'] Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[65, 12, 87, 17], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [65, 87, 5] Generated Node #0,0: 91:[65, 87, 5] Operation: 17-12=5 Exploring Operation: 65+12=77, Resulting Numbers: [87, 17, 77] Generated Node #0,1: 91:[87, 17, 77] Operation: 65+12=77 Exploring Operation: 87-65=22, Resulting Numbers: [12, 17, 22] Generated Node #0,2: 91:[12, 17, 22] Operation: 87-65=22 Exploring Operation: 65+17=82, Resulting Numbers: [12, 87, 82] Generated Node #0,3: 91:[12, 87, 82] Operation: 65+17=82 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[12, 17, 22], Operations: ['87-65=22'] Exploring Operation: 22-17=5, Resulting Numbers: [12, 5] Generated Node #0,2,0: 91:[12, 5] Operation: 22-17=5 Exploring Operation: 22-12=10, Resulting Numbers: [17, 10] Generated Node #0,2,1: 91:[17, 10] Operation: 22-12=10 Exploring Operation: 12+17=29, Resulting Numbers: [22, 29] Generated Node #0,2,2: 91:[22, 29] Operation: 12+17=29 Exploring Operation: 17-12=5, Resulting Numbers: [22, 5] Generated Node #0,2,3: 91:[22, 5] Operation: 17-12=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[12, 5], Operations: ['87-65=22', '22-17=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,91 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[17, 10], Operations: ['87-65=22', '22-12=10'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 91:[22, 5], Operations: ['87-65=22', '17-12=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[22, 29], Operations: ['87-65=22', '12+17=29'] Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 22*29=638, Resulting Numbers: [638] 638,91 unequal: No Solution Exploring Operation: 22+29=51, Resulting Numbers: [51] 51,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[12, 87, 82], Operations: ['65+17=82'] Exploring Operation: 87-82=5, Resulting Numbers: [12, 5] Generated Node #0,3,0: 91:[12, 5] Operation: 87-82=5 Exploring Operation: 87-12=75, Resulting Numbers: [82, 75] Generated Node #0,3,1: 91:[82, 75] Operation: 87-12=75 Exploring Operation: 12+87=99, Resulting Numbers: [82, 99] Generated Node #0,3,2: 91:[82, 99] Operation: 12+87=99 Exploring Operation: 12+82=94, Resulting Numbers: [87, 94] Generated Node #0,3,3: 91:[87, 94] Operation: 12+82=94 Moving to Node #0,3,0 Current State: 91:[12, 5], Operations: ['65+17=82', '87-82=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[87, 94], Operations: ['65+17=82', '12+82=94'] Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 87*94=8178, Resulting Numbers: [8178] 8178,91 unequal: No Solution Exploring Operation: 87+94=181, Resulting Numbers: [181] 181,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[82, 99], Operations: ['65+17=82', '12+87=99'] Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 82*99=8118, Resulting Numbers: [8118] 8118,91 unequal: No Solution Exploring Operation: 82+99=181, Resulting Numbers: [181] 181,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[82, 75], Operations: ['65+17=82', '87-12=75'] Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,91 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[87, 17, 77], Operations: ['65+12=77'] Exploring Operation: 87-77=10, Resulting Numbers: [17, 10] Generated Node #0,1,0: 91:[17, 10] Operation: 87-77=10 Exploring Operation: 87+17=104, Resulting Numbers: [77, 104] Generated Node #0,1,1: 91:[77, 104] Operation: 87+17=104 Exploring Operation: 17+77=94, Resulting Numbers: [87, 94] Generated Node #0,1,2: 91:[87, 94] Operation: 17+77=94 Exploring Operation: 87-17=70, Resulting Numbers: [77, 70] Generated Node #0,1,3: 91:[77, 70] Operation: 87-17=70 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[17, 10], Operations: ['65+12=77', '87-77=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,91 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[87, 94], Operations: ['65+12=77', '17+77=94'] Exploring Operation: 87*94=8178, Resulting Numbers: [8178] 8178,91 unequal: No Solution Exploring Operation: 87+94=181, Resulting Numbers: [181] 181,91 unequal: No Solution Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[77, 104], Operations: ['65+12=77', '87+17=104'] Exploring Operation: 77+104=181, Resulting Numbers: [181] 181,91 unequal: No Solution Exploring Operation: 104-77=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 77*104=8008, Resulting Numbers: [8008] 8008,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 91:[77, 70], Operations: ['65+12=77', '87-17=70'] Exploring Operation: 77*70=5390, Resulting Numbers: [5390] 5390,91 unequal: No Solution Exploring Operation: 77+70=147, Resulting Numbers: [147] 147,91 unequal: No Solution Exploring Operation: 77-70=7, Resulting Numbers: [7] 7,91 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:[65, 87, 5], Operations: ['17-12=5'] Exploring Operation: 87-65=22, Resulting Numbers: [5, 22] Generated Node #0,0,0: 91:[5, 22] Operation: 87-65=22 Exploring Operation: 65/5=13, Resulting Numbers: [87, 13] Generated Node #0,0,1: 91:[87, 13] Operation: 65/5=13 Exploring Operation: 87+5=92, Resulting Numbers: [65, 92] Generated Node #0,0,2: 91:[65, 92] Operation: 87+5=92 Exploring Operation: 65+5=70, Resulting Numbers: [87, 70] Generated Node #0,0,3: 91:[87, 70] Operation: 65+5=70 Moving to Node #0,0,1 Current State: 91:[87, 13], Operations: ['17-12=5', '65/5=13'] Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,91 unequal: No Solution Exploring Operation: 87+13=100, Resulting Numbers: [100] 100,91 unequal: No Solution Exploring Operation: 87*13=1131, Resulting Numbers: [1131] 1131,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[5, 22], Operations: ['17-12=5', '87-65=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,91 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[87, 70], Operations: ['17-12=5', '65+5=70'] Exploring Operation: 87*70=6090, Resulting Numbers: [6090] 6090,91 unequal: No Solution Exploring Operation: 87-70=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 87+70=157, Resulting Numbers: [157] 157,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[65, 92], Operations: ['17-12=5', '87+5=92'] Exploring Operation: 65+92=157, Resulting Numbers: [157] 157,91 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,91 unequal: No Solution Exploring Operation: 65*92=5980, Resulting Numbers: [5980] 5980,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 18, 15, 6, 29 ]
32
[ "18-15=3", "6+29=35", "35-3=32" ]
Current State: 32:[18, 15, 6, 29], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [6, 29, 3] Generated Node #2: [6, 29, 3] from Operation: 18-15=3 Current State: 32:[6, 29, 3], Operations: ['18-15=3'] Exploring Operation: 6+29=35, Resulting Numbers: [3, 35] Generated Node #3: [3, 35] from Operation: 6+29=35 Current State: 32:[3, 35], Operations: ['18-15=3', '6+29=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[18, 15, 6, 29], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [6, 29, 3] Generated Node #0,0: 32:[6, 29, 3] Operation: 18-15=3 Exploring Operation: 18/6=3, Resulting Numbers: [15, 29, 3] Generated Node #0,1: 32:[15, 29, 3] Operation: 18/6=3 Exploring Operation: 29-18=11, Resulting Numbers: [15, 6, 11] Generated Node #0,2: 32:[15, 6, 11] Operation: 29-18=11 Exploring Operation: 15-6=9, Resulting Numbers: [18, 29, 9] Generated Node #0,3: 32:[18, 29, 9] Operation: 15-6=9 Exploring Operation: 18+15=33, Resulting Numbers: [6, 29, 33] Generated Node #0,4: 32:[6, 29, 33] Operation: 18+15=33 Moving to Node #0,1 Current State: 32:[15, 29, 3], Operations: ['18/6=3'] Exploring Operation: 15/3=5, Resulting Numbers: [29, 5] Generated Node #0,1,0: 32:[29, 5] Operation: 15/3=5 Exploring Operation: 29-15=14, Resulting Numbers: [3, 14] Generated Node #0,1,1: 32:[3, 14] Operation: 29-15=14 Exploring Operation: 15+3=18, Resulting Numbers: [29, 18] Generated Node #0,1,2: 32:[29, 18] Operation: 15+3=18 Exploring Operation: 15-3=12, Resulting Numbers: [29, 12] Generated Node #0,1,3: 32:[29, 12] Operation: 15-3=12 Exploring Operation: 29+3=32, Resulting Numbers: [15, 32] Generated Node #0,1,4: 32:[15, 32] Operation: 29+3=32 Moving to Node #0,2 Current State: 32:[15, 6, 11], Operations: ['29-18=11'] Exploring Operation: 11-6=5, Resulting Numbers: [15, 5] Generated Node #0,2,0: 32:[15, 5] Operation: 11-6=5 Exploring Operation: 15-11=4, Resulting Numbers: [6, 4] Generated Node #0,2,1: 32:[6, 4] Operation: 15-11=4 Exploring Operation: 15-6=9, Resulting Numbers: [11, 9] Generated Node #0,2,2: 32:[11, 9] Operation: 15-6=9 Exploring Operation: 15+6=21, Resulting Numbers: [11, 21] Generated Node #0,2,3: 32:[11, 21] Operation: 15+6=21 Exploring Operation: 6+11=17, Resulting Numbers: [15, 17] Generated Node #0,2,4: 32:[15, 17] Operation: 6+11=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[15, 5], Operations: ['29-18=11', '11-6=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,32 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[6, 4], Operations: ['29-18=11', '15-11=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 32:[15, 17], Operations: ['29-18=11', '6+11=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[18, 15, 6, 29], Operations: [] Exploring Operation: 29-18=11, Resulting Numbers: [15, 6, 11] Generated Node #0,2: 32:[15, 6, 11] Operation: 29-18=11 Moving to Node #0,2 Current State: 32:[15, 6, 11], Operations: ['29-18=11'] Exploring Operation: 6+11=17, Resulting Numbers: [15, 17] Generated Node #0,2,4: 32:[15, 17] Operation: 6+11=17 Moving to Node #0,2,4 Current State: 32:[15, 17], Operations: ['29-18=11', '6+11=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
mult_heuristic
[ 36, 23, 46, 32 ]
94
[ "36*32=1152", "23*46=1058", "1152-1058=94" ]
Current State: 94:[36, 23, 46, 32], Operations: [] Exploring Operation: 36*32=1152, Resulting Numbers: [23, 46, 1152] Generated Node #2: [23, 46, 1152] from Operation: 36*32=1152 Current State: 94:[23, 46, 1152], Operations: ['36*32=1152'] Exploring Operation: 23*46=1058, Resulting Numbers: [1152, 1058] Generated Node #3: [1152, 1058] from Operation: 23*46=1058 Current State: 94:[1152, 1058], Operations: ['36*32=1152', '23*46=1058'] Exploring Operation: 1152-1058=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[36, 23, 46, 32], Operations: [] Exploring Operation: 23+32=55, Resulting Numbers: [36, 46, 55] Generated Node #0,0: 94:[36, 46, 55] Operation: 23+32=55 Exploring Operation: 32-23=9, Resulting Numbers: [36, 46, 9] Generated Node #0,1: 94:[36, 46, 9] Operation: 32-23=9 Exploring Operation: 36-32=4, Resulting Numbers: [23, 46, 4] Generated Node #0,2: 94:[23, 46, 4] Operation: 36-32=4 Moving to Node #0,1 Current State: 94:[36, 46, 9], Operations: ['32-23=9'] Exploring Operation: 36+9=45, Resulting Numbers: [46, 45] Generated Node #0,1,0: 94:[46, 45] Operation: 36+9=45 Exploring Operation: 46-36=10, Resulting Numbers: [9, 10] Generated Node #0,1,1: 94:[9, 10] Operation: 46-36=10 Exploring Operation: 36/9=4, Resulting Numbers: [46, 4] Generated Node #0,1,2: 94:[46, 4] Operation: 36/9=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[46, 45], Operations: ['32-23=9', '36+9=45'] Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,94 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 46+45=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 #0,1,2 Current State: 94:[46, 4], Operations: ['32-23=9', '36/9=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,94 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,94 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 #0,1,1 Current State: 94:[9, 10], Operations: ['32-23=9', '46-36=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,94 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,94 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:[36, 46, 55], Operations: ['23+32=55'] Exploring Operation: 46-36=10, Resulting Numbers: [55, 10] Generated Node #0,0,0: 94:[55, 10] Operation: 46-36=10 Exploring Operation: 55-36=19, Resulting Numbers: [46, 19] Generated Node #0,0,1: 94:[46, 19] Operation: 55-36=19 Exploring Operation: 36+55=91, Resulting Numbers: [46, 91] Generated Node #0,0,2: 94:[46, 91] Operation: 36+55=91 Moving to Node #0,2 Current State: 94:[23, 46, 4], Operations: ['36-32=4'] Exploring Operation: 23*4=92, Resulting Numbers: [46, 92] Generated Node #0,2,0: 94:[46, 92] Operation: 23*4=92 Exploring Operation: 23-4=19, Resulting Numbers: [46, 19] Generated Node #0,2,1: 94:[46, 19] Operation: 23-4=19 Exploring Operation: 46/23=2, Resulting Numbers: [4, 2] Generated Node #0,2,2: 94:[4, 2] Operation: 46/23=2 Moving to Node #0,2,2 Current State: 94:[4, 2], Operations: ['36-32=4', '46/23=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,2,0 Current State: 94:[46, 92], Operations: ['36-32=4', '23*4=92'] Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 46+92=138, Resulting Numbers: [138] 138,94 unequal: No Solution Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[46, 91], Operations: ['23+32=55', '36+55=91'] Exploring Operation: 46+91=137, Resulting Numbers: [137] 137,94 unequal: No Solution Exploring Operation: 91-46=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 46*91=4186, Resulting Numbers: [4186] 4186,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[55, 10], Operations: ['23+32=55', '46-36=10'] Exploring Operation: 55+10=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 55*10=550, Resulting Numbers: [550] 550,94 unequal: No Solution Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[46, 19], Operations: ['36-32=4', '23-4=19'] Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,94 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[46, 19], Operations: ['23+32=55', '55-36=19'] Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,94 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,94 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 12, 89, 32, 3 ]
21
[ "12*3=36", "89-32=57", "57-36=21" ]
Current State: 21:[12, 89, 32, 3], Operations: [] Exploring Operation: 12*3=36, Resulting Numbers: [89, 32, 36] Generated Node #2: [89, 32, 36] from Operation: 12*3=36 Current State: 21:[89, 32, 36], Operations: ['12*3=36'] Exploring Operation: 89-32=57, Resulting Numbers: [36, 57] Generated Node #3: [36, 57] from Operation: 89-32=57 Current State: 21:[36, 57], Operations: ['12*3=36', '89-32=57'] Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[12, 89, 32, 3], Operations: [] Exploring Operation: 89-32=57, Resulting Numbers: [12, 3, 57] Generated Node #0,0: 21:[12, 3, 57] Operation: 89-32=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[12, 3, 57], Operations: ['89-32=57'] Exploring Operation: 57/3=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 21:[12, 19] Operation: 57/3=19 Moving to Node #0,0,0 Current State: 21:[12, 19], Operations: ['89-32=57', '57/3=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,21 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
[ 18, 25, 49, 13 ]
20
[ "25-18=7", "49/7=7", "13+7=20" ]
Current State: 20:[18, 25, 49, 13], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [49, 13, 7] Generated Node #2: [49, 13, 7] from Operation: 25-18=7 Current State: 20:[49, 13, 7], Operations: ['25-18=7'] Exploring Operation: 49/7=7, Resulting Numbers: [13, 7] Generated Node #3: [13, 7] from Operation: 49/7=7 Current State: 20:[13, 7], Operations: ['25-18=7', '49/7=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[18, 25, 49, 13], Operations: [] Exploring Operation: 49-18=31, Resulting Numbers: [25, 13, 31] Generated Node #0,0: 20:[25, 13, 31] Operation: 49-18=31 Exploring Operation: 49-25=24, Resulting Numbers: [18, 13, 24] Generated Node #0,1: 20:[18, 13, 24] Operation: 49-25=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[18, 13, 24], Operations: ['49-25=24'] Exploring Operation: 24-13=11, Resulting Numbers: [18, 11] Generated Node #0,1,0: 20:[18, 11] Operation: 24-13=11 Exploring Operation: 18-13=5, Resulting Numbers: [24, 5] Generated Node #0,1,1: 20:[24, 5] Operation: 18-13=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[18, 11], Operations: ['49-25=24', '24-13=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,20 unequal: No Solution No 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: 20:[24, 5], Operations: ['49-25=24', '18-13=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,20 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: 20:[25, 13, 31], Operations: ['49-18=31'] Exploring Operation: 31-25=6, Resulting Numbers: [13, 6] Generated Node #0,0,0: 20:[13, 6] Operation: 31-25=6 Exploring Operation: 31-13=18, Resulting Numbers: [25, 18] Generated Node #0,0,1: 20:[25, 18] Operation: 31-13=18 Moving to Node #0,0,0 Current State: 20:[13, 6], Operations: ['49-18=31', '31-25=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,20 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[25, 18], Operations: ['49-18=31', '31-13=18'] Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,20 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
[ 8, 50, 52, 46 ]
98
[ "52-46=6", "8*6=48", "50+48=98" ]
Current State: 98:[8, 50, 52, 46], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [8, 50, 6] Generated Node #2: [8, 50, 6] from Operation: 52-46=6 Current State: 98:[8, 50, 6], Operations: ['52-46=6'] Exploring Operation: 8*6=48, Resulting Numbers: [50, 48] Generated Node #3: [50, 48] from Operation: 8*6=48 Current State: 98:[50, 48], Operations: ['52-46=6', '8*6=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[8, 50, 52, 46], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [8, 50, 6] Generated Node #0,0: 98:[8, 50, 6] Operation: 52-46=6 Exploring Operation: 50+46=96, Resulting Numbers: [8, 52, 96] Generated Node #0,1: 98:[8, 52, 96] Operation: 50+46=96 Exploring Operation: 50-46=4, Resulting Numbers: [8, 52, 4] Generated Node #0,2: 98:[8, 52, 4] Operation: 50-46=4 Exploring Operation: 52-50=2, Resulting Numbers: [8, 46, 2] Generated Node #0,3: 98:[8, 46, 2] Operation: 52-50=2 Exploring Operation: 52+46=98, Resulting Numbers: [8, 50, 98] Generated Node #0,4: 98:[8, 50, 98] Operation: 52+46=98 Moving to Node #0,4 Current State: 98:[8, 50, 98], Operations: ['52+46=98'] Exploring Operation: 8+50=58, Resulting Numbers: [98, 58] Generated Node #0,4,0: 98:[98, 58] Operation: 8+50=58 Exploring Operation: 50-8=42, Resulting Numbers: [98, 42] Generated Node #0,4,1: 98:[98, 42] Operation: 50-8=42 Exploring Operation: 8+98=106, Resulting Numbers: [50, 106] Generated Node #0,4,2: 98:[50, 106] Operation: 8+98=106 Exploring Operation: 98-8=90, Resulting Numbers: [50, 90] Generated Node #0,4,3: 98:[50, 90] Operation: 98-8=90 Exploring Operation: 98-50=48, Resulting Numbers: [8, 48] Generated Node #0,4,4: 98:[8, 48] Operation: 98-50=48 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 98:[8, 48], Operations: ['52+46=98', '98-50=48'] Exploring Operation: 8*48=384, Resulting Numbers: [384] 384,98 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,98 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 98:[98, 42], Operations: ['52+46=98', '50-8=42'] Exploring Operation: 98*42=4116, Resulting Numbers: [4116] 4116,98 unequal: No Solution Exploring Operation: 98+42=140, Resulting Numbers: [140] 140,98 unequal: No Solution Exploring Operation: 98-42=56, Resulting Numbers: [56] 56,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 98:[98, 58], Operations: ['52+46=98', '8+50=58'] Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 98*58=5684, Resulting Numbers: [5684] 5684,98 unequal: No Solution Exploring Operation: 98+58=156, Resulting Numbers: [156] 156,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 98:[50, 106], Operations: ['52+46=98', '8+98=106'] Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,98 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,98 unequal: No Solution Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 98:[50, 90], Operations: ['52+46=98', '98-8=90'] Exploring Operation: 50*90=4500, Resulting Numbers: [4500] 4500,98 unequal: No Solution Exploring Operation: 50+90=140, Resulting Numbers: [140] 140,98 unequal: No Solution Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,98 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: 98:[8, 50, 6], Operations: ['52-46=6'] Exploring Operation: 8*6=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 98:[50, 48] Operation: 8*6=48 Exploring Operation: 8+6=14, Resulting Numbers: [50, 14] Generated Node #0,0,1: 98:[50, 14] Operation: 8+6=14 Exploring Operation: 50-6=44, Resulting Numbers: [8, 44] Generated Node #0,0,2: 98:[8, 44] Operation: 50-6=44 Exploring Operation: 8-6=2, Resulting Numbers: [50, 2] Generated Node #0,0,3: 98:[50, 2] Operation: 8-6=2 Exploring Operation: 50-8=42, Resulting Numbers: [6, 42] Generated Node #0,0,4: 98:[6, 42] Operation: 50-8=42 Moving to Node #0,3 Current State: 98:[8, 46, 2], Operations: ['52-50=2'] Exploring Operation: 8-2=6, Resulting Numbers: [46, 6] Generated Node #0,3,0: 98:[46, 6] Operation: 8-2=6 Exploring Operation: 8/2=4, Resulting Numbers: [46, 4] Generated Node #0,3,1: 98:[46, 4] Operation: 8/2=4 Exploring Operation: 8*2=16, Resulting Numbers: [46, 16] Generated Node #0,3,2: 98:[46, 16] Operation: 8*2=16 Exploring Operation: 8+46=54, Resulting Numbers: [2, 54] Generated Node #0,3,3: 98:[2, 54] Operation: 8+46=54 Exploring Operation: 46+2=48, Resulting Numbers: [8, 48] Generated Node #0,3,4: 98:[8, 48] Operation: 46+2=48 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 98:[8, 48], Operations: ['52-50=2', '46+2=48'] Exploring Operation: 8*48=384, Resulting Numbers: [384] 384,98 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,98 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 98:[46, 6], Operations: ['52-50=2', '8-2=6'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,98 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 98:[46, 4], Operations: ['52-50=2', '8/2=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 98:[46, 16], Operations: ['52-50=2', '8*2=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,98 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[2, 54], Operations: ['52-50=2', '8+46=54'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,98 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,98 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,98 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,98 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: 98:[8, 52, 96], Operations: ['50+46=96'] Exploring Operation: 8+96=104, Resulting Numbers: [52, 104] Generated Node #0,1,0: 98:[52, 104] Operation: 8+96=104 Exploring Operation: 96/8=12, Resulting Numbers: [52, 12] Generated Node #0,1,1: 98:[52, 12] Operation: 96/8=12 Exploring Operation: 8+52=60, Resulting Numbers: [96, 60] Generated Node #0,1,2: 98:[96, 60] Operation: 8+52=60 Exploring Operation: 52-8=44, Resulting Numbers: [96, 44] Generated Node #0,1,3: 98:[96, 44] Operation: 52-8=44 Exploring Operation: 96-52=44, Resulting Numbers: [8, 44] Generated Node #0,1,4: 98:[8, 44] Operation: 96-52=44 Moving to Node #0,2 Current State: 98:[8, 52, 4], Operations: ['50-46=4'] Exploring Operation: 8-4=4, Resulting Numbers: [52, 4] Generated Node #0,2,0: 98:[52, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [52, 2] Generated Node #0,2,1: 98:[52, 2] Operation: 8/4=2 Exploring Operation: 52/4=13, Resulting Numbers: [8, 13] Generated Node #0,2,2: 98:[8, 13] Operation: 52/4=13 Exploring Operation: 8+4=12, Resulting Numbers: [52, 12] Generated Node #0,2,3: 98:[52, 12] Operation: 8+4=12 Exploring Operation: 52-4=48, Resulting Numbers: [8, 48] Generated Node #0,2,4: 98:[8, 48] Operation: 52-4=48 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[8, 13], Operations: ['50-46=4', '52/4=13'] Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,98 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 98:[8, 48], Operations: ['50-46=4', '52-4=48'] Exploring Operation: 8*48=384, Resulting Numbers: [384] 384,98 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,98 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[52, 2], Operations: ['50-46=4', '8/4=2'] Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,98 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,98 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[52, 4], Operations: ['50-46=4', '8-4=4'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,98 unequal: No Solution Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,98 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 98:[52, 12], Operations: ['50-46=4', '8+4=12'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,98 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,98 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: 98:[50, 14], Operations: ['52-46=6', '8+6=14'] Exploring Operation: 50*14=700, Resulting Numbers: [700] 700,98 unequal: No Solution Exploring Operation: 50+14=64, Resulting Numbers: [64] 64,98 unequal: No Solution Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[50, 2], Operations: ['52-46=6', '8-6=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,98 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[50, 48], Operations: ['52-46=6', '8*6=48'] Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,98 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[8, 50, 52, 46], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [8, 50, 6] Generated Node #0,0: 98:[8, 50, 6] Operation: 52-46=6 Moving to Node #0,0 Current State: 98:[8, 50, 6], Operations: ['52-46=6'] Exploring Operation: 8*6=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 98:[50, 48] Operation: 8*6=48 Moving to Node #0,0,0 Current State: 98:[50, 48], Operations: ['52-46=6', '8*6=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.918403
hs_5
mult_heuristic
[ 11, 64, 55, 71 ]
73
[ "64-11=53", "55+71=126", "126-53=73" ]
Current State: 73:[11, 64, 55, 71], Operations: [] Exploring Operation: 64-11=53, Resulting Numbers: [55, 71, 53] Generated Node #2: [55, 71, 53] from Operation: 64-11=53 Current State: 73:[55, 71, 53], Operations: ['64-11=53'] Exploring Operation: 55+71=126, Resulting Numbers: [53, 126] Generated Node #3: [53, 126] from Operation: 55+71=126 Current State: 73:[53, 126], Operations: ['64-11=53', '55+71=126'] Exploring Operation: 126-53=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[11, 64, 55, 71], Operations: [] Exploring Operation: 11+55=66, Resulting Numbers: [64, 71, 66] Generated Node #0,0: 73:[64, 71, 66] Operation: 11+55=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[64, 71, 66], Operations: ['11+55=66'] Exploring Operation: 64+66=130, Resulting Numbers: [71, 130] Generated Node #0,0,0: 73:[71, 130] Operation: 64+66=130 Moving to Node #0,0,0 Current State: 73:[71, 130], Operations: ['11+55=66', '64+66=130'] Exploring Operation: 130-71=59, Resulting Numbers: [59] 59,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 3, 28, 37, 27 ]
34
[ "37-3=34", "28-27=1", "34*1=34" ]
Current State: 34:[3, 28, 37, 27], Operations: [] Exploring Operation: 37-3=34, Resulting Numbers: [28, 27, 34] Generated Node #2: [28, 27, 34] from Operation: 37-3=34 Current State: 34:[28, 27, 34], Operations: ['37-3=34'] Exploring Operation: 28-27=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 28-27=1 Current State: 34:[34, 1], Operations: ['37-3=34', '28-27=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[3, 28, 37, 27], Operations: [] Exploring Operation: 3+28=31, Resulting Numbers: [37, 27, 31] Generated Node #0,0: 34:[37, 27, 31] Operation: 3+28=31 Exploring Operation: 28-27=1, Resulting Numbers: [3, 37, 1] Generated Node #0,1: 34:[3, 37, 1] Operation: 28-27=1 Exploring Operation: 37-3=34, Resulting Numbers: [28, 27, 34] Generated Node #0,2: 34:[28, 27, 34] Operation: 37-3=34 Moving to Node #0,1 Current State: 34:[3, 37, 1], Operations: ['28-27=1'] Exploring Operation: 37-3=34, Resulting Numbers: [1, 34] Generated Node #0,1,0: 34:[1, 34] Operation: 37-3=34 Exploring Operation: 3-1=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 34:[37, 2] Operation: 3-1=2 Exploring Operation: 37-1=36, Resulting Numbers: [3, 36] Generated Node #0,1,2: 34:[3, 36] Operation: 37-1=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[1, 34], Operations: ['28-27=1', '37-3=34'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[3, 28, 37, 27], Operations: [] Exploring Operation: 28-27=1, Resulting Numbers: [3, 37, 1] Generated Node #0,1: 34:[3, 37, 1] Operation: 28-27=1 Moving to Node #0,1 Current State: 34:[3, 37, 1], Operations: ['28-27=1'] Exploring Operation: 37-3=34, Resulting Numbers: [1, 34] Generated Node #0,1,0: 34:[1, 34] Operation: 37-3=34 Moving to Node #0,1,0 Current State: 34:[1, 34], Operations: ['28-27=1', '37-3=34'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 60, 17, 19, 73 ]
49
[ "60-17=43", "19+73=92", "92-43=49" ]
Current State: 49:[60, 17, 19, 73], Operations: [] Exploring Operation: 60-17=43, Resulting Numbers: [19, 73, 43] Generated Node #2: [19, 73, 43] from Operation: 60-17=43 Current State: 49:[19, 73, 43], Operations: ['60-17=43'] Exploring Operation: 19+73=92, Resulting Numbers: [43, 92] Generated Node #3: [43, 92] from Operation: 19+73=92 Current State: 49:[43, 92], Operations: ['60-17=43', '19+73=92'] Exploring Operation: 92-43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[60, 17, 19, 73], Operations: [] Exploring Operation: 73-17=56, Resulting Numbers: [60, 19, 56] Generated Node #0,0: 49:[60, 19, 56] Operation: 73-17=56 Exploring Operation: 73-60=13, Resulting Numbers: [17, 19, 13] Generated Node #0,1: 49:[17, 19, 13] Operation: 73-60=13 Exploring Operation: 73-19=54, Resulting Numbers: [60, 17, 54] Generated Node #0,2: 49:[60, 17, 54] Operation: 73-19=54 Exploring Operation: 19-17=2, Resulting Numbers: [60, 73, 2] Generated Node #0,3: 49:[60, 73, 2] Operation: 19-17=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[60, 17, 54], Operations: ['73-19=54'] Exploring Operation: 60+17=77, Resulting Numbers: [54, 77] Generated Node #0,2,0: 49:[54, 77] Operation: 60+17=77 Exploring Operation: 60-54=6, Resulting Numbers: [17, 6] Generated Node #0,2,1: 49:[17, 6] Operation: 60-54=6 Exploring Operation: 54-17=37, Resulting Numbers: [60, 37] Generated Node #0,2,2: 49:[60, 37] Operation: 54-17=37 Exploring Operation: 60-17=43, Resulting Numbers: [54, 43] Generated Node #0,2,3: 49:[54, 43] Operation: 60-17=43 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[17, 6], Operations: ['73-19=54', '60-54=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,49 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,49 unequal: No Solution No 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: 49:[54, 43], Operations: ['73-19=54', '60-17=43'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,49 unequal: No Solution No 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: 49:[60, 37], Operations: ['73-19=54', '54-17=37'] Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,49 unequal: No Solution Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,49 unequal: No Solution Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,49 unequal: No Solution No 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: 49:[54, 77], Operations: ['73-19=54', '60+17=77'] Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,49 unequal: No Solution Exploring Operation: 54+77=131, Resulting Numbers: [131] 131,49 unequal: No Solution Exploring Operation: 54*77=4158, Resulting Numbers: [4158] 4158,49 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: 49:[17, 19, 13], Operations: ['73-60=13'] Exploring Operation: 19-17=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 49:[13, 2] Operation: 19-17=2 Exploring Operation: 17+19=36, Resulting Numbers: [13, 36] Generated Node #0,1,1: 49:[13, 36] Operation: 17+19=36 Exploring Operation: 17-13=4, Resulting Numbers: [19, 4] Generated Node #0,1,2: 49:[19, 4] Operation: 17-13=4 Exploring Operation: 19-13=6, Resulting Numbers: [17, 6] Generated Node #0,1,3: 49:[17, 6] Operation: 19-13=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[13, 2], Operations: ['73-60=13', '19-17=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,49 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,49 unequal: No Solution No 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: 49:[17, 6], Operations: ['73-60=13', '19-13=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,49 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,49 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,49 unequal: No Solution No 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: 49:[19, 4], Operations: ['73-60=13', '17-13=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,49 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,49 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,49 unequal: No Solution No 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: 49:[13, 36], Operations: ['73-60=13', '17+19=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[60, 17, 19, 73], Operations: [] Exploring Operation: 73-60=13, Resulting Numbers: [17, 19, 13] Generated Node #0,1: 49:[17, 19, 13] Operation: 73-60=13 Moving to Node #0,1 Current State: 49:[17, 19, 13], Operations: ['73-60=13'] Exploring Operation: 17+19=36, Resulting Numbers: [13, 36] Generated Node #0,1,1: 49:[13, 36] Operation: 17+19=36 Moving to Node #0,1,1 Current State: 49:[13, 36], Operations: ['73-60=13', '17+19=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_4
mult_heuristic
[ 29, 40, 39, 2 ]
27
[ "29-2=27", "40-39=1", "27*1=27" ]
Current State: 27:[29, 40, 39, 2], Operations: [] Exploring Operation: 29-2=27, Resulting Numbers: [40, 39, 27] Generated Node #2: [40, 39, 27] from Operation: 29-2=27 Current State: 27:[40, 39, 27], Operations: ['29-2=27'] Exploring Operation: 40-39=1, Resulting Numbers: [27, 1] Generated Node #3: [27, 1] from Operation: 40-39=1 Current State: 27:[27, 1], Operations: ['29-2=27', '40-39=1'] Exploring Operation: 27*1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[29, 40, 39, 2], Operations: [] Exploring Operation: 40-39=1, Resulting Numbers: [29, 2, 1] Generated Node #0,0: 27:[29, 2, 1] Operation: 40-39=1 Moving to Node #0,0 Current State: 27:[29, 2, 1], Operations: ['40-39=1'] Exploring Operation: 29-2=27, Resulting Numbers: [1, 27] Generated Node #0,0,0: 27:[1, 27] Operation: 29-2=27 Moving to Node #0,0,0 Current State: 27:[1, 27], Operations: ['40-39=1', '29-2=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[29, 40, 39, 2], Operations: [] Exploring Operation: 40-39=1, Resulting Numbers: [29, 2, 1] Generated Node #0,0: 27:[29, 2, 1] Operation: 40-39=1 Moving to Node #0,0 Current State: 27:[29, 2, 1], Operations: ['40-39=1'] Exploring Operation: 29-2=27, Resulting Numbers: [1, 27] Generated Node #0,0,0: 27:[1, 27] Operation: 29-2=27 Moving to Node #0,0,0 Current State: 27:[1, 27], Operations: ['40-39=1', '29-2=27'] Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 6, 9, 34, 15 ]
69
[ "6*34=204", "9*15=135", "204-135=69" ]
Current State: 69:[6, 9, 34, 15], Operations: [] Exploring Operation: 6*34=204, Resulting Numbers: [9, 15, 204] Generated Node #2: [9, 15, 204] from Operation: 6*34=204 Current State: 69:[9, 15, 204], Operations: ['6*34=204'] Exploring Operation: 9*15=135, Resulting Numbers: [204, 135] Generated Node #3: [204, 135] from Operation: 9*15=135 Current State: 69:[204, 135], Operations: ['6*34=204', '9*15=135'] Exploring Operation: 204-135=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[6, 9, 34, 15], Operations: [] Exploring Operation: 34-9=25, Resulting Numbers: [6, 15, 25] Generated Node #0,0: 69:[6, 15, 25] Operation: 34-9=25 Moving to Node #0,0 Current State: 69:[6, 15, 25], Operations: ['34-9=25'] Exploring Operation: 6+15=21, Resulting Numbers: [25, 21] Generated Node #0,0,0: 69:[25, 21] Operation: 6+15=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[25, 21], Operations: ['34-9=25', '6+15=21'] Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 13, 50, 59, 48 ]
74
[ "13+50=63", "59-48=11", "63+11=74" ]
Current State: 74:[13, 50, 59, 48], Operations: [] Exploring Operation: 13+50=63, Resulting Numbers: [59, 48, 63] Generated Node #2: [59, 48, 63] from Operation: 13+50=63 Current State: 74:[59, 48, 63], Operations: ['13+50=63'] Exploring Operation: 59-48=11, Resulting Numbers: [63, 11] Generated Node #3: [63, 11] from Operation: 59-48=11 Current State: 74:[63, 11], Operations: ['13+50=63', '59-48=11'] Exploring Operation: 63+11=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[13, 50, 59, 48], Operations: [] Exploring Operation: 50-13=37, Resulting Numbers: [59, 48, 37] Generated Node #0,0: 74:[59, 48, 37] Operation: 50-13=37 Moving to Node #0,0 Current State: 74:[59, 48, 37], Operations: ['50-13=37'] Exploring Operation: 59-48=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 74:[37, 11] Operation: 59-48=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[37, 11], Operations: ['50-13=37', '59-48=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,74 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
[ 29, 90, 76, 30 ]
35
[ "29+76=105", "90/30=3", "105/3=35" ]
Current State: 35:[29, 90, 76, 30], Operations: [] Exploring Operation: 29+76=105, Resulting Numbers: [90, 30, 105] Generated Node #2: [90, 30, 105] from Operation: 29+76=105 Current State: 35:[90, 30, 105], Operations: ['29+76=105'] Exploring Operation: 90/30=3, Resulting Numbers: [105, 3] Generated Node #3: [105, 3] from Operation: 90/30=3 Current State: 35:[105, 3], Operations: ['29+76=105', '90/30=3'] Exploring Operation: 105/3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[29, 90, 76, 30], Operations: [] Exploring Operation: 90-76=14, Resulting Numbers: [29, 30, 14] Generated Node #0,0: 35:[29, 30, 14] Operation: 90-76=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[29, 30, 14], Operations: ['90-76=14'] Exploring Operation: 30-29=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 35:[14, 1] Operation: 30-29=1 Moving to Node #0,0,0 Current State: 35:[14, 1], Operations: ['90-76=14', '30-29=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,35 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
[ 65, 43, 67, 66 ]
20
[ "67-65=2", "43*2=86", "86-66=20" ]
Current State: 20:[65, 43, 67, 66], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [43, 66, 2] Generated Node #2: [43, 66, 2] from Operation: 67-65=2 Current State: 20:[43, 66, 2], Operations: ['67-65=2'] Exploring Operation: 43*2=86, Resulting Numbers: [66, 86] Generated Node #3: [66, 86] from Operation: 43*2=86 Current State: 20:[66, 86], Operations: ['67-65=2', '43*2=86'] Exploring Operation: 86-66=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[65, 43, 67, 66], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [43, 66, 2] Generated Node #0,0: 20:[43, 66, 2] Operation: 67-65=2 Moving to Node #0,0 Current State: 20:[43, 66, 2], Operations: ['67-65=2'] Exploring Operation: 66-43=23, Resulting Numbers: [2, 23] Generated Node #0,0,0: 20:[2, 23] Operation: 66-43=23 Moving to Node #0,0,0 Current State: 20:[2, 23], Operations: ['67-65=2', '66-43=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,20 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 87, 9, 97, 8 ]
76
[ "97-9=88", "88/8=11", "87-11=76" ]
Current State: 76:[87, 9, 97, 8], Operations: [] Exploring Operation: 97-9=88, Resulting Numbers: [87, 8, 88] Generated Node #2: [87, 8, 88] from Operation: 97-9=88 Current State: 76:[87, 8, 88], Operations: ['97-9=88'] Exploring Operation: 88/8=11, Resulting Numbers: [87, 11] Generated Node #3: [87, 11] from Operation: 88/8=11 Current State: 76:[87, 11], Operations: ['97-9=88', '88/8=11'] Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[87, 9, 97, 8], Operations: [] Exploring Operation: 97-9=88, Resulting Numbers: [87, 8, 88] Generated Node #0,0: 76:[87, 8, 88] Operation: 97-9=88 Exploring Operation: 87-9=78, Resulting Numbers: [97, 8, 78] Generated Node #0,1: 76:[97, 8, 78] Operation: 87-9=78 Exploring Operation: 97-87=10, Resulting Numbers: [9, 8, 10] Generated Node #0,2: 76:[9, 8, 10] Operation: 97-87=10 Moving to Node #0,2 Current State: 76:[9, 8, 10], Operations: ['97-87=10'] Exploring Operation: 9+10=19, Resulting Numbers: [8, 19] Generated Node #0,2,0: 76:[8, 19] Operation: 9+10=19 Exploring Operation: 10-8=2, Resulting Numbers: [9, 2] Generated Node #0,2,1: 76:[9, 2] Operation: 10-8=2 Exploring Operation: 10-9=1, Resulting Numbers: [8, 1] Generated Node #0,2,2: 76:[8, 1] Operation: 10-9=1 Moving to Node #0,0 Current State: 76:[87, 8, 88], Operations: ['97-9=88'] Exploring Operation: 88-87=1, Resulting Numbers: [8, 1] Generated Node #0,0,0: 76:[8, 1] Operation: 88-87=1 Exploring Operation: 88-8=80, Resulting Numbers: [87, 80] Generated Node #0,0,1: 76:[87, 80] Operation: 88-8=80 Exploring Operation: 87-8=79, Resulting Numbers: [88, 79] Generated Node #0,0,2: 76:[88, 79] Operation: 87-8=79 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[8, 1], Operations: ['97-9=88', '88-87=1'] Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,76 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 #0,0,1 Current State: 76:[87, 80], Operations: ['97-9=88', '88-8=80'] Exploring Operation: 87*80=6960, Resulting Numbers: [6960] 6960,76 unequal: No Solution Exploring Operation: 87+80=167, Resulting Numbers: [167] 167,76 unequal: No Solution Exploring Operation: 87-80=7, Resulting Numbers: [7] 7,76 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 #0,0,2 Current State: 76:[88, 79], Operations: ['97-9=88', '87-8=79'] Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 88+79=167, Resulting Numbers: [167] 167,76 unequal: No Solution Exploring Operation: 88*79=6952, Resulting Numbers: [6952] 6952,76 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: 76:[97, 8, 78], Operations: ['87-9=78'] Exploring Operation: 78-8=70, Resulting Numbers: [97, 70] Generated Node #0,1,0: 76:[97, 70] Operation: 78-8=70 Exploring Operation: 97-78=19, Resulting Numbers: [8, 19] Generated Node #0,1,1: 76:[8, 19] Operation: 97-78=19 Exploring Operation: 97-8=89, Resulting Numbers: [78, 89] Generated Node #0,1,2: 76:[78, 89] Operation: 97-8=89 Moving to Node #0,2,0 Current State: 76:[8, 19], Operations: ['97-87=10', '9+10=19'] Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,76 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[8, 19], Operations: ['87-9=78', '97-78=19'] Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,76 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[8, 1], Operations: ['97-87=10', '10-9=1'] Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[9, 2], Operations: ['97-87=10', '10-8=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[78, 89], Operations: ['87-9=78', '97-8=89'] Exploring Operation: 78*89=6942, Resulting Numbers: [6942] 6942,76 unequal: No Solution Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 78+89=167, Resulting Numbers: [167] 167,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[97, 70], Operations: ['87-9=78', '78-8=70'] Exploring Operation: 97*70=6790, Resulting Numbers: [6790] 6790,76 unequal: No Solution Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 97+70=167, Resulting Numbers: [167] 167,76 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 98, 90, 4, 88 ]
20
[ "98-90=8", "88-8=80", "80/4=20" ]
Current State: 20:[98, 90, 4, 88], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [4, 88, 8] Generated Node #2: [4, 88, 8] from Operation: 98-90=8 Current State: 20:[4, 88, 8], Operations: ['98-90=8'] Exploring Operation: 88-8=80, Resulting Numbers: [4, 80] Generated Node #3: [4, 80] from Operation: 88-8=80 Current State: 20:[4, 80], Operations: ['98-90=8', '88-8=80'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[98, 90, 4, 88], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [90, 4, 10] Generated Node #0,0: 20:[90, 4, 10] Operation: 98-88=10 Exploring Operation: 98-4=94, Resulting Numbers: [90, 88, 94] Generated Node #0,1: 20:[90, 88, 94] Operation: 98-4=94 Exploring Operation: 88/4=22, Resulting Numbers: [98, 90, 22] Generated Node #0,2: 20:[98, 90, 22] Operation: 88/4=22 Exploring Operation: 90-88=2, Resulting Numbers: [98, 4, 2] Generated Node #0,3: 20:[98, 4, 2] Operation: 90-88=2 Exploring Operation: 98-90=8, Resulting Numbers: [4, 88, 8] Generated Node #0,4: 20:[4, 88, 8] Operation: 98-90=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[90, 4, 10], Operations: ['98-88=10'] Exploring Operation: 90/10=9, Resulting Numbers: [4, 9] Generated Node #0,0,0: 20:[4, 9] Operation: 90/10=9 Exploring Operation: 90-4=86, Resulting Numbers: [10, 86] Generated Node #0,0,1: 20:[10, 86] Operation: 90-4=86 Exploring Operation: 90+4=94, Resulting Numbers: [10, 94] Generated Node #0,0,2: 20:[10, 94] Operation: 90+4=94 Exploring Operation: 90-10=80, Resulting Numbers: [4, 80] Generated Node #0,0,3: 20:[4, 80] Operation: 90-10=80 Exploring Operation: 10-4=6, Resulting Numbers: [90, 6] Generated Node #0,0,4: 20:[90, 6] Operation: 10-4=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[4, 9], Operations: ['98-88=10', '90/10=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,20 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,20 unequal: No Solution No 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: 20:[4, 80], Operations: ['98-88=10', '90-10=80'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,20 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[98, 90, 4, 88], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [90, 4, 10] Generated Node #0,0: 20:[90, 4, 10] Operation: 98-88=10 Moving to Node #0,0 Current State: 20:[90, 4, 10], Operations: ['98-88=10'] Exploring Operation: 90-10=80, Resulting Numbers: [4, 80] Generated Node #0,0,3: 20:[4, 80] Operation: 90-10=80 Moving to Node #0,0,3 Current State: 20:[4, 80], Operations: ['98-88=10', '90-10=80'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 44, 31, 41, 56 ]
37
[ "44-41=3", "31*3=93", "93-56=37" ]
Current State: 37:[44, 31, 41, 56], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [31, 56, 3] Generated Node #2: [31, 56, 3] from Operation: 44-41=3 Current State: 37:[31, 56, 3], Operations: ['44-41=3'] Exploring Operation: 31*3=93, Resulting Numbers: [56, 93] Generated Node #3: [56, 93] from Operation: 31*3=93 Current State: 37:[56, 93], Operations: ['44-41=3', '31*3=93'] Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[44, 31, 41, 56], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [44, 41, 25] Generated Node #0,0: 37:[44, 41, 25] Operation: 56-31=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[44, 41, 25], Operations: ['56-31=25'] Exploring Operation: 44-25=19, Resulting Numbers: [41, 19] Generated Node #0,0,0: 37:[41, 19] Operation: 44-25=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[41, 19], Operations: ['56-31=25', '44-25=19'] Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 82, 68, 14, 94 ]
34
[ "82+14=96", "96-94=2", "68/2=34" ]
Current State: 34:[82, 68, 14, 94], Operations: [] Exploring Operation: 82+14=96, Resulting Numbers: [68, 94, 96] Generated Node #2: [68, 94, 96] from Operation: 82+14=96 Current State: 34:[68, 94, 96], Operations: ['82+14=96'] Exploring Operation: 96-94=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 96-94=2 Current State: 34:[68, 2], Operations: ['82+14=96', '96-94=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[82, 68, 14, 94], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [82, 14, 26] Generated Node #0,0: 34:[82, 14, 26] Operation: 94-68=26 Exploring Operation: 82-68=14, Resulting Numbers: [14, 94, 14] Generated Node #0,1: 34:[14, 94, 14] Operation: 82-68=14 Exploring Operation: 94-82=12, Resulting Numbers: [68, 14, 12] Generated Node #0,2: 34:[68, 14, 12] Operation: 94-82=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[68, 14, 12], Operations: ['94-82=12'] Exploring Operation: 14-12=2, Resulting Numbers: [68, 2] Generated Node #0,2,0: 34:[68, 2] Operation: 14-12=2 Exploring Operation: 68-14=54, Resulting Numbers: [12, 54] Generated Node #0,2,1: 34:[12, 54] Operation: 68-14=54 Exploring Operation: 68-12=56, Resulting Numbers: [14, 56] Generated Node #0,2,2: 34:[14, 56] Operation: 68-12=56 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 34:[12, 54], Operations: ['94-82=12', '68-14=54'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 12+54=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 12*54=648, Resulting Numbers: [648] 648,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[14, 56], Operations: ['94-82=12', '68-12=56'] Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,34 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[68, 2], Operations: ['94-82=12', '14-12=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[82, 68, 14, 94], Operations: [] Exploring Operation: 94-82=12, Resulting Numbers: [68, 14, 12] Generated Node #0,2: 34:[68, 14, 12] Operation: 94-82=12 Moving to Node #0,2 Current State: 34:[68, 14, 12], Operations: ['94-82=12'] Exploring Operation: 14-12=2, Resulting Numbers: [68, 2] Generated Node #0,2,0: 34:[68, 2] Operation: 14-12=2 Moving to Node #0,2,0 Current State: 34:[68, 2], Operations: ['94-82=12', '14-12=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 51, 28, 25, 81 ]
24
[ "28-25=3", "81/3=27", "51-27=24" ]
Current State: 24:[51, 28, 25, 81], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [51, 81, 3] Generated Node #2: [51, 81, 3] from Operation: 28-25=3 Current State: 24:[51, 81, 3], Operations: ['28-25=3'] Exploring Operation: 81/3=27, Resulting Numbers: [51, 27] Generated Node #3: [51, 27] from Operation: 81/3=27 Current State: 24:[51, 27], Operations: ['28-25=3', '81/3=27'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[51, 28, 25, 81], Operations: [] Exploring Operation: 81-51=30, Resulting Numbers: [28, 25, 30] Generated Node #0,0: 24:[28, 25, 30] Operation: 81-51=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[28, 25, 30], Operations: ['81-51=30'] Exploring Operation: 30-28=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 24:[25, 2] Operation: 30-28=2 Moving to Node #0,0,0 Current State: 24:[25, 2], Operations: ['81-51=30', '30-28=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 59, 2, 94 ]
71
[ "59-35=24", "94/2=47", "24+47=71" ]
Current State: 71:[35, 59, 2, 94], Operations: [] Exploring Operation: 59-35=24, Resulting Numbers: [2, 94, 24] Generated Node #2: [2, 94, 24] from Operation: 59-35=24 Current State: 71:[2, 94, 24], Operations: ['59-35=24'] Exploring Operation: 94/2=47, Resulting Numbers: [24, 47] Generated Node #3: [24, 47] from Operation: 94/2=47 Current State: 71:[24, 47], Operations: ['59-35=24', '94/2=47'] Exploring Operation: 24+47=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[35, 59, 2, 94], Operations: [] Exploring Operation: 35*2=70, Resulting Numbers: [59, 94, 70] Generated Node #0,0: 71:[59, 94, 70] Operation: 35*2=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[59, 94, 70], Operations: ['35*2=70'] Exploring Operation: 94-59=35, Resulting Numbers: [70, 35] Generated Node #0,0,0: 71:[70, 35] Operation: 94-59=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[70, 35], Operations: ['35*2=70', '94-59=35'] Exploring Operation: 70+35=105, Resulting Numbers: [105] 105,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 91, 20, 11, 42 ]
87
[ "91+42=133", "20*11=220", "220-133=87" ]
Current State: 87:[91, 20, 11, 42], Operations: [] Exploring Operation: 91+42=133, Resulting Numbers: [20, 11, 133] Generated Node #2: [20, 11, 133] from Operation: 91+42=133 Current State: 87:[20, 11, 133], Operations: ['91+42=133'] Exploring Operation: 20*11=220, Resulting Numbers: [133, 220] Generated Node #3: [133, 220] from Operation: 20*11=220 Current State: 87:[133, 220], Operations: ['91+42=133', '20*11=220'] Exploring Operation: 220-133=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[91, 20, 11, 42], Operations: [] Exploring Operation: 42-11=31, Resulting Numbers: [91, 20, 31] Generated Node #0,0: 87:[91, 20, 31] Operation: 42-11=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[91, 20, 31], Operations: ['42-11=31'] Exploring Operation: 31-20=11, Resulting Numbers: [91, 11] Generated Node #0,0,0: 87:[91, 11] Operation: 31-20=11 Moving to Node #0,0,0 Current State: 87:[91, 11], Operations: ['42-11=31', '31-20=11'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,87 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
[ 76, 56, 34, 32 ]
22
[ "76-56=20", "34-32=2", "20+2=22" ]
Current State: 22:[76, 56, 34, 32], Operations: [] Exploring Operation: 76-56=20, Resulting Numbers: [34, 32, 20] Generated Node #2: [34, 32, 20] from Operation: 76-56=20 Current State: 22:[34, 32, 20], Operations: ['76-56=20'] Exploring Operation: 34-32=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 34-32=2 Current State: 22:[20, 2], Operations: ['76-56=20', '34-32=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[76, 56, 34, 32], Operations: [] Exploring Operation: 76-56=20, Resulting Numbers: [34, 32, 20] Generated Node #0,0: 22:[34, 32, 20] Operation: 76-56=20 Exploring Operation: 56-34=22, Resulting Numbers: [76, 32, 22] Generated Node #0,1: 22:[76, 32, 22] Operation: 56-34=22 Exploring Operation: 76-32=44, Resulting Numbers: [56, 34, 44] Generated Node #0,2: 22:[56, 34, 44] Operation: 76-32=44 Exploring Operation: 76-34=42, Resulting Numbers: [56, 32, 42] Generated Node #0,3: 22:[56, 32, 42] Operation: 76-34=42 Moving to Node #0,0 Current State: 22:[34, 32, 20], Operations: ['76-56=20'] Exploring Operation: 32-20=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 22:[34, 12] Operation: 32-20=12 Exploring Operation: 34-20=14, Resulting Numbers: [32, 14] Generated Node #0,0,1: 22:[32, 14] Operation: 34-20=14 Exploring Operation: 34-32=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 22:[20, 2] Operation: 34-32=2 Exploring Operation: 34+20=54, Resulting Numbers: [32, 54] Generated Node #0,0,3: 22:[32, 54] Operation: 34+20=54 Moving to Node #0,3 Current State: 22:[56, 32, 42], Operations: ['76-34=42'] Exploring Operation: 56-42=14, Resulting Numbers: [32, 14] Generated Node #0,3,0: 22:[32, 14] Operation: 56-42=14 Exploring Operation: 56-32=24, Resulting Numbers: [42, 24] Generated Node #0,3,1: 22:[42, 24] Operation: 56-32=24 Exploring Operation: 42-32=10, Resulting Numbers: [56, 10] Generated Node #0,3,2: 22:[56, 10] Operation: 42-32=10 Exploring Operation: 56+32=88, Resulting Numbers: [42, 88] Generated Node #0,3,3: 22:[42, 88] Operation: 56+32=88 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 22:[32, 14], Operations: ['76-34=42', '56-42=14'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,22 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 22:[42, 24], Operations: ['76-34=42', '56-32=24'] Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,22 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 22:[56, 10], Operations: ['76-34=42', '42-32=10'] Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 22:[42, 88], Operations: ['76-34=42', '56+32=88'] Exploring Operation: 42*88=3696, Resulting Numbers: [3696] 3696,22 unequal: No Solution Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 42+88=130, Resulting Numbers: [130] 130,22 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: 22:[76, 32, 22], Operations: ['56-34=22'] Exploring Operation: 76-32=44, Resulting Numbers: [22, 44] Generated Node #0,1,0: 22:[22, 44] Operation: 76-32=44 Exploring Operation: 76+32=108, Resulting Numbers: [22, 108] Generated Node #0,1,1: 22:[22, 108] Operation: 76+32=108 Exploring Operation: 76-22=54, Resulting Numbers: [32, 54] Generated Node #0,1,2: 22:[32, 54] Operation: 76-22=54 Exploring Operation: 32-22=10, Resulting Numbers: [76, 10] Generated Node #0,1,3: 22:[76, 10] Operation: 32-22=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[22, 44], Operations: ['56-34=22', '76-32=44'] Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,22 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,22 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[76, 56, 34, 32], Operations: [] Exploring Operation: 56-34=22, Resulting Numbers: [76, 32, 22] Generated Node #0,1: 22:[76, 32, 22] Operation: 56-34=22 Moving to Node #0,1 Current State: 22:[76, 32, 22], Operations: ['56-34=22'] Exploring Operation: 76-32=44, Resulting Numbers: [22, 44] Generated Node #0,1,0: 22:[22, 44] Operation: 76-32=44 Moving to Node #0,1,0 Current State: 22:[22, 44], Operations: ['56-34=22', '76-32=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 33, 69, 21, 67 ]
24
[ "33-21=12", "69-67=2", "12*2=24" ]
Current State: 24:[33, 69, 21, 67], Operations: [] Exploring Operation: 33-21=12, Resulting Numbers: [69, 67, 12] Generated Node #2: [69, 67, 12] from Operation: 33-21=12 Current State: 24:[69, 67, 12], Operations: ['33-21=12'] Exploring Operation: 69-67=2, Resulting Numbers: [12, 2] Generated Node #3: [12, 2] from Operation: 69-67=2 Current State: 24:[12, 2], Operations: ['33-21=12', '69-67=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[33, 69, 21, 67], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [33, 21, 2] Generated Node #0,0: 24:[33, 21, 2] Operation: 69-67=2 Moving to Node #0,0 Current State: 24:[33, 21, 2], Operations: ['69-67=2'] Exploring Operation: 33-21=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 33-21=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['69-67=2', '33-21=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[33, 69, 21, 67], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [33, 21, 2] Generated Node #0,0: 24:[33, 21, 2] Operation: 69-67=2 Moving to Node #0,0 Current State: 24:[33, 21, 2], Operations: ['69-67=2'] Exploring Operation: 33-21=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 24:[2, 12] Operation: 33-21=12 Moving to Node #0,0,0 Current State: 24:[2, 12], Operations: ['69-67=2', '33-21=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 35, 68, 7, 3 ]
30
[ "35*3=105", "68+7=75", "105-75=30" ]
Current State: 30:[35, 68, 7, 3], Operations: [] Exploring Operation: 35*3=105, Resulting Numbers: [68, 7, 105] Generated Node #2: [68, 7, 105] from Operation: 35*3=105 Current State: 30:[68, 7, 105], Operations: ['35*3=105'] Exploring Operation: 68+7=75, Resulting Numbers: [105, 75] Generated Node #3: [105, 75] from Operation: 68+7=75 Current State: 30:[105, 75], Operations: ['35*3=105', '68+7=75'] Exploring Operation: 105-75=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[35, 68, 7, 3], Operations: [] Exploring Operation: 68-7=61, Resulting Numbers: [35, 3, 61] Generated Node #0,0: 30:[35, 3, 61] Operation: 68-7=61 Exploring Operation: 68-35=33, Resulting Numbers: [7, 3, 33] Generated Node #0,1: 30:[7, 3, 33] Operation: 68-35=33 Moving to Node #0,1 Current State: 30:[7, 3, 33], Operations: ['68-35=33'] Exploring Operation: 33/3=11, Resulting Numbers: [7, 11] Generated Node #0,1,0: 30:[7, 11] Operation: 33/3=11 Exploring Operation: 33-3=30, Resulting Numbers: [7, 30] Generated Node #0,1,1: 30:[7, 30] Operation: 33-3=30 Moving to Node #0,0 Current State: 30:[35, 3, 61], Operations: ['68-7=61'] Exploring Operation: 35-3=32, Resulting Numbers: [61, 32] Generated Node #0,0,0: 30:[61, 32] Operation: 35-3=32 Exploring Operation: 61-35=26, Resulting Numbers: [3, 26] Generated Node #0,0,1: 30:[3, 26] Operation: 61-35=26 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[3, 26], Operations: ['68-7=61', '61-35=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[61, 32], Operations: ['68-7=61', '35-3=32'] Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,30 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:[7, 30], Operations: ['68-35=33', '33-3=30'] Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,30 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[7, 11], Operations: ['68-35=33', '33/3=11'] Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 30, 35, 75, 90 ]
12
[ "35*90=3150", "3150/75=42", "42-30=12" ]
Current State: 12:[30, 35, 75, 90], Operations: [] Exploring Operation: 35*90=3150, Resulting Numbers: [30, 75, 3150] Generated Node #2: [30, 75, 3150] from Operation: 35*90=3150 Current State: 12:[30, 75, 3150], Operations: ['35*90=3150'] Exploring Operation: 3150/75=42, Resulting Numbers: [30, 42] Generated Node #3: [30, 42] from Operation: 3150/75=42 Current State: 12:[30, 42], Operations: ['35*90=3150', '3150/75=42'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[30, 35, 75, 90], Operations: [] Exploring Operation: 90-75=15, Resulting Numbers: [30, 35, 15] Generated Node #0,0: 12:[30, 35, 15] Operation: 90-75=15 Exploring Operation: 90/30=3, Resulting Numbers: [35, 75, 3] Generated Node #0,1: 12:[35, 75, 3] Operation: 90/30=3 Exploring Operation: 75-35=40, Resulting Numbers: [30, 90, 40] Generated Node #0,2: 12:[30, 90, 40] Operation: 75-35=40 Exploring Operation: 90-35=55, Resulting Numbers: [30, 75, 55] Generated Node #0,3: 12:[30, 75, 55] Operation: 90-35=55 Exploring Operation: 75-30=45, Resulting Numbers: [35, 90, 45] Generated Node #0,4: 12:[35, 90, 45] Operation: 75-30=45 Moving to Node #0,0 Current State: 12:[30, 35, 15], Operations: ['90-75=15'] Exploring Operation: 30-15=15, Resulting Numbers: [35, 15] Generated Node #0,0,0: 12:[35, 15] Operation: 30-15=15 Exploring Operation: 35-30=5, Resulting Numbers: [15, 5] Generated Node #0,0,1: 12:[15, 5] Operation: 35-30=5 Exploring Operation: 30+35=65, Resulting Numbers: [15, 65] Generated Node #0,0,2: 12:[15, 65] Operation: 30+35=65 Exploring Operation: 35-15=20, Resulting Numbers: [30, 20] Generated Node #0,0,3: 12:[30, 20] Operation: 35-15=20 Exploring Operation: 30/15=2, Resulting Numbers: [35, 2] Generated Node #0,0,4: 12:[35, 2] Operation: 30/15=2 Moving to Node #0,1 Current State: 12:[35, 75, 3], Operations: ['90/30=3'] Exploring Operation: 75-35=40, Resulting Numbers: [3, 40] Generated Node #0,1,0: 12:[3, 40] Operation: 75-35=40 Exploring Operation: 75-3=72, Resulting Numbers: [35, 72] Generated Node #0,1,1: 12:[35, 72] Operation: 75-3=72 Exploring Operation: 75/3=25, Resulting Numbers: [35, 25] Generated Node #0,1,2: 12:[35, 25] Operation: 75/3=25 Exploring Operation: 35+3=38, Resulting Numbers: [75, 38] Generated Node #0,1,3: 12:[75, 38] Operation: 35+3=38 Exploring Operation: 35-3=32, Resulting Numbers: [75, 32] Generated Node #0,1,4: 12:[75, 32] Operation: 35-3=32 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[3, 40], Operations: ['90/30=3', '75-35=40'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,12 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 #0,1,2 Current State: 12:[35, 25], Operations: ['90/30=3', '75/3=25'] Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,12 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,12 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 #0,1,1 Current State: 12:[35, 72], Operations: ['90/30=3', '75-3=72'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 35+72=107, Resulting Numbers: [107] 107,12 unequal: No Solution Exploring Operation: 35*72=2520, Resulting Numbers: [2520] 2520,12 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 #0,1,4 Current State: 12:[75, 32], Operations: ['90/30=3', '35-3=32'] Exploring Operation: 75*32=2400, Resulting Numbers: [2400] 2400,12 unequal: No Solution Exploring Operation: 75+32=107, Resulting Numbers: [107] 107,12 unequal: No Solution Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,12 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 #0,1,3 Current State: 12:[75, 38], Operations: ['90/30=3', '35+3=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,12 unequal: No Solution Exploring Operation: 75*38=2850, Resulting Numbers: [2850] 2850,12 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: 12:[30, 90, 40], Operations: ['75-35=40'] Exploring Operation: 90/30=3, Resulting Numbers: [40, 3] Generated Node #0,2,0: 12:[40, 3] Operation: 90/30=3 Exploring Operation: 40-30=10, Resulting Numbers: [90, 10] Generated Node #0,2,1: 12:[90, 10] Operation: 40-30=10 Exploring Operation: 90-40=50, Resulting Numbers: [30, 50] Generated Node #0,2,2: 12:[30, 50] Operation: 90-40=50 Exploring Operation: 90-30=60, Resulting Numbers: [40, 60] Generated Node #0,2,3: 12:[40, 60] Operation: 90-30=60 Exploring Operation: 30+90=120, Resulting Numbers: [40, 120] Generated Node #0,2,4: 12:[40, 120] Operation: 30+90=120 Moving to Node #0,3 Current State: 12:[30, 75, 55], Operations: ['90-35=55'] Exploring Operation: 75-30=45, Resulting Numbers: [55, 45] Generated Node #0,3,0: 12:[55, 45] Operation: 75-30=45 Exploring Operation: 75-55=20, Resulting Numbers: [30, 20] Generated Node #0,3,1: 12:[30, 20] Operation: 75-55=20 Exploring Operation: 30+55=85, Resulting Numbers: [75, 85] Generated Node #0,3,2: 12:[75, 85] Operation: 30+55=85 Exploring Operation: 30+75=105, Resulting Numbers: [55, 105] Generated Node #0,3,3: 12:[55, 105] Operation: 30+75=105 Exploring Operation: 55-30=25, Resulting Numbers: [75, 25] Generated Node #0,3,4: 12:[75, 25] Operation: 55-30=25 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 12:[30, 20], Operations: ['90-35=55', '75-55=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,12 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[55, 45], Operations: ['90-35=55', '75-30=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,12 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 12:[75, 25], Operations: ['90-35=55', '55-30=25'] Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 75+25=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 75*25=1875, Resulting Numbers: [1875] 1875,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 12:[75, 85], Operations: ['90-35=55', '30+55=85'] Exploring Operation: 75*85=6375, Resulting Numbers: [6375] 6375,12 unequal: No Solution Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 75+85=160, Resulting Numbers: [160] 160,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 12:[55, 105], Operations: ['90-35=55', '30+75=105'] Exploring Operation: 55*105=5775, Resulting Numbers: [5775] 5775,12 unequal: No Solution Exploring Operation: 105-55=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 55+105=160, Resulting Numbers: [160] 160,12 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: 12:[35, 90, 45], Operations: ['75-30=45'] Exploring Operation: 35+90=125, Resulting Numbers: [45, 125] Generated Node #0,4,0: 12:[45, 125] Operation: 35+90=125 Exploring Operation: 90/45=2, Resulting Numbers: [35, 2] Generated Node #0,4,1: 12:[35, 2] Operation: 90/45=2 Exploring Operation: 90-35=55, Resulting Numbers: [45, 55] Generated Node #0,4,2: 12:[45, 55] Operation: 90-35=55 Exploring Operation: 90-45=45, Resulting Numbers: [35, 45] Generated Node #0,4,3: 12:[35, 45] Operation: 90-45=45 Exploring Operation: 45-35=10, Resulting Numbers: [90, 10] Generated Node #0,4,4: 12:[90, 10] Operation: 45-35=10 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 12:[35, 2], Operations: ['75-30=45', '90/45=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,12 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 12:[35, 45], Operations: ['75-30=45', '90-45=45'] Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 12:[45, 55], Operations: ['75-30=45', '90-35=55'] Exploring Operation: 45+55=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 45*55=2475, Resulting Numbers: [2475] 2475,12 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 12:[90, 10], Operations: ['75-30=45', '45-35=10'] Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,12 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 12:[45, 125], Operations: ['75-30=45', '35+90=125'] Exploring Operation: 125-45=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 45*125=5625, Resulting Numbers: [5625] 5625,12 unequal: No Solution Exploring Operation: 45+125=170, Resulting Numbers: [170] 170,12 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: 12:[15, 5], Operations: ['90-75=15', '35-30=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,12 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,12 unequal: No Solution Moving to Node #0,0,4 Current State: 12:[35, 2], Operations: ['90-75=15', '30/15=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,12 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[35, 15], Operations: ['90-75=15', '30-15=15'] Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[30, 20], Operations: ['90-75=15', '35-15=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,12 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[40, 3], Operations: ['75-35=40', '90/30=3'] Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[30, 50], Operations: ['75-35=40', '90-40=50'] Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[15, 65], Operations: ['90-75=15', '30+35=65'] Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,12 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[40, 60], Operations: ['75-35=40', '90-30=60'] Exploring Operation: 40+60=100, Resulting Numbers: [100] 100,12 unequal: No Solution Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 40*60=2400, Resulting Numbers: [2400] 2400,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[90, 10], Operations: ['75-35=40', '40-30=10'] Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,12 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[40, 120], Operations: ['75-35=40', '30+90=120'] Exploring Operation: 120/40=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 40+120=160, Resulting Numbers: [160] 160,12 unequal: No Solution Exploring Operation: 120-40=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 40*120=4800, Resulting Numbers: [4800] 4800,12 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 49, 74, 77, 79 ]
99
[ "79-77=2", "74*2=148", "148-49=99" ]
Current State: 99:[49, 74, 77, 79], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [49, 74, 2] Generated Node #2: [49, 74, 2] from Operation: 79-77=2 Current State: 99:[49, 74, 2], Operations: ['79-77=2'] Exploring Operation: 74*2=148, Resulting Numbers: [49, 148] Generated Node #3: [49, 148] from Operation: 74*2=148 Current State: 99:[49, 148], Operations: ['79-77=2', '74*2=148'] Exploring Operation: 148-49=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[49, 74, 77, 79], Operations: [] Exploring Operation: 77-74=3, Resulting Numbers: [49, 79, 3] Generated Node #0,0: 99:[49, 79, 3] Operation: 77-74=3 Moving to Node #0,0 Current State: 99:[49, 79, 3], Operations: ['77-74=3'] Exploring Operation: 79-49=30, Resulting Numbers: [3, 30] Generated Node #0,0,0: 99:[3, 30] Operation: 79-49=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[3, 30], Operations: ['77-74=3', '79-49=30'] Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,99 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
[ 42, 14, 11, 57 ]
90
[ "42/14=3", "11*3=33", "57+33=90" ]
Current State: 90:[42, 14, 11, 57], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [11, 57, 3] Generated Node #2: [11, 57, 3] from Operation: 42/14=3 Current State: 90:[11, 57, 3], Operations: ['42/14=3'] Exploring Operation: 11*3=33, Resulting Numbers: [57, 33] Generated Node #3: [57, 33] from Operation: 11*3=33 Current State: 90:[57, 33], Operations: ['42/14=3', '11*3=33'] Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[42, 14, 11, 57], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [14, 11, 15] Generated Node #0,0: 90:[14, 11, 15] Operation: 57-42=15 Exploring Operation: 57-11=46, Resulting Numbers: [42, 14, 46] Generated Node #0,1: 90:[42, 14, 46] Operation: 57-11=46 Exploring Operation: 57-14=43, Resulting Numbers: [42, 11, 43] Generated Node #0,2: 90:[42, 11, 43] Operation: 57-14=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[14, 11, 15], Operations: ['57-42=15'] Exploring Operation: 14+15=29, Resulting Numbers: [11, 29] Generated Node #0,0,0: 90:[11, 29] Operation: 14+15=29 Exploring Operation: 14-11=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 90:[15, 3] Operation: 14-11=3 Exploring Operation: 15-14=1, Resulting Numbers: [11, 1] Generated Node #0,0,2: 90:[11, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[15, 3], Operations: ['57-42=15', '14-11=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,90 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:[11, 29], Operations: ['57-42=15', '14+15=29'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 11*29=319, Resulting Numbers: [319] 319,90 unequal: No Solution Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,90 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 #0,0,2 Current State: 90:[11, 1], Operations: ['57-42=15', '15-14=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[42, 14, 46], Operations: ['57-11=46'] Exploring Operation: 46-42=4, Resulting Numbers: [14, 4] Generated Node #0,1,0: 90:[14, 4] Operation: 46-42=4 Exploring Operation: 42/14=3, Resulting Numbers: [46, 3] Generated Node #0,1,1: 90:[46, 3] Operation: 42/14=3 Exploring Operation: 42-14=28, Resulting Numbers: [46, 28] Generated Node #0,1,2: 90:[46, 28] Operation: 42-14=28 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[46, 3], Operations: ['57-11=46', '42/14=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,90 unequal: No Solution Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,90 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:[14, 4], Operations: ['57-11=46', '46-42=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,90 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 #0,1,2 Current State: 90:[46, 28], Operations: ['57-11=46', '42-14=28'] Exploring Operation: 46*28=1288, Resulting Numbers: [1288] 1288,90 unequal: No Solution Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,90 unequal: No Solution Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,90 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:[42, 11, 43], Operations: ['57-14=43'] Exploring Operation: 42-11=31, Resulting Numbers: [43, 31] Generated Node #0,2,0: 90:[43, 31] Operation: 42-11=31 Exploring Operation: 43-11=32, Resulting Numbers: [42, 32] Generated Node #0,2,1: 90:[42, 32] Operation: 43-11=32 Exploring Operation: 43-42=1, Resulting Numbers: [11, 1] Generated Node #0,2,2: 90:[11, 1] Operation: 43-42=1 Moving to Node #0,2,2 Current State: 90:[11, 1], Operations: ['57-14=43', '43-42=1'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[43, 31], Operations: ['57-14=43', '42-11=31'] Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 43*31=1333, Resulting Numbers: [1333] 1333,90 unequal: No Solution Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[42, 32], Operations: ['57-14=43', '43-11=32'] Exploring Operation: 42*32=1344, Resulting Numbers: [1344] 1344,90 unequal: No Solution Exploring Operation: 42-32=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 42+32=74, Resulting Numbers: [74] 74,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 54, 84, 32, 6 ]
72
[ "54+32=86", "84/6=14", "86-14=72" ]
Current State: 72:[54, 84, 32, 6], Operations: [] Exploring Operation: 54+32=86, Resulting Numbers: [84, 6, 86] Generated Node #2: [84, 6, 86] from Operation: 54+32=86 Current State: 72:[84, 6, 86], Operations: ['54+32=86'] Exploring Operation: 84/6=14, Resulting Numbers: [86, 14] Generated Node #3: [86, 14] from Operation: 84/6=14 Current State: 72:[86, 14], Operations: ['54+32=86', '84/6=14'] Exploring Operation: 86-14=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[54, 84, 32, 6], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [84, 32, 9] Generated Node #0,0: 72:[84, 32, 9] Operation: 54/6=9 Exploring Operation: 84-54=30, Resulting Numbers: [32, 6, 30] Generated Node #0,1: 72:[32, 6, 30] Operation: 84-54=30 Exploring Operation: 84/6=14, Resulting Numbers: [54, 32, 14] Generated Node #0,2: 72:[54, 32, 14] Operation: 84/6=14 Exploring Operation: 54-32=22, Resulting Numbers: [84, 6, 22] Generated Node #0,3: 72:[84, 6, 22] Operation: 54-32=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[32, 6, 30], Operations: ['84-54=30'] Exploring Operation: 6+30=36, Resulting Numbers: [32, 36] Generated Node #0,1,0: 72:[32, 36] Operation: 6+30=36 Exploring Operation: 30/6=5, Resulting Numbers: [32, 5] Generated Node #0,1,1: 72:[32, 5] Operation: 30/6=5 Exploring Operation: 32-30=2, Resulting Numbers: [6, 2] Generated Node #0,1,2: 72:[6, 2] Operation: 32-30=2 Exploring Operation: 30-6=24, Resulting Numbers: [32, 24] Generated Node #0,1,3: 72:[32, 24] Operation: 30-6=24 Moving to Node #0,1,2 Current State: 72:[6, 2], Operations: ['84-54=30', '32-30=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[32, 24], Operations: ['84-54=30', '30-6=24'] Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[32, 36], Operations: ['84-54=30', '6+30=36'] Exploring Operation: 32+36=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 32*36=1152, Resulting Numbers: [1152] 1152,72 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[32, 5], Operations: ['84-54=30', '30/6=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,72 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,72 unequal: No Solution No 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: 72:[84, 6, 22], Operations: ['54-32=22'] Exploring Operation: 84-22=62, Resulting Numbers: [6, 62] Generated Node #0,3,0: 72:[6, 62] Operation: 84-22=62 Exploring Operation: 84/6=14, Resulting Numbers: [22, 14] Generated Node #0,3,1: 72:[22, 14] Operation: 84/6=14 Exploring Operation: 84-6=78, Resulting Numbers: [22, 78] Generated Node #0,3,2: 72:[22, 78] Operation: 84-6=78 Exploring Operation: 22-6=16, Resulting Numbers: [84, 16] Generated Node #0,3,3: 72:[84, 16] Operation: 22-6=16 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[22, 14], Operations: ['54-32=22', '84/6=14'] Exploring Operation: 22*14=308, Resulting Numbers: [308] 308,72 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,72 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 #0,3,2 Current State: 72:[22, 78], Operations: ['54-32=22', '84-6=78'] Exploring Operation: 22*78=1716, Resulting Numbers: [1716] 1716,72 unequal: No Solution Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,72 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 #0,3,0 Current State: 72:[6, 62], Operations: ['54-32=22', '84-22=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,72 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,72 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 #0,3,3 Current State: 72:[84, 16], Operations: ['54-32=22', '22-6=16'] Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,72 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,72 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:[84, 32, 9], Operations: ['54/6=9'] Exploring Operation: 84-9=75, Resulting Numbers: [32, 75] Generated Node #0,0,0: 72:[32, 75] Operation: 84-9=75 Exploring Operation: 84-32=52, Resulting Numbers: [9, 52] Generated Node #0,0,1: 72:[9, 52] Operation: 84-32=52 Exploring Operation: 32-9=23, Resulting Numbers: [84, 23] Generated Node #0,0,2: 72:[84, 23] Operation: 32-9=23 Exploring Operation: 32+9=41, Resulting Numbers: [84, 41] Generated Node #0,0,3: 72:[84, 41] Operation: 32+9=41 Moving to Node #0,0,0 Current State: 72:[32, 75], Operations: ['54/6=9', '84-9=75'] Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 32+75=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 32*75=2400, Resulting Numbers: [2400] 2400,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[84, 23], Operations: ['54/6=9', '32-9=23'] Exploring Operation: 84*23=1932, Resulting Numbers: [1932] 1932,72 unequal: No Solution Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,72 unequal: No Solution Exploring Operation: 84+23=107, Resulting Numbers: [107] 107,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[9, 52], Operations: ['54/6=9', '84-32=52'] Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,72 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[84, 41], Operations: ['54/6=9', '32+9=41'] Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,72 unequal: No Solution Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,72 unequal: No Solution No 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: 72:[54, 32, 14], Operations: ['84/6=14'] Exploring Operation: 54-14=40, Resulting Numbers: [32, 40] Generated Node #0,2,0: 72:[32, 40] Operation: 54-14=40 Exploring Operation: 54-32=22, Resulting Numbers: [14, 22] Generated Node #0,2,1: 72:[14, 22] Operation: 54-32=22 Exploring Operation: 54+14=68, Resulting Numbers: [32, 68] Generated Node #0,2,2: 72:[32, 68] Operation: 54+14=68 Exploring Operation: 54+32=86, Resulting Numbers: [14, 86] Generated Node #0,2,3: 72:[14, 86] Operation: 54+32=86 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[14, 22], Operations: ['84/6=14', '54-32=22'] Exploring Operation: 14+22=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 14*22=308, Resulting Numbers: [308] 308,72 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 #0,2,0 Current State: 72:[32, 40], Operations: ['84/6=14', '54-14=40'] Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,72 unequal: No Solution Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[54, 84, 32, 6], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [54, 32, 14] Generated Node #0,2: 72:[54, 32, 14] Operation: 84/6=14 Moving to Node #0,2 Current State: 72:[54, 32, 14], Operations: ['84/6=14'] Exploring Operation: 54-14=40, Resulting Numbers: [32, 40] Generated Node #0,2,0: 72:[32, 40] Operation: 54-14=40 Moving to Node #0,2,0 Current State: 72:[32, 40], Operations: ['84/6=14', '54-14=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.94184
hs_4
mult_heuristic
[ 43, 22, 24, 1 ]
26
[ "43+1=44", "44/22=2", "24+2=26" ]
Current State: 26:[43, 22, 24, 1], Operations: [] Exploring Operation: 43+1=44, Resulting Numbers: [22, 24, 44] Generated Node #2: [22, 24, 44] from Operation: 43+1=44 Current State: 26:[22, 24, 44], Operations: ['43+1=44'] Exploring Operation: 44/22=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 44/22=2 Current State: 26:[24, 2], Operations: ['43+1=44', '44/22=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[43, 22, 24, 1], Operations: [] Exploring Operation: 43-24=19, Resulting Numbers: [22, 1, 19] Generated Node #0,0: 26:[22, 1, 19] Operation: 43-24=19 Exploring Operation: 43-22=21, Resulting Numbers: [24, 1, 21] Generated Node #0,1: 26:[24, 1, 21] Operation: 43-22=21 Moving to Node #0,1 Current State: 26:[24, 1, 21], Operations: ['43-22=21'] Exploring Operation: 24+1=25, Resulting Numbers: [21, 25] Generated Node #0,1,0: 26:[21, 25] Operation: 24+1=25 Exploring Operation: 24-21=3, Resulting Numbers: [1, 3] Generated Node #0,1,1: 26:[1, 3] Operation: 24-21=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[1, 3], Operations: ['43-22=21', '24-21=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[21, 25], Operations: ['43-22=21', '24+1=25'] Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,26 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: 26:[22, 1, 19], Operations: ['43-24=19'] Exploring Operation: 22-19=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 26:[1, 3] Operation: 22-19=3 Exploring Operation: 22+1=23, Resulting Numbers: [19, 23] Generated Node #0,0,1: 26:[19, 23] Operation: 22+1=23 Moving to Node #0,0,0 Current State: 26:[1, 3], Operations: ['43-24=19', '22-19=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[19, 23], Operations: ['43-24=19', '22+1=23'] Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,26 unequal: No Solution Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,26 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 27, 54, 47, 3 ]
37
[ "27+54=81", "47-3=44", "81-44=37" ]
Current State: 37:[27, 54, 47, 3], Operations: [] Exploring Operation: 27+54=81, Resulting Numbers: [47, 3, 81] Generated Node #2: [47, 3, 81] from Operation: 27+54=81 Current State: 37:[47, 3, 81], Operations: ['27+54=81'] Exploring Operation: 47-3=44, Resulting Numbers: [81, 44] Generated Node #3: [81, 44] from Operation: 47-3=44 Current State: 37:[81, 44], Operations: ['27+54=81', '47-3=44'] Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[27, 54, 47, 3], Operations: [] Exploring Operation: 54-3=51, Resulting Numbers: [27, 47, 51] Generated Node #0,0: 37:[27, 47, 51] Operation: 54-3=51 Exploring Operation: 27+3=30, Resulting Numbers: [54, 47, 30] Generated Node #0,1: 37:[54, 47, 30] Operation: 27+3=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[27, 47, 51], Operations: ['54-3=51'] Exploring Operation: 51-27=24, Resulting Numbers: [47, 24] Generated Node #0,0,0: 37:[47, 24] Operation: 51-27=24 Exploring Operation: 47-27=20, Resulting Numbers: [51, 20] Generated Node #0,0,1: 37:[51, 20] Operation: 47-27=20 Moving to Node #0,0,0 Current State: 37:[47, 24], Operations: ['54-3=51', '51-27=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[51, 20], Operations: ['54-3=51', '47-27=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,37 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[54, 47, 30], Operations: ['27+3=30'] Exploring Operation: 54-30=24, Resulting Numbers: [47, 24] Generated Node #0,1,0: 37:[47, 24] Operation: 54-30=24 Exploring Operation: 54-47=7, Resulting Numbers: [30, 7] Generated Node #0,1,1: 37:[30, 7] Operation: 54-47=7 Moving to Node #0,1,0 Current State: 37:[47, 24], Operations: ['27+3=30', '54-30=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[30, 7], Operations: ['27+3=30', '54-47=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[27, 54, 47, 3], Operations: [] Exploring Operation: 27+3=30, Resulting Numbers: [54, 47, 30] Generated Node #0,1: 37:[54, 47, 30] Operation: 27+3=30 Moving to Node #0,1 Current State: 37:[54, 47, 30], Operations: ['27+3=30'] Exploring Operation: 54-47=7, Resulting Numbers: [30, 7] Generated Node #0,1,1: 37:[30, 7] Operation: 54-47=7 Moving to Node #0,1,1 Current State: 37:[30, 7], Operations: ['27+3=30', '54-47=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 71, 28, 54, 30 ]
67
[ "71-28=43", "54-30=24", "43+24=67" ]
Current State: 67:[71, 28, 54, 30], Operations: [] Exploring Operation: 71-28=43, Resulting Numbers: [54, 30, 43] Generated Node #2: [54, 30, 43] from Operation: 71-28=43 Current State: 67:[54, 30, 43], Operations: ['71-28=43'] Exploring Operation: 54-30=24, Resulting Numbers: [43, 24] Generated Node #3: [43, 24] from Operation: 54-30=24 Current State: 67:[43, 24], Operations: ['71-28=43', '54-30=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[71, 28, 54, 30], Operations: [] Exploring Operation: 28+30=58, Resulting Numbers: [71, 54, 58] Generated Node #0,0: 67:[71, 54, 58] Operation: 28+30=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[71, 54, 58], Operations: ['28+30=58'] Exploring Operation: 54+58=112, Resulting Numbers: [71, 112] Generated Node #0,0,0: 67:[71, 112] Operation: 54+58=112 Moving to Node #0,0,0 Current State: 67:[71, 112], Operations: ['28+30=58', '54+58=112'] Exploring Operation: 112-71=41, Resulting Numbers: [41] 41,67 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
[ 20, 39, 54, 27 ]
86
[ "20+39=59", "54-27=27", "59+27=86" ]
Current State: 86:[20, 39, 54, 27], Operations: [] Exploring Operation: 20+39=59, Resulting Numbers: [54, 27, 59] Generated Node #2: [54, 27, 59] from Operation: 20+39=59 Current State: 86:[54, 27, 59], Operations: ['20+39=59'] Exploring Operation: 54-27=27, Resulting Numbers: [59, 27] Generated Node #3: [59, 27] from Operation: 54-27=27 Current State: 86:[59, 27], Operations: ['20+39=59', '54-27=27'] Exploring Operation: 59+27=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[20, 39, 54, 27], Operations: [] Exploring Operation: 20+27=47, Resulting Numbers: [39, 54, 47] Generated Node #0,0: 86:[39, 54, 47] Operation: 20+27=47 Moving to Node #0,0 Current State: 86:[39, 54, 47], Operations: ['20+27=47'] Exploring Operation: 54-47=7, Resulting Numbers: [39, 7] Generated Node #0,0,0: 86:[39, 7] Operation: 54-47=7 Moving to Node #0,0,0 Current State: 86:[39, 7], Operations: ['20+27=47', '54-47=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,86 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 74, 72, 5, 20 ]
45
[ "74-72=2", "20*2=40", "5+40=45" ]
Current State: 45:[74, 72, 5, 20], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [5, 20, 2] Generated Node #2: [5, 20, 2] from Operation: 74-72=2 Current State: 45:[5, 20, 2], Operations: ['74-72=2'] Exploring Operation: 20*2=40, Resulting Numbers: [5, 40] Generated Node #3: [5, 40] from Operation: 20*2=40 Current State: 45:[5, 40], Operations: ['74-72=2', '20*2=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[74, 72, 5, 20], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [5, 20, 2] Generated Node #0,0: 45:[5, 20, 2] Operation: 74-72=2 Exploring Operation: 74-20=54, Resulting Numbers: [72, 5, 54] Generated Node #0,1: 45:[72, 5, 54] Operation: 74-20=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[5, 20, 2], Operations: ['74-72=2'] Exploring Operation: 20/2=10, Resulting Numbers: [5, 10] Generated Node #0,0,0: 45:[5, 10] Operation: 20/2=10 Exploring Operation: 20-5=15, Resulting Numbers: [2, 15] Generated Node #0,0,1: 45:[2, 15] Operation: 20-5=15 Moving to Node #0,0,0 Current State: 45:[5, 10], Operations: ['74-72=2', '20/2=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[2, 15], Operations: ['74-72=2', '20-5=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,45 unequal: No Solution No 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:[72, 5, 54], Operations: ['74-20=54'] Exploring Operation: 72-5=67, Resulting Numbers: [54, 67] Generated Node #0,1,0: 45:[54, 67] Operation: 72-5=67 Exploring Operation: 72-54=18, Resulting Numbers: [5, 18] Generated Node #0,1,1: 45:[5, 18] Operation: 72-54=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[5, 18], Operations: ['74-20=54', '72-54=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,45 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 #0,1,0 Current State: 45:[54, 67], Operations: ['74-20=54', '72-5=67'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 54+67=121, Resulting Numbers: [121] 121,45 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 No solution found.
0
hs_2
mult_heuristic
[ 2, 88, 21, 14 ]
32
[ "2*21=42", "88-14=74", "74-42=32" ]
Current State: 32:[2, 88, 21, 14], Operations: [] Exploring Operation: 2*21=42, Resulting Numbers: [88, 14, 42] Generated Node #2: [88, 14, 42] from Operation: 2*21=42 Current State: 32:[88, 14, 42], Operations: ['2*21=42'] Exploring Operation: 88-14=74, Resulting Numbers: [42, 74] Generated Node #3: [42, 74] from Operation: 88-14=74 Current State: 32:[42, 74], Operations: ['2*21=42', '88-14=74'] Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[2, 88, 21, 14], Operations: [] Exploring Operation: 88-14=74, Resulting Numbers: [2, 21, 74] Generated Node #0,0: 32:[2, 21, 74] Operation: 88-14=74 Exploring Operation: 21+14=35, Resulting Numbers: [2, 88, 35] Generated Node #0,1: 32:[2, 88, 35] Operation: 21+14=35 Exploring Operation: 21-14=7, Resulting Numbers: [2, 88, 7] Generated Node #0,2: 32:[2, 88, 7] Operation: 21-14=7 Exploring Operation: 88/2=44, Resulting Numbers: [21, 14, 44] Generated Node #0,3: 32:[21, 14, 44] Operation: 88/2=44 Exploring Operation: 88-21=67, Resulting Numbers: [2, 14, 67] Generated Node #0,4: 32:[2, 14, 67] Operation: 88-21=67 Moving to Node #0,3 Current State: 32:[21, 14, 44], Operations: ['88/2=44'] Exploring Operation: 21-14=7, Resulting Numbers: [44, 7] Generated Node #0,3,0: 32:[44, 7] Operation: 21-14=7 Exploring Operation: 21+14=35, Resulting Numbers: [44, 35] Generated Node #0,3,1: 32:[44, 35] Operation: 21+14=35 Exploring Operation: 14+44=58, Resulting Numbers: [21, 58] Generated Node #0,3,2: 32:[21, 58] Operation: 14+44=58 Exploring Operation: 44-14=30, Resulting Numbers: [21, 30] Generated Node #0,3,3: 32:[21, 30] Operation: 44-14=30 Exploring Operation: 44-21=23, Resulting Numbers: [14, 23] Generated Node #0,3,4: 32:[14, 23] Operation: 44-21=23 Moving to Node #0,4 Current State: 32:[2, 14, 67], Operations: ['88-21=67'] Exploring Operation: 2+14=16, Resulting Numbers: [67, 16] Generated Node #0,4,0: 32:[67, 16] Operation: 2+14=16 Exploring Operation: 67-14=53, Resulting Numbers: [2, 53] Generated Node #0,4,1: 32:[2, 53] Operation: 67-14=53 Exploring Operation: 14/2=7, Resulting Numbers: [67, 7] Generated Node #0,4,2: 32:[67, 7] Operation: 14/2=7 Exploring Operation: 2*14=28, Resulting Numbers: [67, 28] Generated Node #0,4,3: 32:[67, 28] Operation: 2*14=28 Exploring Operation: 67-2=65, Resulting Numbers: [14, 65] Generated Node #0,4,4: 32:[14, 65] Operation: 67-2=65 Moving to Node #0,0 Current State: 32:[2, 21, 74], Operations: ['88-14=74'] Exploring Operation: 2+21=23, Resulting Numbers: [74, 23] Generated Node #0,0,0: 32:[74, 23] Operation: 2+21=23 Exploring Operation: 21-2=19, Resulting Numbers: [74, 19] Generated Node #0,0,1: 32:[74, 19] Operation: 21-2=19 Exploring Operation: 74-2=72, Resulting Numbers: [21, 72] Generated Node #0,0,2: 32:[21, 72] Operation: 74-2=72 Exploring Operation: 74/2=37, Resulting Numbers: [21, 37] Generated Node #0,0,3: 32:[21, 37] Operation: 74/2=37 Exploring Operation: 74-21=53, Resulting Numbers: [2, 53] Generated Node #0,0,4: 32:[2, 53] Operation: 74-21=53 Moving to Node #0,2 Current State: 32:[2, 88, 7], Operations: ['21-14=7'] Exploring Operation: 7-2=5, Resulting Numbers: [88, 5] Generated Node #0,2,0: 32:[88, 5] Operation: 7-2=5 Exploring Operation: 88/2=44, Resulting Numbers: [7, 44] Generated Node #0,2,1: 32:[7, 44] Operation: 88/2=44 Exploring Operation: 88-7=81, Resulting Numbers: [2, 81] Generated Node #0,2,2: 32:[2, 81] Operation: 88-7=81 Exploring Operation: 2+7=9, Resulting Numbers: [88, 9] Generated Node #0,2,3: 32:[88, 9] Operation: 2+7=9 Exploring Operation: 88-2=86, Resulting Numbers: [7, 86] Generated Node #0,2,4: 32:[7, 86] Operation: 88-2=86 Moving to Node #0,1 Current State: 32:[2, 88, 35], Operations: ['21+14=35'] Exploring Operation: 2+88=90, Resulting Numbers: [35, 90] Generated Node #0,1,0: 32:[35, 90] Operation: 2+88=90 Exploring Operation: 35-2=33, Resulting Numbers: [88, 33] Generated Node #0,1,1: 32:[88, 33] Operation: 35-2=33 Exploring Operation: 88/2=44, Resulting Numbers: [35, 44] Generated Node #0,1,2: 32:[35, 44] Operation: 88/2=44 Exploring Operation: 88-35=53, Resulting Numbers: [2, 53] Generated Node #0,1,3: 32:[2, 53] Operation: 88-35=53 Exploring Operation: 88-2=86, Resulting Numbers: [35, 86] Generated Node #0,1,4: 32:[35, 86] Operation: 88-2=86 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[35, 44], Operations: ['21+14=35', '88/2=44'] Exploring Operation: 35+44=79, Resulting Numbers: [79] 79,32 unequal: No Solution Exploring Operation: 35*44=1540, Resulting Numbers: [1540] 1540,32 unequal: No Solution Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[2, 53], Operations: ['21+14=35', '88-35=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,32 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[88, 33], Operations: ['21+14=35', '35-2=33'] Exploring Operation: 88+33=121, Resulting Numbers: [121] 121,32 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 88*33=2904, Resulting Numbers: [2904] 2904,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 32:[35, 86], Operations: ['21+14=35', '88-2=86'] Exploring Operation: 35+86=121, Resulting Numbers: [121] 121,32 unequal: No Solution Exploring Operation: 35*86=3010, Resulting Numbers: [3010] 3010,32 unequal: No Solution Exploring Operation: 86-35=51, Resulting Numbers: [51] 51,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[35, 90], Operations: ['21+14=35', '2+88=90'] Exploring Operation: 90-35=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 35*90=3150, Resulting Numbers: [3150] 3150,32 unequal: No Solution Exploring Operation: 35+90=125, Resulting Numbers: [125] 125,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 32:[21, 30], Operations: ['88/2=44', '44-14=30'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,32 unequal: No Solution Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,3,4 Current State: 32:[14, 23], Operations: ['88/2=44', '44-21=23'] Exploring Operation: 14*23=322, Resulting Numbers: [322] 322,32 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 14+23=37, Resulting Numbers: [37] 37,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[21, 37], Operations: ['88-14=74', '74/2=37'] Exploring Operation: 21*37=777, Resulting Numbers: [777] 777,32 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[44, 7], Operations: ['88/2=44', '21-14=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,32 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[7, 44], Operations: ['21-14=7', '88/2=44'] Exploring Operation: 7+44=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 7*44=308, Resulting Numbers: [308] 308,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[44, 35], Operations: ['88/2=44', '21+14=35'] Exploring Operation: 44+35=79, Resulting Numbers: [79] 79,32 unequal: No Solution Exploring Operation: 44*35=1540, Resulting Numbers: [1540] 1540,32 unequal: No Solution Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,32 unequal: No Solution Moving to Node #0,4,1 Current State: 32:[2, 53], Operations: ['88-21=67', '67-14=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,32 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,32 unequal: No Solution Moving to Node #0,0,4 Current State: 32:[2, 53], Operations: ['88-14=74', '74-21=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,32 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[21, 58], Operations: ['88/2=44', '14+44=58'] Exploring Operation: 21+58=79, Resulting Numbers: [79] 79,32 unequal: No Solution Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 21*58=1218, Resulting Numbers: [1218] 1218,32 unequal: No Solution Moving to Node #0,4,0 Current State: 32:[67, 16], Operations: ['88-21=67', '2+14=16'] Exploring Operation: 67*16=1072, Resulting Numbers: [1072] 1072,32 unequal: No Solution Exploring Operation: 67+16=83, Resulting Numbers: [83] 83,32 unequal: No Solution Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,4,4 Current State: 32:[14, 65], Operations: ['88-21=67', '67-2=65'] Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,32 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,32 unequal: No Solution Moving to Node #0,4,2 Current State: 32:[67, 7], Operations: ['88-21=67', '14/2=7'] Exploring Operation: 67+7=74, Resulting Numbers: [74] 74,32 unequal: No Solution Exploring Operation: 67*7=469, Resulting Numbers: [469] 469,32 unequal: No Solution Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,32 unequal: No Solution Moving to Node #0,4,3 Current State: 32:[67, 28], Operations: ['88-21=67', '2*14=28'] Exploring Operation: 67*28=1876, Resulting Numbers: [1876] 1876,32 unequal: No Solution Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,32 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[21, 72], Operations: ['88-14=74', '74-2=72'] Exploring Operation: 21*72=1512, Resulting Numbers: [1512] 1512,32 unequal: No Solution Exploring Operation: 21+72=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[74, 19], Operations: ['88-14=74', '21-2=19'] Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,32 unequal: No Solution Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[74, 23], Operations: ['88-14=74', '2+21=23'] Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,32 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,32 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,2,2 Current State: 32:[2, 81], Operations: ['21-14=7', '88-7=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,32 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,32 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,32 unequal: No Solution Moving to Node #0,2,4 Current State: 32:[7, 86], Operations: ['21-14=7', '88-2=86'] Exploring Operation: 7*86=602, Resulting Numbers: [602] 602,32 unequal: No Solution Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,32 unequal: No Solution Exploring Operation: 7+86=93, Resulting Numbers: [93] 93,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[88, 9], Operations: ['21-14=7', '2+7=9'] Exploring Operation: 88+9=97, Resulting Numbers: [97] 97,32 unequal: No Solution Exploring Operation: 88*9=792, Resulting Numbers: [792] 792,32 unequal: No Solution Exploring Operation: 88-9=79, Resulting Numbers: [79] 79,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[88, 5], Operations: ['21-14=7', '7-2=5'] Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,32 unequal: No Solution Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,32 unequal: No Solution Exploring Operation: 88*5=440, Resulting Numbers: [440] 440,32 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 5, 14, 20 ]
53
[ "61-14=47", "5*20=100", "100-47=53" ]
Current State: 53:[61, 5, 14, 20], Operations: [] Exploring Operation: 61-14=47, Resulting Numbers: [5, 20, 47] Generated Node #2: [5, 20, 47] from Operation: 61-14=47 Current State: 53:[5, 20, 47], Operations: ['61-14=47'] Exploring Operation: 5*20=100, Resulting Numbers: [47, 100] Generated Node #3: [47, 100] from Operation: 5*20=100 Current State: 53:[47, 100], Operations: ['61-14=47', '5*20=100'] Exploring Operation: 100-47=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[61, 5, 14, 20], Operations: [] Exploring Operation: 61-5=56, Resulting Numbers: [14, 20, 56] Generated Node #0,0: 53:[14, 20, 56] Operation: 61-5=56 Exploring Operation: 5+14=19, Resulting Numbers: [61, 20, 19] Generated Node #0,1: 53:[61, 20, 19] Operation: 5+14=19 Exploring Operation: 5*14=70, Resulting Numbers: [61, 20, 70] Generated Node #0,2: 53:[61, 20, 70] Operation: 5*14=70 Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[61, 20, 70], Operations: ['5*14=70'] Exploring Operation: 70-20=50, Resulting Numbers: [61, 50] Generated Node #0,2,0: 53:[61, 50] Operation: 70-20=50 Exploring Operation: 61-20=41, Resulting Numbers: [70, 41] Generated Node #0,2,1: 53:[70, 41] Operation: 61-20=41 Exploring Operation: 61+20=81, Resulting Numbers: [70, 81] Generated Node #0,2,2: 53:[70, 81] Operation: 61+20=81 Moving to Node #0,2,0 Current State: 53:[61, 50], Operations: ['5*14=70', '70-20=50'] Exploring Operation: 61+50=111, Resulting Numbers: [111] 111,53 unequal: No Solution Exploring Operation: 61-50=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 61*50=3050, Resulting Numbers: [3050] 3050,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[70, 41], Operations: ['5*14=70', '61-20=41'] Exploring Operation: 70*41=2870, Resulting Numbers: [2870] 2870,53 unequal: No Solution Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,53 unequal: No Solution Exploring Operation: 70+41=111, Resulting Numbers: [111] 111,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[70, 81], Operations: ['5*14=70', '61+20=81'] Exploring Operation: 70*81=5670, Resulting Numbers: [5670] 5670,53 unequal: No Solution Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 70+81=151, Resulting Numbers: [151] 151,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[14, 20, 56], Operations: ['61-5=56'] Exploring Operation: 20-14=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 53:[56, 6] Operation: 20-14=6 Exploring Operation: 14+20=34, Resulting Numbers: [56, 34] Generated Node #0,0,1: 53:[56, 34] Operation: 14+20=34 Exploring Operation: 56-14=42, Resulting Numbers: [20, 42] Generated Node #0,0,2: 53:[20, 42] Operation: 56-14=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[56, 34], Operations: ['61-5=56', '14+20=34'] Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,53 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 56*34=1904, Resulting Numbers: [1904] 1904,53 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 #0,0,2 Current State: 53:[20, 42], Operations: ['61-5=56', '56-14=42'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 20*42=840, Resulting Numbers: [840] 840,53 unequal: No Solution Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,53 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:[56, 6], Operations: ['61-5=56', '20-14=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,53 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,53 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:[61, 20, 19], Operations: ['5+14=19'] Exploring Operation: 61-20=41, Resulting Numbers: [19, 41] Generated Node #0,1,0: 53:[19, 41] Operation: 61-20=41 Exploring Operation: 20+19=39, Resulting Numbers: [61, 39] Generated Node #0,1,1: 53:[61, 39] Operation: 20+19=39 Exploring Operation: 61-19=42, Resulting Numbers: [20, 42] Generated Node #0,1,2: 53:[20, 42] Operation: 61-19=42 Moving to Node #0,1,1 Current State: 53:[61, 39], Operations: ['5+14=19', '20+19=39'] Exploring Operation: 61+39=100, Resulting Numbers: [100] 100,53 unequal: No Solution Exploring Operation: 61*39=2379, Resulting Numbers: [2379] 2379,53 unequal: No Solution Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[20, 42], Operations: ['5+14=19', '61-19=42'] Exploring Operation: 20*42=840, Resulting Numbers: [840] 840,53 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[19, 41], Operations: ['5+14=19', '61-20=41'] Exploring Operation: 19*41=779, Resulting Numbers: [779] 779,53 unequal: No Solution Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 19+41=60, Resulting Numbers: [60] 60,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 31, 62, 85, 47 ]
19
[ "62/31=2", "85-47=38", "38/2=19" ]
Current State: 19:[31, 62, 85, 47], Operations: [] Exploring Operation: 62/31=2, Resulting Numbers: [85, 47, 2] Generated Node #2: [85, 47, 2] from Operation: 62/31=2 Current State: 19:[85, 47, 2], Operations: ['62/31=2'] Exploring Operation: 85-47=38, Resulting Numbers: [2, 38] Generated Node #3: [2, 38] from Operation: 85-47=38 Current State: 19:[2, 38], Operations: ['62/31=2', '85-47=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[31, 62, 85, 47], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [31, 47, 23] Generated Node #0,0: 19:[31, 47, 23] Operation: 85-62=23 Moving to Node #0,0 Current State: 19:[31, 47, 23], Operations: ['85-62=23'] Exploring Operation: 47-31=16, Resulting Numbers: [23, 16] Generated Node #0,0,0: 19:[23, 16] Operation: 47-31=16 Moving to Node #0,0,0 Current State: 19:[23, 16], Operations: ['85-62=23', '47-31=16'] Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,19 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 76, 18, 12, 91 ]
21
[ "76-18=58", "91-12=79", "79-58=21" ]
Current State: 21:[76, 18, 12, 91], Operations: [] Exploring Operation: 76-18=58, Resulting Numbers: [12, 91, 58] Generated Node #2: [12, 91, 58] from Operation: 76-18=58 Current State: 21:[12, 91, 58], Operations: ['76-18=58'] Exploring Operation: 91-12=79, Resulting Numbers: [58, 79] Generated Node #3: [58, 79] from Operation: 91-12=79 Current State: 21:[58, 79], Operations: ['76-18=58', '91-12=79'] Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[76, 18, 12, 91], Operations: [] Exploring Operation: 91-76=15, Resulting Numbers: [18, 12, 15] Generated Node #0,0: 21:[18, 12, 15] Operation: 91-76=15 Moving to Node #0,0 Current State: 21:[18, 12, 15], Operations: ['91-76=15'] Exploring Operation: 15-12=3, Resulting Numbers: [18, 3] Generated Node #0,0,0: 21:[18, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 21:[18, 3], Operations: ['91-76=15', '15-12=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[76, 18, 12, 91], Operations: [] Exploring Operation: 91-76=15, Resulting Numbers: [18, 12, 15] Generated Node #0,0: 21:[18, 12, 15] Operation: 91-76=15 Moving to Node #0,0 Current State: 21:[18, 12, 15], Operations: ['91-76=15'] Exploring Operation: 15-12=3, Resulting Numbers: [18, 3] Generated Node #0,0,0: 21:[18, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 21:[18, 3], Operations: ['91-76=15', '15-12=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 10, 53, 91, 30 ]
41
[ "30/10=3", "91-53=38", "3+38=41" ]
Current State: 41:[10, 53, 91, 30], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [53, 91, 3] Generated Node #2: [53, 91, 3] from Operation: 30/10=3 Current State: 41:[53, 91, 3], Operations: ['30/10=3'] Exploring Operation: 91-53=38, Resulting Numbers: [3, 38] Generated Node #3: [3, 38] from Operation: 91-53=38 Current State: 41:[3, 38], Operations: ['30/10=3', '91-53=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[10, 53, 91, 30], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [91, 30, 43] Generated Node #0,0: 41:[91, 30, 43] Operation: 53-10=43 Exploring Operation: 91-53=38, Resulting Numbers: [10, 30, 38] Generated Node #0,1: 41:[10, 30, 38] Operation: 91-53=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[10, 30, 38], Operations: ['91-53=38'] Exploring Operation: 10+30=40, Resulting Numbers: [38, 40] Generated Node #0,1,0: 41:[38, 40] Operation: 10+30=40 Exploring Operation: 10+38=48, Resulting Numbers: [30, 48] Generated Node #0,1,1: 41:[30, 48] Operation: 10+38=48 Moving to Node #0,1,0 Current State: 41:[38, 40], Operations: ['91-53=38', '10+30=40'] Exploring Operation: 38+40=78, Resulting Numbers: [78] 78,41 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[30, 48], Operations: ['91-53=38', '10+38=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[91, 30, 43], Operations: ['53-10=43'] Exploring Operation: 91-43=48, Resulting Numbers: [30, 48] Generated Node #0,0,0: 41:[30, 48] Operation: 91-43=48 Exploring Operation: 91-30=61, Resulting Numbers: [43, 61] Generated Node #0,0,1: 41:[43, 61] Operation: 91-30=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[30, 48], Operations: ['53-10=43', '91-43=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[43, 61], Operations: ['53-10=43', '91-30=61'] Exploring Operation: 61-43=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 43+61=104, Resulting Numbers: [104] 104,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 17, 33, 71, 34 ]
36
[ "34/17=2", "71-33=38", "38-2=36" ]
Current State: 36:[17, 33, 71, 34], Operations: [] Exploring Operation: 34/17=2, Resulting Numbers: [33, 71, 2] Generated Node #2: [33, 71, 2] from Operation: 34/17=2 Current State: 36:[33, 71, 2], Operations: ['34/17=2'] Exploring Operation: 71-33=38, Resulting Numbers: [2, 38] Generated Node #3: [2, 38] from Operation: 71-33=38 Current State: 36:[2, 38], Operations: ['34/17=2', '71-33=38'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[17, 33, 71, 34], Operations: [] Exploring Operation: 71-33=38, Resulting Numbers: [17, 34, 38] Generated Node #0,0: 36:[17, 34, 38] Operation: 71-33=38 Moving to Node #0,0 Current State: 36:[17, 34, 38], Operations: ['71-33=38'] Exploring Operation: 38-34=4, Resulting Numbers: [17, 4] Generated Node #0,0,0: 36:[17, 4] Operation: 38-34=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[17, 4], Operations: ['71-33=38', '38-34=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 56, 48, 26, 16 ]
39
[ "56+16=72", "26*72=1872", "1872/48=39" ]
Current State: 39:[56, 48, 26, 16], Operations: [] Exploring Operation: 56+16=72, Resulting Numbers: [48, 26, 72] Generated Node #2: [48, 26, 72] from Operation: 56+16=72 Current State: 39:[48, 26, 72], Operations: ['56+16=72'] Exploring Operation: 26*72=1872, Resulting Numbers: [48, 1872] Generated Node #3: [48, 1872] from Operation: 26*72=1872 Current State: 39:[48, 1872], Operations: ['56+16=72', '26*72=1872'] Exploring Operation: 1872/48=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[56, 48, 26, 16], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [56, 16, 22] Generated Node #0,0: 39:[56, 16, 22] Operation: 48-26=22 Exploring Operation: 56-48=8, Resulting Numbers: [26, 16, 8] Generated Node #0,1: 39:[26, 16, 8] Operation: 56-48=8 Exploring Operation: 26+16=42, Resulting Numbers: [56, 48, 42] Generated Node #0,2: 39:[56, 48, 42] Operation: 26+16=42 Exploring Operation: 56-26=30, Resulting Numbers: [48, 16, 30] Generated Node #0,3: 39:[48, 16, 30] Operation: 56-26=30 Exploring Operation: 56-16=40, Resulting Numbers: [48, 26, 40] Generated Node #0,4: 39:[48, 26, 40] Operation: 56-16=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[26, 16, 8], Operations: ['56-48=8'] Exploring Operation: 26+8=34, Resulting Numbers: [16, 34] Generated Node #0,1,0: 39:[16, 34] Operation: 26+8=34 Exploring Operation: 26+16=42, Resulting Numbers: [8, 42] Generated Node #0,1,1: 39:[8, 42] Operation: 26+16=42 Exploring Operation: 26-16=10, Resulting Numbers: [8, 10] Generated Node #0,1,2: 39:[8, 10] Operation: 26-16=10 Exploring Operation: 26-8=18, Resulting Numbers: [16, 18] Generated Node #0,1,3: 39:[16, 18] Operation: 26-8=18 Exploring Operation: 16/8=2, Resulting Numbers: [26, 2] Generated Node #0,1,4: 39:[26, 2] Operation: 16/8=2 Moving to Node #0,1,0 Current State: 39:[16, 34], Operations: ['56-48=8', '26+8=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,39 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[8, 10], Operations: ['56-48=8', '26-16=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[8, 42], Operations: ['56-48=8', '26+16=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[16, 18], Operations: ['56-48=8', '26-8=18'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,39 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,39 unequal: No Solution Moving to Node #0,1,4 Current State: 39:[26, 2], Operations: ['56-48=8', '16/8=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,39 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 Current State: 39:[48, 16, 30], Operations: ['56-26=30'] Exploring Operation: 48-16=32, Resulting Numbers: [30, 32] Generated Node #0,3,0: 39:[30, 32] Operation: 48-16=32 Exploring Operation: 16+30=46, Resulting Numbers: [48, 46] Generated Node #0,3,1: 39:[48, 46] Operation: 16+30=46 Exploring Operation: 48-30=18, Resulting Numbers: [16, 18] Generated Node #0,3,2: 39:[16, 18] Operation: 48-30=18 Exploring Operation: 48/16=3, Resulting Numbers: [30, 3] Generated Node #0,3,3: 39:[30, 3] Operation: 48/16=3 Exploring Operation: 30-16=14, Resulting Numbers: [48, 14] Generated Node #0,3,4: 39:[48, 14] Operation: 30-16=14 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 39:[16, 18], Operations: ['56-26=30', '48-30=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,39 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 39:[30, 3], Operations: ['56-26=30', '48/16=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,39 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 39:[48, 14], Operations: ['56-26=30', '30-16=14'] Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,39 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 39:[30, 32], Operations: ['56-26=30', '48-16=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,39 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 39:[48, 46], Operations: ['56-26=30', '16+30=46'] Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,39 unequal: No Solution Exploring Operation: 48-46=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 48*46=2208, Resulting Numbers: [2208] 2208,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[48, 26, 40], Operations: ['56-16=40'] Exploring Operation: 48-26=22, Resulting Numbers: [40, 22] Generated Node #0,4,0: 39:[40, 22] Operation: 48-26=22 Exploring Operation: 48-40=8, Resulting Numbers: [26, 8] Generated Node #0,4,1: 39:[26, 8] Operation: 48-40=8 Exploring Operation: 40-26=14, Resulting Numbers: [48, 14] Generated Node #0,4,2: 39:[48, 14] Operation: 40-26=14 Exploring Operation: 48+26=74, Resulting Numbers: [40, 74] Generated Node #0,4,3: 39:[40, 74] Operation: 48+26=74 Exploring Operation: 26+40=66, Resulting Numbers: [48, 66] Generated Node #0,4,4: 39:[48, 66] Operation: 26+40=66 Moving to Node #0,4,0 Current State: 39:[40, 22], Operations: ['56-16=40', '48-26=22'] Exploring Operation: 40*22=880, Resulting Numbers: [880] 880,39 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 40+22=62, Resulting Numbers: [62] 62,39 unequal: No Solution Moving to Node #0,4,2 Current State: 39:[48, 14], Operations: ['56-16=40', '40-26=14'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,39 unequal: No Solution Moving to Node #0,4,1 Current State: 39:[26, 8], Operations: ['56-16=40', '48-40=8'] Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,39 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[40, 74], Operations: ['56-16=40', '48+26=74'] Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,39 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,39 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,39 unequal: No Solution Moving to Node #0,4,4 Current State: 39:[48, 66], Operations: ['56-16=40', '26+40=66'] Exploring Operation: 66-48=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 48*66=3168, Resulting Numbers: [3168] 3168,39 unequal: No Solution Exploring Operation: 48+66=114, Resulting Numbers: [114] 114,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[56, 16, 22], Operations: ['48-26=22'] Exploring Operation: 56-22=34, Resulting Numbers: [16, 34] Generated Node #0,0,0: 39:[16, 34] Operation: 56-22=34 Exploring Operation: 56+16=72, Resulting Numbers: [22, 72] Generated Node #0,0,1: 39:[22, 72] Operation: 56+16=72 Exploring Operation: 22-16=6, Resulting Numbers: [56, 6] Generated Node #0,0,2: 39:[56, 6] Operation: 22-16=6 Exploring Operation: 16+22=38, Resulting Numbers: [56, 38] Generated Node #0,0,3: 39:[56, 38] Operation: 16+22=38 Exploring Operation: 56-16=40, Resulting Numbers: [22, 40] Generated Node #0,0,4: 39:[22, 40] Operation: 56-16=40 Moving to Node #0,0,0 Current State: 39:[16, 34], Operations: ['48-26=22', '56-22=34'] Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,39 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[22, 40], Operations: ['48-26=22', '56-16=40'] Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,39 unequal: No Solution Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[56, 38], Operations: ['48-26=22', '16+22=38'] Exploring Operation: 56*38=2128, Resulting Numbers: [2128] 2128,39 unequal: No Solution Exploring Operation: 56+38=94, Resulting Numbers: [94] 94,39 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[56, 6], Operations: ['48-26=22', '22-16=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[22, 72], Operations: ['48-26=22', '56+16=72'] Exploring Operation: 22*72=1584, Resulting Numbers: [1584] 1584,39 unequal: No Solution Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 22+72=94, Resulting Numbers: [94] 94,39 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 #0,2 Current State: 39:[56, 48, 42], Operations: ['26+16=42'] Exploring Operation: 56+42=98, Resulting Numbers: [48, 98] Generated Node #0,2,0: 39:[48, 98] Operation: 56+42=98 Exploring Operation: 48-42=6, Resulting Numbers: [56, 6] Generated Node #0,2,1: 39:[56, 6] Operation: 48-42=6 Exploring Operation: 56-42=14, Resulting Numbers: [48, 14] Generated Node #0,2,2: 39:[48, 14] Operation: 56-42=14 Exploring Operation: 56-48=8, Resulting Numbers: [42, 8] Generated Node #0,2,3: 39:[42, 8] Operation: 56-48=8 Exploring Operation: 56+48=104, Resulting Numbers: [42, 104] Generated Node #0,2,4: 39:[42, 104] Operation: 56+48=104 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 39:[42, 8], Operations: ['26+16=42', '56-48=8'] Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,39 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 39:[48, 14], Operations: ['26+16=42', '56-42=14'] Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,39 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[56, 6], Operations: ['26+16=42', '48-42=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,39 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,39 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[48, 98], Operations: ['26+16=42', '56+42=98'] Exploring Operation: 48+98=146, Resulting Numbers: [146] 146,39 unequal: No Solution Exploring Operation: 48*98=4704, Resulting Numbers: [4704] 4704,39 unequal: No Solution Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 39:[42, 104], Operations: ['26+16=42', '56+48=104'] Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,39 unequal: No Solution Exploring Operation: 42+104=146, Resulting Numbers: [146] 146,39 unequal: No Solution Exploring Operation: 42*104=4368, Resulting Numbers: [4368] 4368,39 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_5
sum_heuristic
[ 40, 73, 66, 72 ]
39
[ "73-40=33", "72-66=6", "33+6=39" ]
Current State: 39:[40, 73, 66, 72], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [66, 72, 33] Generated Node #2: [66, 72, 33] from Operation: 73-40=33 Current State: 39:[66, 72, 33], Operations: ['73-40=33'] Exploring Operation: 72-66=6, Resulting Numbers: [33, 6] Generated Node #3: [33, 6] from Operation: 72-66=6 Current State: 39:[33, 6], Operations: ['73-40=33', '72-66=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[40, 73, 66, 72], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [66, 72, 33] Generated Node #0,0: 39:[66, 72, 33] Operation: 73-40=33 Exploring Operation: 73-66=7, Resulting Numbers: [40, 72, 7] Generated Node #0,1: 39:[40, 72, 7] Operation: 73-66=7 Exploring Operation: 72-66=6, Resulting Numbers: [40, 73, 6] Generated Node #0,2: 39:[40, 73, 6] Operation: 72-66=6 Exploring Operation: 73-72=1, Resulting Numbers: [40, 66, 1] Generated Node #0,3: 39:[40, 66, 1] Operation: 73-72=1 Moving to Node #0,3 Current State: 39:[40, 66, 1], Operations: ['73-72=1'] Exploring Operation: 40*1=40, Resulting Numbers: [66, 40] Generated Node #0,3,0: 39:[66, 40] Operation: 40*1=40 Exploring Operation: 66-40=26, Resulting Numbers: [1, 26] Generated Node #0,3,1: 39:[1, 26] Operation: 66-40=26 Exploring Operation: 66-1=65, Resulting Numbers: [40, 65] Generated Node #0,3,2: 39:[40, 65] Operation: 66-1=65 Exploring Operation: 40-1=39, Resulting Numbers: [66, 39] Generated Node #0,3,3: 39:[66, 39] Operation: 40-1=39 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[1, 26], Operations: ['73-72=1', '66-40=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,39 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:[40, 65], Operations: ['73-72=1', '66-1=65'] Exploring Operation: 65-40=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 40*65=2600, Resulting Numbers: [2600] 2600,39 unequal: No Solution Exploring Operation: 40+65=105, Resulting Numbers: [105] 105,39 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:[66, 39], Operations: ['73-72=1', '40-1=39'] Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 66*39=2574, Resulting Numbers: [2574] 2574,39 unequal: No Solution Exploring Operation: 66+39=105, Resulting Numbers: [105] 105,39 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:[66, 40], Operations: ['73-72=1', '40*1=40'] Exploring Operation: 66+40=106, Resulting Numbers: [106] 106,39 unequal: No Solution Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,39 unequal: No Solution Exploring Operation: 66*40=2640, Resulting Numbers: [2640] 2640,39 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:[40, 73, 6], Operations: ['72-66=6'] Exploring Operation: 73-40=33, Resulting Numbers: [6, 33] Generated Node #0,2,0: 39:[6, 33] Operation: 73-40=33 Exploring Operation: 40-6=34, Resulting Numbers: [73, 34] Generated Node #0,2,1: 39:[73, 34] Operation: 40-6=34 Exploring Operation: 40+6=46, Resulting Numbers: [73, 46] Generated Node #0,2,2: 39:[73, 46] Operation: 40+6=46 Exploring Operation: 73-6=67, Resulting Numbers: [40, 67] Generated Node #0,2,3: 39:[40, 67] Operation: 73-6=67 Moving to Node #0,1 Current State: 39:[40, 72, 7], Operations: ['73-66=7'] Exploring Operation: 72-40=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 39:[7, 32] Operation: 72-40=32 Exploring Operation: 40-7=33, Resulting Numbers: [72, 33] Generated Node #0,1,1: 39:[72, 33] Operation: 40-7=33 Exploring Operation: 40+7=47, Resulting Numbers: [72, 47] Generated Node #0,1,2: 39:[72, 47] Operation: 40+7=47 Exploring Operation: 72-7=65, Resulting Numbers: [40, 65] Generated Node #0,1,3: 39:[40, 65] Operation: 72-7=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[7, 32], Operations: ['73-66=7', '72-40=32'] Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,39 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[40, 73, 66, 72], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [40, 72, 7] Generated Node #0,1: 39:[40, 72, 7] Operation: 73-66=7 Moving to Node #0,1 Current State: 39:[40, 72, 7], Operations: ['73-66=7'] Exploring Operation: 72-40=32, Resulting Numbers: [7, 32] Generated Node #0,1,0: 39:[7, 32] Operation: 72-40=32 Moving to Node #0,1,0 Current State: 39:[7, 32], Operations: ['73-66=7', '72-40=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 66, 49, 68, 65 ]
57
[ "68-66=2", "49+65=114", "114/2=57" ]
Current State: 57:[66, 49, 68, 65], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [49, 65, 2] Generated Node #2: [49, 65, 2] from Operation: 68-66=2 Current State: 57:[49, 65, 2], Operations: ['68-66=2'] Exploring Operation: 49+65=114, Resulting Numbers: [2, 114] Generated Node #3: [2, 114] from Operation: 49+65=114 Current State: 57:[2, 114], Operations: ['68-66=2', '49+65=114'] Exploring Operation: 114/2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[66, 49, 68, 65], Operations: [] Exploring Operation: 66-49=17, Resulting Numbers: [68, 65, 17] Generated Node #0,0: 57:[68, 65, 17] Operation: 66-49=17 Exploring Operation: 68-65=3, Resulting Numbers: [66, 49, 3] Generated Node #0,1: 57:[66, 49, 3] Operation: 68-65=3 Exploring Operation: 68-66=2, Resulting Numbers: [49, 65, 2] Generated Node #0,2: 57:[49, 65, 2] Operation: 68-66=2 Exploring Operation: 68-49=19, Resulting Numbers: [66, 65, 19] Generated Node #0,3: 57:[66, 65, 19] Operation: 68-49=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[66, 49, 3], Operations: ['68-65=3'] Exploring Operation: 66/3=22, Resulting Numbers: [49, 22] Generated Node #0,1,0: 57:[49, 22] Operation: 66/3=22 Exploring Operation: 66-49=17, Resulting Numbers: [3, 17] Generated Node #0,1,1: 57:[3, 17] Operation: 66-49=17 Exploring Operation: 49+3=52, Resulting Numbers: [66, 52] Generated Node #0,1,2: 57:[66, 52] Operation: 49+3=52 Exploring Operation: 66-3=63, Resulting Numbers: [49, 63] Generated Node #0,1,3: 57:[49, 63] Operation: 66-3=63 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[3, 17], Operations: ['68-65=3', '66-49=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,57 unequal: No Solution No 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: 57:[49, 22], Operations: ['68-65=3', '66/3=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,57 unequal: No Solution Exploring Operation: 49*22=1078, Resulting Numbers: [1078] 1078,57 unequal: No Solution Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,57 unequal: No Solution No 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: 57:[66, 52], Operations: ['68-65=3', '49+3=52'] Exploring Operation: 66+52=118, Resulting Numbers: [118] 118,57 unequal: No Solution Exploring Operation: 66*52=3432, Resulting Numbers: [3432] 3432,57 unequal: No Solution Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,57 unequal: No Solution No 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: 57:[49, 63], Operations: ['68-65=3', '66-3=63'] Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 49*63=3087, Resulting Numbers: [3087] 3087,57 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: 57:[49, 65, 2], Operations: ['68-66=2'] Exploring Operation: 49-2=47, Resulting Numbers: [65, 47] Generated Node #0,2,0: 57:[65, 47] Operation: 49-2=47 Exploring Operation: 49+2=51, Resulting Numbers: [65, 51] Generated Node #0,2,1: 57:[65, 51] Operation: 49+2=51 Exploring Operation: 65-2=63, Resulting Numbers: [49, 63] Generated Node #0,2,2: 57:[49, 63] Operation: 65-2=63 Exploring Operation: 65-49=16, Resulting Numbers: [2, 16] Generated Node #0,2,3: 57:[2, 16] Operation: 65-49=16 Moving to Node #0,2,3 Current State: 57:[2, 16], Operations: ['68-66=2', '65-49=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[49, 63], Operations: ['68-66=2', '65-2=63'] Exploring Operation: 49*63=3087, Resulting Numbers: [3087] 3087,57 unequal: No Solution Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[65, 51], Operations: ['68-66=2', '49+2=51'] Exploring Operation: 65*51=3315, Resulting Numbers: [3315] 3315,57 unequal: No Solution Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 65+51=116, Resulting Numbers: [116] 116,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[65, 47], Operations: ['68-66=2', '49-2=47'] Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,57 unequal: No Solution Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,57 unequal: No Solution No 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: 57:[66, 65, 19], Operations: ['68-49=19'] Exploring Operation: 66-19=47, Resulting Numbers: [65, 47] Generated Node #0,3,0: 57:[65, 47] Operation: 66-19=47 Exploring Operation: 66-65=1, Resulting Numbers: [19, 1] Generated Node #0,3,1: 57:[19, 1] Operation: 66-65=1 Exploring Operation: 66+19=85, Resulting Numbers: [65, 85] Generated Node #0,3,2: 57:[65, 85] Operation: 66+19=85 Exploring Operation: 65-19=46, Resulting Numbers: [66, 46] Generated Node #0,3,3: 57:[66, 46] Operation: 65-19=46 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 57:[19, 1], Operations: ['68-49=19', '66-65=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 57:[65, 47], Operations: ['68-49=19', '66-19=47'] Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,57 unequal: No Solution No 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: 57:[66, 46], Operations: ['68-49=19', '65-19=46'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,57 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,57 unequal: No Solution No 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: 57:[65, 85], Operations: ['68-49=19', '66+19=85'] Exploring Operation: 65*85=5525, Resulting Numbers: [5525] 5525,57 unequal: No Solution Exploring Operation: 85-65=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 65+85=150, Resulting Numbers: [150] 150,57 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: 57:[68, 65, 17], Operations: ['66-49=17'] Exploring Operation: 68-17=51, Resulting Numbers: [65, 51] Generated Node #0,0,0: 57:[65, 51] Operation: 68-17=51 Exploring Operation: 68/17=4, Resulting Numbers: [65, 4] Generated Node #0,0,1: 57:[65, 4] Operation: 68/17=4 Exploring Operation: 65-17=48, Resulting Numbers: [68, 48] Generated Node #0,0,2: 57:[68, 48] Operation: 65-17=48 Exploring Operation: 68-65=3, Resulting Numbers: [17, 3] Generated Node #0,0,3: 57:[17, 3] Operation: 68-65=3 Moving to Node #0,0,3 Current State: 57:[17, 3], Operations: ['66-49=17', '68-65=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[65, 4], Operations: ['66-49=17', '68/17=4'] Exploring Operation: 65*4=260, Resulting Numbers: [260] 260,57 unequal: No Solution Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 65+4=69, Resulting Numbers: [69] 69,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[65, 51], Operations: ['66-49=17', '68-17=51'] Exploring Operation: 65*51=3315, Resulting Numbers: [3315] 3315,57 unequal: No Solution Exploring Operation: 65+51=116, Resulting Numbers: [116] 116,57 unequal: No Solution Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[68, 48], Operations: ['66-49=17', '65-17=48'] Exploring Operation: 68+48=116, Resulting Numbers: [116] 116,57 unequal: No Solution Exploring Operation: 68*48=3264, Resulting Numbers: [3264] 3264,57 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 18, 86, 65, 42 ]
36
[ "18*42=756", "86-65=21", "756/21=36" ]
Current State: 36:[18, 86, 65, 42], Operations: [] Exploring Operation: 18*42=756, Resulting Numbers: [86, 65, 756] Generated Node #2: [86, 65, 756] from Operation: 18*42=756 Current State: 36:[86, 65, 756], Operations: ['18*42=756'] Exploring Operation: 86-65=21, Resulting Numbers: [756, 21] Generated Node #3: [756, 21] from Operation: 86-65=21 Current State: 36:[756, 21], Operations: ['18*42=756', '86-65=21'] Exploring Operation: 756/21=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[18, 86, 65, 42], Operations: [] Exploring Operation: 86-42=44, Resulting Numbers: [18, 65, 44] Generated Node #0,0: 36:[18, 65, 44] Operation: 86-42=44 Exploring Operation: 86-65=21, Resulting Numbers: [18, 42, 21] Generated Node #0,1: 36:[18, 42, 21] Operation: 86-65=21 Moving to Node #0,1 Current State: 36:[18, 42, 21], Operations: ['86-65=21'] Exploring Operation: 42-21=21, Resulting Numbers: [18, 21] Generated Node #0,1,0: 36:[18, 21] Operation: 42-21=21 Exploring Operation: 42/21=2, Resulting Numbers: [18, 2] Generated Node #0,1,1: 36:[18, 2] Operation: 42/21=2 Moving to Node #0,0 Current State: 36:[18, 65, 44], Operations: ['86-42=44'] Exploring Operation: 65-18=47, Resulting Numbers: [44, 47] Generated Node #0,0,0: 36:[44, 47] Operation: 65-18=47 Exploring Operation: 65-44=21, Resulting Numbers: [18, 21] Generated Node #0,0,1: 36:[18, 21] Operation: 65-44=21 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[18, 21], Operations: ['86-42=44', '65-44=21'] Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[44, 47], Operations: ['86-42=44', '65-18=47'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,36 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: 36:[18, 2], Operations: ['86-65=21', '42/21=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[18, 86, 65, 42], Operations: [] Exploring Operation: 86-65=21, Resulting Numbers: [18, 42, 21] Generated Node #0,1: 36:[18, 42, 21] Operation: 86-65=21 Moving to Node #0,1 Current State: 36:[18, 42, 21], Operations: ['86-65=21'] Exploring Operation: 42/21=2, Resulting Numbers: [18, 2] Generated Node #0,1,1: 36:[18, 2] Operation: 42/21=2 Moving to Node #0,1,1 Current State: 36:[18, 2], Operations: ['86-65=21', '42/21=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 51, 1, 2, 52 ]
77
[ "51*1=51", "52/2=26", "51+26=77" ]
Current State: 77:[51, 1, 2, 52], Operations: [] Exploring Operation: 51*1=51, Resulting Numbers: [2, 52, 51] Generated Node #2: [2, 52, 51] from Operation: 51*1=51 Current State: 77:[2, 52, 51], Operations: ['51*1=51'] Exploring Operation: 52/2=26, Resulting Numbers: [51, 26] Generated Node #3: [51, 26] from Operation: 52/2=26 Current State: 77:[51, 26], Operations: ['51*1=51', '52/2=26'] Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[51, 1, 2, 52], Operations: [] Exploring Operation: 51+52=103, Resulting Numbers: [1, 2, 103] Generated Node #0,0: 77:[1, 2, 103] Operation: 51+52=103 Exploring Operation: 52/2=26, Resulting Numbers: [51, 1, 26] Generated Node #0,1: 77:[51, 1, 26] Operation: 52/2=26 Exploring Operation: 51+1=52, Resulting Numbers: [2, 52, 52] Generated Node #0,2: 77:[2, 52, 52] Operation: 51+1=52 Exploring Operation: 52-51=1, Resulting Numbers: [1, 2, 1] Generated Node #0,3: 77:[1, 2, 1] Operation: 52-51=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[1, 2, 1], Operations: ['52-51=1'] Exploring Operation: 2+1=3, Resulting Numbers: [1, 3] Generated Node #0,3,0: 77:[1, 3] Operation: 2+1=3 Exploring Operation: 1*2=2, Resulting Numbers: [1, 2] Generated Node #0,3,1: 77:[1, 2] Operation: 1*2=2 Exploring Operation: 1+2=3, Resulting Numbers: [1, 3] Generated Node #0,3,2: 77:[1, 3] Operation: 1+2=3 Exploring Operation: 1+1=2, Resulting Numbers: [2, 2] Generated Node #0,3,3: 77:[2, 2] Operation: 1+1=2 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 77:[1, 3], Operations: ['52-51=1', '2+1=3'] Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 77:[1, 3], Operations: ['52-51=1', '1+2=3'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 77:[2, 2], Operations: ['52-51=1', '1+1=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 77:[1, 2], Operations: ['52-51=1', '1*2=2'] Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[1, 2, 103], Operations: ['51+52=103'] Exploring Operation: 103-1=102, Resulting Numbers: [2, 102] Generated Node #0,0,0: 77:[2, 102] Operation: 103-1=102 Exploring Operation: 1+2=3, Resulting Numbers: [103, 3] Generated Node #0,0,1: 77:[103, 3] Operation: 1+2=3 Exploring Operation: 1*2=2, Resulting Numbers: [103, 2] Generated Node #0,0,2: 77:[103, 2] Operation: 1*2=2 Exploring Operation: 103-2=101, Resulting Numbers: [1, 101] Generated Node #0,0,3: 77:[1, 101] Operation: 103-2=101 Moving to Node #0,0,0 Current State: 77:[2, 102], Operations: ['51+52=103', '103-1=102'] Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,77 unequal: No Solution Exploring Operation: 2*102=204, Resulting Numbers: [204] 204,77 unequal: No Solution Exploring Operation: 2+102=104, Resulting Numbers: [104] 104,77 unequal: No Solution Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[1, 101], Operations: ['51+52=103', '103-2=101'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,77 unequal: No Solution Exploring Operation: 101/1=101, Resulting Numbers: [101] 101,77 unequal: No Solution Exploring Operation: 1+101=102, Resulting Numbers: [102] 102,77 unequal: No Solution Exploring Operation: 1*101=101, Resulting Numbers: [101] 101,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[103, 3], Operations: ['51+52=103', '1+2=3'] Exploring Operation: 103+3=106, Resulting Numbers: [106] 106,77 unequal: No Solution Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,77 unequal: No Solution Exploring Operation: 103*3=309, Resulting Numbers: [309] 309,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[103, 2], Operations: ['51+52=103', '1*2=2'] Exploring Operation: 103+2=105, Resulting Numbers: [105] 105,77 unequal: No Solution Exploring Operation: 103*2=206, Resulting Numbers: [206] 206,77 unequal: No Solution Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[51, 1, 26], Operations: ['52/2=26'] Exploring Operation: 26-1=25, Resulting Numbers: [51, 25] Generated Node #0,1,0: 77:[51, 25] Operation: 26-1=25 Exploring Operation: 51-26=25, Resulting Numbers: [1, 25] Generated Node #0,1,1: 77:[1, 25] Operation: 51-26=25 Exploring Operation: 51+26=77, Resulting Numbers: [1, 77] Generated Node #0,1,2: 77:[1, 77] Operation: 51+26=77 Exploring Operation: 51+1=52, Resulting Numbers: [26, 52] Generated Node #0,1,3: 77:[26, 52] Operation: 51+1=52 Moving to Node #0,1,2 Current State: 77:[1, 77], Operations: ['52/2=26', '51+26=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[51, 1, 2, 52], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [51, 1, 26] Generated Node #0,1: 77:[51, 1, 26] Operation: 52/2=26 Moving to Node #0,1 Current State: 77:[51, 1, 26], Operations: ['52/2=26'] Exploring Operation: 51+26=77, Resulting Numbers: [1, 77] Generated Node #0,1,2: 77:[1, 77] Operation: 51+26=77 Moving to Node #0,1,2 Current State: 77:[1, 77], Operations: ['52/2=26', '51+26=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
sum_heuristic
[ 25, 86, 12, 12 ]
87
[ "25+86=111", "12+12=24", "111-24=87" ]
Current State: 87:[25, 86, 12, 12], Operations: [] Exploring Operation: 25+86=111, Resulting Numbers: [12, 12, 111] Generated Node #2: [12, 12, 111] from Operation: 25+86=111 Current State: 87:[12, 12, 111], Operations: ['25+86=111'] Exploring Operation: 12+12=24, Resulting Numbers: [111, 24] Generated Node #3: [111, 24] from Operation: 12+12=24 Current State: 87:[111, 24], Operations: ['25+86=111', '12+12=24'] Exploring Operation: 111-24=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[25, 86, 12, 12], Operations: [] Exploring Operation: 12/12=1, Resulting Numbers: [25, 86, 1] Generated Node #0,0: 87:[25, 86, 1] Operation: 12/12=1 Moving to Node #0,0 Current State: 87:[25, 86, 1], Operations: ['12/12=1'] Exploring Operation: 25+1=26, Resulting Numbers: [86, 26] Generated Node #0,0,0: 87:[86, 26] Operation: 25+1=26 Moving to Node #0,0,0 Current State: 87:[86, 26], Operations: ['12/12=1', '25+1=26'] Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,87 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 14, 20, 18, 41 ]
44
[ "20-14=6", "18/6=3", "41+3=44" ]
Current State: 44:[14, 20, 18, 41], Operations: [] Exploring Operation: 20-14=6, Resulting Numbers: [18, 41, 6] Generated Node #2: [18, 41, 6] from Operation: 20-14=6 Current State: 44:[18, 41, 6], Operations: ['20-14=6'] Exploring Operation: 18/6=3, Resulting Numbers: [41, 3] Generated Node #3: [41, 3] from Operation: 18/6=3 Current State: 44:[41, 3], Operations: ['20-14=6', '18/6=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[14, 20, 18, 41], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [14, 41, 2] Generated Node #0,0: 44:[14, 41, 2] Operation: 20-18=2 Exploring Operation: 41-18=23, Resulting Numbers: [14, 20, 23] Generated Node #0,1: 44:[14, 20, 23] Operation: 41-18=23 Exploring Operation: 41-20=21, Resulting Numbers: [14, 18, 21] Generated Node #0,2: 44:[14, 18, 21] Operation: 41-20=21 Exploring Operation: 18-14=4, Resulting Numbers: [20, 41, 4] Generated Node #0,3: 44:[20, 41, 4] Operation: 18-14=4 Exploring Operation: 20-14=6, Resulting Numbers: [18, 41, 6] Generated Node #0,4: 44:[18, 41, 6] Operation: 20-14=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[20, 41, 4], Operations: ['18-14=4'] Exploring Operation: 20-4=16, Resulting Numbers: [41, 16] Generated Node #0,3,0: 44:[41, 16] Operation: 20-4=16 Exploring Operation: 20/4=5, Resulting Numbers: [41, 5] Generated Node #0,3,1: 44:[41, 5] Operation: 20/4=5 Exploring Operation: 20+4=24, Resulting Numbers: [41, 24] Generated Node #0,3,2: 44:[41, 24] Operation: 20+4=24 Exploring Operation: 41+4=45, Resulting Numbers: [20, 45] Generated Node #0,3,3: 44:[20, 45] Operation: 41+4=45 Exploring Operation: 41-20=21, Resulting Numbers: [4, 21] Generated Node #0,3,4: 44:[4, 21] Operation: 41-20=21 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 44:[4, 21], Operations: ['18-14=4', '41-20=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,44 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 44:[20, 45], Operations: ['18-14=4', '41+4=45'] Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 44:[41, 5], Operations: ['18-14=4', '20/4=5'] Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 41+5=46, Resulting Numbers: [46] 46,44 unequal: No Solution Exploring Operation: 41*5=205, Resulting Numbers: [205] 205,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 44:[41, 24], Operations: ['18-14=4', '20+4=24'] Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,44 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 44:[41, 16], Operations: ['18-14=4', '20-4=16'] Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,44 unequal: No Solution Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[14, 41, 2], Operations: ['20-18=2'] Exploring Operation: 14/2=7, Resulting Numbers: [41, 7] Generated Node #0,0,0: 44:[41, 7] Operation: 14/2=7 Exploring Operation: 41+2=43, Resulting Numbers: [14, 43] Generated Node #0,0,1: 44:[14, 43] Operation: 41+2=43 Exploring Operation: 14-2=12, Resulting Numbers: [41, 12] Generated Node #0,0,2: 44:[41, 12] Operation: 14-2=12 Exploring Operation: 14+2=16, Resulting Numbers: [41, 16] Generated Node #0,0,3: 44:[41, 16] Operation: 14+2=16 Exploring Operation: 41-14=27, Resulting Numbers: [2, 27] Generated Node #0,0,4: 44:[2, 27] Operation: 41-14=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[14, 43], Operations: ['20-18=2', '41+2=43'] Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,44 unequal: No Solution Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,44 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[41, 12], Operations: ['20-18=2', '14-2=12'] Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,44 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 44:[2, 27], Operations: ['20-18=2', '41-14=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[41, 7], Operations: ['20-18=2', '14/2=7'] Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,44 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 44:[41, 16], Operations: ['20-18=2', '14+2=16'] Exploring Operation: 41*16=656, Resulting Numbers: [656] 656,44 unequal: No Solution Exploring Operation: 41+16=57, Resulting Numbers: [57] 57,44 unequal: No Solution Exploring Operation: 41-16=25, Resulting Numbers: [25] 25,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[14, 20, 23], Operations: ['41-18=23'] Exploring Operation: 23-14=9, Resulting Numbers: [20, 9] Generated Node #0,1,0: 44:[20, 9] Operation: 23-14=9 Exploring Operation: 20-14=6, Resulting Numbers: [23, 6] Generated Node #0,1,1: 44:[23, 6] Operation: 20-14=6 Exploring Operation: 23-20=3, Resulting Numbers: [14, 3] Generated Node #0,1,2: 44:[14, 3] Operation: 23-20=3 Exploring Operation: 20+23=43, Resulting Numbers: [14, 43] Generated Node #0,1,3: 44:[14, 43] Operation: 20+23=43 Exploring Operation: 14+23=37, Resulting Numbers: [20, 37] Generated Node #0,1,4: 44:[20, 37] Operation: 14+23=37 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 44:[23, 6], Operations: ['41-18=23', '20-14=6'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 44:[20, 9], Operations: ['41-18=23', '23-14=9'] Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 44:[14, 3], Operations: ['41-18=23', '23-20=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 44:[14, 43], Operations: ['41-18=23', '20+23=43'] Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,44 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 44:[20, 37], Operations: ['41-18=23', '14+23=37'] Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,44 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,44 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[14, 18, 21], Operations: ['41-20=21'] Exploring Operation: 18-14=4, Resulting Numbers: [21, 4] Generated Node #0,2,0: 44:[21, 4] Operation: 18-14=4 Exploring Operation: 21-14=7, Resulting Numbers: [18, 7] Generated Node #0,2,1: 44:[18, 7] Operation: 21-14=7 Exploring Operation: 14+18=32, Resulting Numbers: [21, 32] Generated Node #0,2,2: 44:[21, 32] Operation: 14+18=32 Exploring Operation: 18+21=39, Resulting Numbers: [14, 39] Generated Node #0,2,3: 44:[14, 39] Operation: 18+21=39 Exploring Operation: 21-18=3, Resulting Numbers: [14, 3] Generated Node #0,2,4: 44:[14, 3] Operation: 21-18=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[21, 4], Operations: ['41-20=21', '18-14=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 44:[14, 3], Operations: ['41-20=21', '21-18=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[18, 7], Operations: ['41-20=21', '21-14=7'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,44 unequal: No Solution Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[14, 39], Operations: ['41-20=21', '18+21=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,44 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,44 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[21, 32], Operations: ['41-20=21', '14+18=32'] Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,44 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,44 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 44:[18, 41, 6], Operations: ['20-14=6'] Exploring Operation: 41-18=23, Resulting Numbers: [6, 23] Generated Node #0,4,0: 44:[6, 23] Operation: 41-18=23 Exploring Operation: 18/6=3, Resulting Numbers: [41, 3] Generated Node #0,4,1: 44:[41, 3] Operation: 18/6=3 Exploring Operation: 18+6=24, Resulting Numbers: [41, 24] Generated Node #0,4,2: 44:[41, 24] Operation: 18+6=24 Exploring Operation: 41+6=47, Resulting Numbers: [18, 47] Generated Node #0,4,3: 44:[18, 47] Operation: 41+6=47 Exploring Operation: 18-6=12, Resulting Numbers: [41, 12] Generated Node #0,4,4: 44:[41, 12] Operation: 18-6=12 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 44:[6, 23], Operations: ['20-14=6', '41-18=23'] Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,44 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 44:[41, 3], Operations: ['20-14=6', '18/6=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[14, 20, 18, 41], Operations: [] Exploring Operation: 20-14=6, Resulting Numbers: [18, 41, 6] Generated Node #0,4: 44:[18, 41, 6] Operation: 20-14=6 Moving to Node #0,4 Current State: 44:[18, 41, 6], Operations: ['20-14=6'] Exploring Operation: 18/6=3, Resulting Numbers: [41, 3] Generated Node #0,4,1: 44:[41, 3] Operation: 18/6=3 Moving to Node #0,4,1 Current State: 44:[41, 3], Operations: ['20-14=6', '18/6=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.914931
hs_5
sum_heuristic
[ 5, 38, 64, 32 ]
28
[ "5*64=320", "320/32=10", "38-10=28" ]
Current State: 28:[5, 38, 64, 32], Operations: [] Exploring Operation: 5*64=320, Resulting Numbers: [38, 32, 320] Generated Node #2: [38, 32, 320] from Operation: 5*64=320 Current State: 28:[38, 32, 320], Operations: ['5*64=320'] Exploring Operation: 320/32=10, Resulting Numbers: [38, 10] Generated Node #3: [38, 10] from Operation: 320/32=10 Current State: 28:[38, 10], Operations: ['5*64=320', '320/32=10'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[5, 38, 64, 32], Operations: [] Exploring Operation: 64/32=2, Resulting Numbers: [5, 38, 2] Generated Node #0,0: 28:[5, 38, 2] Operation: 64/32=2 Exploring Operation: 64-38=26, Resulting Numbers: [5, 32, 26] Generated Node #0,1: 28:[5, 32, 26] Operation: 64-38=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[5, 32, 26], Operations: ['64-38=26'] Exploring Operation: 32-26=6, Resulting Numbers: [5, 6] Generated Node #0,1,0: 28:[5, 6] Operation: 32-26=6 Exploring Operation: 32-5=27, Resulting Numbers: [26, 27] Generated Node #0,1,1: 28:[26, 27] Operation: 32-5=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[5, 6], Operations: ['64-38=26', '32-26=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,28 unequal: No Solution No 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: 28:[26, 27], Operations: ['64-38=26', '32-5=27'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 26+27=53, Resulting Numbers: [53] 53,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[5, 38, 2], Operations: ['64/32=2'] Exploring Operation: 38/2=19, Resulting Numbers: [5, 19] Generated Node #0,0,0: 28:[5, 19] Operation: 38/2=19 Exploring Operation: 38-5=33, Resulting Numbers: [2, 33] Generated Node #0,0,1: 28:[2, 33] Operation: 38-5=33 Moving to Node #0,0,1 Current State: 28:[2, 33], Operations: ['64/32=2', '38-5=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[5, 19], Operations: ['64/32=2', '38/2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,28 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
[ 19, 15, 25, 27 ]
53
[ "27-25=2", "19*2=38", "15+38=53" ]
Current State: 53:[19, 15, 25, 27], Operations: [] Exploring Operation: 27-25=2, Resulting Numbers: [19, 15, 2] Generated Node #2: [19, 15, 2] from Operation: 27-25=2 Current State: 53:[19, 15, 2], Operations: ['27-25=2'] Exploring Operation: 19*2=38, Resulting Numbers: [15, 38] Generated Node #3: [15, 38] from Operation: 19*2=38 Current State: 53:[15, 38], Operations: ['27-25=2', '19*2=38'] Exploring Operation: 15+38=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[19, 15, 25, 27], Operations: [] Exploring Operation: 19+15=34, Resulting Numbers: [25, 27, 34] Generated Node #0,0: 53:[25, 27, 34] Operation: 19+15=34 Exploring Operation: 19+25=44, Resulting Numbers: [15, 27, 44] Generated Node #0,1: 53:[15, 27, 44] Operation: 19+25=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[25, 27, 34], Operations: ['19+15=34'] Exploring Operation: 25+34=59, Resulting Numbers: [27, 59] Generated Node #0,0,0: 53:[27, 59] Operation: 25+34=59 Exploring Operation: 25+27=52, Resulting Numbers: [34, 52] Generated Node #0,0,1: 53:[34, 52] Operation: 25+27=52 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[34, 52], Operations: ['19+15=34', '25+27=52'] Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,53 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:[27, 59], Operations: ['19+15=34', '25+34=59'] Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,53 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:[15, 27, 44], Operations: ['19+25=44'] Exploring Operation: 15+44=59, Resulting Numbers: [27, 59] Generated Node #0,1,0: 53:[27, 59] Operation: 15+44=59 Exploring Operation: 15+27=42, Resulting Numbers: [44, 42] Generated Node #0,1,1: 53:[44, 42] Operation: 15+27=42 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[44, 42], Operations: ['19+25=44', '15+27=42'] Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,53 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[27, 59], Operations: ['19+25=44', '15+44=59'] Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,53 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,53 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
sum_heuristic
[ 3, 71, 87, 54 ]
67
[ "3+71=74", "87+54=141", "141-74=67" ]
Current State: 67:[3, 71, 87, 54], Operations: [] Exploring Operation: 3+71=74, Resulting Numbers: [87, 54, 74] Generated Node #2: [87, 54, 74] from Operation: 3+71=74 Current State: 67:[87, 54, 74], Operations: ['3+71=74'] Exploring Operation: 87+54=141, Resulting Numbers: [74, 141] Generated Node #3: [74, 141] from Operation: 87+54=141 Current State: 67:[74, 141], Operations: ['3+71=74', '87+54=141'] Exploring Operation: 141-74=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[3, 71, 87, 54], Operations: [] Exploring Operation: 3+71=74, Resulting Numbers: [87, 54, 74] Generated Node #0,0: 67:[87, 54, 74] Operation: 3+71=74 Exploring Operation: 87-3=84, Resulting Numbers: [71, 54, 84] Generated Node #0,1: 67:[71, 54, 84] Operation: 87-3=84 Exploring Operation: 71-3=68, Resulting Numbers: [87, 54, 68] Generated Node #0,2: 67:[87, 54, 68] Operation: 71-3=68 Exploring Operation: 3+54=57, Resulting Numbers: [71, 87, 57] Generated Node #0,3: 67:[71, 87, 57] Operation: 3+54=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[71, 54, 84], Operations: ['87-3=84'] Exploring Operation: 71-54=17, Resulting Numbers: [84, 17] Generated Node #0,1,0: 67:[84, 17] Operation: 71-54=17 Exploring Operation: 71+54=125, Resulting Numbers: [84, 125] Generated Node #0,1,1: 67:[84, 125] Operation: 71+54=125 Exploring Operation: 84-71=13, Resulting Numbers: [54, 13] Generated Node #0,1,2: 67:[54, 13] Operation: 84-71=13 Exploring Operation: 84-54=30, Resulting Numbers: [71, 30] Generated Node #0,1,3: 67:[71, 30] Operation: 84-54=30 Moving to Node #0,1,3 Current State: 67:[71, 30], Operations: ['87-3=84', '84-54=30'] Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 71+30=101, Resulting Numbers: [101] 101,67 unequal: No Solution Exploring Operation: 71*30=2130, Resulting Numbers: [2130] 2130,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[54, 13], Operations: ['87-3=84', '84-71=13'] Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[3, 71, 87, 54], Operations: [] Exploring Operation: 87-3=84, Resulting Numbers: [71, 54, 84] Generated Node #0,1: 67:[71, 54, 84] Operation: 87-3=84 Moving to Node #0,1 Current State: 67:[71, 54, 84], Operations: ['87-3=84'] Exploring Operation: 84-71=13, Resulting Numbers: [54, 13] Generated Node #0,1,2: 67:[54, 13] Operation: 84-71=13 Moving to Node #0,1,2 Current State: 67:[54, 13], Operations: ['87-3=84', '84-71=13'] Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 44, 61, 50, 48 ]
27
[ "50-48=2", "44*2=88", "88-61=27" ]
Current State: 27:[44, 61, 50, 48], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [44, 61, 2] Generated Node #2: [44, 61, 2] from Operation: 50-48=2 Current State: 27:[44, 61, 2], Operations: ['50-48=2'] Exploring Operation: 44*2=88, Resulting Numbers: [61, 88] Generated Node #3: [61, 88] from Operation: 44*2=88 Current State: 27:[61, 88], Operations: ['50-48=2', '44*2=88'] Exploring Operation: 88-61=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[44, 61, 50, 48], Operations: [] Exploring Operation: 61-50=11, Resulting Numbers: [44, 48, 11] Generated Node #0,0: 27:[44, 48, 11] Operation: 61-50=11 Moving to Node #0,0 Current State: 27:[44, 48, 11], Operations: ['61-50=11'] Exploring Operation: 48-44=4, Resulting Numbers: [11, 4] Generated Node #0,0,0: 27:[11, 4] Operation: 48-44=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[11, 4], Operations: ['61-50=11', '48-44=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 3, 22, 26, 84 ]
11
[ "84/3=28", "28-26=2", "22/2=11" ]
Current State: 11:[3, 22, 26, 84], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [22, 26, 28] Generated Node #2: [22, 26, 28] from Operation: 84/3=28 Current State: 11:[22, 26, 28], Operations: ['84/3=28'] Exploring Operation: 28-26=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 28-26=2 Current State: 11:[22, 2], Operations: ['84/3=28', '28-26=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[3, 22, 26, 84], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [22, 26, 28] Generated Node #0,0: 11:[22, 26, 28] Operation: 84/3=28 Exploring Operation: 84-26=58, Resulting Numbers: [3, 22, 58] Generated Node #0,1: 11:[3, 22, 58] Operation: 84-26=58 Moving to Node #0,0 Current State: 11:[22, 26, 28], Operations: ['84/3=28'] Exploring Operation: 28-22=6, Resulting Numbers: [26, 6] Generated Node #0,0,0: 11:[26, 6] Operation: 28-22=6 Exploring Operation: 28-26=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 11:[22, 2] Operation: 28-26=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[26, 6], Operations: ['84/3=28', '28-22=6'] Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,11 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[22, 2], Operations: ['84/3=28', '28-26=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[3, 22, 26, 84], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [22, 26, 28] Generated Node #0,0: 11:[22, 26, 28] Operation: 84/3=28 Moving to Node #0,0 Current State: 11:[22, 26, 28], Operations: ['84/3=28'] Exploring Operation: 28-26=2, Resulting Numbers: [22, 2] Generated Node #0,0,1: 11:[22, 2] Operation: 28-26=2 Moving to Node #0,0,1 Current State: 11:[22, 2], Operations: ['84/3=28', '28-26=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 72, 20, 63, 59 ]
67
[ "63-59=4", "20/4=5", "72-5=67" ]
Current State: 67:[72, 20, 63, 59], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [72, 20, 4] Generated Node #2: [72, 20, 4] from Operation: 63-59=4 Current State: 67:[72, 20, 4], Operations: ['63-59=4'] Exploring Operation: 20/4=5, Resulting Numbers: [72, 5] Generated Node #3: [72, 5] from Operation: 20/4=5 Current State: 67:[72, 5], Operations: ['63-59=4', '20/4=5'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[72, 20, 63, 59], Operations: [] Exploring Operation: 72-20=52, Resulting Numbers: [63, 59, 52] Generated Node #0,0: 67:[63, 59, 52] Operation: 72-20=52 Exploring Operation: 20+63=83, Resulting Numbers: [72, 59, 83] Generated Node #0,1: 67:[72, 59, 83] Operation: 20+63=83 Exploring Operation: 20+59=79, Resulting Numbers: [72, 63, 79] Generated Node #0,2: 67:[72, 63, 79] Operation: 20+59=79 Exploring Operation: 72+20=92, Resulting Numbers: [63, 59, 92] Generated Node #0,3: 67:[63, 59, 92] Operation: 72+20=92 Exploring Operation: 63-20=43, Resulting Numbers: [72, 59, 43] Generated Node #0,4: 67:[72, 59, 43] Operation: 63-20=43 Moving to Node #0,2 Current State: 67:[72, 63, 79], Operations: ['20+59=79'] Exploring Operation: 79-63=16, Resulting Numbers: [72, 16] Generated Node #0,2,0: 67:[72, 16] Operation: 79-63=16 Exploring Operation: 72+63=135, Resulting Numbers: [79, 135] Generated Node #0,2,1: 67:[79, 135] Operation: 72+63=135 Exploring Operation: 72-63=9, Resulting Numbers: [79, 9] Generated Node #0,2,2: 67:[79, 9] Operation: 72-63=9 Exploring Operation: 79-72=7, Resulting Numbers: [63, 7] Generated Node #0,2,3: 67:[63, 7] Operation: 79-72=7 Exploring Operation: 63+79=142, Resulting Numbers: [72, 142] Generated Node #0,2,4: 67:[72, 142] Operation: 63+79=142 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[72, 16], Operations: ['20+59=79', '79-63=16'] Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,67 unequal: No Solution No 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: 67:[63, 7], Operations: ['20+59=79', '79-72=7'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,67 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,67 unequal: No Solution No 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: 67:[79, 9], Operations: ['20+59=79', '72-63=9'] Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,67 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,67 unequal: No Solution No 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: 67:[79, 135], Operations: ['20+59=79', '72+63=135'] Exploring Operation: 79+135=214, Resulting Numbers: [214] 214,67 unequal: No Solution Exploring Operation: 135-79=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 79*135=10665, Resulting Numbers: [10665] 10665,67 unequal: No Solution No 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: 67:[72, 142], Operations: ['20+59=79', '63+79=142'] Exploring Operation: 142-72=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 72*142=10224, Resulting Numbers: [10224] 10224,67 unequal: No Solution Exploring Operation: 72+142=214, Resulting Numbers: [214] 214,67 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: 67:[63, 59, 52], Operations: ['72-20=52'] Exploring Operation: 59-52=7, Resulting Numbers: [63, 7] Generated Node #0,0,0: 67:[63, 7] Operation: 59-52=7 Exploring Operation: 63-52=11, Resulting Numbers: [59, 11] Generated Node #0,0,1: 67:[59, 11] Operation: 63-52=11 Exploring Operation: 63+52=115, Resulting Numbers: [59, 115] Generated Node #0,0,2: 67:[59, 115] Operation: 63+52=115 Exploring Operation: 59+52=111, Resulting Numbers: [63, 111] Generated Node #0,0,3: 67:[63, 111] Operation: 59+52=111 Exploring Operation: 63+59=122, Resulting Numbers: [52, 122] Generated Node #0,0,4: 67:[52, 122] Operation: 63+59=122 Moving to Node #0,1 Current State: 67:[72, 59, 83], Operations: ['20+63=83'] Exploring Operation: 83-59=24, Resulting Numbers: [72, 24] Generated Node #0,1,0: 67:[72, 24] Operation: 83-59=24 Exploring Operation: 83-72=11, Resulting Numbers: [59, 11] Generated Node #0,1,1: 67:[59, 11] Operation: 83-72=11 Exploring Operation: 59+83=142, Resulting Numbers: [72, 142] Generated Node #0,1,2: 67:[72, 142] Operation: 59+83=142 Exploring Operation: 72-59=13, Resulting Numbers: [83, 13] Generated Node #0,1,3: 67:[83, 13] Operation: 72-59=13 Exploring Operation: 72+59=131, Resulting Numbers: [83, 131] Generated Node #0,1,4: 67:[83, 131] Operation: 72+59=131 Moving to Node #0,3 Current State: 67:[63, 59, 92], Operations: ['72+20=92'] Exploring Operation: 92-63=29, Resulting Numbers: [59, 29] Generated Node #0,3,0: 67:[59, 29] Operation: 92-63=29 Exploring Operation: 63+59=122, Resulting Numbers: [92, 122] Generated Node #0,3,1: 67:[92, 122] Operation: 63+59=122 Exploring Operation: 63-59=4, Resulting Numbers: [92, 4] Generated Node #0,3,2: 67:[92, 4] Operation: 63-59=4 Exploring Operation: 59+92=151, Resulting Numbers: [63, 151] Generated Node #0,3,3: 67:[63, 151] Operation: 59+92=151 Exploring Operation: 92-59=33, Resulting Numbers: [63, 33] Generated Node #0,3,4: 67:[63, 33] Operation: 92-59=33 Moving to Node #0,4 Current State: 67:[72, 59, 43], Operations: ['63-20=43'] Exploring Operation: 72+43=115, Resulting Numbers: [59, 115] Generated Node #0,4,0: 67:[59, 115] Operation: 72+43=115 Exploring Operation: 59+43=102, Resulting Numbers: [72, 102] Generated Node #0,4,1: 67:[72, 102] Operation: 59+43=102 Exploring Operation: 59-43=16, Resulting Numbers: [72, 16] Generated Node #0,4,2: 67:[72, 16] Operation: 59-43=16 Exploring Operation: 72-43=29, Resulting Numbers: [59, 29] Generated Node #0,4,3: 67:[59, 29] Operation: 72-43=29 Exploring Operation: 72-59=13, Resulting Numbers: [43, 13] Generated Node #0,4,4: 67:[43, 13] Operation: 72-59=13 Moving to Node #0,3,4 Current State: 67:[63, 33], Operations: ['72+20=92', '92-59=33'] Exploring Operation: 63+33=96, Resulting Numbers: [96] 96,67 unequal: No Solution Exploring Operation: 63*33=2079, Resulting Numbers: [2079] 2079,67 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,4,1 Current State: 67:[72, 102], Operations: ['63-20=43', '59+43=102'] Exploring Operation: 72+102=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 72*102=7344, Resulting Numbers: [7344] 7344,67 unequal: No Solution Exploring Operation: 102-72=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[59, 29], Operations: ['72+20=92', '92-63=29'] Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,67 unequal: No Solution Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,4,3 Current State: 67:[59, 29], Operations: ['63-20=43', '72-43=29'] Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,67 unequal: No Solution Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[72, 24], Operations: ['20+63=83', '83-59=24'] Exploring Operation: 72*24=1728, Resulting Numbers: [1728] 1728,67 unequal: No Solution Exploring Operation: 72+24=96, Resulting Numbers: [96] 96,67 unequal: No Solution Exploring Operation: 72/24=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[63, 111], Operations: ['72-20=52', '59+52=111'] Exploring Operation: 111-63=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 63*111=6993, Resulting Numbers: [6993] 6993,67 unequal: No Solution Exploring Operation: 63+111=174, Resulting Numbers: [174] 174,67 unequal: No Solution Moving to Node #0,4,2 Current State: 67:[72, 16], Operations: ['63-20=43', '59-43=16'] Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,67 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[59, 115], Operations: ['72-20=52', '63+52=115'] Exploring Operation: 115-59=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 59+115=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 59*115=6785, Resulting Numbers: [6785] 6785,67 unequal: No Solution Moving to Node #0,4,0 Current State: 67:[59, 115], Operations: ['63-20=43', '72+43=115'] Exploring Operation: 59+115=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 59*115=6785, Resulting Numbers: [6785] 6785,67 unequal: No Solution Exploring Operation: 115-59=56, Resulting Numbers: [56] 56,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[59, 11], Operations: ['20+63=83', '83-72=11'] Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 59*11=649, Resulting Numbers: [649] 649,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[63, 7], Operations: ['72-20=52', '59-52=7'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[59, 11], Operations: ['72-20=52', '63-52=11'] Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 59*11=649, Resulting Numbers: [649] 649,67 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[83, 13], Operations: ['20+63=83', '72-59=13'] Exploring Operation: 83*13=1079, Resulting Numbers: [1079] 1079,67 unequal: No Solution Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,67 unequal: No Solution Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,67 unequal: No Solution Moving to Node #0,0,4 Current State: 67:[52, 122], Operations: ['72-20=52', '63+59=122'] Exploring Operation: 52+122=174, Resulting Numbers: [174] 174,67 unequal: No Solution Exploring Operation: 122-52=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 52*122=6344, Resulting Numbers: [6344] 6344,67 unequal: No Solution Moving to Node #0,4,4 Current State: 67:[43, 13], Operations: ['63-20=43', '72-59=13'] Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,67 unequal: No Solution Exploring Operation: 43*13=559, Resulting Numbers: [559] 559,67 unequal: No Solution Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[83, 131], Operations: ['20+63=83', '72+59=131'] Exploring Operation: 131-83=48, Resulting Numbers: [48] 48,67 unequal: No Solution Exploring Operation: 83*131=10873, Resulting Numbers: [10873] 10873,67 unequal: No Solution Exploring Operation: 83+131=214, Resulting Numbers: [214] 214,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[92, 122], Operations: ['72+20=92', '63+59=122'] Exploring Operation: 92+122=214, Resulting Numbers: [214] 214,67 unequal: No Solution Exploring Operation: 92*122=11224, Resulting Numbers: [11224] 11224,67 unequal: No Solution Exploring Operation: 122-92=30, Resulting Numbers: [30] 30,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[72, 142], Operations: ['20+63=83', '59+83=142'] Exploring Operation: 142-72=70, Resulting Numbers: [70] 70,67 unequal: No Solution Exploring Operation: 72+142=214, Resulting Numbers: [214] 214,67 unequal: No Solution Exploring Operation: 72*142=10224, Resulting Numbers: [10224] 10224,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[92, 4], Operations: ['72+20=92', '63-59=4'] Exploring Operation: 92*4=368, Resulting Numbers: [368] 368,67 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,67 unequal: No Solution Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,67 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[63, 151], Operations: ['72+20=92', '59+92=151'] Exploring Operation: 63+151=214, Resulting Numbers: [214] 214,67 unequal: No Solution Exploring Operation: 63*151=9513, Resulting Numbers: [9513] 9513,67 unequal: No Solution Exploring Operation: 151-63=88, Resulting Numbers: [88] 88,67 unequal: No Solution No solution found.
0
hs_5
sum_heuristic