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
[ 49, 19, 80, 75 ]
32
[ "49-19=30", "80*30=2400", "2400/75=32" ]
Current State: 32:[49, 19, 80, 75], Operations: [] Exploring Operation: 49-19=30, Resulting Numbers: [80, 75, 30] Generated Node #2: [80, 75, 30] from Operation: 49-19=30 Current State: 32:[80, 75, 30], Operations: ['49-19=30'] Exploring Operation: 80*30=2400, Resulting Numbers: [75, 2400] Generated Node #3: [75, 2400] from Operation: 80*30=2400 Current State: 32:[75, 2400], Operations: ['49-19=30', '80*30=2400'] Exploring Operation: 2400/75=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[49, 19, 80, 75], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [49, 19, 5] Generated Node #0,0: 32:[49, 19, 5] Operation: 80-75=5 Exploring Operation: 75-49=26, Resulting Numbers: [19, 80, 26] Generated Node #0,1: 32:[19, 80, 26] Operation: 75-49=26 Exploring Operation: 80-19=61, Resulting Numbers: [49, 75, 61] Generated Node #0,2: 32:[49, 75, 61] Operation: 80-19=61 Exploring Operation: 80-49=31, Resulting Numbers: [19, 75, 31] Generated Node #0,3: 32:[19, 75, 31] Operation: 80-49=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[49, 19, 5], Operations: ['80-75=5'] Exploring Operation: 49+5=54, Resulting Numbers: [19, 54] Generated Node #0,0,0: 32:[19, 54] Operation: 49+5=54 Exploring Operation: 19-5=14, Resulting Numbers: [49, 14] Generated Node #0,0,1: 32:[49, 14] Operation: 19-5=14 Exploring Operation: 49-19=30, Resulting Numbers: [5, 30] Generated Node #0,0,2: 32:[5, 30] Operation: 49-19=30 Exploring Operation: 49-5=44, Resulting Numbers: [19, 44] Generated Node #0,0,3: 32:[19, 44] Operation: 49-5=44 Moving to Node #0,0,2 Current State: 32:[5, 30], Operations: ['80-75=5', '49-19=30'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 5*30=150, Resulting Numbers: [150] 150,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[19, 44], Operations: ['80-75=5', '49-5=44'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,32 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[49, 14], Operations: ['80-75=5', '19-5=14'] Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,32 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[19, 54], Operations: ['80-75=5', '49+5=54'] Exploring Operation: 19+54=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 19*54=1026, Resulting Numbers: [1026] 1026,32 unequal: No Solution Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,32 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 Current State: 32:[19, 75, 31], Operations: ['80-49=31'] Exploring Operation: 19+31=50, Resulting Numbers: [75, 50] Generated Node #0,3,0: 32:[75, 50] Operation: 19+31=50 Exploring Operation: 75-19=56, Resulting Numbers: [31, 56] Generated Node #0,3,1: 32:[31, 56] Operation: 75-19=56 Exploring Operation: 75-31=44, Resulting Numbers: [19, 44] Generated Node #0,3,2: 32:[19, 44] Operation: 75-31=44 Exploring Operation: 31-19=12, Resulting Numbers: [75, 12] Generated Node #0,3,3: 32:[75, 12] Operation: 31-19=12 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 32:[19, 44], Operations: ['80-49=31', '75-31=44'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,32 unequal: No Solution Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,32 unequal: No Solution No 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: 32:[31, 56], Operations: ['80-49=31', '75-19=56'] Exploring Operation: 31+56=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 31*56=1736, Resulting Numbers: [1736] 1736,32 unequal: No Solution Exploring Operation: 56-31=25, Resulting Numbers: [25] 25,32 unequal: No Solution No 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: 32:[75, 12], Operations: ['80-49=31', '31-19=12'] Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,32 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,32 unequal: No Solution No 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: 32:[75, 50], Operations: ['80-49=31', '19+31=50'] Exploring Operation: 75*50=3750, Resulting Numbers: [3750] 3750,32 unequal: No Solution Exploring Operation: 75+50=125, Resulting Numbers: [125] 125,32 unequal: No Solution Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,32 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: 32:[19, 80, 26], Operations: ['75-49=26'] Exploring Operation: 19+26=45, Resulting Numbers: [80, 45] Generated Node #0,1,0: 32:[80, 45] Operation: 19+26=45 Exploring Operation: 26-19=7, Resulting Numbers: [80, 7] Generated Node #0,1,1: 32:[80, 7] Operation: 26-19=7 Exploring Operation: 80-19=61, Resulting Numbers: [26, 61] Generated Node #0,1,2: 32:[26, 61] Operation: 80-19=61 Exploring Operation: 80-26=54, Resulting Numbers: [19, 54] Generated Node #0,1,3: 32:[19, 54] Operation: 80-26=54 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 32:[19, 54], Operations: ['75-49=26', '80-26=54'] Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 19*54=1026, Resulting Numbers: [1026] 1026,32 unequal: No Solution Exploring Operation: 19+54=73, Resulting Numbers: [73] 73,32 unequal: No Solution No 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: 32:[26, 61], Operations: ['75-49=26', '80-19=61'] Exploring Operation: 26*61=1586, Resulting Numbers: [1586] 1586,32 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,32 unequal: No Solution No 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: 32:[80, 7], Operations: ['75-49=26', '26-19=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,32 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,32 unequal: No Solution No 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: 32:[80, 45], Operations: ['75-49=26', '19+26=45'] Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,32 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,32 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: 32:[49, 75, 61], Operations: ['80-19=61'] Exploring Operation: 49+75=124, Resulting Numbers: [61, 124] Generated Node #0,2,0: 32:[61, 124] Operation: 49+75=124 Exploring Operation: 75-61=14, Resulting Numbers: [49, 14] Generated Node #0,2,1: 32:[49, 14] Operation: 75-61=14 Exploring Operation: 75-49=26, Resulting Numbers: [61, 26] Generated Node #0,2,2: 32:[61, 26] Operation: 75-49=26 Exploring Operation: 61-49=12, Resulting Numbers: [75, 12] Generated Node #0,2,3: 32:[75, 12] Operation: 61-49=12 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 32:[49, 14], Operations: ['80-19=61', '75-61=14'] Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,32 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,32 unequal: No Solution No 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: 32:[61, 26], Operations: ['80-19=61', '75-49=26'] Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,32 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,32 unequal: No Solution No 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: 32:[75, 12], Operations: ['80-19=61', '61-49=12'] Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,32 unequal: No Solution Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,32 unequal: No Solution No 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: 32:[61, 124], Operations: ['80-19=61', '49+75=124'] Exploring Operation: 61*124=7564, Resulting Numbers: [7564] 7564,32 unequal: No Solution Exploring Operation: 124-61=63, Resulting Numbers: [63] 63,32 unequal: No Solution Exploring Operation: 61+124=185, Resulting Numbers: [185] 185,32 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
[ 7, 22, 45, 95 ]
65
[ "22-7=15", "95-45=50", "15+50=65" ]
Current State: 65:[7, 22, 45, 95], Operations: [] Exploring Operation: 22-7=15, Resulting Numbers: [45, 95, 15] Generated Node #2: [45, 95, 15] from Operation: 22-7=15 Current State: 65:[45, 95, 15], Operations: ['22-7=15'] Exploring Operation: 95-45=50, Resulting Numbers: [15, 50] Generated Node #3: [15, 50] from Operation: 95-45=50 Current State: 65:[15, 50], Operations: ['22-7=15', '95-45=50'] Exploring Operation: 15+50=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[7, 22, 45, 95], Operations: [] Exploring Operation: 95-22=73, Resulting Numbers: [7, 45, 73] Generated Node #0,0: 65:[7, 45, 73] Operation: 95-22=73 Exploring Operation: 45-22=23, Resulting Numbers: [7, 95, 23] Generated Node #0,1: 65:[7, 95, 23] Operation: 45-22=23 Exploring Operation: 95-45=50, Resulting Numbers: [7, 22, 50] Generated Node #0,2: 65:[7, 22, 50] Operation: 95-45=50 Exploring Operation: 22+45=67, Resulting Numbers: [7, 95, 67] Generated Node #0,3: 65:[7, 95, 67] Operation: 22+45=67 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[7, 22, 50], Operations: ['95-45=50'] Exploring Operation: 22+50=72, Resulting Numbers: [7, 72] Generated Node #0,2,0: 65:[7, 72] Operation: 22+50=72 Exploring Operation: 50-22=28, Resulting Numbers: [7, 28] Generated Node #0,2,1: 65:[7, 28] Operation: 50-22=28 Exploring Operation: 22-7=15, Resulting Numbers: [50, 15] Generated Node #0,2,2: 65:[50, 15] Operation: 22-7=15 Exploring Operation: 7+50=57, Resulting Numbers: [22, 57] Generated Node #0,2,3: 65:[22, 57] Operation: 7+50=57 Moving to Node #0,2,0 Current State: 65:[7, 72], Operations: ['95-45=50', '22+50=72'] Exploring Operation: 7*72=504, Resulting Numbers: [504] 504,65 unequal: No Solution Exploring Operation: 7+72=79, Resulting Numbers: [79] 79,65 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[7, 22, 45, 95], Operations: [] Exploring Operation: 95-45=50, Resulting Numbers: [7, 22, 50] Generated Node #0,2: 65:[7, 22, 50] Operation: 95-45=50 Moving to Node #0,2 Current State: 65:[7, 22, 50], Operations: ['95-45=50'] Exploring Operation: 22+50=72, Resulting Numbers: [7, 72] Generated Node #0,2,0: 65:[7, 72] Operation: 22+50=72 Moving to Node #0,2,0 Current State: 65:[7, 72], Operations: ['95-45=50', '22+50=72'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 72, 38, 54, 80 ]
84
[ "72+38=110", "80-54=26", "110-26=84" ]
Current State: 84:[72, 38, 54, 80], Operations: [] Exploring Operation: 72+38=110, Resulting Numbers: [54, 80, 110] Generated Node #2: [54, 80, 110] from Operation: 72+38=110 Current State: 84:[54, 80, 110], Operations: ['72+38=110'] Exploring Operation: 80-54=26, Resulting Numbers: [110, 26] Generated Node #3: [110, 26] from Operation: 80-54=26 Current State: 84:[110, 26], Operations: ['72+38=110', '80-54=26'] Exploring Operation: 110-26=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[72, 38, 54, 80], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [38, 54, 8] Generated Node #0,0: 84:[38, 54, 8] Operation: 80-72=8 Exploring Operation: 72-54=18, Resulting Numbers: [38, 80, 18] Generated Node #0,1: 84:[38, 80, 18] Operation: 72-54=18 Moving to Node #0,1 Current State: 84:[38, 80, 18], Operations: ['72-54=18'] Exploring Operation: 80-38=42, Resulting Numbers: [18, 42] Generated Node #0,1,0: 84:[18, 42] Operation: 80-38=42 Exploring Operation: 38-18=20, Resulting Numbers: [80, 20] Generated Node #0,1,1: 84:[80, 20] Operation: 38-18=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[18, 42], Operations: ['72-54=18', '80-38=42'] Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[80, 20], Operations: ['72-54=18', '38-18=20'] Exploring Operation: 80+20=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,84 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: 84:[38, 54, 8], Operations: ['80-72=8'] Exploring Operation: 54-8=46, Resulting Numbers: [38, 46] Generated Node #0,0,0: 84:[38, 46] Operation: 54-8=46 Exploring Operation: 54-38=16, Resulting Numbers: [8, 16] Generated Node #0,0,1: 84:[8, 16] Operation: 54-38=16 Moving to Node #0,0,1 Current State: 84:[8, 16], Operations: ['80-72=8', '54-38=16'] Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[38, 46], Operations: ['80-72=8', '54-8=46'] Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[72, 38, 54, 80], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [38, 54, 8] Generated Node #0,0: 84:[38, 54, 8] Operation: 80-72=8 Moving to Node #0,0 Current State: 84:[38, 54, 8], Operations: ['80-72=8'] Exploring Operation: 54-8=46, Resulting Numbers: [38, 46] Generated Node #0,0,0: 84:[38, 46] Operation: 54-8=46 Moving to Node #0,0,0 Current State: 84:[38, 46], Operations: ['80-72=8', '54-8=46'] Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 96, 31, 48, 64 ]
47
[ "96-31=65", "48+64=112", "112-65=47" ]
Current State: 47:[96, 31, 48, 64], Operations: [] Exploring Operation: 96-31=65, Resulting Numbers: [48, 64, 65] Generated Node #2: [48, 64, 65] from Operation: 96-31=65 Current State: 47:[48, 64, 65], Operations: ['96-31=65'] Exploring Operation: 48+64=112, Resulting Numbers: [65, 112] Generated Node #3: [65, 112] from Operation: 48+64=112 Current State: 47:[65, 112], Operations: ['96-31=65', '48+64=112'] Exploring Operation: 112-65=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[96, 31, 48, 64], Operations: [] Exploring Operation: 96-48=48, Resulting Numbers: [31, 64, 48] Generated Node #0,0: 47:[31, 64, 48] Operation: 96-48=48 Exploring Operation: 96-31=65, Resulting Numbers: [48, 64, 65] Generated Node #0,1: 47:[48, 64, 65] Operation: 96-31=65 Exploring Operation: 96-64=32, Resulting Numbers: [31, 48, 32] Generated Node #0,2: 47:[31, 48, 32] Operation: 96-64=32 Moving to Node #0,2 Current State: 47:[31, 48, 32], Operations: ['96-64=32'] Exploring Operation: 48-31=17, Resulting Numbers: [32, 17] Generated Node #0,2,0: 47:[32, 17] Operation: 48-31=17 Exploring Operation: 31+32=63, Resulting Numbers: [48, 63] Generated Node #0,2,1: 47:[48, 63] Operation: 31+32=63 Exploring Operation: 31+48=79, Resulting Numbers: [32, 79] Generated Node #0,2,2: 47:[32, 79] Operation: 31+48=79 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[48, 63], Operations: ['96-64=32', '31+32=63'] Exploring Operation: 48+63=111, Resulting Numbers: [111] 111,47 unequal: No Solution Exploring Operation: 48*63=3024, Resulting Numbers: [3024] 3024,47 unequal: No Solution Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[32, 17], Operations: ['96-64=32', '48-31=17'] Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,47 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[32, 79], Operations: ['96-64=32', '31+48=79'] Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[96, 31, 48, 64], Operations: [] Exploring Operation: 96-64=32, Resulting Numbers: [31, 48, 32] Generated Node #0,2: 47:[31, 48, 32] Operation: 96-64=32 Moving to Node #0,2 Current State: 47:[31, 48, 32], Operations: ['96-64=32'] Exploring Operation: 31+48=79, Resulting Numbers: [32, 79] Generated Node #0,2,2: 47:[32, 79] Operation: 31+48=79 Moving to Node #0,2,2 Current State: 47:[32, 79], Operations: ['96-64=32', '31+48=79'] Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 33, 45, 60, 12 ]
99
[ "60-45=15", "15-12=3", "33*3=99" ]
Current State: 99:[33, 45, 60, 12], Operations: [] Exploring Operation: 60-45=15, Resulting Numbers: [33, 12, 15] Generated Node #2: [33, 12, 15] from Operation: 60-45=15 Current State: 99:[33, 12, 15], Operations: ['60-45=15'] Exploring Operation: 15-12=3, Resulting Numbers: [33, 3] Generated Node #3: [33, 3] from Operation: 15-12=3 Current State: 99:[33, 3], Operations: ['60-45=15', '15-12=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[33, 45, 60, 12], Operations: [] Exploring Operation: 60-45=15, Resulting Numbers: [33, 12, 15] Generated Node #0,0: 99:[33, 12, 15] Operation: 60-45=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[33, 12, 15], Operations: ['60-45=15'] Exploring Operation: 15-12=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 99:[33, 3] Operation: 15-12=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[33, 3], Operations: ['60-45=15', '15-12=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[33, 45, 60, 12], Operations: [] Exploring Operation: 60-45=15, Resulting Numbers: [33, 12, 15] Generated Node #0,0: 99:[33, 12, 15] Operation: 60-45=15 Moving to Node #0,0 Current State: 99:[33, 12, 15], Operations: ['60-45=15'] Exploring Operation: 15-12=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 99:[33, 3] Operation: 15-12=3 Moving to Node #0,0,0 Current State: 99:[33, 3], Operations: ['60-45=15', '15-12=3'] Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 84, 49, 16, 72 ]
91
[ "84-49=35", "72-16=56", "35+56=91" ]
Current State: 91:[84, 49, 16, 72], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [16, 72, 35] Generated Node #2: [16, 72, 35] from Operation: 84-49=35 Current State: 91:[16, 72, 35], Operations: ['84-49=35'] Exploring Operation: 72-16=56, Resulting Numbers: [35, 56] Generated Node #3: [35, 56] from Operation: 72-16=56 Current State: 91:[35, 56], Operations: ['84-49=35', '72-16=56'] Exploring Operation: 35+56=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[84, 49, 16, 72], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [84, 16, 23] Generated Node #0,0: 91:[84, 16, 23] Operation: 72-49=23 Exploring Operation: 84-72=12, Resulting Numbers: [49, 16, 12] Generated Node #0,1: 91:[49, 16, 12] Operation: 84-72=12 Exploring Operation: 49+72=121, Resulting Numbers: [84, 16, 121] Generated Node #0,2: 91:[84, 16, 121] Operation: 49+72=121 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[84, 16, 23], Operations: ['72-49=23'] Exploring Operation: 84+16=100, Resulting Numbers: [23, 100] Generated Node #0,0,0: 91:[23, 100] Operation: 84+16=100 Exploring Operation: 23-16=7, Resulting Numbers: [84, 7] Generated Node #0,0,1: 91:[84, 7] Operation: 23-16=7 Exploring Operation: 84+23=107, Resulting Numbers: [16, 107] Generated Node #0,0,2: 91:[16, 107] Operation: 84+23=107 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[84, 7], Operations: ['72-49=23', '23-16=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[84, 49, 16, 72], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [84, 16, 23] Generated Node #0,0: 91:[84, 16, 23] Operation: 72-49=23 Moving to Node #0,0 Current State: 91:[84, 16, 23], Operations: ['72-49=23'] Exploring Operation: 23-16=7, Resulting Numbers: [84, 7] Generated Node #0,0,1: 91:[84, 7] Operation: 23-16=7 Moving to Node #0,0,1 Current State: 91:[84, 7], Operations: ['72-49=23', '23-16=7'] Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 6, 45, 35, 33 ]
15
[ "35-33=2", "6/2=3", "45/3=15" ]
Current State: 15:[6, 45, 35, 33], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [6, 45, 2] Generated Node #2: [6, 45, 2] from Operation: 35-33=2 Current State: 15:[6, 45, 2], Operations: ['35-33=2'] Exploring Operation: 6/2=3, Resulting Numbers: [45, 3] Generated Node #3: [45, 3] from Operation: 6/2=3 Current State: 15:[45, 3], Operations: ['35-33=2', '6/2=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[6, 45, 35, 33], Operations: [] Exploring Operation: 45-33=12, Resulting Numbers: [6, 35, 12] Generated Node #0,0: 15:[6, 35, 12] Operation: 45-33=12 Exploring Operation: 45-35=10, Resulting Numbers: [6, 33, 10] Generated Node #0,1: 15:[6, 33, 10] Operation: 45-35=10 Exploring Operation: 35-33=2, Resulting Numbers: [6, 45, 2] Generated Node #0,2: 15:[6, 45, 2] Operation: 35-33=2 Exploring Operation: 45-6=39, Resulting Numbers: [35, 33, 39] Generated Node #0,3: 15:[35, 33, 39] Operation: 45-6=39 Exploring Operation: 35-6=29, Resulting Numbers: [45, 33, 29] Generated Node #0,4: 15:[45, 33, 29] Operation: 35-6=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[6, 35, 12], Operations: ['45-33=12'] Exploring Operation: 35-12=23, Resulting Numbers: [6, 23] Generated Node #0,0,0: 15:[6, 23] Operation: 35-12=23 Exploring Operation: 12/6=2, Resulting Numbers: [35, 2] Generated Node #0,0,1: 15:[35, 2] Operation: 12/6=2 Exploring Operation: 6+12=18, Resulting Numbers: [35, 18] Generated Node #0,0,2: 15:[35, 18] Operation: 6+12=18 Exploring Operation: 35-6=29, Resulting Numbers: [12, 29] Generated Node #0,0,3: 15:[12, 29] Operation: 35-6=29 Exploring Operation: 12-6=6, Resulting Numbers: [35, 6] Generated Node #0,0,4: 15:[35, 6] Operation: 12-6=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[6, 23], Operations: ['45-33=12', '35-12=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,15 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 15:[12, 29], Operations: ['45-33=12', '35-6=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,15 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[35, 2], Operations: ['45-33=12', '12/6=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,15 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,15 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 15:[35, 6], Operations: ['45-33=12', '12-6=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 15:[35, 18], Operations: ['45-33=12', '6+12=18'] Exploring Operation: 35*18=630, Resulting Numbers: [630] 630,15 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 35+18=53, Resulting Numbers: [53] 53,15 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: 15:[6, 33, 10], Operations: ['45-35=10'] Exploring Operation: 33-6=27, Resulting Numbers: [10, 27] Generated Node #0,1,0: 15:[10, 27] Operation: 33-6=27 Exploring Operation: 6+10=16, Resulting Numbers: [33, 16] Generated Node #0,1,1: 15:[33, 16] Operation: 6+10=16 Exploring Operation: 33-10=23, Resulting Numbers: [6, 23] Generated Node #0,1,2: 15:[6, 23] Operation: 33-10=23 Exploring Operation: 10-6=4, Resulting Numbers: [33, 4] Generated Node #0,1,3: 15:[33, 4] Operation: 10-6=4 Exploring Operation: 6+33=39, Resulting Numbers: [10, 39] Generated Node #0,1,4: 15:[10, 39] Operation: 6+33=39 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 15:[6, 23], Operations: ['45-35=10', '33-10=23'] Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,15 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[10, 27], Operations: ['45-35=10', '33-6=27'] Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,15 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 15:[33, 16], Operations: ['45-35=10', '6+10=16'] Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,15 unequal: No Solution Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,15 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 15:[33, 4], Operations: ['45-35=10', '10-6=4'] Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,15 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,15 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 15:[10, 39], Operations: ['45-35=10', '6+33=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,15 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,15 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: 15:[6, 45, 2], Operations: ['35-33=2'] Exploring Operation: 6/2=3, Resulting Numbers: [45, 3] Generated Node #0,2,0: 15:[45, 3] Operation: 6/2=3 Exploring Operation: 45-6=39, Resulting Numbers: [2, 39] Generated Node #0,2,1: 15:[2, 39] Operation: 45-6=39 Exploring Operation: 6-2=4, Resulting Numbers: [45, 4] Generated Node #0,2,2: 15:[45, 4] Operation: 6-2=4 Exploring Operation: 45-2=43, Resulting Numbers: [6, 43] Generated Node #0,2,3: 15:[6, 43] Operation: 45-2=43 Exploring Operation: 6+2=8, Resulting Numbers: [45, 8] Generated Node #0,2,4: 15:[45, 8] Operation: 6+2=8 Moving to Node #0,2,1 Current State: 15:[2, 39], Operations: ['35-33=2', '45-6=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,15 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[6, 43], Operations: ['35-33=2', '45-2=43'] Exploring Operation: 6*43=258, Resulting Numbers: [258] 258,15 unequal: No Solution Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,15 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[45, 3], Operations: ['35-33=2', '6/2=3'] Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,15 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[6, 45, 35, 33], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [6, 45, 2] Generated Node #0,2: 15:[6, 45, 2] Operation: 35-33=2 Moving to Node #0,2 Current State: 15:[6, 45, 2], Operations: ['35-33=2'] Exploring Operation: 6/2=3, Resulting Numbers: [45, 3] Generated Node #0,2,0: 15:[45, 3] Operation: 6/2=3 Moving to Node #0,2,0 Current State: 15:[45, 3], Operations: ['35-33=2', '6/2=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
sum_heuristic
[ 91, 80, 29, 8 ]
10
[ "91-80=11", "29-8=21", "21-11=10" ]
Current State: 10:[91, 80, 29, 8], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [29, 8, 11] Generated Node #2: [29, 8, 11] from Operation: 91-80=11 Current State: 10:[29, 8, 11], Operations: ['91-80=11'] Exploring Operation: 29-8=21, Resulting Numbers: [11, 21] Generated Node #3: [11, 21] from Operation: 29-8=21 Current State: 10:[11, 21], Operations: ['91-80=11', '29-8=21'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[91, 80, 29, 8], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [91, 29, 10] Generated Node #0,0: 10:[91, 29, 10] Operation: 80/8=10 Exploring Operation: 91-80=11, Resulting Numbers: [29, 8, 11] Generated Node #0,1: 10:[29, 8, 11] Operation: 91-80=11 Moving to Node #0,1 Current State: 10:[29, 8, 11], Operations: ['91-80=11'] Exploring Operation: 29-11=18, Resulting Numbers: [8, 18] Generated Node #0,1,0: 10:[8, 18] Operation: 29-11=18 Exploring Operation: 29-8=21, Resulting Numbers: [11, 21] Generated Node #0,1,1: 10:[11, 21] Operation: 29-8=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[8, 18], Operations: ['91-80=11', '29-11=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[91, 80, 29, 8], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [29, 8, 11] Generated Node #0,1: 10:[29, 8, 11] Operation: 91-80=11 Moving to Node #0,1 Current State: 10:[29, 8, 11], Operations: ['91-80=11'] Exploring Operation: 29-11=18, Resulting Numbers: [8, 18] Generated Node #0,1,0: 10:[8, 18] Operation: 29-11=18 Moving to Node #0,1,0 Current State: 10:[8, 18], Operations: ['91-80=11', '29-11=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 45, 90, 11, 8 ]
64
[ "90-45=45", "11+8=19", "45+19=64" ]
Current State: 64:[45, 90, 11, 8], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [11, 8, 45] Generated Node #2: [11, 8, 45] from Operation: 90-45=45 Current State: 64:[11, 8, 45], Operations: ['90-45=45'] Exploring Operation: 11+8=19, Resulting Numbers: [45, 19] Generated Node #3: [45, 19] from Operation: 11+8=19 Current State: 64:[45, 19], Operations: ['90-45=45', '11+8=19'] Exploring Operation: 45+19=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[45, 90, 11, 8], Operations: [] Exploring Operation: 90/45=2, Resulting Numbers: [11, 8, 2] Generated Node #0,0: 64:[11, 8, 2] Operation: 90/45=2 Exploring Operation: 90-45=45, Resulting Numbers: [11, 8, 45] Generated Node #0,1: 64:[11, 8, 45] Operation: 90-45=45 Moving to Node #0,0 Current State: 64:[11, 8, 2], Operations: ['90/45=2'] Exploring Operation: 11-2=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 64:[8, 9] Operation: 11-2=9 Exploring Operation: 11-8=3, Resulting Numbers: [2, 3] Generated Node #0,0,1: 64:[2, 3] Operation: 11-8=3 Moving to Node #0,1 Current State: 64:[11, 8, 45], Operations: ['90-45=45'] Exploring Operation: 45-11=34, Resulting Numbers: [8, 34] Generated Node #0,1,0: 64:[8, 34] Operation: 45-11=34 Exploring Operation: 11+45=56, Resulting Numbers: [8, 56] Generated Node #0,1,1: 64:[8, 56] Operation: 11+45=56 Moving to Node #0,0,0 Current State: 64:[8, 9], Operations: ['90/45=2', '11-2=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,64 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[2, 3], Operations: ['90/45=2', '11-8=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[8, 34], Operations: ['90-45=45', '45-11=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[8, 56], Operations: ['90-45=45', '11+45=56'] Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,64 unequal: No Solution Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[45, 90, 11, 8], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [11, 8, 45] Generated Node #0,1: 64:[11, 8, 45] Operation: 90-45=45 Moving to Node #0,1 Current State: 64:[11, 8, 45], Operations: ['90-45=45'] Exploring Operation: 11+45=56, Resulting Numbers: [8, 56] Generated Node #0,1,1: 64:[8, 56] Operation: 11+45=56 Moving to Node #0,1,1 Current State: 64:[8, 56], Operations: ['90-45=45', '11+45=56'] Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.984375
hs_2
sum_heuristic
[ 33, 37, 28, 33 ]
79
[ "37-33=4", "28*4=112", "112-33=79" ]
Current State: 79:[33, 37, 28, 33], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [28, 4] Generated Node #2: [28, 4] from Operation: 37-33=4 Current State: 79:[28, 4], Operations: ['37-33=4'] Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,79 equal: Goal Reached Exploring Operation: 112-33=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[33, 37, 28, 33], Operations: [] Exploring Operation: 33+37=70, Resulting Numbers: [28, 33, 70] Generated Node #0,0: 79:[28, 33, 70] Operation: 33+37=70 Exploring Operation: 33+28=61, Resulting Numbers: [37, 33, 61] Generated Node #0,1: 79:[37, 33, 61] Operation: 33+28=61 Exploring Operation: 33+33=66, Resulting Numbers: [37, 28, 66] Generated Node #0,2: 79:[37, 28, 66] Operation: 33+33=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[28, 33, 70], Operations: ['33+37=70'] Exploring Operation: 28+33=61, Resulting Numbers: [70, 61] Generated Node #0,0,0: 79:[70, 61] Operation: 28+33=61 Exploring Operation: 33+70=103, Resulting Numbers: [28, 103] Generated Node #0,0,1: 79:[28, 103] Operation: 33+70=103 Exploring Operation: 28+70=98, Resulting Numbers: [33, 98] Generated Node #0,0,2: 79:[33, 98] Operation: 28+70=98 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[70, 61], Operations: ['33+37=70', '28+33=61'] Exploring Operation: 70+61=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 70*61=4270, Resulting Numbers: [4270] 4270,79 unequal: No Solution Exploring Operation: 70-61=9, Resulting Numbers: [9] 9,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[33, 98], Operations: ['33+37=70', '28+70=98'] Exploring Operation: 98-33=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 33+98=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 33*98=3234, Resulting Numbers: [3234] 3234,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[28, 103], Operations: ['33+37=70', '33+70=103'] Exploring Operation: 28+103=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 28*103=2884, Resulting Numbers: [2884] 2884,79 unequal: No Solution Exploring Operation: 103-28=75, Resulting Numbers: [75] 75,79 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: 79:[37, 33, 61], Operations: ['33+28=61'] Exploring Operation: 37+33=70, Resulting Numbers: [61, 70] Generated Node #0,1,0: 79:[61, 70] Operation: 37+33=70 Exploring Operation: 33+61=94, Resulting Numbers: [37, 94] Generated Node #0,1,1: 79:[37, 94] Operation: 33+61=94 Exploring Operation: 37+61=98, Resulting Numbers: [33, 98] Generated Node #0,1,2: 79:[33, 98] Operation: 37+61=98 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[61, 70], Operations: ['33+28=61', '37+33=70'] Exploring Operation: 70-61=9, Resulting Numbers: [9] 9,79 unequal: No Solution Exploring Operation: 61+70=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 61*70=4270, Resulting Numbers: [4270] 4270,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[37, 94], Operations: ['33+28=61', '33+61=94'] Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,79 unequal: No Solution Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[33, 98], Operations: ['33+28=61', '37+61=98'] Exploring Operation: 33*98=3234, Resulting Numbers: [3234] 3234,79 unequal: No Solution Exploring Operation: 33+98=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 98-33=65, Resulting Numbers: [65] 65,79 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: 79:[37, 28, 66], Operations: ['33+33=66'] Exploring Operation: 37+28=65, Resulting Numbers: [66, 65] Generated Node #0,2,0: 79:[66, 65] Operation: 37+28=65 Exploring Operation: 28+66=94, Resulting Numbers: [37, 94] Generated Node #0,2,1: 79:[37, 94] Operation: 28+66=94 Exploring Operation: 37+66=103, Resulting Numbers: [28, 103] Generated Node #0,2,2: 79:[28, 103] Operation: 37+66=103 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[66, 65], Operations: ['33+33=66', '37+28=65'] Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,79 unequal: No Solution Exploring Operation: 66+65=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 66*65=4290, Resulting Numbers: [4290] 4290,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 79:[37, 94], Operations: ['33+33=66', '28+66=94'] Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,79 unequal: No Solution Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[28, 103], Operations: ['33+33=66', '37+66=103'] Exploring Operation: 28*103=2884, Resulting Numbers: [2884] 2884,79 unequal: No Solution Exploring Operation: 103-28=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 28+103=131, Resulting Numbers: [131] 131,79 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
[ 99, 44, 66, 97 ]
20
[ "99+44=143", "66+97=163", "163-143=20" ]
Current State: 20:[99, 44, 66, 97], Operations: [] Exploring Operation: 99+44=143, Resulting Numbers: [66, 97, 143] Generated Node #2: [66, 97, 143] from Operation: 99+44=143 Current State: 20:[66, 97, 143], Operations: ['99+44=143'] Exploring Operation: 66+97=163, Resulting Numbers: [143, 163] Generated Node #3: [143, 163] from Operation: 66+97=163 Current State: 20:[143, 163], Operations: ['99+44=143', '66+97=163'] Exploring Operation: 163-143=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[99, 44, 66, 97], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [44, 66, 2] Generated Node #0,0: 20:[44, 66, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 20:[44, 66, 2], Operations: ['99-97=2'] Exploring Operation: 66-44=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 20:[2, 22] Operation: 66-44=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[2, 22], Operations: ['99-97=2', '66-44=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[99, 44, 66, 97], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [44, 66, 2] Generated Node #0,0: 20:[44, 66, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 20:[44, 66, 2], Operations: ['99-97=2'] Exploring Operation: 66-44=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 20:[2, 22] Operation: 66-44=22 Moving to Node #0,0,0 Current State: 20:[2, 22], Operations: ['99-97=2', '66-44=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 19, 22, 83, 2 ]
96
[ "22*83=1826", "1826-2=1824", "1824/19=96" ]
Current State: 96:[19, 22, 83, 2], Operations: [] Exploring Operation: 22*83=1826, Resulting Numbers: [19, 2, 1826] Generated Node #2: [19, 2, 1826] from Operation: 22*83=1826 Current State: 96:[19, 2, 1826], Operations: ['22*83=1826'] Exploring Operation: 1826-2=1824, Resulting Numbers: [19, 1824] Generated Node #3: [19, 1824] from Operation: 1826-2=1824 Current State: 96:[19, 1824], Operations: ['22*83=1826', '1826-2=1824'] Exploring Operation: 1824/19=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[19, 22, 83, 2], Operations: [] Exploring Operation: 19+83=102, Resulting Numbers: [22, 2, 102] Generated Node #0,0: 96:[22, 2, 102] Operation: 19+83=102 Exploring Operation: 22+83=105, Resulting Numbers: [19, 2, 105] Generated Node #0,1: 96:[19, 2, 105] Operation: 22+83=105 Moving to Node #0,0 Current State: 96:[22, 2, 102], Operations: ['19+83=102'] Exploring Operation: 22+2=24, Resulting Numbers: [102, 24] Generated Node #0,0,0: 96:[102, 24] Operation: 22+2=24 Exploring Operation: 102/2=51, Resulting Numbers: [22, 51] Generated Node #0,0,1: 96:[22, 51] Operation: 102/2=51 Moving to Node #0,1 Current State: 96:[19, 2, 105], Operations: ['22+83=105'] Exploring Operation: 105-19=86, Resulting Numbers: [2, 86] Generated Node #0,1,0: 96:[2, 86] Operation: 105-19=86 Exploring Operation: 19-2=17, Resulting Numbers: [105, 17] Generated Node #0,1,1: 96:[105, 17] Operation: 19-2=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[2, 86], Operations: ['22+83=105', '105-19=86'] Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,96 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,96 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 #0,1,1 Current State: 96:[105, 17], Operations: ['22+83=105', '19-2=17'] Exploring Operation: 105+17=122, Resulting Numbers: [122] 122,96 unequal: No Solution Exploring Operation: 105-17=88, Resulting Numbers: [88] 88,96 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: 96:[22, 51], Operations: ['19+83=102', '102/2=51'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 22+51=73, Resulting Numbers: [73] 73,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[102, 24], Operations: ['19+83=102', '22+2=24'] Exploring Operation: 102-24=78, Resulting Numbers: [78] 78,96 unequal: No Solution Exploring Operation: 102+24=126, Resulting Numbers: [126] 126,96 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 54, 75, 81, 71 ]
62
[ "81-75=6", "54/6=9", "71-9=62" ]
Current State: 62:[54, 75, 81, 71], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [54, 71, 6] Generated Node #2: [54, 71, 6] from Operation: 81-75=6 Current State: 62:[54, 71, 6], Operations: ['81-75=6'] Exploring Operation: 54/6=9, Resulting Numbers: [71, 9] Generated Node #3: [71, 9] from Operation: 54/6=9 Current State: 62:[71, 9], Operations: ['81-75=6', '54/6=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[54, 75, 81, 71], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [54, 71, 6] Generated Node #0,0: 62:[54, 71, 6] Operation: 81-75=6 Exploring Operation: 75-71=4, Resulting Numbers: [54, 81, 4] Generated Node #0,1: 62:[54, 81, 4] Operation: 75-71=4 Exploring Operation: 81-71=10, Resulting Numbers: [54, 75, 10] Generated Node #0,2: 62:[54, 75, 10] Operation: 81-71=10 Exploring Operation: 81-54=27, Resulting Numbers: [75, 71, 27] Generated Node #0,3: 62:[75, 71, 27] Operation: 81-54=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[54, 71, 6], Operations: ['81-75=6'] Exploring Operation: 71-6=65, Resulting Numbers: [54, 65] Generated Node #0,0,0: 62:[54, 65] Operation: 71-6=65 Exploring Operation: 54+6=60, Resulting Numbers: [71, 60] Generated Node #0,0,1: 62:[71, 60] Operation: 54+6=60 Exploring Operation: 54/6=9, Resulting Numbers: [71, 9] Generated Node #0,0,2: 62:[71, 9] Operation: 54/6=9 Exploring Operation: 71-54=17, Resulting Numbers: [6, 17] Generated Node #0,0,3: 62:[6, 17] Operation: 71-54=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[54, 65], Operations: ['81-75=6', '71-6=65'] Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,62 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,62 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[71, 60], Operations: ['81-75=6', '54+6=60'] Exploring Operation: 71*60=4260, Resulting Numbers: [4260] 4260,62 unequal: No Solution Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 71+60=131, Resulting Numbers: [131] 131,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[71, 9], Operations: ['81-75=6', '54/6=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[54, 75, 81, 71], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [54, 71, 6] Generated Node #0,0: 62:[54, 71, 6] Operation: 81-75=6 Moving to Node #0,0 Current State: 62:[54, 71, 6], Operations: ['81-75=6'] Exploring Operation: 54/6=9, Resulting Numbers: [71, 9] Generated Node #0,0,2: 62:[71, 9] Operation: 54/6=9 Moving to Node #0,0,2 Current State: 62:[71, 9], Operations: ['81-75=6', '54/6=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 33, 26, 83, 24 ]
100
[ "33-26=7", "83+24=107", "107-7=100" ]
Current State: 100:[33, 26, 83, 24], Operations: [] Exploring Operation: 33-26=7, Resulting Numbers: [83, 24, 7] Generated Node #2: [83, 24, 7] from Operation: 33-26=7 Current State: 100:[83, 24, 7], Operations: ['33-26=7'] Exploring Operation: 83+24=107, Resulting Numbers: [7, 107] Generated Node #3: [7, 107] from Operation: 83+24=107 Current State: 100:[7, 107], Operations: ['33-26=7', '83+24=107'] Exploring Operation: 107-7=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[33, 26, 83, 24], Operations: [] Exploring Operation: 83+24=107, Resulting Numbers: [33, 26, 107] Generated Node #0,0: 100:[33, 26, 107] Operation: 83+24=107 Exploring Operation: 83-26=57, Resulting Numbers: [33, 24, 57] Generated Node #0,1: 100:[33, 24, 57] Operation: 83-26=57 Exploring Operation: 83-33=50, Resulting Numbers: [26, 24, 50] Generated Node #0,2: 100:[26, 24, 50] Operation: 83-33=50 Moving to Node #0,2 Current State: 100:[26, 24, 50], Operations: ['83-33=50'] Exploring Operation: 50-26=24, Resulting Numbers: [24, 24] Generated Node #0,2,0: 100:[24, 24] Operation: 50-26=24 Exploring Operation: 26-24=2, Resulting Numbers: [50, 2] Generated Node #0,2,1: 100:[50, 2] Operation: 26-24=2 Exploring Operation: 26+24=50, Resulting Numbers: [50, 50] Generated Node #0,2,2: 100:[50, 50] Operation: 26+24=50 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[50, 2], Operations: ['83-33=50', '26-24=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[33, 26, 83, 24], Operations: [] Exploring Operation: 83-33=50, Resulting Numbers: [26, 24, 50] Generated Node #0,2: 100:[26, 24, 50] Operation: 83-33=50 Moving to Node #0,2 Current State: 100:[26, 24, 50], Operations: ['83-33=50'] Exploring Operation: 26-24=2, Resulting Numbers: [50, 2] Generated Node #0,2,1: 100:[50, 2] Operation: 26-24=2 Moving to Node #0,2,1 Current State: 100:[50, 2], Operations: ['83-33=50', '26-24=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 36, 39, 77, 18 ]
58
[ "36/18=2", "39+77=116", "116/2=58" ]
Current State: 58:[36, 39, 77, 18], Operations: [] Exploring Operation: 36/18=2, Resulting Numbers: [39, 77, 2] Generated Node #2: [39, 77, 2] from Operation: 36/18=2 Current State: 58:[39, 77, 2], Operations: ['36/18=2'] Exploring Operation: 39+77=116, Resulting Numbers: [2, 116] Generated Node #3: [2, 116] from Operation: 39+77=116 Current State: 58:[2, 116], Operations: ['36/18=2', '39+77=116'] Exploring Operation: 116/2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[36, 39, 77, 18], Operations: [] Exploring Operation: 77-18=59, Resulting Numbers: [36, 39, 59] Generated Node #0,0: 58:[36, 39, 59] Operation: 77-18=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[36, 39, 59], Operations: ['77-18=59'] Exploring Operation: 39-36=3, Resulting Numbers: [59, 3] Generated Node #0,0,0: 58:[59, 3] Operation: 39-36=3 Moving to Node #0,0,0 Current State: 58:[59, 3], Operations: ['77-18=59', '39-36=3'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,58 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
[ 42, 29, 85, 78 ]
78
[ "42+29=71", "85-78=7", "71+7=78" ]
Current State: 78:[42, 29, 85, 78], Operations: [] Exploring Operation: 42+29=71, Resulting Numbers: [85, 78, 71] Generated Node #2: [85, 78, 71] from Operation: 42+29=71 Current State: 78:[85, 78, 71], Operations: ['42+29=71'] Exploring Operation: 85-78=7, Resulting Numbers: [71, 7] Generated Node #3: [71, 7] from Operation: 85-78=7 Current State: 78:[71, 7], Operations: ['42+29=71', '85-78=7'] Exploring Operation: 71+7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[42, 29, 85, 78], Operations: [] Exploring Operation: 42-29=13, Resulting Numbers: [85, 78, 13] Generated Node #0,0: 78:[85, 78, 13] Operation: 42-29=13 Exploring Operation: 85-42=43, Resulting Numbers: [29, 78, 43] Generated Node #0,1: 78:[29, 78, 43] Operation: 85-42=43 Moving to Node #0,0 Current State: 78:[85, 78, 13], Operations: ['42-29=13'] Exploring Operation: 85-13=72, Resulting Numbers: [78, 72] Generated Node #0,0,0: 78:[78, 72] Operation: 85-13=72 Exploring Operation: 85-78=7, Resulting Numbers: [13, 7] Generated Node #0,0,1: 78:[13, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[13, 7], Operations: ['42-29=13', '85-78=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,78 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[78, 72], Operations: ['42-29=13', '85-13=72'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 78+72=150, Resulting Numbers: [150] 150,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 78:[29, 78, 43], Operations: ['85-42=43'] Exploring Operation: 29+43=72, Resulting Numbers: [78, 72] Generated Node #0,1,0: 78:[78, 72] Operation: 29+43=72 Exploring Operation: 43-29=14, Resulting Numbers: [78, 14] Generated Node #0,1,1: 78:[78, 14] Operation: 43-29=14 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[78, 14], Operations: ['85-42=43', '43-29=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,78 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[78, 72], Operations: ['85-42=43', '29+43=72'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 78+72=150, Resulting Numbers: [150] 150,78 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
[ 24, 63, 70, 30 ]
61
[ "63-24=39", "70+30=100", "100-39=61" ]
Current State: 61:[24, 63, 70, 30], Operations: [] Exploring Operation: 63-24=39, Resulting Numbers: [70, 30, 39] Generated Node #2: [70, 30, 39] from Operation: 63-24=39 Current State: 61:[70, 30, 39], Operations: ['63-24=39'] Exploring Operation: 70+30=100, Resulting Numbers: [39, 100] Generated Node #3: [39, 100] from Operation: 70+30=100 Current State: 61:[39, 100], Operations: ['63-24=39', '70+30=100'] Exploring Operation: 100-39=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[24, 63, 70, 30], Operations: [] Exploring Operation: 70-24=46, Resulting Numbers: [63, 30, 46] Generated Node #0,0: 61:[63, 30, 46] Operation: 70-24=46 Exploring Operation: 24+63=87, Resulting Numbers: [70, 30, 87] Generated Node #0,1: 61:[70, 30, 87] Operation: 24+63=87 Exploring Operation: 63-24=39, Resulting Numbers: [70, 30, 39] Generated Node #0,2: 61:[70, 30, 39] Operation: 63-24=39 Exploring Operation: 24+30=54, Resulting Numbers: [63, 70, 54] Generated Node #0,3: 61:[63, 70, 54] Operation: 24+30=54 Exploring Operation: 70-30=40, Resulting Numbers: [24, 63, 40] Generated Node #0,4: 61:[24, 63, 40] Operation: 70-30=40 Moving to Node #0,3 Current State: 61:[63, 70, 54], Operations: ['24+30=54'] Exploring Operation: 70-54=16, Resulting Numbers: [63, 16] Generated Node #0,3,0: 61:[63, 16] Operation: 70-54=16 Exploring Operation: 70-63=7, Resulting Numbers: [54, 7] Generated Node #0,3,1: 61:[54, 7] Operation: 70-63=7 Exploring Operation: 63+54=117, Resulting Numbers: [70, 117] Generated Node #0,3,2: 61:[70, 117] Operation: 63+54=117 Exploring Operation: 63-54=9, Resulting Numbers: [70, 9] Generated Node #0,3,3: 61:[70, 9] Operation: 63-54=9 Exploring Operation: 70+54=124, Resulting Numbers: [63, 124] Generated Node #0,3,4: 61:[63, 124] Operation: 70+54=124 Moving to Node #0,0 Current State: 61:[63, 30, 46], Operations: ['70-24=46'] Exploring Operation: 63-30=33, Resulting Numbers: [46, 33] Generated Node #0,0,0: 61:[46, 33] Operation: 63-30=33 Exploring Operation: 30+46=76, Resulting Numbers: [63, 76] Generated Node #0,0,1: 61:[63, 76] Operation: 30+46=76 Exploring Operation: 63+30=93, Resulting Numbers: [46, 93] Generated Node #0,0,2: 61:[46, 93] Operation: 63+30=93 Exploring Operation: 46-30=16, Resulting Numbers: [63, 16] Generated Node #0,0,3: 61:[63, 16] Operation: 46-30=16 Exploring Operation: 63-46=17, Resulting Numbers: [30, 17] Generated Node #0,0,4: 61:[30, 17] Operation: 63-46=17 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[63, 76], Operations: ['70-24=46', '30+46=76'] Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 63*76=4788, Resulting Numbers: [4788] 4788,61 unequal: No Solution Exploring Operation: 63+76=139, Resulting Numbers: [139] 139,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[46, 33], Operations: ['70-24=46', '63-30=33'] Exploring Operation: 46*33=1518, Resulting Numbers: [1518] 1518,61 unequal: No Solution Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[46, 93], Operations: ['70-24=46', '63+30=93'] Exploring Operation: 46*93=4278, Resulting Numbers: [4278] 4278,61 unequal: No Solution Exploring Operation: 46+93=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 93-46=47, Resulting Numbers: [47] 47,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[63, 16], Operations: ['70-24=46', '46-30=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 61:[30, 17], Operations: ['70-24=46', '63-46=17'] Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,61 unequal: No Solution Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,61 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: 61:[24, 63, 40], Operations: ['70-30=40'] Exploring Operation: 24+40=64, Resulting Numbers: [63, 64] Generated Node #0,4,0: 61:[63, 64] Operation: 24+40=64 Exploring Operation: 24+63=87, Resulting Numbers: [40, 87] Generated Node #0,4,1: 61:[40, 87] Operation: 24+63=87 Exploring Operation: 63-24=39, Resulting Numbers: [40, 39] Generated Node #0,4,2: 61:[40, 39] Operation: 63-24=39 Exploring Operation: 40-24=16, Resulting Numbers: [63, 16] Generated Node #0,4,3: 61:[63, 16] Operation: 40-24=16 Exploring Operation: 63-40=23, Resulting Numbers: [24, 23] Generated Node #0,4,4: 61:[24, 23] Operation: 63-40=23 Moving to Node #0,2 Current State: 61:[70, 30, 39], Operations: ['63-24=39'] Exploring Operation: 39-30=9, Resulting Numbers: [70, 9] Generated Node #0,2,0: 61:[70, 9] Operation: 39-30=9 Exploring Operation: 70-39=31, Resulting Numbers: [30, 31] Generated Node #0,2,1: 61:[30, 31] Operation: 70-39=31 Exploring Operation: 70+30=100, Resulting Numbers: [39, 100] Generated Node #0,2,2: 61:[39, 100] Operation: 70+30=100 Exploring Operation: 70-30=40, Resulting Numbers: [39, 40] Generated Node #0,2,3: 61:[39, 40] Operation: 70-30=40 Exploring Operation: 30+39=69, Resulting Numbers: [70, 69] Generated Node #0,2,4: 61:[70, 69] Operation: 30+39=69 Moving to Node #0,1 Current State: 61:[70, 30, 87], Operations: ['24+63=87'] Exploring Operation: 70+30=100, Resulting Numbers: [87, 100] Generated Node #0,1,0: 61:[87, 100] Operation: 70+30=100 Exploring Operation: 87-70=17, Resulting Numbers: [30, 17] Generated Node #0,1,1: 61:[30, 17] Operation: 87-70=17 Exploring Operation: 30+87=117, Resulting Numbers: [70, 117] Generated Node #0,1,2: 61:[70, 117] Operation: 30+87=117 Exploring Operation: 70-30=40, Resulting Numbers: [87, 40] Generated Node #0,1,3: 61:[87, 40] Operation: 70-30=40 Exploring Operation: 87-30=57, Resulting Numbers: [70, 57] Generated Node #0,1,4: 61:[70, 57] Operation: 87-30=57 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 61:[70, 57], Operations: ['24+63=87', '87-30=57'] Exploring Operation: 70+57=127, Resulting Numbers: [127] 127,61 unequal: No Solution Exploring Operation: 70*57=3990, Resulting Numbers: [3990] 3990,61 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 61:[87, 40], Operations: ['24+63=87', '70-30=40'] Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 87*40=3480, Resulting Numbers: [3480] 3480,61 unequal: No Solution Exploring Operation: 87+40=127, Resulting Numbers: [127] 127,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[87, 100], Operations: ['24+63=87', '70+30=100'] Exploring Operation: 87+100=187, Resulting Numbers: [187] 187,61 unequal: No Solution Exploring Operation: 100-87=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 87*100=8700, Resulting Numbers: [8700] 8700,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[70, 117], Operations: ['24+63=87', '30+87=117'] Exploring Operation: 70*117=8190, Resulting Numbers: [8190] 8190,61 unequal: No Solution Exploring Operation: 117-70=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 70+117=187, Resulting Numbers: [187] 187,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[30, 17], Operations: ['24+63=87', '87-70=17'] Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,61 unequal: No Solution Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 61:[63, 64], Operations: ['70-30=40', '24+40=64'] Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,61 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,61 unequal: No Solution Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,2,4 Current State: 61:[70, 69], Operations: ['63-24=39', '30+39=69'] Exploring Operation: 70*69=4830, Resulting Numbers: [4830] 4830,61 unequal: No Solution Exploring Operation: 70+69=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[40, 39], Operations: ['70-30=40', '63-24=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[39, 40], Operations: ['63-24=39', '70-30=40'] Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,61 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[63, 16], Operations: ['24+30=54', '70-54=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Moving to Node #0,4,1 Current State: 61:[40, 87], Operations: ['70-30=40', '24+63=87'] Exploring Operation: 40*87=3480, Resulting Numbers: [3480] 3480,61 unequal: No Solution Exploring Operation: 40+87=127, Resulting Numbers: [127] 127,61 unequal: No Solution Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,61 unequal: No Solution Moving to Node #0,4,3 Current State: 61:[63, 16], Operations: ['70-30=40', '40-24=16'] Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,61 unequal: No Solution Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[30, 31], Operations: ['63-24=39', '70-39=31'] Exploring Operation: 30*31=930, Resulting Numbers: [930] 930,61 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[24, 63, 70, 30], Operations: [] Exploring Operation: 63-24=39, Resulting Numbers: [70, 30, 39] Generated Node #0,2: 61:[70, 30, 39] Operation: 63-24=39 Moving to Node #0,2 Current State: 61:[70, 30, 39], Operations: ['63-24=39'] Exploring Operation: 70-39=31, Resulting Numbers: [30, 31] Generated Node #0,2,1: 61:[30, 31] Operation: 70-39=31 Moving to Node #0,2,1 Current State: 61:[30, 31], Operations: ['63-24=39', '70-39=31'] Exploring Operation: 30+31=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.923611
hs_5
sum_heuristic
[ 68, 84, 48, 4 ]
55
[ "68+48=116", "116/4=29", "84-29=55" ]
Current State: 55:[68, 84, 48, 4], Operations: [] Exploring Operation: 68+48=116, Resulting Numbers: [84, 4, 116] Generated Node #2: [84, 4, 116] from Operation: 68+48=116 Current State: 55:[84, 4, 116], Operations: ['68+48=116'] Exploring Operation: 116/4=29, Resulting Numbers: [84, 29] Generated Node #3: [84, 29] from Operation: 116/4=29 Current State: 55:[84, 29], Operations: ['68+48=116', '116/4=29'] Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[68, 84, 48, 4], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [48, 4, 16] Generated Node #0,0: 55:[48, 4, 16] Operation: 84-68=16 Exploring Operation: 84-48=36, Resulting Numbers: [68, 4, 36] Generated Node #0,1: 55:[68, 4, 36] Operation: 84-48=36 Exploring Operation: 84/4=21, Resulting Numbers: [68, 48, 21] Generated Node #0,2: 55:[68, 48, 21] Operation: 84/4=21 Moving to Node #0,0 Current State: 55:[48, 4, 16], Operations: ['84-68=16'] Exploring Operation: 48/4=12, Resulting Numbers: [16, 12] Generated Node #0,0,0: 55:[16, 12] Operation: 48/4=12 Exploring Operation: 48/16=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 55:[4, 3] Operation: 48/16=3 Exploring Operation: 48+4=52, Resulting Numbers: [16, 52] Generated Node #0,0,2: 55:[16, 52] Operation: 48+4=52 Moving to Node #0,2 Current State: 55:[68, 48, 21], Operations: ['84/4=21'] Exploring Operation: 68-21=47, Resulting Numbers: [48, 47] Generated Node #0,2,0: 55:[48, 47] Operation: 68-21=47 Exploring Operation: 68-48=20, Resulting Numbers: [21, 20] Generated Node #0,2,1: 55:[21, 20] Operation: 68-48=20 Exploring Operation: 48+21=69, Resulting Numbers: [68, 69] Generated Node #0,2,2: 55:[68, 69] Operation: 48+21=69 Moving to Node #0,1 Current State: 55:[68, 4, 36], Operations: ['84-48=36'] Exploring Operation: 68/4=17, Resulting Numbers: [36, 17] Generated Node #0,1,0: 55:[36, 17] Operation: 68/4=17 Exploring Operation: 36/4=9, Resulting Numbers: [68, 9] Generated Node #0,1,1: 55:[68, 9] Operation: 36/4=9 Exploring Operation: 68-36=32, Resulting Numbers: [4, 32] Generated Node #0,1,2: 55:[4, 32] Operation: 68-36=32 Moving to Node #0,0,1 Current State: 55:[4, 3], Operations: ['84-68=16', '48/16=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[16, 12], Operations: ['84-68=16', '48/4=12'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,55 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[16, 52], Operations: ['84-68=16', '48+4=52'] Exploring Operation: 52-16=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 16*52=832, Resulting Numbers: [832] 832,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[68, 9], Operations: ['84-48=36', '36/4=9'] Exploring Operation: 68+9=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 68*9=612, Resulting Numbers: [612] 612,55 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,55 unequal: No Solution Moving to Node #0,2,0 Current State: 55:[48, 47], Operations: ['84/4=21', '68-21=47'] Exploring Operation: 48+47=95, Resulting Numbers: [95] 95,55 unequal: No Solution Exploring Operation: 48*47=2256, Resulting Numbers: [2256] 2256,55 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[21, 20], Operations: ['84/4=21', '68-48=20'] Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,55 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[4, 32], Operations: ['84-48=36', '68-36=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[36, 17], Operations: ['84-48=36', '68/4=17'] Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,55 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,55 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[68, 69], Operations: ['84/4=21', '48+21=69'] Exploring Operation: 68*69=4692, Resulting Numbers: [4692] 4692,55 unequal: No Solution Exploring Operation: 68+69=137, Resulting Numbers: [137] 137,55 unequal: No Solution Exploring Operation: 69-68=1, Resulting Numbers: [1] 1,55 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 35, 52, 18, 7 ]
75
[ "35/7=5", "52+18=70", "5+70=75" ]
Current State: 75:[35, 52, 18, 7], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [52, 18, 5] Generated Node #2: [52, 18, 5] from Operation: 35/7=5 Current State: 75:[52, 18, 5], Operations: ['35/7=5'] Exploring Operation: 52+18=70, Resulting Numbers: [5, 70] Generated Node #3: [5, 70] from Operation: 52+18=70 Current State: 75:[5, 70], Operations: ['35/7=5', '52+18=70'] Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[35, 52, 18, 7], Operations: [] Exploring Operation: 52-35=17, Resulting Numbers: [18, 7, 17] Generated Node #0,0: 75:[18, 7, 17] Operation: 52-35=17 Exploring Operation: 52+18=70, Resulting Numbers: [35, 7, 70] Generated Node #0,1: 75:[35, 7, 70] Operation: 52+18=70 Exploring Operation: 52-18=34, Resulting Numbers: [35, 7, 34] Generated Node #0,2: 75:[35, 7, 34] Operation: 52-18=34 Exploring Operation: 35+52=87, Resulting Numbers: [18, 7, 87] Generated Node #0,3: 75:[18, 7, 87] Operation: 35+52=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[18, 7, 17], Operations: ['52-35=17'] Exploring Operation: 7+17=24, Resulting Numbers: [18, 24] Generated Node #0,0,0: 75:[18, 24] Operation: 7+17=24 Exploring Operation: 18+7=25, Resulting Numbers: [17, 25] Generated Node #0,0,1: 75:[17, 25] Operation: 18+7=25 Exploring Operation: 18-7=11, Resulting Numbers: [17, 11] Generated Node #0,0,2: 75:[17, 11] Operation: 18-7=11 Exploring Operation: 18-17=1, Resulting Numbers: [7, 1] Generated Node #0,0,3: 75:[7, 1] Operation: 18-17=1 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[17, 25], Operations: ['52-35=17', '18+7=25'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,75 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,75 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:[18, 24], Operations: ['52-35=17', '7+17=24'] Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,75 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,75 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,75 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:[7, 1], Operations: ['52-35=17', '18-17=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,75 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:[17, 11], Operations: ['52-35=17', '18-7=11'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,75 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:[35, 7, 70], Operations: ['52+18=70'] Exploring Operation: 35/7=5, Resulting Numbers: [70, 5] Generated Node #0,1,0: 75:[70, 5] Operation: 35/7=5 Exploring Operation: 70/35=2, Resulting Numbers: [7, 2] Generated Node #0,1,1: 75:[7, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [7, 35] Generated Node #0,1,2: 75:[7, 35] Operation: 70-35=35 Exploring Operation: 35-7=28, Resulting Numbers: [70, 28] Generated Node #0,1,3: 75:[70, 28] Operation: 35-7=28 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[7, 2], Operations: ['52+18=70', '70/35=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,75 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 #0,1,0 Current State: 75:[70, 5], Operations: ['52+18=70', '35/7=5'] Exploring Operation: 70*5=350, Resulting Numbers: [350] 350,75 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,75 unequal: No Solution Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[35, 52, 18, 7], Operations: [] Exploring Operation: 52+18=70, Resulting Numbers: [35, 7, 70] Generated Node #0,1: 75:[35, 7, 70] Operation: 52+18=70 Moving to Node #0,1 Current State: 75:[35, 7, 70], Operations: ['52+18=70'] Exploring Operation: 35/7=5, Resulting Numbers: [70, 5] Generated Node #0,1,0: 75:[70, 5] Operation: 35/7=5 Moving to Node #0,1,0 Current State: 75:[70, 5], Operations: ['52+18=70', '35/7=5'] Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_4
mult_heuristic
[ 49, 2, 50, 59 ]
11
[ "49*2=98", "50+59=109", "109-98=11" ]
Current State: 11:[49, 2, 50, 59], Operations: [] Exploring Operation: 49*2=98, Resulting Numbers: [50, 59, 98] Generated Node #2: [50, 59, 98] from Operation: 49*2=98 Current State: 11:[50, 59, 98], Operations: ['49*2=98'] Exploring Operation: 50+59=109, Resulting Numbers: [98, 109] Generated Node #3: [98, 109] from Operation: 50+59=109 Current State: 11:[98, 109], Operations: ['49*2=98', '50+59=109'] Exploring Operation: 109-98=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[49, 2, 50, 59], Operations: [] Exploring Operation: 59-49=10, Resulting Numbers: [2, 50, 10] Generated Node #0,0: 11:[2, 50, 10] Operation: 59-49=10 Exploring Operation: 49-2=47, Resulting Numbers: [50, 59, 47] Generated Node #0,1: 11:[50, 59, 47] Operation: 49-2=47 Exploring Operation: 50/2=25, Resulting Numbers: [49, 59, 25] Generated Node #0,2: 11:[49, 59, 25] Operation: 50/2=25 Exploring Operation: 59-50=9, Resulting Numbers: [49, 2, 9] Generated Node #0,3: 11:[49, 2, 9] Operation: 59-50=9 Exploring Operation: 50-49=1, Resulting Numbers: [2, 59, 1] Generated Node #0,4: 11:[2, 59, 1] Operation: 50-49=1 Moving to Node #0,0 Current State: 11:[2, 50, 10], Operations: ['59-49=10'] Exploring Operation: 50/2=25, Resulting Numbers: [10, 25] Generated Node #0,0,0: 11:[10, 25] Operation: 50/2=25 Exploring Operation: 50-2=48, Resulting Numbers: [10, 48] Generated Node #0,0,1: 11:[10, 48] Operation: 50-2=48 Exploring Operation: 2+10=12, Resulting Numbers: [50, 12] Generated Node #0,0,2: 11:[50, 12] Operation: 2+10=12 Exploring Operation: 50/10=5, Resulting Numbers: [2, 5] Generated Node #0,0,3: 11:[2, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [2, 40] Generated Node #0,0,4: 11:[2, 40] Operation: 50-10=40 Moving to Node #0,3 Current State: 11:[49, 2, 9], Operations: ['59-50=9'] Exploring Operation: 49-9=40, Resulting Numbers: [2, 40] Generated Node #0,3,0: 11:[2, 40] Operation: 49-9=40 Exploring Operation: 9-2=7, Resulting Numbers: [49, 7] Generated Node #0,3,1: 11:[49, 7] Operation: 9-2=7 Exploring Operation: 2+9=11, Resulting Numbers: [49, 11] Generated Node #0,3,2: 11:[49, 11] Operation: 2+9=11 Exploring Operation: 49-2=47, Resulting Numbers: [9, 47] Generated Node #0,3,3: 11:[9, 47] Operation: 49-2=47 Exploring Operation: 49+2=51, Resulting Numbers: [9, 51] Generated Node #0,3,4: 11:[9, 51] Operation: 49+2=51 Moving to Node #0,4 Current State: 11:[2, 59, 1], Operations: ['50-49=1'] Exploring Operation: 59-2=57, Resulting Numbers: [1, 57] Generated Node #0,4,0: 11:[1, 57] Operation: 59-2=57 Exploring Operation: 2+1=3, Resulting Numbers: [59, 3] Generated Node #0,4,1: 11:[59, 3] Operation: 2+1=3 Exploring Operation: 2*1=2, Resulting Numbers: [59, 2] Generated Node #0,4,2: 11:[59, 2] Operation: 2*1=2 Exploring Operation: 2/1=2, Resulting Numbers: [59, 2] Generated Node #0,4,3: 11:[59, 2] Operation: 2/1=2 Exploring Operation: 59-1=58, Resulting Numbers: [2, 58] Generated Node #0,4,4: 11:[2, 58] Operation: 59-1=58 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 11:[1, 57], Operations: ['50-49=1', '59-2=57'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,11 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,11 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 11:[59, 3], Operations: ['50-49=1', '2+1=3'] Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,11 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 11:[2, 58], Operations: ['50-49=1', '59-1=58'] Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,11 unequal: No Solution Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 11:[59, 2], Operations: ['50-49=1', '2*1=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 59*2=118, Resulting Numbers: [118] 118,11 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 11:[59, 2], Operations: ['50-49=1', '2/1=2'] Exploring Operation: 59*2=118, Resulting Numbers: [118] 118,11 unequal: No Solution Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 11:[49, 59, 25], Operations: ['50/2=25'] Exploring Operation: 49-25=24, Resulting Numbers: [59, 24] Generated Node #0,2,0: 11:[59, 24] Operation: 49-25=24 Exploring Operation: 49+25=74, Resulting Numbers: [59, 74] Generated Node #0,2,1: 11:[59, 74] Operation: 49+25=74 Exploring Operation: 59-49=10, Resulting Numbers: [25, 10] Generated Node #0,2,2: 11:[25, 10] Operation: 59-49=10 Exploring Operation: 59-25=34, Resulting Numbers: [49, 34] Generated Node #0,2,3: 11:[49, 34] Operation: 59-25=34 Exploring Operation: 49+59=108, Resulting Numbers: [25, 108] Generated Node #0,2,4: 11:[25, 108] Operation: 49+59=108 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[25, 10], Operations: ['50/2=25', '59-49=10'] Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,11 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[59, 24], Operations: ['50/2=25', '49-25=24'] Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 59*24=1416, Resulting Numbers: [1416] 1416,11 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[49, 34], Operations: ['50/2=25', '59-25=34'] Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,11 unequal: No Solution Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,11 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[59, 74], Operations: ['50/2=25', '49+25=74'] Exploring Operation: 74-59=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 59*74=4366, Resulting Numbers: [4366] 4366,11 unequal: No Solution Exploring Operation: 59+74=133, Resulting Numbers: [133] 133,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 11:[25, 108], Operations: ['50/2=25', '49+59=108'] Exploring Operation: 25+108=133, Resulting Numbers: [133] 133,11 unequal: No Solution Exploring Operation: 25*108=2700, Resulting Numbers: [2700] 2700,11 unequal: No Solution Exploring Operation: 108-25=83, Resulting Numbers: [83] 83,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 11:[50, 59, 47], Operations: ['49-2=47'] Exploring Operation: 50+59=109, Resulting Numbers: [47, 109] Generated Node #0,1,0: 11:[47, 109] Operation: 50+59=109 Exploring Operation: 50+47=97, Resulting Numbers: [59, 97] Generated Node #0,1,1: 11:[59, 97] Operation: 50+47=97 Exploring Operation: 59-50=9, Resulting Numbers: [47, 9] Generated Node #0,1,2: 11:[47, 9] Operation: 59-50=9 Exploring Operation: 50-47=3, Resulting Numbers: [59, 3] Generated Node #0,1,3: 11:[59, 3] Operation: 50-47=3 Exploring Operation: 59-47=12, Resulting Numbers: [50, 12] Generated Node #0,1,4: 11:[50, 12] Operation: 59-47=12 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[47, 9], Operations: ['49-2=47', '59-50=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,11 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 11:[50, 12], Operations: ['49-2=47', '59-47=12'] Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,11 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 11:[59, 3], Operations: ['49-2=47', '50-47=3'] Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,11 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[47, 109], Operations: ['49-2=47', '50+59=109'] Exploring Operation: 109-47=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 47*109=5123, Resulting Numbers: [5123] 5123,11 unequal: No Solution Exploring Operation: 47+109=156, Resulting Numbers: [156] 156,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[59, 97], Operations: ['49-2=47', '50+47=97'] Exploring Operation: 59*97=5723, Resulting Numbers: [5723] 5723,11 unequal: No Solution Exploring Operation: 97-59=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 59+97=156, Resulting Numbers: [156] 156,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 11:[10, 25], Operations: ['59-49=10', '50/2=25'] Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,11 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,11 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[2, 5], Operations: ['59-49=10', '50/10=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[10, 48], Operations: ['59-49=10', '50-2=48'] Exploring Operation: 10*48=480, Resulting Numbers: [480] 480,11 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[49, 11], Operations: ['59-50=9', '2+9=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,11 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[2, 40], Operations: ['59-50=9', '49-9=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,11 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[2, 40], Operations: ['59-49=10', '50-10=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[9, 47], Operations: ['59-50=9', '49-2=47'] Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,11 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,11 unequal: No Solution Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[50, 12], Operations: ['59-49=10', '2+10=12'] Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,11 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,11 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[49, 7], Operations: ['59-50=9', '9-2=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,11 unequal: No Solution Moving to Node #0,3,4 Current State: 11:[9, 51], Operations: ['59-50=9', '49+2=51'] Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,11 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 44, 61, 17, 67 ]
33
[ "61-44=17", "67-17=50", "50-17=33" ]
Current State: 33:[44, 61, 17, 67], Operations: [] Exploring Operation: 61-44=17, Resulting Numbers: [17, 67, 17] Generated Node #2: [17, 67, 17] from Operation: 61-44=17 Current State: 33:[17, 67, 17], Operations: ['61-44=17'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,33 equal: Goal Reached Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[44, 61, 17, 67], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [44, 17, 6] Generated Node #0,0: 33:[44, 17, 6] Operation: 67-61=6 Exploring Operation: 67-44=23, Resulting Numbers: [61, 17, 23] Generated Node #0,1: 33:[61, 17, 23] Operation: 67-44=23 Moving to Node #0,0 Current State: 33:[44, 17, 6], Operations: ['67-61=6'] Exploring Operation: 44-17=27, Resulting Numbers: [6, 27] Generated Node #0,0,0: 33:[6, 27] Operation: 44-17=27 Exploring Operation: 44-6=38, Resulting Numbers: [17, 38] Generated Node #0,0,1: 33:[17, 38] Operation: 44-6=38 Moving to Node #0,1 Current State: 33:[61, 17, 23], Operations: ['67-44=23'] Exploring Operation: 61-17=44, Resulting Numbers: [23, 44] Generated Node #0,1,0: 33:[23, 44] Operation: 61-17=44 Exploring Operation: 61-23=38, Resulting Numbers: [17, 38] Generated Node #0,1,1: 33:[17, 38] Operation: 61-23=38 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[17, 38], Operations: ['67-44=23', '61-23=38'] Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,33 unequal: No Solution Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[23, 44], Operations: ['67-44=23', '61-17=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,33 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,33 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: 33:[6, 27], Operations: ['67-61=6', '44-17=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[44, 61, 17, 67], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [44, 17, 6] Generated Node #0,0: 33:[44, 17, 6] Operation: 67-61=6 Moving to Node #0,0 Current State: 33:[44, 17, 6], Operations: ['67-61=6'] Exploring Operation: 44-17=27, Resulting Numbers: [6, 27] Generated Node #0,0,0: 33:[6, 27] Operation: 44-17=27 Moving to Node #0,0,0 Current State: 33:[6, 27], Operations: ['67-61=6', '44-17=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 25, 36, 44, 99 ]
82
[ "25+36=61", "44+99=143", "143-61=82" ]
Current State: 82:[25, 36, 44, 99], Operations: [] Exploring Operation: 25+36=61, Resulting Numbers: [44, 99, 61] Generated Node #2: [44, 99, 61] from Operation: 25+36=61 Current State: 82:[44, 99, 61], Operations: ['25+36=61'] Exploring Operation: 44+99=143, Resulting Numbers: [61, 143] Generated Node #3: [61, 143] from Operation: 44+99=143 Current State: 82:[61, 143], Operations: ['25+36=61', '44+99=143'] Exploring Operation: 143-61=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[25, 36, 44, 99], Operations: [] Exploring Operation: 36+44=80, Resulting Numbers: [25, 99, 80] Generated Node #0,0: 82:[25, 99, 80] Operation: 36+44=80 Exploring Operation: 25+44=69, Resulting Numbers: [36, 99, 69] Generated Node #0,1: 82:[36, 99, 69] Operation: 25+44=69 Exploring Operation: 99-44=55, Resulting Numbers: [25, 36, 55] Generated Node #0,2: 82:[25, 36, 55] Operation: 99-44=55 Exploring Operation: 99-25=74, Resulting Numbers: [36, 44, 74] Generated Node #0,3: 82:[36, 44, 74] Operation: 99-25=74 Exploring Operation: 36-25=11, Resulting Numbers: [44, 99, 11] Generated Node #0,4: 82:[44, 99, 11] Operation: 36-25=11 Moving to Node #0,3 Current State: 82:[36, 44, 74], Operations: ['99-25=74'] Exploring Operation: 74-36=38, Resulting Numbers: [44, 38] Generated Node #0,3,0: 82:[44, 38] Operation: 74-36=38 Exploring Operation: 44-36=8, Resulting Numbers: [74, 8] Generated Node #0,3,1: 82:[74, 8] Operation: 44-36=8 Exploring Operation: 36+44=80, Resulting Numbers: [74, 80] Generated Node #0,3,2: 82:[74, 80] Operation: 36+44=80 Exploring Operation: 36+74=110, Resulting Numbers: [44, 110] Generated Node #0,3,3: 82:[44, 110] Operation: 36+74=110 Exploring Operation: 74-44=30, Resulting Numbers: [36, 30] Generated Node #0,3,4: 82:[36, 30] Operation: 74-44=30 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 82:[44, 38], Operations: ['99-25=74', '74-36=38'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[25, 36, 44, 99], Operations: [] Exploring Operation: 99-25=74, Resulting Numbers: [36, 44, 74] Generated Node #0,3: 82:[36, 44, 74] Operation: 99-25=74 Moving to Node #0,3 Current State: 82:[36, 44, 74], Operations: ['99-25=74'] Exploring Operation: 74-36=38, Resulting Numbers: [44, 38] Generated Node #0,3,0: 82:[44, 38] Operation: 74-36=38 Moving to Node #0,3,0 Current State: 82:[44, 38], Operations: ['99-25=74', '74-36=38'] Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 69, 30, 93, 46 ]
52
[ "69+30=99", "93-46=47", "99-47=52" ]
Current State: 52:[69, 30, 93, 46], Operations: [] Exploring Operation: 69+30=99, Resulting Numbers: [93, 46, 99] Generated Node #2: [93, 46, 99] from Operation: 69+30=99 Current State: 52:[93, 46, 99], Operations: ['69+30=99'] Exploring Operation: 93-46=47, Resulting Numbers: [99, 47] Generated Node #3: [99, 47] from Operation: 93-46=47 Current State: 52:[99, 47], Operations: ['69+30=99', '93-46=47'] Exploring Operation: 99-47=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[69, 30, 93, 46], Operations: [] Exploring Operation: 93-30=63, Resulting Numbers: [69, 46, 63] Generated Node #0,0: 52:[69, 46, 63] Operation: 93-30=63 Exploring Operation: 69-46=23, Resulting Numbers: [30, 93, 23] Generated Node #0,1: 52:[30, 93, 23] Operation: 69-46=23 Exploring Operation: 93-69=24, Resulting Numbers: [30, 46, 24] Generated Node #0,2: 52:[30, 46, 24] Operation: 93-69=24 Exploring Operation: 93-46=47, Resulting Numbers: [69, 30, 47] Generated Node #0,3: 52:[69, 30, 47] Operation: 93-46=47 Moving to Node #0,2 Current State: 52:[30, 46, 24], Operations: ['93-69=24'] Exploring Operation: 46-30=16, Resulting Numbers: [24, 16] Generated Node #0,2,0: 52:[24, 16] Operation: 46-30=16 Exploring Operation: 30+24=54, Resulting Numbers: [46, 54] Generated Node #0,2,1: 52:[46, 54] Operation: 30+24=54 Exploring Operation: 46-24=22, Resulting Numbers: [30, 22] Generated Node #0,2,2: 52:[30, 22] Operation: 46-24=22 Exploring Operation: 30-24=6, Resulting Numbers: [46, 6] Generated Node #0,2,3: 52:[46, 6] Operation: 30-24=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 52:[24, 16], Operations: ['93-69=24', '46-30=16'] Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 52:[46, 54], Operations: ['93-69=24', '30+24=54'] Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 46+54=100, Resulting Numbers: [100] 100,52 unequal: No Solution Exploring Operation: 46*54=2484, Resulting Numbers: [2484] 2484,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 52:[30, 22], Operations: ['93-69=24', '46-24=22'] Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,52 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[69, 30, 93, 46], Operations: [] Exploring Operation: 93-69=24, Resulting Numbers: [30, 46, 24] Generated Node #0,2: 52:[30, 46, 24] Operation: 93-69=24 Moving to Node #0,2 Current State: 52:[30, 46, 24], Operations: ['93-69=24'] Exploring Operation: 46-24=22, Resulting Numbers: [30, 22] Generated Node #0,2,2: 52:[30, 22] Operation: 46-24=22 Moving to Node #0,2,2 Current State: 52:[30, 22], Operations: ['93-69=24', '46-24=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 5, 15, 23, 46 ]
69
[ "15/5=3", "46-23=23", "3*23=69" ]
Current State: 69:[5, 15, 23, 46], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [23, 46, 3] Generated Node #2: [23, 46, 3] from Operation: 15/5=3 Current State: 69:[23, 46, 3], Operations: ['15/5=3'] Exploring Operation: 46-23=23, Resulting Numbers: [3, 23] Generated Node #3: [3, 23] from Operation: 46-23=23 Current State: 69:[3, 23], Operations: ['15/5=3', '46-23=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[5, 15, 23, 46], Operations: [] Exploring Operation: 46-23=23, Resulting Numbers: [5, 15, 23] Generated Node #0,0: 69:[5, 15, 23] Operation: 46-23=23 Exploring Operation: 15+46=61, Resulting Numbers: [5, 23, 61] Generated Node #0,1: 69:[5, 23, 61] Operation: 15+46=61 Exploring Operation: 23+46=69, Resulting Numbers: [5, 15, 69] Generated Node #0,2: 69:[5, 15, 69] Operation: 23+46=69 Exploring Operation: 46-15=31, Resulting Numbers: [5, 23, 31] Generated Node #0,3: 69:[5, 23, 31] Operation: 46-15=31 Moving to Node #0,0 Current State: 69:[5, 15, 23], Operations: ['46-23=23'] Exploring Operation: 5+15=20, Resulting Numbers: [23, 20] Generated Node #0,0,0: 69:[23, 20] Operation: 5+15=20 Exploring Operation: 15-5=10, Resulting Numbers: [23, 10] Generated Node #0,0,1: 69:[23, 10] Operation: 15-5=10 Exploring Operation: 15/5=3, Resulting Numbers: [23, 3] Generated Node #0,0,2: 69:[23, 3] Operation: 15/5=3 Exploring Operation: 5*15=75, Resulting Numbers: [23, 75] Generated Node #0,0,3: 69:[23, 75] Operation: 5*15=75 Moving to Node #0,2 Current State: 69:[5, 15, 69], Operations: ['23+46=69'] Exploring Operation: 15/5=3, Resulting Numbers: [69, 3] Generated Node #0,2,0: 69:[69, 3] Operation: 15/5=3 Exploring Operation: 15-5=10, Resulting Numbers: [69, 10] Generated Node #0,2,1: 69:[69, 10] Operation: 15-5=10 Exploring Operation: 5*15=75, Resulting Numbers: [69, 75] Generated Node #0,2,2: 69:[69, 75] Operation: 5*15=75 Exploring Operation: 5+15=20, Resulting Numbers: [69, 20] Generated Node #0,2,3: 69:[69, 20] Operation: 5+15=20 Moving to Node #0,1 Current State: 69:[5, 23, 61], Operations: ['15+46=61'] Exploring Operation: 61-5=56, Resulting Numbers: [23, 56] Generated Node #0,1,0: 69:[23, 56] Operation: 61-5=56 Exploring Operation: 23-5=18, Resulting Numbers: [61, 18] Generated Node #0,1,1: 69:[61, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [61, 28] Generated Node #0,1,2: 69:[61, 28] Operation: 5+23=28 Exploring Operation: 5+61=66, Resulting Numbers: [23, 66] Generated Node #0,1,3: 69:[23, 66] Operation: 5+61=66 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[23, 66], Operations: ['15+46=61', '5+61=66'] Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,69 unequal: No Solution Exploring Operation: 23+66=89, Resulting Numbers: [89] 89,69 unequal: No Solution Exploring Operation: 23*66=1518, Resulting Numbers: [1518] 1518,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[23, 56], Operations: ['15+46=61', '61-5=56'] Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 23+56=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 23*56=1288, Resulting Numbers: [1288] 1288,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[61, 18], Operations: ['15+46=61', '23-5=18'] Exploring Operation: 61*18=1098, Resulting Numbers: [1098] 1098,69 unequal: No Solution Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[61, 28], Operations: ['15+46=61', '5+23=28'] Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,69 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,69 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: 69:[5, 23, 31], Operations: ['46-15=31'] Exploring Operation: 31-23=8, Resulting Numbers: [5, 8] Generated Node #0,3,0: 69:[5, 8] Operation: 31-23=8 Exploring Operation: 31-5=26, Resulting Numbers: [23, 26] Generated Node #0,3,1: 69:[23, 26] Operation: 31-5=26 Exploring Operation: 23-5=18, Resulting Numbers: [31, 18] Generated Node #0,3,2: 69:[31, 18] Operation: 23-5=18 Exploring Operation: 5+23=28, Resulting Numbers: [31, 28] Generated Node #0,3,3: 69:[31, 28] Operation: 5+23=28 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 69:[23, 26], Operations: ['46-15=31', '31-5=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,69 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[5, 8], Operations: ['46-15=31', '31-23=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[31, 18], Operations: ['46-15=31', '23-5=18'] Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,69 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[31, 28], Operations: ['46-15=31', '5+23=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,69 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 69:[23, 3], Operations: ['46-23=23', '15/5=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[5, 15, 23, 46], Operations: [] Exploring Operation: 46-23=23, Resulting Numbers: [5, 15, 23] Generated Node #0,0: 69:[5, 15, 23] Operation: 46-23=23 Moving to Node #0,0 Current State: 69:[5, 15, 23], Operations: ['46-23=23'] Exploring Operation: 15/5=3, Resulting Numbers: [23, 3] Generated Node #0,0,2: 69:[23, 3] Operation: 15/5=3 Moving to Node #0,0,2 Current State: 69:[23, 3], Operations: ['46-23=23', '15/5=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 4, 99, 83, 56 ]
30
[ "56/4=14", "99-83=16", "14+16=30" ]
Current State: 30:[4, 99, 83, 56], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [99, 83, 14] Generated Node #2: [99, 83, 14] from Operation: 56/4=14 Current State: 30:[99, 83, 14], Operations: ['56/4=14'] Exploring Operation: 99-83=16, Resulting Numbers: [14, 16] Generated Node #3: [14, 16] from Operation: 99-83=16 Current State: 30:[14, 16], Operations: ['56/4=14', '99-83=16'] Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 99, 83, 56], Operations: [] Exploring Operation: 99-56=43, Resulting Numbers: [4, 83, 43] Generated Node #0,0: 30:[4, 83, 43] Operation: 99-56=43 Exploring Operation: 99-83=16, Resulting Numbers: [4, 56, 16] Generated Node #0,1: 30:[4, 56, 16] Operation: 99-83=16 Exploring Operation: 83-56=27, Resulting Numbers: [4, 99, 27] Generated Node #0,2: 30:[4, 99, 27] Operation: 83-56=27 Exploring Operation: 99-4=95, Resulting Numbers: [83, 56, 95] Generated Node #0,3: 30:[83, 56, 95] Operation: 99-4=95 Exploring Operation: 56/4=14, Resulting Numbers: [99, 83, 14] Generated Node #0,4: 30:[99, 83, 14] Operation: 56/4=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[4, 56, 16], Operations: ['99-83=16'] Exploring Operation: 56/4=14, Resulting Numbers: [16, 14] Generated Node #0,1,0: 30:[16, 14] Operation: 56/4=14 Exploring Operation: 16/4=4, Resulting Numbers: [56, 4] Generated Node #0,1,1: 30:[56, 4] Operation: 16/4=4 Exploring Operation: 56-4=52, Resulting Numbers: [16, 52] Generated Node #0,1,2: 30:[16, 52] Operation: 56-4=52 Exploring Operation: 56-16=40, Resulting Numbers: [4, 40] Generated Node #0,1,3: 30:[4, 40] Operation: 56-16=40 Exploring Operation: 16-4=12, Resulting Numbers: [56, 12] Generated Node #0,1,4: 30:[56, 12] Operation: 16-4=12 Moving to Node #0,1,0 Current State: 30:[16, 14], Operations: ['99-83=16', '56/4=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,30 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[4, 99, 83, 56], Operations: [] Exploring Operation: 99-83=16, Resulting Numbers: [4, 56, 16] Generated Node #0,1: 30:[4, 56, 16] Operation: 99-83=16 Moving to Node #0,1 Current State: 30:[4, 56, 16], Operations: ['99-83=16'] Exploring Operation: 56/4=14, Resulting Numbers: [16, 14] Generated Node #0,1,0: 30:[16, 14] Operation: 56/4=14 Moving to Node #0,1,0 Current State: 30:[16, 14], Operations: ['99-83=16', '56/4=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 4, 38, 62, 50 ]
54
[ "4+38=42", "62-50=12", "42+12=54" ]
Current State: 54:[4, 38, 62, 50], Operations: [] Exploring Operation: 4+38=42, Resulting Numbers: [62, 50, 42] Generated Node #2: [62, 50, 42] from Operation: 4+38=42 Current State: 54:[62, 50, 42], Operations: ['4+38=42'] Exploring Operation: 62-50=12, Resulting Numbers: [42, 12] Generated Node #3: [42, 12] from Operation: 62-50=12 Current State: 54:[42, 12], Operations: ['4+38=42', '62-50=12'] Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[4, 38, 62, 50], Operations: [] Exploring Operation: 38-4=34, Resulting Numbers: [62, 50, 34] Generated Node #0,0: 54:[62, 50, 34] Operation: 38-4=34 Exploring Operation: 62-50=12, Resulting Numbers: [4, 38, 12] Generated Node #0,1: 54:[4, 38, 12] Operation: 62-50=12 Exploring Operation: 50-38=12, Resulting Numbers: [4, 62, 12] Generated Node #0,2: 54:[4, 62, 12] Operation: 50-38=12 Exploring Operation: 62-38=24, Resulting Numbers: [4, 50, 24] Generated Node #0,3: 54:[4, 50, 24] Operation: 62-38=24 Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[4, 50, 24], Operations: ['62-38=24'] Exploring Operation: 4+50=54, Resulting Numbers: [24, 54] Generated Node #0,3,0: 54:[24, 54] Operation: 4+50=54 Exploring Operation: 4+24=28, Resulting Numbers: [50, 28] Generated Node #0,3,1: 54:[50, 28] Operation: 4+24=28 Exploring Operation: 50-24=26, Resulting Numbers: [4, 26] Generated Node #0,3,2: 54:[4, 26] Operation: 50-24=26 Exploring Operation: 24/4=6, Resulting Numbers: [50, 6] Generated Node #0,3,3: 54:[50, 6] Operation: 24/4=6 Moving to Node #0,3,2 Current State: 54:[4, 26], Operations: ['62-38=24', '50-24=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[24, 54], Operations: ['62-38=24', '4+50=54'] Exploring Operation: 24+54=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 24*54=1296, Resulting Numbers: [1296] 1296,54 unequal: No Solution Moving to Node #0,3,3 Current State: 54:[50, 6], Operations: ['62-38=24', '24/4=6'] Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,54 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[50, 28], Operations: ['62-38=24', '4+24=28'] Exploring Operation: 50*28=1400, Resulting Numbers: [1400] 1400,54 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 50+28=78, Resulting Numbers: [78] 78,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[4, 62, 12], Operations: ['50-38=12'] Exploring Operation: 12-4=8, Resulting Numbers: [62, 8] Generated Node #0,2,0: 54:[62, 8] Operation: 12-4=8 Exploring Operation: 62-4=58, Resulting Numbers: [12, 58] Generated Node #0,2,1: 54:[12, 58] Operation: 62-4=58 Exploring Operation: 12/4=3, Resulting Numbers: [62, 3] Generated Node #0,2,2: 54:[62, 3] Operation: 12/4=3 Exploring Operation: 62-12=50, Resulting Numbers: [4, 50] Generated Node #0,2,3: 54:[4, 50] Operation: 62-12=50 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 54:[4, 50], Operations: ['50-38=12', '62-12=50'] Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,54 unequal: No Solution Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[4, 38, 62, 50], Operations: [] Exploring Operation: 50-38=12, Resulting Numbers: [4, 62, 12] Generated Node #0,2: 54:[4, 62, 12] Operation: 50-38=12 Moving to Node #0,2 Current State: 54:[4, 62, 12], Operations: ['50-38=12'] Exploring Operation: 62-12=50, Resulting Numbers: [4, 50] Generated Node #0,2,3: 54:[4, 50] Operation: 62-12=50 Moving to Node #0,2,3 Current State: 54:[4, 50], Operations: ['50-38=12', '62-12=50'] Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 80, 78, 84, 22 ]
95
[ "80-78=2", "22/2=11", "84+11=95" ]
Current State: 95:[80, 78, 84, 22], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [84, 22, 2] Generated Node #2: [84, 22, 2] from Operation: 80-78=2 Current State: 95:[84, 22, 2], Operations: ['80-78=2'] Exploring Operation: 22/2=11, Resulting Numbers: [84, 11] Generated Node #3: [84, 11] from Operation: 22/2=11 Current State: 95:[84, 11], Operations: ['80-78=2', '22/2=11'] Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[80, 78, 84, 22], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [80, 22, 6] Generated Node #0,0: 95:[80, 22, 6] Operation: 84-78=6 Exploring Operation: 80-78=2, Resulting Numbers: [84, 22, 2] Generated Node #0,1: 95:[84, 22, 2] Operation: 80-78=2 Exploring Operation: 78+22=100, Resulting Numbers: [80, 84, 100] Generated Node #0,2: 95:[80, 84, 100] Operation: 78+22=100 Exploring Operation: 84-80=4, Resulting Numbers: [78, 22, 4] Generated Node #0,3: 95:[78, 22, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[84, 22, 2], Operations: ['80-78=2'] Exploring Operation: 84-2=82, Resulting Numbers: [22, 82] Generated Node #0,1,0: 95:[22, 82] Operation: 84-2=82 Exploring Operation: 84+2=86, Resulting Numbers: [22, 86] Generated Node #0,1,1: 95:[22, 86] Operation: 84+2=86 Exploring Operation: 22-2=20, Resulting Numbers: [84, 20] Generated Node #0,1,2: 95:[84, 20] Operation: 22-2=20 Exploring Operation: 84+22=106, Resulting Numbers: [2, 106] Generated Node #0,1,3: 95:[2, 106] Operation: 84+22=106 Moving to Node #0,1,1 Current State: 95:[22, 86], Operations: ['80-78=2', '84+2=86'] Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 22+86=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 22*86=1892, Resulting Numbers: [1892] 1892,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[84, 20], Operations: ['80-78=2', '22-2=20'] Exploring Operation: 84+20=104, Resulting Numbers: [104] 104,95 unequal: No Solution Exploring Operation: 84*20=1680, Resulting Numbers: [1680] 1680,95 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[2, 106], Operations: ['80-78=2', '84+22=106'] Exploring Operation: 2+106=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 106/2=53, Resulting Numbers: [53] 53,95 unequal: No Solution Exploring Operation: 106-2=104, Resulting Numbers: [104] 104,95 unequal: No Solution Exploring Operation: 2*106=212, Resulting Numbers: [212] 212,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[22, 82], Operations: ['80-78=2', '84-2=82'] Exploring Operation: 22*82=1804, Resulting Numbers: [1804] 1804,95 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,95 unequal: No Solution Exploring Operation: 22+82=104, Resulting Numbers: [104] 104,95 unequal: No Solution No 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: 95:[80, 22, 6], Operations: ['84-78=6'] Exploring Operation: 80+22=102, Resulting Numbers: [6, 102] Generated Node #0,0,0: 95:[6, 102] Operation: 80+22=102 Exploring Operation: 80-6=74, Resulting Numbers: [22, 74] Generated Node #0,0,1: 95:[22, 74] Operation: 80-6=74 Exploring Operation: 22-6=16, Resulting Numbers: [80, 16] Generated Node #0,0,2: 95:[80, 16] Operation: 22-6=16 Exploring Operation: 80+6=86, Resulting Numbers: [22, 86] Generated Node #0,0,3: 95:[22, 86] Operation: 80+6=86 Moving to Node #0,0,0 Current State: 95:[6, 102], Operations: ['84-78=6', '80+22=102'] Exploring Operation: 102/6=17, Resulting Numbers: [17] 17,95 unequal: No Solution Exploring Operation: 102-6=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 6+102=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 6*102=612, Resulting Numbers: [612] 612,95 unequal: No Solution Moving to Node #0,0,3 Current State: 95:[22, 86], Operations: ['84-78=6', '80+6=86'] Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 22+86=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 22*86=1892, Resulting Numbers: [1892] 1892,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[80, 16], Operations: ['84-78=6', '22-6=16'] Exploring Operation: 80*16=1280, Resulting Numbers: [1280] 1280,95 unequal: No Solution Exploring Operation: 80+16=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[22, 74], Operations: ['84-78=6', '80-6=74'] Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,95 unequal: No Solution Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,95 unequal: No Solution No 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: 95:[78, 22, 4], Operations: ['84-80=4'] Exploring Operation: 22-4=18, Resulting Numbers: [78, 18] Generated Node #0,3,0: 95:[78, 18] Operation: 22-4=18 Exploring Operation: 78+22=100, Resulting Numbers: [4, 100] Generated Node #0,3,1: 95:[4, 100] Operation: 78+22=100 Exploring Operation: 78-4=74, Resulting Numbers: [22, 74] Generated Node #0,3,2: 95:[22, 74] Operation: 78-4=74 Exploring Operation: 78+4=82, Resulting Numbers: [22, 82] Generated Node #0,3,3: 95:[22, 82] Operation: 78+4=82 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 95:[4, 100], Operations: ['84-80=4', '78+22=100'] Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 4*100=400, Resulting Numbers: [400] 400,95 unequal: No Solution Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,95 unequal: No Solution Exploring Operation: 4+100=104, Resulting Numbers: [104] 104,95 unequal: No Solution No 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: 95:[22, 82], Operations: ['84-80=4', '78+4=82'] Exploring Operation: 22+82=104, Resulting Numbers: [104] 104,95 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,95 unequal: No Solution Exploring Operation: 22*82=1804, Resulting Numbers: [1804] 1804,95 unequal: No Solution No 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: 95:[78, 18], Operations: ['84-80=4', '22-4=18'] Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,95 unequal: No Solution Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,95 unequal: No Solution No 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: 95:[22, 74], Operations: ['84-80=4', '78-4=74'] Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,95 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: 95:[80, 84, 100], Operations: ['78+22=100'] Exploring Operation: 84-80=4, Resulting Numbers: [100, 4] Generated Node #0,2,0: 95:[100, 4] Operation: 84-80=4 Exploring Operation: 100-84=16, Resulting Numbers: [80, 16] Generated Node #0,2,1: 95:[80, 16] Operation: 100-84=16 Exploring Operation: 100-80=20, Resulting Numbers: [84, 20] Generated Node #0,2,2: 95:[84, 20] Operation: 100-80=20 Exploring Operation: 80+84=164, Resulting Numbers: [100, 164] Generated Node #0,2,3: 95:[100, 164] Operation: 80+84=164 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 95:[100, 4], Operations: ['78+22=100', '84-80=4'] Exploring Operation: 100*4=400, Resulting Numbers: [400] 400,95 unequal: No Solution Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,95 unequal: No Solution Exploring Operation: 100+4=104, Resulting Numbers: [104] 104,95 unequal: No Solution No 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: 95:[84, 20], Operations: ['78+22=100', '100-80=20'] Exploring Operation: 84*20=1680, Resulting Numbers: [1680] 1680,95 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 84+20=104, Resulting Numbers: [104] 104,95 unequal: No Solution No 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: 95:[80, 16], Operations: ['78+22=100', '100-84=16'] Exploring Operation: 80+16=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 80*16=1280, Resulting Numbers: [1280] 1280,95 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,95 unequal: No Solution No 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: 95:[100, 164], Operations: ['78+22=100', '80+84=164'] Exploring Operation: 164-100=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 100+164=264, Resulting Numbers: [264] 264,95 unequal: No Solution Exploring Operation: 100*164=16400, Resulting Numbers: [16400] 16400,95 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
[ 13, 28, 25, 2 ]
38
[ "28-13=15", "25-2=23", "15+23=38" ]
Current State: 38:[13, 28, 25, 2], Operations: [] Exploring Operation: 28-13=15, Resulting Numbers: [25, 2, 15] Generated Node #2: [25, 2, 15] from Operation: 28-13=15 Current State: 38:[25, 2, 15], Operations: ['28-13=15'] Exploring Operation: 25-2=23, Resulting Numbers: [15, 23] Generated Node #3: [15, 23] from Operation: 25-2=23 Current State: 38:[15, 23], Operations: ['28-13=15', '25-2=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[13, 28, 25, 2], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [13, 2, 3] Generated Node #0,0: 38:[13, 2, 3] Operation: 28-25=3 Moving to Node #0,0 Current State: 38:[13, 2, 3], Operations: ['28-25=3'] Exploring Operation: 13*3=39, Resulting Numbers: [2, 39] Generated Node #0,0,0: 38:[2, 39] Operation: 13*3=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[2, 39], Operations: ['28-25=3', '13*3=39'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,38 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
[ 48, 82, 4, 79 ]
60
[ "82-79=3", "4*3=12", "48+12=60" ]
Current State: 60:[48, 82, 4, 79], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [48, 4, 3] Generated Node #2: [48, 4, 3] from Operation: 82-79=3 Current State: 60:[48, 4, 3], Operations: ['82-79=3'] Exploring Operation: 4*3=12, Resulting Numbers: [48, 12] Generated Node #3: [48, 12] from Operation: 4*3=12 Current State: 60:[48, 12], Operations: ['82-79=3', '4*3=12'] Exploring Operation: 48+12=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[48, 82, 4, 79], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [48, 4, 3] Generated Node #0,0: 60:[48, 4, 3] Operation: 82-79=3 Exploring Operation: 82-48=34, Resulting Numbers: [4, 79, 34] Generated Node #0,1: 60:[4, 79, 34] Operation: 82-48=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[48, 4, 3], Operations: ['82-79=3'] Exploring Operation: 48/4=12, Resulting Numbers: [3, 12] Generated Node #0,0,0: 60:[3, 12] Operation: 48/4=12 Exploring Operation: 48/3=16, Resulting Numbers: [4, 16] Generated Node #0,0,1: 60:[4, 16] Operation: 48/3=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[3, 12], Operations: ['82-79=3', '48/4=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,60 unequal: No Solution No 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: 60:[4, 16], Operations: ['82-79=3', '48/3=16'] Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,60 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,60 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: 60:[4, 79, 34], Operations: ['82-48=34'] Exploring Operation: 79-34=45, Resulting Numbers: [4, 45] Generated Node #0,1,0: 60:[4, 45] Operation: 79-34=45 Exploring Operation: 79-4=75, Resulting Numbers: [34, 75] Generated Node #0,1,1: 60:[34, 75] Operation: 79-4=75 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 60:[4, 45], Operations: ['82-48=34', '79-34=45'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,60 unequal: No Solution No 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: 60:[34, 75], Operations: ['82-48=34', '79-4=75'] Exploring Operation: 75-34=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 34+75=109, Resulting Numbers: [109] 109,60 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
[ 81, 98, 93, 19 ]
91
[ "98-81=17", "93-19=74", "17+74=91" ]
Current State: 91:[81, 98, 93, 19], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [93, 19, 17] Generated Node #2: [93, 19, 17] from Operation: 98-81=17 Current State: 91:[93, 19, 17], Operations: ['98-81=17'] Exploring Operation: 93-19=74, Resulting Numbers: [17, 74] Generated Node #3: [17, 74] from Operation: 93-19=74 Current State: 91:[17, 74], Operations: ['98-81=17', '93-19=74'] Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[81, 98, 93, 19], Operations: [] Exploring Operation: 93-81=12, Resulting Numbers: [98, 19, 12] Generated Node #0,0: 91:[98, 19, 12] Operation: 93-81=12 Exploring Operation: 98-81=17, Resulting Numbers: [93, 19, 17] Generated Node #0,1: 91:[93, 19, 17] Operation: 98-81=17 Exploring Operation: 81+19=100, Resulting Numbers: [98, 93, 100] Generated Node #0,2: 91:[98, 93, 100] Operation: 81+19=100 Exploring Operation: 98-93=5, Resulting Numbers: [81, 19, 5] Generated Node #0,3: 91:[81, 19, 5] Operation: 98-93=5 Moving to Node #0,1 Current State: 91:[93, 19, 17], Operations: ['98-81=17'] Exploring Operation: 93+19=112, Resulting Numbers: [17, 112] Generated Node #0,1,0: 91:[17, 112] Operation: 93+19=112 Exploring Operation: 93-17=76, Resulting Numbers: [19, 76] Generated Node #0,1,1: 91:[19, 76] Operation: 93-17=76 Exploring Operation: 19-17=2, Resulting Numbers: [93, 2] Generated Node #0,1,2: 91:[93, 2] Operation: 19-17=2 Exploring Operation: 93-19=74, Resulting Numbers: [17, 74] Generated Node #0,1,3: 91:[17, 74] Operation: 93-19=74 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 91:[93, 2], Operations: ['98-81=17', '19-17=2'] Exploring Operation: 93*2=186, Resulting Numbers: [186] 186,91 unequal: No Solution Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,91 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[81, 98, 93, 19], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [93, 19, 17] Generated Node #0,1: 91:[93, 19, 17] Operation: 98-81=17 Moving to Node #0,1 Current State: 91:[93, 19, 17], Operations: ['98-81=17'] Exploring Operation: 19-17=2, Resulting Numbers: [93, 2] Generated Node #0,1,2: 91:[93, 2] Operation: 19-17=2 Moving to Node #0,1,2 Current State: 91:[93, 2], Operations: ['98-81=17', '19-17=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 72, 3, 44, 62 ]
14
[ "72-62=10", "3*10=30", "44-30=14" ]
Current State: 14:[72, 3, 44, 62], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [3, 44, 10] Generated Node #2: [3, 44, 10] from Operation: 72-62=10 Current State: 14:[3, 44, 10], Operations: ['72-62=10'] Exploring Operation: 3*10=30, Resulting Numbers: [44, 30] Generated Node #3: [44, 30] from Operation: 3*10=30 Current State: 14:[44, 30], Operations: ['72-62=10', '3*10=30'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[72, 3, 44, 62], Operations: [] Exploring Operation: 72-44=28, Resulting Numbers: [3, 62, 28] Generated Node #0,0: 14:[3, 62, 28] Operation: 72-44=28 Exploring Operation: 62-44=18, Resulting Numbers: [72, 3, 18] Generated Node #0,1: 14:[72, 3, 18] Operation: 62-44=18 Exploring Operation: 72/3=24, Resulting Numbers: [44, 62, 24] Generated Node #0,2: 14:[44, 62, 24] Operation: 72/3=24 Exploring Operation: 72-62=10, Resulting Numbers: [3, 44, 10] Generated Node #0,3: 14:[3, 44, 10] Operation: 72-62=10 Exploring Operation: 72-3=69, Resulting Numbers: [44, 62, 69] Generated Node #0,4: 14:[44, 62, 69] Operation: 72-3=69 Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[3, 44, 10], Operations: ['72-62=10'] Exploring Operation: 44-10=34, Resulting Numbers: [3, 34] Generated Node #0,3,0: 14:[3, 34] Operation: 44-10=34 Exploring Operation: 3+44=47, Resulting Numbers: [10, 47] Generated Node #0,3,1: 14:[10, 47] Operation: 3+44=47 Exploring Operation: 44-3=41, Resulting Numbers: [10, 41] Generated Node #0,3,2: 14:[10, 41] Operation: 44-3=41 Exploring Operation: 3+10=13, Resulting Numbers: [44, 13] Generated Node #0,3,3: 14:[44, 13] Operation: 3+10=13 Exploring Operation: 10-3=7, Resulting Numbers: [44, 7] Generated Node #0,3,4: 14:[44, 7] Operation: 10-3=7 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 14:[3, 34], Operations: ['72-62=10', '44-10=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,14 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,14 unequal: No Solution No 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: 14:[10, 41], Operations: ['72-62=10', '44-3=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,14 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,14 unequal: No Solution No 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: 14:[44, 7], Operations: ['72-62=10', '10-3=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,14 unequal: No Solution Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,14 unequal: No Solution No 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: 14:[44, 13], Operations: ['72-62=10', '3+10=13'] Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,14 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,14 unequal: No Solution No 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: 14:[10, 47], Operations: ['72-62=10', '3+44=47'] Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,14 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,14 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: 14:[3, 62, 28], Operations: ['72-44=28'] Exploring Operation: 3+28=31, Resulting Numbers: [62, 31] Generated Node #0,0,0: 14:[62, 31] Operation: 3+28=31 Exploring Operation: 28-3=25, Resulting Numbers: [62, 25] Generated Node #0,0,1: 14:[62, 25] Operation: 28-3=25 Exploring Operation: 3+62=65, Resulting Numbers: [28, 65] Generated Node #0,0,2: 14:[28, 65] Operation: 3+62=65 Exploring Operation: 62-3=59, Resulting Numbers: [28, 59] Generated Node #0,0,3: 14:[28, 59] Operation: 62-3=59 Exploring Operation: 62-28=34, Resulting Numbers: [3, 34] Generated Node #0,0,4: 14:[3, 34] Operation: 62-28=34 Moving to Node #0,0,4 Current State: 14:[3, 34], Operations: ['72-44=28', '62-28=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[28, 59], Operations: ['72-44=28', '62-3=59'] Exploring Operation: 28*59=1652, Resulting Numbers: [1652] 1652,14 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 28+59=87, Resulting Numbers: [87] 87,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[62, 25], Operations: ['72-44=28', '28-3=25'] Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,14 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,14 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[62, 31], Operations: ['72-44=28', '3+28=31'] Exploring Operation: 62+31=93, Resulting Numbers: [93] 93,14 unequal: No Solution Exploring Operation: 62-31=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 62*31=1922, Resulting Numbers: [1922] 1922,14 unequal: No Solution Exploring Operation: 62/31=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[28, 65], Operations: ['72-44=28', '3+62=65'] Exploring Operation: 28*65=1820, Resulting Numbers: [1820] 1820,14 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 28+65=93, Resulting Numbers: [93] 93,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[72, 3, 18], Operations: ['62-44=18'] Exploring Operation: 72/18=4, Resulting Numbers: [3, 4] Generated Node #0,1,0: 14:[3, 4] Operation: 72/18=4 Exploring Operation: 18-3=15, Resulting Numbers: [72, 15] Generated Node #0,1,1: 14:[72, 15] Operation: 18-3=15 Exploring Operation: 72/3=24, Resulting Numbers: [18, 24] Generated Node #0,1,2: 14:[18, 24] Operation: 72/3=24 Exploring Operation: 72-18=54, Resulting Numbers: [3, 54] Generated Node #0,1,3: 14:[3, 54] Operation: 72-18=54 Exploring Operation: 72-3=69, Resulting Numbers: [18, 69] Generated Node #0,1,4: 14:[18, 69] Operation: 72-3=69 Moving to Node #0,1,0 Current State: 14:[3, 4], Operations: ['62-44=18', '72/18=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[18, 24], Operations: ['62-44=18', '72/3=24'] Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,14 unequal: No Solution Moving to Node #0,1,3 Current State: 14:[3, 54], Operations: ['62-44=18', '72-18=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,14 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,14 unequal: No Solution Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[72, 15], Operations: ['62-44=18', '18-3=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,14 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,14 unequal: No Solution Moving to Node #0,1,4 Current State: 14:[18, 69], Operations: ['62-44=18', '72-3=69'] Exploring Operation: 18+69=87, Resulting Numbers: [87] 87,14 unequal: No Solution Exploring Operation: 18*69=1242, Resulting Numbers: [1242] 1242,14 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[44, 62, 24], Operations: ['72/3=24'] Exploring Operation: 62-24=38, Resulting Numbers: [44, 38] Generated Node #0,2,0: 14:[44, 38] Operation: 62-24=38 Exploring Operation: 44-24=20, Resulting Numbers: [62, 20] Generated Node #0,2,1: 14:[62, 20] Operation: 44-24=20 Exploring Operation: 44+62=106, Resulting Numbers: [24, 106] Generated Node #0,2,2: 14:[24, 106] Operation: 44+62=106 Exploring Operation: 62-44=18, Resulting Numbers: [24, 18] Generated Node #0,2,3: 14:[24, 18] Operation: 62-44=18 Exploring Operation: 44+24=68, Resulting Numbers: [62, 68] Generated Node #0,2,4: 14:[62, 68] Operation: 44+24=68 Moving to Node #0,2,3 Current State: 14:[24, 18], Operations: ['72/3=24', '62-44=18'] Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,14 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[62, 20], Operations: ['72/3=24', '44-24=20'] Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,14 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[44, 38], Operations: ['72/3=24', '62-24=38'] Exploring Operation: 44*38=1672, Resulting Numbers: [1672] 1672,14 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,14 unequal: No Solution Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,14 unequal: No Solution Moving to Node #0,2,2 Current State: 14:[24, 106], Operations: ['72/3=24', '44+62=106'] Exploring Operation: 24+106=130, Resulting Numbers: [130] 130,14 unequal: No Solution Exploring Operation: 24*106=2544, Resulting Numbers: [2544] 2544,14 unequal: No Solution Exploring Operation: 106-24=82, Resulting Numbers: [82] 82,14 unequal: No Solution Moving to Node #0,2,4 Current State: 14:[62, 68], Operations: ['72/3=24', '44+24=68'] Exploring Operation: 62*68=4216, Resulting Numbers: [4216] 4216,14 unequal: No Solution Exploring Operation: 68-62=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 62+68=130, Resulting Numbers: [130] 130,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 14:[44, 62, 69], Operations: ['72-3=69'] Exploring Operation: 69-44=25, Resulting Numbers: [62, 25] Generated Node #0,4,0: 14:[62, 25] Operation: 69-44=25 Exploring Operation: 69-62=7, Resulting Numbers: [44, 7] Generated Node #0,4,1: 14:[44, 7] Operation: 69-62=7 Exploring Operation: 62-44=18, Resulting Numbers: [69, 18] Generated Node #0,4,2: 14:[69, 18] Operation: 62-44=18 Exploring Operation: 44+62=106, Resulting Numbers: [69, 106] Generated Node #0,4,3: 14:[69, 106] Operation: 44+62=106 Exploring Operation: 44+69=113, Resulting Numbers: [62, 113] Generated Node #0,4,4: 14:[62, 113] Operation: 44+69=113 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 14:[44, 7], Operations: ['72-3=69', '69-62=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,14 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 14:[62, 25], Operations: ['72-3=69', '69-44=25'] Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,14 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 14:[69, 18], Operations: ['72-3=69', '62-44=18'] Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,14 unequal: No Solution Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,14 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 14:[69, 106], Operations: ['72-3=69', '44+62=106'] Exploring Operation: 69+106=175, Resulting Numbers: [175] 175,14 unequal: No Solution Exploring Operation: 106-69=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 69*106=7314, Resulting Numbers: [7314] 7314,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 14:[62, 113], Operations: ['72-3=69', '44+69=113'] Exploring Operation: 113-62=51, Resulting Numbers: [51] 51,14 unequal: No Solution Exploring Operation: 62+113=175, Resulting Numbers: [175] 175,14 unequal: No Solution Exploring Operation: 62*113=7006, Resulting Numbers: [7006] 7006,14 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
[ 37, 59, 85, 23 ]
84
[ "59-37=22", "85-23=62", "22+62=84" ]
Current State: 84:[37, 59, 85, 23], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [85, 23, 22] Generated Node #2: [85, 23, 22] from Operation: 59-37=22 Current State: 84:[85, 23, 22], Operations: ['59-37=22'] Exploring Operation: 85-23=62, Resulting Numbers: [22, 62] Generated Node #3: [22, 62] from Operation: 85-23=62 Current State: 84:[22, 62], Operations: ['59-37=22', '85-23=62'] Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[37, 59, 85, 23], Operations: [] Exploring Operation: 85-59=26, Resulting Numbers: [37, 23, 26] Generated Node #0,0: 84:[37, 23, 26] Operation: 85-59=26 Exploring Operation: 37+59=96, Resulting Numbers: [85, 23, 96] Generated Node #0,1: 84:[85, 23, 96] Operation: 37+59=96 Exploring Operation: 59+23=82, Resulting Numbers: [37, 85, 82] Generated Node #0,2: 84:[37, 85, 82] Operation: 59+23=82 Exploring Operation: 59-37=22, Resulting Numbers: [85, 23, 22] Generated Node #0,3: 84:[85, 23, 22] Operation: 59-37=22 Exploring Operation: 59-23=36, Resulting Numbers: [37, 85, 36] Generated Node #0,4: 84:[37, 85, 36] Operation: 59-23=36 Moving to Node #0,3 Current State: 84:[85, 23, 22], Operations: ['59-37=22'] Exploring Operation: 23+22=45, Resulting Numbers: [85, 45] Generated Node #0,3,0: 84:[85, 45] Operation: 23+22=45 Exploring Operation: 85-23=62, Resulting Numbers: [22, 62] Generated Node #0,3,1: 84:[22, 62] Operation: 85-23=62 Exploring Operation: 23-22=1, Resulting Numbers: [85, 1] Generated Node #0,3,2: 84:[85, 1] Operation: 23-22=1 Exploring Operation: 85-22=63, Resulting Numbers: [23, 63] Generated Node #0,3,3: 84:[23, 63] Operation: 85-22=63 Exploring Operation: 85+23=108, Resulting Numbers: [22, 108] Generated Node #0,3,4: 84:[22, 108] Operation: 85+23=108 Moving to Node #0,2 Current State: 84:[37, 85, 82], Operations: ['59+23=82'] Exploring Operation: 82-37=45, Resulting Numbers: [85, 45] Generated Node #0,2,0: 84:[85, 45] Operation: 82-37=45 Exploring Operation: 85-37=48, Resulting Numbers: [82, 48] Generated Node #0,2,1: 84:[82, 48] Operation: 85-37=48 Exploring Operation: 85-82=3, Resulting Numbers: [37, 3] Generated Node #0,2,2: 84:[37, 3] Operation: 85-82=3 Exploring Operation: 37+82=119, Resulting Numbers: [85, 119] Generated Node #0,2,3: 84:[85, 119] Operation: 37+82=119 Exploring Operation: 37+85=122, Resulting Numbers: [82, 122] Generated Node #0,2,4: 84:[82, 122] Operation: 37+85=122 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[85, 45], Operations: ['59+23=82', '82-37=45'] Exploring Operation: 85+45=130, Resulting Numbers: [130] 130,84 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 85*45=3825, Resulting Numbers: [3825] 3825,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[37, 3], Operations: ['59+23=82', '85-82=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,84 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[82, 48], Operations: ['59+23=82', '85-37=48'] Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,84 unequal: No Solution Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[85, 119], Operations: ['59+23=82', '37+82=119'] Exploring Operation: 85+119=204, Resulting Numbers: [204] 204,84 unequal: No Solution Exploring Operation: 85*119=10115, Resulting Numbers: [10115] 10115,84 unequal: No Solution Exploring Operation: 119-85=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 84:[82, 122], Operations: ['59+23=82', '37+85=122'] Exploring Operation: 82*122=10004, Resulting Numbers: [10004] 10004,84 unequal: No Solution Exploring Operation: 82+122=204, Resulting Numbers: [204] 204,84 unequal: No Solution Exploring Operation: 122-82=40, Resulting Numbers: [40] 40,84 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: 84:[37, 23, 26], Operations: ['85-59=26'] Exploring Operation: 23+26=49, Resulting Numbers: [37, 49] Generated Node #0,0,0: 84:[37, 49] Operation: 23+26=49 Exploring Operation: 37-23=14, Resulting Numbers: [26, 14] Generated Node #0,0,1: 84:[26, 14] Operation: 37-23=14 Exploring Operation: 37-26=11, Resulting Numbers: [23, 11] Generated Node #0,0,2: 84:[23, 11] Operation: 37-26=11 Exploring Operation: 26-23=3, Resulting Numbers: [37, 3] Generated Node #0,0,3: 84:[37, 3] Operation: 26-23=3 Exploring Operation: 37+23=60, Resulting Numbers: [26, 60] Generated Node #0,0,4: 84:[26, 60] Operation: 37+23=60 Moving to Node #0,4 Current State: 84:[37, 85, 36], Operations: ['59-23=36'] Exploring Operation: 85-37=48, Resulting Numbers: [36, 48] Generated Node #0,4,0: 84:[36, 48] Operation: 85-37=48 Exploring Operation: 85-36=49, Resulting Numbers: [37, 49] Generated Node #0,4,1: 84:[37, 49] Operation: 85-36=49 Exploring Operation: 37+36=73, Resulting Numbers: [85, 73] Generated Node #0,4,2: 84:[85, 73] Operation: 37+36=73 Exploring Operation: 37-36=1, Resulting Numbers: [85, 1] Generated Node #0,4,3: 84:[85, 1] Operation: 37-36=1 Exploring Operation: 85+36=121, Resulting Numbers: [37, 121] Generated Node #0,4,4: 84:[37, 121] Operation: 85+36=121 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 84:[85, 1], Operations: ['59-23=36', '37-36=1'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 85*1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[37, 59, 85, 23], Operations: [] Exploring Operation: 59-23=36, Resulting Numbers: [37, 85, 36] Generated Node #0,4: 84:[37, 85, 36] Operation: 59-23=36 Moving to Node #0,4 Current State: 84:[37, 85, 36], Operations: ['59-23=36'] Exploring Operation: 37-36=1, Resulting Numbers: [85, 1] Generated Node #0,4,3: 84:[85, 1] Operation: 37-36=1 Moving to Node #0,4,3 Current State: 84:[85, 1], Operations: ['59-23=36', '37-36=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 99, 37, 96, 41 ]
87
[ "99*37=3663", "3663-96=3567", "3567/41=87" ]
Current State: 87:[99, 37, 96, 41], Operations: [] Exploring Operation: 99*37=3663, Resulting Numbers: [96, 41, 3663] Generated Node #2: [96, 41, 3663] from Operation: 99*37=3663 Current State: 87:[96, 41, 3663], Operations: ['99*37=3663'] Exploring Operation: 3663-96=3567, Resulting Numbers: [41, 3567] Generated Node #3: [41, 3567] from Operation: 3663-96=3567 Current State: 87:[41, 3567], Operations: ['99*37=3663', '3663-96=3567'] Exploring Operation: 3567/41=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[99, 37, 96, 41], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [99, 96, 4] Generated Node #0,0: 87:[99, 96, 4] Operation: 41-37=4 Exploring Operation: 99-96=3, Resulting Numbers: [37, 41, 3] Generated Node #0,1: 87:[37, 41, 3] Operation: 99-96=3 Exploring Operation: 37+41=78, Resulting Numbers: [99, 96, 78] Generated Node #0,2: 87:[99, 96, 78] Operation: 37+41=78 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[37, 41, 3], Operations: ['99-96=3'] Exploring Operation: 37-3=34, Resulting Numbers: [41, 34] Generated Node #0,1,0: 87:[41, 34] Operation: 37-3=34 Exploring Operation: 41-37=4, Resulting Numbers: [3, 4] Generated Node #0,1,1: 87:[3, 4] Operation: 41-37=4 Exploring Operation: 37+41=78, Resulting Numbers: [3, 78] Generated Node #0,1,2: 87:[3, 78] Operation: 37+41=78 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[3, 4], Operations: ['99-96=3', '41-37=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[3, 78], Operations: ['99-96=3', '37+41=78'] Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,87 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[41, 34], Operations: ['99-96=3', '37-3=34'] Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,87 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[99, 96, 4], Operations: ['41-37=4'] Exploring Operation: 99-4=95, Resulting Numbers: [96, 95] Generated Node #0,0,0: 87:[96, 95] Operation: 99-4=95 Exploring Operation: 99-96=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 87:[4, 3] Operation: 99-96=3 Exploring Operation: 96-4=92, Resulting Numbers: [99, 92] Generated Node #0,0,2: 87:[99, 92] Operation: 96-4=92 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[4, 3], Operations: ['41-37=4', '99-96=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[96, 95], Operations: ['41-37=4', '99-4=95'] Exploring Operation: 96+95=191, Resulting Numbers: [191] 191,87 unequal: No Solution Exploring Operation: 96*95=9120, Resulting Numbers: [9120] 9120,87 unequal: No Solution Exploring Operation: 96-95=1, Resulting Numbers: [1] 1,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[99, 92], Operations: ['41-37=4', '96-4=92'] Exploring Operation: 99-92=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 99*92=9108, Resulting Numbers: [9108] 9108,87 unequal: No Solution Exploring Operation: 99+92=191, Resulting Numbers: [191] 191,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[99, 96, 78], Operations: ['37+41=78'] Exploring Operation: 96-78=18, Resulting Numbers: [99, 18] Generated Node #0,2,0: 87:[99, 18] Operation: 96-78=18 Exploring Operation: 99-96=3, Resulting Numbers: [78, 3] Generated Node #0,2,1: 87:[78, 3] Operation: 99-96=3 Exploring Operation: 99-78=21, Resulting Numbers: [96, 21] Generated Node #0,2,2: 87:[96, 21] Operation: 99-78=21 Moving to Node #0,2,1 Current State: 87:[78, 3], Operations: ['37+41=78', '99-96=3'] Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,87 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[96, 21], Operations: ['37+41=78', '99-78=21'] Exploring Operation: 96+21=117, Resulting Numbers: [117] 117,87 unequal: No Solution Exploring Operation: 96*21=2016, Resulting Numbers: [2016] 2016,87 unequal: No Solution Exploring Operation: 96-21=75, Resulting Numbers: [75] 75,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[99, 18], Operations: ['37+41=78', '96-78=18'] Exploring Operation: 99-18=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 99*18=1782, Resulting Numbers: [1782] 1782,87 unequal: No Solution Exploring Operation: 99+18=117, Resulting Numbers: [117] 117,87 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
[ 26, 21, 12, 12 ]
60
[ "26*12=312", "21*12=252", "312-252=60" ]
Current State: 60:[26, 21, 12, 12], Operations: [] Exploring Operation: 26*12=312, Resulting Numbers: [21, 312] Generated Node #2: [21, 312] from Operation: 26*12=312 Current State: 60:[21, 312], Operations: ['26*12=312'] Exploring Operation: 21*12=252, Resulting Numbers: [312, 252] Generated Node #3: [312, 252] from Operation: 21*12=252 Current State: 60:[312, 252], Operations: ['26*12=312', '21*12=252'] Exploring Operation: 312-252=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[26, 21, 12, 12], Operations: [] Exploring Operation: 26-21=5, Resulting Numbers: [12, 12, 5] Generated Node #0,0: 60:[12, 12, 5] Operation: 26-21=5 Moving to Node #0,0 Current State: 60:[12, 12, 5], Operations: ['26-21=5'] Exploring Operation: 12*5=60, Resulting Numbers: [12, 60] Generated Node #0,0,0: 60:[12, 60] Operation: 12*5=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[12, 60], Operations: ['26-21=5', '12*5=60'] Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,60 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
[ 84, 68, 44, 14 ]
76
[ "68+44=112", "112/14=8", "84-8=76" ]
Current State: 76:[84, 68, 44, 14], Operations: [] Exploring Operation: 68+44=112, Resulting Numbers: [84, 14, 112] Generated Node #2: [84, 14, 112] from Operation: 68+44=112 Current State: 76:[84, 14, 112], Operations: ['68+44=112'] Exploring Operation: 112/14=8, Resulting Numbers: [84, 8] Generated Node #3: [84, 8] from Operation: 112/14=8 Current State: 76:[84, 8], Operations: ['68+44=112', '112/14=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[84, 68, 44, 14], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [44, 14, 16] Generated Node #0,0: 76:[44, 14, 16] Operation: 84-68=16 Exploring Operation: 84-44=40, Resulting Numbers: [68, 14, 40] Generated Node #0,1: 76:[68, 14, 40] Operation: 84-44=40 Moving to Node #0,0 Current State: 76:[44, 14, 16], Operations: ['84-68=16'] Exploring Operation: 44-14=30, Resulting Numbers: [16, 30] Generated Node #0,0,0: 76:[16, 30] Operation: 44-14=30 Exploring Operation: 16-14=2, Resulting Numbers: [44, 2] Generated Node #0,0,1: 76:[44, 2] Operation: 16-14=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[44, 2], Operations: ['84-68=16', '16-14=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,76 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 #0,0,0 Current State: 76:[16, 30], Operations: ['84-68=16', '44-14=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,76 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:[68, 14, 40], Operations: ['84-44=40'] Exploring Operation: 68+14=82, Resulting Numbers: [40, 82] Generated Node #0,1,0: 76:[40, 82] Operation: 68+14=82 Exploring Operation: 68-40=28, Resulting Numbers: [14, 28] Generated Node #0,1,1: 76:[14, 28] Operation: 68-40=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[40, 82], Operations: ['84-44=40', '68+14=82'] Exploring Operation: 40+82=122, Resulting Numbers: [122] 122,76 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[14, 28], Operations: ['84-44=40', '68-40=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 69, 72, 10, 84 ]
97
[ "72-69=3", "10+84=94", "3+94=97" ]
Current State: 97:[69, 72, 10, 84], Operations: [] Exploring Operation: 72-69=3, Resulting Numbers: [10, 84, 3] Generated Node #2: [10, 84, 3] from Operation: 72-69=3 Current State: 97:[10, 84, 3], Operations: ['72-69=3'] Exploring Operation: 10+84=94, Resulting Numbers: [3, 94] Generated Node #3: [3, 94] from Operation: 10+84=94 Current State: 97:[3, 94], Operations: ['72-69=3', '10+84=94'] Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[69, 72, 10, 84], Operations: [] Exploring Operation: 69+10=79, Resulting Numbers: [72, 84, 79] Generated Node #0,0: 97:[72, 84, 79] Operation: 69+10=79 Moving to Node #0,0 Current State: 97:[72, 84, 79], Operations: ['69+10=79'] Exploring Operation: 72+79=151, Resulting Numbers: [84, 151] Generated Node #0,0,0: 97:[84, 151] Operation: 72+79=151 Moving to Node #0,0,0 Current State: 97:[84, 151], Operations: ['69+10=79', '72+79=151'] Exploring Operation: 151-84=67, Resulting Numbers: [67] 67,97 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 38, 17, 11, 39 ]
27
[ "38+17=55", "39-11=28", "55-28=27" ]
Current State: 27:[38, 17, 11, 39], Operations: [] Exploring Operation: 38+17=55, Resulting Numbers: [11, 39, 55] Generated Node #2: [11, 39, 55] from Operation: 38+17=55 Current State: 27:[11, 39, 55], Operations: ['38+17=55'] Exploring Operation: 39-11=28, Resulting Numbers: [55, 28] Generated Node #3: [55, 28] from Operation: 39-11=28 Current State: 27:[55, 28], Operations: ['38+17=55', '39-11=28'] Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[38, 17, 11, 39], Operations: [] Exploring Operation: 39-38=1, Resulting Numbers: [17, 11, 1] Generated Node #0,0: 27:[17, 11, 1] Operation: 39-38=1 Moving to Node #0,0 Current State: 27:[17, 11, 1], Operations: ['39-38=1'] Exploring Operation: 17+11=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 17+11=28 Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['39-38=1', '17+11=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[38, 17, 11, 39], Operations: [] Exploring Operation: 39-38=1, Resulting Numbers: [17, 11, 1] Generated Node #0,0: 27:[17, 11, 1] Operation: 39-38=1 Moving to Node #0,0 Current State: 27:[17, 11, 1], Operations: ['39-38=1'] Exploring Operation: 17+11=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 17+11=28 Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['39-38=1', '17+11=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 5, 23, 53, 62 ]
92
[ "5+53=58", "62-58=4", "23*4=92" ]
Current State: 92:[5, 23, 53, 62], Operations: [] Exploring Operation: 5+53=58, Resulting Numbers: [23, 62, 58] Generated Node #2: [23, 62, 58] from Operation: 5+53=58 Current State: 92:[23, 62, 58], Operations: ['5+53=58'] Exploring Operation: 62-58=4, Resulting Numbers: [23, 4] Generated Node #3: [23, 4] from Operation: 62-58=4 Current State: 92:[23, 4], Operations: ['5+53=58', '62-58=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[5, 23, 53, 62], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [5, 23, 9] Generated Node #0,0: 92:[5, 23, 9] Operation: 62-53=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[5, 23, 9], Operations: ['62-53=9'] Exploring Operation: 9-5=4, Resulting Numbers: [23, 4] Generated Node #0,0,0: 92:[23, 4] Operation: 9-5=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[23, 4], Operations: ['62-53=9', '9-5=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[5, 23, 53, 62], Operations: [] Exploring Operation: 62-53=9, Resulting Numbers: [5, 23, 9] Generated Node #0,0: 92:[5, 23, 9] Operation: 62-53=9 Moving to Node #0,0 Current State: 92:[5, 23, 9], Operations: ['62-53=9'] Exploring Operation: 9-5=4, Resulting Numbers: [23, 4] Generated Node #0,0,0: 92:[23, 4] Operation: 9-5=4 Moving to Node #0,0,0 Current State: 92:[23, 4], Operations: ['62-53=9', '9-5=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 75, 23, 41, 5 ]
81
[ "75-41=34", "23*5=115", "115-34=81" ]
Current State: 81:[75, 23, 41, 5], Operations: [] Exploring Operation: 75-41=34, Resulting Numbers: [23, 5, 34] Generated Node #2: [23, 5, 34] from Operation: 75-41=34 Current State: 81:[23, 5, 34], Operations: ['75-41=34'] Exploring Operation: 23*5=115, Resulting Numbers: [34, 115] Generated Node #3: [34, 115] from Operation: 23*5=115 Current State: 81:[34, 115], Operations: ['75-41=34', '23*5=115'] Exploring Operation: 115-34=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[75, 23, 41, 5], Operations: [] Exploring Operation: 41-23=18, Resulting Numbers: [75, 5, 18] Generated Node #0,0: 81:[75, 5, 18] Operation: 41-23=18 Exploring Operation: 23+5=28, Resulting Numbers: [75, 41, 28] Generated Node #0,1: 81:[75, 41, 28] Operation: 23+5=28 Exploring Operation: 41-5=36, Resulting Numbers: [75, 23, 36] Generated Node #0,2: 81:[75, 23, 36] Operation: 41-5=36 Exploring Operation: 75+5=80, Resulting Numbers: [23, 41, 80] Generated Node #0,3: 81:[23, 41, 80] Operation: 75+5=80 Exploring Operation: 75-41=34, Resulting Numbers: [23, 5, 34] Generated Node #0,4: 81:[23, 5, 34] Operation: 75-41=34 Moving to Node #0,4 Current State: 81:[23, 5, 34], Operations: ['75-41=34'] Exploring Operation: 34-5=29, Resulting Numbers: [23, 29] Generated Node #0,4,0: 81:[23, 29] Operation: 34-5=29 Exploring Operation: 34-23=11, Resulting Numbers: [5, 11] Generated Node #0,4,1: 81:[5, 11] Operation: 34-23=11 Exploring Operation: 5+34=39, Resulting Numbers: [23, 39] Generated Node #0,4,2: 81:[23, 39] Operation: 5+34=39 Exploring Operation: 23-5=18, Resulting Numbers: [34, 18] Generated Node #0,4,3: 81:[34, 18] Operation: 23-5=18 Exploring Operation: 23+5=28, Resulting Numbers: [34, 28] Generated Node #0,4,4: 81:[34, 28] Operation: 23+5=28 Moving to Node #0,0 Current State: 81:[75, 5, 18], Operations: ['41-23=18'] Exploring Operation: 5+18=23, Resulting Numbers: [75, 23] Generated Node #0,0,0: 81:[75, 23] Operation: 5+18=23 Exploring Operation: 75+18=93, Resulting Numbers: [5, 93] Generated Node #0,0,1: 81:[5, 93] Operation: 75+18=93 Exploring Operation: 75+5=80, Resulting Numbers: [18, 80] Generated Node #0,0,2: 81:[18, 80] Operation: 75+5=80 Exploring Operation: 75/5=15, Resulting Numbers: [18, 15] Generated Node #0,0,3: 81:[18, 15] Operation: 75/5=15 Exploring Operation: 18-5=13, Resulting Numbers: [75, 13] Generated Node #0,0,4: 81:[75, 13] Operation: 18-5=13 Moving to Node #0,2 Current State: 81:[75, 23, 36], Operations: ['41-5=36'] Exploring Operation: 75-36=39, Resulting Numbers: [23, 39] Generated Node #0,2,0: 81:[23, 39] Operation: 75-36=39 Exploring Operation: 75+23=98, Resulting Numbers: [36, 98] Generated Node #0,2,1: 81:[36, 98] Operation: 75+23=98 Exploring Operation: 75-23=52, Resulting Numbers: [36, 52] Generated Node #0,2,2: 81:[36, 52] Operation: 75-23=52 Exploring Operation: 23+36=59, Resulting Numbers: [75, 59] Generated Node #0,2,3: 81:[75, 59] Operation: 23+36=59 Exploring Operation: 36-23=13, Resulting Numbers: [75, 13] Generated Node #0,2,4: 81:[75, 13] Operation: 36-23=13 Moving to Node #0,3 Current State: 81:[23, 41, 80], Operations: ['75+5=80'] Exploring Operation: 80-41=39, Resulting Numbers: [23, 39] Generated Node #0,3,0: 81:[23, 39] Operation: 80-41=39 Exploring Operation: 80-23=57, Resulting Numbers: [41, 57] Generated Node #0,3,1: 81:[41, 57] Operation: 80-23=57 Exploring Operation: 41-23=18, Resulting Numbers: [80, 18] Generated Node #0,3,2: 81:[80, 18] Operation: 41-23=18 Exploring Operation: 23+41=64, Resulting Numbers: [80, 64] Generated Node #0,3,3: 81:[80, 64] Operation: 23+41=64 Exploring Operation: 23+80=103, Resulting Numbers: [41, 103] Generated Node #0,3,4: 81:[41, 103] Operation: 23+80=103 Moving to Node #0,1 Current State: 81:[75, 41, 28], Operations: ['23+5=28'] Exploring Operation: 41-28=13, Resulting Numbers: [75, 13] Generated Node #0,1,0: 81:[75, 13] Operation: 41-28=13 Exploring Operation: 41+28=69, Resulting Numbers: [75, 69] Generated Node #0,1,1: 81:[75, 69] Operation: 41+28=69 Exploring Operation: 75-41=34, Resulting Numbers: [28, 34] Generated Node #0,1,2: 81:[28, 34] Operation: 75-41=34 Exploring Operation: 75-28=47, Resulting Numbers: [41, 47] Generated Node #0,1,3: 81:[41, 47] Operation: 75-28=47 Exploring Operation: 75+41=116, Resulting Numbers: [28, 116] Generated Node #0,1,4: 81:[28, 116] Operation: 75+41=116 Moving to Node #0,4,1 Current State: 81:[5, 11], Operations: ['75-41=34', '34-23=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,81 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,81 unequal: No Solution Moving to Node #0,4,0 Current State: 81:[23, 29], Operations: ['75-41=34', '34-5=29'] Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,81 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,81 unequal: No Solution Moving to Node #0,4,4 Current State: 81:[34, 28], Operations: ['75-41=34', '23+5=28'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 34*28=952, Resulting Numbers: [952] 952,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[28, 34], Operations: ['23+5=28', '75-41=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[18, 80], Operations: ['41-23=18', '75+5=80'] Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[75, 23], Operations: ['41-23=18', '5+18=23'] Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,81 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,81 unequal: No Solution Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[75, 13], Operations: ['23+5=28', '41-28=13'] Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,81 unequal: No Solution Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,2,4 Current State: 81:[75, 13], Operations: ['41-5=36', '36-23=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,81 unequal: No Solution Moving to Node #0,0,4 Current State: 81:[75, 13], Operations: ['41-23=18', '18-5=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,81 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,81 unequal: No Solution Moving to Node #0,3,2 Current State: 81:[80, 18], Operations: ['75+5=80', '41-23=18'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[5, 93], Operations: ['41-23=18', '75+18=93'] Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 5*93=465, Resulting Numbers: [465] 465,81 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[18, 15], Operations: ['41-23=18', '75/5=15'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,81 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[23, 39], Operations: ['41-5=36', '75-36=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,81 unequal: No Solution Moving to Node #0,4,3 Current State: 81:[34, 18], Operations: ['75-41=34', '23-5=18'] Exploring Operation: 34*18=612, Resulting Numbers: [612] 612,81 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,81 unequal: No Solution Moving to Node #0,3,0 Current State: 81:[23, 39], Operations: ['75+5=80', '80-41=39'] Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,81 unequal: No Solution Moving to Node #0,4,2 Current State: 81:[23, 39], Operations: ['75-41=34', '5+34=39'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[75, 69], Operations: ['23+5=28', '41+28=69'] Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,81 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[80, 64], Operations: ['75+5=80', '23+41=64'] Exploring Operation: 80*64=5120, Resulting Numbers: [5120] 5120,81 unequal: No Solution Exploring Operation: 80+64=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[36, 98], Operations: ['41-5=36', '75+23=98'] Exploring Operation: 36*98=3528, Resulting Numbers: [3528] 3528,81 unequal: No Solution Exploring Operation: 98-36=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 36+98=134, Resulting Numbers: [134] 134,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[75, 59], Operations: ['41-5=36', '23+36=59'] Exploring Operation: 75-59=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 75+59=134, Resulting Numbers: [134] 134,81 unequal: No Solution Exploring Operation: 75*59=4425, Resulting Numbers: [4425] 4425,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[36, 52], Operations: ['41-5=36', '75-23=52'] Exploring Operation: 36+52=88, Resulting Numbers: [88] 88,81 unequal: No Solution Exploring Operation: 36*52=1872, Resulting Numbers: [1872] 1872,81 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[41, 47], Operations: ['23+5=28', '75-28=47'] Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,81 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,3,4 Current State: 81:[41, 103], Operations: ['75+5=80', '23+80=103'] Exploring Operation: 103-41=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 41*103=4223, Resulting Numbers: [4223] 4223,81 unequal: No Solution Exploring Operation: 41+103=144, Resulting Numbers: [144] 144,81 unequal: No Solution Moving to Node #0,1,4 Current State: 81:[28, 116], Operations: ['23+5=28', '75+41=116'] Exploring Operation: 28+116=144, Resulting Numbers: [144] 144,81 unequal: No Solution Exploring Operation: 28*116=3248, Resulting Numbers: [3248] 3248,81 unequal: No Solution Exploring Operation: 116-28=88, Resulting Numbers: [88] 88,81 unequal: No Solution Moving to Node #0,3,1 Current State: 81:[41, 57], Operations: ['75+5=80', '80-23=57'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,81 unequal: No Solution Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,81 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 45, 81, 60, 7 ]
15
[ "45*7=315", "81-60=21", "315/21=15" ]
Current State: 15:[45, 81, 60, 7], Operations: [] Exploring Operation: 45*7=315, Resulting Numbers: [81, 60, 315] Generated Node #2: [81, 60, 315] from Operation: 45*7=315 Current State: 15:[81, 60, 315], Operations: ['45*7=315'] Exploring Operation: 81-60=21, Resulting Numbers: [315, 21] Generated Node #3: [315, 21] from Operation: 81-60=21 Current State: 15:[315, 21], Operations: ['45*7=315', '81-60=21'] Exploring Operation: 315/21=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[45, 81, 60, 7], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [45, 7, 21] Generated Node #0,0: 15:[45, 7, 21] Operation: 81-60=21 Exploring Operation: 81-45=36, Resulting Numbers: [60, 7, 36] Generated Node #0,1: 15:[60, 7, 36] Operation: 81-45=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[45, 7, 21], Operations: ['81-60=21'] Exploring Operation: 45-21=24, Resulting Numbers: [7, 24] Generated Node #0,0,0: 15:[7, 24] Operation: 45-21=24 Exploring Operation: 45-7=38, Resulting Numbers: [21, 38] Generated Node #0,0,1: 15:[21, 38] Operation: 45-7=38 Moving to Node #0,0,0 Current State: 15:[7, 24], Operations: ['81-60=21', '45-21=24'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[21, 38], Operations: ['81-60=21', '45-7=38'] Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[60, 7, 36], Operations: ['81-45=36'] Exploring Operation: 60-36=24, Resulting Numbers: [7, 24] Generated Node #0,1,0: 15:[7, 24] Operation: 60-36=24 Exploring Operation: 60-7=53, Resulting Numbers: [36, 53] Generated Node #0,1,1: 15:[36, 53] Operation: 60-7=53 Moving to Node #0,1,0 Current State: 15:[7, 24], Operations: ['81-45=36', '60-36=24'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[36, 53], Operations: ['81-45=36', '60-7=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,15 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,15 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
[ 33, 43, 45, 85 ]
59
[ "33+85=118", "45-43=2", "118/2=59" ]
Current State: 59:[33, 43, 45, 85], Operations: [] Exploring Operation: 33+85=118, Resulting Numbers: [43, 45, 118] Generated Node #2: [43, 45, 118] from Operation: 33+85=118 Current State: 59:[43, 45, 118], Operations: ['33+85=118'] Exploring Operation: 45-43=2, Resulting Numbers: [118, 2] Generated Node #3: [118, 2] from Operation: 45-43=2 Current State: 59:[118, 2], Operations: ['33+85=118', '45-43=2'] Exploring Operation: 118/2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[33, 43, 45, 85], Operations: [] Exploring Operation: 85-33=52, Resulting Numbers: [43, 45, 52] Generated Node #0,0: 59:[43, 45, 52] Operation: 85-33=52 Exploring Operation: 85-43=42, Resulting Numbers: [33, 45, 42] Generated Node #0,1: 59:[33, 45, 42] Operation: 85-43=42 Exploring Operation: 33+43=76, Resulting Numbers: [45, 85, 76] Generated Node #0,2: 59:[45, 85, 76] Operation: 33+43=76 Exploring Operation: 33+45=78, Resulting Numbers: [43, 85, 78] Generated Node #0,3: 59:[43, 85, 78] Operation: 33+45=78 Moving to Node #0,0 Current State: 59:[43, 45, 52], Operations: ['85-33=52'] Exploring Operation: 43+52=95, Resulting Numbers: [45, 95] Generated Node #0,0,0: 59:[45, 95] Operation: 43+52=95 Exploring Operation: 45+52=97, Resulting Numbers: [43, 97] Generated Node #0,0,1: 59:[43, 97] Operation: 45+52=97 Exploring Operation: 45-43=2, Resulting Numbers: [52, 2] Generated Node #0,0,2: 59:[52, 2] Operation: 45-43=2 Exploring Operation: 43+45=88, Resulting Numbers: [52, 88] Generated Node #0,0,3: 59:[52, 88] Operation: 43+45=88 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[52, 88], Operations: ['85-33=52', '43+45=88'] Exploring Operation: 52*88=4576, Resulting Numbers: [4576] 4576,59 unequal: No Solution Exploring Operation: 88-52=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 52+88=140, Resulting Numbers: [140] 140,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[45, 95], Operations: ['85-33=52', '43+52=95'] Exploring Operation: 45*95=4275, Resulting Numbers: [4275] 4275,59 unequal: No Solution Exploring Operation: 45+95=140, Resulting Numbers: [140] 140,59 unequal: No Solution Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[43, 97], Operations: ['85-33=52', '45+52=97'] Exploring Operation: 43+97=140, Resulting Numbers: [140] 140,59 unequal: No Solution Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 43*97=4171, Resulting Numbers: [4171] 4171,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[52, 2], Operations: ['85-33=52', '45-43=2'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,59 unequal: No Solution Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[45, 85, 76], Operations: ['33+43=76'] Exploring Operation: 85-45=40, Resulting Numbers: [76, 40] Generated Node #0,2,0: 59:[76, 40] Operation: 85-45=40 Exploring Operation: 45+85=130, Resulting Numbers: [76, 130] Generated Node #0,2,1: 59:[76, 130] Operation: 45+85=130 Exploring Operation: 85-76=9, Resulting Numbers: [45, 9] Generated Node #0,2,2: 59:[45, 9] Operation: 85-76=9 Exploring Operation: 76-45=31, Resulting Numbers: [85, 31] Generated Node #0,2,3: 59:[85, 31] Operation: 76-45=31 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[76, 40], Operations: ['33+43=76', '85-45=40'] Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 76*40=3040, Resulting Numbers: [3040] 3040,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[85, 31], Operations: ['33+43=76', '76-45=31'] Exploring Operation: 85-31=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 85+31=116, Resulting Numbers: [116] 116,59 unequal: No Solution Exploring Operation: 85*31=2635, Resulting Numbers: [2635] 2635,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[45, 9], Operations: ['33+43=76', '85-76=9'] Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 45*9=405, Resulting Numbers: [405] 405,59 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 45+9=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[76, 130], Operations: ['33+43=76', '45+85=130'] Exploring Operation: 76+130=206, Resulting Numbers: [206] 206,59 unequal: No Solution Exploring Operation: 130-76=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 76*130=9880, Resulting Numbers: [9880] 9880,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[33, 45, 42], Operations: ['85-43=42'] Exploring Operation: 45+42=87, Resulting Numbers: [33, 87] Generated Node #0,1,0: 59:[33, 87] Operation: 45+42=87 Exploring Operation: 45-33=12, Resulting Numbers: [42, 12] Generated Node #0,1,1: 59:[42, 12] Operation: 45-33=12 Exploring Operation: 33+42=75, Resulting Numbers: [45, 75] Generated Node #0,1,2: 59:[45, 75] Operation: 33+42=75 Exploring Operation: 33+45=78, Resulting Numbers: [42, 78] Generated Node #0,1,3: 59:[42, 78] Operation: 33+45=78 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[45, 75], Operations: ['85-43=42', '33+42=75'] Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,59 unequal: No Solution Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 59:[42, 78], Operations: ['85-43=42', '33+45=78'] Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 42+78=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 42*78=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[33, 87], Operations: ['85-43=42', '45+42=87'] Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,59 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[42, 12], Operations: ['85-43=42', '45-33=12'] Exploring Operation: 42*12=504, Resulting Numbers: [504] 504,59 unequal: No Solution Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 59:[43, 85, 78], Operations: ['33+45=78'] Exploring Operation: 43+85=128, Resulting Numbers: [78, 128] Generated Node #0,3,0: 59:[78, 128] Operation: 43+85=128 Exploring Operation: 78-43=35, Resulting Numbers: [85, 35] Generated Node #0,3,1: 59:[85, 35] Operation: 78-43=35 Exploring Operation: 85-43=42, Resulting Numbers: [78, 42] Generated Node #0,3,2: 59:[78, 42] Operation: 85-43=42 Exploring Operation: 85-78=7, Resulting Numbers: [43, 7] Generated Node #0,3,3: 59:[43, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[78, 42], Operations: ['33+45=78', '85-43=42'] Exploring Operation: 78*42=3276, Resulting Numbers: [3276] 3276,59 unequal: No Solution Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 78+42=120, Resulting Numbers: [120] 120,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[85, 35], Operations: ['33+45=78', '78-43=35'] Exploring Operation: 85-35=50, Resulting Numbers: [50] 50,59 unequal: No Solution Exploring Operation: 85*35=2975, Resulting Numbers: [2975] 2975,59 unequal: No Solution Exploring Operation: 85+35=120, Resulting Numbers: [120] 120,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[43, 7], Operations: ['33+45=78', '85-78=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,59 unequal: No Solution Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[78, 128], Operations: ['33+45=78', '43+85=128'] Exploring Operation: 128-78=50, Resulting Numbers: [50] 50,59 unequal: No Solution Exploring Operation: 78*128=9984, Resulting Numbers: [9984] 9984,59 unequal: No Solution Exploring Operation: 78+128=206, Resulting Numbers: [206] 206,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 53, 85, 40, 27 ]
35
[ "85-53=32", "40+27=67", "67-32=35" ]
Current State: 35:[53, 85, 40, 27], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [40, 27, 32] Generated Node #2: [40, 27, 32] from Operation: 85-53=32 Current State: 35:[40, 27, 32], Operations: ['85-53=32'] Exploring Operation: 40+27=67, Resulting Numbers: [32, 67] Generated Node #3: [32, 67] from Operation: 40+27=67 Current State: 35:[32, 67], Operations: ['85-53=32', '40+27=67'] Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[53, 85, 40, 27], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [40, 27, 32] Generated Node #0,0: 35:[40, 27, 32] Operation: 85-53=32 Exploring Operation: 85-27=58, Resulting Numbers: [53, 40, 58] Generated Node #0,1: 35:[53, 40, 58] Operation: 85-27=58 Exploring Operation: 85-40=45, Resulting Numbers: [53, 27, 45] Generated Node #0,2: 35:[53, 27, 45] Operation: 85-40=45 Moving to Node #0,0 Current State: 35:[40, 27, 32], Operations: ['85-53=32'] Exploring Operation: 32-27=5, Resulting Numbers: [40, 5] Generated Node #0,0,0: 35:[40, 5] Operation: 32-27=5 Exploring Operation: 40-32=8, Resulting Numbers: [27, 8] Generated Node #0,0,1: 35:[27, 8] Operation: 40-32=8 Exploring Operation: 40-27=13, Resulting Numbers: [32, 13] Generated Node #0,0,2: 35:[32, 13] Operation: 40-27=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[40, 5], Operations: ['85-53=32', '32-27=5'] Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[53, 85, 40, 27], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [40, 27, 32] Generated Node #0,0: 35:[40, 27, 32] Operation: 85-53=32 Moving to Node #0,0 Current State: 35:[40, 27, 32], Operations: ['85-53=32'] Exploring Operation: 32-27=5, Resulting Numbers: [40, 5] Generated Node #0,0,0: 35:[40, 5] Operation: 32-27=5 Moving to Node #0,0,0 Current State: 35:[40, 5], Operations: ['85-53=32', '32-27=5'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 42, 57, 93, 54 ]
11
[ "57-54=3", "93/3=31", "42-31=11" ]
Current State: 11:[42, 57, 93, 54], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [42, 93, 3] Generated Node #2: [42, 93, 3] from Operation: 57-54=3 Current State: 11:[42, 93, 3], Operations: ['57-54=3'] Exploring Operation: 93/3=31, Resulting Numbers: [42, 31] Generated Node #3: [42, 31] from Operation: 93/3=31 Current State: 11:[42, 31], Operations: ['57-54=3', '93/3=31'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[42, 57, 93, 54], Operations: [] Exploring Operation: 93-54=39, Resulting Numbers: [42, 57, 39] Generated Node #0,0: 11:[42, 57, 39] Operation: 93-54=39 Exploring Operation: 93-42=51, Resulting Numbers: [57, 54, 51] Generated Node #0,1: 11:[57, 54, 51] Operation: 93-42=51 Exploring Operation: 93-57=36, Resulting Numbers: [42, 54, 36] Generated Node #0,2: 11:[42, 54, 36] Operation: 93-57=36 Exploring Operation: 57-42=15, Resulting Numbers: [93, 54, 15] Generated Node #0,3: 11:[93, 54, 15] Operation: 57-42=15 Exploring Operation: 57-54=3, Resulting Numbers: [42, 93, 3] Generated Node #0,4: 11:[42, 93, 3] Operation: 57-54=3 Moving to Node #0,2 Current State: 11:[42, 54, 36], Operations: ['93-57=36'] Exploring Operation: 54-42=12, Resulting Numbers: [36, 12] Generated Node #0,2,0: 11:[36, 12] Operation: 54-42=12 Exploring Operation: 42-36=6, Resulting Numbers: [54, 6] Generated Node #0,2,1: 11:[54, 6] Operation: 42-36=6 Exploring Operation: 42+54=96, Resulting Numbers: [36, 96] Generated Node #0,2,2: 11:[36, 96] Operation: 42+54=96 Exploring Operation: 54-36=18, Resulting Numbers: [42, 18] Generated Node #0,2,3: 11:[42, 18] Operation: 54-36=18 Exploring Operation: 42+36=78, Resulting Numbers: [54, 78] Generated Node #0,2,4: 11:[54, 78] Operation: 42+36=78 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[36, 12], Operations: ['93-57=36', '54-42=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 36*12=432, Resulting Numbers: [432] 432,11 unequal: No Solution Exploring Operation: 36+12=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[42, 18], Operations: ['93-57=36', '54-36=18'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,11 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[54, 6], Operations: ['93-57=36', '42-36=6'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,11 unequal: No Solution Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[36, 96], Operations: ['93-57=36', '42+54=96'] Exploring Operation: 96-36=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 36*96=3456, Resulting Numbers: [3456] 3456,11 unequal: No Solution Exploring Operation: 36+96=132, Resulting Numbers: [132] 132,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 11:[54, 78], Operations: ['93-57=36', '42+36=78'] Exploring Operation: 54+78=132, Resulting Numbers: [132] 132,11 unequal: No Solution Exploring Operation: 54*78=4212, Resulting Numbers: [4212] 4212,11 unequal: No Solution Exploring Operation: 78-54=24, Resulting Numbers: [24] 24,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 11:[42, 57, 39], Operations: ['93-54=39'] Exploring Operation: 42-39=3, Resulting Numbers: [57, 3] Generated Node #0,0,0: 11:[57, 3] Operation: 42-39=3 Exploring Operation: 57-42=15, Resulting Numbers: [39, 15] Generated Node #0,0,1: 11:[39, 15] Operation: 57-42=15 Exploring Operation: 57-39=18, Resulting Numbers: [42, 18] Generated Node #0,0,2: 11:[42, 18] Operation: 57-39=18 Exploring Operation: 42+57=99, Resulting Numbers: [39, 99] Generated Node #0,0,3: 11:[39, 99] Operation: 42+57=99 Exploring Operation: 42+39=81, Resulting Numbers: [57, 81] Generated Node #0,0,4: 11:[57, 81] Operation: 42+39=81 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[39, 15], Operations: ['93-54=39', '57-42=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,11 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[42, 18], Operations: ['93-54=39', '57-39=18'] Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,11 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[57, 3], Operations: ['93-54=39', '42-39=3'] Exploring Operation: 57+3=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 57*3=171, Resulting Numbers: [171] 171,11 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 #0,0,3 Current State: 11:[39, 99], Operations: ['93-54=39', '42+57=99'] Exploring Operation: 99-39=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 39+99=138, Resulting Numbers: [138] 138,11 unequal: No Solution Exploring Operation: 39*99=3861, Resulting Numbers: [3861] 3861,11 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 #0,0,4 Current State: 11:[57, 81], Operations: ['93-54=39', '42+39=81'] Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 57+81=138, Resulting Numbers: [138] 138,11 unequal: No Solution Exploring Operation: 57*81=4617, Resulting Numbers: [4617] 4617,11 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: 11:[42, 93, 3], Operations: ['57-54=3'] Exploring Operation: 93-42=51, Resulting Numbers: [3, 51] Generated Node #0,4,0: 11:[3, 51] Operation: 93-42=51 Exploring Operation: 93/3=31, Resulting Numbers: [42, 31] Generated Node #0,4,1: 11:[42, 31] Operation: 93/3=31 Exploring Operation: 42-3=39, Resulting Numbers: [93, 39] Generated Node #0,4,2: 11:[93, 39] Operation: 42-3=39 Exploring Operation: 42/3=14, Resulting Numbers: [93, 14] Generated Node #0,4,3: 11:[93, 14] Operation: 42/3=14 Exploring Operation: 93-3=90, Resulting Numbers: [42, 90] Generated Node #0,4,4: 11:[42, 90] Operation: 93-3=90 Moving to Node #0,1 Current State: 11:[57, 54, 51], Operations: ['93-42=51'] Exploring Operation: 57-51=6, Resulting Numbers: [54, 6] Generated Node #0,1,0: 11:[54, 6] Operation: 57-51=6 Exploring Operation: 57-54=3, Resulting Numbers: [51, 3] Generated Node #0,1,1: 11:[51, 3] Operation: 57-54=3 Exploring Operation: 57+51=108, Resulting Numbers: [54, 108] Generated Node #0,1,2: 11:[54, 108] Operation: 57+51=108 Exploring Operation: 57+54=111, Resulting Numbers: [51, 111] Generated Node #0,1,3: 11:[51, 111] Operation: 57+54=111 Exploring Operation: 54-51=3, Resulting Numbers: [57, 3] Generated Node #0,1,4: 11:[57, 3] Operation: 54-51=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[54, 6], Operations: ['93-42=51', '57-51=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,11 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[51, 3], Operations: ['93-42=51', '57-54=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,11 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 11:[57, 3], Operations: ['93-42=51', '54-51=3'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 57+3=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 57*3=171, Resulting Numbers: [171] 171,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[54, 108], Operations: ['93-42=51', '57+51=108'] Exploring Operation: 54*108=5832, Resulting Numbers: [5832] 5832,11 unequal: No Solution Exploring Operation: 108/54=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 54+108=162, Resulting Numbers: [162] 162,11 unequal: No Solution Exploring Operation: 108-54=54, Resulting Numbers: [54] 54,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 11:[51, 111], Operations: ['93-42=51', '57+54=111'] Exploring Operation: 51*111=5661, Resulting Numbers: [5661] 5661,11 unequal: No Solution Exploring Operation: 111-51=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 51+111=162, Resulting Numbers: [162] 162,11 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: 11:[93, 54, 15], Operations: ['57-42=15'] Exploring Operation: 93-54=39, Resulting Numbers: [15, 39] Generated Node #0,3,0: 11:[15, 39] Operation: 93-54=39 Exploring Operation: 93+15=108, Resulting Numbers: [54, 108] Generated Node #0,3,1: 11:[54, 108] Operation: 93+15=108 Exploring Operation: 54-15=39, Resulting Numbers: [93, 39] Generated Node #0,3,2: 11:[93, 39] Operation: 54-15=39 Exploring Operation: 93-15=78, Resulting Numbers: [54, 78] Generated Node #0,3,3: 11:[54, 78] Operation: 93-15=78 Exploring Operation: 93+54=147, Resulting Numbers: [15, 147] Generated Node #0,3,4: 11:[15, 147] Operation: 93+54=147 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[15, 39], Operations: ['57-42=15', '93-54=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[93, 39], Operations: ['57-42=15', '54-15=39'] Exploring Operation: 93+39=132, Resulting Numbers: [132] 132,11 unequal: No Solution Exploring Operation: 93*39=3627, Resulting Numbers: [3627] 3627,11 unequal: No Solution Exploring Operation: 93-39=54, Resulting Numbers: [54] 54,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[54, 78], Operations: ['57-42=15', '93-15=78'] Exploring Operation: 54+78=132, Resulting Numbers: [132] 132,11 unequal: No Solution Exploring Operation: 78-54=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 54*78=4212, Resulting Numbers: [4212] 4212,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[54, 108], Operations: ['57-42=15', '93+15=108'] Exploring Operation: 54+108=162, Resulting Numbers: [162] 162,11 unequal: No Solution Exploring Operation: 54*108=5832, Resulting Numbers: [5832] 5832,11 unequal: No Solution Exploring Operation: 108-54=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 108/54=2, Resulting Numbers: [2] 2,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 11:[15, 147], Operations: ['57-42=15', '93+54=147'] Exploring Operation: 15*147=2205, Resulting Numbers: [2205] 2205,11 unequal: No Solution Exploring Operation: 147-15=132, Resulting Numbers: [132] 132,11 unequal: No Solution Exploring Operation: 15+147=162, Resulting Numbers: [162] 162,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 11:[3, 51], Operations: ['57-54=3', '93-42=51'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,11 unequal: No Solution Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,11 unequal: No Solution Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[42, 31], Operations: ['57-54=3', '93/3=31'] Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,11 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[42, 57, 93, 54], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [42, 93, 3] Generated Node #0,4: 11:[42, 93, 3] Operation: 57-54=3 Moving to Node #0,4 Current State: 11:[42, 93, 3], Operations: ['57-54=3'] Exploring Operation: 93/3=31, Resulting Numbers: [42, 31] Generated Node #0,4,1: 11:[42, 31] Operation: 93/3=31 Moving to Node #0,4,1 Current State: 11:[42, 31], Operations: ['57-54=3', '93/3=31'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.905382
hs_5
mult_heuristic
[ 3, 22, 48, 90 ]
44
[ "48-3=45", "22*90=1980", "1980/45=44" ]
Current State: 44:[3, 22, 48, 90], Operations: [] Exploring Operation: 48-3=45, Resulting Numbers: [22, 90, 45] Generated Node #2: [22, 90, 45] from Operation: 48-3=45 Current State: 44:[22, 90, 45], Operations: ['48-3=45'] Exploring Operation: 22*90=1980, Resulting Numbers: [45, 1980] Generated Node #3: [45, 1980] from Operation: 22*90=1980 Current State: 44:[45, 1980], Operations: ['48-3=45', '22*90=1980'] Exploring Operation: 1980/45=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[3, 22, 48, 90], Operations: [] Exploring Operation: 90-48=42, Resulting Numbers: [3, 22, 42] Generated Node #0,0: 44:[3, 22, 42] Operation: 90-48=42 Moving to Node #0,0 Current State: 44:[3, 22, 42], Operations: ['90-48=42'] Exploring Operation: 3+42=45, Resulting Numbers: [22, 45] Generated Node #0,0,0: 44:[22, 45] Operation: 3+42=45 Moving to Node #0,0,0 Current State: 44:[22, 45], Operations: ['90-48=42', '3+42=45'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,44 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 14, 57, 4, 59 ]
64
[ "57-14=43", "59-43=16", "4*16=64" ]
Current State: 64:[14, 57, 4, 59], Operations: [] Exploring Operation: 57-14=43, Resulting Numbers: [4, 59, 43] Generated Node #2: [4, 59, 43] from Operation: 57-14=43 Current State: 64:[4, 59, 43], Operations: ['57-14=43'] Exploring Operation: 59-43=16, Resulting Numbers: [4, 16] Generated Node #3: [4, 16] from Operation: 59-43=16 Current State: 64:[4, 16], Operations: ['57-14=43', '59-43=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[14, 57, 4, 59], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [14, 4, 2] Generated Node #0,0: 64:[14, 4, 2] Operation: 59-57=2 Exploring Operation: 14+57=71, Resulting Numbers: [4, 59, 71] Generated Node #0,1: 64:[4, 59, 71] Operation: 14+57=71 Exploring Operation: 4+59=63, Resulting Numbers: [14, 57, 63] Generated Node #0,2: 64:[14, 57, 63] Operation: 4+59=63 Exploring Operation: 57+4=61, Resulting Numbers: [14, 59, 61] Generated Node #0,3: 64:[14, 59, 61] Operation: 57+4=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[14, 4, 2], Operations: ['59-57=2'] Exploring Operation: 14-4=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 64:[2, 10] Operation: 14-4=10 Exploring Operation: 14+2=16, Resulting Numbers: [4, 16] Generated Node #0,0,1: 64:[4, 16] Operation: 14+2=16 Exploring Operation: 14+4=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 64:[2, 18] Operation: 14+4=18 Exploring Operation: 14/2=7, Resulting Numbers: [4, 7] Generated Node #0,0,3: 64:[4, 7] Operation: 14/2=7 Moving to Node #0,0,1 Current State: 64:[4, 16], Operations: ['59-57=2', '14+2=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[14, 57, 4, 59], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [14, 4, 2] Generated Node #0,0: 64:[14, 4, 2] Operation: 59-57=2 Moving to Node #0,0 Current State: 64:[14, 4, 2], Operations: ['59-57=2'] Exploring Operation: 14+2=16, Resulting Numbers: [4, 16] Generated Node #0,0,1: 64:[4, 16] Operation: 14+2=16 Moving to Node #0,0,1 Current State: 64:[4, 16], Operations: ['59-57=2', '14+2=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 76, 5, 21, 10 ]
82
[ "76-5=71", "21-10=11", "71+11=82" ]
Current State: 82:[76, 5, 21, 10], Operations: [] Exploring Operation: 76-5=71, Resulting Numbers: [21, 10, 71] Generated Node #2: [21, 10, 71] from Operation: 76-5=71 Current State: 82:[21, 10, 71], Operations: ['76-5=71'] Exploring Operation: 21-10=11, Resulting Numbers: [71, 11] Generated Node #3: [71, 11] from Operation: 21-10=11 Current State: 82:[71, 11], Operations: ['76-5=71', '21-10=11'] Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[76, 5, 21, 10], Operations: [] Exploring Operation: 21+10=31, Resulting Numbers: [76, 5, 31] Generated Node #0,0: 82:[76, 5, 31] Operation: 21+10=31 Exploring Operation: 10/5=2, Resulting Numbers: [76, 21, 2] Generated Node #0,1: 82:[76, 21, 2] Operation: 10/5=2 Exploring Operation: 21-10=11, Resulting Numbers: [76, 5, 11] Generated Node #0,2: 82:[76, 5, 11] Operation: 21-10=11 Exploring Operation: 76-21=55, Resulting Numbers: [5, 10, 55] Generated Node #0,3: 82:[5, 10, 55] Operation: 76-21=55 Moving to Node #0,2 Current State: 82:[76, 5, 11], Operations: ['21-10=11'] Exploring Operation: 76+5=81, Resulting Numbers: [11, 81] Generated Node #0,2,0: 82:[11, 81] Operation: 76+5=81 Exploring Operation: 11-5=6, Resulting Numbers: [76, 6] Generated Node #0,2,1: 82:[76, 6] Operation: 11-5=6 Exploring Operation: 76+11=87, Resulting Numbers: [5, 87] Generated Node #0,2,2: 82:[5, 87] Operation: 76+11=87 Exploring Operation: 76-5=71, Resulting Numbers: [11, 71] Generated Node #0,2,3: 82:[11, 71] Operation: 76-5=71 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[5, 87], Operations: ['21-10=11', '76+11=87'] Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[76, 5, 21, 10], Operations: [] Exploring Operation: 21-10=11, Resulting Numbers: [76, 5, 11] Generated Node #0,2: 82:[76, 5, 11] Operation: 21-10=11 Moving to Node #0,2 Current State: 82:[76, 5, 11], Operations: ['21-10=11'] Exploring Operation: 76+11=87, Resulting Numbers: [5, 87] Generated Node #0,2,2: 82:[5, 87] Operation: 76+11=87 Moving to Node #0,2,2 Current State: 82:[5, 87], Operations: ['21-10=11', '76+11=87'] Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 2, 24, 42, 77 ]
32
[ "42/2=21", "77-24=53", "53-21=32" ]
Current State: 32:[2, 24, 42, 77], Operations: [] Exploring Operation: 42/2=21, Resulting Numbers: [24, 77, 21] Generated Node #2: [24, 77, 21] from Operation: 42/2=21 Current State: 32:[24, 77, 21], Operations: ['42/2=21'] Exploring Operation: 77-24=53, Resulting Numbers: [21, 53] Generated Node #3: [21, 53] from Operation: 77-24=53 Current State: 32:[21, 53], Operations: ['42/2=21', '77-24=53'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[2, 24, 42, 77], Operations: [] Exploring Operation: 77-42=35, Resulting Numbers: [2, 24, 35] Generated Node #0,0: 32:[2, 24, 35] Operation: 77-42=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[2, 24, 35], Operations: ['77-42=35'] Exploring Operation: 35-24=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 32:[2, 11] Operation: 35-24=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[2, 11], Operations: ['77-42=35', '35-24=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,32 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
[ 74, 24, 64, 52 ]
86
[ "74+24=98", "64-52=12", "98-12=86" ]
Current State: 86:[74, 24, 64, 52], Operations: [] Exploring Operation: 74+24=98, Resulting Numbers: [64, 52, 98] Generated Node #2: [64, 52, 98] from Operation: 74+24=98 Current State: 86:[64, 52, 98], Operations: ['74+24=98'] Exploring Operation: 64-52=12, Resulting Numbers: [98, 12] Generated Node #3: [98, 12] from Operation: 64-52=12 Current State: 86:[98, 12], Operations: ['74+24=98', '64-52=12'] Exploring Operation: 98-12=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[74, 24, 64, 52], Operations: [] Exploring Operation: 24+64=88, Resulting Numbers: [74, 52, 88] Generated Node #0,0: 86:[74, 52, 88] Operation: 24+64=88 Exploring Operation: 64-24=40, Resulting Numbers: [74, 52, 40] Generated Node #0,1: 86:[74, 52, 40] Operation: 64-24=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[74, 52, 88], Operations: ['24+64=88'] Exploring Operation: 88-74=14, Resulting Numbers: [52, 14] Generated Node #0,0,0: 86:[52, 14] Operation: 88-74=14 Exploring Operation: 88-52=36, Resulting Numbers: [74, 36] Generated Node #0,0,1: 86:[74, 36] Operation: 88-52=36 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[74, 36], Operations: ['24+64=88', '88-52=36'] Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 74+36=110, Resulting Numbers: [110] 110,86 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 #0,0,0 Current State: 86:[52, 14], Operations: ['24+64=88', '88-74=14'] Exploring Operation: 52+14=66, Resulting Numbers: [66] 66,86 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,86 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:[74, 52, 40], Operations: ['64-24=40'] Exploring Operation: 52+40=92, Resulting Numbers: [74, 92] Generated Node #0,1,0: 86:[74, 92] Operation: 52+40=92 Exploring Operation: 74-40=34, Resulting Numbers: [52, 34] Generated Node #0,1,1: 86:[52, 34] Operation: 74-40=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[74, 92], Operations: ['64-24=40', '52+40=92'] Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 74+92=166, Resulting Numbers: [166] 166,86 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 #0,1,1 Current State: 86:[52, 34], Operations: ['64-24=40', '74-40=34'] Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[74, 24, 64, 52], Operations: [] Exploring Operation: 64-24=40, Resulting Numbers: [74, 52, 40] Generated Node #0,1: 86:[74, 52, 40] Operation: 64-24=40 Moving to Node #0,1 Current State: 86:[74, 52, 40], Operations: ['64-24=40'] Exploring Operation: 74-40=34, Resulting Numbers: [52, 34] Generated Node #0,1,1: 86:[52, 34] Operation: 74-40=34 Moving to Node #0,1,1 Current State: 86:[52, 34], Operations: ['64-24=40', '74-40=34'] Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 54, 98, 80, 37 ]
53
[ "80*37=2960", "2960-98=2862", "2862/54=53" ]
Current State: 53:[54, 98, 80, 37], Operations: [] Exploring Operation: 80*37=2960, Resulting Numbers: [54, 98, 2960] Generated Node #2: [54, 98, 2960] from Operation: 80*37=2960 Current State: 53:[54, 98, 2960], Operations: ['80*37=2960'] Exploring Operation: 2960-98=2862, Resulting Numbers: [54, 2862] Generated Node #3: [54, 2862] from Operation: 2960-98=2862 Current State: 53:[54, 2862], Operations: ['80*37=2960', '2960-98=2862'] Exploring Operation: 2862/54=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[54, 98, 80, 37], Operations: [] Exploring Operation: 98-37=61, Resulting Numbers: [54, 80, 61] Generated Node #0,0: 53:[54, 80, 61] Operation: 98-37=61 Moving to Node #0,0 Current State: 53:[54, 80, 61], Operations: ['98-37=61'] Exploring Operation: 80-54=26, Resulting Numbers: [61, 26] Generated Node #0,0,0: 53:[61, 26] Operation: 80-54=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[61, 26], Operations: ['98-37=61', '80-54=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 56, 49, 58, 22 ]
25
[ "56+49=105", "58+22=80", "105-80=25" ]
Current State: 25:[56, 49, 58, 22], Operations: [] Exploring Operation: 56+49=105, Resulting Numbers: [58, 22, 105] Generated Node #2: [58, 22, 105] from Operation: 56+49=105 Current State: 25:[58, 22, 105], Operations: ['56+49=105'] Exploring Operation: 58+22=80, Resulting Numbers: [105, 80] Generated Node #3: [105, 80] from Operation: 58+22=80 Current State: 25:[105, 80], Operations: ['56+49=105', '58+22=80'] Exploring Operation: 105-80=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[56, 49, 58, 22], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [49, 22, 2] Generated Node #0,0: 25:[49, 22, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 25:[49, 22, 2], Operations: ['58-56=2'] Exploring Operation: 49-22=27, Resulting Numbers: [2, 27] Generated Node #0,0,0: 25:[2, 27] Operation: 49-22=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[2, 27], Operations: ['58-56=2', '49-22=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[56, 49, 58, 22], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [49, 22, 2] Generated Node #0,0: 25:[49, 22, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 25:[49, 22, 2], Operations: ['58-56=2'] Exploring Operation: 49-22=27, Resulting Numbers: [2, 27] Generated Node #0,0,0: 25:[2, 27] Operation: 49-22=27 Moving to Node #0,0,0 Current State: 25:[2, 27], Operations: ['58-56=2', '49-22=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 31, 2, 12, 4 ]
38
[ "31-12=19", "4-2=2", "19*2=38" ]
Current State: 38:[31, 2, 12, 4], Operations: [] Exploring Operation: 31-12=19, Resulting Numbers: [2, 4, 19] Generated Node #2: [2, 4, 19] from Operation: 31-12=19 Current State: 38:[2, 4, 19], Operations: ['31-12=19'] Exploring Operation: 4-2=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 4-2=2 Current State: 38:[19, 2], Operations: ['31-12=19', '4-2=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[31, 2, 12, 4], Operations: [] Exploring Operation: 31-12=19, Resulting Numbers: [2, 4, 19] Generated Node #0,0: 38:[2, 4, 19] Operation: 31-12=19 Moving to Node #0,0 Current State: 38:[2, 4, 19], Operations: ['31-12=19'] Exploring Operation: 4-2=2, Resulting Numbers: [19, 2] Generated Node #0,0,0: 38:[19, 2] Operation: 4-2=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[19, 2], Operations: ['31-12=19', '4-2=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[31, 2, 12, 4], Operations: [] Exploring Operation: 31-12=19, Resulting Numbers: [2, 4, 19] Generated Node #0,0: 38:[2, 4, 19] Operation: 31-12=19 Moving to Node #0,0 Current State: 38:[2, 4, 19], Operations: ['31-12=19'] Exploring Operation: 4-2=2, Resulting Numbers: [19, 2] Generated Node #0,0,0: 38:[19, 2] Operation: 4-2=2 Moving to Node #0,0,0 Current State: 38:[19, 2], Operations: ['31-12=19', '4-2=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 12, 5, 46, 9 ]
97
[ "12*5=60", "46-9=37", "60+37=97" ]
Current State: 97:[12, 5, 46, 9], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [46, 9, 60] Generated Node #2: [46, 9, 60] from Operation: 12*5=60 Current State: 97:[46, 9, 60], Operations: ['12*5=60'] Exploring Operation: 46-9=37, Resulting Numbers: [60, 37] Generated Node #3: [60, 37] from Operation: 46-9=37 Current State: 97:[60, 37], Operations: ['12*5=60', '46-9=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[12, 5, 46, 9], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [46, 9, 60] Generated Node #0,0: 97:[46, 9, 60] Operation: 12*5=60 Exploring Operation: 12*9=108, Resulting Numbers: [5, 46, 108] Generated Node #0,1: 97:[5, 46, 108] Operation: 12*9=108 Exploring Operation: 5*9=45, Resulting Numbers: [12, 46, 45] Generated Node #0,2: 97:[12, 46, 45] Operation: 5*9=45 Exploring Operation: 12+46=58, Resulting Numbers: [5, 9, 58] Generated Node #0,3: 97:[5, 9, 58] Operation: 12+46=58 Exploring Operation: 12+5=17, Resulting Numbers: [46, 9, 17] Generated Node #0,4: 97:[46, 9, 17] Operation: 12+5=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[5, 46, 108], Operations: ['12*9=108'] Exploring Operation: 108-5=103, Resulting Numbers: [46, 103] Generated Node #0,1,0: 97:[46, 103] Operation: 108-5=103 Exploring Operation: 5+108=113, Resulting Numbers: [46, 113] Generated Node #0,1,1: 97:[46, 113] Operation: 5+108=113 Exploring Operation: 5+46=51, Resulting Numbers: [108, 51] Generated Node #0,1,2: 97:[108, 51] Operation: 5+46=51 Exploring Operation: 108-46=62, Resulting Numbers: [5, 62] Generated Node #0,1,3: 97:[5, 62] Operation: 108-46=62 Exploring Operation: 46-5=41, Resulting Numbers: [108, 41] Generated Node #0,1,4: 97:[108, 41] Operation: 46-5=41 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[46, 103], Operations: ['12*9=108', '108-5=103'] Exploring Operation: 46+103=149, Resulting Numbers: [149] 149,97 unequal: No Solution Exploring Operation: 103-46=57, Resulting Numbers: [57] 57,97 unequal: No Solution Exploring Operation: 46*103=4738, Resulting Numbers: [4738] 4738,97 unequal: No Solution No 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: 97:[108, 51], Operations: ['12*9=108', '5+46=51'] Exploring Operation: 108*51=5508, Resulting Numbers: [5508] 5508,97 unequal: No Solution Exploring Operation: 108-51=57, Resulting Numbers: [57] 57,97 unequal: No Solution Exploring Operation: 108+51=159, Resulting Numbers: [159] 159,97 unequal: No Solution No 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: 97:[46, 113], Operations: ['12*9=108', '5+108=113'] Exploring Operation: 113-46=67, Resulting Numbers: [67] 67,97 unequal: No Solution Exploring Operation: 46*113=5198, Resulting Numbers: [5198] 5198,97 unequal: No Solution Exploring Operation: 46+113=159, Resulting Numbers: [159] 159,97 unequal: No Solution No 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: 97:[108, 41], Operations: ['12*9=108', '46-5=41'] Exploring Operation: 108*41=4428, Resulting Numbers: [4428] 4428,97 unequal: No Solution Exploring Operation: 108-41=67, Resulting Numbers: [67] 67,97 unequal: No Solution Exploring Operation: 108+41=149, Resulting Numbers: [149] 149,97 unequal: No Solution No 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: 97:[5, 62], Operations: ['12*9=108', '108-46=62'] Exploring Operation: 5+62=67, Resulting Numbers: [67] 67,97 unequal: No Solution Exploring Operation: 5*62=310, Resulting Numbers: [310] 310,97 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,97 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: 97:[46, 9, 60], Operations: ['12*5=60'] Exploring Operation: 46+9=55, Resulting Numbers: [60, 55] Generated Node #0,0,0: 97:[60, 55] Operation: 46+9=55 Exploring Operation: 9+60=69, Resulting Numbers: [46, 69] Generated Node #0,0,1: 97:[46, 69] Operation: 9+60=69 Exploring Operation: 46-9=37, Resulting Numbers: [60, 37] Generated Node #0,0,2: 97:[60, 37] Operation: 46-9=37 Exploring Operation: 46+60=106, Resulting Numbers: [9, 106] Generated Node #0,0,3: 97:[9, 106] Operation: 46+60=106 Exploring Operation: 60-9=51, Resulting Numbers: [46, 51] Generated Node #0,0,4: 97:[46, 51] Operation: 60-9=51 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[60, 55], Operations: ['12*5=60', '46+9=55'] Exploring Operation: 60*55=3300, Resulting Numbers: [3300] 3300,97 unequal: No Solution Exploring Operation: 60+55=115, Resulting Numbers: [115] 115,97 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,97 unequal: No Solution No 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: 97:[46, 69], Operations: ['12*5=60', '9+60=69'] Exploring Operation: 46+69=115, Resulting Numbers: [115] 115,97 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,97 unequal: No Solution Exploring Operation: 46*69=3174, Resulting Numbers: [3174] 3174,97 unequal: No Solution No 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: 97:[60, 37], Operations: ['12*5=60', '46-9=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[12, 5, 46, 9], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [46, 9, 60] Generated Node #0,0: 97:[46, 9, 60] Operation: 12*5=60 Moving to Node #0,0 Current State: 97:[46, 9, 60], Operations: ['12*5=60'] Exploring Operation: 46-9=37, Resulting Numbers: [60, 37] Generated Node #0,0,2: 97:[60, 37] Operation: 46-9=37 Moving to Node #0,0,2 Current State: 97:[60, 37], Operations: ['12*5=60', '46-9=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 26, 7, 26, 31 ]
61
[ "31-26=5", "7*5=35", "26+35=61" ]
Current State: 61:[26, 7, 26, 31], Operations: [] Exploring Operation: 31-26=5, Resulting Numbers: [7, 5] Generated Node #2: [7, 5] from Operation: 31-26=5 Current State: 61:[7, 5], Operations: ['31-26=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,61 equal: Goal Reached Exploring Operation: 26+35=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[26, 7, 26, 31], Operations: [] Exploring Operation: 7+26=33, Resulting Numbers: [26, 31, 33] Generated Node #0,0: 61:[26, 31, 33] Operation: 7+26=33 Exploring Operation: 26+31=57, Resulting Numbers: [7, 26, 57] Generated Node #0,1: 61:[7, 26, 57] Operation: 26+31=57 Exploring Operation: 26+7=33, Resulting Numbers: [26, 31, 33] Generated Node #0,2: 61:[26, 31, 33] Operation: 26+7=33 Exploring Operation: 26+26=52, Resulting Numbers: [7, 31, 52] Generated Node #0,3: 61:[7, 31, 52] Operation: 26+26=52 Moving to Node #0,0 Current State: 61:[26, 31, 33], Operations: ['7+26=33'] Exploring Operation: 31-26=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 61:[33, 5] Operation: 31-26=5 Exploring Operation: 26+31=57, Resulting Numbers: [33, 57] Generated Node #0,0,1: 61:[33, 57] Operation: 26+31=57 Exploring Operation: 26+33=59, Resulting Numbers: [31, 59] Generated Node #0,0,2: 61:[31, 59] Operation: 26+33=59 Exploring Operation: 31+33=64, Resulting Numbers: [26, 64] Generated Node #0,0,3: 61:[26, 64] Operation: 31+33=64 Moving to Node #0,2 Current State: 61:[26, 31, 33], Operations: ['26+7=33'] Exploring Operation: 31+33=64, Resulting Numbers: [26, 64] Generated Node #0,2,0: 61:[26, 64] Operation: 31+33=64 Exploring Operation: 26+31=57, Resulting Numbers: [33, 57] Generated Node #0,2,1: 61:[33, 57] Operation: 26+31=57 Exploring Operation: 31-26=5, Resulting Numbers: [33, 5] Generated Node #0,2,2: 61:[33, 5] Operation: 31-26=5 Exploring Operation: 26+33=59, Resulting Numbers: [31, 59] Generated Node #0,2,3: 61:[31, 59] Operation: 26+33=59 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[33, 57], Operations: ['26+7=33', '26+31=57'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 61:[31, 59], Operations: ['26+7=33', '26+33=59'] Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 31*59=1829, Resulting Numbers: [1829] 1829,61 unequal: No Solution Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[26, 64], Operations: ['26+7=33', '31+33=64'] Exploring Operation: 26*64=1664, Resulting Numbers: [1664] 1664,61 unequal: No Solution Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[33, 5], Operations: ['26+7=33', '31-26=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,61 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 61:[7, 26, 57], Operations: ['26+31=57'] Exploring Operation: 7+26=33, Resulting Numbers: [57, 33] Generated Node #0,1,0: 61:[57, 33] Operation: 7+26=33 Exploring Operation: 57-7=50, Resulting Numbers: [26, 50] Generated Node #0,1,1: 61:[26, 50] Operation: 57-7=50 Exploring Operation: 7+57=64, Resulting Numbers: [26, 64] Generated Node #0,1,2: 61:[26, 64] Operation: 7+57=64 Exploring Operation: 26-7=19, Resulting Numbers: [57, 19] Generated Node #0,1,3: 61:[57, 19] Operation: 26-7=19 Moving to Node #0,3 Current State: 61:[7, 31, 52], Operations: ['26+26=52'] Exploring Operation: 52-7=45, Resulting Numbers: [31, 45] Generated Node #0,3,0: 61:[31, 45] Operation: 52-7=45 Exploring Operation: 7+31=38, Resulting Numbers: [52, 38] Generated Node #0,3,1: 61:[52, 38] Operation: 7+31=38 Exploring Operation: 7+52=59, Resulting Numbers: [31, 59] Generated Node #0,3,2: 61:[31, 59] Operation: 7+52=59 Exploring Operation: 31-7=24, Resulting Numbers: [52, 24] Generated Node #0,3,3: 61:[52, 24] Operation: 31-7=24 Moving to Node #0,0,1 Current State: 61:[33, 57], Operations: ['7+26=33', '26+31=57'] Exploring Operation: 33*57=1881, Resulting Numbers: [1881] 1881,61 unequal: No Solution Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 33+57=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[31, 59], Operations: ['7+26=33', '26+33=59'] Exploring Operation: 31*59=1829, Resulting Numbers: [1829] 1829,61 unequal: No Solution Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[57, 33], Operations: ['26+31=57', '7+26=33'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,61 unequal: No Solution Exploring Operation: 57*33=1881, Resulting Numbers: [1881] 1881,61 unequal: No Solution Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[31, 59], Operations: ['26+26=52', '7+52=59'] Exploring Operation: 31+59=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 31*59=1829, Resulting Numbers: [1829] 1829,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[52, 38], Operations: ['26+26=52', '7+31=38'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 52*38=1976, Resulting Numbers: [1976] 1976,61 unequal: No Solution Exploring Operation: 52+38=90, Resulting Numbers: [90] 90,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[26, 64], Operations: ['7+26=33', '31+33=64'] Exploring Operation: 26*64=1664, Resulting Numbers: [1664] 1664,61 unequal: No Solution Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[26, 64], Operations: ['26+31=57', '7+57=64'] Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 26*64=1664, Resulting Numbers: [1664] 1664,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[26, 50], Operations: ['26+31=57', '57-7=50'] Exploring Operation: 26+50=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 26*50=1300, Resulting Numbers: [1300] 1300,61 unequal: No Solution Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[52, 24], Operations: ['26+26=52', '31-7=24'] Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,61 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[57, 19], Operations: ['26+31=57', '26-7=19'] Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,61 unequal: No Solution Exploring Operation: 57+19=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 57*19=1083, Resulting Numbers: [1083] 1083,61 unequal: No Solution Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[31, 45], Operations: ['26+26=52', '52-7=45'] Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 31*45=1395, Resulting Numbers: [1395] 1395,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[33, 5], Operations: ['7+26=33', '31-26=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,61 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,61 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 72, 30, 6, 50 ]
92
[ "72/6=12", "30+50=80", "12+80=92" ]
Current State: 92:[72, 30, 6, 50], Operations: [] Exploring Operation: 72/6=12, Resulting Numbers: [30, 50, 12] Generated Node #2: [30, 50, 12] from Operation: 72/6=12 Current State: 92:[30, 50, 12], Operations: ['72/6=12'] Exploring Operation: 30+50=80, Resulting Numbers: [12, 80] Generated Node #3: [12, 80] from Operation: 30+50=80 Current State: 92:[12, 80], Operations: ['72/6=12', '30+50=80'] Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[72, 30, 6, 50], Operations: [] Exploring Operation: 72-30=42, Resulting Numbers: [6, 50, 42] Generated Node #0,0: 92:[6, 50, 42] Operation: 72-30=42 Exploring Operation: 72+30=102, Resulting Numbers: [6, 50, 102] Generated Node #0,1: 92:[6, 50, 102] Operation: 72+30=102 Exploring Operation: 72-50=22, Resulting Numbers: [30, 6, 22] Generated Node #0,2: 92:[30, 6, 22] Operation: 72-50=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[6, 50, 42], Operations: ['72-30=42'] Exploring Operation: 50+42=92, Resulting Numbers: [6, 92] Generated Node #0,0,0: 92:[6, 92] Operation: 50+42=92 Exploring Operation: 6+42=48, Resulting Numbers: [50, 48] Generated Node #0,0,1: 92:[50, 48] Operation: 6+42=48 Exploring Operation: 50-6=44, Resulting Numbers: [42, 44] Generated Node #0,0,2: 92:[42, 44] Operation: 50-6=44 Moving to Node #0,0,0 Current State: 92:[6, 92], Operations: ['72-30=42', '50+42=92'] Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,92 unequal: No Solution Exploring Operation: 6*92=552, Resulting Numbers: [552] 552,92 unequal: No Solution Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[50, 48], Operations: ['72-30=42', '6+42=48'] Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,92 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[42, 44], Operations: ['72-30=42', '50-6=44'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[30, 6, 22], Operations: ['72-50=22'] Exploring Operation: 30/6=5, Resulting Numbers: [22, 5] Generated Node #0,2,0: 92:[22, 5] Operation: 30/6=5 Exploring Operation: 30-6=24, Resulting Numbers: [22, 24] Generated Node #0,2,1: 92:[22, 24] Operation: 30-6=24 Exploring Operation: 30-22=8, Resulting Numbers: [6, 8] Generated Node #0,2,2: 92:[6, 8] Operation: 30-22=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 92:[22, 5], Operations: ['72-50=22', '30/6=5'] Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,92 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,92 unequal: No Solution No 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: 92:[22, 24], Operations: ['72-50=22', '30-6=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,92 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,92 unequal: No Solution No 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: 92:[6, 8], Operations: ['72-50=22', '30-22=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,92 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[6, 50, 102], Operations: ['72+30=102'] Exploring Operation: 102-6=96, Resulting Numbers: [50, 96] Generated Node #0,1,0: 92:[50, 96] Operation: 102-6=96 Exploring Operation: 102/6=17, Resulting Numbers: [50, 17] Generated Node #0,1,1: 92:[50, 17] Operation: 102/6=17 Exploring Operation: 102-50=52, Resulting Numbers: [6, 52] Generated Node #0,1,2: 92:[6, 52] Operation: 102-50=52 Moving to Node #0,1,0 Current State: 92:[50, 96], Operations: ['72+30=102', '102-6=96'] Exploring Operation: 50+96=146, Resulting Numbers: [146] 146,92 unequal: No Solution Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 50*96=4800, Resulting Numbers: [4800] 4800,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[6, 52], Operations: ['72+30=102', '102-50=52'] Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,92 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[50, 17], Operations: ['72+30=102', '102/6=17'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,92 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,92 unequal: No Solution Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,92 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
[ 88, 6, 46, 31 ]
67
[ "88-6=82", "46-31=15", "82-15=67" ]
Current State: 67:[88, 6, 46, 31], Operations: [] Exploring Operation: 88-6=82, Resulting Numbers: [46, 31, 82] Generated Node #2: [46, 31, 82] from Operation: 88-6=82 Current State: 67:[46, 31, 82], Operations: ['88-6=82'] Exploring Operation: 46-31=15, Resulting Numbers: [82, 15] Generated Node #3: [82, 15] from Operation: 46-31=15 Current State: 67:[82, 15], Operations: ['88-6=82', '46-31=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[88, 6, 46, 31], Operations: [] Exploring Operation: 88-6=82, Resulting Numbers: [46, 31, 82] Generated Node #0,0: 67:[46, 31, 82] Operation: 88-6=82 Exploring Operation: 88+6=94, Resulting Numbers: [46, 31, 94] Generated Node #0,1: 67:[46, 31, 94] Operation: 88+6=94 Exploring Operation: 6+46=52, Resulting Numbers: [88, 31, 52] Generated Node #0,2: 67:[88, 31, 52] Operation: 6+46=52 Exploring Operation: 6+31=37, Resulting Numbers: [88, 46, 37] Generated Node #0,3: 67:[88, 46, 37] Operation: 6+31=37 Exploring Operation: 46-6=40, Resulting Numbers: [88, 31, 40] Generated Node #0,4: 67:[88, 31, 40] Operation: 46-6=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[46, 31, 82], Operations: ['88-6=82'] Exploring Operation: 82-31=51, Resulting Numbers: [46, 51] Generated Node #0,0,0: 67:[46, 51] Operation: 82-31=51 Exploring Operation: 46+31=77, Resulting Numbers: [82, 77] Generated Node #0,0,1: 67:[82, 77] Operation: 46+31=77 Exploring Operation: 46-31=15, Resulting Numbers: [82, 15] Generated Node #0,0,2: 67:[82, 15] Operation: 46-31=15 Exploring Operation: 82-46=36, Resulting Numbers: [31, 36] Generated Node #0,0,3: 67:[31, 36] Operation: 82-46=36 Exploring Operation: 31+82=113, Resulting Numbers: [46, 113] Generated Node #0,0,4: 67:[46, 113] Operation: 31+82=113 Moving to Node #0,0,1 Current State: 67:[82, 77], Operations: ['88-6=82', '46+31=77'] Exploring Operation: 82+77=159, Resulting Numbers: [159] 159,67 unequal: No Solution Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 82*77=6314, Resulting Numbers: [6314] 6314,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[46, 51], Operations: ['88-6=82', '82-31=51'] Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 46*51=2346, Resulting Numbers: [2346] 2346,67 unequal: No Solution Exploring Operation: 46+51=97, Resulting Numbers: [97] 97,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[82, 15], Operations: ['88-6=82', '46-31=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[88, 6, 46, 31], Operations: [] Exploring Operation: 88-6=82, Resulting Numbers: [46, 31, 82] Generated Node #0,0: 67:[46, 31, 82] Operation: 88-6=82 Moving to Node #0,0 Current State: 67:[46, 31, 82], Operations: ['88-6=82'] Exploring Operation: 46-31=15, Resulting Numbers: [82, 15] Generated Node #0,0,2: 67:[82, 15] Operation: 46-31=15 Moving to Node #0,0,2 Current State: 67:[82, 15], Operations: ['88-6=82', '46-31=15'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 53, 61, 30, 75 ]
97
[ "61-53=8", "30+75=105", "105-8=97" ]
Current State: 97:[53, 61, 30, 75], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [30, 75, 8] Generated Node #2: [30, 75, 8] from Operation: 61-53=8 Current State: 97:[30, 75, 8], Operations: ['61-53=8'] Exploring Operation: 30+75=105, Resulting Numbers: [8, 105] Generated Node #3: [8, 105] from Operation: 30+75=105 Current State: 97:[8, 105], Operations: ['61-53=8', '30+75=105'] Exploring Operation: 105-8=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[53, 61, 30, 75], Operations: [] Exploring Operation: 53+30=83, Resulting Numbers: [61, 75, 83] Generated Node #0,0: 97:[61, 75, 83] Operation: 53+30=83 Moving to Node #0,0 Current State: 97:[61, 75, 83], Operations: ['53+30=83'] Exploring Operation: 61+75=136, Resulting Numbers: [83, 136] Generated Node #0,0,0: 97:[83, 136] Operation: 61+75=136 Moving to Node #0,0,0 Current State: 97:[83, 136], Operations: ['53+30=83', '61+75=136'] Exploring Operation: 136-83=53, Resulting Numbers: [53] 53,97 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 8, 8, 99, 4 ]
75
[ "8+99=107", "8*4=32", "107-32=75" ]
Current State: 75:[8, 8, 99, 4], Operations: [] Exploring Operation: 8+99=107, Resulting Numbers: [4, 107] Generated Node #2: [4, 107] from Operation: 8+99=107 Current State: 75:[4, 107], Operations: ['8+99=107'] Exploring Operation: 8*4=32, Resulting Numbers: [107, 32] Generated Node #3: [107, 32] from Operation: 8*4=32 Current State: 75:[107, 32], Operations: ['8+99=107', '8*4=32'] Exploring Operation: 107-32=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[8, 8, 99, 4], Operations: [] Exploring Operation: 99-8=91, Resulting Numbers: [8, 4, 91] Generated Node #0,0: 75:[8, 4, 91] Operation: 99-8=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[8, 4, 91], Operations: ['99-8=91'] Exploring Operation: 91-8=83, Resulting Numbers: [4, 83] Generated Node #0,0,0: 75:[4, 83] Operation: 91-8=83 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[4, 83], Operations: ['99-8=91', '91-8=83'] Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,75 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 No solution found.
0
hs_1
mult_heuristic
[ 5, 55, 28, 30 ]
18
[ "5+28=33", "30*33=990", "990/55=18" ]
Current State: 18:[5, 55, 28, 30], Operations: [] Exploring Operation: 5+28=33, Resulting Numbers: [55, 30, 33] Generated Node #2: [55, 30, 33] from Operation: 5+28=33 Current State: 18:[55, 30, 33], Operations: ['5+28=33'] Exploring Operation: 30*33=990, Resulting Numbers: [55, 990] Generated Node #3: [55, 990] from Operation: 30*33=990 Current State: 18:[55, 990], Operations: ['5+28=33', '30*33=990'] Exploring Operation: 990/55=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[5, 55, 28, 30], Operations: [] Exploring Operation: 55-30=25, Resulting Numbers: [5, 28, 25] Generated Node #0,0: 18:[5, 28, 25] Operation: 55-30=25 Exploring Operation: 55/5=11, Resulting Numbers: [28, 30, 11] Generated Node #0,1: 18:[28, 30, 11] Operation: 55/5=11 Exploring Operation: 55-28=27, Resulting Numbers: [5, 30, 27] Generated Node #0,2: 18:[5, 30, 27] Operation: 55-28=27 Moving to Node #0,0 Current State: 18:[5, 28, 25], Operations: ['55-30=25'] Exploring Operation: 25/5=5, Resulting Numbers: [28, 5] Generated Node #0,0,0: 18:[28, 5] Operation: 25/5=5 Exploring Operation: 28-5=23, Resulting Numbers: [25, 23] Generated Node #0,0,1: 18:[25, 23] Operation: 28-5=23 Exploring Operation: 28-25=3, Resulting Numbers: [5, 3] Generated Node #0,0,2: 18:[5, 3] Operation: 28-25=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[5, 3], Operations: ['55-30=25', '28-25=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,18 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[28, 5], Operations: ['55-30=25', '25/5=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[25, 23], Operations: ['55-30=25', '28-5=23'] Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 25*23=575, Resulting Numbers: [575] 575,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 18:[5, 30, 27], Operations: ['55-28=27'] Exploring Operation: 30/5=6, Resulting Numbers: [27, 6] Generated Node #0,2,0: 18:[27, 6] Operation: 30/5=6 Exploring Operation: 30-5=25, Resulting Numbers: [27, 25] Generated Node #0,2,1: 18:[27, 25] Operation: 30-5=25 Exploring Operation: 30-27=3, Resulting Numbers: [5, 3] Generated Node #0,2,2: 18:[5, 3] Operation: 30-27=3 Moving to Node #0,1 Current State: 18:[28, 30, 11], Operations: ['55/5=11'] Exploring Operation: 28-11=17, Resulting Numbers: [30, 17] Generated Node #0,1,0: 18:[30, 17] Operation: 28-11=17 Exploring Operation: 30-11=19, Resulting Numbers: [28, 19] Generated Node #0,1,1: 18:[28, 19] Operation: 30-11=19 Exploring Operation: 30-28=2, Resulting Numbers: [11, 2] Generated Node #0,1,2: 18:[11, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[11, 2], Operations: ['55/5=11', '30-28=2'] Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[28, 19], Operations: ['55/5=11', '30-11=19'] Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 28*19=532, Resulting Numbers: [532] 532,18 unequal: No Solution Exploring Operation: 28+19=47, Resulting Numbers: [47] 47,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[30, 17], Operations: ['55/5=11', '28-11=17'] Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,18 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 18:[5, 3], Operations: ['55-28=27', '30-27=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[27, 6], Operations: ['55-28=27', '30/5=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,18 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[27, 25], Operations: ['55-28=27', '30-5=25'] Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,18 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 80, 56, 59, 6 ]
63
[ "80-56=24", "24/6=4", "59+4=63" ]
Current State: 63:[80, 56, 59, 6], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [59, 6, 24] Generated Node #2: [59, 6, 24] from Operation: 80-56=24 Current State: 63:[59, 6, 24], Operations: ['80-56=24'] Exploring Operation: 24/6=4, Resulting Numbers: [59, 4] Generated Node #3: [59, 4] from Operation: 24/6=4 Current State: 63:[59, 4], Operations: ['80-56=24', '24/6=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[80, 56, 59, 6], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [59, 6, 24] Generated Node #0,0: 63:[59, 6, 24] Operation: 80-56=24 Exploring Operation: 56+6=62, Resulting Numbers: [80, 59, 62] Generated Node #0,1: 63:[80, 59, 62] Operation: 56+6=62 Exploring Operation: 80-59=21, Resulting Numbers: [56, 6, 21] Generated Node #0,2: 63:[56, 6, 21] Operation: 80-59=21 Exploring Operation: 59-56=3, Resulting Numbers: [80, 6, 3] Generated Node #0,3: 63:[80, 6, 3] Operation: 59-56=3 Exploring Operation: 80-6=74, Resulting Numbers: [56, 59, 74] Generated Node #0,4: 63:[56, 59, 74] Operation: 80-6=74 Moving to Node #0,0 Current State: 63:[59, 6, 24], Operations: ['80-56=24'] Exploring Operation: 59-6=53, Resulting Numbers: [24, 53] Generated Node #0,0,0: 63:[24, 53] Operation: 59-6=53 Exploring Operation: 59+6=65, Resulting Numbers: [24, 65] Generated Node #0,0,1: 63:[24, 65] Operation: 59+6=65 Exploring Operation: 24/6=4, Resulting Numbers: [59, 4] Generated Node #0,0,2: 63:[59, 4] Operation: 24/6=4 Exploring Operation: 6+24=30, Resulting Numbers: [59, 30] Generated Node #0,0,3: 63:[59, 30] Operation: 6+24=30 Exploring Operation: 24-6=18, Resulting Numbers: [59, 18] Generated Node #0,0,4: 63:[59, 18] Operation: 24-6=18 Moving to Node #0,2 Current State: 63:[56, 6, 21], Operations: ['80-59=21'] Exploring Operation: 56+21=77, Resulting Numbers: [6, 77] Generated Node #0,2,0: 63:[6, 77] Operation: 56+21=77 Exploring Operation: 56-6=50, Resulting Numbers: [21, 50] Generated Node #0,2,1: 63:[21, 50] Operation: 56-6=50 Exploring Operation: 6+21=27, Resulting Numbers: [56, 27] Generated Node #0,2,2: 63:[56, 27] Operation: 6+21=27 Exploring Operation: 21-6=15, Resulting Numbers: [56, 15] Generated Node #0,2,3: 63:[56, 15] Operation: 21-6=15 Exploring Operation: 56+6=62, Resulting Numbers: [21, 62] Generated Node #0,2,4: 63:[21, 62] Operation: 56+6=62 Moving to Node #0,3 Current State: 63:[80, 6, 3], Operations: ['59-56=3'] Exploring Operation: 6/3=2, Resulting Numbers: [80, 2] Generated Node #0,3,0: 63:[80, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [80, 3] Generated Node #0,3,1: 63:[80, 3] Operation: 6-3=3 Exploring Operation: 80-3=77, Resulting Numbers: [6, 77] Generated Node #0,3,2: 63:[6, 77] Operation: 80-3=77 Exploring Operation: 80-6=74, Resulting Numbers: [3, 74] Generated Node #0,3,3: 63:[3, 74] Operation: 80-6=74 Exploring Operation: 6+3=9, Resulting Numbers: [80, 9] Generated Node #0,3,4: 63:[80, 9] Operation: 6+3=9 Moving to Node #0,1 Current State: 63:[80, 59, 62], Operations: ['56+6=62'] Exploring Operation: 80+59=139, Resulting Numbers: [62, 139] Generated Node #0,1,0: 63:[62, 139] Operation: 80+59=139 Exploring Operation: 80-59=21, Resulting Numbers: [62, 21] Generated Node #0,1,1: 63:[62, 21] Operation: 80-59=21 Exploring Operation: 80-62=18, Resulting Numbers: [59, 18] Generated Node #0,1,2: 63:[59, 18] Operation: 80-62=18 Exploring Operation: 59+62=121, Resulting Numbers: [80, 121] Generated Node #0,1,3: 63:[80, 121] Operation: 59+62=121 Exploring Operation: 62-59=3, Resulting Numbers: [80, 3] Generated Node #0,1,4: 63:[80, 3] Operation: 62-59=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[62, 21], Operations: ['56+6=62', '80-59=21'] Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,63 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 62*21=1302, Resulting Numbers: [1302] 1302,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[59, 18], Operations: ['56+6=62', '80-62=18'] Exploring Operation: 59-18=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 59+18=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 59*18=1062, Resulting Numbers: [1062] 1062,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 63:[80, 3], Operations: ['56+6=62', '62-59=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,63 unequal: No Solution Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 63:[80, 121], Operations: ['56+6=62', '59+62=121'] Exploring Operation: 80+121=201, Resulting Numbers: [201] 201,63 unequal: No Solution Exploring Operation: 121-80=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 80*121=9680, Resulting Numbers: [9680] 9680,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[62, 139], Operations: ['56+6=62', '80+59=139'] Exploring Operation: 139-62=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 62+139=201, Resulting Numbers: [201] 201,63 unequal: No Solution Exploring Operation: 62*139=8618, Resulting Numbers: [8618] 8618,63 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: 63:[56, 59, 74], Operations: ['80-6=74'] Exploring Operation: 56+74=130, Resulting Numbers: [59, 130] Generated Node #0,4,0: 63:[59, 130] Operation: 56+74=130 Exploring Operation: 59-56=3, Resulting Numbers: [74, 3] Generated Node #0,4,1: 63:[74, 3] Operation: 59-56=3 Exploring Operation: 74-59=15, Resulting Numbers: [56, 15] Generated Node #0,4,2: 63:[56, 15] Operation: 74-59=15 Exploring Operation: 56+59=115, Resulting Numbers: [74, 115] Generated Node #0,4,3: 63:[74, 115] Operation: 56+59=115 Exploring Operation: 74-56=18, Resulting Numbers: [59, 18] Generated Node #0,4,4: 63:[59, 18] Operation: 74-56=18 Moving to Node #0,2,4 Current State: 63:[21, 62], Operations: ['80-59=21', '56+6=62'] Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,63 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 21*62=1302, Resulting Numbers: [1302] 1302,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[24, 65], Operations: ['80-56=24', '59+6=65'] Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,63 unequal: No Solution Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[59, 4], Operations: ['80-56=24', '24/6=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[80, 56, 59, 6], Operations: [] Exploring Operation: 80-56=24, Resulting Numbers: [59, 6, 24] Generated Node #0,0: 63:[59, 6, 24] Operation: 80-56=24 Moving to Node #0,0 Current State: 63:[59, 6, 24], Operations: ['80-56=24'] Exploring Operation: 24/6=4, Resulting Numbers: [59, 4] Generated Node #0,0,2: 63:[59, 4] Operation: 24/6=4 Moving to Node #0,0,2 Current State: 63:[59, 4], Operations: ['80-56=24', '24/6=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.951389
hs_5
mult_heuristic
[ 64, 46, 58, 56 ]
96
[ "64-46=18", "58+56=114", "114-18=96" ]
Current State: 96:[64, 46, 58, 56], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [58, 56, 18] Generated Node #2: [58, 56, 18] from Operation: 64-46=18 Current State: 96:[58, 56, 18], Operations: ['64-46=18'] Exploring Operation: 58+56=114, Resulting Numbers: [18, 114] Generated Node #3: [18, 114] from Operation: 58+56=114 Current State: 96:[18, 114], Operations: ['64-46=18', '58+56=114'] Exploring Operation: 114-18=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[64, 46, 58, 56], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [46, 56, 6] Generated Node #0,0: 96:[46, 56, 6] Operation: 64-58=6 Exploring Operation: 64-56=8, Resulting Numbers: [46, 58, 8] Generated Node #0,1: 96:[46, 58, 8] Operation: 64-56=8 Exploring Operation: 58-46=12, Resulting Numbers: [64, 56, 12] Generated Node #0,2: 96:[64, 56, 12] Operation: 58-46=12 Exploring Operation: 58-56=2, Resulting Numbers: [64, 46, 2] Generated Node #0,3: 96:[64, 46, 2] Operation: 58-56=2 Exploring Operation: 64-46=18, Resulting Numbers: [58, 56, 18] Generated Node #0,4: 96:[58, 56, 18] Operation: 64-46=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[46, 56, 6], Operations: ['64-58=6'] Exploring Operation: 46-6=40, Resulting Numbers: [56, 40] Generated Node #0,0,0: 96:[56, 40] Operation: 46-6=40 Exploring Operation: 56-46=10, Resulting Numbers: [6, 10] Generated Node #0,0,1: 96:[6, 10] Operation: 56-46=10 Exploring Operation: 56-6=50, Resulting Numbers: [46, 50] Generated Node #0,0,2: 96:[46, 50] Operation: 56-6=50 Exploring Operation: 46+6=52, Resulting Numbers: [56, 52] Generated Node #0,0,3: 96:[56, 52] Operation: 46+6=52 Exploring Operation: 46+56=102, Resulting Numbers: [6, 102] Generated Node #0,0,4: 96:[6, 102] Operation: 46+56=102 Moving to Node #0,0,1 Current State: 96:[6, 10], Operations: ['64-58=6', '56-46=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[46, 50], Operations: ['64-58=6', '56-6=50'] Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 46+50=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[64, 46, 58, 56], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [46, 56, 6] Generated Node #0,0: 96:[46, 56, 6] Operation: 64-58=6 Moving to Node #0,0 Current State: 96:[46, 56, 6], Operations: ['64-58=6'] Exploring Operation: 56-6=50, Resulting Numbers: [46, 50] Generated Node #0,0,2: 96:[46, 50] Operation: 56-6=50 Moving to Node #0,0,2 Current State: 96:[46, 50], Operations: ['64-58=6', '56-6=50'] Exploring Operation: 46+50=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 58, 62, 93, 32 ]
60
[ "58+32=90", "62*90=5580", "5580/93=60" ]
Current State: 60:[58, 62, 93, 32], Operations: [] Exploring Operation: 58+32=90, Resulting Numbers: [62, 93, 90] Generated Node #2: [62, 93, 90] from Operation: 58+32=90 Current State: 60:[62, 93, 90], Operations: ['58+32=90'] Exploring Operation: 62*90=5580, Resulting Numbers: [93, 5580] Generated Node #3: [93, 5580] from Operation: 62*90=5580 Current State: 60:[93, 5580], Operations: ['58+32=90', '62*90=5580'] Exploring Operation: 5580/93=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[58, 62, 93, 32], Operations: [] Exploring Operation: 93-32=61, Resulting Numbers: [58, 62, 61] Generated Node #0,0: 60:[58, 62, 61] Operation: 93-32=61 Exploring Operation: 93-58=35, Resulting Numbers: [62, 32, 35] Generated Node #0,1: 60:[62, 32, 35] Operation: 93-58=35 Exploring Operation: 93-62=31, Resulting Numbers: [58, 32, 31] Generated Node #0,2: 60:[58, 32, 31] Operation: 93-62=31 Exploring Operation: 62-58=4, Resulting Numbers: [93, 32, 4] Generated Node #0,3: 60:[93, 32, 4] Operation: 62-58=4 Moving to Node #0,0 Current State: 60:[58, 62, 61], Operations: ['93-32=61'] Exploring Operation: 62-61=1, Resulting Numbers: [58, 1] Generated Node #0,0,0: 60:[58, 1] Operation: 62-61=1 Exploring Operation: 58+62=120, Resulting Numbers: [61, 120] Generated Node #0,0,1: 60:[61, 120] Operation: 58+62=120 Exploring Operation: 61-58=3, Resulting Numbers: [62, 3] Generated Node #0,0,2: 60:[62, 3] Operation: 61-58=3 Exploring Operation: 62-58=4, Resulting Numbers: [61, 4] Generated Node #0,0,3: 60:[61, 4] Operation: 62-58=4 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[61, 4], Operations: ['93-32=61', '62-58=4'] Exploring Operation: 61*4=244, Resulting Numbers: [244] 244,60 unequal: No Solution Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,60 unequal: No Solution No 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: 60:[62, 3], Operations: ['93-32=61', '61-58=3'] Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,60 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,60 unequal: No Solution No 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: 60:[58, 1], Operations: ['93-32=61', '62-61=1'] Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,60 unequal: No Solution No 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: 60:[61, 120], Operations: ['93-32=61', '58+62=120'] Exploring Operation: 61*120=7320, Resulting Numbers: [7320] 7320,60 unequal: No Solution Exploring Operation: 120-61=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 61+120=181, Resulting Numbers: [181] 181,60 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: 60:[58, 32, 31], Operations: ['93-62=31'] Exploring Operation: 32+31=63, Resulting Numbers: [58, 63] Generated Node #0,2,0: 60:[58, 63] Operation: 32+31=63 Exploring Operation: 58-32=26, Resulting Numbers: [31, 26] Generated Node #0,2,1: 60:[31, 26] Operation: 58-32=26 Exploring Operation: 32-31=1, Resulting Numbers: [58, 1] Generated Node #0,2,2: 60:[58, 1] Operation: 32-31=1 Exploring Operation: 58-31=27, Resulting Numbers: [32, 27] Generated Node #0,2,3: 60:[32, 27] Operation: 58-31=27 Moving to Node #0,1 Current State: 60:[62, 32, 35], Operations: ['93-58=35'] Exploring Operation: 62-35=27, Resulting Numbers: [32, 27] Generated Node #0,1,0: 60:[32, 27] Operation: 62-35=27 Exploring Operation: 35-32=3, Resulting Numbers: [62, 3] Generated Node #0,1,1: 60:[62, 3] Operation: 35-32=3 Exploring Operation: 32+35=67, Resulting Numbers: [62, 67] Generated Node #0,1,2: 60:[62, 67] Operation: 32+35=67 Exploring Operation: 62-32=30, Resulting Numbers: [35, 30] Generated Node #0,1,3: 60:[35, 30] Operation: 62-32=30 Moving to Node #0,3 Current State: 60:[93, 32, 4], Operations: ['62-58=4'] Exploring Operation: 93-4=89, Resulting Numbers: [32, 89] Generated Node #0,3,0: 60:[32, 89] Operation: 93-4=89 Exploring Operation: 93-32=61, Resulting Numbers: [4, 61] Generated Node #0,3,1: 60:[4, 61] Operation: 93-32=61 Exploring Operation: 32-4=28, Resulting Numbers: [93, 28] Generated Node #0,3,2: 60:[93, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [93, 8] Generated Node #0,3,3: 60:[93, 8] Operation: 32/4=8 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[4, 61], Operations: ['62-58=4', '93-32=61'] Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,60 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,60 unequal: No Solution No 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: 60:[32, 89], Operations: ['62-58=4', '93-4=89'] Exploring Operation: 32+89=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 32*89=2848, Resulting Numbers: [2848] 2848,60 unequal: No Solution Exploring Operation: 89-32=57, Resulting Numbers: [57] 57,60 unequal: No Solution No 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: 60:[93, 28], Operations: ['62-58=4', '32-4=28'] Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 93+28=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 93*28=2604, Resulting Numbers: [2604] 2604,60 unequal: No Solution No 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: 60:[93, 8], Operations: ['62-58=4', '32/4=8'] Exploring Operation: 93*8=744, Resulting Numbers: [744] 744,60 unequal: No Solution Exploring Operation: 93+8=101, Resulting Numbers: [101] 101,60 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,60 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: 60:[62, 3], Operations: ['93-58=35', '35-32=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,60 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[58, 1], Operations: ['93-62=31', '32-31=1'] Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[31, 26], Operations: ['93-62=31', '58-32=26'] Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,60 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,60 unequal: No Solution Moving to Node #0,1,0 Current State: 60:[32, 27], Operations: ['93-58=35', '62-35=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,60 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[35, 30], Operations: ['93-58=35', '62-32=30'] Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 35*30=1050, Resulting Numbers: [1050] 1050,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[58, 63], Operations: ['93-62=31', '32+31=63'] Exploring Operation: 58+63=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 58*63=3654, Resulting Numbers: [3654] 3654,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[32, 27], Operations: ['93-62=31', '58-31=27'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[62, 67], Operations: ['93-58=35', '32+35=67'] Exploring Operation: 62+67=129, Resulting Numbers: [129] 129,60 unequal: No Solution Exploring Operation: 67-62=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 62*67=4154, Resulting Numbers: [4154] 4154,60 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 42, 56, 40, 29 ]
59
[ "42*40=1680", "1680/56=30", "29+30=59" ]
Current State: 59:[42, 56, 40, 29], Operations: [] Exploring Operation: 42*40=1680, Resulting Numbers: [56, 29, 1680] Generated Node #2: [56, 29, 1680] from Operation: 42*40=1680 Current State: 59:[56, 29, 1680], Operations: ['42*40=1680'] Exploring Operation: 1680/56=30, Resulting Numbers: [29, 30] Generated Node #3: [29, 30] from Operation: 1680/56=30 Current State: 59:[29, 30], Operations: ['42*40=1680', '1680/56=30'] Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[42, 56, 40, 29], Operations: [] Exploring Operation: 40+29=69, Resulting Numbers: [42, 56, 69] Generated Node #0,0: 59:[42, 56, 69] Operation: 40+29=69 Moving to Node #0,0 Current State: 59:[42, 56, 69], Operations: ['40+29=69'] Exploring Operation: 69-42=27, Resulting Numbers: [56, 27] Generated Node #0,0,0: 59:[56, 27] Operation: 69-42=27 Moving to Node #0,0,0 Current State: 59:[56, 27], Operations: ['40+29=69', '69-42=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,59 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 11, 20, 23, 41 ]
90
[ "41-11=30", "23-20=3", "30*3=90" ]
Current State: 90:[11, 20, 23, 41], Operations: [] Exploring Operation: 41-11=30, Resulting Numbers: [20, 23, 30] Generated Node #2: [20, 23, 30] from Operation: 41-11=30 Current State: 90:[20, 23, 30], Operations: ['41-11=30'] Exploring Operation: 23-20=3, Resulting Numbers: [30, 3] Generated Node #3: [30, 3] from Operation: 23-20=3 Current State: 90:[30, 3], Operations: ['41-11=30', '23-20=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[11, 20, 23, 41], Operations: [] Exploring Operation: 20+23=43, Resulting Numbers: [11, 41, 43] Generated Node #0,0: 90:[11, 41, 43] Operation: 20+23=43 Exploring Operation: 41-11=30, Resulting Numbers: [20, 23, 30] Generated Node #0,1: 90:[20, 23, 30] Operation: 41-11=30 Exploring Operation: 23-20=3, Resulting Numbers: [11, 41, 3] Generated Node #0,2: 90:[11, 41, 3] Operation: 23-20=3 Exploring Operation: 23-11=12, Resulting Numbers: [20, 41, 12] Generated Node #0,3: 90:[20, 41, 12] Operation: 23-11=12 Exploring Operation: 41-23=18, Resulting Numbers: [11, 20, 18] Generated Node #0,4: 90:[11, 20, 18] Operation: 41-23=18 Start Sub Search at level 1: Moving to Node #0,4 Current State: 90:[11, 20, 18], Operations: ['41-23=18'] Exploring Operation: 18-11=7, Resulting Numbers: [20, 7] Generated Node #0,4,0: 90:[20, 7] Operation: 18-11=7 Exploring Operation: 11+18=29, Resulting Numbers: [20, 29] Generated Node #0,4,1: 90:[20, 29] Operation: 11+18=29 Exploring Operation: 20-11=9, Resulting Numbers: [18, 9] Generated Node #0,4,2: 90:[18, 9] Operation: 20-11=9 Exploring Operation: 20-18=2, Resulting Numbers: [11, 2] Generated Node #0,4,3: 90:[11, 2] Operation: 20-18=2 Exploring Operation: 11+20=31, Resulting Numbers: [18, 31] Generated Node #0,4,4: 90:[18, 31] Operation: 11+20=31 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 90:[18, 9], Operations: ['41-23=18', '20-11=9'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,90 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,90 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 #0,4,3 Current State: 90:[11, 2], Operations: ['41-23=18', '20-18=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,90 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,90 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 #0,4,4 Current State: 90:[18, 31], Operations: ['41-23=18', '11+20=31'] Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,90 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,90 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 #0,4,0 Current State: 90:[20, 7], Operations: ['41-23=18', '18-11=7'] Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,90 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 90:[20, 29], Operations: ['41-23=18', '11+18=29'] Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,90 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,90 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:[11, 41, 3], Operations: ['23-20=3'] Exploring Operation: 41+3=44, Resulting Numbers: [11, 44] Generated Node #0,2,0: 90:[11, 44] Operation: 41+3=44 Exploring Operation: 11+3=14, Resulting Numbers: [41, 14] Generated Node #0,2,1: 90:[41, 14] Operation: 11+3=14 Exploring Operation: 11+41=52, Resulting Numbers: [3, 52] Generated Node #0,2,2: 90:[3, 52] Operation: 11+41=52 Exploring Operation: 41-11=30, Resulting Numbers: [3, 30] Generated Node #0,2,3: 90:[3, 30] Operation: 41-11=30 Exploring Operation: 11-3=8, Resulting Numbers: [41, 8] Generated Node #0,2,4: 90:[41, 8] Operation: 11-3=8 Moving to Node #0,2,3 Current State: 90:[3, 30], Operations: ['23-20=3', '41-11=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[11, 20, 23, 41], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [11, 41, 3] Generated Node #0,2: 90:[11, 41, 3] Operation: 23-20=3 Moving to Node #0,2 Current State: 90:[11, 41, 3], Operations: ['23-20=3'] Exploring Operation: 41-11=30, Resulting Numbers: [3, 30] Generated Node #0,2,3: 90:[3, 30] Operation: 41-11=30 Moving to Node #0,2,3 Current State: 90:[3, 30], Operations: ['23-20=3', '41-11=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 35, 75, 2, 97 ]
51
[ "75+97=172", "172/2=86", "86-35=51" ]
Current State: 51:[35, 75, 2, 97], Operations: [] Exploring Operation: 75+97=172, Resulting Numbers: [35, 2, 172] Generated Node #2: [35, 2, 172] from Operation: 75+97=172 Current State: 51:[35, 2, 172], Operations: ['75+97=172'] Exploring Operation: 172/2=86, Resulting Numbers: [35, 86] Generated Node #3: [35, 86] from Operation: 172/2=86 Current State: 51:[35, 86], Operations: ['75+97=172', '172/2=86'] Exploring Operation: 86-35=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[35, 75, 2, 97], Operations: [] Exploring Operation: 97-35=62, Resulting Numbers: [75, 2, 62] Generated Node #0,0: 51:[75, 2, 62] Operation: 97-35=62 Exploring Operation: 35+2=37, Resulting Numbers: [75, 97, 37] Generated Node #0,1: 51:[75, 97, 37] Operation: 35+2=37 Exploring Operation: 75-35=40, Resulting Numbers: [2, 97, 40] Generated Node #0,2: 51:[2, 97, 40] Operation: 75-35=40 Exploring Operation: 97-75=22, Resulting Numbers: [35, 2, 22] Generated Node #0,3: 51:[35, 2, 22] Operation: 97-75=22 Exploring Operation: 75-2=73, Resulting Numbers: [35, 97, 73] Generated Node #0,4: 51:[35, 97, 73] Operation: 75-2=73 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[35, 2, 22], Operations: ['97-75=22'] Exploring Operation: 35-2=33, Resulting Numbers: [22, 33] Generated Node #0,3,0: 51:[22, 33] Operation: 35-2=33 Exploring Operation: 35-22=13, Resulting Numbers: [2, 13] Generated Node #0,3,1: 51:[2, 13] Operation: 35-22=13 Exploring Operation: 35+2=37, Resulting Numbers: [22, 37] Generated Node #0,3,2: 51:[22, 37] Operation: 35+2=37 Exploring Operation: 35+22=57, Resulting Numbers: [2, 57] Generated Node #0,3,3: 51:[2, 57] Operation: 35+22=57 Exploring Operation: 22-2=20, Resulting Numbers: [35, 20] Generated Node #0,3,4: 51:[35, 20] Operation: 22-2=20 Moving to Node #0,3,1 Current State: 51:[2, 13], Operations: ['97-75=22', '35-22=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[2, 57], Operations: ['97-75=22', '35+22=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,51 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,51 unequal: No Solution Moving to Node #0,3,2 Current State: 51:[22, 37], Operations: ['97-75=22', '35+2=37'] Exploring Operation: 22*37=814, Resulting Numbers: [814] 814,51 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 22+37=59, Resulting Numbers: [59] 59,51 unequal: No Solution Moving to Node #0,3,4 Current State: 51:[35, 20], Operations: ['97-75=22', '22-2=20'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[22, 33], Operations: ['97-75=22', '35-2=33'] Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,51 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[75, 2, 62], Operations: ['97-35=62'] Exploring Operation: 62-2=60, Resulting Numbers: [75, 60] Generated Node #0,0,0: 51:[75, 60] Operation: 62-2=60 Exploring Operation: 75-2=73, Resulting Numbers: [62, 73] Generated Node #0,0,1: 51:[62, 73] Operation: 75-2=73 Exploring Operation: 75+2=77, Resulting Numbers: [62, 77] Generated Node #0,0,2: 51:[62, 77] Operation: 75+2=77 Exploring Operation: 75-62=13, Resulting Numbers: [2, 13] Generated Node #0,0,3: 51:[2, 13] Operation: 75-62=13 Exploring Operation: 2+62=64, Resulting Numbers: [75, 64] Generated Node #0,0,4: 51:[75, 64] Operation: 2+62=64 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 51:[2, 13], Operations: ['97-35=62', '75-62=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[75, 60], Operations: ['97-35=62', '62-2=60'] Exploring Operation: 75+60=135, Resulting Numbers: [135] 135,51 unequal: No Solution Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 75*60=4500, Resulting Numbers: [4500] 4500,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[62, 73], Operations: ['97-35=62', '75-2=73'] Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 62*73=4526, Resulting Numbers: [4526] 4526,51 unequal: No Solution Exploring Operation: 62+73=135, Resulting Numbers: [135] 135,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[62, 77], Operations: ['97-35=62', '75+2=77'] Exploring Operation: 62+77=139, Resulting Numbers: [139] 139,51 unequal: No Solution Exploring Operation: 62*77=4774, Resulting Numbers: [4774] 4774,51 unequal: No Solution Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 51:[75, 64], Operations: ['97-35=62', '2+62=64'] Exploring Operation: 75*64=4800, Resulting Numbers: [4800] 4800,51 unequal: No Solution Exploring Operation: 75+64=139, Resulting Numbers: [139] 139,51 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[2, 97, 40], Operations: ['75-35=40'] Exploring Operation: 2+40=42, Resulting Numbers: [97, 42] Generated Node #0,2,0: 51:[97, 42] Operation: 2+40=42 Exploring Operation: 97-40=57, Resulting Numbers: [2, 57] Generated Node #0,2,1: 51:[2, 57] Operation: 97-40=57 Exploring Operation: 2+97=99, Resulting Numbers: [40, 99] Generated Node #0,2,2: 51:[40, 99] Operation: 2+97=99 Exploring Operation: 97-2=95, Resulting Numbers: [40, 95] Generated Node #0,2,3: 51:[40, 95] Operation: 97-2=95 Exploring Operation: 40/2=20, Resulting Numbers: [97, 20] Generated Node #0,2,4: 51:[97, 20] Operation: 40/2=20 Moving to Node #0,2,1 Current State: 51:[2, 57], Operations: ['75-35=40', '97-40=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,51 unequal: No Solution Moving to Node #0,2,4 Current State: 51:[97, 20], Operations: ['75-35=40', '40/2=20'] Exploring Operation: 97*20=1940, Resulting Numbers: [1940] 1940,51 unequal: No Solution Exploring Operation: 97+20=117, Resulting Numbers: [117] 117,51 unequal: No Solution Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[97, 42], Operations: ['75-35=40', '2+40=42'] Exploring Operation: 97*42=4074, Resulting Numbers: [4074] 4074,51 unequal: No Solution Exploring Operation: 97+42=139, Resulting Numbers: [139] 139,51 unequal: No Solution Exploring Operation: 97-42=55, Resulting Numbers: [55] 55,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[40, 95], Operations: ['75-35=40', '97-2=95'] Exploring Operation: 40*95=3800, Resulting Numbers: [3800] 3800,51 unequal: No Solution Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 40+95=135, Resulting Numbers: [135] 135,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[40, 99], Operations: ['75-35=40', '2+97=99'] Exploring Operation: 40+99=139, Resulting Numbers: [139] 139,51 unequal: No Solution Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 40*99=3960, Resulting Numbers: [3960] 3960,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[75, 97, 37], Operations: ['35+2=37'] Exploring Operation: 75-37=38, Resulting Numbers: [97, 38] Generated Node #0,1,0: 51:[97, 38] Operation: 75-37=38 Exploring Operation: 75+37=112, Resulting Numbers: [97, 112] Generated Node #0,1,1: 51:[97, 112] Operation: 75+37=112 Exploring Operation: 97-37=60, Resulting Numbers: [75, 60] Generated Node #0,1,2: 51:[75, 60] Operation: 97-37=60 Exploring Operation: 97+37=134, Resulting Numbers: [75, 134] Generated Node #0,1,3: 51:[75, 134] Operation: 97+37=134 Exploring Operation: 97-75=22, Resulting Numbers: [37, 22] Generated Node #0,1,4: 51:[37, 22] Operation: 97-75=22 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 51:[37, 22], Operations: ['35+2=37', '97-75=22'] Exploring Operation: 37*22=814, Resulting Numbers: [814] 814,51 unequal: No Solution Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 51:[75, 60], Operations: ['35+2=37', '97-37=60'] Exploring Operation: 75*60=4500, Resulting Numbers: [4500] 4500,51 unequal: No Solution Exploring Operation: 75+60=135, Resulting Numbers: [135] 135,51 unequal: No Solution Exploring Operation: 75-60=15, Resulting Numbers: [15] 15,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[97, 38], Operations: ['35+2=37', '75-37=38'] Exploring Operation: 97*38=3686, Resulting Numbers: [3686] 3686,51 unequal: No Solution Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 97+38=135, Resulting Numbers: [135] 135,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[97, 112], Operations: ['35+2=37', '75+37=112'] Exploring Operation: 97+112=209, Resulting Numbers: [209] 209,51 unequal: No Solution Exploring Operation: 97*112=10864, Resulting Numbers: [10864] 10864,51 unequal: No Solution Exploring Operation: 112-97=15, Resulting Numbers: [15] 15,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 51:[75, 134], Operations: ['35+2=37', '97+37=134'] Exploring Operation: 134-75=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 75*134=10050, Resulting Numbers: [10050] 10050,51 unequal: No Solution Exploring Operation: 75+134=209, Resulting Numbers: [209] 209,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 51:[35, 97, 73], Operations: ['75-2=73'] Exploring Operation: 97-73=24, Resulting Numbers: [35, 24] Generated Node #0,4,0: 51:[35, 24] Operation: 97-73=24 Exploring Operation: 97-35=62, Resulting Numbers: [73, 62] Generated Node #0,4,1: 51:[73, 62] Operation: 97-35=62 Exploring Operation: 35+97=132, Resulting Numbers: [73, 132] Generated Node #0,4,2: 51:[73, 132] Operation: 35+97=132 Exploring Operation: 35+73=108, Resulting Numbers: [97, 108] Generated Node #0,4,3: 51:[97, 108] Operation: 35+73=108 Exploring Operation: 73-35=38, Resulting Numbers: [97, 38] Generated Node #0,4,4: 51:[97, 38] Operation: 73-35=38 Moving to Node #0,4,0 Current State: 51:[35, 24], Operations: ['75-2=73', '97-73=24'] Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,51 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,51 unequal: No Solution Moving to Node #0,4,1 Current State: 51:[73, 62], Operations: ['75-2=73', '97-35=62'] Exploring Operation: 73*62=4526, Resulting Numbers: [4526] 4526,51 unequal: No Solution Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 73+62=135, Resulting Numbers: [135] 135,51 unequal: No Solution Moving to Node #0,4,4 Current State: 51:[97, 38], Operations: ['75-2=73', '73-35=38'] Exploring Operation: 97*38=3686, Resulting Numbers: [3686] 3686,51 unequal: No Solution Exploring Operation: 97-38=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 97+38=135, Resulting Numbers: [135] 135,51 unequal: No Solution Moving to Node #0,4,2 Current State: 51:[73, 132], Operations: ['75-2=73', '35+97=132'] Exploring Operation: 132-73=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 73+132=205, Resulting Numbers: [205] 205,51 unequal: No Solution Exploring Operation: 73*132=9636, Resulting Numbers: [9636] 9636,51 unequal: No Solution Moving to Node #0,4,3 Current State: 51:[97, 108], Operations: ['75-2=73', '35+73=108'] Exploring Operation: 97*108=10476, Resulting Numbers: [10476] 10476,51 unequal: No Solution Exploring Operation: 97+108=205, Resulting Numbers: [205] 205,51 unequal: No Solution Exploring Operation: 108-97=11, Resulting Numbers: [11] 11,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 8, 18, 46, 25 ]
73
[ "8*18=144", "46+25=71", "144-71=73" ]
Current State: 73:[8, 18, 46, 25], Operations: [] Exploring Operation: 8*18=144, Resulting Numbers: [46, 25, 144] Generated Node #2: [46, 25, 144] from Operation: 8*18=144 Current State: 73:[46, 25, 144], Operations: ['8*18=144'] Exploring Operation: 46+25=71, Resulting Numbers: [144, 71] Generated Node #3: [144, 71] from Operation: 46+25=71 Current State: 73:[144, 71], Operations: ['8*18=144', '46+25=71'] Exploring Operation: 144-71=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[8, 18, 46, 25], Operations: [] Exploring Operation: 8+18=26, Resulting Numbers: [46, 25, 26] Generated Node #0,0: 73:[46, 25, 26] Operation: 8+18=26 Exploring Operation: 8+46=54, Resulting Numbers: [18, 25, 54] Generated Node #0,1: 73:[18, 25, 54] Operation: 8+46=54 Moving to Node #0,0 Current State: 73:[46, 25, 26], Operations: ['8+18=26'] Exploring Operation: 46+26=72, Resulting Numbers: [25, 72] Generated Node #0,0,0: 73:[25, 72] Operation: 46+26=72 Exploring Operation: 46+25=71, Resulting Numbers: [26, 71] Generated Node #0,0,1: 73:[26, 71] Operation: 46+25=71 Moving to Node #0,1 Current State: 73:[18, 25, 54], Operations: ['8+46=54'] Exploring Operation: 18+54=72, Resulting Numbers: [25, 72] Generated Node #0,1,0: 73:[25, 72] Operation: 18+54=72 Exploring Operation: 18+25=43, Resulting Numbers: [54, 43] Generated Node #0,1,1: 73:[54, 43] Operation: 18+25=43 Moving to Node #0,0,0 Current State: 73:[25, 72], Operations: ['8+18=26', '46+26=72'] Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[25, 72], Operations: ['8+46=54', '18+54=72'] Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[26, 71], Operations: ['8+18=26', '46+25=71'] Exploring Operation: 26+71=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 71-26=45, Resulting Numbers: [45] 45,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[54, 43], Operations: ['8+46=54', '18+25=43'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,73 unequal: No Solution Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,73 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 78, 36, 84 ]
14
[ "2*36=72", "78-72=6", "84/6=14" ]
Current State: 14:[2, 78, 36, 84], Operations: [] Exploring Operation: 2*36=72, Resulting Numbers: [78, 84, 72] Generated Node #2: [78, 84, 72] from Operation: 2*36=72 Current State: 14:[78, 84, 72], Operations: ['2*36=72'] Exploring Operation: 78-72=6, Resulting Numbers: [84, 6] Generated Node #3: [84, 6] from Operation: 78-72=6 Current State: 14:[84, 6], Operations: ['2*36=72', '78-72=6'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[2, 78, 36, 84], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [2, 36, 6] Generated Node #0,0: 14:[2, 36, 6] Operation: 84-78=6 Moving to Node #0,0 Current State: 14:[2, 36, 6], Operations: ['84-78=6'] Exploring Operation: 36/6=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 14:[2, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[2, 6], Operations: ['84-78=6', '36/6=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,14 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
[ 98, 2, 8, 91 ]
34
[ "98/2=49", "91-8=83", "83-49=34" ]
Current State: 34:[98, 2, 8, 91], Operations: [] Exploring Operation: 98/2=49, Resulting Numbers: [8, 91, 49] Generated Node #2: [8, 91, 49] from Operation: 98/2=49 Current State: 34:[8, 91, 49], Operations: ['98/2=49'] Exploring Operation: 91-8=83, Resulting Numbers: [49, 83] Generated Node #3: [49, 83] from Operation: 91-8=83 Current State: 34:[49, 83], Operations: ['98/2=49', '91-8=83'] Exploring Operation: 83-49=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[98, 2, 8, 91], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [2, 8, 7] Generated Node #0,0: 34:[2, 8, 7] Operation: 98-91=7 Exploring Operation: 98/2=49, Resulting Numbers: [8, 91, 49] Generated Node #0,1: 34:[8, 91, 49] Operation: 98/2=49 Moving to Node #0,0 Current State: 34:[2, 8, 7], Operations: ['98-91=7'] Exploring Operation: 8+7=15, Resulting Numbers: [2, 15] Generated Node #0,0,0: 34:[2, 15] Operation: 8+7=15 Exploring Operation: 8-7=1, Resulting Numbers: [2, 1] Generated Node #0,0,1: 34:[2, 1] Operation: 8-7=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[2, 1], Operations: ['98-91=7', '8-7=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,34 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 #0,0,0 Current State: 34:[2, 15], Operations: ['98-91=7', '8+7=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,34 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:[8, 91, 49], Operations: ['98/2=49'] Exploring Operation: 91-8=83, Resulting Numbers: [49, 83] Generated Node #0,1,0: 34:[49, 83] Operation: 91-8=83 Exploring Operation: 91-49=42, Resulting Numbers: [8, 42] Generated Node #0,1,1: 34:[8, 42] Operation: 91-49=42 Moving to Node #0,1,1 Current State: 34:[8, 42], Operations: ['98/2=49', '91-49=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[98, 2, 8, 91], Operations: [] Exploring Operation: 98/2=49, Resulting Numbers: [8, 91, 49] Generated Node #0,1: 34:[8, 91, 49] Operation: 98/2=49 Moving to Node #0,1 Current State: 34:[8, 91, 49], Operations: ['98/2=49'] Exploring Operation: 91-49=42, Resulting Numbers: [8, 42] Generated Node #0,1,1: 34:[8, 42] Operation: 91-49=42 Moving to Node #0,1,1 Current State: 34:[8, 42], Operations: ['98/2=49', '91-49=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 28, 45, 18, 56 ]
65
[ "56/28=2", "45+18=63", "2+63=65" ]
Current State: 65:[28, 45, 18, 56], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [45, 18, 2] Generated Node #2: [45, 18, 2] from Operation: 56/28=2 Current State: 65:[45, 18, 2], Operations: ['56/28=2'] Exploring Operation: 45+18=63, Resulting Numbers: [2, 63] Generated Node #3: [2, 63] from Operation: 45+18=63 Current State: 65:[2, 63], Operations: ['56/28=2', '45+18=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[28, 45, 18, 56], Operations: [] Exploring Operation: 28+45=73, Resulting Numbers: [18, 56, 73] Generated Node #0,0: 65:[18, 56, 73] Operation: 28+45=73 Exploring Operation: 45-28=17, Resulting Numbers: [18, 56, 17] Generated Node #0,1: 65:[18, 56, 17] Operation: 45-28=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[18, 56, 17], Operations: ['45-28=17'] Exploring Operation: 18+56=74, Resulting Numbers: [17, 74] Generated Node #0,1,0: 65:[17, 74] Operation: 18+56=74 Exploring Operation: 18-17=1, Resulting Numbers: [56, 1] Generated Node #0,1,1: 65:[56, 1] Operation: 18-17=1 Moving to Node #0,1,0 Current State: 65:[17, 74], Operations: ['45-28=17', '18+56=74'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,65 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[56, 1], Operations: ['45-28=17', '18-17=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,65 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,65 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:[18, 56, 73], Operations: ['28+45=73'] Exploring Operation: 73-56=17, Resulting Numbers: [18, 17] Generated Node #0,0,0: 65:[18, 17] Operation: 73-56=17 Exploring Operation: 18+56=74, Resulting Numbers: [73, 74] Generated Node #0,0,1: 65:[73, 74] Operation: 18+56=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[18, 17], Operations: ['28+45=73', '73-56=17'] Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,65 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,65 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:[73, 74], Operations: ['28+45=73', '18+56=74'] Exploring Operation: 74-73=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 73+74=147, Resulting Numbers: [147] 147,65 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_2
mult_heuristic
[ 9, 1, 65, 18 ]
57
[ "9+1=10", "65-18=47", "10+47=57" ]
Current State: 57:[9, 1, 65, 18], Operations: [] Exploring Operation: 9+1=10, Resulting Numbers: [65, 18, 10] Generated Node #2: [65, 18, 10] from Operation: 9+1=10 Current State: 57:[65, 18, 10], Operations: ['9+1=10'] Exploring Operation: 65-18=47, Resulting Numbers: [10, 47] Generated Node #3: [10, 47] from Operation: 65-18=47 Current State: 57:[10, 47], Operations: ['9+1=10', '65-18=47'] Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[9, 1, 65, 18], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [1, 65, 2] Generated Node #0,0: 57:[1, 65, 2] Operation: 18/9=2 Exploring Operation: 65-1=64, Resulting Numbers: [9, 18, 64] Generated Node #0,1: 57:[9, 18, 64] Operation: 65-1=64 Exploring Operation: 65-9=56, Resulting Numbers: [1, 18, 56] Generated Node #0,2: 57:[1, 18, 56] Operation: 65-9=56 Exploring Operation: 9-1=8, Resulting Numbers: [65, 18, 8] Generated Node #0,3: 57:[65, 18, 8] Operation: 9-1=8 Moving to Node #0,2 Current State: 57:[1, 18, 56], Operations: ['65-9=56'] Exploring Operation: 1+56=57, Resulting Numbers: [18, 57] Generated Node #0,2,0: 57:[18, 57] Operation: 1+56=57 Exploring Operation: 1*18=18, Resulting Numbers: [56, 18] Generated Node #0,2,1: 57:[56, 18] Operation: 1*18=18 Exploring Operation: 18/1=18, Resulting Numbers: [56, 18] Generated Node #0,2,2: 57:[56, 18] Operation: 18/1=18 Exploring Operation: 1+18=19, Resulting Numbers: [56, 19] Generated Node #0,2,3: 57:[56, 19] Operation: 1+18=19 Moving to Node #0,0 Current State: 57:[1, 65, 2], Operations: ['18/9=2'] Exploring Operation: 65-2=63, Resulting Numbers: [1, 63] Generated Node #0,0,0: 57:[1, 63] Operation: 65-2=63 Exploring Operation: 1*65=65, Resulting Numbers: [2, 65] Generated Node #0,0,1: 57:[2, 65] Operation: 1*65=65 Exploring Operation: 1+2=3, Resulting Numbers: [65, 3] Generated Node #0,0,2: 57:[65, 3] Operation: 1+2=3 Exploring Operation: 65-1=64, Resulting Numbers: [2, 64] Generated Node #0,0,3: 57:[2, 64] Operation: 65-1=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[1, 63], Operations: ['18/9=2', '65-2=63'] Exploring Operation: 1+63=64, Resulting Numbers: [64] 64,57 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 1*63=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,57 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 #0,0,2 Current State: 57:[65, 3], Operations: ['18/9=2', '1+2=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,57 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,57 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 #0,0,3 Current State: 57:[2, 64], Operations: ['18/9=2', '65-1=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,57 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 #0,0,1 Current State: 57:[2, 65], Operations: ['18/9=2', '1*65=65'] Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,57 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,57 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: 57:[65, 18, 8], Operations: ['9-1=8'] Exploring Operation: 18+8=26, Resulting Numbers: [65, 26] Generated Node #0,3,0: 57:[65, 26] Operation: 18+8=26 Exploring Operation: 65-18=47, Resulting Numbers: [8, 47] Generated Node #0,3,1: 57:[8, 47] Operation: 65-18=47 Exploring Operation: 65-8=57, Resulting Numbers: [18, 57] Generated Node #0,3,2: 57:[18, 57] Operation: 65-8=57 Exploring Operation: 18-8=10, Resulting Numbers: [65, 10] Generated Node #0,3,3: 57:[65, 10] Operation: 18-8=10 Moving to Node #0,1 Current State: 57:[9, 18, 64], Operations: ['65-1=64'] Exploring Operation: 64-9=55, Resulting Numbers: [18, 55] Generated Node #0,1,0: 57:[18, 55] Operation: 64-9=55 Exploring Operation: 18/9=2, Resulting Numbers: [64, 2] Generated Node #0,1,1: 57:[64, 2] Operation: 18/9=2 Exploring Operation: 9+18=27, Resulting Numbers: [64, 27] Generated Node #0,1,2: 57:[64, 27] Operation: 9+18=27 Exploring Operation: 18-9=9, Resulting Numbers: [64, 9] Generated Node #0,1,3: 57:[64, 9] Operation: 18-9=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[18, 55], Operations: ['65-1=64', '64-9=55'] Exploring Operation: 18+55=73, Resulting Numbers: [73] 73,57 unequal: No Solution Exploring Operation: 18*55=990, Resulting Numbers: [990] 990,57 unequal: No Solution Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,57 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 #0,1,1 Current State: 57:[64, 2], Operations: ['65-1=64', '18/9=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,57 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,57 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 #0,1,3 Current State: 57:[64, 9], Operations: ['65-1=64', '18-9=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,57 unequal: No Solution Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,57 unequal: No Solution Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,57 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 #0,1,2 Current State: 57:[64, 27], Operations: ['65-1=64', '9+18=27'] Exploring Operation: 64+27=91, Resulting Numbers: [91] 91,57 unequal: No Solution Exploring Operation: 64*27=1728, Resulting Numbers: [1728] 1728,57 unequal: No Solution Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 57:[18, 57], Operations: ['65-9=56', '1+56=57'] Exploring Operation: 18+57=75, Resulting Numbers: [75] 75,57 unequal: No Solution Exploring Operation: 18*57=1026, Resulting Numbers: [1026] 1026,57 unequal: No Solution Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[56, 19], Operations: ['65-9=56', '1+18=19'] Exploring Operation: 56*19=1064, Resulting Numbers: [1064] 1064,57 unequal: No Solution Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[18, 57], Operations: ['9-1=8', '65-8=57'] Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 18+57=75, Resulting Numbers: [75] 75,57 unequal: No Solution Exploring Operation: 18*57=1026, Resulting Numbers: [1026] 1026,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[56, 18], Operations: ['65-9=56', '1*18=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,57 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,57 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[56, 18], Operations: ['65-9=56', '18/1=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,57 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,57 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[65, 26], Operations: ['9-1=8', '18+8=26'] Exploring Operation: 65*26=1690, Resulting Numbers: [1690] 1690,57 unequal: No Solution Exploring Operation: 65+26=91, Resulting Numbers: [91] 91,57 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[8, 47], Operations: ['9-1=8', '65-18=47'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,57 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[65, 10], Operations: ['9-1=8', '18-8=10'] Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,57 unequal: No Solution Exploring Operation: 65*10=650, Resulting Numbers: [650] 650,57 unequal: No Solution Exploring Operation: 65+10=75, Resulting Numbers: [75] 75,57 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 33, 15, 37 ]
76
[ "33*15=495", "37+495=532", "532/7=76" ]
Current State: 76:[7, 33, 15, 37], Operations: [] Exploring Operation: 33*15=495, Resulting Numbers: [7, 37, 495] Generated Node #2: [7, 37, 495] from Operation: 33*15=495 Current State: 76:[7, 37, 495], Operations: ['33*15=495'] Exploring Operation: 37+495=532, Resulting Numbers: [7, 532] Generated Node #3: [7, 532] from Operation: 37+495=532 Current State: 76:[7, 532], Operations: ['33*15=495', '37+495=532'] Exploring Operation: 532/7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[7, 33, 15, 37], Operations: [] Exploring Operation: 33-15=18, Resulting Numbers: [7, 37, 18] Generated Node #0,0: 76:[7, 37, 18] Operation: 33-15=18 Exploring Operation: 37-33=4, Resulting Numbers: [7, 15, 4] Generated Node #0,1: 76:[7, 15, 4] Operation: 37-33=4 Exploring Operation: 7+33=40, Resulting Numbers: [15, 37, 40] Generated Node #0,2: 76:[15, 37, 40] Operation: 7+33=40 Exploring Operation: 7+15=22, Resulting Numbers: [33, 37, 22] Generated Node #0,3: 76:[33, 37, 22] Operation: 7+15=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[7, 37, 18], Operations: ['33-15=18'] Exploring Operation: 18-7=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 76:[37, 11] Operation: 18-7=11 Exploring Operation: 7+37=44, Resulting Numbers: [18, 44] Generated Node #0,0,1: 76:[18, 44] Operation: 7+37=44 Exploring Operation: 7+18=25, Resulting Numbers: [37, 25] Generated Node #0,0,2: 76:[37, 25] Operation: 7+18=25 Exploring Operation: 37-18=19, Resulting Numbers: [7, 19] Generated Node #0,0,3: 76:[7, 19] Operation: 37-18=19 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 76:[7, 19], Operations: ['33-15=18', '37-18=19'] Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,76 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[18, 44], Operations: ['33-15=18', '7+37=44'] Exploring Operation: 18*44=792, Resulting Numbers: [792] 792,76 unequal: No Solution Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 18+44=62, Resulting Numbers: [62] 62,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 76:[37, 25], Operations: ['33-15=18', '7+18=25'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[37, 11], Operations: ['33-15=18', '18-7=11'] Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,76 unequal: No Solution Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,76 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[7, 15, 4], Operations: ['37-33=4'] Exploring Operation: 7-4=3, Resulting Numbers: [15, 3] Generated Node #0,1,0: 76:[15, 3] Operation: 7-4=3 Exploring Operation: 15-7=8, Resulting Numbers: [4, 8] Generated Node #0,1,1: 76:[4, 8] Operation: 15-7=8 Exploring Operation: 15+4=19, Resulting Numbers: [7, 19] Generated Node #0,1,2: 76:[7, 19] Operation: 15+4=19 Exploring Operation: 7+15=22, Resulting Numbers: [4, 22] Generated Node #0,1,3: 76:[4, 22] Operation: 7+15=22 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 76:[7, 19], Operations: ['37-33=4', '15+4=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[4, 22], Operations: ['37-33=4', '7+15=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[4, 8], Operations: ['37-33=4', '15-7=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[15, 3], Operations: ['37-33=4', '7-4=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[15, 37, 40], Operations: ['7+33=40'] Exploring Operation: 40-15=25, Resulting Numbers: [37, 25] Generated Node #0,2,0: 76:[37, 25] Operation: 40-15=25 Exploring Operation: 37+40=77, Resulting Numbers: [15, 77] Generated Node #0,2,1: 76:[15, 77] Operation: 37+40=77 Exploring Operation: 37-15=22, Resulting Numbers: [40, 22] Generated Node #0,2,2: 76:[40, 22] Operation: 37-15=22 Exploring Operation: 40-37=3, Resulting Numbers: [15, 3] Generated Node #0,2,3: 76:[15, 3] Operation: 40-37=3 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[15, 77], Operations: ['7+33=40', '37+40=77'] Exploring Operation: 15*77=1155, Resulting Numbers: [1155] 1155,76 unequal: No Solution Exploring Operation: 77-15=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 15+77=92, Resulting Numbers: [92] 92,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[40, 22], Operations: ['7+33=40', '37-15=22'] Exploring Operation: 40+22=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 40*22=880, Resulting Numbers: [880] 880,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[15, 3], Operations: ['7+33=40', '40-37=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[37, 25], Operations: ['7+33=40', '40-15=25'] Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[33, 37, 22], Operations: ['7+15=22'] Exploring Operation: 33+37=70, Resulting Numbers: [22, 70] Generated Node #0,3,0: 76:[22, 70] Operation: 33+37=70 Exploring Operation: 33-22=11, Resulting Numbers: [37, 11] Generated Node #0,3,1: 76:[37, 11] Operation: 33-22=11 Exploring Operation: 37-33=4, Resulting Numbers: [22, 4] Generated Node #0,3,2: 76:[22, 4] Operation: 37-33=4 Exploring Operation: 37-22=15, Resulting Numbers: [33, 15] Generated Node #0,3,3: 76:[33, 15] Operation: 37-22=15 Moving to Node #0,3,2 Current State: 76:[22, 4], Operations: ['7+15=22', '37-33=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[37, 11], Operations: ['7+15=22', '33-22=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,76 unequal: No Solution Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,76 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[33, 15], Operations: ['7+15=22', '37-22=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,76 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,76 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[22, 70], Operations: ['7+15=22', '33+37=70'] Exploring Operation: 22+70=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 22*70=1540, Resulting Numbers: [1540] 1540,76 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,76 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
[ 46, 30, 6, 4 ]
31
[ "6-4=2", "30/2=15", "46-15=31" ]
Current State: 31:[46, 30, 6, 4], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [46, 30, 2] Generated Node #2: [46, 30, 2] from Operation: 6-4=2 Current State: 31:[46, 30, 2], Operations: ['6-4=2'] Exploring Operation: 30/2=15, Resulting Numbers: [46, 15] Generated Node #3: [46, 15] from Operation: 30/2=15 Current State: 31:[46, 15], Operations: ['6-4=2', '30/2=15'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[46, 30, 6, 4], Operations: [] Exploring Operation: 6*4=24, Resulting Numbers: [46, 30, 24] Generated Node #0,0: 31:[46, 30, 24] Operation: 6*4=24 Exploring Operation: 46-6=40, Resulting Numbers: [30, 4, 40] Generated Node #0,1: 31:[30, 4, 40] Operation: 46-6=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[46, 30, 24], Operations: ['6*4=24'] Exploring Operation: 46-30=16, Resulting Numbers: [24, 16] Generated Node #0,0,0: 31:[24, 16] Operation: 46-30=16 Exploring Operation: 46-24=22, Resulting Numbers: [30, 22] Generated Node #0,0,1: 31:[30, 22] Operation: 46-24=22 Moving to Node #0,0,1 Current State: 31:[30, 22], Operations: ['6*4=24', '46-24=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[24, 16], Operations: ['6*4=24', '46-30=16'] Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,31 unequal: No Solution No 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:[30, 4, 40], Operations: ['46-6=40'] Exploring Operation: 40-4=36, Resulting Numbers: [30, 36] Generated Node #0,1,0: 31:[30, 36] Operation: 40-4=36 Exploring Operation: 30+4=34, Resulting Numbers: [40, 34] Generated Node #0,1,1: 31:[40, 34] Operation: 30+4=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[30, 36], Operations: ['46-6=40', '40-4=36'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,31 unequal: No Solution Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,31 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:[40, 34], Operations: ['46-6=40', '30+4=34'] Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,31 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,31 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
mult_heuristic
[ 19, 82, 16, 2 ]
69
[ "19+82=101", "16*2=32", "101-32=69" ]
Current State: 69:[19, 82, 16, 2], Operations: [] Exploring Operation: 19+82=101, Resulting Numbers: [16, 2, 101] Generated Node #2: [16, 2, 101] from Operation: 19+82=101 Current State: 69:[16, 2, 101], Operations: ['19+82=101'] Exploring Operation: 16*2=32, Resulting Numbers: [101, 32] Generated Node #3: [101, 32] from Operation: 16*2=32 Current State: 69:[101, 32], Operations: ['19+82=101', '16*2=32'] Exploring Operation: 101-32=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[19, 82, 16, 2], Operations: [] Exploring Operation: 19-16=3, Resulting Numbers: [82, 2, 3] Generated Node #0,0: 69:[82, 2, 3] Operation: 19-16=3 Exploring Operation: 82-19=63, Resulting Numbers: [16, 2, 63] Generated Node #0,1: 69:[16, 2, 63] Operation: 82-19=63 Exploring Operation: 82-16=66, Resulting Numbers: [19, 2, 66] Generated Node #0,2: 69:[19, 2, 66] Operation: 82-16=66 Exploring Operation: 19+2=21, Resulting Numbers: [82, 16, 21] Generated Node #0,3: 69:[82, 16, 21] Operation: 19+2=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[19, 2, 66], Operations: ['82-16=66'] Exploring Operation: 66-2=64, Resulting Numbers: [19, 64] Generated Node #0,2,0: 69:[19, 64] Operation: 66-2=64 Exploring Operation: 19-2=17, Resulting Numbers: [66, 17] Generated Node #0,2,1: 69:[66, 17] Operation: 19-2=17 Exploring Operation: 19+2=21, Resulting Numbers: [66, 21] Generated Node #0,2,2: 69:[66, 21] Operation: 19+2=21 Exploring Operation: 2+66=68, Resulting Numbers: [19, 68] Generated Node #0,2,3: 69:[19, 68] Operation: 2+66=68 Moving to Node #0,2,2 Current State: 69:[66, 21], Operations: ['82-16=66', '19+2=21'] Exploring Operation: 66*21=1386, Resulting Numbers: [1386] 1386,69 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[19, 68], Operations: ['82-16=66', '2+66=68'] Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 19+68=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 19*68=1292, Resulting Numbers: [1292] 1292,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[66, 17], Operations: ['82-16=66', '19-2=17'] Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,69 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[19, 64], Operations: ['82-16=66', '66-2=64'] Exploring Operation: 19*64=1216, Resulting Numbers: [1216] 1216,69 unequal: No Solution Exploring Operation: 64-19=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 19+64=83, Resulting Numbers: [83] 83,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[82, 2, 3], Operations: ['19-16=3'] Exploring Operation: 82-2=80, Resulting Numbers: [3, 80] Generated Node #0,0,0: 69:[3, 80] Operation: 82-2=80 Exploring Operation: 82+2=84, Resulting Numbers: [3, 84] Generated Node #0,0,1: 69:[3, 84] Operation: 82+2=84 Exploring Operation: 82-3=79, Resulting Numbers: [2, 79] Generated Node #0,0,2: 69:[2, 79] Operation: 82-3=79 Exploring Operation: 2+3=5, Resulting Numbers: [82, 5] Generated Node #0,0,3: 69:[82, 5] Operation: 2+3=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[3, 80], Operations: ['19-16=3', '82-2=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,69 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[2, 79], Operations: ['19-16=3', '82-3=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,69 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[3, 84], Operations: ['19-16=3', '82+2=84'] Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 3*84=252, Resulting Numbers: [252] 252,69 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 69:[82, 5], Operations: ['19-16=3', '2+3=5'] Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,69 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[16, 2, 63], Operations: ['82-19=63'] Exploring Operation: 16+2=18, Resulting Numbers: [63, 18] Generated Node #0,1,0: 69:[63, 18] Operation: 16+2=18 Exploring Operation: 16+63=79, Resulting Numbers: [2, 79] Generated Node #0,1,1: 69:[2, 79] Operation: 16+63=79 Exploring Operation: 16/2=8, Resulting Numbers: [63, 8] Generated Node #0,1,2: 69:[63, 8] Operation: 16/2=8 Exploring Operation: 2+63=65, Resulting Numbers: [16, 65] Generated Node #0,1,3: 69:[16, 65] Operation: 2+63=65 Moving to Node #0,1,0 Current State: 69:[63, 18], Operations: ['82-19=63', '16+2=18'] Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 63*18=1134, Resulting Numbers: [1134] 1134,69 unequal: No Solution Exploring Operation: 63+18=81, Resulting Numbers: [81] 81,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[63, 8], Operations: ['82-19=63', '16/2=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,69 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[2, 79], Operations: ['82-19=63', '16+63=79'] Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,69 unequal: No Solution Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,69 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[16, 65], Operations: ['82-19=63', '2+63=65'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 16*65=1040, Resulting Numbers: [1040] 1040,69 unequal: No Solution Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[82, 16, 21], Operations: ['19+2=21'] Exploring Operation: 82-21=61, Resulting Numbers: [16, 61] Generated Node #0,3,0: 69:[16, 61] Operation: 82-21=61 Exploring Operation: 21-16=5, Resulting Numbers: [82, 5] Generated Node #0,3,1: 69:[82, 5] Operation: 21-16=5 Exploring Operation: 82-16=66, Resulting Numbers: [21, 66] Generated Node #0,3,2: 69:[21, 66] Operation: 82-16=66 Exploring Operation: 16+21=37, Resulting Numbers: [82, 37] Generated Node #0,3,3: 69:[82, 37] Operation: 16+21=37 Moving to Node #0,3,2 Current State: 69:[21, 66], Operations: ['19+2=21', '82-16=66'] Exploring Operation: 21+66=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 21*66=1386, Resulting Numbers: [1386] 1386,69 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[82, 5], Operations: ['19+2=21', '21-16=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,69 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[16, 61], Operations: ['19+2=21', '82-21=61'] Exploring Operation: 16+61=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 16*61=976, Resulting Numbers: [976] 976,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[82, 37], Operations: ['19+2=21', '16+21=37'] Exploring Operation: 82-37=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 82+37=119, Resulting Numbers: [119] 119,69 unequal: No Solution Exploring Operation: 82*37=3034, Resulting Numbers: [3034] 3034,69 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
[ 43, 31, 21, 5 ]
79
[ "43-21=22", "5*22=110", "110-31=79" ]
Current State: 79:[43, 31, 21, 5], Operations: [] Exploring Operation: 43-21=22, Resulting Numbers: [31, 5, 22] Generated Node #2: [31, 5, 22] from Operation: 43-21=22 Current State: 79:[31, 5, 22], Operations: ['43-21=22'] Exploring Operation: 5*22=110, Resulting Numbers: [31, 110] Generated Node #3: [31, 110] from Operation: 5*22=110 Current State: 79:[31, 110], Operations: ['43-21=22', '5*22=110'] Exploring Operation: 110-31=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[43, 31, 21, 5], Operations: [] Exploring Operation: 21*5=105, Resulting Numbers: [43, 31, 105] Generated Node #0,0: 79:[43, 31, 105] Operation: 21*5=105 Moving to Node #0,0 Current State: 79:[43, 31, 105], Operations: ['21*5=105'] Exploring Operation: 43+31=74, Resulting Numbers: [105, 74] Generated Node #0,0,0: 79:[105, 74] Operation: 43+31=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[105, 74], Operations: ['21*5=105', '43+31=74'] Exploring Operation: 105-74=31, Resulting Numbers: [31] 31,79 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
[ 45, 68, 18, 60 ]
65
[ "68-45=23", "60-18=42", "23+42=65" ]
Current State: 65:[45, 68, 18, 60], Operations: [] Exploring Operation: 68-45=23, Resulting Numbers: [18, 60, 23] Generated Node #2: [18, 60, 23] from Operation: 68-45=23 Current State: 65:[18, 60, 23], Operations: ['68-45=23'] Exploring Operation: 60-18=42, Resulting Numbers: [23, 42] Generated Node #3: [23, 42] from Operation: 60-18=42 Current State: 65:[23, 42], Operations: ['68-45=23', '60-18=42'] Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[45, 68, 18, 60], Operations: [] Exploring Operation: 45+18=63, Resulting Numbers: [68, 60, 63] Generated Node #0,0: 65:[68, 60, 63] Operation: 45+18=63 Moving to Node #0,0 Current State: 65:[68, 60, 63], Operations: ['45+18=63'] Exploring Operation: 68-60=8, Resulting Numbers: [63, 8] Generated Node #0,0,0: 65:[63, 8] Operation: 68-60=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[63, 8], Operations: ['45+18=63', '68-60=8'] Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,65 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
[ 88, 43, 37, 31 ]
90
[ "43+31=74", "74/37=2", "88+2=90" ]
Current State: 90:[88, 43, 37, 31], Operations: [] Exploring Operation: 43+31=74, Resulting Numbers: [88, 37, 74] Generated Node #2: [88, 37, 74] from Operation: 43+31=74 Current State: 90:[88, 37, 74], Operations: ['43+31=74'] Exploring Operation: 74/37=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 74/37=2 Current State: 90:[88, 2], Operations: ['43+31=74', '74/37=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[88, 43, 37, 31], Operations: [] Exploring Operation: 43-37=6, Resulting Numbers: [88, 31, 6] Generated Node #0,0: 90:[88, 31, 6] Operation: 43-37=6 Exploring Operation: 88-37=51, Resulting Numbers: [43, 31, 51] Generated Node #0,1: 90:[43, 31, 51] Operation: 88-37=51 Exploring Operation: 37-31=6, Resulting Numbers: [88, 43, 6] Generated Node #0,2: 90:[88, 43, 6] Operation: 37-31=6 Exploring Operation: 88-43=45, Resulting Numbers: [37, 31, 45] Generated Node #0,3: 90:[37, 31, 45] Operation: 88-43=45 Moving to Node #0,0 Current State: 90:[88, 31, 6], Operations: ['43-37=6'] Exploring Operation: 31+6=37, Resulting Numbers: [88, 37] Generated Node #0,0,0: 90:[88, 37] Operation: 31+6=37 Exploring Operation: 88-6=82, Resulting Numbers: [31, 82] Generated Node #0,0,1: 90:[31, 82] Operation: 88-6=82 Exploring Operation: 31-6=25, Resulting Numbers: [88, 25] Generated Node #0,0,2: 90:[88, 25] Operation: 31-6=25 Exploring Operation: 88+6=94, Resulting Numbers: [31, 94] Generated Node #0,0,3: 90:[31, 94] Operation: 88+6=94 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[31, 94], Operations: ['43-37=6', '88+6=94'] Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 31+94=125, Resulting Numbers: [125] 125,90 unequal: No Solution Exploring Operation: 31*94=2914, Resulting Numbers: [2914] 2914,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[88, 25], Operations: ['43-37=6', '31-6=25'] Exploring Operation: 88*25=2200, Resulting Numbers: [2200] 2200,90 unequal: No Solution Exploring Operation: 88+25=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[88, 37], Operations: ['43-37=6', '31+6=37'] Exploring Operation: 88*37=3256, Resulting Numbers: [3256] 3256,90 unequal: No Solution Exploring Operation: 88+37=125, Resulting Numbers: [125] 125,90 unequal: No Solution Exploring Operation: 88-37=51, Resulting Numbers: [51] 51,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[31, 82], Operations: ['43-37=6', '88-6=82'] Exploring Operation: 31*82=2542, Resulting Numbers: [2542] 2542,90 unequal: No Solution Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,90 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: 90:[88, 43, 6], Operations: ['37-31=6'] Exploring Operation: 43+6=49, Resulting Numbers: [88, 49] Generated Node #0,2,0: 90:[88, 49] Operation: 43+6=49 Exploring Operation: 88+6=94, Resulting Numbers: [43, 94] Generated Node #0,2,1: 90:[43, 94] Operation: 88+6=94 Exploring Operation: 88-43=45, Resulting Numbers: [6, 45] Generated Node #0,2,2: 90:[6, 45] Operation: 88-43=45 Exploring Operation: 43-6=37, Resulting Numbers: [88, 37] Generated Node #0,2,3: 90:[88, 37] Operation: 43-6=37 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[6, 45], Operations: ['37-31=6', '88-43=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,90 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[88, 49], Operations: ['37-31=6', '43+6=49'] Exploring Operation: 88*49=4312, Resulting Numbers: [4312] 4312,90 unequal: No Solution Exploring Operation: 88+49=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[43, 94], Operations: ['37-31=6', '88+6=94'] Exploring Operation: 43+94=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 43*94=4042, Resulting Numbers: [4042] 4042,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[88, 37], Operations: ['37-31=6', '43-6=37'] Exploring Operation: 88+37=125, Resulting Numbers: [125] 125,90 unequal: No Solution Exploring Operation: 88*37=3256, Resulting Numbers: [3256] 3256,90 unequal: No Solution Exploring Operation: 88-37=51, Resulting Numbers: [51] 51,90 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: 90:[37, 31, 45], Operations: ['88-43=45'] Exploring Operation: 37-31=6, Resulting Numbers: [45, 6] Generated Node #0,3,0: 90:[45, 6] Operation: 37-31=6 Exploring Operation: 45-37=8, Resulting Numbers: [31, 8] Generated Node #0,3,1: 90:[31, 8] Operation: 45-37=8 Exploring Operation: 45-31=14, Resulting Numbers: [37, 14] Generated Node #0,3,2: 90:[37, 14] Operation: 45-31=14 Exploring Operation: 37+45=82, Resulting Numbers: [31, 82] Generated Node #0,3,3: 90:[31, 82] Operation: 37+45=82 Moving to Node #0,1 Current State: 90:[43, 31, 51], Operations: ['88-37=51'] Exploring Operation: 43+51=94, Resulting Numbers: [31, 94] Generated Node #0,1,0: 90:[31, 94] Operation: 43+51=94 Exploring Operation: 51-43=8, Resulting Numbers: [31, 8] Generated Node #0,1,1: 90:[31, 8] Operation: 51-43=8 Exploring Operation: 43-31=12, Resulting Numbers: [51, 12] Generated Node #0,1,2: 90:[51, 12] Operation: 43-31=12 Exploring Operation: 51-31=20, Resulting Numbers: [43, 20] Generated Node #0,1,3: 90:[43, 20] Operation: 51-31=20 Moving to Node #0,3,0 Current State: 90:[45, 6], Operations: ['88-43=45', '37-31=6'] Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,90 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[31, 8], Operations: ['88-43=45', '45-37=8'] Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,90 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[31, 8], Operations: ['88-37=51', '51-43=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,90 unequal: No Solution Moving to Node #0,1,3 Current State: 90:[43, 20], Operations: ['88-37=51', '51-31=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,90 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[31, 94], Operations: ['88-37=51', '43+51=94'] Exploring Operation: 31*94=2914, Resulting Numbers: [2914] 2914,90 unequal: No Solution Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 31+94=125, Resulting Numbers: [125] 125,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[37, 14], Operations: ['88-43=45', '45-31=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,90 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[51, 12], Operations: ['88-37=51', '43-31=12'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[31, 82], Operations: ['88-43=45', '37+45=82'] Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,90 unequal: No Solution Exploring Operation: 31*82=2542, Resulting Numbers: [2542] 2542,90 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 14, 53, 66, 62 ]
63
[ "14+53=67", "66-62=4", "67-4=63" ]
Current State: 63:[14, 53, 66, 62], Operations: [] Exploring Operation: 14+53=67, Resulting Numbers: [66, 62, 67] Generated Node #2: [66, 62, 67] from Operation: 14+53=67 Current State: 63:[66, 62, 67], Operations: ['14+53=67'] Exploring Operation: 66-62=4, Resulting Numbers: [67, 4] Generated Node #3: [67, 4] from Operation: 66-62=4 Current State: 63:[67, 4], Operations: ['14+53=67', '66-62=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[14, 53, 66, 62], Operations: [] Exploring Operation: 66-53=13, Resulting Numbers: [14, 62, 13] Generated Node #0,0: 63:[14, 62, 13] Operation: 66-53=13 Exploring Operation: 14+53=67, Resulting Numbers: [66, 62, 67] Generated Node #0,1: 63:[66, 62, 67] Operation: 14+53=67 Exploring Operation: 53-14=39, Resulting Numbers: [66, 62, 39] Generated Node #0,2: 63:[66, 62, 39] Operation: 53-14=39 Exploring Operation: 66-62=4, Resulting Numbers: [14, 53, 4] Generated Node #0,3: 63:[14, 53, 4] Operation: 66-62=4 Exploring Operation: 62-53=9, Resulting Numbers: [14, 66, 9] Generated Node #0,4: 63:[14, 66, 9] Operation: 62-53=9 Moving to Node #0,1 Current State: 63:[66, 62, 67], Operations: ['14+53=67'] Exploring Operation: 66-62=4, Resulting Numbers: [67, 4] Generated Node #0,1,0: 63:[67, 4] Operation: 66-62=4 Exploring Operation: 67-62=5, Resulting Numbers: [66, 5] Generated Node #0,1,1: 63:[66, 5] Operation: 67-62=5 Exploring Operation: 62+67=129, Resulting Numbers: [66, 129] Generated Node #0,1,2: 63:[66, 129] Operation: 62+67=129 Exploring Operation: 66+62=128, Resulting Numbers: [67, 128] Generated Node #0,1,3: 63:[67, 128] Operation: 66+62=128 Exploring Operation: 67-66=1, Resulting Numbers: [62, 1] Generated Node #0,1,4: 63:[62, 1] Operation: 67-66=1 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 63:[62, 1], Operations: ['14+53=67', '67-66=1'] Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[14, 53, 66, 62], Operations: [] Exploring Operation: 14+53=67, Resulting Numbers: [66, 62, 67] Generated Node #0,1: 63:[66, 62, 67] Operation: 14+53=67 Moving to Node #0,1 Current State: 63:[66, 62, 67], Operations: ['14+53=67'] Exploring Operation: 67-66=1, Resulting Numbers: [62, 1] Generated Node #0,1,4: 63:[62, 1] Operation: 67-66=1 Moving to Node #0,1,4 Current State: 63:[62, 1], Operations: ['14+53=67', '67-66=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 70, 54, 38, 65 ]
35
[ "65-38=27", "70*27=1890", "1890/54=35" ]
Current State: 35:[70, 54, 38, 65], Operations: [] Exploring Operation: 65-38=27, Resulting Numbers: [70, 54, 27] Generated Node #2: [70, 54, 27] from Operation: 65-38=27 Current State: 35:[70, 54, 27], Operations: ['65-38=27'] Exploring Operation: 70*27=1890, Resulting Numbers: [54, 1890] Generated Node #3: [54, 1890] from Operation: 70*27=1890 Current State: 35:[54, 1890], Operations: ['65-38=27', '70*27=1890'] Exploring Operation: 1890/54=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[70, 54, 38, 65], Operations: [] Exploring Operation: 70-65=5, Resulting Numbers: [54, 38, 5] Generated Node #0,0: 35:[54, 38, 5] Operation: 70-65=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[54, 38, 5], Operations: ['70-65=5'] Exploring Operation: 54-38=16, Resulting Numbers: [5, 16] Generated Node #0,0,0: 35:[5, 16] Operation: 54-38=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[5, 16], Operations: ['70-65=5', '54-38=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,35 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
[ 10, 58, 43, 64 ]
59
[ "58-10=48", "43+64=107", "107-48=59" ]
Current State: 59:[10, 58, 43, 64], Operations: [] Exploring Operation: 58-10=48, Resulting Numbers: [43, 64, 48] Generated Node #2: [43, 64, 48] from Operation: 58-10=48 Current State: 59:[43, 64, 48], Operations: ['58-10=48'] Exploring Operation: 43+64=107, Resulting Numbers: [48, 107] Generated Node #3: [48, 107] from Operation: 43+64=107 Current State: 59:[48, 107], Operations: ['58-10=48', '43+64=107'] Exploring Operation: 107-48=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[10, 58, 43, 64], Operations: [] Exploring Operation: 10+43=53, Resulting Numbers: [58, 64, 53] Generated Node #0,0: 59:[58, 64, 53] Operation: 10+43=53 Moving to Node #0,0 Current State: 59:[58, 64, 53], Operations: ['10+43=53'] Exploring Operation: 64-53=11, Resulting Numbers: [58, 11] Generated Node #0,0,0: 59:[58, 11] Operation: 64-53=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[58, 11], Operations: ['10+43=53', '64-53=11'] Exploring Operation: 58+11=69, Resulting Numbers: [69] 69,59 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
[ 2, 14, 72, 39 ]
45
[ "14-2=12", "72-39=33", "12+33=45" ]
Current State: 45:[2, 14, 72, 39], Operations: [] Exploring Operation: 14-2=12, Resulting Numbers: [72, 39, 12] Generated Node #2: [72, 39, 12] from Operation: 14-2=12 Current State: 45:[72, 39, 12], Operations: ['14-2=12'] Exploring Operation: 72-39=33, Resulting Numbers: [12, 33] Generated Node #3: [12, 33] from Operation: 72-39=33 Current State: 45:[12, 33], Operations: ['14-2=12', '72-39=33'] Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[2, 14, 72, 39], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [2, 14, 33] Generated Node #0,0: 45:[2, 14, 33] Operation: 72-39=33 Exploring Operation: 72/2=36, Resulting Numbers: [14, 39, 36] Generated Node #0,1: 45:[14, 39, 36] Operation: 72/2=36 Exploring Operation: 72-14=58, Resulting Numbers: [2, 39, 58] Generated Node #0,2: 45:[2, 39, 58] Operation: 72-14=58 Exploring Operation: 72-2=70, Resulting Numbers: [14, 39, 70] Generated Node #0,3: 45:[14, 39, 70] Operation: 72-2=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[2, 14, 33], Operations: ['72-39=33'] Exploring Operation: 2+14=16, Resulting Numbers: [33, 16] Generated Node #0,0,0: 45:[33, 16] Operation: 2+14=16 Exploring Operation: 14+33=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 45:[2, 47] Operation: 14+33=47 Exploring Operation: 33-14=19, Resulting Numbers: [2, 19] Generated Node #0,0,2: 45:[2, 19] Operation: 33-14=19 Exploring Operation: 2+33=35, Resulting Numbers: [14, 35] Generated Node #0,0,3: 45:[14, 35] Operation: 2+33=35 Moving to Node #0,0,1 Current State: 45:[2, 47], Operations: ['72-39=33', '14+33=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,45 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,45 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[2, 14, 72, 39], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [2, 14, 33] Generated Node #0,0: 45:[2, 14, 33] Operation: 72-39=33 Moving to Node #0,0 Current State: 45:[2, 14, 33], Operations: ['72-39=33'] Exploring Operation: 14+33=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 45:[2, 47] Operation: 14+33=47 Moving to Node #0,0,1 Current State: 45:[2, 47], Operations: ['72-39=33', '14+33=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 28, 46, 23, 4 ]
18
[ "28+46=74", "23*4=92", "92-74=18" ]
Current State: 18:[28, 46, 23, 4], Operations: [] Exploring Operation: 28+46=74, Resulting Numbers: [23, 4, 74] Generated Node #2: [23, 4, 74] from Operation: 28+46=74 Current State: 18:[23, 4, 74], Operations: ['28+46=74'] Exploring Operation: 23*4=92, Resulting Numbers: [74, 92] Generated Node #3: [74, 92] from Operation: 23*4=92 Current State: 18:[74, 92], Operations: ['28+46=74', '23*4=92'] Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[28, 46, 23, 4], Operations: [] Exploring Operation: 46/23=2, Resulting Numbers: [28, 4, 2] Generated Node #0,0: 18:[28, 4, 2] Operation: 46/23=2 Exploring Operation: 46-28=18, Resulting Numbers: [23, 4, 18] Generated Node #0,1: 18:[23, 4, 18] Operation: 46-28=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[23, 4, 18], Operations: ['46-28=18'] Exploring Operation: 23-18=5, Resulting Numbers: [4, 5] Generated Node #0,1,0: 18:[4, 5] Operation: 23-18=5 Exploring Operation: 23-4=19, Resulting Numbers: [18, 19] Generated Node #0,1,1: 18:[18, 19] Operation: 23-4=19 Moving to Node #0,1,1 Current State: 18:[18, 19], Operations: ['46-28=18', '23-4=19'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[4, 5], Operations: ['46-28=18', '23-18=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[28, 4, 2], Operations: ['46/23=2'] Exploring Operation: 28/4=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 18:[2, 7] Operation: 28/4=7 Exploring Operation: 28/2=14, Resulting Numbers: [4, 14] Generated Node #0,0,1: 18:[4, 14] Operation: 28/2=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[2, 7], Operations: ['46/23=2', '28/4=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[4, 14], Operations: ['46/23=2', '28/2=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[28, 46, 23, 4], Operations: [] Exploring Operation: 46/23=2, Resulting Numbers: [28, 4, 2] Generated Node #0,0: 18:[28, 4, 2] Operation: 46/23=2 Moving to Node #0,0 Current State: 18:[28, 4, 2], Operations: ['46/23=2'] Exploring Operation: 28/2=14, Resulting Numbers: [4, 14] Generated Node #0,0,1: 18:[4, 14] Operation: 28/2=14 Moving to Node #0,0,1 Current State: 18:[4, 14], Operations: ['46/23=2', '28/2=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 32, 11, 79, 11 ]
74
[ "79-32=47", "11*11=121", "121-47=74" ]
Current State: 74:[32, 11, 79, 11], Operations: [] Exploring Operation: 79-32=47, Resulting Numbers: [11, 11, 47] Generated Node #2: [11, 11, 47] from Operation: 79-32=47 Current State: 74:[11, 11, 47], Operations: ['79-32=47'] Exploring Operation: 11*11=121, Resulting Numbers: [47, 121] Generated Node #3: [47, 121] from Operation: 11*11=121 Current State: 74:[47, 121], Operations: ['79-32=47', '11*11=121'] Exploring Operation: 121-47=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[32, 11, 79, 11], Operations: [] Exploring Operation: 79-11=68, Resulting Numbers: [32, 11, 68] Generated Node #0,0: 74:[32, 11, 68] Operation: 79-11=68 Exploring Operation: 32+11=43, Resulting Numbers: [11, 79, 43] Generated Node #0,1: 74:[11, 79, 43] Operation: 32+11=43 Exploring Operation: 11-11=0, Resulting Numbers: [32, 79, 0] Generated Node #0,2: 74:[32, 79, 0] Operation: 11-11=0 Exploring Operation: 32+11=43, Resulting Numbers: [79, 11, 43] Generated Node #0,3: 74:[79, 11, 43] Operation: 32+11=43 Exploring Operation: 11/11=1, Resulting Numbers: [32, 79, 1] Generated Node #0,4: 74:[32, 79, 1] Operation: 11/11=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 74:[32, 79, 1], Operations: ['11/11=1'] Exploring Operation: 79-1=78, Resulting Numbers: [32, 78] Generated Node #0,4,0: 74:[32, 78] Operation: 79-1=78 Exploring Operation: 32*1=32, Resulting Numbers: [79, 32] Generated Node #0,4,1: 74:[79, 32] Operation: 32*1=32 Exploring Operation: 32+1=33, Resulting Numbers: [79, 33] Generated Node #0,4,2: 74:[79, 33] Operation: 32+1=33 Exploring Operation: 32/1=32, Resulting Numbers: [79, 32] Generated Node #0,4,3: 74:[79, 32] Operation: 32/1=32 Exploring Operation: 79*1=79, Resulting Numbers: [32, 79] Generated Node #0,4,4: 74:[32, 79] Operation: 79*1=79 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 74:[32, 78], Operations: ['11/11=1', '79-1=78'] Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,74 unequal: No Solution Exploring Operation: 32*78=2496, Resulting Numbers: [2496] 2496,74 unequal: No Solution Exploring Operation: 32+78=110, Resulting Numbers: [110] 110,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 74:[79, 33], Operations: ['11/11=1', '32+1=33'] Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,74 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,74 unequal: No Solution Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 74:[79, 32], Operations: ['11/11=1', '32*1=32'] Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 74:[79, 32], Operations: ['11/11=1', '32/1=32'] Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 74:[32, 79], Operations: ['11/11=1', '79*1=79'] Exploring Operation: 32+79=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 32*79=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[32, 79, 0], Operations: ['11-11=0'] Exploring Operation: 32+0=32, Resulting Numbers: [79, 32] Generated Node #0,2,0: 74:[79, 32] Operation: 32+0=32 Exploring Operation: 79+0=79, Resulting Numbers: [32, 79] Generated Node #0,2,1: 74:[32, 79] Operation: 79+0=79 Exploring Operation: 32*0=0, Resulting Numbers: [79, 0] Generated Node #0,2,2: 74:[79, 0] Operation: 32*0=0 Exploring Operation: 79*0=0, Resulting Numbers: [32, 0] Generated Node #0,2,3: 74:[32, 0] Operation: 79*0=0 Exploring Operation: 32-0=32, Resulting Numbers: [79, 32] Generated Node #0,2,4: 74:[79, 32] Operation: 32-0=32 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[79, 0], Operations: ['11-11=0', '32*0=0'] Exploring Operation: 79+0=79, Resulting Numbers: [79] 79,74 unequal: No Solution Exploring Operation: 79*0=0, Resulting Numbers: [0] 0,74 unequal: No Solution Exploring Operation: 79-0=79, Resulting Numbers: [79] 79,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 74:[32, 0], Operations: ['11-11=0', '79*0=0'] Exploring Operation: 32+0=32, Resulting Numbers: [32] 32,74 unequal: No Solution Exploring Operation: 32*0=0, Resulting Numbers: [0] 0,74 unequal: No Solution Exploring Operation: 32-0=32, Resulting Numbers: [32] 32,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[79, 32], Operations: ['11-11=0', '32+0=32'] Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[32, 79], Operations: ['11-11=0', '79+0=79'] Exploring Operation: 32+79=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 32*79=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 74:[79, 32], Operations: ['11-11=0', '32-0=32'] Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[32, 11, 68], Operations: ['79-11=68'] Exploring Operation: 32+11=43, Resulting Numbers: [68, 43] Generated Node #0,0,0: 74:[68, 43] Operation: 32+11=43 Exploring Operation: 32-11=21, Resulting Numbers: [68, 21] Generated Node #0,0,1: 74:[68, 21] Operation: 32-11=21 Exploring Operation: 68-11=57, Resulting Numbers: [32, 57] Generated Node #0,0,2: 74:[32, 57] Operation: 68-11=57 Exploring Operation: 68-32=36, Resulting Numbers: [11, 36] Generated Node #0,0,3: 74:[11, 36] Operation: 68-32=36 Exploring Operation: 11+68=79, Resulting Numbers: [32, 79] Generated Node #0,0,4: 74:[32, 79] Operation: 11+68=79 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 74:[11, 36], Operations: ['79-11=68', '68-32=36'] Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 74:[32, 79], Operations: ['79-11=68', '11+68=79'] Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 32+79=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 32*79=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[68, 43], Operations: ['79-11=68', '32+11=43'] Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 68*43=2924, Resulting Numbers: [2924] 2924,74 unequal: No Solution Exploring Operation: 68+43=111, Resulting Numbers: [111] 111,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[68, 21], Operations: ['79-11=68', '32-11=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,74 unequal: No Solution Exploring Operation: 68*21=1428, Resulting Numbers: [1428] 1428,74 unequal: No Solution Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 74:[32, 57], Operations: ['79-11=68', '68-11=57'] Exploring Operation: 32*57=1824, Resulting Numbers: [1824] 1824,74 unequal: No Solution Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 32+57=89, Resulting Numbers: [89] 89,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[11, 79, 43], Operations: ['32+11=43'] Exploring Operation: 11+43=54, Resulting Numbers: [79, 54] Generated Node #0,1,0: 74:[79, 54] Operation: 11+43=54 Exploring Operation: 43-11=32, Resulting Numbers: [79, 32] Generated Node #0,1,1: 74:[79, 32] Operation: 43-11=32 Exploring Operation: 79-43=36, Resulting Numbers: [11, 36] Generated Node #0,1,2: 74:[11, 36] Operation: 79-43=36 Exploring Operation: 11+79=90, Resulting Numbers: [43, 90] Generated Node #0,1,3: 74:[43, 90] Operation: 11+79=90 Exploring Operation: 79-11=68, Resulting Numbers: [43, 68] Generated Node #0,1,4: 74:[43, 68] Operation: 79-11=68 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[79, 32], Operations: ['32+11=43', '43-11=32'] Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 74:[11, 36], Operations: ['32+11=43', '79-43=36'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 74:[43, 68], Operations: ['32+11=43', '79-11=68'] Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,74 unequal: No Solution Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,74 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[79, 54], Operations: ['32+11=43', '11+43=54'] Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,74 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,74 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 74:[43, 90], Operations: ['32+11=43', '11+79=90'] Exploring Operation: 43+90=133, Resulting Numbers: [133] 133,74 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 43*90=3870, Resulting Numbers: [3870] 3870,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[79, 11, 43], Operations: ['32+11=43'] Exploring Operation: 11+43=54, Resulting Numbers: [79, 54] Generated Node #0,3,0: 74:[79, 54] Operation: 11+43=54 Exploring Operation: 79+11=90, Resulting Numbers: [43, 90] Generated Node #0,3,1: 74:[43, 90] Operation: 79+11=90 Exploring Operation: 79-43=36, Resulting Numbers: [11, 36] Generated Node #0,3,2: 74:[11, 36] Operation: 79-43=36 Exploring Operation: 43-11=32, Resulting Numbers: [79, 32] Generated Node #0,3,3: 74:[79, 32] Operation: 43-11=32 Exploring Operation: 79-11=68, Resulting Numbers: [43, 68] Generated Node #0,3,4: 74:[43, 68] Operation: 79-11=68 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 74:[11, 36], Operations: ['32+11=43', '79-43=36'] Exploring Operation: 11*36=396, Resulting Numbers: [396] 396,74 unequal: No Solution Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 74:[79, 32], Operations: ['32+11=43', '43-11=32'] Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,74 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,74 unequal: No Solution Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 74:[43, 68], Operations: ['32+11=43', '79-11=68'] Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 43*68=2924, Resulting Numbers: [2924] 2924,74 unequal: No Solution Exploring Operation: 43+68=111, Resulting Numbers: [111] 111,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 74:[79, 54], Operations: ['32+11=43', '11+43=54'] Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,74 unequal: No Solution Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 74:[43, 90], Operations: ['32+11=43', '79+11=90'] Exploring Operation: 43+90=133, Resulting Numbers: [133] 133,74 unequal: No Solution Exploring Operation: 43*90=3870, Resulting Numbers: [3870] 3870,74 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 80, 69, 71, 14 ]
73
[ "71-69=2", "14/2=7", "80-7=73" ]
Current State: 73:[80, 69, 71, 14], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [80, 14, 2] Generated Node #2: [80, 14, 2] from Operation: 71-69=2 Current State: 73:[80, 14, 2], Operations: ['71-69=2'] Exploring Operation: 14/2=7, Resulting Numbers: [80, 7] Generated Node #3: [80, 7] from Operation: 14/2=7 Current State: 73:[80, 7], Operations: ['71-69=2', '14/2=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[80, 69, 71, 14], Operations: [] Exploring Operation: 80-14=66, Resulting Numbers: [69, 71, 66] Generated Node #0,0: 73:[69, 71, 66] Operation: 80-14=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[69, 71, 66], Operations: ['80-14=66'] Exploring Operation: 69+66=135, Resulting Numbers: [71, 135] Generated Node #0,0,0: 73:[71, 135] Operation: 69+66=135 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[71, 135], Operations: ['80-14=66', '69+66=135'] Exploring Operation: 135-71=64, Resulting Numbers: [64] 64,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 11, 83, 62, 77 ]
79
[ "11+83=94", "77-62=15", "94-15=79" ]
Current State: 79:[11, 83, 62, 77], Operations: [] Exploring Operation: 11+83=94, Resulting Numbers: [62, 77, 94] Generated Node #2: [62, 77, 94] from Operation: 11+83=94 Current State: 79:[62, 77, 94], Operations: ['11+83=94'] Exploring Operation: 77-62=15, Resulting Numbers: [94, 15] Generated Node #3: [94, 15] from Operation: 77-62=15 Current State: 79:[94, 15], Operations: ['11+83=94', '77-62=15'] Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[11, 83, 62, 77], Operations: [] Exploring Operation: 11+62=73, Resulting Numbers: [83, 77, 73] Generated Node #0,0: 79:[83, 77, 73] Operation: 11+62=73 Exploring Operation: 83-11=72, Resulting Numbers: [62, 77, 72] Generated Node #0,1: 79:[62, 77, 72] Operation: 83-11=72 Exploring Operation: 11+83=94, Resulting Numbers: [62, 77, 94] Generated Node #0,2: 79:[62, 77, 94] Operation: 11+83=94 Exploring Operation: 11+77=88, Resulting Numbers: [83, 62, 88] Generated Node #0,3: 79:[83, 62, 88] Operation: 11+77=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[83, 77, 73], Operations: ['11+62=73'] Exploring Operation: 83-73=10, Resulting Numbers: [77, 10] Generated Node #0,0,0: 79:[77, 10] Operation: 83-73=10 Exploring Operation: 77+73=150, Resulting Numbers: [83, 150] Generated Node #0,0,1: 79:[83, 150] Operation: 77+73=150 Exploring Operation: 83+73=156, Resulting Numbers: [77, 156] Generated Node #0,0,2: 79:[77, 156] Operation: 83+73=156 Exploring Operation: 83-77=6, Resulting Numbers: [73, 6] Generated Node #0,0,3: 79:[73, 6] Operation: 83-77=6 Moving to Node #0,0,0 Current State: 79:[77, 10], Operations: ['11+62=73', '83-73=10'] Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,79 unequal: No Solution Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,79 unequal: No Solution Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[83, 150], Operations: ['11+62=73', '77+73=150'] Exploring Operation: 83+150=233, Resulting Numbers: [233] 233,79 unequal: No Solution Exploring Operation: 150-83=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 83*150=12450, Resulting Numbers: [12450] 12450,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[73, 6], Operations: ['11+62=73', '83-77=6'] Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[11, 83, 62, 77], Operations: [] Exploring Operation: 11+62=73, Resulting Numbers: [83, 77, 73] Generated Node #0,0: 79:[83, 77, 73] Operation: 11+62=73 Moving to Node #0,0 Current State: 79:[83, 77, 73], Operations: ['11+62=73'] Exploring Operation: 83-77=6, Resulting Numbers: [73, 6] Generated Node #0,0,3: 79:[73, 6] Operation: 83-77=6 Moving to Node #0,0,3 Current State: 79:[73, 6], Operations: ['11+62=73', '83-77=6'] Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 92, 2, 16, 11 ]
62
[ "16-2=14", "11*14=154", "154-92=62" ]
Current State: 62:[92, 2, 16, 11], Operations: [] Exploring Operation: 16-2=14, Resulting Numbers: [92, 11, 14] Generated Node #2: [92, 11, 14] from Operation: 16-2=14 Current State: 62:[92, 11, 14], Operations: ['16-2=14'] Exploring Operation: 11*14=154, Resulting Numbers: [92, 154] Generated Node #3: [92, 154] from Operation: 11*14=154 Current State: 62:[92, 154], Operations: ['16-2=14', '11*14=154'] Exploring Operation: 154-92=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[92, 2, 16, 11], Operations: [] Exploring Operation: 92-11=81, Resulting Numbers: [2, 16, 81] Generated Node #0,0: 62:[2, 16, 81] Operation: 92-11=81 Exploring Operation: 92-16=76, Resulting Numbers: [2, 11, 76] Generated Node #0,1: 62:[2, 11, 76] Operation: 92-16=76 Exploring Operation: 16+11=27, Resulting Numbers: [92, 2, 27] Generated Node #0,2: 62:[92, 2, 27] Operation: 16+11=27 Exploring Operation: 16-11=5, Resulting Numbers: [92, 2, 5] Generated Node #0,3: 62:[92, 2, 5] Operation: 16-11=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[2, 11, 76], Operations: ['92-16=76'] Exploring Operation: 76-11=65, Resulting Numbers: [2, 65] Generated Node #0,1,0: 62:[2, 65] Operation: 76-11=65 Exploring Operation: 76/2=38, Resulting Numbers: [11, 38] Generated Node #0,1,1: 62:[11, 38] Operation: 76/2=38 Exploring Operation: 76-2=74, Resulting Numbers: [11, 74] Generated Node #0,1,2: 62:[11, 74] Operation: 76-2=74 Exploring Operation: 11-2=9, Resulting Numbers: [76, 9] Generated Node #0,1,3: 62:[76, 9] Operation: 11-2=9 Moving to Node #0,1,0 Current State: 62:[2, 65], Operations: ['92-16=76', '76-11=65'] Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,62 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[11, 38], Operations: ['92-16=76', '76/2=38'] Exploring Operation: 11*38=418, Resulting Numbers: [418] 418,62 unequal: No Solution Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 11+38=49, Resulting Numbers: [49] 49,62 unequal: No Solution Moving to Node #0,1,3 Current State: 62:[76, 9], Operations: ['92-16=76', '11-2=9'] Exploring Operation: 76+9=85, Resulting Numbers: [85] 85,62 unequal: No Solution Exploring Operation: 76-9=67, Resulting Numbers: [67] 67,62 unequal: No Solution Exploring Operation: 76*9=684, Resulting Numbers: [684] 684,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[11, 74], Operations: ['92-16=76', '76-2=74'] Exploring Operation: 11*74=814, Resulting Numbers: [814] 814,62 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[2, 16, 81], Operations: ['92-11=81'] Exploring Operation: 16/2=8, Resulting Numbers: [81, 8] Generated Node #0,0,0: 62:[81, 8] Operation: 16/2=8 Exploring Operation: 2*16=32, Resulting Numbers: [81, 32] Generated Node #0,0,1: 62:[81, 32] Operation: 2*16=32 Exploring Operation: 16-2=14, Resulting Numbers: [81, 14] Generated Node #0,0,2: 62:[81, 14] Operation: 16-2=14 Exploring Operation: 81-16=65, Resulting Numbers: [2, 65] Generated Node #0,0,3: 62:[2, 65] Operation: 81-16=65 Moving to Node #0,0,3 Current State: 62:[2, 65], Operations: ['92-11=81', '81-16=65'] Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,62 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[81, 32], Operations: ['92-11=81', '2*16=32'] Exploring Operation: 81+32=113, Resulting Numbers: [113] 113,62 unequal: No Solution Exploring Operation: 81*32=2592, Resulting Numbers: [2592] 2592,62 unequal: No Solution Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[81, 8], Operations: ['92-11=81', '16/2=8'] Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,62 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[81, 14], Operations: ['92-11=81', '16-2=14'] Exploring Operation: 81+14=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 81*14=1134, Resulting Numbers: [1134] 1134,62 unequal: No Solution Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[92, 2, 5], Operations: ['16-11=5'] Exploring Operation: 5-2=3, Resulting Numbers: [92, 3] Generated Node #0,3,0: 62:[92, 3] Operation: 5-2=3 Exploring Operation: 92/2=46, Resulting Numbers: [5, 46] Generated Node #0,3,1: 62:[5, 46] Operation: 92/2=46 Exploring Operation: 92-5=87, Resulting Numbers: [2, 87] Generated Node #0,3,2: 62:[2, 87] Operation: 92-5=87 Exploring Operation: 92-2=90, Resulting Numbers: [5, 90] Generated Node #0,3,3: 62:[5, 90] Operation: 92-2=90 Moving to Node #0,3,1 Current State: 62:[5, 46], Operations: ['16-11=5', '92/2=46'] Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,62 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[2, 87], Operations: ['16-11=5', '92-5=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,62 unequal: No Solution Exploring Operation: 2*87=174, Resulting Numbers: [174] 174,62 unequal: No Solution Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[5, 90], Operations: ['16-11=5', '92-2=90'] Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,62 unequal: No Solution Exploring Operation: 5*90=450, Resulting Numbers: [450] 450,62 unequal: No Solution Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,62 unequal: No Solution Moving to Node #0,3,0 Current State: 62:[92, 3], Operations: ['16-11=5', '5-2=3'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,62 unequal: No Solution Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 92*3=276, Resulting Numbers: [276] 276,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[92, 2, 27], Operations: ['16+11=27'] Exploring Operation: 92-2=90, Resulting Numbers: [27, 90] Generated Node #0,2,0: 62:[27, 90] Operation: 92-2=90 Exploring Operation: 92-27=65, Resulting Numbers: [2, 65] Generated Node #0,2,1: 62:[2, 65] Operation: 92-27=65 Exploring Operation: 92/2=46, Resulting Numbers: [27, 46] Generated Node #0,2,2: 62:[27, 46] Operation: 92/2=46 Exploring Operation: 2+27=29, Resulting Numbers: [92, 29] Generated Node #0,2,3: 62:[92, 29] Operation: 2+27=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[2, 65], Operations: ['16+11=27', '92-27=65'] Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,62 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[27, 46], Operations: ['16+11=27', '92/2=46'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 27*46=1242, Resulting Numbers: [1242] 1242,62 unequal: No Solution Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[27, 90], Operations: ['16+11=27', '92-2=90'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 27+90=117, Resulting Numbers: [117] 117,62 unequal: No Solution Exploring Operation: 27*90=2430, Resulting Numbers: [2430] 2430,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 62:[92, 29], Operations: ['16+11=27', '2+27=29'] Exploring Operation: 92+29=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 92*29=2668, Resulting Numbers: [2668] 2668,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 30, 59, 32, 8 ]
24
[ "59-30=29", "32-29=3", "8*3=24" ]
Current State: 24:[30, 59, 32, 8], Operations: [] Exploring Operation: 59-30=29, Resulting Numbers: [32, 8, 29] Generated Node #2: [32, 8, 29] from Operation: 59-30=29 Current State: 24:[32, 8, 29], Operations: ['59-30=29'] Exploring Operation: 32-29=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 32-29=3 Current State: 24:[8, 3], Operations: ['59-30=29', '32-29=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[30, 59, 32, 8], Operations: [] Exploring Operation: 59-32=27, Resulting Numbers: [30, 8, 27] Generated Node #0,0: 24:[30, 8, 27] Operation: 59-32=27 Exploring Operation: 59-30=29, Resulting Numbers: [32, 8, 29] Generated Node #0,1: 24:[32, 8, 29] Operation: 59-30=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[30, 8, 27], Operations: ['59-32=27'] Exploring Operation: 30-27=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 24:[8, 3] Operation: 30-27=3 Exploring Operation: 30-8=22, Resulting Numbers: [27, 22] Generated Node #0,0,1: 24:[27, 22] Operation: 30-8=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[8, 3], Operations: ['59-32=27', '30-27=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[30, 59, 32, 8], Operations: [] Exploring Operation: 59-32=27, Resulting Numbers: [30, 8, 27] Generated Node #0,0: 24:[30, 8, 27] Operation: 59-32=27 Moving to Node #0,0 Current State: 24:[30, 8, 27], Operations: ['59-32=27'] Exploring Operation: 30-27=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 24:[8, 3] Operation: 30-27=3 Moving to Node #0,0,0 Current State: 24:[8, 3], Operations: ['59-32=27', '30-27=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 87, 43, 99, 78 ]
32
[ "87-78=9", "99/9=11", "43-11=32" ]
Current State: 32:[87, 43, 99, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [43, 99, 9] Generated Node #2: [43, 99, 9] from Operation: 87-78=9 Current State: 32:[43, 99, 9], Operations: ['87-78=9'] Exploring Operation: 99/9=11, Resulting Numbers: [43, 11] Generated Node #3: [43, 11] from Operation: 99/9=11 Current State: 32:[43, 11], Operations: ['87-78=9', '99/9=11'] Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[87, 43, 99, 78], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [43, 78, 12] Generated Node #0,0: 32:[43, 78, 12] Operation: 99-87=12 Moving to Node #0,0 Current State: 32:[43, 78, 12], Operations: ['99-87=12'] Exploring Operation: 78-43=35, Resulting Numbers: [12, 35] Generated Node #0,0,0: 32:[12, 35] Operation: 78-43=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[12, 35], Operations: ['99-87=12', '78-43=35'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 62, 4, 94, 99 ]
60
[ "62+94=156", "156/4=39", "99-39=60" ]
Current State: 60:[62, 4, 94, 99], Operations: [] Exploring Operation: 62+94=156, Resulting Numbers: [4, 99, 156] Generated Node #2: [4, 99, 156] from Operation: 62+94=156 Current State: 60:[4, 99, 156], Operations: ['62+94=156'] Exploring Operation: 156/4=39, Resulting Numbers: [99, 39] Generated Node #3: [99, 39] from Operation: 156/4=39 Current State: 60:[99, 39], Operations: ['62+94=156', '156/4=39'] Exploring Operation: 99-39=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[62, 4, 94, 99], Operations: [] Exploring Operation: 94-62=32, Resulting Numbers: [4, 99, 32] Generated Node #0,0: 60:[4, 99, 32] Operation: 94-62=32 Exploring Operation: 99-94=5, Resulting Numbers: [62, 4, 5] Generated Node #0,1: 60:[62, 4, 5] Operation: 99-94=5 Moving to Node #0,1 Current State: 60:[62, 4, 5], Operations: ['99-94=5'] Exploring Operation: 4*5=20, Resulting Numbers: [62, 20] Generated Node #0,1,0: 60:[62, 20] Operation: 4*5=20 Exploring Operation: 62-4=58, Resulting Numbers: [5, 58] Generated Node #0,1,1: 60:[5, 58] Operation: 62-4=58 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[62, 20], Operations: ['99-94=5', '4*5=20'] Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,60 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,60 unequal: No Solution No 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: 60:[5, 58], Operations: ['99-94=5', '62-4=58'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,60 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,60 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: 60:[4, 99, 32], Operations: ['94-62=32'] Exploring Operation: 99-32=67, Resulting Numbers: [4, 67] Generated Node #0,0,0: 60:[4, 67] Operation: 99-32=67 Exploring Operation: 99-4=95, Resulting Numbers: [32, 95] Generated Node #0,0,1: 60:[32, 95] Operation: 99-4=95 Moving to Node #0,0,0 Current State: 60:[4, 67], Operations: ['94-62=32', '99-32=67'] Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,60 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[32, 95], Operations: ['94-62=32', '99-4=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,60 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,60 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 7, 2, 1, 48 ]
23
[ "2+1=3", "48/3=16", "7+16=23" ]
Current State: 23:[7, 2, 1, 48], Operations: [] Exploring Operation: 2+1=3, Resulting Numbers: [7, 48, 3] Generated Node #2: [7, 48, 3] from Operation: 2+1=3 Current State: 23:[7, 48, 3], Operations: ['2+1=3'] Exploring Operation: 48/3=16, Resulting Numbers: [7, 16] Generated Node #3: [7, 16] from Operation: 48/3=16 Current State: 23:[7, 16], Operations: ['2+1=3', '48/3=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[7, 2, 1, 48], Operations: [] Exploring Operation: 7*2=14, Resulting Numbers: [1, 48, 14] Generated Node #0,0: 23:[1, 48, 14] Operation: 7*2=14 Exploring Operation: 48/2=24, Resulting Numbers: [7, 1, 24] Generated Node #0,1: 23:[7, 1, 24] Operation: 48/2=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[7, 1, 24], Operations: ['48/2=24'] Exploring Operation: 24-1=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 23:[7, 23] Operation: 24-1=23 Exploring Operation: 7+1=8, Resulting Numbers: [24, 8] Generated Node #0,1,1: 23:[24, 8] Operation: 7+1=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[7, 23], Operations: ['48/2=24', '24-1=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,23 unequal: No Solution No 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: 23:[24, 8], Operations: ['48/2=24', '7+1=8'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,23 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: 23:[1, 48, 14], Operations: ['7*2=14'] Exploring Operation: 1+14=15, Resulting Numbers: [48, 15] Generated Node #0,0,0: 23:[48, 15] Operation: 1+14=15 Exploring Operation: 48-1=47, Resulting Numbers: [14, 47] Generated Node #0,0,1: 23:[14, 47] Operation: 48-1=47 Moving to Node #0,0,0 Current State: 23:[48, 15], Operations: ['7*2=14', '1+14=15'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[14, 47], Operations: ['7*2=14', '48-1=47'] Exploring Operation: 14+47=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,23 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
[ 18, 77, 25, 47 ]
23
[ "18+77=95", "25+47=72", "95-72=23" ]
Current State: 23:[18, 77, 25, 47], Operations: [] Exploring Operation: 18+77=95, Resulting Numbers: [25, 47, 95] Generated Node #2: [25, 47, 95] from Operation: 18+77=95 Current State: 23:[25, 47, 95], Operations: ['18+77=95'] Exploring Operation: 25+47=72, Resulting Numbers: [95, 72] Generated Node #3: [95, 72] from Operation: 25+47=72 Current State: 23:[95, 72], Operations: ['18+77=95', '25+47=72'] Exploring Operation: 95-72=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[18, 77, 25, 47], Operations: [] Exploring Operation: 77-47=30, Resulting Numbers: [18, 25, 30] Generated Node #0,0: 23:[18, 25, 30] Operation: 77-47=30 Exploring Operation: 47-25=22, Resulting Numbers: [18, 77, 22] Generated Node #0,1: 23:[18, 77, 22] Operation: 47-25=22 Exploring Operation: 77-18=59, Resulting Numbers: [25, 47, 59] Generated Node #0,2: 23:[25, 47, 59] Operation: 77-18=59 Exploring Operation: 77-25=52, Resulting Numbers: [18, 47, 52] Generated Node #0,3: 23:[18, 47, 52] Operation: 77-25=52 Moving to Node #0,0 Current State: 23:[18, 25, 30], Operations: ['77-47=30'] Exploring Operation: 25-18=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 23:[30, 7] Operation: 25-18=7 Exploring Operation: 30-18=12, Resulting Numbers: [25, 12] Generated Node #0,0,1: 23:[25, 12] Operation: 30-18=12 Exploring Operation: 30-25=5, Resulting Numbers: [18, 5] Generated Node #0,0,2: 23:[18, 5] Operation: 30-25=5 Exploring Operation: 18+25=43, Resulting Numbers: [30, 43] Generated Node #0,0,3: 23:[30, 43] Operation: 18+25=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 23:[25, 12], Operations: ['77-47=30', '30-18=12'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,23 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[30, 7], Operations: ['77-47=30', '25-18=7'] Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,23 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[18, 77, 25, 47], Operations: [] Exploring Operation: 77-47=30, Resulting Numbers: [18, 25, 30] Generated Node #0,0: 23:[18, 25, 30] Operation: 77-47=30 Moving to Node #0,0 Current State: 23:[18, 25, 30], Operations: ['77-47=30'] Exploring Operation: 25-18=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 23:[30, 7] Operation: 25-18=7 Moving to Node #0,0,0 Current State: 23:[30, 7], Operations: ['77-47=30', '25-18=7'] Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 7, 84, 47, 40 ]
19
[ "84/7=12", "47-40=7", "12+7=19" ]
Current State: 19:[7, 84, 47, 40], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [47, 40, 12] Generated Node #2: [47, 40, 12] from Operation: 84/7=12 Current State: 19:[47, 40, 12], Operations: ['84/7=12'] Exploring Operation: 47-40=7, Resulting Numbers: [12, 7] Generated Node #3: [12, 7] from Operation: 47-40=7 Current State: 19:[12, 7], Operations: ['84/7=12', '47-40=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[7, 84, 47, 40], Operations: [] Exploring Operation: 84-7=77, Resulting Numbers: [47, 40, 77] Generated Node #0,0: 19:[47, 40, 77] Operation: 84-7=77 Exploring Operation: 84/7=12, Resulting Numbers: [47, 40, 12] Generated Node #0,1: 19:[47, 40, 12] Operation: 84/7=12 Exploring Operation: 47-40=7, Resulting Numbers: [7, 84, 7] Generated Node #0,2: 19:[7, 84, 7] Operation: 47-40=7 Exploring Operation: 84-40=44, Resulting Numbers: [7, 47, 44] Generated Node #0,3: 19:[7, 47, 44] Operation: 84-40=44 Exploring Operation: 84-47=37, Resulting Numbers: [7, 40, 37] Generated Node #0,4: 19:[7, 40, 37] Operation: 84-47=37 Moving to Node #0,4 Current State: 19:[7, 40, 37], Operations: ['84-47=37'] Exploring Operation: 40-37=3, Resulting Numbers: [7, 3] Generated Node #0,4,0: 19:[7, 3] Operation: 40-37=3 Exploring Operation: 37-7=30, Resulting Numbers: [40, 30] Generated Node #0,4,1: 19:[40, 30] Operation: 37-7=30 Exploring Operation: 7+40=47, Resulting Numbers: [37, 47] Generated Node #0,4,2: 19:[37, 47] Operation: 7+40=47 Exploring Operation: 40-7=33, Resulting Numbers: [37, 33] Generated Node #0,4,3: 19:[37, 33] Operation: 40-7=33 Exploring Operation: 7+37=44, Resulting Numbers: [40, 44] Generated Node #0,4,4: 19:[40, 44] Operation: 7+37=44 Moving to Node #0,1 Current State: 19:[47, 40, 12], Operations: ['84/7=12'] Exploring Operation: 40-12=28, Resulting Numbers: [47, 28] Generated Node #0,1,0: 19:[47, 28] Operation: 40-12=28 Exploring Operation: 47-12=35, Resulting Numbers: [40, 35] Generated Node #0,1,1: 19:[40, 35] Operation: 47-12=35 Exploring Operation: 47+12=59, Resulting Numbers: [40, 59] Generated Node #0,1,2: 19:[40, 59] Operation: 47+12=59 Exploring Operation: 47-40=7, Resulting Numbers: [12, 7] Generated Node #0,1,3: 19:[12, 7] Operation: 47-40=7 Exploring Operation: 40+12=52, Resulting Numbers: [47, 52] Generated Node #0,1,4: 19:[47, 52] Operation: 40+12=52 Moving to Node #0,3 Current State: 19:[7, 47, 44], Operations: ['84-40=44'] Exploring Operation: 7+44=51, Resulting Numbers: [47, 51] Generated Node #0,3,0: 19:[47, 51] Operation: 7+44=51 Exploring Operation: 7+47=54, Resulting Numbers: [44, 54] Generated Node #0,3,1: 19:[44, 54] Operation: 7+47=54 Exploring Operation: 44-7=37, Resulting Numbers: [47, 37] Generated Node #0,3,2: 19:[47, 37] Operation: 44-7=37 Exploring Operation: 47-7=40, Resulting Numbers: [44, 40] Generated Node #0,3,3: 19:[44, 40] Operation: 47-7=40 Exploring Operation: 47-44=3, Resulting Numbers: [7, 3] Generated Node #0,3,4: 19:[7, 3] Operation: 47-44=3 Moving to Node #0,2 Current State: 19:[7, 84, 7], Operations: ['47-40=7'] Exploring Operation: 84/7=12, Resulting Numbers: [7, 12] Generated Node #0,2,0: 19:[7, 12] Operation: 84/7=12 Exploring Operation: 7+7=14, Resulting Numbers: [84, 14] Generated Node #0,2,1: 19:[84, 14] Operation: 7+7=14 Exploring Operation: 84/7=12, Resulting Numbers: [7, 12] Generated Node #0,2,2: 19:[7, 12] Operation: 84/7=12 Exploring Operation: 84-7=77, Resulting Numbers: [7, 77] Generated Node #0,2,3: 19:[7, 77] Operation: 84-7=77 Exploring Operation: 84-7=77, Resulting Numbers: [7, 77] Generated Node #0,2,4: 19:[7, 77] Operation: 84-7=77 Moving to Node #0,0 Current State: 19:[47, 40, 77], Operations: ['84-7=77'] Exploring Operation: 47+77=124, Resulting Numbers: [40, 124] Generated Node #0,0,0: 19:[40, 124] Operation: 47+77=124 Exploring Operation: 47+40=87, Resulting Numbers: [77, 87] Generated Node #0,0,1: 19:[77, 87] Operation: 47+40=87 Exploring Operation: 77-47=30, Resulting Numbers: [40, 30] Generated Node #0,0,2: 19:[40, 30] Operation: 77-47=30 Exploring Operation: 77-40=37, Resulting Numbers: [47, 37] Generated Node #0,0,3: 19:[47, 37] Operation: 77-40=37 Exploring Operation: 47-40=7, Resulting Numbers: [77, 7] Generated Node #0,0,4: 19:[77, 7] Operation: 47-40=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 19:[40, 30], Operations: ['84-7=77', '77-47=30'] Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,19 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,19 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:[47, 37], Operations: ['84-7=77', '77-40=37'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,19 unequal: No Solution Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,19 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:[77, 7], Operations: ['84-7=77', '47-40=7'] Exploring Operation: 77+7=84, Resulting Numbers: [84] 84,19 unequal: No Solution Exploring Operation: 77*7=539, Resulting Numbers: [539] 539,19 unequal: No Solution Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,19 unequal: No Solution Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,19 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:[40, 124], Operations: ['84-7=77', '47+77=124'] Exploring Operation: 40*124=4960, Resulting Numbers: [4960] 4960,19 unequal: No Solution Exploring Operation: 124-40=84, Resulting Numbers: [84] 84,19 unequal: No Solution Exploring Operation: 40+124=164, Resulting Numbers: [164] 164,19 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:[77, 87], Operations: ['84-7=77', '47+40=87'] Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 77*87=6699, Resulting Numbers: [6699] 6699,19 unequal: No Solution Exploring Operation: 77+87=164, Resulting Numbers: [164] 164,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 19:[12, 7], Operations: ['84/7=12', '47-40=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[7, 84, 47, 40], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [47, 40, 12] Generated Node #0,1: 19:[47, 40, 12] Operation: 84/7=12 Moving to Node #0,1 Current State: 19:[47, 40, 12], Operations: ['84/7=12'] Exploring Operation: 47-40=7, Resulting Numbers: [12, 7] Generated Node #0,1,3: 19:[12, 7] Operation: 47-40=7 Moving to Node #0,1,3 Current State: 19:[12, 7], Operations: ['84/7=12', '47-40=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.955729
hs_5
mult_heuristic
[ 54, 16, 40, 26 ]
32
[ "54+26=80", "16*80=1280", "1280/40=32" ]
Current State: 32:[54, 16, 40, 26], Operations: [] Exploring Operation: 54+26=80, Resulting Numbers: [16, 40, 80] Generated Node #2: [16, 40, 80] from Operation: 54+26=80 Current State: 32:[16, 40, 80], Operations: ['54+26=80'] Exploring Operation: 16*80=1280, Resulting Numbers: [40, 1280] Generated Node #3: [40, 1280] from Operation: 16*80=1280 Current State: 32:[40, 1280], Operations: ['54+26=80', '16*80=1280'] Exploring Operation: 1280/40=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[54, 16, 40, 26], Operations: [] Exploring Operation: 54-26=28, Resulting Numbers: [16, 40, 28] Generated Node #0,0: 32:[16, 40, 28] Operation: 54-26=28 Exploring Operation: 54-16=38, Resulting Numbers: [40, 26, 38] Generated Node #0,1: 32:[40, 26, 38] Operation: 54-16=38 Exploring Operation: 54-40=14, Resulting Numbers: [16, 26, 14] Generated Node #0,2: 32:[16, 26, 14] Operation: 54-40=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[16, 26, 14], Operations: ['54-40=14'] Exploring Operation: 26-16=10, Resulting Numbers: [14, 10] Generated Node #0,2,0: 32:[14, 10] Operation: 26-16=10 Exploring Operation: 16-14=2, Resulting Numbers: [26, 2] Generated Node #0,2,1: 32:[26, 2] Operation: 16-14=2 Exploring Operation: 26-14=12, Resulting Numbers: [16, 12] Generated Node #0,2,2: 32:[16, 12] Operation: 26-14=12 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[14, 10], Operations: ['54-40=14', '26-16=10'] Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 14*10=140, Resulting Numbers: [140] 140,32 unequal: No Solution No 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: 32:[16, 12], Operations: ['54-40=14', '26-14=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,32 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,32 unequal: No Solution No 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: 32:[26, 2], Operations: ['54-40=14', '16-14=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,32 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: 32:[16, 40, 28], Operations: ['54-26=28'] Exploring Operation: 40-16=24, Resulting Numbers: [28, 24] Generated Node #0,0,0: 32:[28, 24] Operation: 40-16=24 Exploring Operation: 28-16=12, Resulting Numbers: [40, 12] Generated Node #0,0,1: 32:[40, 12] Operation: 28-16=12 Exploring Operation: 40-28=12, Resulting Numbers: [16, 12] Generated Node #0,0,2: 32:[16, 12] Operation: 40-28=12 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[16, 12], Operations: ['54-26=28', '40-28=12'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,32 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,32 unequal: No Solution No 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: 32:[28, 24], Operations: ['54-26=28', '40-16=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,32 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,32 unequal: No Solution No 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: 32:[40, 12], Operations: ['54-26=28', '28-16=12'] Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,32 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,32 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: 32:[40, 26, 38], Operations: ['54-16=38'] Exploring Operation: 38-26=12, Resulting Numbers: [40, 12] Generated Node #0,1,0: 32:[40, 12] Operation: 38-26=12 Exploring Operation: 40-26=14, Resulting Numbers: [38, 14] Generated Node #0,1,1: 32:[38, 14] Operation: 40-26=14 Exploring Operation: 40-38=2, Resulting Numbers: [26, 2] Generated Node #0,1,2: 32:[26, 2] Operation: 40-38=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 32:[26, 2], Operations: ['54-16=38', '40-38=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,32 unequal: No Solution No 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: 32:[38, 14], Operations: ['54-16=38', '40-26=14'] Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,32 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,32 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,32 unequal: No Solution No 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: 32:[40, 12], Operations: ['54-16=38', '38-26=12'] Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,32 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 2, 11, 31, 72 ]
94
[ "11-2=9", "31+72=103", "103-9=94" ]
Current State: 94:[2, 11, 31, 72], Operations: [] Exploring Operation: 11-2=9, Resulting Numbers: [31, 72, 9] Generated Node #2: [31, 72, 9] from Operation: 11-2=9 Current State: 94:[31, 72, 9], Operations: ['11-2=9'] Exploring Operation: 31+72=103, Resulting Numbers: [9, 103] Generated Node #3: [9, 103] from Operation: 31+72=103 Current State: 94:[9, 103], Operations: ['11-2=9', '31+72=103'] Exploring Operation: 103-9=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[2, 11, 31, 72], Operations: [] Exploring Operation: 72-31=41, Resulting Numbers: [2, 11, 41] Generated Node #0,0: 94:[2, 11, 41] Operation: 72-31=41 Exploring Operation: 11+31=42, Resulting Numbers: [2, 72, 42] Generated Node #0,1: 94:[2, 72, 42] Operation: 11+31=42 Exploring Operation: 31+72=103, Resulting Numbers: [2, 11, 103] Generated Node #0,2: 94:[2, 11, 103] Operation: 31+72=103 Moving to Node #0,0 Current State: 94:[2, 11, 41], Operations: ['72-31=41'] Exploring Operation: 11+41=52, Resulting Numbers: [2, 52] Generated Node #0,0,0: 94:[2, 52] Operation: 11+41=52 Exploring Operation: 11-2=9, Resulting Numbers: [41, 9] Generated Node #0,0,1: 94:[41, 9] Operation: 11-2=9 Exploring Operation: 2+41=43, Resulting Numbers: [11, 43] Generated Node #0,0,2: 94:[11, 43] Operation: 2+41=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[2, 52], Operations: ['72-31=41', '11+41=52'] Exploring Operation: 2*52=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,94 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[41, 9], Operations: ['72-31=41', '11-2=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,94 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[11, 43], Operations: ['72-31=41', '2+41=43'] Exploring Operation: 11*43=473, Resulting Numbers: [473] 473,94 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 11+43=54, Resulting Numbers: [54] 54,94 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: 94:[2, 11, 103], Operations: ['31+72=103'] Exploring Operation: 103-2=101, Resulting Numbers: [11, 101] Generated Node #0,2,0: 94:[11, 101] Operation: 103-2=101 Exploring Operation: 11-2=9, Resulting Numbers: [103, 9] Generated Node #0,2,1: 94:[103, 9] Operation: 11-2=9 Exploring Operation: 103-11=92, Resulting Numbers: [2, 92] Generated Node #0,2,2: 94:[2, 92] Operation: 103-11=92 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[2, 92], Operations: ['31+72=103', '103-11=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[2, 11, 31, 72], Operations: [] Exploring Operation: 31+72=103, Resulting Numbers: [2, 11, 103] Generated Node #0,2: 94:[2, 11, 103] Operation: 31+72=103 Moving to Node #0,2 Current State: 94:[2, 11, 103], Operations: ['31+72=103'] Exploring Operation: 103-11=92, Resulting Numbers: [2, 92] Generated Node #0,2,2: 94:[2, 92] Operation: 103-11=92 Moving to Node #0,2,2 Current State: 94:[2, 92], Operations: ['31+72=103', '103-11=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 4, 37, 7, 21 ]
25
[ "4*21=84", "84/7=12", "37-12=25" ]
Current State: 25:[4, 37, 7, 21], Operations: [] Exploring Operation: 4*21=84, Resulting Numbers: [37, 7, 84] Generated Node #2: [37, 7, 84] from Operation: 4*21=84 Current State: 25:[37, 7, 84], Operations: ['4*21=84'] Exploring Operation: 84/7=12, Resulting Numbers: [37, 12] Generated Node #3: [37, 12] from Operation: 84/7=12 Current State: 25:[37, 12], Operations: ['4*21=84', '84/7=12'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[4, 37, 7, 21], Operations: [] Exploring Operation: 37-21=16, Resulting Numbers: [4, 7, 16] Generated Node #0,0: 25:[4, 7, 16] Operation: 37-21=16 Exploring Operation: 37-7=30, Resulting Numbers: [4, 21, 30] Generated Node #0,1: 25:[4, 21, 30] Operation: 37-7=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[4, 21, 30], Operations: ['37-7=30'] Exploring Operation: 30-4=26, Resulting Numbers: [21, 26] Generated Node #0,1,0: 25:[21, 26] Operation: 30-4=26 Exploring Operation: 4+21=25, Resulting Numbers: [30, 25] Generated Node #0,1,1: 25:[30, 25] Operation: 4+21=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[21, 26], Operations: ['37-7=30', '30-4=26'] Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[30, 25], Operations: ['37-7=30', '4+21=25'] Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,25 unequal: No Solution Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[4, 7, 16], Operations: ['37-21=16'] Exploring Operation: 7+16=23, Resulting Numbers: [4, 23] Generated Node #0,0,0: 25:[4, 23] Operation: 7+16=23 Exploring Operation: 16/4=4, Resulting Numbers: [7, 4] Generated Node #0,0,1: 25:[7, 4] Operation: 16/4=4 Moving to Node #0,0,0 Current State: 25:[4, 23], Operations: ['37-21=16', '7+16=23'] Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[7, 4], Operations: ['37-21=16', '16/4=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,25 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,25 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
[ 7, 63, 72, 69 ]
67
[ "7+63=70", "72-69=3", "70-3=67" ]
Current State: 67:[7, 63, 72, 69], Operations: [] Exploring Operation: 7+63=70, Resulting Numbers: [72, 69, 70] Generated Node #2: [72, 69, 70] from Operation: 7+63=70 Current State: 67:[72, 69, 70], Operations: ['7+63=70'] Exploring Operation: 72-69=3, Resulting Numbers: [70, 3] Generated Node #3: [70, 3] from Operation: 72-69=3 Current State: 67:[70, 3], Operations: ['7+63=70', '72-69=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[7, 63, 72, 69], Operations: [] Exploring Operation: 72-7=65, Resulting Numbers: [63, 69, 65] Generated Node #0,0: 67:[63, 69, 65] Operation: 72-7=65 Moving to Node #0,0 Current State: 67:[63, 69, 65], Operations: ['72-7=65'] Exploring Operation: 69-63=6, Resulting Numbers: [65, 6] Generated Node #0,0,0: 67:[65, 6] Operation: 69-63=6 Moving to Node #0,0,0 Current State: 67:[65, 6], Operations: ['72-7=65', '69-63=6'] Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,67 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 68, 74, 16, 74 ]
85
[ "68+16=84", "74/74=1", "84+1=85" ]
Current State: 85:[68, 74, 16, 74], Operations: [] Exploring Operation: 68+16=84, Resulting Numbers: [74, 74, 84] Generated Node #2: [74, 74, 84] from Operation: 68+16=84 Current State: 85:[74, 74, 84], Operations: ['68+16=84'] Exploring Operation: 74/74=1, Resulting Numbers: [84, 1] Generated Node #3: [84, 1] from Operation: 74/74=1 Current State: 85:[84, 1], Operations: ['68+16=84', '74/74=1'] Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[68, 74, 16, 74], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [74, 16, 6] Generated Node #0,0: 85:[74, 16, 6] Operation: 74-68=6 Exploring Operation: 68+16=84, Resulting Numbers: [74, 74, 84] Generated Node #0,1: 85:[74, 74, 84] Operation: 68+16=84 Exploring Operation: 74/74=1, Resulting Numbers: [68, 16, 1] Generated Node #0,2: 85:[68, 16, 1] Operation: 74/74=1 Exploring Operation: 74-68=6, Resulting Numbers: [16, 74, 6] Generated Node #0,3: 85:[16, 74, 6] Operation: 74-68=6 Moving to Node #0,0 Current State: 85:[74, 16, 6], Operations: ['74-68=6'] Exploring Operation: 74+6=80, Resulting Numbers: [16, 80] Generated Node #0,0,0: 85:[16, 80] Operation: 74+6=80 Exploring Operation: 16-6=10, Resulting Numbers: [74, 10] Generated Node #0,0,1: 85:[74, 10] Operation: 16-6=10 Exploring Operation: 16+6=22, Resulting Numbers: [74, 22] Generated Node #0,0,2: 85:[74, 22] Operation: 16+6=22 Exploring Operation: 74+16=90, Resulting Numbers: [6, 90] Generated Node #0,0,3: 85:[6, 90] Operation: 74+16=90 Moving to Node #0,3 Current State: 85:[16, 74, 6], Operations: ['74-68=6'] Exploring Operation: 16-6=10, Resulting Numbers: [74, 10] Generated Node #0,3,0: 85:[74, 10] Operation: 16-6=10 Exploring Operation: 16+6=22, Resulting Numbers: [74, 22] Generated Node #0,3,1: 85:[74, 22] Operation: 16+6=22 Exploring Operation: 16+74=90, Resulting Numbers: [6, 90] Generated Node #0,3,2: 85:[6, 90] Operation: 16+74=90 Exploring Operation: 74+6=80, Resulting Numbers: [16, 80] Generated Node #0,3,3: 85:[16, 80] Operation: 74+6=80 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[6, 90], Operations: ['74-68=6', '16+74=90'] Exploring Operation: 90/6=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 6*90=540, Resulting Numbers: [540] 540,85 unequal: No Solution Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 6+90=96, Resulting Numbers: [96] 96,85 unequal: No Solution No 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: 85:[16, 80], Operations: ['74-68=6', '74+6=80'] Exploring Operation: 16*80=1280, Resulting Numbers: [1280] 1280,85 unequal: No Solution Exploring Operation: 16+80=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,85 unequal: No Solution No 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: 85:[74, 10], Operations: ['74-68=6', '16-6=10'] Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,85 unequal: No Solution Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,85 unequal: No Solution No 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: 85:[74, 22], Operations: ['74-68=6', '16+6=22'] Exploring Operation: 74*22=1628, Resulting Numbers: [1628] 1628,85 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,85 unequal: No Solution Exploring Operation: 74+22=96, Resulting Numbers: [96] 96,85 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: 85:[68, 16, 1], Operations: ['74/74=1'] Exploring Operation: 16+1=17, Resulting Numbers: [68, 17] Generated Node #0,2,0: 85:[68, 17] Operation: 16+1=17 Exploring Operation: 68*1=68, Resulting Numbers: [16, 68] Generated Node #0,2,1: 85:[16, 68] Operation: 68*1=68 Exploring Operation: 68+1=69, Resulting Numbers: [16, 69] Generated Node #0,2,2: 85:[16, 69] Operation: 68+1=69 Exploring Operation: 68+16=84, Resulting Numbers: [1, 84] Generated Node #0,2,3: 85:[1, 84] Operation: 68+16=84 Moving to Node #0,1 Current State: 85:[74, 74, 84], Operations: ['68+16=84'] Exploring Operation: 74-74=0, Resulting Numbers: [84, 0] Generated Node #0,1,0: 85:[84, 0] Operation: 74-74=0 Exploring Operation: 84-74=10, Resulting Numbers: [74, 10] Generated Node #0,1,1: 85:[74, 10] Operation: 84-74=10 Exploring Operation: 74/74=1, Resulting Numbers: [84, 1] Generated Node #0,1,2: 85:[84, 1] Operation: 74/74=1 Exploring Operation: 84-74=10, Resulting Numbers: [74, 10] Generated Node #0,1,3: 85:[74, 10] Operation: 84-74=10 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 85:[84, 1], Operations: ['68+16=84', '74/74=1'] Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[68, 74, 16, 74], Operations: [] Exploring Operation: 68+16=84, Resulting Numbers: [74, 74, 84] Generated Node #0,1: 85:[74, 74, 84] Operation: 68+16=84 Moving to Node #0,1 Current State: 85:[74, 74, 84], Operations: ['68+16=84'] Exploring Operation: 74/74=1, Resulting Numbers: [84, 1] Generated Node #0,1,2: 85:[84, 1] Operation: 74/74=1 Moving to Node #0,1,2 Current State: 85:[84, 1], Operations: ['68+16=84', '74/74=1'] Exploring Operation: 84+1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
sum_heuristic
[ 88, 18, 40, 79 ]
38
[ "88-79=9", "18/9=2", "40-2=38" ]
Current State: 38:[88, 18, 40, 79], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [18, 40, 9] Generated Node #2: [18, 40, 9] from Operation: 88-79=9 Current State: 38:[18, 40, 9], Operations: ['88-79=9'] Exploring Operation: 18/9=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 18/9=2 Current State: 38:[40, 2], Operations: ['88-79=9', '18/9=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[88, 18, 40, 79], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [18, 40, 9] Generated Node #0,0: 38:[18, 40, 9] Operation: 88-79=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[18, 40, 9], Operations: ['88-79=9'] Exploring Operation: 18/9=2, Resulting Numbers: [40, 2] Generated Node #0,0,0: 38:[40, 2] Operation: 18/9=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[40, 2], Operations: ['88-79=9', '18/9=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[88, 18, 40, 79], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [18, 40, 9] Generated Node #0,0: 38:[18, 40, 9] Operation: 88-79=9 Moving to Node #0,0 Current State: 38:[18, 40, 9], Operations: ['88-79=9'] Exploring Operation: 18/9=2, Resulting Numbers: [40, 2] Generated Node #0,0,0: 38:[40, 2] Operation: 18/9=2 Moving to Node #0,0,0 Current State: 38:[40, 2], Operations: ['88-79=9', '18/9=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 3, 5, 5, 80 ]
51
[ "5+80=85", "3*85=255", "255/5=51" ]
Current State: 51:[3, 5, 5, 80], Operations: [] Exploring Operation: 5+80=85, Resulting Numbers: [3, 85] Generated Node #2: [3, 85] from Operation: 5+80=85 Current State: 51:[3, 85], Operations: ['5+80=85'] Exploring Operation: 3*85=255, Resulting Numbers: [255] 255,51 equal: Goal Reached Exploring Operation: 255/5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[3, 5, 5, 80], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [3, 5, 16] Generated Node #0,0: 51:[3, 5, 16] Operation: 80/5=16 Exploring Operation: 80/5=16, Resulting Numbers: [3, 5, 16] Generated Node #0,1: 51:[3, 5, 16] Operation: 80/5=16 Moving to Node #0,0 Current State: 51:[3, 5, 16], Operations: ['80/5=16'] Exploring Operation: 3*5=15, Resulting Numbers: [16, 15] Generated Node #0,0,0: 51:[16, 15] Operation: 3*5=15 Exploring Operation: 5-3=2, Resulting Numbers: [16, 2] Generated Node #0,0,1: 51:[16, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[16, 2], Operations: ['80/5=16', '5-3=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[16, 15], Operations: ['80/5=16', '3*5=15'] Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,51 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: 51:[3, 5, 16], Operations: ['80/5=16'] Exploring Operation: 3*5=15, Resulting Numbers: [16, 15] Generated Node #0,1,0: 51:[16, 15] Operation: 3*5=15 Exploring Operation: 5-3=2, Resulting Numbers: [16, 2] Generated Node #0,1,1: 51:[16, 2] Operation: 5-3=2 Moving to Node #0,1,1 Current State: 51:[16, 2], Operations: ['80/5=16', '5-3=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[16, 15], Operations: ['80/5=16', '3*5=15'] Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,51 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 27, 46, 50, 86 ]
43
[ "50-27=23", "46/23=2", "86/2=43" ]
Current State: 43:[27, 46, 50, 86], Operations: [] Exploring Operation: 50-27=23, Resulting Numbers: [46, 86, 23] Generated Node #2: [46, 86, 23] from Operation: 50-27=23 Current State: 43:[46, 86, 23], Operations: ['50-27=23'] Exploring Operation: 46/23=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 46/23=2 Current State: 43:[86, 2], Operations: ['50-27=23', '46/23=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[27, 46, 50, 86], Operations: [] Exploring Operation: 86-46=40, Resulting Numbers: [27, 50, 40] Generated Node #0,0: 43:[27, 50, 40] Operation: 86-46=40 Exploring Operation: 86-27=59, Resulting Numbers: [46, 50, 59] Generated Node #0,1: 43:[46, 50, 59] Operation: 86-27=59 Moving to Node #0,0 Current State: 43:[27, 50, 40], Operations: ['86-46=40'] Exploring Operation: 50-27=23, Resulting Numbers: [40, 23] Generated Node #0,0,0: 43:[40, 23] Operation: 50-27=23 Exploring Operation: 27+40=67, Resulting Numbers: [50, 67] Generated Node #0,0,1: 43:[50, 67] Operation: 27+40=67 Moving to Node #0,1 Current State: 43:[46, 50, 59], Operations: ['86-27=59'] Exploring Operation: 59-46=13, Resulting Numbers: [50, 13] Generated Node #0,1,0: 43:[50, 13] Operation: 59-46=13 Exploring Operation: 59-50=9, Resulting Numbers: [46, 9] Generated Node #0,1,1: 43:[46, 9] Operation: 59-50=9 Moving to Node #0,0,0 Current State: 43:[40, 23], Operations: ['86-46=40', '50-27=23'] Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[50, 67], Operations: ['86-46=40', '27+40=67'] Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,43 unequal: No Solution Exploring Operation: 50+67=117, Resulting Numbers: [117] 117,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[46, 9], Operations: ['86-27=59', '59-50=9'] Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[50, 13], Operations: ['86-27=59', '59-46=13'] Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,43 unequal: No Solution Exploring Operation: 50+13=63, Resulting Numbers: [63] 63,43 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 15, 52, 57, 41 ]
53
[ "52-15=37", "57-41=16", "37+16=53" ]
Current State: 53:[15, 52, 57, 41], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [57, 41, 37] Generated Node #2: [57, 41, 37] from Operation: 52-15=37 Current State: 53:[57, 41, 37], Operations: ['52-15=37'] Exploring Operation: 57-41=16, Resulting Numbers: [37, 16] Generated Node #3: [37, 16] from Operation: 57-41=16 Current State: 53:[37, 16], Operations: ['52-15=37', '57-41=16'] Exploring Operation: 37+16=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[15, 52, 57, 41], Operations: [] Exploring Operation: 15+52=67, Resulting Numbers: [57, 41, 67] Generated Node #0,0: 53:[57, 41, 67] Operation: 15+52=67 Exploring Operation: 57-15=42, Resulting Numbers: [52, 41, 42] Generated Node #0,1: 53:[52, 41, 42] Operation: 57-15=42 Exploring Operation: 15+41=56, Resulting Numbers: [52, 57, 56] Generated Node #0,2: 53:[52, 57, 56] Operation: 15+41=56 Moving to Node #0,2 Current State: 53:[52, 57, 56], Operations: ['15+41=56'] Exploring Operation: 57-56=1, Resulting Numbers: [52, 1] Generated Node #0,2,0: 53:[52, 1] Operation: 57-56=1 Exploring Operation: 56-52=4, Resulting Numbers: [57, 4] Generated Node #0,2,1: 53:[57, 4] Operation: 56-52=4 Exploring Operation: 57-52=5, Resulting Numbers: [56, 5] Generated Node #0,2,2: 53:[56, 5] Operation: 57-52=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 53:[56, 5], Operations: ['15+41=56', '57-52=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,53 unequal: No Solution Exploring Operation: 56*5=280, Resulting Numbers: [280] 280,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[52, 1], Operations: ['15+41=56', '57-56=1'] Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[15, 52, 57, 41], Operations: [] Exploring Operation: 15+41=56, Resulting Numbers: [52, 57, 56] Generated Node #0,2: 53:[52, 57, 56] Operation: 15+41=56 Moving to Node #0,2 Current State: 53:[52, 57, 56], Operations: ['15+41=56'] Exploring Operation: 57-56=1, Resulting Numbers: [52, 1] Generated Node #0,2,0: 53:[52, 1] Operation: 57-56=1 Moving to Node #0,2,0 Current State: 53:[52, 1], Operations: ['15+41=56', '57-56=1'] Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 84, 50, 20, 44 ]
95
[ "84*50=4200", "4200-20=4180", "4180/44=95" ]
Current State: 95:[84, 50, 20, 44], Operations: [] Exploring Operation: 84*50=4200, Resulting Numbers: [20, 44, 4200] Generated Node #2: [20, 44, 4200] from Operation: 84*50=4200 Current State: 95:[20, 44, 4200], Operations: ['84*50=4200'] Exploring Operation: 4200-20=4180, Resulting Numbers: [44, 4180] Generated Node #3: [44, 4180] from Operation: 4200-20=4180 Current State: 95:[44, 4180], Operations: ['84*50=4200', '4200-20=4180'] Exploring Operation: 4180/44=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[84, 50, 20, 44], Operations: [] Exploring Operation: 50-44=6, Resulting Numbers: [84, 20, 6] Generated Node #0,0: 95:[84, 20, 6] Operation: 50-44=6 Exploring Operation: 50+44=94, Resulting Numbers: [84, 20, 94] Generated Node #0,1: 95:[84, 20, 94] Operation: 50+44=94 Moving to Node #0,0 Current State: 95:[84, 20, 6], Operations: ['50-44=6'] Exploring Operation: 84/6=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 95:[20, 14] Operation: 84/6=14 Exploring Operation: 84+6=90, Resulting Numbers: [20, 90] Generated Node #0,0,1: 95:[20, 90] Operation: 84+6=90 Moving to Node #0,1 Current State: 95:[84, 20, 94], Operations: ['50+44=94'] Exploring Operation: 94-84=10, Resulting Numbers: [20, 10] Generated Node #0,1,0: 95:[20, 10] Operation: 94-84=10 Exploring Operation: 84+20=104, Resulting Numbers: [94, 104] Generated Node #0,1,1: 95:[94, 104] Operation: 84+20=104 Moving to Node #0,0,0 Current State: 95:[20, 14], Operations: ['50-44=6', '84/6=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[20, 10], Operations: ['50+44=94', '94-84=10'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,95 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[20, 90], Operations: ['50-44=6', '84+6=90'] Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 20+90=110, Resulting Numbers: [110] 110,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[94, 104], Operations: ['50+44=94', '84+20=104'] Exploring Operation: 94+104=198, Resulting Numbers: [198] 198,95 unequal: No Solution Exploring Operation: 104-94=10, Resulting Numbers: [10] 10,95 unequal: No Solution No solution found.
0
hs_2
mult_heuristic