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
[ 44, 35, 90, 31 ]
50
[ "44-35=9", "90-31=59", "59-9=50" ]
Current State: 50:[44, 35, 90, 31], Operations: [] Exploring Operation: 44-35=9, Resulting Numbers: [90, 31, 9] Generated Node #2: [90, 31, 9] from Operation: 44-35=9 Current State: 50:[90, 31, 9], Operations: ['44-35=9'] Exploring Operation: 90-31=59, Resulting Numbers: [9, 59] Generated Node #3: [9, 59] from Operation: 90-31=59 Current State: 50:[9, 59], Operations: ['44-35=9', '90-31=59'] Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[44, 35, 90, 31], Operations: [] Exploring Operation: 90-31=59, Resulting Numbers: [44, 35, 59] Generated Node #0,0: 50:[44, 35, 59] Operation: 90-31=59 Exploring Operation: 44-35=9, Resulting Numbers: [90, 31, 9] Generated Node #0,1: 50:[90, 31, 9] Operation: 44-35=9 Exploring Operation: 90-44=46, Resulting Numbers: [35, 31, 46] Generated Node #0,2: 50:[35, 31, 46] Operation: 90-44=46 Exploring Operation: 90-35=55, Resulting Numbers: [44, 31, 55] Generated Node #0,3: 50:[44, 31, 55] Operation: 90-35=55 Start Sub Search at level 1: Moving to Node #0,3 Current State: 50:[44, 31, 55], Operations: ['90-35=55'] Exploring Operation: 55-31=24, Resulting Numbers: [44, 24] Generated Node #0,3,0: 50:[44, 24] Operation: 55-31=24 Exploring Operation: 55-44=11, Resulting Numbers: [31, 11] Generated Node #0,3,1: 50:[31, 11] Operation: 55-44=11 Exploring Operation: 44-31=13, Resulting Numbers: [55, 13] Generated Node #0,3,2: 50:[55, 13] Operation: 44-31=13 Exploring Operation: 44+31=75, Resulting Numbers: [55, 75] Generated Node #0,3,3: 50:[55, 75] Operation: 44+31=75 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 50:[44, 24], Operations: ['90-35=55', '55-31=24'] Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,50 unequal: No Solution Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,50 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,50 unequal: No Solution No 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: 50:[31, 11], Operations: ['90-35=55', '55-44=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,50 unequal: No Solution No 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: 50:[55, 13], Operations: ['90-35=55', '44-31=13'] Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,50 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,50 unequal: No Solution Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,50 unequal: No Solution No 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: 50:[55, 75], Operations: ['90-35=55', '44+31=75'] Exploring Operation: 55+75=130, Resulting Numbers: [130] 130,50 unequal: No Solution Exploring Operation: 55*75=4125, Resulting Numbers: [4125] 4125,50 unequal: No Solution Exploring Operation: 75-55=20, Resulting Numbers: [20] 20,50 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: 50:[35, 31, 46], Operations: ['90-44=46'] Exploring Operation: 46-31=15, Resulting Numbers: [35, 15] Generated Node #0,2,0: 50:[35, 15] Operation: 46-31=15 Exploring Operation: 46-35=11, Resulting Numbers: [31, 11] Generated Node #0,2,1: 50:[31, 11] Operation: 46-35=11 Exploring Operation: 35-31=4, Resulting Numbers: [46, 4] Generated Node #0,2,2: 50:[46, 4] Operation: 35-31=4 Exploring Operation: 35+31=66, Resulting Numbers: [46, 66] Generated Node #0,2,3: 50:[46, 66] Operation: 35+31=66 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 50:[46, 4], Operations: ['90-44=46', '35-31=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[44, 35, 90, 31], Operations: [] Exploring Operation: 90-44=46, Resulting Numbers: [35, 31, 46] Generated Node #0,2: 50:[35, 31, 46] Operation: 90-44=46 Moving to Node #0,2 Current State: 50:[35, 31, 46], Operations: ['90-44=46'] Exploring Operation: 35-31=4, Resulting Numbers: [46, 4] Generated Node #0,2,2: 50:[46, 4] Operation: 35-31=4 Moving to Node #0,2,2 Current State: 50:[46, 4], Operations: ['90-44=46', '35-31=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 96, 68, 44, 27 ]
24
[ "44-27=17", "96*17=1632", "1632/68=24" ]
Current State: 24:[96, 68, 44, 27], Operations: [] Exploring Operation: 44-27=17, Resulting Numbers: [96, 68, 17] Generated Node #2: [96, 68, 17] from Operation: 44-27=17 Current State: 24:[96, 68, 17], Operations: ['44-27=17'] Exploring Operation: 96*17=1632, Resulting Numbers: [68, 1632] Generated Node #3: [68, 1632] from Operation: 96*17=1632 Current State: 24:[68, 1632], Operations: ['44-27=17', '96*17=1632'] Exploring Operation: 1632/68=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[96, 68, 44, 27], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [96, 27, 24] Generated Node #0,0: 24:[96, 27, 24] Operation: 68-44=24 Exploring Operation: 96-27=69, Resulting Numbers: [68, 44, 69] Generated Node #0,1: 24:[68, 44, 69] Operation: 96-27=69 Exploring Operation: 96-44=52, Resulting Numbers: [68, 27, 52] Generated Node #0,2: 24:[68, 27, 52] Operation: 96-44=52 Exploring Operation: 96-68=28, Resulting Numbers: [44, 27, 28] Generated Node #0,3: 24:[44, 27, 28] Operation: 96-68=28 Exploring Operation: 68-27=41, Resulting Numbers: [96, 44, 41] Generated Node #0,4: 24:[96, 44, 41] Operation: 68-27=41 Moving to Node #0,3 Current State: 24:[44, 27, 28], Operations: ['96-68=28'] Exploring Operation: 44-27=17, Resulting Numbers: [28, 17] Generated Node #0,3,0: 24:[28, 17] Operation: 44-27=17 Exploring Operation: 44+27=71, Resulting Numbers: [28, 71] Generated Node #0,3,1: 24:[28, 71] Operation: 44+27=71 Exploring Operation: 44+28=72, Resulting Numbers: [27, 72] Generated Node #0,3,2: 24:[27, 72] Operation: 44+28=72 Exploring Operation: 28-27=1, Resulting Numbers: [44, 1] Generated Node #0,3,3: 24:[44, 1] Operation: 28-27=1 Exploring Operation: 44-28=16, Resulting Numbers: [27, 16] Generated Node #0,3,4: 24:[27, 16] Operation: 44-28=16 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 24:[27, 16], Operations: ['96-68=28', '44-28=16'] Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,24 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 24:[28, 17], Operations: ['96-68=28', '44-27=17'] Exploring Operation: 28+17=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 28*17=476, Resulting Numbers: [476] 476,24 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 24:[44, 1], Operations: ['96-68=28', '28-27=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 24:[28, 71], Operations: ['96-68=28', '44+27=71'] Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 28+71=99, Resulting Numbers: [99] 99,24 unequal: No Solution Exploring Operation: 28*71=1988, Resulting Numbers: [1988] 1988,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 24:[27, 72], Operations: ['96-68=28', '44+28=72'] Exploring Operation: 27*72=1944, Resulting Numbers: [1944] 1944,24 unequal: No Solution Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,24 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: 24:[68, 27, 52], Operations: ['96-44=52'] Exploring Operation: 68+27=95, Resulting Numbers: [52, 95] Generated Node #0,2,0: 24:[52, 95] Operation: 68+27=95 Exploring Operation: 52-27=25, Resulting Numbers: [68, 25] Generated Node #0,2,1: 24:[68, 25] Operation: 52-27=25 Exploring Operation: 68+52=120, Resulting Numbers: [27, 120] Generated Node #0,2,2: 24:[27, 120] Operation: 68+52=120 Exploring Operation: 68-27=41, Resulting Numbers: [52, 41] Generated Node #0,2,3: 24:[52, 41] Operation: 68-27=41 Exploring Operation: 68-52=16, Resulting Numbers: [27, 16] Generated Node #0,2,4: 24:[27, 16] Operation: 68-52=16 Moving to Node #0,0 Current State: 24:[96, 27, 24], Operations: ['68-44=24'] Exploring Operation: 96-24=72, Resulting Numbers: [27, 72] Generated Node #0,0,0: 24:[27, 72] Operation: 96-24=72 Exploring Operation: 27-24=3, Resulting Numbers: [96, 3] Generated Node #0,0,1: 24:[96, 3] Operation: 27-24=3 Exploring Operation: 96/24=4, Resulting Numbers: [27, 4] Generated Node #0,0,2: 24:[27, 4] Operation: 96/24=4 Exploring Operation: 96+27=123, Resulting Numbers: [24, 123] Generated Node #0,0,3: 24:[24, 123] Operation: 96+27=123 Exploring Operation: 96-27=69, Resulting Numbers: [24, 69] Generated Node #0,0,4: 24:[24, 69] Operation: 96-27=69 Moving to Node #0,1 Current State: 24:[68, 44, 69], Operations: ['96-27=69'] Exploring Operation: 69-44=25, Resulting Numbers: [68, 25] Generated Node #0,1,0: 24:[68, 25] Operation: 69-44=25 Exploring Operation: 68+44=112, Resulting Numbers: [69, 112] Generated Node #0,1,1: 24:[69, 112] Operation: 68+44=112 Exploring Operation: 68+69=137, Resulting Numbers: [44, 137] Generated Node #0,1,2: 24:[44, 137] Operation: 68+69=137 Exploring Operation: 68-44=24, Resulting Numbers: [69, 24] Generated Node #0,1,3: 24:[69, 24] Operation: 68-44=24 Exploring Operation: 69-68=1, Resulting Numbers: [44, 1] Generated Node #0,1,4: 24:[44, 1] Operation: 69-68=1 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 24:[44, 1], Operations: ['96-27=69', '69-68=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[68, 25], Operations: ['96-27=69', '69-44=25'] Exploring Operation: 68*25=1700, Resulting Numbers: [1700] 1700,24 unequal: No Solution Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[69, 24], Operations: ['96-27=69', '68-44=24'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 69*24=1656, Resulting Numbers: [1656] 1656,24 unequal: No Solution Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[69, 112], Operations: ['96-27=69', '68+44=112'] Exploring Operation: 69+112=181, Resulting Numbers: [181] 181,24 unequal: No Solution Exploring Operation: 69*112=7728, Resulting Numbers: [7728] 7728,24 unequal: No Solution Exploring Operation: 112-69=43, Resulting Numbers: [43] 43,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[44, 137], Operations: ['96-27=69', '68+69=137'] Exploring Operation: 44+137=181, Resulting Numbers: [181] 181,24 unequal: No Solution Exploring Operation: 44*137=6028, Resulting Numbers: [6028] 6028,24 unequal: No Solution Exploring Operation: 137-44=93, Resulting Numbers: [93] 93,24 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: 24:[96, 44, 41], Operations: ['68-27=41'] Exploring Operation: 96-41=55, Resulting Numbers: [44, 55] Generated Node #0,4,0: 24:[44, 55] Operation: 96-41=55 Exploring Operation: 96+41=137, Resulting Numbers: [44, 137] Generated Node #0,4,1: 24:[44, 137] Operation: 96+41=137 Exploring Operation: 96+44=140, Resulting Numbers: [41, 140] Generated Node #0,4,2: 24:[41, 140] Operation: 96+44=140 Exploring Operation: 44-41=3, Resulting Numbers: [96, 3] Generated Node #0,4,3: 24:[96, 3] Operation: 44-41=3 Exploring Operation: 96-44=52, Resulting Numbers: [41, 52] Generated Node #0,4,4: 24:[41, 52] Operation: 96-44=52 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 24:[41, 52], Operations: ['68-27=41', '96-44=52'] Exploring Operation: 41+52=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 41*52=2132, Resulting Numbers: [2132] 2132,24 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 24:[44, 55], Operations: ['68-27=41', '96-41=55'] Exploring Operation: 44*55=2420, Resulting Numbers: [2420] 2420,24 unequal: No Solution Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 44+55=99, Resulting Numbers: [99] 99,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 24:[96, 3], Operations: ['68-27=41', '44-41=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 96*3=288, Resulting Numbers: [288] 288,24 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 24:[44, 137], Operations: ['68-27=41', '96+41=137'] Exploring Operation: 44*137=6028, Resulting Numbers: [6028] 6028,24 unequal: No Solution Exploring Operation: 137-44=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 44+137=181, Resulting Numbers: [181] 181,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 24:[41, 140], Operations: ['68-27=41', '96+44=140'] Exploring Operation: 41+140=181, Resulting Numbers: [181] 181,24 unequal: No Solution Exploring Operation: 140-41=99, Resulting Numbers: [99] 99,24 unequal: No Solution Exploring Operation: 41*140=5740, Resulting Numbers: [5740] 5740,24 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: 24:[27, 4], Operations: ['68-44=24', '96/24=4'] Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,24 unequal: No Solution Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,24 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,24 unequal: No Solution Moving to Node #0,2,4 Current State: 24:[27, 16], Operations: ['96-44=52', '68-52=16'] Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,24 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,24 unequal: No Solution Moving to Node #0,0,4 Current State: 24:[24, 69], Operations: ['68-44=24', '96-27=69'] Exploring Operation: 24*69=1656, Resulting Numbers: [1656] 1656,24 unequal: No Solution Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 24+69=93, Resulting Numbers: [93] 93,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[52, 41], Operations: ['96-44=52', '68-27=41'] Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 52*41=2132, Resulting Numbers: [2132] 2132,24 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[68, 25], Operations: ['96-44=52', '52-27=25'] Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 68*25=1700, Resulting Numbers: [1700] 1700,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[27, 72], Operations: ['68-44=24', '96-24=72'] Exploring Operation: 27*72=1944, Resulting Numbers: [1944] 1944,24 unequal: No Solution Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,24 unequal: No Solution Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[96, 3], Operations: ['68-44=24', '27-24=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 96*3=288, Resulting Numbers: [288] 288,24 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[52, 95], Operations: ['96-44=52', '68+27=95'] Exploring Operation: 52+95=147, Resulting Numbers: [147] 147,24 unequal: No Solution Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 52*95=4940, Resulting Numbers: [4940] 4940,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[27, 120], Operations: ['96-44=52', '68+52=120'] Exploring Operation: 120-27=93, Resulting Numbers: [93] 93,24 unequal: No Solution Exploring Operation: 27+120=147, Resulting Numbers: [147] 147,24 unequal: No Solution Exploring Operation: 27*120=3240, Resulting Numbers: [3240] 3240,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[24, 123], Operations: ['68-44=24', '96+27=123'] Exploring Operation: 24*123=2952, Resulting Numbers: [2952] 2952,24 unequal: No Solution Exploring Operation: 123-24=99, Resulting Numbers: [99] 99,24 unequal: No Solution Exploring Operation: 24+123=147, Resulting Numbers: [147] 147,24 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 15, 67, 43, 51 ]
60
[ "67-15=52", "51-43=8", "52+8=60" ]
Current State: 60:[15, 67, 43, 51], Operations: [] Exploring Operation: 67-15=52, Resulting Numbers: [43, 51, 52] Generated Node #2: [43, 51, 52] from Operation: 67-15=52 Current State: 60:[43, 51, 52], Operations: ['67-15=52'] Exploring Operation: 51-43=8, Resulting Numbers: [52, 8] Generated Node #3: [52, 8] from Operation: 51-43=8 Current State: 60:[52, 8], Operations: ['67-15=52', '51-43=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[15, 67, 43, 51], Operations: [] Exploring Operation: 51-43=8, Resulting Numbers: [15, 67, 8] Generated Node #0,0: 60:[15, 67, 8] Operation: 51-43=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[15, 67, 8], Operations: ['51-43=8'] Exploring Operation: 67-8=59, Resulting Numbers: [15, 59] Generated Node #0,0,0: 60:[15, 59] Operation: 67-8=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[15, 59], Operations: ['51-43=8', '67-8=59'] Exploring Operation: 15+59=74, Resulting Numbers: [74] 74,60 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_1
mult_heuristic
[ 51, 13, 9, 6 ]
79
[ "51+13=64", "9+6=15", "64+15=79" ]
Current State: 79:[51, 13, 9, 6], Operations: [] Exploring Operation: 51+13=64, Resulting Numbers: [9, 6, 64] Generated Node #2: [9, 6, 64] from Operation: 51+13=64 Current State: 79:[9, 6, 64], Operations: ['51+13=64'] Exploring Operation: 9+6=15, Resulting Numbers: [64, 15] Generated Node #3: [64, 15] from Operation: 9+6=15 Current State: 79:[64, 15], Operations: ['51+13=64', '9+6=15'] Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[51, 13, 9, 6], Operations: [] Exploring Operation: 13*9=117, Resulting Numbers: [51, 6, 117] Generated Node #0,0: 79:[51, 6, 117] Operation: 13*9=117 Exploring Operation: 13*6=78, Resulting Numbers: [51, 9, 78] Generated Node #0,1: 79:[51, 9, 78] Operation: 13*6=78 Exploring Operation: 9*6=54, Resulting Numbers: [51, 13, 54] Generated Node #0,2: 79:[51, 13, 54] Operation: 9*6=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[51, 9, 78], Operations: ['13*6=78'] Exploring Operation: 51+9=60, Resulting Numbers: [78, 60] Generated Node #0,1,0: 79:[78, 60] Operation: 51+9=60 Exploring Operation: 9+78=87, Resulting Numbers: [51, 87] Generated Node #0,1,1: 79:[51, 87] Operation: 9+78=87 Exploring Operation: 51-9=42, Resulting Numbers: [78, 42] Generated Node #0,1,2: 79:[78, 42] Operation: 51-9=42 Moving to Node #0,1,0 Current State: 79:[78, 60], Operations: ['13*6=78', '51+9=60'] Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,79 unequal: No Solution Exploring Operation: 78+60=138, Resulting Numbers: [138] 138,79 unequal: No Solution Exploring Operation: 78*60=4680, Resulting Numbers: [4680] 4680,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[51, 87], Operations: ['13*6=78', '9+78=87'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,79 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,79 unequal: No Solution Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[78, 42], Operations: ['13*6=78', '51-9=42'] Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,79 unequal: No Solution Exploring Operation: 78+42=120, Resulting Numbers: [120] 120,79 unequal: No Solution Exploring Operation: 78*42=3276, Resulting Numbers: [3276] 3276,79 unequal: No Solution No 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:[51, 13, 54], Operations: ['9*6=54'] Exploring Operation: 13+54=67, Resulting Numbers: [51, 67] Generated Node #0,2,0: 79:[51, 67] Operation: 13+54=67 Exploring Operation: 51+13=64, Resulting Numbers: [54, 64] Generated Node #0,2,1: 79:[54, 64] Operation: 51+13=64 Exploring Operation: 51-13=38, Resulting Numbers: [54, 38] Generated Node #0,2,2: 79:[54, 38] Operation: 51-13=38 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[51, 67], Operations: ['9*6=54', '13+54=67'] Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,79 unequal: No Solution Exploring Operation: 51*67=3417, Resulting Numbers: [3417] 3417,79 unequal: No Solution Exploring Operation: 51+67=118, Resulting Numbers: [118] 118,79 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:[54, 64], Operations: ['9*6=54', '51+13=64'] Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,79 unequal: No Solution Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,79 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:[54, 38], Operations: ['9*6=54', '51-13=38'] Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,79 unequal: No Solution Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,79 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,79 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 #0,0 Current State: 79:[51, 6, 117], Operations: ['13*9=117'] Exploring Operation: 51-6=45, Resulting Numbers: [117, 45] Generated Node #0,0,0: 79:[117, 45] Operation: 51-6=45 Exploring Operation: 51+6=57, Resulting Numbers: [117, 57] Generated Node #0,0,1: 79:[117, 57] Operation: 51+6=57 Exploring Operation: 117-6=111, Resulting Numbers: [51, 111] Generated Node #0,0,2: 79:[51, 111] Operation: 117-6=111 Moving to Node #0,0,1 Current State: 79:[117, 57], Operations: ['13*9=117', '51+6=57'] Exploring Operation: 117+57=174, Resulting Numbers: [174] 174,79 unequal: No Solution Exploring Operation: 117-57=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 117*57=6669, Resulting Numbers: [6669] 6669,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[51, 111], Operations: ['13*9=117', '117-6=111'] Exploring Operation: 111-51=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 51+111=162, Resulting Numbers: [162] 162,79 unequal: No Solution Exploring Operation: 51*111=5661, Resulting Numbers: [5661] 5661,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[117, 45], Operations: ['13*9=117', '51-6=45'] Exploring Operation: 117+45=162, Resulting Numbers: [162] 162,79 unequal: No Solution Exploring Operation: 117*45=5265, Resulting Numbers: [5265] 5265,79 unequal: No Solution Exploring Operation: 117-45=72, Resulting Numbers: [72] 72,79 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
[ 82, 4, 41, 88 ]
19
[ "82-41=41", "88/4=22", "41-22=19" ]
Current State: 19:[82, 4, 41, 88], Operations: [] Exploring Operation: 82-41=41, Resulting Numbers: [4, 88, 41] Generated Node #2: [4, 88, 41] from Operation: 82-41=41 Current State: 19:[4, 88, 41], Operations: ['82-41=41'] Exploring Operation: 88/4=22, Resulting Numbers: [41, 22] Generated Node #3: [41, 22] from Operation: 88/4=22 Current State: 19:[41, 22], Operations: ['82-41=41', '88/4=22'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[82, 4, 41, 88], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [82, 41, 22] Generated Node #0,0: 19:[82, 41, 22] Operation: 88/4=22 Exploring Operation: 82/41=2, Resulting Numbers: [4, 88, 2] Generated Node #0,1: 19:[4, 88, 2] Operation: 82/41=2 Exploring Operation: 82-41=41, Resulting Numbers: [4, 88, 41] Generated Node #0,2: 19:[4, 88, 41] Operation: 82-41=41 Exploring Operation: 88-82=6, Resulting Numbers: [4, 41, 6] Generated Node #0,3: 19:[4, 41, 6] Operation: 88-82=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[4, 41, 6], Operations: ['88-82=6'] Exploring Operation: 4*6=24, Resulting Numbers: [41, 24] Generated Node #0,3,0: 19:[41, 24] Operation: 4*6=24 Exploring Operation: 41-6=35, Resulting Numbers: [4, 35] Generated Node #0,3,1: 19:[4, 35] Operation: 41-6=35 Exploring Operation: 41-4=37, Resulting Numbers: [6, 37] Generated Node #0,3,2: 19:[6, 37] Operation: 41-4=37 Exploring Operation: 4+6=10, Resulting Numbers: [41, 10] Generated Node #0,3,3: 19:[41, 10] Operation: 4+6=10 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 19:[41, 24], Operations: ['88-82=6', '4*6=24'] Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,19 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,19 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,19 unequal: No Solution No 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: 19:[4, 35], Operations: ['88-82=6', '41-6=35'] Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,19 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,19 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,19 unequal: No Solution No 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: 19:[6, 37], Operations: ['88-82=6', '41-4=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,19 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,19 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,19 unequal: No Solution No 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: 19:[41, 10], Operations: ['88-82=6', '4+6=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,19 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,19 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,19 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: 19:[82, 41, 22], Operations: ['88/4=22'] Exploring Operation: 82-22=60, Resulting Numbers: [41, 60] Generated Node #0,0,0: 19:[41, 60] Operation: 82-22=60 Exploring Operation: 82-41=41, Resulting Numbers: [22, 41] Generated Node #0,0,1: 19:[22, 41] Operation: 82-41=41 Exploring Operation: 41-22=19, Resulting Numbers: [82, 19] Generated Node #0,0,2: 19:[82, 19] Operation: 41-22=19 Exploring Operation: 82/41=2, Resulting Numbers: [22, 2] Generated Node #0,0,3: 19:[22, 2] Operation: 82/41=2 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 19:[22, 2], Operations: ['88/4=22', '82/41=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,19 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,19 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,19 unequal: No Solution No 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: 19:[22, 41], Operations: ['88/4=22', '82-41=41'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[82, 4, 41, 88], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [82, 41, 22] Generated Node #0,0: 19:[82, 41, 22] Operation: 88/4=22 Moving to Node #0,0 Current State: 19:[82, 41, 22], Operations: ['88/4=22'] Exploring Operation: 82-41=41, Resulting Numbers: [22, 41] Generated Node #0,0,1: 19:[22, 41] Operation: 82-41=41 Moving to Node #0,0,1 Current State: 19:[22, 41], Operations: ['88/4=22', '82-41=41'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 77, 11, 19, 48 ]
60
[ "77/11=7", "19+48=67", "67-7=60" ]
Current State: 60:[77, 11, 19, 48], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [19, 48, 7] Generated Node #2: [19, 48, 7] from Operation: 77/11=7 Current State: 60:[19, 48, 7], Operations: ['77/11=7'] Exploring Operation: 19+48=67, Resulting Numbers: [7, 67] Generated Node #3: [7, 67] from Operation: 19+48=67 Current State: 60:[7, 67], Operations: ['77/11=7', '19+48=67'] Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[77, 11, 19, 48], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [11, 19, 29] Generated Node #0,0: 60:[11, 19, 29] Operation: 77-48=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[11, 19, 29], Operations: ['77-48=29'] Exploring Operation: 11+19=30, Resulting Numbers: [29, 30] Generated Node #0,0,0: 60:[29, 30] Operation: 11+19=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[29, 30], Operations: ['77-48=29', '11+19=30'] Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,60 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_1
sum_heuristic
[ 21, 88, 39, 35 ]
35
[ "21+88=109", "39+35=74", "109-74=35" ]
Current State: 35:[21, 88, 39, 35], Operations: [] Exploring Operation: 21+88=109, Resulting Numbers: [39, 35, 109] Generated Node #2: [39, 35, 109] from Operation: 21+88=109 Current State: 35:[39, 35, 109], Operations: ['21+88=109'] Exploring Operation: 39+35=74, Resulting Numbers: [109, 74] Generated Node #3: [109, 74] from Operation: 39+35=74 Current State: 35:[109, 74], Operations: ['21+88=109', '39+35=74'] Exploring Operation: 109-74=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[21, 88, 39, 35], Operations: [] Exploring Operation: 88-39=49, Resulting Numbers: [21, 35, 49] Generated Node #0,0: 35:[21, 35, 49] Operation: 88-39=49 Exploring Operation: 88-21=67, Resulting Numbers: [39, 35, 67] Generated Node #0,1: 35:[39, 35, 67] Operation: 88-21=67 Moving to Node #0,0 Current State: 35:[21, 35, 49], Operations: ['88-39=49'] Exploring Operation: 35-21=14, Resulting Numbers: [49, 14] Generated Node #0,0,0: 35:[49, 14] Operation: 35-21=14 Exploring Operation: 49-21=28, Resulting Numbers: [35, 28] Generated Node #0,0,1: 35:[35, 28] Operation: 49-21=28 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[35, 28], Operations: ['88-39=49', '49-21=28'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[49, 14], Operations: ['88-39=49', '35-21=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[21, 88, 39, 35], Operations: [] Exploring Operation: 88-39=49, Resulting Numbers: [21, 35, 49] Generated Node #0,0: 35:[21, 35, 49] Operation: 88-39=49 Moving to Node #0,0 Current State: 35:[21, 35, 49], Operations: ['88-39=49'] Exploring Operation: 35-21=14, Resulting Numbers: [49, 14] Generated Node #0,0,0: 35:[49, 14] Operation: 35-21=14 Moving to Node #0,0,0 Current State: 35:[49, 14], Operations: ['88-39=49', '35-21=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 30, 26, 1, 28 ]
85
[ "30+26=56", "1+28=29", "56+29=85" ]
Current State: 85:[30, 26, 1, 28], Operations: [] Exploring Operation: 30+26=56, Resulting Numbers: [1, 28, 56] Generated Node #2: [1, 28, 56] from Operation: 30+26=56 Current State: 85:[1, 28, 56], Operations: ['30+26=56'] Exploring Operation: 1+28=29, Resulting Numbers: [56, 29] Generated Node #3: [56, 29] from Operation: 1+28=29 Current State: 85:[56, 29], Operations: ['30+26=56', '1+28=29'] Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[30, 26, 1, 28], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [26, 1, 2] Generated Node #0,0: 85:[26, 1, 2] Operation: 30-28=2 Exploring Operation: 30-26=4, Resulting Numbers: [1, 28, 4] Generated Node #0,1: 85:[1, 28, 4] Operation: 30-26=4 Exploring Operation: 28-26=2, Resulting Numbers: [30, 1, 2] Generated Node #0,2: 85:[30, 1, 2] Operation: 28-26=2 Exploring Operation: 26-1=25, Resulting Numbers: [30, 28, 25] Generated Node #0,3: 85:[30, 28, 25] Operation: 26-1=25 Exploring Operation: 30-1=29, Resulting Numbers: [26, 28, 29] Generated Node #0,4: 85:[26, 28, 29] Operation: 30-1=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[26, 1, 2], Operations: ['30-28=2'] Exploring Operation: 26/2=13, Resulting Numbers: [1, 13] Generated Node #0,0,0: 85:[1, 13] Operation: 26/2=13 Exploring Operation: 26-1=25, Resulting Numbers: [2, 25] Generated Node #0,0,1: 85:[2, 25] Operation: 26-1=25 Exploring Operation: 26-2=24, Resulting Numbers: [1, 24] Generated Node #0,0,2: 85:[1, 24] Operation: 26-2=24 Exploring Operation: 1+2=3, Resulting Numbers: [26, 3] Generated Node #0,0,3: 85:[26, 3] Operation: 1+2=3 Exploring Operation: 26*1=26, Resulting Numbers: [2, 26] Generated Node #0,0,4: 85:[2, 26] Operation: 26*1=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[1, 13], Operations: ['30-28=2', '26/2=13'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[2, 25], Operations: ['30-28=2', '26-1=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,85 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[1, 24], Operations: ['30-28=2', '26-2=24'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 85:[26, 3], Operations: ['30-28=2', '1+2=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 85:[2, 26], Operations: ['30-28=2', '26*1=26'] Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,85 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[1, 28, 4], Operations: ['30-26=4'] Exploring Operation: 28-1=27, Resulting Numbers: [4, 27] Generated Node #0,1,0: 85:[4, 27] Operation: 28-1=27 Exploring Operation: 28/4=7, Resulting Numbers: [1, 7] Generated Node #0,1,1: 85:[1, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [1, 24] Generated Node #0,1,2: 85:[1, 24] Operation: 28-4=24 Exploring Operation: 1+4=5, Resulting Numbers: [28, 5] Generated Node #0,1,3: 85:[28, 5] Operation: 1+4=5 Exploring Operation: 1*28=28, Resulting Numbers: [4, 28] Generated Node #0,1,4: 85:[4, 28] Operation: 1*28=28 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[1, 7], Operations: ['30-26=4', '28/4=7'] Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[4, 27], Operations: ['30-26=4', '28-1=27'] Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,85 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 85:[1, 24], Operations: ['30-26=4', '28-4=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 85:[28, 5], Operations: ['30-26=4', '1+4=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 85:[4, 28], Operations: ['30-26=4', '1*28=28'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,85 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[30, 1, 2], Operations: ['28-26=2'] Exploring Operation: 30/2=15, Resulting Numbers: [1, 15] Generated Node #0,2,0: 85:[1, 15] Operation: 30/2=15 Exploring Operation: 30*1=30, Resulting Numbers: [2, 30] Generated Node #0,2,1: 85:[2, 30] Operation: 30*1=30 Exploring Operation: 30-2=28, Resulting Numbers: [1, 28] Generated Node #0,2,2: 85:[1, 28] Operation: 30-2=28 Exploring Operation: 30-1=29, Resulting Numbers: [2, 29] Generated Node #0,2,3: 85:[2, 29] Operation: 30-1=29 Exploring Operation: 1+2=3, Resulting Numbers: [30, 3] Generated Node #0,2,4: 85:[30, 3] Operation: 1+2=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 85:[1, 15], Operations: ['28-26=2', '30/2=15'] Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 85:[1, 28], Operations: ['28-26=2', '30-2=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 85:[2, 29], Operations: ['28-26=2', '30-1=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 85:[30, 3], Operations: ['28-26=2', '1+2=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[2, 30], Operations: ['28-26=2', '30*1=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[30, 28, 25], Operations: ['26-1=25'] Exploring Operation: 30+25=55, Resulting Numbers: [28, 55] Generated Node #0,3,0: 85:[28, 55] Operation: 30+25=55 Exploring Operation: 30-25=5, Resulting Numbers: [28, 5] Generated Node #0,3,1: 85:[28, 5] Operation: 30-25=5 Exploring Operation: 28-25=3, Resulting Numbers: [30, 3] Generated Node #0,3,2: 85:[30, 3] Operation: 28-25=3 Exploring Operation: 30+28=58, Resulting Numbers: [25, 58] Generated Node #0,3,3: 85:[25, 58] Operation: 30+28=58 Exploring Operation: 30-28=2, Resulting Numbers: [25, 2] Generated Node #0,3,4: 85:[25, 2] Operation: 30-28=2 Moving to Node #0,3,1 Current State: 85:[28, 5], Operations: ['26-1=25', '30-25=5'] Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,85 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[25, 2], Operations: ['26-1=25', '30-28=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[30, 3], Operations: ['26-1=25', '28-25=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[25, 58], Operations: ['26-1=25', '30+28=58'] Exploring Operation: 25+58=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 25*58=1450, Resulting Numbers: [1450] 1450,85 unequal: No Solution Exploring Operation: 58-25=33, Resulting Numbers: [33] 33,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[28, 55], Operations: ['26-1=25', '30+25=55'] Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,85 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,85 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 #0,4 Current State: 85:[26, 28, 29], Operations: ['30-1=29'] Exploring Operation: 29-26=3, Resulting Numbers: [28, 3] Generated Node #0,4,0: 85:[28, 3] Operation: 29-26=3 Exploring Operation: 28-26=2, Resulting Numbers: [29, 2] Generated Node #0,4,1: 85:[29, 2] Operation: 28-26=2 Exploring Operation: 28+29=57, Resulting Numbers: [26, 57] Generated Node #0,4,2: 85:[26, 57] Operation: 28+29=57 Exploring Operation: 26+29=55, Resulting Numbers: [28, 55] Generated Node #0,4,3: 85:[28, 55] Operation: 26+29=55 Exploring Operation: 29-28=1, Resulting Numbers: [26, 1] Generated Node #0,4,4: 85:[26, 1] Operation: 29-28=1 Moving to Node #0,4,0 Current State: 85:[28, 3], Operations: ['30-1=29', '29-26=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[26, 1], Operations: ['30-1=29', '29-28=1'] Exploring Operation: 26*1=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[29, 2], Operations: ['30-1=29', '28-26=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[26, 57], Operations: ['30-1=29', '28+29=57'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 26*57=1482, Resulting Numbers: [1482] 1482,85 unequal: No Solution Exploring Operation: 26+57=83, Resulting Numbers: [83] 83,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[28, 55], Operations: ['30-1=29', '26+29=55'] Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,85 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 8, 74, 88, 62 ]
23
[ "88/8=11", "74-62=12", "11+12=23" ]
Current State: 23:[8, 74, 88, 62], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [74, 62, 11] Generated Node #2: [74, 62, 11] from Operation: 88/8=11 Current State: 23:[74, 62, 11], Operations: ['88/8=11'] Exploring Operation: 74-62=12, Resulting Numbers: [11, 12] Generated Node #3: [11, 12] from Operation: 74-62=12 Current State: 23:[11, 12], Operations: ['88/8=11', '74-62=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[8, 74, 88, 62], Operations: [] Exploring Operation: 88-74=14, Resulting Numbers: [8, 62, 14] Generated Node #0,0: 23:[8, 62, 14] Operation: 88-74=14 Exploring Operation: 88-62=26, Resulting Numbers: [8, 74, 26] Generated Node #0,1: 23:[8, 74, 26] Operation: 88-62=26 Exploring Operation: 74-62=12, Resulting Numbers: [8, 88, 12] Generated Node #0,2: 23:[8, 88, 12] Operation: 74-62=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[8, 62, 14], Operations: ['88-74=14'] Exploring Operation: 8+14=22, Resulting Numbers: [62, 22] Generated Node #0,0,0: 23:[62, 22] Operation: 8+14=22 Exploring Operation: 62-14=48, Resulting Numbers: [8, 48] Generated Node #0,0,1: 23:[8, 48] Operation: 62-14=48 Exploring Operation: 62-8=54, Resulting Numbers: [14, 54] Generated Node #0,0,2: 23:[14, 54] Operation: 62-8=54 Moving to Node #0,0,0 Current State: 23:[62, 22], Operations: ['88-74=14', '8+14=22'] Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,23 unequal: No Solution Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,23 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[8, 48], Operations: ['88-74=14', '62-14=48'] Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,23 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[14, 54], Operations: ['88-74=14', '62-8=54'] Exploring Operation: 14+54=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 14*54=756, Resulting Numbers: [756] 756,23 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[8, 74, 26], Operations: ['88-62=26'] Exploring Operation: 26-8=18, Resulting Numbers: [74, 18] Generated Node #0,1,0: 23:[74, 18] Operation: 26-8=18 Exploring Operation: 74-8=66, Resulting Numbers: [26, 66] Generated Node #0,1,1: 23:[26, 66] Operation: 74-8=66 Exploring Operation: 74-26=48, Resulting Numbers: [8, 48] Generated Node #0,1,2: 23:[8, 48] Operation: 74-26=48 Moving to Node #0,1,2 Current State: 23:[8, 48], Operations: ['88-62=26', '74-26=48'] Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,23 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[26, 66], Operations: ['88-62=26', '74-8=66'] Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,23 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[74, 18], Operations: ['88-62=26', '26-8=18'] Exploring Operation: 74-18=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 74*18=1332, Resulting Numbers: [1332] 1332,23 unequal: No Solution Exploring Operation: 74+18=92, Resulting Numbers: [92] 92,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[8, 88, 12], Operations: ['74-62=12'] Exploring Operation: 8+12=20, Resulting Numbers: [88, 20] Generated Node #0,2,0: 23:[88, 20] Operation: 8+12=20 Exploring Operation: 88-8=80, Resulting Numbers: [12, 80] Generated Node #0,2,1: 23:[12, 80] Operation: 88-8=80 Exploring Operation: 88/8=11, Resulting Numbers: [12, 11] Generated Node #0,2,2: 23:[12, 11] Operation: 88/8=11 Moving to Node #0,2,2 Current State: 23:[12, 11], Operations: ['74-62=12', '88/8=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[8, 74, 88, 62], Operations: [] Exploring Operation: 74-62=12, Resulting Numbers: [8, 88, 12] Generated Node #0,2: 23:[8, 88, 12] Operation: 74-62=12 Moving to Node #0,2 Current State: 23:[8, 88, 12], Operations: ['74-62=12'] Exploring Operation: 88/8=11, Resulting Numbers: [12, 11] Generated Node #0,2,2: 23:[12, 11] Operation: 88/8=11 Moving to Node #0,2,2 Current State: 23:[12, 11], Operations: ['74-62=12', '88/8=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 1, 85, 10, 4 ]
87
[ "1+4=5", "10/5=2", "85+2=87" ]
Current State: 87:[1, 85, 10, 4], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [85, 10, 5] Generated Node #2: [85, 10, 5] from Operation: 1+4=5 Current State: 87:[85, 10, 5], Operations: ['1+4=5'] Exploring Operation: 10/5=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 10/5=2 Current State: 87:[85, 2], Operations: ['1+4=5', '10/5=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[1, 85, 10, 4], Operations: [] Exploring Operation: 10-4=6, Resulting Numbers: [1, 85, 6] Generated Node #0,0: 87:[1, 85, 6] Operation: 10-4=6 Exploring Operation: 1+85=86, Resulting Numbers: [10, 4, 86] Generated Node #0,1: 87:[10, 4, 86] Operation: 1+85=86 Moving to Node #0,0 Current State: 87:[1, 85, 6], Operations: ['10-4=6'] Exploring Operation: 1+85=86, Resulting Numbers: [6, 86] Generated Node #0,0,0: 87:[6, 86] Operation: 1+85=86 Exploring Operation: 6-1=5, Resulting Numbers: [85, 5] Generated Node #0,0,1: 87:[85, 5] Operation: 6-1=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[6, 86], Operations: ['10-4=6', '1+85=86'] Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,87 unequal: No Solution No 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: 87:[85, 5], Operations: ['10-4=6', '6-1=5'] Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,87 unequal: No Solution Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,87 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: 87:[10, 4, 86], Operations: ['1+85=86'] Exploring Operation: 10+86=96, Resulting Numbers: [4, 96] Generated Node #0,1,0: 87:[4, 96] Operation: 10+86=96 Exploring Operation: 10-4=6, Resulting Numbers: [86, 6] Generated Node #0,1,1: 87:[86, 6] Operation: 10-4=6 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[86, 6], Operations: ['1+85=86', '10-4=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,87 unequal: No Solution No 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: 87:[4, 96], Operations: ['1+85=86', '10+86=96'] Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,87 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
[ 3, 92, 86, 86 ]
68
[ "92-86=6", "3*6=18", "86-18=68" ]
Current State: 68:[3, 92, 86, 86], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [3, 6] Generated Node #2: [3, 6] from Operation: 92-86=6 Current State: 68:[3, 6], Operations: ['92-86=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,68 equal: Goal Reached Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[3, 92, 86, 86], Operations: [] Exploring Operation: 86/86=1, Resulting Numbers: [3, 92, 1] Generated Node #0,0: 68:[3, 92, 1] Operation: 86/86=1 Exploring Operation: 92-86=6, Resulting Numbers: [3, 86, 6] Generated Node #0,1: 68:[3, 86, 6] Operation: 92-86=6 Exploring Operation: 92-86=6, Resulting Numbers: [3, 86, 6] Generated Node #0,2: 68:[3, 86, 6] Operation: 92-86=6 Exploring Operation: 86-86=0, Resulting Numbers: [3, 92, 0] Generated Node #0,3: 68:[3, 92, 0] Operation: 86-86=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[3, 86, 6], Operations: ['92-86=6'] Exploring Operation: 86-3=83, Resulting Numbers: [6, 83] Generated Node #0,1,0: 68:[6, 83] Operation: 86-3=83 Exploring Operation: 6/3=2, Resulting Numbers: [86, 2] Generated Node #0,1,1: 68:[86, 2] Operation: 6/3=2 Exploring Operation: 86-6=80, Resulting Numbers: [3, 80] Generated Node #0,1,2: 68:[3, 80] Operation: 86-6=80 Exploring Operation: 3*6=18, Resulting Numbers: [86, 18] Generated Node #0,1,3: 68:[86, 18] Operation: 3*6=18 Moving to Node #0,1,2 Current State: 68:[3, 80], Operations: ['92-86=6', '86-6=80'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,68 unequal: No Solution Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[6, 83], Operations: ['92-86=6', '86-3=83'] Exploring Operation: 6*83=498, Resulting Numbers: [498] 498,68 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[86, 2], Operations: ['92-86=6', '6/3=2'] Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,68 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,68 unequal: No Solution Exploring Operation: 86*2=172, Resulting Numbers: [172] 172,68 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[86, 18], Operations: ['92-86=6', '3*6=18'] Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[3, 92, 86, 86], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [3, 86, 6] Generated Node #0,1: 68:[3, 86, 6] Operation: 92-86=6 Moving to Node #0,1 Current State: 68:[3, 86, 6], Operations: ['92-86=6'] Exploring Operation: 3*6=18, Resulting Numbers: [86, 18] Generated Node #0,1,3: 68:[86, 18] Operation: 3*6=18 Moving to Node #0,1,3 Current State: 68:[86, 18], Operations: ['92-86=6', '3*6=18'] Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 5, 24, 22, 40 ]
43
[ "24-5=19", "22+40=62", "62-19=43" ]
Current State: 43:[5, 24, 22, 40], Operations: [] Exploring Operation: 24-5=19, Resulting Numbers: [22, 40, 19] Generated Node #2: [22, 40, 19] from Operation: 24-5=19 Current State: 43:[22, 40, 19], Operations: ['24-5=19'] Exploring Operation: 22+40=62, Resulting Numbers: [19, 62] Generated Node #3: [19, 62] from Operation: 22+40=62 Current State: 43:[19, 62], Operations: ['24-5=19', '22+40=62'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[5, 24, 22, 40], Operations: [] Exploring Operation: 5+40=45, Resulting Numbers: [24, 22, 45] Generated Node #0,0: 43:[24, 22, 45] Operation: 5+40=45 Exploring Operation: 24+22=46, Resulting Numbers: [5, 40, 46] Generated Node #0,1: 43:[5, 40, 46] Operation: 24+22=46 Exploring Operation: 5+22=27, Resulting Numbers: [24, 40, 27] Generated Node #0,2: 43:[24, 40, 27] Operation: 5+22=27 Exploring Operation: 24-5=19, Resulting Numbers: [22, 40, 19] Generated Node #0,3: 43:[22, 40, 19] Operation: 24-5=19 Exploring Operation: 5+24=29, Resulting Numbers: [22, 40, 29] Generated Node #0,4: 43:[22, 40, 29] Operation: 5+24=29 Moving to Node #0,2 Current State: 43:[24, 40, 27], Operations: ['5+22=27'] Exploring Operation: 24+27=51, Resulting Numbers: [40, 51] Generated Node #0,2,0: 43:[40, 51] Operation: 24+27=51 Exploring Operation: 24+40=64, Resulting Numbers: [27, 64] Generated Node #0,2,1: 43:[27, 64] Operation: 24+40=64 Exploring Operation: 27-24=3, Resulting Numbers: [40, 3] Generated Node #0,2,2: 43:[40, 3] Operation: 27-24=3 Exploring Operation: 40+27=67, Resulting Numbers: [24, 67] Generated Node #0,2,3: 43:[24, 67] Operation: 40+27=67 Exploring Operation: 40-24=16, Resulting Numbers: [27, 16] Generated Node #0,2,4: 43:[27, 16] Operation: 40-24=16 Moving to Node #0,4 Current State: 43:[22, 40, 29], Operations: ['5+24=29'] Exploring Operation: 40-22=18, Resulting Numbers: [29, 18] Generated Node #0,4,0: 43:[29, 18] Operation: 40-22=18 Exploring Operation: 22+29=51, Resulting Numbers: [40, 51] Generated Node #0,4,1: 43:[40, 51] Operation: 22+29=51 Exploring Operation: 29-22=7, Resulting Numbers: [40, 7] Generated Node #0,4,2: 43:[40, 7] Operation: 29-22=7 Exploring Operation: 40+29=69, Resulting Numbers: [22, 69] Generated Node #0,4,3: 43:[22, 69] Operation: 40+29=69 Exploring Operation: 22+40=62, Resulting Numbers: [29, 62] Generated Node #0,4,4: 43:[29, 62] Operation: 22+40=62 Moving to Node #0,0 Current State: 43:[24, 22, 45], Operations: ['5+40=45'] Exploring Operation: 45-22=23, Resulting Numbers: [24, 23] Generated Node #0,0,0: 43:[24, 23] Operation: 45-22=23 Exploring Operation: 45-24=21, Resulting Numbers: [22, 21] Generated Node #0,0,1: 43:[22, 21] Operation: 45-24=21 Exploring Operation: 22+45=67, Resulting Numbers: [24, 67] Generated Node #0,0,2: 43:[24, 67] Operation: 22+45=67 Exploring Operation: 24-22=2, Resulting Numbers: [45, 2] Generated Node #0,0,3: 43:[45, 2] Operation: 24-22=2 Exploring Operation: 24+22=46, Resulting Numbers: [45, 46] Generated Node #0,0,4: 43:[45, 46] Operation: 24+22=46 Moving to Node #0,1 Current State: 43:[5, 40, 46], Operations: ['24+22=46'] Exploring Operation: 40-5=35, Resulting Numbers: [46, 35] Generated Node #0,1,0: 43:[46, 35] Operation: 40-5=35 Exploring Operation: 5+40=45, Resulting Numbers: [46, 45] Generated Node #0,1,1: 43:[46, 45] Operation: 5+40=45 Exploring Operation: 5+46=51, Resulting Numbers: [40, 51] Generated Node #0,1,2: 43:[40, 51] Operation: 5+46=51 Exploring Operation: 46-5=41, Resulting Numbers: [40, 41] Generated Node #0,1,3: 43:[40, 41] Operation: 46-5=41 Exploring Operation: 40/5=8, Resulting Numbers: [46, 8] Generated Node #0,1,4: 43:[46, 8] Operation: 40/5=8 Moving to Node #0,3 Current State: 43:[22, 40, 19], Operations: ['24-5=19'] Exploring Operation: 40-19=21, Resulting Numbers: [22, 21] Generated Node #0,3,0: 43:[22, 21] Operation: 40-19=21 Exploring Operation: 40+19=59, Resulting Numbers: [22, 59] Generated Node #0,3,1: 43:[22, 59] Operation: 40+19=59 Exploring Operation: 22+40=62, Resulting Numbers: [19, 62] Generated Node #0,3,2: 43:[19, 62] Operation: 22+40=62 Exploring Operation: 22-19=3, Resulting Numbers: [40, 3] Generated Node #0,3,3: 43:[40, 3] Operation: 22-19=3 Exploring Operation: 22+19=41, Resulting Numbers: [40, 41] Generated Node #0,3,4: 43:[40, 41] Operation: 22+19=41 Moving to Node #0,0,4 Current State: 43:[45, 46], Operations: ['5+40=45', '24+22=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,43 unequal: No Solution Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[46, 45], Operations: ['24+22=46', '5+40=45'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,43 unequal: No Solution Moving to Node #0,3,4 Current State: 43:[40, 41], Operations: ['24-5=19', '22+19=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,43 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[40, 41], Operations: ['24+22=46', '46-5=41'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[40, 51], Operations: ['5+24=29', '22+29=51'] Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,43 unequal: No Solution Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[46, 35], Operations: ['24+22=46', '40-5=35'] Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[40, 51], Operations: ['24+22=46', '5+46=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,43 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[40, 51], Operations: ['5+22=27', '24+27=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,43 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[29, 62], Operations: ['5+24=29', '22+40=62'] Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 29*62=1798, Resulting Numbers: [1798] 1798,43 unequal: No Solution Exploring Operation: 29+62=91, Resulting Numbers: [91] 91,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[22, 59], Operations: ['24-5=19', '40+19=59'] Exploring Operation: 22*59=1298, Resulting Numbers: [1298] 1298,43 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[27, 64], Operations: ['5+22=27', '24+40=64'] Exploring Operation: 27*64=1728, Resulting Numbers: [1728] 1728,43 unequal: No Solution Exploring Operation: 27+64=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 64-27=37, Resulting Numbers: [37] 37,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[46, 8], Operations: ['24+22=46', '40/5=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[24, 23], Operations: ['5+40=45', '45-22=23'] Exploring Operation: 24+23=47, Resulting Numbers: [47] 47,43 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 24*23=552, Resulting Numbers: [552] 552,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[40, 7], Operations: ['5+24=29', '29-22=7'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,43 unequal: No Solution Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,43 unequal: No Solution Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[29, 18], Operations: ['5+24=29', '40-22=18'] Exploring Operation: 29*18=522, Resulting Numbers: [522] 522,43 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[45, 2], Operations: ['5+40=45', '24-22=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[5, 24, 22, 40], Operations: [] Exploring Operation: 5+40=45, Resulting Numbers: [24, 22, 45] Generated Node #0,0: 43:[24, 22, 45] Operation: 5+40=45 Moving to Node #0,0 Current State: 43:[24, 22, 45], Operations: ['5+40=45'] Exploring Operation: 24-22=2, Resulting Numbers: [45, 2] Generated Node #0,0,3: 43:[45, 2] Operation: 24-22=2 Moving to Node #0,0,3 Current State: 43:[45, 2], Operations: ['5+40=45', '24-22=2'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
0.929688
hs_5
mult_heuristic
[ 53, 32, 2, 6 ]
13
[ "53-32=21", "2+6=8", "21-8=13" ]
Current State: 13:[53, 32, 2, 6], Operations: [] Exploring Operation: 53-32=21, Resulting Numbers: [2, 6, 21] Generated Node #2: [2, 6, 21] from Operation: 53-32=21 Current State: 13:[2, 6, 21], Operations: ['53-32=21'] Exploring Operation: 2+6=8, Resulting Numbers: [21, 8] Generated Node #3: [21, 8] from Operation: 2+6=8 Current State: 13:[21, 8], Operations: ['53-32=21', '2+6=8'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[53, 32, 2, 6], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [53, 6, 16] Generated Node #0,0: 13:[53, 6, 16] Operation: 32/2=16 Exploring Operation: 53-32=21, Resulting Numbers: [2, 6, 21] Generated Node #0,1: 13:[2, 6, 21] Operation: 53-32=21 Exploring Operation: 53-6=47, Resulting Numbers: [32, 2, 47] Generated Node #0,2: 13:[32, 2, 47] Operation: 53-6=47 Exploring Operation: 2*6=12, Resulting Numbers: [53, 32, 12] Generated Node #0,3: 13:[53, 32, 12] Operation: 2*6=12 Exploring Operation: 53-2=51, Resulting Numbers: [32, 6, 51] Generated Node #0,4: 13:[32, 6, 51] Operation: 53-2=51 Moving to Node #0,1 Current State: 13:[2, 6, 21], Operations: ['53-32=21'] Exploring Operation: 21-2=19, Resulting Numbers: [6, 19] Generated Node #0,1,0: 13:[6, 19] Operation: 21-2=19 Exploring Operation: 2*6=12, Resulting Numbers: [21, 12] Generated Node #0,1,1: 13:[21, 12] Operation: 2*6=12 Exploring Operation: 6-2=4, Resulting Numbers: [21, 4] Generated Node #0,1,2: 13:[21, 4] Operation: 6-2=4 Exploring Operation: 21-6=15, Resulting Numbers: [2, 15] Generated Node #0,1,3: 13:[2, 15] Operation: 21-6=15 Exploring Operation: 2+6=8, Resulting Numbers: [21, 8] Generated Node #0,1,4: 13:[21, 8] Operation: 2+6=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[21, 12], Operations: ['53-32=21', '2*6=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,13 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,13 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[6, 19], Operations: ['53-32=21', '21-2=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,13 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[53, 32, 2, 6], Operations: [] Exploring Operation: 53-32=21, Resulting Numbers: [2, 6, 21] Generated Node #0,1: 13:[2, 6, 21] Operation: 53-32=21 Moving to Node #0,1 Current State: 13:[2, 6, 21], Operations: ['53-32=21'] Exploring Operation: 21-2=19, Resulting Numbers: [6, 19] Generated Node #0,1,0: 13:[6, 19] Operation: 21-2=19 Moving to Node #0,1,0 Current State: 13:[6, 19], Operations: ['53-32=21', '21-2=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 72, 20, 37, 15 ]
59
[ "72*20=1440", "1440/15=96", "96-37=59" ]
Current State: 59:[72, 20, 37, 15], Operations: [] Exploring Operation: 72*20=1440, Resulting Numbers: [37, 15, 1440] Generated Node #2: [37, 15, 1440] from Operation: 72*20=1440 Current State: 59:[37, 15, 1440], Operations: ['72*20=1440'] Exploring Operation: 1440/15=96, Resulting Numbers: [37, 96] Generated Node #3: [37, 96] from Operation: 1440/15=96 Current State: 59:[37, 96], Operations: ['72*20=1440', '1440/15=96'] Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[72, 20, 37, 15], Operations: [] Exploring Operation: 20+15=35, Resulting Numbers: [72, 37, 35] Generated Node #0,0: 59:[72, 37, 35] Operation: 20+15=35 Exploring Operation: 20+37=57, Resulting Numbers: [72, 15, 57] Generated Node #0,1: 59:[72, 15, 57] Operation: 20+37=57 Exploring Operation: 37+15=52, Resulting Numbers: [72, 20, 52] Generated Node #0,2: 59:[72, 20, 52] Operation: 37+15=52 Moving to Node #0,0 Current State: 59:[72, 37, 35], Operations: ['20+15=35'] Exploring Operation: 72-35=37, Resulting Numbers: [37, 37] Generated Node #0,0,0: 59:[37, 37] Operation: 72-35=37 Exploring Operation: 37+35=72, Resulting Numbers: [72, 72] Generated Node #0,0,1: 59:[72, 72] Operation: 37+35=72 Exploring Operation: 72-37=35, Resulting Numbers: [35, 35] Generated Node #0,0,2: 59:[35, 35] Operation: 72-37=35 Moving to Node #0,1 Current State: 59:[72, 15, 57], Operations: ['20+37=57'] Exploring Operation: 72+15=87, Resulting Numbers: [57, 87] Generated Node #0,1,0: 59:[57, 87] Operation: 72+15=87 Exploring Operation: 72-15=57, Resulting Numbers: [57, 57] Generated Node #0,1,1: 59:[57, 57] Operation: 72-15=57 Exploring Operation: 15+57=72, Resulting Numbers: [72, 72] Generated Node #0,1,2: 59:[72, 72] Operation: 15+57=72 Moving to Node #0,2 Current State: 59:[72, 20, 52], Operations: ['37+15=52'] Exploring Operation: 72+20=92, Resulting Numbers: [52, 92] Generated Node #0,2,0: 59:[52, 92] Operation: 72+20=92 Exploring Operation: 72-20=52, Resulting Numbers: [52, 52] Generated Node #0,2,1: 59:[52, 52] Operation: 72-20=52 Exploring Operation: 20+52=72, Resulting Numbers: [72, 72] Generated Node #0,2,2: 59:[72, 72] Operation: 20+52=72 Moving to Node #0,1,1 Current State: 59:[57, 57], Operations: ['20+37=57', '72-15=57'] Exploring Operation: 57/57=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 57-57=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 57+57=114, Resulting Numbers: [114] 114,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[52, 52], Operations: ['37+15=52', '72-20=52'] Exploring Operation: 52-52=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 52/52=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 52+52=104, Resulting Numbers: [104] 104,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[72, 72], Operations: ['20+15=35', '37+35=72'] Exploring Operation: 72+72=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 72/72=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 72-72=0, Resulting Numbers: [0] 0,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[72, 72], Operations: ['20+37=57', '15+57=72'] Exploring Operation: 72/72=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 72+72=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 72-72=0, Resulting Numbers: [0] 0,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[72, 72], Operations: ['37+15=52', '20+52=72'] Exploring Operation: 72+72=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 72-72=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 72/72=1, Resulting Numbers: [1] 1,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[57, 87], Operations: ['20+37=57', '72+15=87'] Exploring Operation: 57+87=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 57*87=4959, Resulting Numbers: [4959] 4959,59 unequal: No Solution Exploring Operation: 87-57=30, Resulting Numbers: [30] 30,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[52, 92], Operations: ['37+15=52', '72+20=92'] Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 52+92=144, Resulting Numbers: [144] 144,59 unequal: No Solution Exploring Operation: 52*92=4784, Resulting Numbers: [4784] 4784,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[37, 37], Operations: ['20+15=35', '72-35=37'] Exploring Operation: 37+37=74, Resulting Numbers: [74] 74,59 unequal: No Solution Exploring Operation: 37-37=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 37/37=1, Resulting Numbers: [1] 1,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[35, 35], Operations: ['20+15=35', '72-37=35'] Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,59 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 4, 62, 87, 4 ]
84
[ "4+62=66", "87-66=21", "4*21=84" ]
Current State: 84:[4, 62, 87, 4], Operations: [] Exploring Operation: 4+62=66, Resulting Numbers: [87, 66] Generated Node #2: [87, 66] from Operation: 4+62=66 Current State: 84:[87, 66], Operations: ['4+62=66'] Exploring Operation: 87-66=21, Resulting Numbers: [21] 21,84 equal: Goal Reached Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[4, 62, 87, 4], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [4, 4, 25] Generated Node #0,0: 84:[4, 4, 25] Operation: 87-62=25 Moving to Node #0,0 Current State: 84:[4, 4, 25], Operations: ['87-62=25'] Exploring Operation: 25-4=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 84:[4, 21] Operation: 25-4=21 Moving to Node #0,0,0 Current State: 84:[4, 21], Operations: ['87-62=25', '25-4=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[4, 62, 87, 4], Operations: [] Exploring Operation: 87-62=25, Resulting Numbers: [4, 4, 25] Generated Node #0,0: 84:[4, 4, 25] Operation: 87-62=25 Moving to Node #0,0 Current State: 84:[4, 4, 25], Operations: ['87-62=25'] Exploring Operation: 25-4=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 84:[4, 21] Operation: 25-4=21 Moving to Node #0,0,0 Current State: 84:[4, 21], Operations: ['87-62=25', '25-4=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 24, 19, 40, 16 ]
46
[ "19*40=760", "760-24=736", "736/16=46" ]
Current State: 46:[24, 19, 40, 16], Operations: [] Exploring Operation: 19*40=760, Resulting Numbers: [24, 16, 760] Generated Node #2: [24, 16, 760] from Operation: 19*40=760 Current State: 46:[24, 16, 760], Operations: ['19*40=760'] Exploring Operation: 760-24=736, Resulting Numbers: [16, 736] Generated Node #3: [16, 736] from Operation: 760-24=736 Current State: 46:[16, 736], Operations: ['19*40=760', '760-24=736'] Exploring Operation: 736/16=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[24, 19, 40, 16], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [24, 16, 21] Generated Node #0,0: 46:[24, 16, 21] Operation: 40-19=21 Exploring Operation: 24+19=43, Resulting Numbers: [40, 16, 43] Generated Node #0,1: 46:[40, 16, 43] Operation: 24+19=43 Exploring Operation: 40+16=56, Resulting Numbers: [24, 19, 56] Generated Node #0,2: 46:[24, 19, 56] Operation: 40+16=56 Exploring Operation: 19-16=3, Resulting Numbers: [24, 40, 3] Generated Node #0,3: 46:[24, 40, 3] Operation: 19-16=3 Exploring Operation: 40-16=24, Resulting Numbers: [24, 19, 24] Generated Node #0,4: 46:[24, 19, 24] Operation: 40-16=24 Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[24, 19, 24], Operations: ['40-16=24'] Exploring Operation: 24/24=1, Resulting Numbers: [19, 1] Generated Node #0,4,0: 46:[19, 1] Operation: 24/24=1 Exploring Operation: 24-19=5, Resulting Numbers: [24, 5] Generated Node #0,4,1: 46:[24, 5] Operation: 24-19=5 Exploring Operation: 24+19=43, Resulting Numbers: [24, 43] Generated Node #0,4,2: 46:[24, 43] Operation: 24+19=43 Exploring Operation: 19+24=43, Resulting Numbers: [24, 43] Generated Node #0,4,3: 46:[24, 43] Operation: 19+24=43 Exploring Operation: 24-19=5, Resulting Numbers: [24, 5] Generated Node #0,4,4: 46:[24, 5] Operation: 24-19=5 Moving to Node #0,4,1 Current State: 46:[24, 5], Operations: ['40-16=24', '24-19=5'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,46 unequal: No Solution Moving to Node #0,4,3 Current State: 46:[24, 43], Operations: ['40-16=24', '19+24=43'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,46 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,46 unequal: No Solution Moving to Node #0,4,2 Current State: 46:[24, 43], Operations: ['40-16=24', '24+19=43'] Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,46 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[24, 5], Operations: ['40-16=24', '24-19=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,46 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,46 unequal: No Solution Moving to Node #0,4,0 Current State: 46:[19, 1], Operations: ['40-16=24', '24/24=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,46 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[24, 40, 3], Operations: ['19-16=3'] Exploring Operation: 40-3=37, Resulting Numbers: [24, 37] Generated Node #0,3,0: 46:[24, 37] Operation: 40-3=37 Exploring Operation: 24+3=27, Resulting Numbers: [40, 27] Generated Node #0,3,1: 46:[40, 27] Operation: 24+3=27 Exploring Operation: 40+3=43, Resulting Numbers: [24, 43] Generated Node #0,3,2: 46:[24, 43] Operation: 40+3=43 Exploring Operation: 40-24=16, Resulting Numbers: [3, 16] Generated Node #0,3,3: 46:[3, 16] Operation: 40-24=16 Exploring Operation: 24-3=21, Resulting Numbers: [40, 21] Generated Node #0,3,4: 46:[40, 21] Operation: 24-3=21 Moving to Node #0,3,2 Current State: 46:[24, 43], Operations: ['19-16=3', '40+3=43'] Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,46 unequal: No Solution Moving to Node #0,3,4 Current State: 46:[40, 21], Operations: ['19-16=3', '24-3=21'] Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,46 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,46 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[3, 16], Operations: ['19-16=3', '40-24=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[24, 37], Operations: ['19-16=3', '40-3=37'] Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,46 unequal: No Solution Exploring Operation: 24*37=888, Resulting Numbers: [888] 888,46 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[40, 27], Operations: ['19-16=3', '24+3=27'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 40*27=1080, Resulting Numbers: [1080] 1080,46 unequal: No Solution Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[24, 16, 21], Operations: ['40-19=21'] Exploring Operation: 24-21=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 46:[16, 3] Operation: 24-21=3 Exploring Operation: 24+21=45, Resulting Numbers: [16, 45] Generated Node #0,0,1: 46:[16, 45] Operation: 24+21=45 Exploring Operation: 21-16=5, Resulting Numbers: [24, 5] Generated Node #0,0,2: 46:[24, 5] Operation: 21-16=5 Exploring Operation: 24+16=40, Resulting Numbers: [21, 40] Generated Node #0,0,3: 46:[21, 40] Operation: 24+16=40 Exploring Operation: 24-16=8, Resulting Numbers: [21, 8] Generated Node #0,0,4: 46:[21, 8] Operation: 24-16=8 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 46:[24, 5], Operations: ['40-19=21', '21-16=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,46 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,46 unequal: No Solution No 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: 46:[16, 3], Operations: ['40-19=21', '24-21=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,46 unequal: No Solution No 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: 46:[16, 45], Operations: ['40-19=21', '24+21=45'] Exploring Operation: 16*45=720, Resulting Numbers: [720] 720,46 unequal: No Solution Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 16+45=61, Resulting Numbers: [61] 61,46 unequal: No Solution No 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: 46:[21, 40], Operations: ['40-19=21', '24+16=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,46 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,46 unequal: No Solution No 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: 46:[21, 8], Operations: ['40-19=21', '24-16=8'] Exploring Operation: 21*8=168, Resulting Numbers: [168] 168,46 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,46 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: 46:[24, 19, 56], Operations: ['40+16=56'] Exploring Operation: 24-19=5, Resulting Numbers: [56, 5] Generated Node #0,2,0: 46:[56, 5] Operation: 24-19=5 Exploring Operation: 56-19=37, Resulting Numbers: [24, 37] Generated Node #0,2,1: 46:[24, 37] Operation: 56-19=37 Exploring Operation: 24+19=43, Resulting Numbers: [56, 43] Generated Node #0,2,2: 46:[56, 43] Operation: 24+19=43 Exploring Operation: 56-24=32, Resulting Numbers: [19, 32] Generated Node #0,2,3: 46:[19, 32] Operation: 56-24=32 Exploring Operation: 19+56=75, Resulting Numbers: [24, 75] Generated Node #0,2,4: 46:[24, 75] Operation: 19+56=75 Moving to Node #0,2,1 Current State: 46:[24, 37], Operations: ['40+16=56', '56-19=37'] Exploring Operation: 24*37=888, Resulting Numbers: [888] 888,46 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[56, 43], Operations: ['40+16=56', '24+19=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,46 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[56, 5], Operations: ['40+16=56', '24-19=5'] Exploring Operation: 56*5=280, Resulting Numbers: [280] 280,46 unequal: No Solution Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,46 unequal: No Solution Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[19, 32], Operations: ['40+16=56', '56-24=32'] Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,46 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,2,4 Current State: 46:[24, 75], Operations: ['40+16=56', '19+56=75'] Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,46 unequal: No Solution Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[40, 16, 43], Operations: ['24+19=43'] Exploring Operation: 16+43=59, Resulting Numbers: [40, 59] Generated Node #0,1,0: 46:[40, 59] Operation: 16+43=59 Exploring Operation: 43-16=27, Resulting Numbers: [40, 27] Generated Node #0,1,1: 46:[40, 27] Operation: 43-16=27 Exploring Operation: 43-40=3, Resulting Numbers: [16, 3] Generated Node #0,1,2: 46:[16, 3] Operation: 43-40=3 Exploring Operation: 40-16=24, Resulting Numbers: [43, 24] Generated Node #0,1,3: 46:[43, 24] Operation: 40-16=24 Exploring Operation: 40+16=56, Resulting Numbers: [43, 56] Generated Node #0,1,4: 46:[43, 56] Operation: 40+16=56 Moving to Node #0,1,3 Current State: 46:[43, 24], Operations: ['24+19=43', '40-16=24'] Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,46 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[16, 3], Operations: ['24+19=43', '43-40=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[40, 27], Operations: ['24+19=43', '43-16=27'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 40*27=1080, Resulting Numbers: [1080] 1080,46 unequal: No Solution Moving to Node #0,1,4 Current State: 46:[43, 56], Operations: ['24+19=43', '40+16=56'] Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,46 unequal: No Solution Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[40, 59], Operations: ['24+19=43', '16+43=59'] Exploring Operation: 59-40=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 40+59=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 40*59=2360, Resulting Numbers: [2360] 2360,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 44, 39, 64, 73 ]
84
[ "44*73=3212", "64+3212=3276", "3276/39=84" ]
Current State: 84:[44, 39, 64, 73], Operations: [] Exploring Operation: 44*73=3212, Resulting Numbers: [39, 64, 3212] Generated Node #2: [39, 64, 3212] from Operation: 44*73=3212 Current State: 84:[39, 64, 3212], Operations: ['44*73=3212'] Exploring Operation: 64+3212=3276, Resulting Numbers: [39, 3276] Generated Node #3: [39, 3276] from Operation: 64+3212=3276 Current State: 84:[39, 3276], Operations: ['44*73=3212', '64+3212=3276'] Exploring Operation: 3276/39=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[44, 39, 64, 73], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [44, 39, 9] Generated Node #0,0: 84:[44, 39, 9] Operation: 73-64=9 Exploring Operation: 64-44=20, Resulting Numbers: [39, 73, 20] Generated Node #0,1: 84:[39, 73, 20] Operation: 64-44=20 Exploring Operation: 73-44=29, Resulting Numbers: [39, 64, 29] Generated Node #0,2: 84:[39, 64, 29] Operation: 73-44=29 Exploring Operation: 64-39=25, Resulting Numbers: [44, 73, 25] Generated Node #0,3: 84:[44, 73, 25] Operation: 64-39=25 Moving to Node #0,0 Current State: 84:[44, 39, 9], Operations: ['73-64=9'] Exploring Operation: 39+9=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 84:[44, 48] Operation: 39+9=48 Exploring Operation: 44-39=5, Resulting Numbers: [9, 5] Generated Node #0,0,1: 84:[9, 5] Operation: 44-39=5 Exploring Operation: 39-9=30, Resulting Numbers: [44, 30] Generated Node #0,0,2: 84:[44, 30] Operation: 39-9=30 Exploring Operation: 44+39=83, Resulting Numbers: [9, 83] Generated Node #0,0,3: 84:[9, 83] Operation: 44+39=83 Moving to Node #0,1 Current State: 84:[39, 73, 20], Operations: ['64-44=20'] Exploring Operation: 73+20=93, Resulting Numbers: [39, 93] Generated Node #0,1,0: 84:[39, 93] Operation: 73+20=93 Exploring Operation: 73-20=53, Resulting Numbers: [39, 53] Generated Node #0,1,1: 84:[39, 53] Operation: 73-20=53 Exploring Operation: 39-20=19, Resulting Numbers: [73, 19] Generated Node #0,1,2: 84:[73, 19] Operation: 39-20=19 Exploring Operation: 73-39=34, Resulting Numbers: [20, 34] Generated Node #0,1,3: 84:[20, 34] Operation: 73-39=34 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[20, 34], Operations: ['64-44=20', '73-39=34'] Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,84 unequal: No Solution Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,84 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 #0,1,0 Current State: 84:[39, 93], Operations: ['64-44=20', '73+20=93'] Exploring Operation: 39+93=132, Resulting Numbers: [132] 132,84 unequal: No Solution Exploring Operation: 39*93=3627, Resulting Numbers: [3627] 3627,84 unequal: No Solution Exploring Operation: 93-39=54, Resulting Numbers: [54] 54,84 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 #0,1,2 Current State: 84:[73, 19], Operations: ['64-44=20', '39-20=19'] Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,84 unequal: No Solution Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,84 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:[39, 53], Operations: ['64-44=20', '73-20=53'] Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,84 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,84 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: 84:[44, 73, 25], Operations: ['64-39=25'] Exploring Operation: 73-25=48, Resulting Numbers: [44, 48] Generated Node #0,3,0: 84:[44, 48] Operation: 73-25=48 Exploring Operation: 73+25=98, Resulting Numbers: [44, 98] Generated Node #0,3,1: 84:[44, 98] Operation: 73+25=98 Exploring Operation: 73-44=29, Resulting Numbers: [25, 29] Generated Node #0,3,2: 84:[25, 29] Operation: 73-44=29 Exploring Operation: 44-25=19, Resulting Numbers: [73, 19] Generated Node #0,3,3: 84:[73, 19] Operation: 44-25=19 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[25, 29], Operations: ['64-39=25', '73-44=29'] Exploring Operation: 25*29=725, Resulting Numbers: [725] 725,84 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[44, 48], Operations: ['64-39=25', '73-25=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 44*48=2112, Resulting Numbers: [2112] 2112,84 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[73, 19], Operations: ['64-39=25', '44-25=19'] Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,84 unequal: No Solution Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[44, 98], Operations: ['64-39=25', '73+25=98'] Exploring Operation: 44*98=4312, Resulting Numbers: [4312] 4312,84 unequal: No Solution Exploring Operation: 98-44=54, Resulting Numbers: [54] 54,84 unequal: No Solution Exploring Operation: 44+98=142, Resulting Numbers: [142] 142,84 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: 84:[39, 64, 29], Operations: ['73-44=29'] Exploring Operation: 64-39=25, Resulting Numbers: [29, 25] Generated Node #0,2,0: 84:[29, 25] Operation: 64-39=25 Exploring Operation: 39+64=103, Resulting Numbers: [29, 103] Generated Node #0,2,1: 84:[29, 103] Operation: 39+64=103 Exploring Operation: 64+29=93, Resulting Numbers: [39, 93] Generated Node #0,2,2: 84:[39, 93] Operation: 64+29=93 Exploring Operation: 64-29=35, Resulting Numbers: [39, 35] Generated Node #0,2,3: 84:[39, 35] Operation: 64-29=35 Moving to Node #0,0,1 Current State: 84:[9, 5], Operations: ['73-64=9', '44-39=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[9, 83], Operations: ['73-64=9', '44+39=83'] Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,84 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[44, 30], Operations: ['73-64=9', '39-9=30'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 44*30=1320, Resulting Numbers: [1320] 1320,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[29, 25], Operations: ['73-44=29', '64-39=25'] Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,84 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[44, 48], Operations: ['73-64=9', '39+9=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 44*48=2112, Resulting Numbers: [2112] 2112,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[39, 35], Operations: ['73-44=29', '64-29=35'] Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,84 unequal: No Solution Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[39, 93], Operations: ['73-44=29', '64+29=93'] Exploring Operation: 93-39=54, Resulting Numbers: [54] 54,84 unequal: No Solution Exploring Operation: 39*93=3627, Resulting Numbers: [3627] 3627,84 unequal: No Solution Exploring Operation: 39+93=132, Resulting Numbers: [132] 132,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[29, 103], Operations: ['73-44=29', '39+64=103'] Exploring Operation: 103-29=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 29+103=132, Resulting Numbers: [132] 132,84 unequal: No Solution Exploring Operation: 29*103=2987, Resulting Numbers: [2987] 2987,84 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 50, 26, 89, 94 ]
71
[ "50+26=76", "94-89=5", "76-5=71" ]
Current State: 71:[50, 26, 89, 94], Operations: [] Exploring Operation: 50+26=76, Resulting Numbers: [89, 94, 76] Generated Node #2: [89, 94, 76] from Operation: 50+26=76 Current State: 71:[89, 94, 76], Operations: ['50+26=76'] Exploring Operation: 94-89=5, Resulting Numbers: [76, 5] Generated Node #3: [76, 5] from Operation: 94-89=5 Current State: 71:[76, 5], Operations: ['50+26=76', '94-89=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[50, 26, 89, 94], Operations: [] Exploring Operation: 94-26=68, Resulting Numbers: [50, 89, 68] Generated Node #0,0: 71:[50, 89, 68] Operation: 94-26=68 Exploring Operation: 50+26=76, Resulting Numbers: [89, 94, 76] Generated Node #0,1: 71:[89, 94, 76] Operation: 50+26=76 Exploring Operation: 89-26=63, Resulting Numbers: [50, 94, 63] Generated Node #0,2: 71:[50, 94, 63] Operation: 89-26=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[50, 89, 68], Operations: ['94-26=68'] Exploring Operation: 89-50=39, Resulting Numbers: [68, 39] Generated Node #0,0,0: 71:[68, 39] Operation: 89-50=39 Exploring Operation: 50+89=139, Resulting Numbers: [68, 139] Generated Node #0,0,1: 71:[68, 139] Operation: 50+89=139 Exploring Operation: 50+68=118, Resulting Numbers: [89, 118] Generated Node #0,0,2: 71:[89, 118] Operation: 50+68=118 Moving to Node #0,0,0 Current State: 71:[68, 39], Operations: ['94-26=68', '89-50=39'] Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,71 unequal: No Solution Exploring Operation: 68*39=2652, Resulting Numbers: [2652] 2652,71 unequal: No Solution Exploring Operation: 68+39=107, Resulting Numbers: [107] 107,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[89, 118], Operations: ['94-26=68', '50+68=118'] Exploring Operation: 89+118=207, Resulting Numbers: [207] 207,71 unequal: No Solution Exploring Operation: 89*118=10502, Resulting Numbers: [10502] 10502,71 unequal: No Solution Exploring Operation: 118-89=29, Resulting Numbers: [29] 29,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[68, 139], Operations: ['94-26=68', '50+89=139'] Exploring Operation: 68+139=207, Resulting Numbers: [207] 207,71 unequal: No Solution Exploring Operation: 68*139=9452, Resulting Numbers: [9452] 9452,71 unequal: No Solution Exploring Operation: 139-68=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[50, 26, 89, 94], Operations: [] Exploring Operation: 94-26=68, Resulting Numbers: [50, 89, 68] Generated Node #0,0: 71:[50, 89, 68] Operation: 94-26=68 Moving to Node #0,0 Current State: 71:[50, 89, 68], Operations: ['94-26=68'] Exploring Operation: 50+89=139, Resulting Numbers: [68, 139] Generated Node #0,0,1: 71:[68, 139] Operation: 50+89=139 Moving to Node #0,0,1 Current State: 71:[68, 139], Operations: ['94-26=68', '50+89=139'] Exploring Operation: 139-68=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 91, 2, 39, 38 ]
88
[ "91-2=89", "39-38=1", "89-1=88" ]
Current State: 88:[91, 2, 39, 38], Operations: [] Exploring Operation: 91-2=89, Resulting Numbers: [39, 38, 89] Generated Node #2: [39, 38, 89] from Operation: 91-2=89 Current State: 88:[39, 38, 89], Operations: ['91-2=89'] Exploring Operation: 39-38=1, Resulting Numbers: [89, 1] Generated Node #3: [89, 1] from Operation: 39-38=1 Current State: 88:[89, 1], Operations: ['91-2=89', '39-38=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[91, 2, 39, 38], Operations: [] Exploring Operation: 91-2=89, Resulting Numbers: [39, 38, 89] Generated Node #0,0: 88:[39, 38, 89] Operation: 91-2=89 Exploring Operation: 38/2=19, Resulting Numbers: [91, 39, 19] Generated Node #0,1: 88:[91, 39, 19] Operation: 38/2=19 Exploring Operation: 39-38=1, Resulting Numbers: [91, 2, 1] Generated Node #0,2: 88:[91, 2, 1] Operation: 39-38=1 Exploring Operation: 2+39=41, Resulting Numbers: [91, 38, 41] Generated Node #0,3: 88:[91, 38, 41] Operation: 2+39=41 Exploring Operation: 2+38=40, Resulting Numbers: [91, 39, 40] Generated Node #0,4: 88:[91, 39, 40] Operation: 2+38=40 Moving to Node #0,2 Current State: 88:[91, 2, 1], Operations: ['39-38=1'] Exploring Operation: 91-1=90, Resulting Numbers: [2, 90] Generated Node #0,2,0: 88:[2, 90] Operation: 91-1=90 Exploring Operation: 91/1=91, Resulting Numbers: [2, 91] Generated Node #0,2,1: 88:[2, 91] Operation: 91/1=91 Exploring Operation: 91-2=89, Resulting Numbers: [1, 89] Generated Node #0,2,2: 88:[1, 89] Operation: 91-2=89 Exploring Operation: 2*1=2, Resulting Numbers: [91, 2] Generated Node #0,2,3: 88:[91, 2] Operation: 2*1=2 Exploring Operation: 91*1=91, Resulting Numbers: [2, 91] Generated Node #0,2,4: 88:[2, 91] Operation: 91*1=91 Moving to Node #0,1 Current State: 88:[91, 39, 19], Operations: ['38/2=19'] Exploring Operation: 39-19=20, Resulting Numbers: [91, 20] Generated Node #0,1,0: 88:[91, 20] Operation: 39-19=20 Exploring Operation: 91+19=110, Resulting Numbers: [39, 110] Generated Node #0,1,1: 88:[39, 110] Operation: 91+19=110 Exploring Operation: 39+19=58, Resulting Numbers: [91, 58] Generated Node #0,1,2: 88:[91, 58] Operation: 39+19=58 Exploring Operation: 91-19=72, Resulting Numbers: [39, 72] Generated Node #0,1,3: 88:[39, 72] Operation: 91-19=72 Exploring Operation: 91-39=52, Resulting Numbers: [19, 52] Generated Node #0,1,4: 88:[19, 52] Operation: 91-39=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[91, 20], Operations: ['38/2=19', '39-19=20'] Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 91*20=1820, Resulting Numbers: [1820] 1820,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 88:[19, 52], Operations: ['38/2=19', '91-39=52'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,88 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[91, 58], Operations: ['38/2=19', '39+19=58'] Exploring Operation: 91*58=5278, Resulting Numbers: [5278] 5278,88 unequal: No Solution Exploring Operation: 91-58=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 91+58=149, Resulting Numbers: [149] 149,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[39, 72], Operations: ['38/2=19', '91-19=72'] Exploring Operation: 72-39=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 39+72=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 39*72=2808, Resulting Numbers: [2808] 2808,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[39, 110], Operations: ['38/2=19', '91+19=110'] Exploring Operation: 110-39=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 39+110=149, Resulting Numbers: [149] 149,88 unequal: No Solution Exploring Operation: 39*110=4290, Resulting Numbers: [4290] 4290,88 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: 88:[39, 38, 89], Operations: ['91-2=89'] Exploring Operation: 89-39=50, Resulting Numbers: [38, 50] Generated Node #0,0,0: 88:[38, 50] Operation: 89-39=50 Exploring Operation: 89-38=51, Resulting Numbers: [39, 51] Generated Node #0,0,1: 88:[39, 51] Operation: 89-38=51 Exploring Operation: 39+38=77, Resulting Numbers: [89, 77] Generated Node #0,0,2: 88:[89, 77] Operation: 39+38=77 Exploring Operation: 38+89=127, Resulting Numbers: [39, 127] Generated Node #0,0,3: 88:[39, 127] Operation: 38+89=127 Exploring Operation: 39-38=1, Resulting Numbers: [89, 1] Generated Node #0,0,4: 88:[89, 1] Operation: 39-38=1 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 88:[89, 1], Operations: ['91-2=89', '39-38=1'] Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[91, 2, 39, 38], Operations: [] Exploring Operation: 91-2=89, Resulting Numbers: [39, 38, 89] Generated Node #0,0: 88:[39, 38, 89] Operation: 91-2=89 Moving to Node #0,0 Current State: 88:[39, 38, 89], Operations: ['91-2=89'] Exploring Operation: 39-38=1, Resulting Numbers: [89, 1] Generated Node #0,0,4: 88:[89, 1] Operation: 39-38=1 Moving to Node #0,0,4 Current State: 88:[89, 1], Operations: ['91-2=89', '39-38=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 21, 98, 95, 71 ]
78
[ "98-95=3", "21/3=7", "71+7=78" ]
Current State: 78:[21, 98, 95, 71], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [21, 71, 3] Generated Node #2: [21, 71, 3] from Operation: 98-95=3 Current State: 78:[21, 71, 3], Operations: ['98-95=3'] Exploring Operation: 21/3=7, Resulting Numbers: [71, 7] Generated Node #3: [71, 7] from Operation: 21/3=7 Current State: 78:[71, 7], Operations: ['98-95=3', '21/3=7'] Exploring Operation: 71+7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[21, 98, 95, 71], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [21, 71, 3] Generated Node #0,0: 78:[21, 71, 3] Operation: 98-95=3 Exploring Operation: 98-71=27, Resulting Numbers: [21, 95, 27] Generated Node #0,1: 78:[21, 95, 27] Operation: 98-71=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[21, 71, 3], Operations: ['98-95=3'] Exploring Operation: 21+3=24, Resulting Numbers: [71, 24] Generated Node #0,0,0: 78:[71, 24] Operation: 21+3=24 Exploring Operation: 21/3=7, Resulting Numbers: [71, 7] Generated Node #0,0,1: 78:[71, 7] Operation: 21/3=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[71, 7], Operations: ['98-95=3', '21/3=7'] Exploring Operation: 71+7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[21, 98, 95, 71], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [21, 71, 3] Generated Node #0,0: 78:[21, 71, 3] Operation: 98-95=3 Moving to Node #0,0 Current State: 78:[21, 71, 3], Operations: ['98-95=3'] Exploring Operation: 21/3=7, Resulting Numbers: [71, 7] Generated Node #0,0,1: 78:[71, 7] Operation: 21/3=7 Moving to Node #0,0,1 Current State: 78:[71, 7], Operations: ['98-95=3', '21/3=7'] Exploring Operation: 71+7=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 99, 55, 20, 76 ]
12
[ "99-55=44", "76-20=56", "56-44=12" ]
Current State: 12:[99, 55, 20, 76], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [20, 76, 44] Generated Node #2: [20, 76, 44] from Operation: 99-55=44 Current State: 12:[20, 76, 44], Operations: ['99-55=44'] Exploring Operation: 76-20=56, Resulting Numbers: [44, 56] Generated Node #3: [44, 56] from Operation: 76-20=56 Current State: 12:[44, 56], Operations: ['99-55=44', '76-20=56'] Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[99, 55, 20, 76], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [20, 76, 44] Generated Node #0,0: 12:[20, 76, 44] Operation: 99-55=44 Exploring Operation: 99-76=23, Resulting Numbers: [55, 20, 23] Generated Node #0,1: 12:[55, 20, 23] Operation: 99-76=23 Moving to Node #0,1 Current State: 12:[55, 20, 23], Operations: ['99-76=23'] Exploring Operation: 55-20=35, Resulting Numbers: [23, 35] Generated Node #0,1,0: 12:[23, 35] Operation: 55-20=35 Exploring Operation: 55-23=32, Resulting Numbers: [20, 32] Generated Node #0,1,1: 12:[20, 32] Operation: 55-23=32 Moving to Node #0,0 Current State: 12:[20, 76, 44], Operations: ['99-55=44'] Exploring Operation: 76-20=56, Resulting Numbers: [44, 56] Generated Node #0,0,0: 12:[44, 56] Operation: 76-20=56 Exploring Operation: 76-44=32, Resulting Numbers: [20, 32] Generated Node #0,0,1: 12:[20, 32] Operation: 76-44=32 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[20, 32], Operations: ['99-55=44', '76-44=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,12 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[99, 55, 20, 76], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [20, 76, 44] Generated Node #0,0: 12:[20, 76, 44] Operation: 99-55=44 Moving to Node #0,0 Current State: 12:[20, 76, 44], Operations: ['99-55=44'] Exploring Operation: 76-44=32, Resulting Numbers: [20, 32] Generated Node #0,0,1: 12:[20, 32] Operation: 76-44=32 Moving to Node #0,0,1 Current State: 12:[20, 32], Operations: ['99-55=44', '76-44=32'] Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 52, 40, 44, 33 ]
15
[ "52+40=92", "44+33=77", "92-77=15" ]
Current State: 15:[52, 40, 44, 33], Operations: [] Exploring Operation: 52+40=92, Resulting Numbers: [44, 33, 92] Generated Node #2: [44, 33, 92] from Operation: 52+40=92 Current State: 15:[44, 33, 92], Operations: ['52+40=92'] Exploring Operation: 44+33=77, Resulting Numbers: [92, 77] Generated Node #3: [92, 77] from Operation: 44+33=77 Current State: 15:[92, 77], Operations: ['52+40=92', '44+33=77'] Exploring Operation: 92-77=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[52, 40, 44, 33], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [52, 33, 4] Generated Node #0,0: 15:[52, 33, 4] Operation: 44-40=4 Exploring Operation: 52-44=8, Resulting Numbers: [40, 33, 8] Generated Node #0,1: 15:[40, 33, 8] Operation: 52-44=8 Exploring Operation: 52-40=12, Resulting Numbers: [44, 33, 12] Generated Node #0,2: 15:[44, 33, 12] Operation: 52-40=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[40, 33, 8], Operations: ['52-44=8'] Exploring Operation: 40/8=5, Resulting Numbers: [33, 5] Generated Node #0,1,0: 15:[33, 5] Operation: 40/8=5 Exploring Operation: 40-8=32, Resulting Numbers: [33, 32] Generated Node #0,1,1: 15:[33, 32] Operation: 40-8=32 Exploring Operation: 40-33=7, Resulting Numbers: [8, 7] Generated Node #0,1,2: 15:[8, 7] Operation: 40-33=7 Moving to Node #0,1,2 Current State: 15:[8, 7], Operations: ['52-44=8', '40-33=7'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[52, 40, 44, 33], Operations: [] Exploring Operation: 52-44=8, Resulting Numbers: [40, 33, 8] Generated Node #0,1: 15:[40, 33, 8] Operation: 52-44=8 Moving to Node #0,1 Current State: 15:[40, 33, 8], Operations: ['52-44=8'] Exploring Operation: 40-33=7, Resulting Numbers: [8, 7] Generated Node #0,1,2: 15:[8, 7] Operation: 40-33=7 Moving to Node #0,1,2 Current State: 15:[8, 7], Operations: ['52-44=8', '40-33=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 8, 37, 89, 26 ]
34
[ "37-8=29", "89-26=63", "63-29=34" ]
Current State: 34:[8, 37, 89, 26], Operations: [] Exploring Operation: 37-8=29, Resulting Numbers: [89, 26, 29] Generated Node #2: [89, 26, 29] from Operation: 37-8=29 Current State: 34:[89, 26, 29], Operations: ['37-8=29'] Exploring Operation: 89-26=63, Resulting Numbers: [29, 63] Generated Node #3: [29, 63] from Operation: 89-26=63 Current State: 34:[29, 63], Operations: ['37-8=29', '89-26=63'] Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[8, 37, 89, 26], Operations: [] Exploring Operation: 89-37=52, Resulting Numbers: [8, 26, 52] Generated Node #0,0: 34:[8, 26, 52] Operation: 89-37=52 Moving to Node #0,0 Current State: 34:[8, 26, 52], Operations: ['89-37=52'] Exploring Operation: 52/26=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 34:[8, 2] Operation: 52/26=2 Moving to Node #0,0,0 Current State: 34:[8, 2], Operations: ['89-37=52', '52/26=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,34 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 38, 42, 72, 93 ]
40
[ "93-72=21", "42/21=2", "38+2=40" ]
Current State: 40:[38, 42, 72, 93], Operations: [] Exploring Operation: 93-72=21, Resulting Numbers: [38, 42, 21] Generated Node #2: [38, 42, 21] from Operation: 93-72=21 Current State: 40:[38, 42, 21], Operations: ['93-72=21'] Exploring Operation: 42/21=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 42/21=2 Current State: 40:[38, 2], Operations: ['93-72=21', '42/21=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[38, 42, 72, 93], Operations: [] Exploring Operation: 93-42=51, Resulting Numbers: [38, 72, 51] Generated Node #0,0: 40:[38, 72, 51] Operation: 93-42=51 Exploring Operation: 93-72=21, Resulting Numbers: [38, 42, 21] Generated Node #0,1: 40:[38, 42, 21] Operation: 93-72=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[38, 42, 21], Operations: ['93-72=21'] Exploring Operation: 42-38=4, Resulting Numbers: [21, 4] Generated Node #0,1,0: 40:[21, 4] Operation: 42-38=4 Exploring Operation: 42/21=2, Resulting Numbers: [38, 2] Generated Node #0,1,1: 40:[38, 2] Operation: 42/21=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[21, 4], Operations: ['93-72=21', '42-38=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,40 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,40 unequal: No Solution No 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: 40:[38, 2], Operations: ['93-72=21', '42/21=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,40 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[38, 42, 72, 93], Operations: [] Exploring Operation: 93-72=21, Resulting Numbers: [38, 42, 21] Generated Node #0,1: 40:[38, 42, 21] Operation: 93-72=21 Moving to Node #0,1 Current State: 40:[38, 42, 21], Operations: ['93-72=21'] Exploring Operation: 42/21=2, Resulting Numbers: [38, 2] Generated Node #0,1,1: 40:[38, 2] Operation: 42/21=2 Moving to Node #0,1,1 Current State: 40:[38, 2], Operations: ['93-72=21', '42/21=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 52, 19, 68, 15 ]
26
[ "19+15=34", "52*34=1768", "1768/68=26" ]
Current State: 26:[52, 19, 68, 15], Operations: [] Exploring Operation: 19+15=34, Resulting Numbers: [52, 68, 34] Generated Node #2: [52, 68, 34] from Operation: 19+15=34 Current State: 26:[52, 68, 34], Operations: ['19+15=34'] Exploring Operation: 52*34=1768, Resulting Numbers: [68, 1768] Generated Node #3: [68, 1768] from Operation: 52*34=1768 Current State: 26:[68, 1768], Operations: ['19+15=34', '52*34=1768'] Exploring Operation: 1768/68=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[52, 19, 68, 15], Operations: [] Exploring Operation: 52-19=33, Resulting Numbers: [68, 15, 33] Generated Node #0,0: 26:[68, 15, 33] Operation: 52-19=33 Exploring Operation: 68-52=16, Resulting Numbers: [19, 15, 16] Generated Node #0,1: 26:[19, 15, 16] Operation: 68-52=16 Exploring Operation: 68-19=49, Resulting Numbers: [52, 15, 49] Generated Node #0,2: 26:[52, 15, 49] Operation: 68-19=49 Moving to Node #0,1 Current State: 26:[19, 15, 16], Operations: ['68-52=16'] Exploring Operation: 19-15=4, Resulting Numbers: [16, 4] Generated Node #0,1,0: 26:[16, 4] Operation: 19-15=4 Exploring Operation: 16-15=1, Resulting Numbers: [19, 1] Generated Node #0,1,1: 26:[19, 1] Operation: 16-15=1 Exploring Operation: 19-16=3, Resulting Numbers: [15, 3] Generated Node #0,1,2: 26:[15, 3] Operation: 19-16=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[15, 3], Operations: ['68-52=16', '19-16=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[16, 4], Operations: ['68-52=16', '19-15=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[19, 1], Operations: ['68-52=16', '16-15=1'] Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 26:[68, 15, 33], Operations: ['52-19=33'] Exploring Operation: 68-15=53, Resulting Numbers: [33, 53] Generated Node #0,0,0: 26:[33, 53] Operation: 68-15=53 Exploring Operation: 33-15=18, Resulting Numbers: [68, 18] Generated Node #0,0,1: 26:[68, 18] Operation: 33-15=18 Exploring Operation: 68-33=35, Resulting Numbers: [15, 35] Generated Node #0,0,2: 26:[15, 35] Operation: 68-33=35 Moving to Node #0,2 Current State: 26:[52, 15, 49], Operations: ['68-19=49'] Exploring Operation: 52-49=3, Resulting Numbers: [15, 3] Generated Node #0,2,0: 26:[15, 3] Operation: 52-49=3 Exploring Operation: 52-15=37, Resulting Numbers: [49, 37] Generated Node #0,2,1: 26:[49, 37] Operation: 52-15=37 Exploring Operation: 49-15=34, Resulting Numbers: [52, 34] Generated Node #0,2,2: 26:[52, 34] Operation: 49-15=34 Moving to Node #0,2,0 Current State: 26:[15, 3], Operations: ['68-19=49', '52-49=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[15, 35], Operations: ['52-19=33', '68-33=35'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[52, 34], Operations: ['68-19=49', '49-15=34'] Exploring Operation: 52*34=1768, Resulting Numbers: [1768] 1768,26 unequal: No Solution Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 52+34=86, Resulting Numbers: [86] 86,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[49, 37], Operations: ['68-19=49', '52-15=37'] Exploring Operation: 49*37=1813, Resulting Numbers: [1813] 1813,26 unequal: No Solution Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,26 unequal: No Solution Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[33, 53], Operations: ['52-19=33', '68-15=53'] Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,26 unequal: No Solution Exploring Operation: 33*53=1749, Resulting Numbers: [1749] 1749,26 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[68, 18], Operations: ['52-19=33', '33-15=18'] Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 68*18=1224, Resulting Numbers: [1224] 1224,26 unequal: No Solution Exploring Operation: 68+18=86, Resulting Numbers: [86] 86,26 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 22, 42, 42, 26 ]
88
[ "42-22=20", "42+26=68", "20+68=88" ]
Current State: 88:[22, 42, 42, 26], Operations: [] Exploring Operation: 42-22=20, Resulting Numbers: [26, 20] Generated Node #2: [26, 20] from Operation: 42-22=20 Current State: 88:[26, 20], Operations: ['42-22=20'] Exploring Operation: 42+26=68, Resulting Numbers: [20, 68] Generated Node #3: [20, 68] from Operation: 42+26=68 Current State: 88:[20, 68], Operations: ['42-22=20', '42+26=68'] Exploring Operation: 20+68=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[22, 42, 42, 26], Operations: [] Exploring Operation: 42-42=0, Resulting Numbers: [22, 26, 0] Generated Node #0,0: 88:[22, 26, 0] Operation: 42-42=0 Exploring Operation: 42-26=16, Resulting Numbers: [22, 42, 16] Generated Node #0,1: 88:[22, 42, 16] Operation: 42-26=16 Exploring Operation: 26-22=4, Resulting Numbers: [42, 42, 4] Generated Node #0,2: 88:[42, 42, 4] Operation: 26-22=4 Exploring Operation: 42/42=1, Resulting Numbers: [22, 26, 1] Generated Node #0,3: 88:[22, 26, 1] Operation: 42/42=1 Moving to Node #0,2 Current State: 88:[42, 42, 4], Operations: ['26-22=4'] Exploring Operation: 42+4=46, Resulting Numbers: [42, 46] Generated Node #0,2,0: 88:[42, 46] Operation: 42+4=46 Exploring Operation: 42-42=0, Resulting Numbers: [4, 0] Generated Node #0,2,1: 88:[4, 0] Operation: 42-42=0 Exploring Operation: 42+42=84, Resulting Numbers: [4, 84] Generated Node #0,2,2: 88:[4, 84] Operation: 42+42=84 Exploring Operation: 42/42=1, Resulting Numbers: [4, 1] Generated Node #0,2,3: 88:[4, 1] Operation: 42/42=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[4, 1], Operations: ['26-22=4', '42/42=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[4, 0], Operations: ['26-22=4', '42-42=0'] Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,88 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[42, 46], Operations: ['26-22=4', '42+4=46'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[22, 42, 42, 26], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [42, 42, 4] Generated Node #0,2: 88:[42, 42, 4] Operation: 26-22=4 Moving to Node #0,2 Current State: 88:[42, 42, 4], Operations: ['26-22=4'] Exploring Operation: 42+4=46, Resulting Numbers: [42, 46] Generated Node #0,2,0: 88:[42, 46] Operation: 42+4=46 Moving to Node #0,2,0 Current State: 88:[42, 46], Operations: ['26-22=4', '42+4=46'] Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 48, 12, 2, 89 ]
77
[ "48/2=24", "12+89=101", "101-24=77" ]
Current State: 77:[48, 12, 2, 89], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [12, 89, 24] Generated Node #2: [12, 89, 24] from Operation: 48/2=24 Current State: 77:[12, 89, 24], Operations: ['48/2=24'] Exploring Operation: 12+89=101, Resulting Numbers: [24, 101] Generated Node #3: [24, 101] from Operation: 12+89=101 Current State: 77:[24, 101], Operations: ['48/2=24', '12+89=101'] Exploring Operation: 101-24=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[48, 12, 2, 89], Operations: [] Exploring Operation: 89-12=77, Resulting Numbers: [48, 2, 77] Generated Node #0,0: 77:[48, 2, 77] Operation: 89-12=77 Exploring Operation: 48+12=60, Resulting Numbers: [2, 89, 60] Generated Node #0,1: 77:[2, 89, 60] Operation: 48+12=60 Exploring Operation: 48/12=4, Resulting Numbers: [2, 89, 4] Generated Node #0,2: 77:[2, 89, 4] Operation: 48/12=4 Exploring Operation: 48/2=24, Resulting Numbers: [12, 89, 24] Generated Node #0,3: 77:[12, 89, 24] Operation: 48/2=24 Exploring Operation: 48*2=96, Resulting Numbers: [12, 89, 96] Generated Node #0,4: 77:[12, 89, 96] Operation: 48*2=96 Moving to Node #0,2 Current State: 77:[2, 89, 4], Operations: ['48/12=4'] Exploring Operation: 2+4=6, Resulting Numbers: [89, 6] Generated Node #0,2,0: 77:[89, 6] Operation: 2+4=6 Exploring Operation: 2+89=91, Resulting Numbers: [4, 91] Generated Node #0,2,1: 77:[4, 91] Operation: 2+89=91 Exploring Operation: 2*4=8, Resulting Numbers: [89, 8] Generated Node #0,2,2: 77:[89, 8] Operation: 2*4=8 Exploring Operation: 89-2=87, Resulting Numbers: [4, 87] Generated Node #0,2,3: 77:[4, 87] Operation: 89-2=87 Exploring Operation: 89-4=85, Resulting Numbers: [2, 85] Generated Node #0,2,4: 77:[2, 85] Operation: 89-4=85 Moving to Node #0,3 Current State: 77:[12, 89, 24], Operations: ['48/2=24'] Exploring Operation: 24-12=12, Resulting Numbers: [89, 12] Generated Node #0,3,0: 77:[89, 12] Operation: 24-12=12 Exploring Operation: 89-12=77, Resulting Numbers: [24, 77] Generated Node #0,3,1: 77:[24, 77] Operation: 89-12=77 Exploring Operation: 12+89=101, Resulting Numbers: [24, 101] Generated Node #0,3,2: 77:[24, 101] Operation: 12+89=101 Exploring Operation: 24/12=2, Resulting Numbers: [89, 2] Generated Node #0,3,3: 77:[89, 2] Operation: 24/12=2 Exploring Operation: 89-24=65, Resulting Numbers: [12, 65] Generated Node #0,3,4: 77:[12, 65] Operation: 89-24=65 Moving to Node #0,4 Current State: 77:[12, 89, 96], Operations: ['48*2=96'] Exploring Operation: 12+89=101, Resulting Numbers: [96, 101] Generated Node #0,4,0: 77:[96, 101] Operation: 12+89=101 Exploring Operation: 96-12=84, Resulting Numbers: [89, 84] Generated Node #0,4,1: 77:[89, 84] Operation: 96-12=84 Exploring Operation: 96/12=8, Resulting Numbers: [89, 8] Generated Node #0,4,2: 77:[89, 8] Operation: 96/12=8 Exploring Operation: 89-12=77, Resulting Numbers: [96, 77] Generated Node #0,4,3: 77:[96, 77] Operation: 89-12=77 Exploring Operation: 96-89=7, Resulting Numbers: [12, 7] Generated Node #0,4,4: 77:[12, 7] Operation: 96-89=7 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 77:[12, 7], Operations: ['48*2=96', '96-89=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 77:[89, 8], Operations: ['48*2=96', '96/12=8'] Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,77 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 77:[89, 84], Operations: ['48*2=96', '96-12=84'] Exploring Operation: 89-84=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 89*84=7476, Resulting Numbers: [7476] 7476,77 unequal: No Solution Exploring Operation: 89+84=173, Resulting Numbers: [173] 173,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 77:[96, 77], Operations: ['48*2=96', '89-12=77'] Exploring Operation: 96-77=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 96+77=173, Resulting Numbers: [173] 173,77 unequal: No Solution Exploring Operation: 96*77=7392, Resulting Numbers: [7392] 7392,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 77:[96, 101], Operations: ['48*2=96', '12+89=101'] Exploring Operation: 101-96=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 96+101=197, Resulting Numbers: [197] 197,77 unequal: No Solution Exploring Operation: 96*101=9696, Resulting Numbers: [9696] 9696,77 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: 77:[48, 2, 77], Operations: ['89-12=77'] Exploring Operation: 48*2=96, Resulting Numbers: [77, 96] Generated Node #0,0,0: 77:[77, 96] Operation: 48*2=96 Exploring Operation: 48/2=24, Resulting Numbers: [77, 24] Generated Node #0,0,1: 77:[77, 24] Operation: 48/2=24 Exploring Operation: 48+2=50, Resulting Numbers: [77, 50] Generated Node #0,0,2: 77:[77, 50] Operation: 48+2=50 Exploring Operation: 77-48=29, Resulting Numbers: [2, 29] Generated Node #0,0,3: 77:[2, 29] Operation: 77-48=29 Exploring Operation: 48-2=46, Resulting Numbers: [77, 46] Generated Node #0,0,4: 77:[77, 46] Operation: 48-2=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[77, 24], Operations: ['89-12=77', '48/2=24'] Exploring Operation: 77*24=1848, Resulting Numbers: [1848] 1848,77 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,77 unequal: No Solution Exploring Operation: 77+24=101, Resulting Numbers: [101] 101,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[77, 96], Operations: ['89-12=77', '48*2=96'] Exploring Operation: 77+96=173, Resulting Numbers: [173] 173,77 unequal: No Solution Exploring Operation: 96-77=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 77*96=7392, Resulting Numbers: [7392] 7392,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[2, 29], Operations: ['89-12=77', '77-48=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 77:[77, 50], Operations: ['89-12=77', '48+2=50'] Exploring Operation: 77-50=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 77+50=127, Resulting Numbers: [127] 127,77 unequal: No Solution Exploring Operation: 77*50=3850, Resulting Numbers: [3850] 3850,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 77:[77, 46], Operations: ['89-12=77', '48-2=46'] Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,77 unequal: No Solution Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,77 unequal: No Solution Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,77 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: 77:[2, 89, 60], Operations: ['48+12=60'] Exploring Operation: 2+89=91, Resulting Numbers: [60, 91] Generated Node #0,1,0: 77:[60, 91] Operation: 2+89=91 Exploring Operation: 2+60=62, Resulting Numbers: [89, 62] Generated Node #0,1,1: 77:[89, 62] Operation: 2+60=62 Exploring Operation: 89-60=29, Resulting Numbers: [2, 29] Generated Node #0,1,2: 77:[2, 29] Operation: 89-60=29 Exploring Operation: 89-2=87, Resulting Numbers: [60, 87] Generated Node #0,1,3: 77:[60, 87] Operation: 89-2=87 Exploring Operation: 60-2=58, Resulting Numbers: [89, 58] Generated Node #0,1,4: 77:[89, 58] Operation: 60-2=58 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[2, 29], Operations: ['48+12=60', '89-60=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[89, 62], Operations: ['48+12=60', '2+60=62'] Exploring Operation: 89-62=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 89*62=5518, Resulting Numbers: [5518] 5518,77 unequal: No Solution Exploring Operation: 89+62=151, Resulting Numbers: [151] 151,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 77:[60, 87], Operations: ['48+12=60', '89-2=87'] Exploring Operation: 60+87=147, Resulting Numbers: [147] 147,77 unequal: No Solution Exploring Operation: 60*87=5220, Resulting Numbers: [5220] 5220,77 unequal: No Solution Exploring Operation: 87-60=27, Resulting Numbers: [27] 27,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[60, 91], Operations: ['48+12=60', '2+89=91'] Exploring Operation: 60+91=151, Resulting Numbers: [151] 151,77 unequal: No Solution Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,77 unequal: No Solution Exploring Operation: 60*91=5460, Resulting Numbers: [5460] 5460,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 77:[89, 58], Operations: ['48+12=60', '60-2=58'] Exploring Operation: 89-58=31, Resulting Numbers: [31] 31,77 unequal: No Solution Exploring Operation: 89*58=5162, Resulting Numbers: [5162] 5162,77 unequal: No Solution Exploring Operation: 89+58=147, Resulting Numbers: [147] 147,77 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: 77:[89, 6], Operations: ['48/12=4', '2+4=6'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,77 unequal: No Solution Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,77 unequal: No Solution Exploring Operation: 89*6=534, Resulting Numbers: [534] 534,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[4, 87], Operations: ['48/12=4', '89-2=87'] Exploring Operation: 4+87=91, Resulting Numbers: [91] 91,77 unequal: No Solution Exploring Operation: 4*87=348, Resulting Numbers: [348] 348,77 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[24, 77], Operations: ['48/2=24', '89-12=77'] Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,77 unequal: No Solution Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,77 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[89, 12], Operations: ['48/2=24', '24-12=12'] Exploring Operation: 89*12=1068, Resulting Numbers: [1068] 1068,77 unequal: No Solution Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[48, 12, 2, 89], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [12, 89, 24] Generated Node #0,3: 77:[12, 89, 24] Operation: 48/2=24 Moving to Node #0,3 Current State: 77:[12, 89, 24], Operations: ['48/2=24'] Exploring Operation: 24-12=12, Resulting Numbers: [89, 12] Generated Node #0,3,0: 77:[89, 12] Operation: 24-12=12 Moving to Node #0,3,0 Current State: 77:[89, 12], Operations: ['48/2=24', '24-12=12'] Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.921875
hs_5
sum_heuristic
[ 30, 40, 28, 10 ]
60
[ "30-28=2", "40-10=30", "2*30=60" ]
Current State: 60:[30, 40, 28, 10], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [40, 10, 2] Generated Node #2: [40, 10, 2] from Operation: 30-28=2 Current State: 60:[40, 10, 2], Operations: ['30-28=2'] Exploring Operation: 40-10=30, Resulting Numbers: [2, 30] Generated Node #3: [2, 30] from Operation: 40-10=30 Current State: 60:[2, 30], Operations: ['30-28=2', '40-10=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[30, 40, 28, 10], Operations: [] Exploring Operation: 40-28=12, Resulting Numbers: [30, 10, 12] Generated Node #0,0: 60:[30, 10, 12] Operation: 40-28=12 Exploring Operation: 40-30=10, Resulting Numbers: [28, 10, 10] Generated Node #0,1: 60:[28, 10, 10] Operation: 40-30=10 Moving to Node #0,0 Current State: 60:[30, 10, 12], Operations: ['40-28=12'] Exploring Operation: 30/10=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 60:[12, 3] Operation: 30/10=3 Exploring Operation: 30-10=20, Resulting Numbers: [12, 20] Generated Node #0,0,1: 60:[12, 20] Operation: 30-10=20 Moving to Node #0,1 Current State: 60:[28, 10, 10], Operations: ['40-30=10'] Exploring Operation: 28-10=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 60:[10, 18] Operation: 28-10=18 Exploring Operation: 28-10=18, Resulting Numbers: [10, 18] Generated Node #0,1,1: 60:[10, 18] Operation: 28-10=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[10, 18], Operations: ['40-30=10', '28-10=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,60 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,60 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:[10, 18], Operations: ['40-30=10', '28-10=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,60 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,60 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: 60:[12, 3], Operations: ['40-28=12', '30/10=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[12, 20], Operations: ['40-28=12', '30-10=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,60 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 35, 79, 2, 41 ]
82
[ "35+41=76", "79*2=158", "158-76=82" ]
Current State: 82:[35, 79, 2, 41], Operations: [] Exploring Operation: 35+41=76, Resulting Numbers: [79, 2, 76] Generated Node #2: [79, 2, 76] from Operation: 35+41=76 Current State: 82:[79, 2, 76], Operations: ['35+41=76'] Exploring Operation: 79*2=158, Resulting Numbers: [76, 158] Generated Node #3: [76, 158] from Operation: 79*2=158 Current State: 82:[76, 158], Operations: ['35+41=76', '79*2=158'] Exploring Operation: 158-76=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[35, 79, 2, 41], Operations: [] Exploring Operation: 79-35=44, Resulting Numbers: [2, 41, 44] Generated Node #0,0: 82:[2, 41, 44] Operation: 79-35=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[2, 41, 44], Operations: ['79-35=44'] Exploring Operation: 44-2=42, Resulting Numbers: [41, 42] Generated Node #0,0,0: 82:[41, 42] Operation: 44-2=42 Moving to Node #0,0,0 Current State: 82:[41, 42], Operations: ['79-35=44', '44-2=42'] Exploring Operation: 41+42=83, Resulting Numbers: [83] 83,82 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
[ 58, 68, 3, 59 ]
23
[ "68-58=10", "59+10=69", "69/3=23" ]
Current State: 23:[58, 68, 3, 59], Operations: [] Exploring Operation: 68-58=10, Resulting Numbers: [3, 59, 10] Generated Node #2: [3, 59, 10] from Operation: 68-58=10 Current State: 23:[3, 59, 10], Operations: ['68-58=10'] Exploring Operation: 59+10=69, Resulting Numbers: [3, 69] Generated Node #3: [3, 69] from Operation: 59+10=69 Current State: 23:[3, 69], Operations: ['68-58=10', '59+10=69'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[58, 68, 3, 59], Operations: [] Exploring Operation: 68-58=10, Resulting Numbers: [3, 59, 10] Generated Node #0,0: 23:[3, 59, 10] Operation: 68-58=10 Exploring Operation: 68-59=9, Resulting Numbers: [58, 3, 9] Generated Node #0,1: 23:[58, 3, 9] Operation: 68-59=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[3, 59, 10], Operations: ['68-58=10'] Exploring Operation: 3*10=30, Resulting Numbers: [59, 30] Generated Node #0,0,0: 23:[59, 30] Operation: 3*10=30 Exploring Operation: 59-3=56, Resulting Numbers: [10, 56] Generated Node #0,0,1: 23:[10, 56] Operation: 59-3=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[59, 30], Operations: ['68-58=10', '3*10=30'] Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 59+30=89, Resulting Numbers: [89] 89,23 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 #0,0,1 Current State: 23:[10, 56], Operations: ['68-58=10', '59-3=56'] Exploring Operation: 10+56=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,23 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 #0,1 Current State: 23:[58, 3, 9], Operations: ['68-59=9'] Exploring Operation: 3*9=27, Resulting Numbers: [58, 27] Generated Node #0,1,0: 23:[58, 27] Operation: 3*9=27 Exploring Operation: 58-3=55, Resulting Numbers: [9, 55] Generated Node #0,1,1: 23:[9, 55] Operation: 58-3=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[58, 27], Operations: ['68-59=9', '3*9=27'] Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 58+27=85, Resulting Numbers: [85] 85,23 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:[9, 55], Operations: ['68-59=9', '58-3=55'] Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 9+55=64, Resulting Numbers: [64] 64,23 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 No solution found.
0
hs_2
mult_heuristic
[ 15, 40, 46, 6 ]
65
[ "40-15=25", "46-6=40", "25+40=65" ]
Current State: 65:[15, 40, 46, 6], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [46, 6, 25] Generated Node #2: [46, 6, 25] from Operation: 40-15=25 Current State: 65:[46, 6, 25], Operations: ['40-15=25'] Exploring Operation: 46-6=40, Resulting Numbers: [25, 40] Generated Node #3: [25, 40] from Operation: 46-6=40 Current State: 65:[25, 40], Operations: ['40-15=25', '46-6=40'] Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[15, 40, 46, 6], Operations: [] Exploring Operation: 40+46=86, Resulting Numbers: [15, 6, 86] Generated Node #0,0: 65:[15, 6, 86] Operation: 40+46=86 Exploring Operation: 15+40=55, Resulting Numbers: [46, 6, 55] Generated Node #0,1: 65:[46, 6, 55] Operation: 15+40=55 Exploring Operation: 46-40=6, Resulting Numbers: [15, 6, 6] Generated Node #0,2: 65:[15, 6, 6] Operation: 46-40=6 Moving to Node #0,2 Current State: 65:[15, 6, 6], Operations: ['46-40=6'] Exploring Operation: 15-6=9, Resulting Numbers: [6, 9] Generated Node #0,2,0: 65:[6, 9] Operation: 15-6=9 Exploring Operation: 6+6=12, Resulting Numbers: [15, 12] Generated Node #0,2,1: 65:[15, 12] Operation: 6+6=12 Exploring Operation: 15-6=9, Resulting Numbers: [6, 9] Generated Node #0,2,2: 65:[6, 9] Operation: 15-6=9 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[15, 12], Operations: ['46-40=6', '6+6=12'] Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,65 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[6, 9], Operations: ['46-40=6', '15-6=9'] Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[6, 9], Operations: ['46-40=6', '15-6=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,65 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: 65:[15, 6, 86], Operations: ['40+46=86'] Exploring Operation: 86-15=71, Resulting Numbers: [6, 71] Generated Node #0,0,0: 65:[6, 71] Operation: 86-15=71 Exploring Operation: 86-6=80, Resulting Numbers: [15, 80] Generated Node #0,0,1: 65:[15, 80] Operation: 86-6=80 Exploring Operation: 15-6=9, Resulting Numbers: [86, 9] Generated Node #0,0,2: 65:[86, 9] Operation: 15-6=9 Moving to Node #0,1 Current State: 65:[46, 6, 55], Operations: ['15+40=55'] Exploring Operation: 6+55=61, Resulting Numbers: [46, 61] Generated Node #0,1,0: 65:[46, 61] Operation: 6+55=61 Exploring Operation: 46+6=52, Resulting Numbers: [55, 52] Generated Node #0,1,1: 65:[55, 52] Operation: 46+6=52 Exploring Operation: 55-46=9, Resulting Numbers: [6, 9] Generated Node #0,1,2: 65:[6, 9] Operation: 55-46=9 Moving to Node #0,1,2 Current State: 65:[6, 9], Operations: ['15+40=55', '55-46=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,65 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[6, 71], Operations: ['40+46=86', '86-15=71'] Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,65 unequal: No Solution Exploring Operation: 6*71=426, Resulting Numbers: [426] 426,65 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[15, 40, 46, 6], Operations: [] Exploring Operation: 40+46=86, Resulting Numbers: [15, 6, 86] Generated Node #0,0: 65:[15, 6, 86] Operation: 40+46=86 Moving to Node #0,0 Current State: 65:[15, 6, 86], Operations: ['40+46=86'] Exploring Operation: 86-15=71, Resulting Numbers: [6, 71] Generated Node #0,0,0: 65:[6, 71] Operation: 86-15=71 Moving to Node #0,0,0 Current State: 65:[6, 71], Operations: ['40+46=86', '86-15=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.97309
hs_3
sum_heuristic
[ 35, 9, 45, 67 ]
48
[ "35-9=26", "67-45=22", "26+22=48" ]
Current State: 48:[35, 9, 45, 67], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [45, 67, 26] Generated Node #2: [45, 67, 26] from Operation: 35-9=26 Current State: 48:[45, 67, 26], Operations: ['35-9=26'] Exploring Operation: 67-45=22, Resulting Numbers: [26, 22] Generated Node #3: [26, 22] from Operation: 67-45=22 Current State: 48:[26, 22], Operations: ['35-9=26', '67-45=22'] Exploring Operation: 26+22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[35, 9, 45, 67], Operations: [] Exploring Operation: 67-45=22, Resulting Numbers: [35, 9, 22] Generated Node #0,0: 48:[35, 9, 22] Operation: 67-45=22 Exploring Operation: 67-35=32, Resulting Numbers: [9, 45, 32] Generated Node #0,1: 48:[9, 45, 32] Operation: 67-35=32 Exploring Operation: 45-35=10, Resulting Numbers: [9, 67, 10] Generated Node #0,2: 48:[9, 67, 10] Operation: 45-35=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[9, 45, 32], Operations: ['67-35=32'] Exploring Operation: 45/9=5, Resulting Numbers: [32, 5] Generated Node #0,1,0: 48:[32, 5] Operation: 45/9=5 Exploring Operation: 32-9=23, Resulting Numbers: [45, 23] Generated Node #0,1,1: 48:[45, 23] Operation: 32-9=23 Exploring Operation: 45-32=13, Resulting Numbers: [9, 13] Generated Node #0,1,2: 48:[9, 13] Operation: 45-32=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[9, 13], Operations: ['67-35=32', '45-32=13'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,48 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[45, 23], Operations: ['67-35=32', '32-9=23'] Exploring Operation: 45+23=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 45*23=1035, Resulting Numbers: [1035] 1035,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[32, 5], Operations: ['67-35=32', '45/9=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,48 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[35, 9, 22], Operations: ['67-45=22'] Exploring Operation: 35-22=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 48:[9, 13] Operation: 35-22=13 Exploring Operation: 35-9=26, Resulting Numbers: [22, 26] Generated Node #0,0,1: 48:[22, 26] Operation: 35-9=26 Exploring Operation: 35+9=44, Resulting Numbers: [22, 44] Generated Node #0,0,2: 48:[22, 44] Operation: 35+9=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[9, 13], Operations: ['67-45=22', '35-22=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,48 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[22, 26], Operations: ['67-45=22', '35-9=26'] Exploring Operation: 22*26=572, Resulting Numbers: [572] 572,48 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[35, 9, 45, 67], Operations: [] Exploring Operation: 67-45=22, Resulting Numbers: [35, 9, 22] Generated Node #0,0: 48:[35, 9, 22] Operation: 67-45=22 Moving to Node #0,0 Current State: 48:[35, 9, 22], Operations: ['67-45=22'] Exploring Operation: 35-9=26, Resulting Numbers: [22, 26] Generated Node #0,0,1: 48:[22, 26] Operation: 35-9=26 Moving to Node #0,0,1 Current State: 48:[22, 26], Operations: ['67-45=22', '35-9=26'] Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 78, 22, 84, 21 ]
77
[ "84-78=6", "22*21=462", "462/6=77" ]
Current State: 77:[78, 22, 84, 21], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [22, 21, 6] Generated Node #2: [22, 21, 6] from Operation: 84-78=6 Current State: 77:[22, 21, 6], Operations: ['84-78=6'] Exploring Operation: 22*21=462, Resulting Numbers: [6, 462] Generated Node #3: [6, 462] from Operation: 22*21=462 Current State: 77:[6, 462], Operations: ['84-78=6', '22*21=462'] Exploring Operation: 462/6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[78, 22, 84, 21], Operations: [] Exploring Operation: 22-21=1, Resulting Numbers: [78, 84, 1] Generated Node #0,0: 77:[78, 84, 1] Operation: 22-21=1 Exploring Operation: 84-78=6, Resulting Numbers: [22, 21, 6] Generated Node #0,1: 77:[22, 21, 6] Operation: 84-78=6 Exploring Operation: 84/21=4, Resulting Numbers: [78, 22, 4] Generated Node #0,2: 77:[78, 22, 4] Operation: 84/21=4 Exploring Operation: 84-22=62, Resulting Numbers: [78, 21, 62] Generated Node #0,3: 77:[78, 21, 62] Operation: 84-22=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[78, 84, 1], Operations: ['22-21=1'] Exploring Operation: 84-1=83, Resulting Numbers: [78, 83] Generated Node #0,0,0: 77:[78, 83] Operation: 84-1=83 Exploring Operation: 78-1=77, Resulting Numbers: [84, 77] Generated Node #0,0,1: 77:[84, 77] Operation: 78-1=77 Exploring Operation: 84-78=6, Resulting Numbers: [1, 6] Generated Node #0,0,2: 77:[1, 6] Operation: 84-78=6 Exploring Operation: 78*1=78, Resulting Numbers: [84, 78] Generated Node #0,0,3: 77:[84, 78] Operation: 78*1=78 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[78, 83], Operations: ['22-21=1', '84-1=83'] Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,77 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[84, 77], Operations: ['22-21=1', '78-1=77'] Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,77 unequal: No Solution Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,77 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[1, 6], Operations: ['22-21=1', '84-78=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 77:[84, 78], Operations: ['22-21=1', '78*1=78'] Exploring Operation: 84-78=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 84+78=162, Resulting Numbers: [162] 162,77 unequal: No Solution Exploring Operation: 84*78=6552, Resulting Numbers: [6552] 6552,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[78, 22, 4], Operations: ['84/21=4'] Exploring Operation: 78-4=74, Resulting Numbers: [22, 74] Generated Node #0,2,0: 77:[22, 74] Operation: 78-4=74 Exploring Operation: 22*4=88, Resulting Numbers: [78, 88] Generated Node #0,2,1: 77:[78, 88] Operation: 22*4=88 Exploring Operation: 78+4=82, Resulting Numbers: [22, 82] Generated Node #0,2,2: 77:[22, 82] Operation: 78+4=82 Exploring Operation: 22-4=18, Resulting Numbers: [78, 18] Generated Node #0,2,3: 77:[78, 18] Operation: 22-4=18 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 77:[78, 18], Operations: ['84/21=4', '22-4=18'] Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,77 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[78, 88], Operations: ['84/21=4', '22*4=88'] Exploring Operation: 78*88=6864, Resulting Numbers: [6864] 6864,77 unequal: No Solution Exploring Operation: 78+88=166, Resulting Numbers: [166] 166,77 unequal: No Solution Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[22, 74], Operations: ['84/21=4', '78-4=74'] Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,77 unequal: No Solution Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[22, 82], Operations: ['84/21=4', '78+4=82'] Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,77 unequal: No Solution Exploring Operation: 22+82=104, Resulting Numbers: [104] 104,77 unequal: No Solution Exploring Operation: 22*82=1804, Resulting Numbers: [1804] 1804,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[22, 21, 6], Operations: ['84-78=6'] Exploring Operation: 22-6=16, Resulting Numbers: [21, 16] Generated Node #0,1,0: 77:[21, 16] Operation: 22-6=16 Exploring Operation: 22+6=28, Resulting Numbers: [21, 28] Generated Node #0,1,1: 77:[21, 28] Operation: 22+6=28 Exploring Operation: 21-6=15, Resulting Numbers: [22, 15] Generated Node #0,1,2: 77:[22, 15] Operation: 21-6=15 Exploring Operation: 22-21=1, Resulting Numbers: [6, 1] Generated Node #0,1,3: 77:[6, 1] Operation: 22-21=1 Moving to Node #0,1,3 Current State: 77:[6, 1], Operations: ['84-78=6', '22-21=1'] Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[22, 15], Operations: ['84-78=6', '21-6=15'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,77 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[21, 16], Operations: ['84-78=6', '22-6=16'] Exploring Operation: 21+16=37, Resulting Numbers: [37] 37,77 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 21*16=336, Resulting Numbers: [336] 336,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[21, 28], Operations: ['84-78=6', '22+6=28'] Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,77 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[78, 21, 62], Operations: ['84-22=62'] Exploring Operation: 78-21=57, Resulting Numbers: [62, 57] Generated Node #0,3,0: 77:[62, 57] Operation: 78-21=57 Exploring Operation: 78-62=16, Resulting Numbers: [21, 16] Generated Node #0,3,1: 77:[21, 16] Operation: 78-62=16 Exploring Operation: 62-21=41, Resulting Numbers: [78, 41] Generated Node #0,3,2: 77:[78, 41] Operation: 62-21=41 Exploring Operation: 21+62=83, Resulting Numbers: [78, 83] Generated Node #0,3,3: 77:[78, 83] Operation: 21+62=83 Moving to Node #0,3,3 Current State: 77:[78, 83], Operations: ['84-22=62', '21+62=83'] Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,77 unequal: No Solution Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,77 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[21, 16], Operations: ['84-22=62', '78-62=16'] Exploring Operation: 21+16=37, Resulting Numbers: [37] 37,77 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 21*16=336, Resulting Numbers: [336] 336,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[78, 41], Operations: ['84-22=62', '62-21=41'] Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,77 unequal: No Solution Exploring Operation: 78*41=3198, Resulting Numbers: [3198] 3198,77 unequal: No Solution Exploring Operation: 78+41=119, Resulting Numbers: [119] 119,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[62, 57], Operations: ['84-22=62', '78-21=57'] Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 62+57=119, Resulting Numbers: [119] 119,77 unequal: No Solution Exploring Operation: 62*57=3534, Resulting Numbers: [3534] 3534,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 3, 32, 9, 34 ]
14
[ "32-3=29", "9+34=43", "43-29=14" ]
Current State: 14:[3, 32, 9, 34], Operations: [] Exploring Operation: 32-3=29, Resulting Numbers: [9, 34, 29] Generated Node #2: [9, 34, 29] from Operation: 32-3=29 Current State: 14:[9, 34, 29], Operations: ['32-3=29'] Exploring Operation: 9+34=43, Resulting Numbers: [29, 43] Generated Node #3: [29, 43] from Operation: 9+34=43 Current State: 14:[29, 43], Operations: ['32-3=29', '9+34=43'] Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[3, 32, 9, 34], Operations: [] Exploring Operation: 34-9=25, Resulting Numbers: [3, 32, 25] Generated Node #0,0: 14:[3, 32, 25] Operation: 34-9=25 Exploring Operation: 34-32=2, Resulting Numbers: [3, 9, 2] Generated Node #0,1: 14:[3, 9, 2] Operation: 34-32=2 Exploring Operation: 32-9=23, Resulting Numbers: [3, 34, 23] Generated Node #0,2: 14:[3, 34, 23] Operation: 32-9=23 Moving to Node #0,1 Current State: 14:[3, 9, 2], Operations: ['34-32=2'] Exploring Operation: 9-3=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 14:[2, 6] Operation: 9-3=6 Exploring Operation: 9-2=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 14:[3, 7] Operation: 9-2=7 Exploring Operation: 9/3=3, Resulting Numbers: [2, 3] Generated Node #0,1,2: 14:[2, 3] Operation: 9/3=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[2, 6], Operations: ['34-32=2', '9-3=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,14 unequal: No Solution 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 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[3, 7], Operations: ['34-32=2', '9-2=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,14 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 #0,1,2 Current State: 14:[2, 3], Operations: ['34-32=2', '9/3=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,14 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: 14:[3, 32, 25], Operations: ['34-9=25'] Exploring Operation: 32-25=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 14:[3, 7] Operation: 32-25=7 Exploring Operation: 25-3=22, Resulting Numbers: [32, 22] Generated Node #0,0,1: 14:[32, 22] Operation: 25-3=22 Exploring Operation: 32-3=29, Resulting Numbers: [25, 29] Generated Node #0,0,2: 14:[25, 29] Operation: 32-3=29 Moving to Node #0,2 Current State: 14:[3, 34, 23], Operations: ['32-9=23'] Exploring Operation: 34-3=31, Resulting Numbers: [23, 31] Generated Node #0,2,0: 14:[23, 31] Operation: 34-3=31 Exploring Operation: 34-23=11, Resulting Numbers: [3, 11] Generated Node #0,2,1: 14:[3, 11] Operation: 34-23=11 Exploring Operation: 23-3=20, Resulting Numbers: [34, 20] Generated Node #0,2,2: 14:[34, 20] Operation: 23-3=20 Moving to Node #0,0,0 Current State: 14:[3, 7], Operations: ['34-9=25', '32-25=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[3, 11], Operations: ['32-9=23', '34-23=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[3, 32, 9, 34], Operations: [] Exploring Operation: 32-9=23, Resulting Numbers: [3, 34, 23] Generated Node #0,2: 14:[3, 34, 23] Operation: 32-9=23 Moving to Node #0,2 Current State: 14:[3, 34, 23], Operations: ['32-9=23'] Exploring Operation: 34-23=11, Resulting Numbers: [3, 11] Generated Node #0,2,1: 14:[3, 11] Operation: 34-23=11 Moving to Node #0,2,1 Current State: 14:[3, 11], Operations: ['32-9=23', '34-23=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.974826
hs_3
mult_heuristic
[ 52, 40, 72, 87 ]
85
[ "72-52=20", "40/20=2", "87-2=85" ]
Current State: 85:[52, 40, 72, 87], Operations: [] Exploring Operation: 72-52=20, Resulting Numbers: [40, 87, 20] Generated Node #2: [40, 87, 20] from Operation: 72-52=20 Current State: 85:[40, 87, 20], Operations: ['72-52=20'] Exploring Operation: 40/20=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 40/20=2 Current State: 85:[87, 2], Operations: ['72-52=20', '40/20=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[52, 40, 72, 87], Operations: [] Exploring Operation: 52-40=12, Resulting Numbers: [72, 87, 12] Generated Node #0,0: 85:[72, 87, 12] Operation: 52-40=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[72, 87, 12], Operations: ['52-40=12'] Exploring Operation: 72+12=84, Resulting Numbers: [87, 84] Generated Node #0,0,0: 85:[87, 84] Operation: 72+12=84 Moving to Node #0,0,0 Current State: 85:[87, 84], Operations: ['52-40=12', '72+12=84'] Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,85 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, 3, 80, 33 ]
64
[ "80-45=35", "3*33=99", "99-35=64" ]
Current State: 64:[45, 3, 80, 33], Operations: [] Exploring Operation: 80-45=35, Resulting Numbers: [3, 33, 35] Generated Node #2: [3, 33, 35] from Operation: 80-45=35 Current State: 64:[3, 33, 35], Operations: ['80-45=35'] Exploring Operation: 3*33=99, Resulting Numbers: [35, 99] Generated Node #3: [35, 99] from Operation: 3*33=99 Current State: 64:[35, 99], Operations: ['80-45=35', '3*33=99'] Exploring Operation: 99-35=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[45, 3, 80, 33], Operations: [] Exploring Operation: 45-33=12, Resulting Numbers: [3, 80, 12] Generated Node #0,0: 64:[3, 80, 12] Operation: 45-33=12 Exploring Operation: 80-45=35, Resulting Numbers: [3, 33, 35] Generated Node #0,1: 64:[3, 33, 35] Operation: 80-45=35 Exploring Operation: 45/3=15, Resulting Numbers: [80, 33, 15] Generated Node #0,2: 64:[80, 33, 15] Operation: 45/3=15 Moving to Node #0,1 Current State: 64:[3, 33, 35], Operations: ['80-45=35'] Exploring Operation: 35-33=2, Resulting Numbers: [3, 2] Generated Node #0,1,0: 64:[3, 2] Operation: 35-33=2 Exploring Operation: 35-3=32, Resulting Numbers: [33, 32] Generated Node #0,1,1: 64:[33, 32] Operation: 35-3=32 Exploring Operation: 33-3=30, Resulting Numbers: [35, 30] Generated Node #0,1,2: 64:[35, 30] Operation: 33-3=30 Moving to Node #0,2 Current State: 64:[80, 33, 15], Operations: ['45/3=15'] Exploring Operation: 33-15=18, Resulting Numbers: [80, 18] Generated Node #0,2,0: 64:[80, 18] Operation: 33-15=18 Exploring Operation: 80-33=47, Resulting Numbers: [15, 47] Generated Node #0,2,1: 64:[15, 47] Operation: 80-33=47 Exploring Operation: 80-15=65, Resulting Numbers: [33, 65] Generated Node #0,2,2: 64:[33, 65] Operation: 80-15=65 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 64:[33, 65], Operations: ['45/3=15', '80-15=65'] Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,64 unequal: No Solution Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,64 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 64:[15, 47], Operations: ['45/3=15', '80-33=47'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,64 unequal: No Solution Exploring Operation: 15*47=705, Resulting Numbers: [705] 705,64 unequal: No Solution Exploring Operation: 15+47=62, Resulting Numbers: [62] 62,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 64:[80, 18], Operations: ['45/3=15', '33-15=18'] Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,64 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,64 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,64 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: 64:[3, 80, 12], Operations: ['45-33=12'] Exploring Operation: 12/3=4, Resulting Numbers: [80, 4] Generated Node #0,0,0: 64:[80, 4] Operation: 12/3=4 Exploring Operation: 80-3=77, Resulting Numbers: [12, 77] Generated Node #0,0,1: 64:[12, 77] Operation: 80-3=77 Exploring Operation: 80-12=68, Resulting Numbers: [3, 68] Generated Node #0,0,2: 64:[3, 68] Operation: 80-12=68 Moving to Node #0,1,0 Current State: 64:[3, 2], Operations: ['80-45=35', '35-33=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[33, 32], Operations: ['80-45=35', '35-3=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[35, 30], Operations: ['80-45=35', '33-3=30'] Exploring Operation: 35*30=1050, Resulting Numbers: [1050] 1050,64 unequal: No Solution Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[3, 68], Operations: ['45-33=12', '80-12=68'] Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,64 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[80, 4], Operations: ['45-33=12', '12/3=4'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,64 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,64 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[12, 77], Operations: ['45-33=12', '80-3=77'] Exploring Operation: 12*77=924, Resulting Numbers: [924] 924,64 unequal: No Solution Exploring Operation: 12+77=89, Resulting Numbers: [89] 89,64 unequal: No Solution Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,64 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 32, 12, 41, 5 ]
90
[ "32+12=44", "41+5=46", "44+46=90" ]
Current State: 90:[32, 12, 41, 5], Operations: [] Exploring Operation: 32+12=44, Resulting Numbers: [41, 5, 44] Generated Node #2: [41, 5, 44] from Operation: 32+12=44 Current State: 90:[41, 5, 44], Operations: ['32+12=44'] Exploring Operation: 41+5=46, Resulting Numbers: [44, 46] Generated Node #3: [44, 46] from Operation: 41+5=46 Current State: 90:[44, 46], Operations: ['32+12=44', '41+5=46'] Exploring Operation: 44+46=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[32, 12, 41, 5], Operations: [] Exploring Operation: 41-12=29, Resulting Numbers: [32, 5, 29] Generated Node #0,0: 90:[32, 5, 29] Operation: 41-12=29 Exploring Operation: 41-32=9, Resulting Numbers: [12, 5, 9] Generated Node #0,1: 90:[12, 5, 9] Operation: 41-32=9 Exploring Operation: 32+12=44, Resulting Numbers: [41, 5, 44] Generated Node #0,2: 90:[41, 5, 44] Operation: 32+12=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[12, 5, 9], Operations: ['41-32=9'] Exploring Operation: 12-9=3, Resulting Numbers: [5, 3] Generated Node #0,1,0: 90:[5, 3] Operation: 12-9=3 Exploring Operation: 12-5=7, Resulting Numbers: [9, 7] Generated Node #0,1,1: 90:[9, 7] Operation: 12-5=7 Exploring Operation: 12+5=17, Resulting Numbers: [9, 17] Generated Node #0,1,2: 90:[9, 17] Operation: 12+5=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[5, 3], Operations: ['41-32=9', '12-9=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[9, 7], Operations: ['41-32=9', '12-5=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,90 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[9, 17], Operations: ['41-32=9', '12+5=17'] Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,90 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 #0,0 Current State: 90:[32, 5, 29], Operations: ['41-12=29'] Exploring Operation: 32-5=27, Resulting Numbers: [29, 27] Generated Node #0,0,0: 90:[29, 27] Operation: 32-5=27 Exploring Operation: 5+29=34, Resulting Numbers: [32, 34] Generated Node #0,0,1: 90:[32, 34] Operation: 5+29=34 Exploring Operation: 32-29=3, Resulting Numbers: [5, 3] Generated Node #0,0,2: 90:[5, 3] Operation: 32-29=3 Moving to Node #0,0,2 Current State: 90:[5, 3], Operations: ['41-12=29', '32-29=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[29, 27], Operations: ['41-12=29', '32-5=27'] Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,90 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[32, 34], Operations: ['41-12=29', '5+29=34'] Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,90 unequal: No Solution Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,90 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 Current State: 90:[41, 5, 44], Operations: ['32+12=44'] Exploring Operation: 41+5=46, Resulting Numbers: [44, 46] Generated Node #0,2,0: 90:[44, 46] Operation: 41+5=46 Exploring Operation: 41+44=85, Resulting Numbers: [5, 85] Generated Node #0,2,1: 90:[5, 85] Operation: 41+44=85 Exploring Operation: 44-41=3, Resulting Numbers: [5, 3] Generated Node #0,2,2: 90:[5, 3] Operation: 44-41=3 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[5, 3], Operations: ['32+12=44', '44-41=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[44, 46], Operations: ['32+12=44', '41+5=46'] Exploring Operation: 44+46=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[32, 12, 41, 5], Operations: [] Exploring Operation: 32+12=44, Resulting Numbers: [41, 5, 44] Generated Node #0,2: 90:[41, 5, 44] Operation: 32+12=44 Moving to Node #0,2 Current State: 90:[41, 5, 44], Operations: ['32+12=44'] Exploring Operation: 41+5=46, Resulting Numbers: [44, 46] Generated Node #0,2,0: 90:[44, 46] Operation: 41+5=46 Moving to Node #0,2,0 Current State: 90:[44, 46], Operations: ['32+12=44', '41+5=46'] Exploring Operation: 44+46=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
mult_heuristic
[ 76, 46, 35, 4 ]
73
[ "76+35=111", "46*4=184", "184-111=73" ]
Current State: 73:[76, 46, 35, 4], Operations: [] Exploring Operation: 76+35=111, Resulting Numbers: [46, 4, 111] Generated Node #2: [46, 4, 111] from Operation: 76+35=111 Current State: 73:[46, 4, 111], Operations: ['76+35=111'] Exploring Operation: 46*4=184, Resulting Numbers: [111, 184] Generated Node #3: [111, 184] from Operation: 46*4=184 Current State: 73:[111, 184], Operations: ['76+35=111', '46*4=184'] Exploring Operation: 184-111=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[76, 46, 35, 4], Operations: [] Exploring Operation: 76-4=72, Resulting Numbers: [46, 35, 72] Generated Node #0,0: 73:[46, 35, 72] Operation: 76-4=72 Exploring Operation: 76+4=80, Resulting Numbers: [46, 35, 80] Generated Node #0,1: 73:[46, 35, 80] Operation: 76+4=80 Exploring Operation: 46+4=50, Resulting Numbers: [76, 35, 50] Generated Node #0,2: 73:[76, 35, 50] Operation: 46+4=50 Exploring Operation: 35+4=39, Resulting Numbers: [76, 46, 39] Generated Node #0,3: 73:[76, 46, 39] Operation: 35+4=39 Moving to Node #0,2 Current State: 73:[76, 35, 50], Operations: ['46+4=50'] Exploring Operation: 50-35=15, Resulting Numbers: [76, 15] Generated Node #0,2,0: 73:[76, 15] Operation: 50-35=15 Exploring Operation: 35+50=85, Resulting Numbers: [76, 85] Generated Node #0,2,1: 73:[76, 85] Operation: 35+50=85 Exploring Operation: 76+35=111, Resulting Numbers: [50, 111] Generated Node #0,2,2: 73:[50, 111] Operation: 76+35=111 Exploring Operation: 76-35=41, Resulting Numbers: [50, 41] Generated Node #0,2,3: 73:[50, 41] Operation: 76-35=41 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 73:[76, 85], Operations: ['46+4=50', '35+50=85'] Exploring Operation: 76*85=6460, Resulting Numbers: [6460] 6460,73 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 76+85=161, Resulting Numbers: [161] 161,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 73:[50, 41], Operations: ['46+4=50', '76-35=41'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,73 unequal: No Solution Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 73:[76, 15], Operations: ['46+4=50', '50-35=15'] Exploring Operation: 76*15=1140, Resulting Numbers: [1140] 1140,73 unequal: No Solution Exploring Operation: 76+15=91, Resulting Numbers: [91] 91,73 unequal: No Solution Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 73:[50, 111], Operations: ['46+4=50', '76+35=111'] Exploring Operation: 50+111=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 111-50=61, Resulting Numbers: [61] 61,73 unequal: No Solution Exploring Operation: 50*111=5550, Resulting Numbers: [5550] 5550,73 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: 73:[76, 46, 39], Operations: ['35+4=39'] Exploring Operation: 46+39=85, Resulting Numbers: [76, 85] Generated Node #0,3,0: 73:[76, 85] Operation: 46+39=85 Exploring Operation: 76-39=37, Resulting Numbers: [46, 37] Generated Node #0,3,1: 73:[46, 37] Operation: 76-39=37 Exploring Operation: 46-39=7, Resulting Numbers: [76, 7] Generated Node #0,3,2: 73:[76, 7] Operation: 46-39=7 Exploring Operation: 76+39=115, Resulting Numbers: [46, 115] Generated Node #0,3,3: 73:[46, 115] Operation: 76+39=115 Moving to Node #0,0 Current State: 73:[46, 35, 72], Operations: ['76-4=72'] Exploring Operation: 35+72=107, Resulting Numbers: [46, 107] Generated Node #0,0,0: 73:[46, 107] Operation: 35+72=107 Exploring Operation: 46+35=81, Resulting Numbers: [72, 81] Generated Node #0,0,1: 73:[72, 81] Operation: 46+35=81 Exploring Operation: 72-35=37, Resulting Numbers: [46, 37] Generated Node #0,0,2: 73:[46, 37] Operation: 72-35=37 Exploring Operation: 46-35=11, Resulting Numbers: [72, 11] Generated Node #0,0,3: 73:[72, 11] Operation: 46-35=11 Moving to Node #0,1 Current State: 73:[46, 35, 80], Operations: ['76+4=80'] Exploring Operation: 35+80=115, Resulting Numbers: [46, 115] Generated Node #0,1,0: 73:[46, 115] Operation: 35+80=115 Exploring Operation: 80-35=45, Resulting Numbers: [46, 45] Generated Node #0,1,1: 73:[46, 45] Operation: 80-35=45 Exploring Operation: 46+35=81, Resulting Numbers: [80, 81] Generated Node #0,1,2: 73:[80, 81] Operation: 46+35=81 Exploring Operation: 46-35=11, Resulting Numbers: [80, 11] Generated Node #0,1,3: 73:[80, 11] Operation: 46-35=11 Moving to Node #0,0,1 Current State: 73:[72, 81], Operations: ['76-4=72', '46+35=81'] Exploring Operation: 81-72=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 72*81=5832, Resulting Numbers: [5832] 5832,73 unequal: No Solution Exploring Operation: 72+81=153, Resulting Numbers: [153] 153,73 unequal: No Solution Moving to Node #0,3,0 Current State: 73:[76, 85], Operations: ['35+4=39', '46+39=85'] Exploring Operation: 76*85=6460, Resulting Numbers: [6460] 6460,73 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 76+85=161, Resulting Numbers: [161] 161,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[80, 81], Operations: ['76+4=80', '46+35=81'] Exploring Operation: 81-80=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 80+81=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 80*81=6480, Resulting Numbers: [6480] 6480,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[46, 45], Operations: ['76+4=80', '80-35=45'] Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,73 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[46, 107], Operations: ['76-4=72', '35+72=107'] Exploring Operation: 46*107=4922, Resulting Numbers: [4922] 4922,73 unequal: No Solution Exploring Operation: 46+107=153, Resulting Numbers: [153] 153,73 unequal: No Solution Exploring Operation: 107-46=61, Resulting Numbers: [61] 61,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[46, 37], Operations: ['76-4=72', '72-35=37'] Exploring Operation: 46*37=1702, Resulting Numbers: [1702] 1702,73 unequal: No Solution Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[46, 37], Operations: ['35+4=39', '76-39=37'] Exploring Operation: 46*37=1702, Resulting Numbers: [1702] 1702,73 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[72, 11], Operations: ['76-4=72', '46-35=11'] Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,73 unequal: No Solution Exploring Operation: 72+11=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 72*11=792, Resulting Numbers: [792] 792,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[80, 11], Operations: ['76+4=80', '46-35=11'] Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,73 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[76, 7], Operations: ['35+4=39', '46-39=7'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,73 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[46, 115], Operations: ['76+4=80', '35+80=115'] Exploring Operation: 46*115=5290, Resulting Numbers: [5290] 5290,73 unequal: No Solution Exploring Operation: 46+115=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 115-46=69, Resulting Numbers: [69] 69,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[46, 115], Operations: ['35+4=39', '76+39=115'] Exploring Operation: 115-46=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 46+115=161, Resulting Numbers: [161] 161,73 unequal: No Solution Exploring Operation: 46*115=5290, Resulting Numbers: [5290] 5290,73 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 45, 56, 48, 4 ]
76
[ "45*4=180", "56+48=104", "180-104=76" ]
Current State: 76:[45, 56, 48, 4], Operations: [] Exploring Operation: 45*4=180, Resulting Numbers: [56, 48, 180] Generated Node #2: [56, 48, 180] from Operation: 45*4=180 Current State: 76:[56, 48, 180], Operations: ['45*4=180'] Exploring Operation: 56+48=104, Resulting Numbers: [180, 104] Generated Node #3: [180, 104] from Operation: 56+48=104 Current State: 76:[180, 104], Operations: ['45*4=180', '56+48=104'] Exploring Operation: 180-104=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[45, 56, 48, 4], Operations: [] Exploring Operation: 56-48=8, Resulting Numbers: [45, 4, 8] Generated Node #0,0: 76:[45, 4, 8] Operation: 56-48=8 Exploring Operation: 56-45=11, Resulting Numbers: [48, 4, 11] Generated Node #0,1: 76:[48, 4, 11] Operation: 56-45=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[45, 4, 8], Operations: ['56-48=8'] Exploring Operation: 45-4=41, Resulting Numbers: [8, 41] Generated Node #0,0,0: 76:[8, 41] Operation: 45-4=41 Exploring Operation: 45-8=37, Resulting Numbers: [4, 37] Generated Node #0,0,1: 76:[4, 37] Operation: 45-8=37 Moving to Node #0,0,1 Current State: 76:[4, 37], Operations: ['56-48=8', '45-8=37'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[8, 41], Operations: ['56-48=8', '45-4=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[48, 4, 11], Operations: ['56-45=11'] Exploring Operation: 48-11=37, Resulting Numbers: [4, 37] Generated Node #0,1,0: 76:[4, 37] Operation: 48-11=37 Exploring Operation: 48-4=44, Resulting Numbers: [11, 44] Generated Node #0,1,1: 76:[11, 44] Operation: 48-4=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[4, 37], Operations: ['56-45=11', '48-11=37'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,76 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:[11, 44], Operations: ['56-45=11', '48-4=44'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 44, 36, 31, 1 ]
40
[ "44-36=8", "31+1=32", "8+32=40" ]
Current State: 40:[44, 36, 31, 1], Operations: [] Exploring Operation: 44-36=8, Resulting Numbers: [31, 1, 8] Generated Node #2: [31, 1, 8] from Operation: 44-36=8 Current State: 40:[31, 1, 8], Operations: ['44-36=8'] Exploring Operation: 31+1=32, Resulting Numbers: [8, 32] Generated Node #3: [8, 32] from Operation: 31+1=32 Current State: 40:[8, 32], Operations: ['44-36=8', '31+1=32'] Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[44, 36, 31, 1], Operations: [] Exploring Operation: 36-31=5, Resulting Numbers: [44, 1, 5] Generated Node #0,0: 40:[44, 1, 5] Operation: 36-31=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[44, 1, 5], Operations: ['36-31=5'] Exploring Operation: 44-5=39, Resulting Numbers: [1, 39] Generated Node #0,0,0: 40:[1, 39] Operation: 44-5=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[1, 39], Operations: ['36-31=5', '44-5=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[44, 36, 31, 1], Operations: [] Exploring Operation: 36-31=5, Resulting Numbers: [44, 1, 5] Generated Node #0,0: 40:[44, 1, 5] Operation: 36-31=5 Moving to Node #0,0 Current State: 40:[44, 1, 5], Operations: ['36-31=5'] Exploring Operation: 44-5=39, Resulting Numbers: [1, 39] Generated Node #0,0,0: 40:[1, 39] Operation: 44-5=39 Moving to Node #0,0,0 Current State: 40:[1, 39], Operations: ['36-31=5', '44-5=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 76, 73, 35, 33 ]
65
[ "76-73=3", "35+33=68", "68-3=65" ]
Current State: 65:[76, 73, 35, 33], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [35, 33, 3] Generated Node #2: [35, 33, 3] from Operation: 76-73=3 Current State: 65:[35, 33, 3], Operations: ['76-73=3'] Exploring Operation: 35+33=68, Resulting Numbers: [3, 68] Generated Node #3: [3, 68] from Operation: 35+33=68 Current State: 65:[3, 68], Operations: ['76-73=3', '35+33=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[76, 73, 35, 33], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [35, 33, 3] Generated Node #0,0: 65:[35, 33, 3] Operation: 76-73=3 Exploring Operation: 35-33=2, Resulting Numbers: [76, 73, 2] Generated Node #0,1: 65:[76, 73, 2] Operation: 35-33=2 Exploring Operation: 76-33=43, Resulting Numbers: [73, 35, 43] Generated Node #0,2: 65:[73, 35, 43] Operation: 76-33=43 Exploring Operation: 35+33=68, Resulting Numbers: [76, 73, 68] Generated Node #0,3: 65:[76, 73, 68] Operation: 35+33=68 Exploring Operation: 76-35=41, Resulting Numbers: [73, 33, 41] Generated Node #0,4: 65:[73, 33, 41] Operation: 76-35=41 Moving to Node #0,1 Current State: 65:[76, 73, 2], Operations: ['35-33=2'] Exploring Operation: 76-73=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 65:[2, 3] Operation: 76-73=3 Exploring Operation: 76-2=74, Resulting Numbers: [73, 74] Generated Node #0,1,1: 65:[73, 74] Operation: 76-2=74 Exploring Operation: 76+2=78, Resulting Numbers: [73, 78] Generated Node #0,1,2: 65:[73, 78] Operation: 76+2=78 Exploring Operation: 73-2=71, Resulting Numbers: [76, 71] Generated Node #0,1,3: 65:[76, 71] Operation: 73-2=71 Exploring Operation: 73+2=75, Resulting Numbers: [76, 75] Generated Node #0,1,4: 65:[76, 75] Operation: 73+2=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[2, 3], Operations: ['35-33=2', '76-73=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[73, 74], Operations: ['35-33=2', '76-2=74'] Exploring Operation: 73*74=5402, Resulting Numbers: [5402] 5402,65 unequal: No Solution Exploring Operation: 73+74=147, Resulting Numbers: [147] 147,65 unequal: No Solution Exploring Operation: 74-73=1, Resulting Numbers: [1] 1,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[76, 71], Operations: ['35-33=2', '73-2=71'] Exploring Operation: 76-71=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 76*71=5396, Resulting Numbers: [5396] 5396,65 unequal: No Solution Exploring Operation: 76+71=147, Resulting Numbers: [147] 147,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[73, 78], Operations: ['35-33=2', '76+2=78'] Exploring Operation: 73*78=5694, Resulting Numbers: [5694] 5694,65 unequal: No Solution Exploring Operation: 78-73=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 73+78=151, Resulting Numbers: [151] 151,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 65:[76, 75], Operations: ['35-33=2', '73+2=75'] Exploring Operation: 76-75=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 76+75=151, Resulting Numbers: [151] 151,65 unequal: No Solution Exploring Operation: 76*75=5700, Resulting Numbers: [5700] 5700,65 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: 65:[76, 73, 68], Operations: ['35+33=68'] Exploring Operation: 76+68=144, Resulting Numbers: [73, 144] Generated Node #0,3,0: 65:[73, 144] Operation: 76+68=144 Exploring Operation: 76+73=149, Resulting Numbers: [68, 149] Generated Node #0,3,1: 65:[68, 149] Operation: 76+73=149 Exploring Operation: 76-68=8, Resulting Numbers: [73, 8] Generated Node #0,3,2: 65:[73, 8] Operation: 76-68=8 Exploring Operation: 76-73=3, Resulting Numbers: [68, 3] Generated Node #0,3,3: 65:[68, 3] Operation: 76-73=3 Exploring Operation: 73-68=5, Resulting Numbers: [76, 5] Generated Node #0,3,4: 65:[76, 5] Operation: 73-68=5 Moving to Node #0,0 Current State: 65:[35, 33, 3], Operations: ['76-73=3'] Exploring Operation: 33-3=30, Resulting Numbers: [35, 30] Generated Node #0,0,0: 65:[35, 30] Operation: 33-3=30 Exploring Operation: 35+33=68, Resulting Numbers: [3, 68] Generated Node #0,0,1: 65:[3, 68] Operation: 35+33=68 Exploring Operation: 35-3=32, Resulting Numbers: [33, 32] Generated Node #0,0,2: 65:[33, 32] Operation: 35-3=32 Exploring Operation: 35-33=2, Resulting Numbers: [3, 2] Generated Node #0,0,3: 65:[3, 2] Operation: 35-33=2 Exploring Operation: 33/3=11, Resulting Numbers: [35, 11] Generated Node #0,0,4: 65:[35, 11] Operation: 33/3=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[3, 68], Operations: ['76-73=3', '35+33=68'] Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,65 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[76, 73, 35, 33], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [35, 33, 3] Generated Node #0,0: 65:[35, 33, 3] Operation: 76-73=3 Moving to Node #0,0 Current State: 65:[35, 33, 3], Operations: ['76-73=3'] Exploring Operation: 35+33=68, Resulting Numbers: [3, 68] Generated Node #0,0,1: 65:[3, 68] Operation: 35+33=68 Moving to Node #0,0,1 Current State: 65:[3, 68], Operations: ['76-73=3', '35+33=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 94, 83, 13, 96 ]
93
[ "83+13=96", "96/96=1", "94-1=93" ]
Current State: 93:[94, 83, 13, 96], Operations: [] Exploring Operation: 83+13=96, Resulting Numbers: [94, 96, 96] Generated Node #2: [94, 96, 96] from Operation: 83+13=96 Current State: 93:[94, 96, 96], Operations: ['83+13=96'] Exploring Operation: 96/96=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 96/96=1 Current State: 93:[94, 1], Operations: ['83+13=96', '96/96=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[94, 83, 13, 96], Operations: [] Exploring Operation: 83+13=96, Resulting Numbers: [94, 96, 96] Generated Node #0,0: 93:[94, 96, 96] Operation: 83+13=96 Exploring Operation: 94-83=11, Resulting Numbers: [13, 96, 11] Generated Node #0,1: 93:[13, 96, 11] Operation: 94-83=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[94, 96, 96], Operations: ['83+13=96'] Exploring Operation: 96-94=2, Resulting Numbers: [96, 2] Generated Node #0,0,0: 93:[96, 2] Operation: 96-94=2 Exploring Operation: 96/96=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 96/96=1 Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['83+13=96', '96/96=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[94, 83, 13, 96], Operations: [] Exploring Operation: 83+13=96, Resulting Numbers: [94, 96, 96] Generated Node #0,0: 93:[94, 96, 96] Operation: 83+13=96 Moving to Node #0,0 Current State: 93:[94, 96, 96], Operations: ['83+13=96'] Exploring Operation: 96/96=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 96/96=1 Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['83+13=96', '96/96=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 38, 38, 78, 3 ]
80
[ "38/38=1", "78+3=81", "81-1=80" ]
Current State: 80:[38, 38, 78, 3], Operations: [] Exploring Operation: 38/38=1, Resulting Numbers: [78, 3, 1] Generated Node #2: [78, 3, 1] from Operation: 38/38=1 Current State: 80:[78, 3, 1], Operations: ['38/38=1'] Exploring Operation: 78+3=81, Resulting Numbers: [1, 81] Generated Node #3: [1, 81] from Operation: 78+3=81 Current State: 80:[1, 81], Operations: ['38/38=1', '78+3=81'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[38, 38, 78, 3], Operations: [] Exploring Operation: 78-38=40, Resulting Numbers: [38, 3, 40] Generated Node #0,0: 80:[38, 3, 40] Operation: 78-38=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[38, 3, 40], Operations: ['78-38=40'] Exploring Operation: 38+3=41, Resulting Numbers: [40, 41] Generated Node #0,0,0: 80:[40, 41] Operation: 38+3=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[40, 41], Operations: ['78-38=40', '38+3=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 68, 9, 1, 19 ]
77
[ "68-9=59", "19-1=18", "59+18=77" ]
Current State: 77:[68, 9, 1, 19], Operations: [] Exploring Operation: 68-9=59, Resulting Numbers: [1, 19, 59] Generated Node #2: [1, 19, 59] from Operation: 68-9=59 Current State: 77:[1, 19, 59], Operations: ['68-9=59'] Exploring Operation: 19-1=18, Resulting Numbers: [59, 18] Generated Node #3: [59, 18] from Operation: 19-1=18 Current State: 77:[59, 18], Operations: ['68-9=59', '19-1=18'] Exploring Operation: 59+18=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[68, 9, 1, 19], Operations: [] Exploring Operation: 19-9=10, Resulting Numbers: [68, 1, 10] Generated Node #0,0: 77:[68, 1, 10] Operation: 19-9=10 Exploring Operation: 68+9=77, Resulting Numbers: [1, 19, 77] Generated Node #0,1: 77:[1, 19, 77] Operation: 68+9=77 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[1, 19, 77], Operations: ['68+9=77'] Exploring Operation: 1*19=19, Resulting Numbers: [77, 19] Generated Node #0,1,0: 77:[77, 19] Operation: 1*19=19 Exploring Operation: 19-1=18, Resulting Numbers: [77, 18] Generated Node #0,1,1: 77:[77, 18] Operation: 19-1=18 Moving to Node #0,1,1 Current State: 77:[77, 18], Operations: ['68+9=77', '19-1=18'] Exploring Operation: 77+18=95, Resulting Numbers: [95] 95,77 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[77, 19], Operations: ['68+9=77', '1*19=19'] Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,77 unequal: No Solution Exploring Operation: 77+19=96, Resulting Numbers: [96] 96,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[68, 1, 10], Operations: ['19-9=10'] Exploring Operation: 68+1=69, Resulting Numbers: [10, 69] Generated Node #0,0,0: 77:[10, 69] Operation: 68+1=69 Exploring Operation: 68+10=78, Resulting Numbers: [1, 78] Generated Node #0,0,1: 77:[1, 78] Operation: 68+10=78 Moving to Node #0,0,1 Current State: 77:[1, 78], Operations: ['19-9=10', '68+10=78'] Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[68, 9, 1, 19], Operations: [] Exploring Operation: 19-9=10, Resulting Numbers: [68, 1, 10] Generated Node #0,0: 77:[68, 1, 10] Operation: 19-9=10 Moving to Node #0,0 Current State: 77:[68, 1, 10], Operations: ['19-9=10'] Exploring Operation: 68+10=78, Resulting Numbers: [1, 78] Generated Node #0,0,1: 77:[1, 78] Operation: 68+10=78 Moving to Node #0,0,1 Current State: 77:[1, 78], Operations: ['19-9=10', '68+10=78'] Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 32, 67, 14, 36 ]
57
[ "67-32=35", "36-14=22", "35+22=57" ]
Current State: 57:[32, 67, 14, 36], Operations: [] Exploring Operation: 67-32=35, Resulting Numbers: [14, 36, 35] Generated Node #2: [14, 36, 35] from Operation: 67-32=35 Current State: 57:[14, 36, 35], Operations: ['67-32=35'] Exploring Operation: 36-14=22, Resulting Numbers: [35, 22] Generated Node #3: [35, 22] from Operation: 36-14=22 Current State: 57:[35, 22], Operations: ['67-32=35', '36-14=22'] Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[32, 67, 14, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [67, 14, 4] Generated Node #0,0: 57:[67, 14, 4] Operation: 36-32=4 Exploring Operation: 67-36=31, Resulting Numbers: [32, 14, 31] Generated Node #0,1: 57:[32, 14, 31] Operation: 67-36=31 Exploring Operation: 32-14=18, Resulting Numbers: [67, 36, 18] Generated Node #0,2: 57:[67, 36, 18] Operation: 32-14=18 Exploring Operation: 32+36=68, Resulting Numbers: [67, 14, 68] Generated Node #0,3: 57:[67, 14, 68] Operation: 32+36=68 Exploring Operation: 36-14=22, Resulting Numbers: [32, 67, 22] Generated Node #0,4: 57:[32, 67, 22] Operation: 36-14=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[67, 14, 4], Operations: ['36-32=4'] Exploring Operation: 14+4=18, Resulting Numbers: [67, 18] Generated Node #0,0,0: 57:[67, 18] Operation: 14+4=18 Exploring Operation: 67-14=53, Resulting Numbers: [4, 53] Generated Node #0,0,1: 57:[4, 53] Operation: 67-14=53 Exploring Operation: 14*4=56, Resulting Numbers: [67, 56] Generated Node #0,0,2: 57:[67, 56] Operation: 14*4=56 Exploring Operation: 67-4=63, Resulting Numbers: [14, 63] Generated Node #0,0,3: 57:[14, 63] Operation: 67-4=63 Exploring Operation: 14-4=10, Resulting Numbers: [67, 10] Generated Node #0,0,4: 57:[67, 10] Operation: 14-4=10 Moving to Node #0,0,1 Current State: 57:[4, 53], Operations: ['36-32=4', '67-14=53'] Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 4*53=212, Resulting Numbers: [212] 212,57 unequal: No Solution Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[32, 67, 14, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [67, 14, 4] Generated Node #0,0: 57:[67, 14, 4] Operation: 36-32=4 Moving to Node #0,0 Current State: 57:[67, 14, 4], Operations: ['36-32=4'] Exploring Operation: 67-14=53, Resulting Numbers: [4, 53] Generated Node #0,0,1: 57:[4, 53] Operation: 67-14=53 Moving to Node #0,0,1 Current State: 57:[4, 53], Operations: ['36-32=4', '67-14=53'] Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 33, 30, 51, 60 ]
72
[ "33+30=63", "60-51=9", "63+9=72" ]
Current State: 72:[33, 30, 51, 60], Operations: [] Exploring Operation: 33+30=63, Resulting Numbers: [51, 60, 63] Generated Node #2: [51, 60, 63] from Operation: 33+30=63 Current State: 72:[51, 60, 63], Operations: ['33+30=63'] Exploring Operation: 60-51=9, Resulting Numbers: [63, 9] Generated Node #3: [63, 9] from Operation: 60-51=9 Current State: 72:[63, 9], Operations: ['33+30=63', '60-51=9'] Exploring Operation: 63+9=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[33, 30, 51, 60], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [33, 51, 2] Generated Node #0,0: 72:[33, 51, 2] Operation: 60/30=2 Exploring Operation: 60-33=27, Resulting Numbers: [30, 51, 27] Generated Node #0,1: 72:[30, 51, 27] Operation: 60-33=27 Exploring Operation: 51-33=18, Resulting Numbers: [30, 60, 18] Generated Node #0,2: 72:[30, 60, 18] Operation: 51-33=18 Exploring Operation: 60-51=9, Resulting Numbers: [33, 30, 9] Generated Node #0,3: 72:[33, 30, 9] Operation: 60-51=9 Exploring Operation: 51-30=21, Resulting Numbers: [33, 60, 21] Generated Node #0,4: 72:[33, 60, 21] Operation: 51-30=21 Moving to Node #0,3 Current State: 72:[33, 30, 9], Operations: ['60-51=9'] Exploring Operation: 30+9=39, Resulting Numbers: [33, 39] Generated Node #0,3,0: 72:[33, 39] Operation: 30+9=39 Exploring Operation: 30-9=21, Resulting Numbers: [33, 21] Generated Node #0,3,1: 72:[33, 21] Operation: 30-9=21 Exploring Operation: 33+30=63, Resulting Numbers: [9, 63] Generated Node #0,3,2: 72:[9, 63] Operation: 33+30=63 Exploring Operation: 33-30=3, Resulting Numbers: [9, 3] Generated Node #0,3,3: 72:[9, 3] Operation: 33-30=3 Exploring Operation: 33-9=24, Resulting Numbers: [30, 24] Generated Node #0,3,4: 72:[30, 24] Operation: 33-9=24 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[9, 3], Operations: ['60-51=9', '33-30=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[33, 39], Operations: ['60-51=9', '30+9=39'] Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,72 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[33, 30, 51, 60], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [33, 30, 9] Generated Node #0,3: 72:[33, 30, 9] Operation: 60-51=9 Moving to Node #0,3 Current State: 72:[33, 30, 9], Operations: ['60-51=9'] Exploring Operation: 30+9=39, Resulting Numbers: [33, 39] Generated Node #0,3,0: 72:[33, 39] Operation: 30+9=39 Moving to Node #0,3,0 Current State: 72:[33, 39], Operations: ['60-51=9', '30+9=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 16, 49, 5, 36 ]
81
[ "49-36=13", "5*13=65", "16+65=81" ]
Current State: 81:[16, 49, 5, 36], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [16, 5, 13] Generated Node #2: [16, 5, 13] from Operation: 49-36=13 Current State: 81:[16, 5, 13], Operations: ['49-36=13'] Exploring Operation: 5*13=65, Resulting Numbers: [16, 65] Generated Node #3: [16, 65] from Operation: 5*13=65 Current State: 81:[16, 65], Operations: ['49-36=13', '5*13=65'] Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[16, 49, 5, 36], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [16, 5, 13] Generated Node #0,0: 81:[16, 5, 13] Operation: 49-36=13 Exploring Operation: 49+36=85, Resulting Numbers: [16, 5, 85] Generated Node #0,1: 81:[16, 5, 85] Operation: 49+36=85 Moving to Node #0,0 Current State: 81:[16, 5, 13], Operations: ['49-36=13'] Exploring Operation: 16+13=29, Resulting Numbers: [5, 29] Generated Node #0,0,0: 81:[5, 29] Operation: 16+13=29 Exploring Operation: 16-13=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 81:[5, 3] Operation: 16-13=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[5, 3], Operations: ['49-36=13', '16-13=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,81 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[5, 29], Operations: ['49-36=13', '16+13=29'] Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,81 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: 81:[16, 5, 85], Operations: ['49+36=85'] Exploring Operation: 16-5=11, Resulting Numbers: [85, 11] Generated Node #0,1,0: 81:[85, 11] Operation: 16-5=11 Exploring Operation: 16*5=80, Resulting Numbers: [85, 80] Generated Node #0,1,1: 81:[85, 80] Operation: 16*5=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[85, 80], Operations: ['49+36=85', '16*5=80'] Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 85+80=165, Resulting Numbers: [165] 165,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[85, 11], Operations: ['49+36=85', '16-5=11'] Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,81 unequal: No Solution Exploring Operation: 85+11=96, Resulting Numbers: [96] 96,81 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
[ 89, 56, 7, 8 ]
23
[ "89-56=33", "7*8=56", "56-33=23" ]
Current State: 23:[89, 56, 7, 8], Operations: [] Exploring Operation: 89-56=33, Resulting Numbers: [7, 8, 33] Generated Node #2: [7, 8, 33] from Operation: 89-56=33 Current State: 23:[7, 8, 33], Operations: ['89-56=33'] Exploring Operation: 7*8=56, Resulting Numbers: [33, 56] Generated Node #3: [33, 56] from Operation: 7*8=56 Current State: 23:[33, 56], Operations: ['89-56=33', '7*8=56'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[89, 56, 7, 8], Operations: [] Exploring Operation: 56/7=8, Resulting Numbers: [89, 8, 8] Generated Node #0,0: 23:[89, 8, 8] Operation: 56/7=8 Exploring Operation: 89-7=82, Resulting Numbers: [56, 8, 82] Generated Node #0,1: 23:[56, 8, 82] Operation: 89-7=82 Exploring Operation: 56/8=7, Resulting Numbers: [89, 7, 7] Generated Node #0,2: 23:[89, 7, 7] Operation: 56/8=7 Exploring Operation: 89-56=33, Resulting Numbers: [7, 8, 33] Generated Node #0,3: 23:[7, 8, 33] Operation: 89-56=33 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[7, 8, 33], Operations: ['89-56=33'] Exploring Operation: 33-7=26, Resulting Numbers: [8, 26] Generated Node #0,3,0: 23:[8, 26] Operation: 33-7=26 Exploring Operation: 7+8=15, Resulting Numbers: [33, 15] Generated Node #0,3,1: 23:[33, 15] Operation: 7+8=15 Exploring Operation: 8-7=1, Resulting Numbers: [33, 1] Generated Node #0,3,2: 23:[33, 1] Operation: 8-7=1 Exploring Operation: 33-8=25, Resulting Numbers: [7, 25] Generated Node #0,3,3: 23:[7, 25] Operation: 33-8=25 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 23:[8, 26], Operations: ['89-56=33', '33-7=26'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 8*26=208, Resulting Numbers: [208] 208,23 unequal: No Solution Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,23 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 #0,3,1 Current State: 23:[33, 15], Operations: ['89-56=33', '7+8=15'] Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,23 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,23 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 #0,3,3 Current State: 23:[7, 25], Operations: ['89-56=33', '33-8=25'] Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,23 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,23 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 #0,3,2 Current State: 23:[33, 1], Operations: ['89-56=33', '8-7=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 33-1=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:[89, 8, 8], Operations: ['56/7=8'] Exploring Operation: 89-8=81, Resulting Numbers: [8, 81] Generated Node #0,0,0: 23:[8, 81] Operation: 89-8=81 Exploring Operation: 8/8=1, Resulting Numbers: [89, 1] Generated Node #0,0,1: 23:[89, 1] Operation: 8/8=1 Exploring Operation: 89-8=81, Resulting Numbers: [8, 81] Generated Node #0,0,2: 23:[8, 81] Operation: 89-8=81 Exploring Operation: 8+8=16, Resulting Numbers: [89, 16] Generated Node #0,0,3: 23:[89, 16] Operation: 8+8=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[8, 81], Operations: ['56/7=8', '89-8=81'] Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,23 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,23 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 #0,0,2 Current State: 23:[8, 81], Operations: ['56/7=8', '89-8=81'] Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,23 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,23 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,23 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 #0,0,3 Current State: 23:[89, 16], Operations: ['56/7=8', '8+8=16'] Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,23 unequal: No Solution Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,23 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,23 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 #0,0,1 Current State: 23:[89, 1], Operations: ['56/7=8', '8/8=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,23 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,23 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 #0,2 Current State: 23:[89, 7, 7], Operations: ['56/8=7'] Exploring Operation: 89-7=82, Resulting Numbers: [7, 82] Generated Node #0,2,0: 23:[7, 82] Operation: 89-7=82 Exploring Operation: 7+7=14, Resulting Numbers: [89, 14] Generated Node #0,2,1: 23:[89, 14] Operation: 7+7=14 Exploring Operation: 89-7=82, Resulting Numbers: [7, 82] Generated Node #0,2,2: 23:[7, 82] Operation: 89-7=82 Exploring Operation: 7/7=1, Resulting Numbers: [89, 1] Generated Node #0,2,3: 23:[89, 1] Operation: 7/7=1 Moving to Node #0,2,0 Current State: 23:[7, 82], Operations: ['56/8=7', '89-7=82'] Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,23 unequal: No Solution Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[7, 82], Operations: ['56/8=7', '89-7=82'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,23 unequal: No Solution Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[89, 14], Operations: ['56/8=7', '7+7=14'] Exploring Operation: 89*14=1246, Resulting Numbers: [1246] 1246,23 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,23 unequal: No Solution Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[89, 1], Operations: ['56/8=7', '7/7=1'] Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,23 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[56, 8, 82], Operations: ['89-7=82'] Exploring Operation: 82-8=74, Resulting Numbers: [56, 74] Generated Node #0,1,0: 23:[56, 74] Operation: 82-8=74 Exploring Operation: 56-8=48, Resulting Numbers: [82, 48] Generated Node #0,1,1: 23:[82, 48] Operation: 56-8=48 Exploring Operation: 82-56=26, Resulting Numbers: [8, 26] Generated Node #0,1,2: 23:[8, 26] Operation: 82-56=26 Exploring Operation: 56/8=7, Resulting Numbers: [82, 7] Generated Node #0,1,3: 23:[82, 7] Operation: 56/8=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[8, 26], Operations: ['89-7=82', '82-56=26'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 8*26=208, Resulting Numbers: [208] 208,23 unequal: No Solution Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,23 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 #0,1,3 Current State: 23:[82, 7], Operations: ['89-7=82', '56/8=7'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,23 unequal: No Solution Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 82*7=574, Resulting Numbers: [574] 574,23 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 #0,1,0 Current State: 23:[56, 74], Operations: ['89-7=82', '82-8=74'] Exploring Operation: 56*74=4144, Resulting Numbers: [4144] 4144,23 unequal: No Solution Exploring Operation: 56+74=130, Resulting Numbers: [130] 130,23 unequal: No Solution Exploring Operation: 74-56=18, Resulting Numbers: [18] 18,23 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:[82, 48], Operations: ['89-7=82', '56-8=48'] Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,23 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,23 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 No solution found.
0
hs_4
sum_heuristic
[ 84, 83, 53, 15 ]
39
[ "84-83=1", "53-15=38", "1+38=39" ]
Current State: 39:[84, 83, 53, 15], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [53, 15, 1] Generated Node #2: [53, 15, 1] from Operation: 84-83=1 Current State: 39:[53, 15, 1], Operations: ['84-83=1'] Exploring Operation: 53-15=38, Resulting Numbers: [1, 38] Generated Node #3: [1, 38] from Operation: 53-15=38 Current State: 39:[1, 38], Operations: ['84-83=1', '53-15=38'] Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[84, 83, 53, 15], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [53, 15, 1] Generated Node #0,0: 39:[53, 15, 1] Operation: 84-83=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[53, 15, 1], Operations: ['84-83=1'] Exploring Operation: 53-15=38, Resulting Numbers: [1, 38] Generated Node #0,0,0: 39:[1, 38] Operation: 53-15=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[1, 38], Operations: ['84-83=1', '53-15=38'] Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[84, 83, 53, 15], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [53, 15, 1] Generated Node #0,0: 39:[53, 15, 1] Operation: 84-83=1 Moving to Node #0,0 Current State: 39:[53, 15, 1], Operations: ['84-83=1'] Exploring Operation: 53-15=38, Resulting Numbers: [1, 38] Generated Node #0,0,0: 39:[1, 38] Operation: 53-15=38 Moving to Node #0,0,0 Current State: 39:[1, 38], Operations: ['84-83=1', '53-15=38'] Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 90, 88, 3, 16 ]
50
[ "90-88=2", "3*16=48", "2+48=50" ]
Current State: 50:[90, 88, 3, 16], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [3, 16, 2] Generated Node #2: [3, 16, 2] from Operation: 90-88=2 Current State: 50:[3, 16, 2], Operations: ['90-88=2'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 3*16=48 Current State: 50:[2, 48], Operations: ['90-88=2', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[90, 88, 3, 16], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [3, 16, 2] Generated Node #0,0: 50:[3, 16, 2] Operation: 90-88=2 Exploring Operation: 90-16=74, Resulting Numbers: [88, 3, 74] Generated Node #0,1: 50:[88, 3, 74] Operation: 90-16=74 Exploring Operation: 90/3=30, Resulting Numbers: [88, 16, 30] Generated Node #0,2: 50:[88, 16, 30] Operation: 90/3=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[3, 16, 2], Operations: ['90-88=2'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 3*16=48 Exploring Operation: 16-3=13, Resulting Numbers: [2, 13] Generated Node #0,0,1: 50:[2, 13] Operation: 16-3=13 Exploring Operation: 16/2=8, Resulting Numbers: [3, 8] Generated Node #0,0,2: 50:[3, 8] Operation: 16/2=8 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['90-88=2', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[90, 88, 3, 16], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [3, 16, 2] Generated Node #0,0: 50:[3, 16, 2] Operation: 90-88=2 Moving to Node #0,0 Current State: 50:[3, 16, 2], Operations: ['90-88=2'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 3*16=48 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['90-88=2', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 90, 12, 25, 80 ]
14
[ "25+80=105", "12*105=1260", "1260/90=14" ]
Current State: 14:[90, 12, 25, 80], Operations: [] Exploring Operation: 25+80=105, Resulting Numbers: [90, 12, 105] Generated Node #2: [90, 12, 105] from Operation: 25+80=105 Current State: 14:[90, 12, 105], Operations: ['25+80=105'] Exploring Operation: 12*105=1260, Resulting Numbers: [90, 1260] Generated Node #3: [90, 1260] from Operation: 12*105=1260 Current State: 14:[90, 1260], Operations: ['25+80=105', '12*105=1260'] Exploring Operation: 1260/90=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[90, 12, 25, 80], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [12, 80, 65] Generated Node #0,0: 14:[12, 80, 65] Operation: 90-25=65 Exploring Operation: 90-12=78, Resulting Numbers: [25, 80, 78] Generated Node #0,1: 14:[25, 80, 78] Operation: 90-12=78 Exploring Operation: 80-12=68, Resulting Numbers: [90, 25, 68] Generated Node #0,2: 14:[90, 25, 68] Operation: 80-12=68 Exploring Operation: 80-25=55, Resulting Numbers: [90, 12, 55] Generated Node #0,3: 14:[90, 12, 55] Operation: 80-25=55 Exploring Operation: 90-80=10, Resulting Numbers: [12, 25, 10] Generated Node #0,4: 14:[12, 25, 10] Operation: 90-80=10 Start Sub Search at level 1: Moving to Node #0,4 Current State: 14:[12, 25, 10], Operations: ['90-80=10'] Exploring Operation: 12-10=2, Resulting Numbers: [25, 2] Generated Node #0,4,0: 14:[25, 2] Operation: 12-10=2 Exploring Operation: 25-10=15, Resulting Numbers: [12, 15] Generated Node #0,4,1: 14:[12, 15] Operation: 25-10=15 Exploring Operation: 25+10=35, Resulting Numbers: [12, 35] Generated Node #0,4,2: 14:[12, 35] Operation: 25+10=35 Exploring Operation: 12+10=22, Resulting Numbers: [25, 22] Generated Node #0,4,3: 14:[25, 22] Operation: 12+10=22 Exploring Operation: 25-12=13, Resulting Numbers: [10, 13] Generated Node #0,4,4: 14:[10, 13] Operation: 25-12=13 Moving to Node #0,4,1 Current State: 14:[12, 15], Operations: ['90-80=10', '25-10=15'] Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,14 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,14 unequal: No Solution Moving to Node #0,4,4 Current State: 14:[10, 13], Operations: ['90-80=10', '25-12=13'] Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,14 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,14 unequal: No Solution Moving to Node #0,4,0 Current State: 14:[25, 2], Operations: ['90-80=10', '12-10=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,14 unequal: No Solution Moving to Node #0,4,3 Current State: 14:[25, 22], Operations: ['90-80=10', '12+10=22'] Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,14 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,14 unequal: No Solution Moving to Node #0,4,2 Current State: 14:[12, 35], Operations: ['90-80=10', '25+10=35'] Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,14 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,14 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 #0,0 Current State: 14:[12, 80, 65], Operations: ['90-25=65'] Exploring Operation: 12+65=77, Resulting Numbers: [80, 77] Generated Node #0,0,0: 14:[80, 77] Operation: 12+65=77 Exploring Operation: 65-12=53, Resulting Numbers: [80, 53] Generated Node #0,0,1: 14:[80, 53] Operation: 65-12=53 Exploring Operation: 80-65=15, Resulting Numbers: [12, 15] Generated Node #0,0,2: 14:[12, 15] Operation: 80-65=15 Exploring Operation: 80-12=68, Resulting Numbers: [65, 68] Generated Node #0,0,3: 14:[65, 68] Operation: 80-12=68 Exploring Operation: 12+80=92, Resulting Numbers: [65, 92] Generated Node #0,0,4: 14:[65, 92] Operation: 12+80=92 Moving to Node #0,0,2 Current State: 14:[12, 15], Operations: ['90-25=65', '80-65=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[65, 68], Operations: ['90-25=65', '80-12=68'] Exploring Operation: 65*68=4420, Resulting Numbers: [4420] 4420,14 unequal: No Solution Exploring Operation: 68-65=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 65+68=133, Resulting Numbers: [133] 133,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[80, 53], Operations: ['90-25=65', '65-12=53'] Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 80+53=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 80*53=4240, Resulting Numbers: [4240] 4240,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[80, 77], Operations: ['90-25=65', '12+65=77'] Exploring Operation: 80*77=6160, Resulting Numbers: [6160] 6160,14 unequal: No Solution Exploring Operation: 80+77=157, Resulting Numbers: [157] 157,14 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,14 unequal: No Solution Moving to Node #0,0,4 Current State: 14:[65, 92], Operations: ['90-25=65', '12+80=92'] Exploring Operation: 65+92=157, Resulting Numbers: [157] 157,14 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 65*92=5980, Resulting Numbers: [5980] 5980,14 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 #0,3 Current State: 14:[90, 12, 55], Operations: ['80-25=55'] Exploring Operation: 90-55=35, Resulting Numbers: [12, 35] Generated Node #0,3,0: 14:[12, 35] Operation: 90-55=35 Exploring Operation: 12+55=67, Resulting Numbers: [90, 67] Generated Node #0,3,1: 14:[90, 67] Operation: 12+55=67 Exploring Operation: 90-12=78, Resulting Numbers: [55, 78] Generated Node #0,3,2: 14:[55, 78] Operation: 90-12=78 Exploring Operation: 90+12=102, Resulting Numbers: [55, 102] Generated Node #0,3,3: 14:[55, 102] Operation: 90+12=102 Exploring Operation: 55-12=43, Resulting Numbers: [90, 43] Generated Node #0,3,4: 14:[90, 43] Operation: 55-12=43 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 14:[12, 35], Operations: ['80-25=55', '90-55=35'] Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,14 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,14 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:[55, 78], Operations: ['80-25=55', '90-12=78'] Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 55+78=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 55*78=4290, Resulting Numbers: [4290] 4290,14 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:[90, 43], Operations: ['80-25=55', '55-12=43'] Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,14 unequal: No Solution Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,14 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:[90, 67], Operations: ['80-25=55', '12+55=67'] Exploring Operation: 90-67=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 90*67=6030, Resulting Numbers: [6030] 6030,14 unequal: No Solution Exploring Operation: 90+67=157, Resulting Numbers: [157] 157,14 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:[55, 102], Operations: ['80-25=55', '90+12=102'] Exploring Operation: 55+102=157, Resulting Numbers: [157] 157,14 unequal: No Solution Exploring Operation: 55*102=5610, Resulting Numbers: [5610] 5610,14 unequal: No Solution Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,14 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 #0,1 Current State: 14:[25, 80, 78], Operations: ['90-12=78'] Exploring Operation: 80-78=2, Resulting Numbers: [25, 2] Generated Node #0,1,0: 14:[25, 2] Operation: 80-78=2 Exploring Operation: 25+80=105, Resulting Numbers: [78, 105] Generated Node #0,1,1: 14:[78, 105] Operation: 25+80=105 Exploring Operation: 80-25=55, Resulting Numbers: [78, 55] Generated Node #0,1,2: 14:[78, 55] Operation: 80-25=55 Exploring Operation: 78-25=53, Resulting Numbers: [80, 53] Generated Node #0,1,3: 14:[80, 53] Operation: 78-25=53 Exploring Operation: 25+78=103, Resulting Numbers: [80, 103] Generated Node #0,1,4: 14:[80, 103] Operation: 25+78=103 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[25, 2], Operations: ['90-12=78', '80-78=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,14 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 #0,1,2 Current State: 14:[78, 55], Operations: ['90-12=78', '80-25=55'] Exploring Operation: 78+55=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 78*55=4290, Resulting Numbers: [4290] 4290,14 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 #0,1,3 Current State: 14:[80, 53], Operations: ['90-12=78', '78-25=53'] Exploring Operation: 80+53=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 80*53=4240, Resulting Numbers: [4240] 4240,14 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 #0,1,1 Current State: 14:[78, 105], Operations: ['90-12=78', '25+80=105'] Exploring Operation: 78+105=183, Resulting Numbers: [183] 183,14 unequal: No Solution Exploring Operation: 105-78=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 78*105=8190, Resulting Numbers: [8190] 8190,14 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 #0,1,4 Current State: 14:[80, 103], Operations: ['90-12=78', '25+78=103'] Exploring Operation: 80+103=183, Resulting Numbers: [183] 183,14 unequal: No Solution Exploring Operation: 103-80=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 80*103=8240, Resulting Numbers: [8240] 8240,14 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 #0,2 Current State: 14:[90, 25, 68], Operations: ['80-12=68'] Exploring Operation: 90+68=158, Resulting Numbers: [25, 158] Generated Node #0,2,0: 14:[25, 158] Operation: 90+68=158 Exploring Operation: 90-25=65, Resulting Numbers: [68, 65] Generated Node #0,2,1: 14:[68, 65] Operation: 90-25=65 Exploring Operation: 90-68=22, Resulting Numbers: [25, 22] Generated Node #0,2,2: 14:[25, 22] Operation: 90-68=22 Exploring Operation: 68-25=43, Resulting Numbers: [90, 43] Generated Node #0,2,3: 14:[90, 43] Operation: 68-25=43 Exploring Operation: 90+25=115, Resulting Numbers: [68, 115] Generated Node #0,2,4: 14:[68, 115] Operation: 90+25=115 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 14:[25, 22], Operations: ['80-12=68', '90-68=22'] Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,14 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,14 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,14 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 #0,2,1 Current State: 14:[68, 65], Operations: ['80-12=68', '90-25=65'] Exploring Operation: 68*65=4420, Resulting Numbers: [4420] 4420,14 unequal: No Solution Exploring Operation: 68-65=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 68+65=133, Resulting Numbers: [133] 133,14 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 #0,2,3 Current State: 14:[90, 43], Operations: ['80-12=68', '68-25=43'] Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,14 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,14 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 #0,2,0 Current State: 14:[25, 158], Operations: ['80-12=68', '90+68=158'] Exploring Operation: 158-25=133, Resulting Numbers: [133] 133,14 unequal: No Solution Exploring Operation: 25*158=3950, Resulting Numbers: [3950] 3950,14 unequal: No Solution Exploring Operation: 25+158=183, Resulting Numbers: [183] 183,14 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 #0,2,4 Current State: 14:[68, 115], Operations: ['80-12=68', '90+25=115'] Exploring Operation: 68+115=183, Resulting Numbers: [183] 183,14 unequal: No Solution Exploring Operation: 115-68=47, Resulting Numbers: [47] 47,14 unequal: No Solution Exploring Operation: 68*115=7820, Resulting Numbers: [7820] 7820,14 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
mult_heuristic
[ 5, 23, 10, 12 ]
70
[ "10/5=2", "23+12=35", "2*35=70" ]
Current State: 70:[5, 23, 10, 12], Operations: [] Exploring Operation: 10/5=2, Resulting Numbers: [23, 12, 2] Generated Node #2: [23, 12, 2] from Operation: 10/5=2 Current State: 70:[23, 12, 2], Operations: ['10/5=2'] Exploring Operation: 23+12=35, Resulting Numbers: [2, 35] Generated Node #3: [2, 35] from Operation: 23+12=35 Current State: 70:[2, 35], Operations: ['10/5=2', '23+12=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[5, 23, 10, 12], Operations: [] Exploring Operation: 23+12=35, Resulting Numbers: [5, 10, 35] Generated Node #0,0: 70:[5, 10, 35] Operation: 23+12=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[5, 10, 35], Operations: ['23+12=35'] Exploring Operation: 10-5=5, Resulting Numbers: [35, 5] Generated Node #0,0,0: 70:[35, 5] Operation: 10-5=5 Moving to Node #0,0,0 Current State: 70:[35, 5], Operations: ['23+12=35', '10-5=5'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,70 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
[ 73, 5, 3, 23 ]
49
[ "73+5=78", "78/3=26", "23+26=49" ]
Current State: 49:[73, 5, 3, 23], Operations: [] Exploring Operation: 73+5=78, Resulting Numbers: [3, 23, 78] Generated Node #2: [3, 23, 78] from Operation: 73+5=78 Current State: 49:[3, 23, 78], Operations: ['73+5=78'] Exploring Operation: 78/3=26, Resulting Numbers: [23, 26] Generated Node #3: [23, 26] from Operation: 78/3=26 Current State: 49:[23, 26], Operations: ['73+5=78', '78/3=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[73, 5, 3, 23], Operations: [] Exploring Operation: 73-23=50, Resulting Numbers: [5, 3, 50] Generated Node #0,0: 49:[5, 3, 50] Operation: 73-23=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[5, 3, 50], Operations: ['73-23=50'] Exploring Operation: 5+3=8, Resulting Numbers: [50, 8] Generated Node #0,0,0: 49:[50, 8] Operation: 5+3=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[50, 8], Operations: ['73-23=50', '5+3=8'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 76, 44, 89 ]
84
[ "76-37=39", "89-44=45", "39+45=84" ]
Current State: 84:[37, 76, 44, 89], Operations: [] Exploring Operation: 76-37=39, Resulting Numbers: [44, 89, 39] Generated Node #2: [44, 89, 39] from Operation: 76-37=39 Current State: 84:[44, 89, 39], Operations: ['76-37=39'] Exploring Operation: 89-44=45, Resulting Numbers: [39, 45] Generated Node #3: [39, 45] from Operation: 89-44=45 Current State: 84:[39, 45], Operations: ['76-37=39', '89-44=45'] Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[37, 76, 44, 89], Operations: [] Exploring Operation: 76-37=39, Resulting Numbers: [44, 89, 39] Generated Node #0,0: 84:[44, 89, 39] Operation: 76-37=39 Exploring Operation: 89-76=13, Resulting Numbers: [37, 44, 13] Generated Node #0,1: 84:[37, 44, 13] Operation: 89-76=13 Exploring Operation: 44-37=7, Resulting Numbers: [76, 89, 7] Generated Node #0,2: 84:[76, 89, 7] Operation: 44-37=7 Exploring Operation: 37+44=81, Resulting Numbers: [76, 89, 81] Generated Node #0,3: 84:[76, 89, 81] Operation: 37+44=81 Exploring Operation: 76-44=32, Resulting Numbers: [37, 89, 32] Generated Node #0,4: 84:[37, 89, 32] Operation: 76-44=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[37, 44, 13], Operations: ['89-76=13'] Exploring Operation: 44-13=31, Resulting Numbers: [37, 31] Generated Node #0,1,0: 84:[37, 31] Operation: 44-13=31 Exploring Operation: 37+13=50, Resulting Numbers: [44, 50] Generated Node #0,1,1: 84:[44, 50] Operation: 37+13=50 Exploring Operation: 37-13=24, Resulting Numbers: [44, 24] Generated Node #0,1,2: 84:[44, 24] Operation: 37-13=24 Exploring Operation: 44-37=7, Resulting Numbers: [13, 7] Generated Node #0,1,3: 84:[13, 7] Operation: 44-37=7 Exploring Operation: 37+44=81, Resulting Numbers: [13, 81] Generated Node #0,1,4: 84:[13, 81] Operation: 37+44=81 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 84:[13, 7], Operations: ['89-76=13', '44-37=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,84 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 84:[13, 81], Operations: ['89-76=13', '37+44=81'] Exploring Operation: 13*81=1053, Resulting Numbers: [1053] 1053,84 unequal: No Solution Exploring Operation: 13+81=94, Resulting Numbers: [94] 94,84 unequal: No Solution Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 84:[44, 24], Operations: ['89-76=13', '37-13=24'] Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,84 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 84:[37, 31], Operations: ['89-76=13', '44-13=31'] Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,84 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 84:[44, 50], Operations: ['89-76=13', '37+13=50'] Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,84 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,84 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: 84:[44, 89, 39], Operations: ['76-37=39'] Exploring Operation: 89-44=45, Resulting Numbers: [39, 45] Generated Node #0,0,0: 84:[39, 45] Operation: 89-44=45 Exploring Operation: 44-39=5, Resulting Numbers: [89, 5] Generated Node #0,0,1: 84:[89, 5] Operation: 44-39=5 Exploring Operation: 89-39=50, Resulting Numbers: [44, 50] Generated Node #0,0,2: 84:[44, 50] Operation: 89-39=50 Exploring Operation: 44+39=83, Resulting Numbers: [89, 83] Generated Node #0,0,3: 84:[89, 83] Operation: 44+39=83 Exploring Operation: 89+39=128, Resulting Numbers: [44, 128] Generated Node #0,0,4: 84:[44, 128] Operation: 89+39=128 Moving to Node #0,0,0 Current State: 84:[39, 45], Operations: ['76-37=39', '89-44=45'] Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[37, 76, 44, 89], Operations: [] Exploring Operation: 76-37=39, Resulting Numbers: [44, 89, 39] Generated Node #0,0: 84:[44, 89, 39] Operation: 76-37=39 Moving to Node #0,0 Current State: 84:[44, 89, 39], Operations: ['76-37=39'] Exploring Operation: 89-44=45, Resulting Numbers: [39, 45] Generated Node #0,0,0: 84:[39, 45] Operation: 89-44=45 Moving to Node #0,0,0 Current State: 84:[39, 45], Operations: ['76-37=39', '89-44=45'] Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 6, 92, 39, 79 ]
39
[ "92-79=13", "6*13=78", "78-39=39" ]
Current State: 39:[6, 92, 39, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [6, 39, 13] Generated Node #2: [6, 39, 13] from Operation: 92-79=13 Current State: 39:[6, 39, 13], Operations: ['92-79=13'] Exploring Operation: 6*13=78, Resulting Numbers: [39, 78] Generated Node #3: [39, 78] from Operation: 6*13=78 Current State: 39:[39, 78], Operations: ['92-79=13', '6*13=78'] Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[6, 92, 39, 79], Operations: [] Exploring Operation: 79-39=40, Resulting Numbers: [6, 92, 40] Generated Node #0,0: 39:[6, 92, 40] Operation: 79-39=40 Exploring Operation: 92-6=86, Resulting Numbers: [39, 79, 86] Generated Node #0,1: 39:[39, 79, 86] Operation: 92-6=86 Exploring Operation: 79-6=73, Resulting Numbers: [92, 39, 73] Generated Node #0,2: 39:[92, 39, 73] Operation: 79-6=73 Exploring Operation: 92-39=53, Resulting Numbers: [6, 79, 53] Generated Node #0,3: 39:[6, 79, 53] Operation: 92-39=53 Exploring Operation: 92-79=13, Resulting Numbers: [6, 39, 13] Generated Node #0,4: 39:[6, 39, 13] Operation: 92-79=13 Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[6, 39, 13], Operations: ['92-79=13'] Exploring Operation: 39/13=3, Resulting Numbers: [6, 3] Generated Node #0,4,0: 39:[6, 3] Operation: 39/13=3 Exploring Operation: 39-6=33, Resulting Numbers: [13, 33] Generated Node #0,4,1: 39:[13, 33] Operation: 39-6=33 Exploring Operation: 13-6=7, Resulting Numbers: [39, 7] Generated Node #0,4,2: 39:[39, 7] Operation: 13-6=7 Exploring Operation: 6+13=19, Resulting Numbers: [39, 19] Generated Node #0,4,3: 39:[39, 19] Operation: 6+13=19 Exploring Operation: 6+39=45, Resulting Numbers: [13, 45] Generated Node #0,4,4: 39:[13, 45] Operation: 6+39=45 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 39:[6, 3], Operations: ['92-79=13', '39/13=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 39:[39, 7], Operations: ['92-79=13', '13-6=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 39*7=273, Resulting Numbers: [273] 273,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 39:[13, 33], Operations: ['92-79=13', '39-6=33'] Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,39 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,39 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 39:[39, 19], Operations: ['92-79=13', '6+13=19'] Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,39 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 39:[13, 45], Operations: ['92-79=13', '6+39=45'] Exploring Operation: 45-13=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 13*45=585, Resulting Numbers: [585] 585,39 unequal: No Solution Exploring Operation: 13+45=58, Resulting Numbers: [58] 58,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[6, 92, 40], Operations: ['79-39=40'] Exploring Operation: 92-6=86, Resulting Numbers: [40, 86] Generated Node #0,0,0: 39:[40, 86] Operation: 92-6=86 Exploring Operation: 40-6=34, Resulting Numbers: [92, 34] Generated Node #0,0,1: 39:[92, 34] Operation: 40-6=34 Exploring Operation: 6+92=98, Resulting Numbers: [40, 98] Generated Node #0,0,2: 39:[40, 98] Operation: 6+92=98 Exploring Operation: 92-40=52, Resulting Numbers: [6, 52] Generated Node #0,0,3: 39:[6, 52] Operation: 92-40=52 Exploring Operation: 6+40=46, Resulting Numbers: [92, 46] Generated Node #0,0,4: 39:[92, 46] Operation: 6+40=46 Moving to Node #0,0,3 Current State: 39:[6, 52], Operations: ['79-39=40', '92-40=52'] Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,39 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[40, 86], Operations: ['79-39=40', '92-6=86'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 40+86=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 40*86=3440, Resulting Numbers: [3440] 3440,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[92, 34], Operations: ['79-39=40', '40-6=34'] Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 92*34=3128, Resulting Numbers: [3128] 3128,39 unequal: No Solution Exploring Operation: 92+34=126, Resulting Numbers: [126] 126,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[40, 98], Operations: ['79-39=40', '6+92=98'] Exploring Operation: 40*98=3920, Resulting Numbers: [3920] 3920,39 unequal: No Solution Exploring Operation: 98-40=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 40+98=138, Resulting Numbers: [138] 138,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[92, 46], Operations: ['79-39=40', '6+40=46'] Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 92+46=138, Resulting Numbers: [138] 138,39 unequal: No Solution Exploring Operation: 92*46=4232, Resulting Numbers: [4232] 4232,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[6, 79, 53], Operations: ['92-39=53'] Exploring Operation: 79-6=73, Resulting Numbers: [53, 73] Generated Node #0,3,0: 39:[53, 73] Operation: 79-6=73 Exploring Operation: 6+79=85, Resulting Numbers: [53, 85] Generated Node #0,3,1: 39:[53, 85] Operation: 6+79=85 Exploring Operation: 79-53=26, Resulting Numbers: [6, 26] Generated Node #0,3,2: 39:[6, 26] Operation: 79-53=26 Exploring Operation: 6+53=59, Resulting Numbers: [79, 59] Generated Node #0,3,3: 39:[79, 59] Operation: 6+53=59 Exploring Operation: 53-6=47, Resulting Numbers: [79, 47] Generated Node #0,3,4: 39:[79, 47] Operation: 53-6=47 Moving to Node #0,3,2 Current State: 39:[6, 26], Operations: ['92-39=53', '79-53=26'] Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,39 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,39 unequal: No Solution Moving to Node #0,3,4 Current State: 39:[79, 47], Operations: ['92-39=53', '53-6=47'] Exploring Operation: 79*47=3713, Resulting Numbers: [3713] 3713,39 unequal: No Solution Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 79+47=126, Resulting Numbers: [126] 126,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[53, 73], Operations: ['92-39=53', '79-6=73'] Exploring Operation: 53*73=3869, Resulting Numbers: [3869] 3869,39 unequal: No Solution Exploring Operation: 53+73=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 73-53=20, Resulting Numbers: [20] 20,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[53, 85], Operations: ['92-39=53', '6+79=85'] Exploring Operation: 85-53=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 53*85=4505, Resulting Numbers: [4505] 4505,39 unequal: No Solution Exploring Operation: 53+85=138, Resulting Numbers: [138] 138,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[79, 59], Operations: ['92-39=53', '6+53=59'] Exploring Operation: 79*59=4661, Resulting Numbers: [4661] 4661,39 unequal: No Solution Exploring Operation: 79+59=138, Resulting Numbers: [138] 138,39 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[39, 79, 86], Operations: ['92-6=86'] Exploring Operation: 86-79=7, Resulting Numbers: [39, 7] Generated Node #0,1,0: 39:[39, 7] Operation: 86-79=7 Exploring Operation: 39+79=118, Resulting Numbers: [86, 118] Generated Node #0,1,1: 39:[86, 118] Operation: 39+79=118 Exploring Operation: 86-39=47, Resulting Numbers: [79, 47] Generated Node #0,1,2: 39:[79, 47] Operation: 86-39=47 Exploring Operation: 79-39=40, Resulting Numbers: [86, 40] Generated Node #0,1,3: 39:[86, 40] Operation: 79-39=40 Exploring Operation: 39+86=125, Resulting Numbers: [79, 125] Generated Node #0,1,4: 39:[79, 125] Operation: 39+86=125 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[39, 7], Operations: ['92-6=86', '86-79=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 39*7=273, Resulting Numbers: [273] 273,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 39:[79, 47], Operations: ['92-6=86', '86-39=47'] Exploring Operation: 79+47=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 79*47=3713, Resulting Numbers: [3713] 3713,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 39:[86, 40], Operations: ['92-6=86', '79-39=40'] Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,39 unequal: No Solution Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[86, 118], Operations: ['92-6=86', '39+79=118'] Exploring Operation: 86*118=10148, Resulting Numbers: [10148] 10148,39 unequal: No Solution Exploring Operation: 118-86=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 86+118=204, Resulting Numbers: [204] 204,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 39:[79, 125], Operations: ['92-6=86', '39+86=125'] Exploring Operation: 79*125=9875, Resulting Numbers: [9875] 9875,39 unequal: No Solution Exploring Operation: 79+125=204, Resulting Numbers: [204] 204,39 unequal: No Solution Exploring Operation: 125-79=46, Resulting Numbers: [46] 46,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[92, 39, 73], Operations: ['79-6=73'] Exploring Operation: 92-73=19, Resulting Numbers: [39, 19] Generated Node #0,2,0: 39:[39, 19] Operation: 92-73=19 Exploring Operation: 92+73=165, Resulting Numbers: [39, 165] Generated Node #0,2,1: 39:[39, 165] Operation: 92+73=165 Exploring Operation: 73-39=34, Resulting Numbers: [92, 34] Generated Node #0,2,2: 39:[92, 34] Operation: 73-39=34 Exploring Operation: 92+39=131, Resulting Numbers: [73, 131] Generated Node #0,2,3: 39:[73, 131] Operation: 92+39=131 Exploring Operation: 92-39=53, Resulting Numbers: [73, 53] Generated Node #0,2,4: 39:[73, 53] Operation: 92-39=53 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 39:[39, 19], Operations: ['79-6=73', '92-73=19'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,39 unequal: No Solution Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,39 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 39:[73, 53], Operations: ['79-6=73', '92-39=53'] Exploring Operation: 73+53=126, Resulting Numbers: [126] 126,39 unequal: No Solution Exploring Operation: 73*53=3869, Resulting Numbers: [3869] 3869,39 unequal: No Solution Exploring Operation: 73-53=20, Resulting Numbers: [20] 20,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 39:[92, 34], Operations: ['79-6=73', '73-39=34'] Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 92*34=3128, Resulting Numbers: [3128] 3128,39 unequal: No Solution Exploring Operation: 92+34=126, Resulting Numbers: [126] 126,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 39:[39, 165], Operations: ['79-6=73', '92+73=165'] Exploring Operation: 39+165=204, Resulting Numbers: [204] 204,39 unequal: No Solution Exploring Operation: 39*165=6435, Resulting Numbers: [6435] 6435,39 unequal: No Solution Exploring Operation: 165-39=126, Resulting Numbers: [126] 126,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 39:[73, 131], Operations: ['79-6=73', '92+39=131'] Exploring Operation: 131-73=58, Resulting Numbers: [58] 58,39 unequal: No Solution Exploring Operation: 73*131=9563, Resulting Numbers: [9563] 9563,39 unequal: No Solution Exploring Operation: 73+131=204, Resulting Numbers: [204] 204,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 52, 50, 83, 28 ]
47
[ "52+50=102", "83-28=55", "102-55=47" ]
Current State: 47:[52, 50, 83, 28], Operations: [] Exploring Operation: 52+50=102, Resulting Numbers: [83, 28, 102] Generated Node #2: [83, 28, 102] from Operation: 52+50=102 Current State: 47:[83, 28, 102], Operations: ['52+50=102'] Exploring Operation: 83-28=55, Resulting Numbers: [102, 55] Generated Node #3: [102, 55] from Operation: 83-28=55 Current State: 47:[102, 55], Operations: ['52+50=102', '83-28=55'] Exploring Operation: 102-55=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[52, 50, 83, 28], Operations: [] Exploring Operation: 83-50=33, Resulting Numbers: [52, 28, 33] Generated Node #0,0: 47:[52, 28, 33] Operation: 83-50=33 Exploring Operation: 83-28=55, Resulting Numbers: [52, 50, 55] Generated Node #0,1: 47:[52, 50, 55] Operation: 83-28=55 Exploring Operation: 83-52=31, Resulting Numbers: [50, 28, 31] Generated Node #0,2: 47:[50, 28, 31] Operation: 83-52=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[52, 50, 55], Operations: ['83-28=55'] Exploring Operation: 52-50=2, Resulting Numbers: [55, 2] Generated Node #0,1,0: 47:[55, 2] Operation: 52-50=2 Exploring Operation: 55-52=3, Resulting Numbers: [50, 3] Generated Node #0,1,1: 47:[50, 3] Operation: 55-52=3 Exploring Operation: 55-50=5, Resulting Numbers: [52, 5] Generated Node #0,1,2: 47:[52, 5] Operation: 55-50=5 Moving to Node #0,1,1 Current State: 47:[50, 3], Operations: ['83-28=55', '55-52=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,47 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[52, 50, 83, 28], Operations: [] Exploring Operation: 83-28=55, Resulting Numbers: [52, 50, 55] Generated Node #0,1: 47:[52, 50, 55] Operation: 83-28=55 Moving to Node #0,1 Current State: 47:[52, 50, 55], Operations: ['83-28=55'] Exploring Operation: 55-52=3, Resulting Numbers: [50, 3] Generated Node #0,1,1: 47:[50, 3] Operation: 55-52=3 Moving to Node #0,1,1 Current State: 47:[50, 3], Operations: ['83-28=55', '55-52=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 7, 77, 76, 81 ]
88
[ "7+81=88", "77-76=1", "88*1=88" ]
Current State: 88:[7, 77, 76, 81], Operations: [] Exploring Operation: 7+81=88, Resulting Numbers: [77, 76, 88] Generated Node #2: [77, 76, 88] from Operation: 7+81=88 Current State: 88:[77, 76, 88], Operations: ['7+81=88'] Exploring Operation: 77-76=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 77-76=1 Current State: 88:[88, 1], Operations: ['7+81=88', '77-76=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[7, 77, 76, 81], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [7, 81, 1] Generated Node #0,0: 88:[7, 81, 1] Operation: 77-76=1 Exploring Operation: 81-77=4, Resulting Numbers: [7, 76, 4] Generated Node #0,1: 88:[7, 76, 4] Operation: 81-77=4 Moving to Node #0,0 Current State: 88:[7, 81, 1], Operations: ['77-76=1'] Exploring Operation: 7+81=88, Resulting Numbers: [1, 88] Generated Node #0,0,0: 88:[1, 88] Operation: 7+81=88 Exploring Operation: 7+1=8, Resulting Numbers: [81, 8] Generated Node #0,0,1: 88:[81, 8] Operation: 7+1=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[1, 88], Operations: ['77-76=1', '7+81=88'] Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[7, 77, 76, 81], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [7, 81, 1] Generated Node #0,0: 88:[7, 81, 1] Operation: 77-76=1 Moving to Node #0,0 Current State: 88:[7, 81, 1], Operations: ['77-76=1'] Exploring Operation: 7+81=88, Resulting Numbers: [1, 88] Generated Node #0,0,0: 88:[1, 88] Operation: 7+81=88 Moving to Node #0,0,0 Current State: 88:[1, 88], Operations: ['77-76=1', '7+81=88'] Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 4, 20, 36, 33 ]
29
[ "36-20=16", "16/4=4", "33-4=29" ]
Current State: 29:[4, 20, 36, 33], Operations: [] Exploring Operation: 36-20=16, Resulting Numbers: [4, 33, 16] Generated Node #2: [4, 33, 16] from Operation: 36-20=16 Current State: 29:[4, 33, 16], Operations: ['36-20=16'] Exploring Operation: 16/4=4, Resulting Numbers: [33, 4] Generated Node #3: [33, 4] from Operation: 16/4=4 Current State: 29:[33, 4], Operations: ['36-20=16', '16/4=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[4, 20, 36, 33], Operations: [] Exploring Operation: 20-4=16, Resulting Numbers: [36, 33, 16] Generated Node #0,0: 29:[36, 33, 16] Operation: 20-4=16 Exploring Operation: 4+20=24, Resulting Numbers: [36, 33, 24] Generated Node #0,1: 29:[36, 33, 24] Operation: 4+20=24 Exploring Operation: 36-4=32, Resulting Numbers: [20, 33, 32] Generated Node #0,2: 29:[20, 33, 32] Operation: 36-4=32 Exploring Operation: 33-4=29, Resulting Numbers: [20, 36, 29] Generated Node #0,3: 29:[20, 36, 29] Operation: 33-4=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[36, 33, 24], Operations: ['4+20=24'] Exploring Operation: 33-24=9, Resulting Numbers: [36, 9] Generated Node #0,1,0: 29:[36, 9] Operation: 33-24=9 Exploring Operation: 36+24=60, Resulting Numbers: [33, 60] Generated Node #0,1,1: 29:[33, 60] Operation: 36+24=60 Exploring Operation: 36-33=3, Resulting Numbers: [24, 3] Generated Node #0,1,2: 29:[24, 3] Operation: 36-33=3 Exploring Operation: 36-24=12, Resulting Numbers: [33, 12] Generated Node #0,1,3: 29:[33, 12] Operation: 36-24=12 Moving to Node #0,1,3 Current State: 29:[33, 12], Operations: ['4+20=24', '36-24=12'] Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,29 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,29 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[36, 9], Operations: ['4+20=24', '33-24=9'] Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 36*9=324, Resulting Numbers: [324] 324,29 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 36+9=45, Resulting Numbers: [45] 45,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[24, 3], Operations: ['4+20=24', '36-33=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[33, 60], Operations: ['4+20=24', '36+24=60'] Exploring Operation: 33*60=1980, Resulting Numbers: [1980] 1980,29 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 33+60=93, Resulting Numbers: [93] 93,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[20, 33, 32], Operations: ['36-4=32'] Exploring Operation: 20+33=53, Resulting Numbers: [32, 53] Generated Node #0,2,0: 29:[32, 53] Operation: 20+33=53 Exploring Operation: 20+32=52, Resulting Numbers: [33, 52] Generated Node #0,2,1: 29:[33, 52] Operation: 20+32=52 Exploring Operation: 32-20=12, Resulting Numbers: [33, 12] Generated Node #0,2,2: 29:[33, 12] Operation: 32-20=12 Exploring Operation: 33-20=13, Resulting Numbers: [32, 13] Generated Node #0,2,3: 29:[32, 13] Operation: 33-20=13 Moving to Node #0,2,3 Current State: 29:[32, 13], Operations: ['36-4=32', '33-20=13'] Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,29 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[33, 12], Operations: ['36-4=32', '32-20=12'] Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,29 unequal: No Solution Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,29 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[33, 52], Operations: ['36-4=32', '20+32=52'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,29 unequal: No Solution Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[32, 53], Operations: ['36-4=32', '20+33=53'] Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,29 unequal: No Solution Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 29:[20, 36, 29], Operations: ['33-4=29'] Exploring Operation: 20+36=56, Resulting Numbers: [29, 56] Generated Node #0,3,0: 29:[29, 56] Operation: 20+36=56 Exploring Operation: 20+29=49, Resulting Numbers: [36, 49] Generated Node #0,3,1: 29:[36, 49] Operation: 20+29=49 Exploring Operation: 36-20=16, Resulting Numbers: [29, 16] Generated Node #0,3,2: 29:[29, 16] Operation: 36-20=16 Exploring Operation: 29-20=9, Resulting Numbers: [36, 9] Generated Node #0,3,3: 29:[36, 9] Operation: 29-20=9 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 29:[29, 16], Operations: ['33-4=29', '36-20=16'] Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,29 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,29 unequal: No Solution No 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: 29:[29, 56], Operations: ['33-4=29', '20+36=56'] Exploring Operation: 29*56=1624, Resulting Numbers: [1624] 1624,29 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,29 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,29 unequal: No Solution No 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: 29:[36, 49], Operations: ['33-4=29', '20+29=49'] Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,29 unequal: No Solution Exploring Operation: 36*49=1764, Resulting Numbers: [1764] 1764,29 unequal: No Solution Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,29 unequal: No Solution No 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: 29:[36, 9], Operations: ['33-4=29', '29-20=9'] Exploring Operation: 36*9=324, Resulting Numbers: [324] 324,29 unequal: No Solution Exploring Operation: 36+9=45, Resulting Numbers: [45] 45,29 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,29 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: 29:[36, 33, 16], Operations: ['20-4=16'] Exploring Operation: 33-16=17, Resulting Numbers: [36, 17] Generated Node #0,0,0: 29:[36, 17] Operation: 33-16=17 Exploring Operation: 36-16=20, Resulting Numbers: [33, 20] Generated Node #0,0,1: 29:[33, 20] Operation: 36-16=20 Exploring Operation: 33+16=49, Resulting Numbers: [36, 49] Generated Node #0,0,2: 29:[36, 49] Operation: 33+16=49 Exploring Operation: 36+16=52, Resulting Numbers: [33, 52] Generated Node #0,0,3: 29:[33, 52] Operation: 36+16=52 Moving to Node #0,0,1 Current State: 29:[33, 20], Operations: ['20-4=16', '36-16=20'] Exploring Operation: 33*20=660, Resulting Numbers: [660] 660,29 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 33+20=53, Resulting Numbers: [53] 53,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[36, 17], Operations: ['20-4=16', '33-16=17'] Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,29 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[33, 52], Operations: ['20-4=16', '36+16=52'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,29 unequal: No Solution Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[36, 49], Operations: ['20-4=16', '33+16=49'] Exploring Operation: 36*49=1764, Resulting Numbers: [1764] 1764,29 unequal: No Solution Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 6, 2, 19, 4 ]
61
[ "6/2=3", "19*3=57", "4+57=61" ]
Current State: 61:[6, 2, 19, 4], Operations: [] Exploring Operation: 6/2=3, Resulting Numbers: [19, 4, 3] Generated Node #2: [19, 4, 3] from Operation: 6/2=3 Current State: 61:[19, 4, 3], Operations: ['6/2=3'] Exploring Operation: 19*3=57, Resulting Numbers: [4, 57] Generated Node #3: [4, 57] from Operation: 19*3=57 Current State: 61:[4, 57], Operations: ['6/2=3', '19*3=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[6, 2, 19, 4], Operations: [] Exploring Operation: 2*19=38, Resulting Numbers: [6, 4, 38] Generated Node #0,0: 61:[6, 4, 38] Operation: 2*19=38 Exploring Operation: 19*4=76, Resulting Numbers: [6, 2, 76] Generated Node #0,1: 61:[6, 2, 76] Operation: 19*4=76 Moving to Node #0,1 Current State: 61:[6, 2, 76], Operations: ['19*4=76'] Exploring Operation: 6+2=8, Resulting Numbers: [76, 8] Generated Node #0,1,0: 61:[76, 8] Operation: 6+2=8 Exploring Operation: 6*2=12, Resulting Numbers: [76, 12] Generated Node #0,1,1: 61:[76, 12] Operation: 6*2=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[76, 12], Operations: ['19*4=76', '6*2=12'] Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,61 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:[76, 8], Operations: ['19*4=76', '6+2=8'] Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,61 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,61 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: 61:[6, 4, 38], Operations: ['2*19=38'] Exploring Operation: 6+4=10, Resulting Numbers: [38, 10] Generated Node #0,0,0: 61:[38, 10] Operation: 6+4=10 Exploring Operation: 6*4=24, Resulting Numbers: [38, 24] Generated Node #0,0,1: 61:[38, 24] Operation: 6*4=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[38, 24], Operations: ['2*19=38', '6*4=24'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,61 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:[38, 10], Operations: ['2*19=38', '6+4=10'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 38+10=48, Resulting Numbers: [48] 48,61 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
[ 5, 15, 29, 37 ]
67
[ "5*15=75", "37-29=8", "75-8=67" ]
Current State: 67:[5, 15, 29, 37], Operations: [] Exploring Operation: 5*15=75, Resulting Numbers: [29, 37, 75] Generated Node #2: [29, 37, 75] from Operation: 5*15=75 Current State: 67:[29, 37, 75], Operations: ['5*15=75'] Exploring Operation: 37-29=8, Resulting Numbers: [75, 8] Generated Node #3: [75, 8] from Operation: 37-29=8 Current State: 67:[75, 8], Operations: ['5*15=75', '37-29=8'] Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[5, 15, 29, 37], Operations: [] Exploring Operation: 5+29=34, Resulting Numbers: [15, 37, 34] Generated Node #0,0: 67:[15, 37, 34] Operation: 5+29=34 Exploring Operation: 5+37=42, Resulting Numbers: [15, 29, 42] Generated Node #0,1: 67:[15, 29, 42] Operation: 5+37=42 Exploring Operation: 5+15=20, Resulting Numbers: [29, 37, 20] Generated Node #0,2: 67:[29, 37, 20] Operation: 5+15=20 Exploring Operation: 5*15=75, Resulting Numbers: [29, 37, 75] Generated Node #0,3: 67:[29, 37, 75] Operation: 5*15=75 Moving to Node #0,3 Current State: 67:[29, 37, 75], Operations: ['5*15=75'] Exploring Operation: 75-29=46, Resulting Numbers: [37, 46] Generated Node #0,3,0: 67:[37, 46] Operation: 75-29=46 Exploring Operation: 37-29=8, Resulting Numbers: [75, 8] Generated Node #0,3,1: 67:[75, 8] Operation: 37-29=8 Exploring Operation: 29+75=104, Resulting Numbers: [37, 104] Generated Node #0,3,2: 67:[37, 104] Operation: 29+75=104 Exploring Operation: 29+37=66, Resulting Numbers: [75, 66] Generated Node #0,3,3: 67:[75, 66] Operation: 29+37=66 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 67:[75, 66], Operations: ['5*15=75', '29+37=66'] Exploring Operation: 75+66=141, Resulting Numbers: [141] 141,67 unequal: No Solution Exploring Operation: 75*66=4950, Resulting Numbers: [4950] 4950,67 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[37, 46], Operations: ['5*15=75', '75-29=46'] Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,67 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,67 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[75, 8], Operations: ['5*15=75', '37-29=8'] Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,67 unequal: No Solution Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[5, 15, 29, 37], Operations: [] Exploring Operation: 5*15=75, Resulting Numbers: [29, 37, 75] Generated Node #0,3: 67:[29, 37, 75] Operation: 5*15=75 Moving to Node #0,3 Current State: 67:[29, 37, 75], Operations: ['5*15=75'] Exploring Operation: 37-29=8, Resulting Numbers: [75, 8] Generated Node #0,3,1: 67:[75, 8] Operation: 37-29=8 Moving to Node #0,3,1 Current State: 67:[75, 8], Operations: ['5*15=75', '37-29=8'] Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 21, 48, 8, 47 ]
79
[ "21*48=1008", "1008/8=126", "126-47=79" ]
Current State: 79:[21, 48, 8, 47], Operations: [] Exploring Operation: 21*48=1008, Resulting Numbers: [8, 47, 1008] Generated Node #2: [8, 47, 1008] from Operation: 21*48=1008 Current State: 79:[8, 47, 1008], Operations: ['21*48=1008'] Exploring Operation: 1008/8=126, Resulting Numbers: [47, 126] Generated Node #3: [47, 126] from Operation: 1008/8=126 Current State: 79:[47, 126], Operations: ['21*48=1008', '1008/8=126'] Exploring Operation: 126-47=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[21, 48, 8, 47], Operations: [] Exploring Operation: 21+48=69, Resulting Numbers: [8, 47, 69] Generated Node #0,0: 79:[8, 47, 69] Operation: 21+48=69 Moving to Node #0,0 Current State: 79:[8, 47, 69], Operations: ['21+48=69'] Exploring Operation: 8+47=55, Resulting Numbers: [69, 55] Generated Node #0,0,0: 79:[69, 55] Operation: 8+47=55 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[69, 55], Operations: ['21+48=69', '8+47=55'] Exploring Operation: 69+55=124, Resulting Numbers: [124] 124,79 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
[ 5, 75, 91, 38 ]
17
[ "75-5=70", "91-38=53", "70-53=17" ]
Current State: 17:[5, 75, 91, 38], Operations: [] Exploring Operation: 75-5=70, Resulting Numbers: [91, 38, 70] Generated Node #2: [91, 38, 70] from Operation: 75-5=70 Current State: 17:[91, 38, 70], Operations: ['75-5=70'] Exploring Operation: 91-38=53, Resulting Numbers: [70, 53] Generated Node #3: [70, 53] from Operation: 91-38=53 Current State: 17:[70, 53], Operations: ['75-5=70', '91-38=53'] Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[5, 75, 91, 38], Operations: [] Exploring Operation: 91-38=53, Resulting Numbers: [5, 75, 53] Generated Node #0,0: 17:[5, 75, 53] Operation: 91-38=53 Exploring Operation: 75-5=70, Resulting Numbers: [91, 38, 70] Generated Node #0,1: 17:[91, 38, 70] Operation: 75-5=70 Exploring Operation: 75-38=37, Resulting Numbers: [5, 91, 37] Generated Node #0,2: 17:[5, 91, 37] Operation: 75-38=37 Exploring Operation: 75/5=15, Resulting Numbers: [91, 38, 15] Generated Node #0,3: 17:[91, 38, 15] Operation: 75/5=15 Exploring Operation: 91-75=16, Resulting Numbers: [5, 38, 16] Generated Node #0,4: 17:[5, 38, 16] Operation: 91-75=16 Moving to Node #0,4 Current State: 17:[5, 38, 16], Operations: ['91-75=16'] Exploring Operation: 5+16=21, Resulting Numbers: [38, 21] Generated Node #0,4,0: 17:[38, 21] Operation: 5+16=21 Exploring Operation: 5+38=43, Resulting Numbers: [16, 43] Generated Node #0,4,1: 17:[16, 43] Operation: 5+38=43 Exploring Operation: 38-5=33, Resulting Numbers: [16, 33] Generated Node #0,4,2: 17:[16, 33] Operation: 38-5=33 Exploring Operation: 38-16=22, Resulting Numbers: [5, 22] Generated Node #0,4,3: 17:[5, 22] Operation: 38-16=22 Exploring Operation: 16-5=11, Resulting Numbers: [38, 11] Generated Node #0,4,4: 17:[38, 11] Operation: 16-5=11 Moving to Node #0,3 Current State: 17:[91, 38, 15], Operations: ['75/5=15'] Exploring Operation: 91-38=53, Resulting Numbers: [15, 53] Generated Node #0,3,0: 17:[15, 53] Operation: 91-38=53 Exploring Operation: 38+15=53, Resulting Numbers: [91, 53] Generated Node #0,3,1: 17:[91, 53] Operation: 38+15=53 Exploring Operation: 38-15=23, Resulting Numbers: [91, 23] Generated Node #0,3,2: 17:[91, 23] Operation: 38-15=23 Exploring Operation: 91-15=76, Resulting Numbers: [38, 76] Generated Node #0,3,3: 17:[38, 76] Operation: 91-15=76 Exploring Operation: 91+15=106, Resulting Numbers: [38, 106] Generated Node #0,3,4: 17:[38, 106] Operation: 91+15=106 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 17:[15, 53], Operations: ['75/5=15', '91-38=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[91, 23], Operations: ['75/5=15', '38-15=23'] Exploring Operation: 91+23=114, Resulting Numbers: [114] 114,17 unequal: No Solution Exploring Operation: 91*23=2093, Resulting Numbers: [2093] 2093,17 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 17:[38, 76], Operations: ['75/5=15', '91-15=76'] Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,17 unequal: No Solution Exploring Operation: 38*76=2888, Resulting Numbers: [2888] 2888,17 unequal: No Solution Exploring Operation: 38+76=114, Resulting Numbers: [114] 114,17 unequal: No Solution Exploring Operation: 76/38=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 17:[91, 53], Operations: ['75/5=15', '38+15=53'] Exploring Operation: 91+53=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 91*53=4823, Resulting Numbers: [4823] 4823,17 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 17:[38, 106], Operations: ['75/5=15', '91+15=106'] Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,17 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: 17:[5, 75, 53], Operations: ['91-38=53'] Exploring Operation: 5+75=80, Resulting Numbers: [53, 80] Generated Node #0,0,0: 17:[53, 80] Operation: 5+75=80 Exploring Operation: 75/5=15, Resulting Numbers: [53, 15] Generated Node #0,0,1: 17:[53, 15] Operation: 75/5=15 Exploring Operation: 75-53=22, Resulting Numbers: [5, 22] Generated Node #0,0,2: 17:[5, 22] Operation: 75-53=22 Exploring Operation: 53-5=48, Resulting Numbers: [75, 48] Generated Node #0,0,3: 17:[75, 48] Operation: 53-5=48 Exploring Operation: 75-5=70, Resulting Numbers: [53, 70] Generated Node #0,0,4: 17:[53, 70] Operation: 75-5=70 Moving to Node #0,2 Current State: 17:[5, 91, 37], Operations: ['75-38=37'] Exploring Operation: 37-5=32, Resulting Numbers: [91, 32] Generated Node #0,2,0: 17:[91, 32] Operation: 37-5=32 Exploring Operation: 91-5=86, Resulting Numbers: [37, 86] Generated Node #0,2,1: 17:[37, 86] Operation: 91-5=86 Exploring Operation: 91-37=54, Resulting Numbers: [5, 54] Generated Node #0,2,2: 17:[5, 54] Operation: 91-37=54 Exploring Operation: 5+91=96, Resulting Numbers: [37, 96] Generated Node #0,2,3: 17:[37, 96] Operation: 5+91=96 Exploring Operation: 5+37=42, Resulting Numbers: [91, 42] Generated Node #0,2,4: 17:[91, 42] Operation: 5+37=42 Moving to Node #0,1 Current State: 17:[91, 38, 70], Operations: ['75-5=70'] Exploring Operation: 91-38=53, Resulting Numbers: [70, 53] Generated Node #0,1,0: 17:[70, 53] Operation: 91-38=53 Exploring Operation: 91+70=161, Resulting Numbers: [38, 161] Generated Node #0,1,1: 17:[38, 161] Operation: 91+70=161 Exploring Operation: 91+38=129, Resulting Numbers: [70, 129] Generated Node #0,1,2: 17:[70, 129] Operation: 91+38=129 Exploring Operation: 70-38=32, Resulting Numbers: [91, 32] Generated Node #0,1,3: 17:[91, 32] Operation: 70-38=32 Exploring Operation: 91-70=21, Resulting Numbers: [38, 21] Generated Node #0,1,4: 17:[38, 21] Operation: 91-70=21 Moving to Node #0,4,2 Current State: 17:[16, 33], Operations: ['91-75=16', '38-5=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[5, 75, 91, 38], Operations: [] Exploring Operation: 91-75=16, Resulting Numbers: [5, 38, 16] Generated Node #0,4: 17:[5, 38, 16] Operation: 91-75=16 Moving to Node #0,4 Current State: 17:[5, 38, 16], Operations: ['91-75=16'] Exploring Operation: 38-5=33, Resulting Numbers: [16, 33] Generated Node #0,4,2: 17:[16, 33] Operation: 38-5=33 Moving to Node #0,4,2 Current State: 17:[16, 33], Operations: ['91-75=16', '38-5=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.955729
hs_5
sum_heuristic
[ 19, 15, 23, 42 ]
50
[ "19-15=4", "23*4=92", "92-42=50" ]
Current State: 50:[19, 15, 23, 42], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [23, 42, 4] Generated Node #2: [23, 42, 4] from Operation: 19-15=4 Current State: 50:[23, 42, 4], Operations: ['19-15=4'] Exploring Operation: 23*4=92, Resulting Numbers: [42, 92] Generated Node #3: [42, 92] from Operation: 23*4=92 Current State: 50:[42, 92], Operations: ['19-15=4', '23*4=92'] Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[19, 15, 23, 42], Operations: [] Exploring Operation: 42-19=23, Resulting Numbers: [15, 23, 23] Generated Node #0,0: 50:[15, 23, 23] Operation: 42-19=23 Exploring Operation: 19-15=4, Resulting Numbers: [23, 42, 4] Generated Node #0,1: 50:[23, 42, 4] Operation: 19-15=4 Exploring Operation: 42-15=27, Resulting Numbers: [19, 23, 27] Generated Node #0,2: 50:[19, 23, 27] Operation: 42-15=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[15, 23, 23], Operations: ['42-19=23'] Exploring Operation: 23-15=8, Resulting Numbers: [23, 8] Generated Node #0,0,0: 50:[23, 8] Operation: 23-15=8 Exploring Operation: 23/23=1, Resulting Numbers: [15, 1] Generated Node #0,0,1: 50:[15, 1] Operation: 23/23=1 Exploring Operation: 23-15=8, Resulting Numbers: [23, 8] Generated Node #0,0,2: 50:[23, 8] Operation: 23-15=8 Moving to Node #0,0,0 Current State: 50:[23, 8], Operations: ['42-19=23', '23-15=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,50 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[23, 8], Operations: ['42-19=23', '23-15=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[15, 1], Operations: ['42-19=23', '23/23=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[19, 23, 27], Operations: ['42-15=27'] Exploring Operation: 19+27=46, Resulting Numbers: [23, 46] Generated Node #0,2,0: 50:[23, 46] Operation: 19+27=46 Exploring Operation: 27-19=8, Resulting Numbers: [23, 8] Generated Node #0,2,1: 50:[23, 8] Operation: 27-19=8 Exploring Operation: 23-19=4, Resulting Numbers: [27, 4] Generated Node #0,2,2: 50:[27, 4] Operation: 23-19=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 50:[27, 4], Operations: ['42-15=27', '23-19=4'] Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,50 unequal: No Solution No 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: 50:[23, 8], Operations: ['42-15=27', '27-19=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,50 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,50 unequal: No Solution No 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: 50:[23, 46], Operations: ['42-15=27', '19+27=46'] Exploring Operation: 23+46=69, Resulting Numbers: [69] 69,50 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,50 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: 50:[23, 42, 4], Operations: ['19-15=4'] Exploring Operation: 42+4=46, Resulting Numbers: [23, 46] Generated Node #0,1,0: 50:[23, 46] Operation: 42+4=46 Exploring Operation: 42-23=19, Resulting Numbers: [4, 19] Generated Node #0,1,1: 50:[4, 19] Operation: 42-23=19 Exploring Operation: 23+4=27, Resulting Numbers: [42, 27] Generated Node #0,1,2: 50:[42, 27] Operation: 23+4=27 Moving to Node #0,1,0 Current State: 50:[23, 46], Operations: ['19-15=4', '42+4=46'] Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 23+46=69, Resulting Numbers: [69] 69,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[4, 19], Operations: ['19-15=4', '42-23=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,50 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[42, 27], Operations: ['19-15=4', '23+4=27'] Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,50 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,50 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,50 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
[ 67, 58, 26, 51 ]
100
[ "67+58=125", "51-26=25", "125-25=100" ]
Current State: 100:[67, 58, 26, 51], Operations: [] Exploring Operation: 67+58=125, Resulting Numbers: [26, 51, 125] Generated Node #2: [26, 51, 125] from Operation: 67+58=125 Current State: 100:[26, 51, 125], Operations: ['67+58=125'] Exploring Operation: 51-26=25, Resulting Numbers: [125, 25] Generated Node #3: [125, 25] from Operation: 51-26=25 Current State: 100:[125, 25], Operations: ['67+58=125', '51-26=25'] Exploring Operation: 125-25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[67, 58, 26, 51], Operations: [] Exploring Operation: 67-58=9, Resulting Numbers: [26, 51, 9] Generated Node #0,0: 100:[26, 51, 9] Operation: 67-58=9 Exploring Operation: 67-51=16, Resulting Numbers: [58, 26, 16] Generated Node #0,1: 100:[58, 26, 16] Operation: 67-51=16 Exploring Operation: 67+26=93, Resulting Numbers: [58, 51, 93] Generated Node #0,2: 100:[58, 51, 93] Operation: 67+26=93 Exploring Operation: 67-26=41, Resulting Numbers: [58, 51, 41] Generated Node #0,3: 100:[58, 51, 41] Operation: 67-26=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[26, 51, 9], Operations: ['67-58=9'] Exploring Operation: 26+9=35, Resulting Numbers: [51, 35] Generated Node #0,0,0: 100:[51, 35] Operation: 26+9=35 Exploring Operation: 51-9=42, Resulting Numbers: [26, 42] Generated Node #0,0,1: 100:[26, 42] Operation: 51-9=42 Exploring Operation: 26-9=17, Resulting Numbers: [51, 17] Generated Node #0,0,2: 100:[51, 17] Operation: 26-9=17 Exploring Operation: 51-26=25, Resulting Numbers: [9, 25] Generated Node #0,0,3: 100:[9, 25] Operation: 51-26=25 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 100:[9, 25], Operations: ['67-58=9', '51-26=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 100:[51, 17], Operations: ['67-58=9', '26-9=17'] Exploring Operation: 51+17=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 51*17=867, Resulting Numbers: [867] 867,100 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[26, 42], Operations: ['67-58=9', '51-9=42'] Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,100 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[51, 35], Operations: ['67-58=9', '26+9=35'] Exploring Operation: 51*35=1785, Resulting Numbers: [1785] 1785,100 unequal: No Solution Exploring Operation: 51-35=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 51+35=86, Resulting Numbers: [86] 86,100 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: 100:[58, 26, 16], Operations: ['67-51=16'] Exploring Operation: 26-16=10, Resulting Numbers: [58, 10] Generated Node #0,1,0: 100:[58, 10] Operation: 26-16=10 Exploring Operation: 26+16=42, Resulting Numbers: [58, 42] Generated Node #0,1,1: 100:[58, 42] Operation: 26+16=42 Exploring Operation: 58-16=42, Resulting Numbers: [26, 42] Generated Node #0,1,2: 100:[26, 42] Operation: 58-16=42 Exploring Operation: 58-26=32, Resulting Numbers: [16, 32] Generated Node #0,1,3: 100:[16, 32] Operation: 58-26=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[58, 10], Operations: ['67-51=16', '26-16=10'] Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,100 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 100:[26, 42], Operations: ['67-51=16', '58-16=42'] Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 100:[16, 32], Operations: ['67-51=16', '58-26=32'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 16*32=512, Resulting Numbers: [512] 512,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[58, 42], Operations: ['67-51=16', '26+16=42'] Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[67, 58, 26, 51], Operations: [] Exploring Operation: 67-51=16, Resulting Numbers: [58, 26, 16] Generated Node #0,1: 100:[58, 26, 16] Operation: 67-51=16 Moving to Node #0,1 Current State: 100:[58, 26, 16], Operations: ['67-51=16'] Exploring Operation: 26+16=42, Resulting Numbers: [58, 42] Generated Node #0,1,1: 100:[58, 42] Operation: 26+16=42 Moving to Node #0,1,1 Current State: 100:[58, 42], Operations: ['67-51=16', '26+16=42'] Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 9, 2, 70, 69 ]
86
[ "9+69=78", "2*78=156", "156-70=86" ]
Current State: 86:[9, 2, 70, 69], Operations: [] Exploring Operation: 9+69=78, Resulting Numbers: [2, 70, 78] Generated Node #2: [2, 70, 78] from Operation: 9+69=78 Current State: 86:[2, 70, 78], Operations: ['9+69=78'] Exploring Operation: 2*78=156, Resulting Numbers: [70, 156] Generated Node #3: [70, 156] from Operation: 2*78=156 Current State: 86:[70, 156], Operations: ['9+69=78', '2*78=156'] Exploring Operation: 156-70=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[9, 2, 70, 69], Operations: [] Exploring Operation: 9+70=79, Resulting Numbers: [2, 69, 79] Generated Node #0,0: 86:[2, 69, 79] Operation: 9+70=79 Exploring Operation: 9+69=78, Resulting Numbers: [2, 70, 78] Generated Node #0,1: 86:[2, 70, 78] Operation: 9+69=78 Exploring Operation: 70/2=35, Resulting Numbers: [9, 69, 35] Generated Node #0,2: 86:[9, 69, 35] Operation: 70/2=35 Exploring Operation: 70-69=1, Resulting Numbers: [9, 2, 1] Generated Node #0,3: 86:[9, 2, 1] Operation: 70-69=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[9, 2, 1], Operations: ['70-69=1'] Exploring Operation: 9*1=9, Resulting Numbers: [2, 9] Generated Node #0,3,0: 86:[2, 9] Operation: 9*1=9 Exploring Operation: 9-2=7, Resulting Numbers: [1, 7] Generated Node #0,3,1: 86:[1, 7] Operation: 9-2=7 Exploring Operation: 9/1=9, Resulting Numbers: [2, 9] Generated Node #0,3,2: 86:[2, 9] Operation: 9/1=9 Exploring Operation: 9-1=8, Resulting Numbers: [2, 8] Generated Node #0,3,3: 86:[2, 8] Operation: 9-1=8 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 86:[1, 7], Operations: ['70-69=1', '9-2=7'] Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,86 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 #0,3,3 Current State: 86:[2, 8], Operations: ['70-69=1', '9-1=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,86 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,86 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,86 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 #0,3,0 Current State: 86:[2, 9], Operations: ['70-69=1', '9*1=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,86 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 #0,3,2 Current State: 86:[2, 9], Operations: ['70-69=1', '9/1=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,86 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 #0,0 Current State: 86:[2, 69, 79], Operations: ['9+70=79'] Exploring Operation: 79-69=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 86:[2, 10] Operation: 79-69=10 Exploring Operation: 2+69=71, Resulting Numbers: [79, 71] Generated Node #0,0,1: 86:[79, 71] Operation: 2+69=71 Exploring Operation: 69-2=67, Resulting Numbers: [79, 67] Generated Node #0,0,2: 86:[79, 67] Operation: 69-2=67 Exploring Operation: 2+79=81, Resulting Numbers: [69, 81] Generated Node #0,0,3: 86:[69, 81] Operation: 2+79=81 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[2, 10], Operations: ['9+70=79', '79-69=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[79, 71], Operations: ['9+70=79', '2+69=71'] Exploring Operation: 79+71=150, Resulting Numbers: [150] 150,86 unequal: No Solution Exploring Operation: 79*71=5609, Resulting Numbers: [5609] 5609,86 unequal: No Solution Exploring Operation: 79-71=8, Resulting Numbers: [8] 8,86 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 #0,0,3 Current State: 86:[69, 81], Operations: ['9+70=79', '2+79=81'] Exploring Operation: 69*81=5589, Resulting Numbers: [5589] 5589,86 unequal: No Solution Exploring Operation: 81-69=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 69+81=150, Resulting Numbers: [150] 150,86 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 #0,0,2 Current State: 86:[79, 67], Operations: ['9+70=79', '69-2=67'] Exploring Operation: 79+67=146, Resulting Numbers: [146] 146,86 unequal: No Solution Exploring Operation: 79*67=5293, Resulting Numbers: [5293] 5293,86 unequal: No Solution Exploring Operation: 79-67=12, Resulting Numbers: [12] 12,86 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:[2, 70, 78], Operations: ['9+69=78'] Exploring Operation: 78-70=8, Resulting Numbers: [2, 8] Generated Node #0,1,0: 86:[2, 8] Operation: 78-70=8 Exploring Operation: 78/2=39, Resulting Numbers: [70, 39] Generated Node #0,1,1: 86:[70, 39] Operation: 78/2=39 Exploring Operation: 2+70=72, Resulting Numbers: [78, 72] Generated Node #0,1,2: 86:[78, 72] Operation: 2+70=72 Exploring Operation: 70/2=35, Resulting Numbers: [78, 35] Generated Node #0,1,3: 86:[78, 35] Operation: 70/2=35 Moving to Node #0,1,0 Current State: 86:[2, 8], Operations: ['9+69=78', '78-70=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,86 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,86 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[78, 35], Operations: ['9+69=78', '70/2=35'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,86 unequal: No Solution Exploring Operation: 78*35=2730, Resulting Numbers: [2730] 2730,86 unequal: No Solution Exploring Operation: 78+35=113, Resulting Numbers: [113] 113,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[70, 39], Operations: ['9+69=78', '78/2=39'] Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 70*39=2730, Resulting Numbers: [2730] 2730,86 unequal: No Solution Exploring Operation: 70+39=109, Resulting Numbers: [109] 109,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[78, 72], Operations: ['9+69=78', '2+70=72'] Exploring Operation: 78*72=5616, Resulting Numbers: [5616] 5616,86 unequal: No Solution Exploring Operation: 78+72=150, Resulting Numbers: [150] 150,86 unequal: No Solution Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[9, 69, 35], Operations: ['70/2=35'] Exploring Operation: 69-35=34, Resulting Numbers: [9, 34] Generated Node #0,2,0: 86:[9, 34] Operation: 69-35=34 Exploring Operation: 9+35=44, Resulting Numbers: [69, 44] Generated Node #0,2,1: 86:[69, 44] Operation: 9+35=44 Exploring Operation: 9+69=78, Resulting Numbers: [35, 78] Generated Node #0,2,2: 86:[35, 78] Operation: 9+69=78 Exploring Operation: 69-9=60, Resulting Numbers: [35, 60] Generated Node #0,2,3: 86:[35, 60] Operation: 69-9=60 Moving to Node #0,2,0 Current State: 86:[9, 34], Operations: ['70/2=35', '69-35=34'] Exploring Operation: 9*34=306, Resulting Numbers: [306] 306,86 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[35, 78], Operations: ['70/2=35', '9+69=78'] Exploring Operation: 35+78=113, Resulting Numbers: [113] 113,86 unequal: No Solution Exploring Operation: 35*78=2730, Resulting Numbers: [2730] 2730,86 unequal: No Solution Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[69, 44], Operations: ['70/2=35', '9+35=44'] Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,86 unequal: No Solution Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,86 unequal: No Solution Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[35, 60], Operations: ['70/2=35', '69-9=60'] Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,86 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 9, 45, 61, 84 ]
12
[ "9+45=54", "61-54=7", "84/7=12" ]
Current State: 12:[9, 45, 61, 84], Operations: [] Exploring Operation: 9+45=54, Resulting Numbers: [61, 84, 54] Generated Node #2: [61, 84, 54] from Operation: 9+45=54 Current State: 12:[61, 84, 54], Operations: ['9+45=54'] Exploring Operation: 61-54=7, Resulting Numbers: [84, 7] Generated Node #3: [84, 7] from Operation: 61-54=7 Current State: 12:[84, 7], Operations: ['9+45=54', '61-54=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[9, 45, 61, 84], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [9, 84, 16] Generated Node #0,0: 12:[9, 84, 16] Operation: 61-45=16 Exploring Operation: 84-45=39, Resulting Numbers: [9, 61, 39] Generated Node #0,1: 12:[9, 61, 39] Operation: 84-45=39 Exploring Operation: 84-61=23, Resulting Numbers: [9, 45, 23] Generated Node #0,2: 12:[9, 45, 23] Operation: 84-61=23 Exploring Operation: 45/9=5, Resulting Numbers: [61, 84, 5] Generated Node #0,3: 12:[61, 84, 5] Operation: 45/9=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[9, 45, 23], Operations: ['84-61=23'] Exploring Operation: 45-9=36, Resulting Numbers: [23, 36] Generated Node #0,2,0: 12:[23, 36] Operation: 45-9=36 Exploring Operation: 45/9=5, Resulting Numbers: [23, 5] Generated Node #0,2,1: 12:[23, 5] Operation: 45/9=5 Exploring Operation: 45-23=22, Resulting Numbers: [9, 22] Generated Node #0,2,2: 12:[9, 22] Operation: 45-23=22 Exploring Operation: 23-9=14, Resulting Numbers: [45, 14] Generated Node #0,2,3: 12:[45, 14] Operation: 23-9=14 Moving to Node #0,2,1 Current State: 12:[23, 5], Operations: ['84-61=23', '45/9=5'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,12 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[9, 22], Operations: ['84-61=23', '45-23=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,12 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,12 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[45, 14], Operations: ['84-61=23', '23-9=14'] Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,12 unequal: No Solution Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[23, 36], Operations: ['84-61=23', '45-9=36'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[9, 84, 16], Operations: ['61-45=16'] Exploring Operation: 84-9=75, Resulting Numbers: [16, 75] Generated Node #0,0,0: 12:[16, 75] Operation: 84-9=75 Exploring Operation: 9+84=93, Resulting Numbers: [16, 93] Generated Node #0,0,1: 12:[16, 93] Operation: 9+84=93 Exploring Operation: 16-9=7, Resulting Numbers: [84, 7] Generated Node #0,0,2: 12:[84, 7] Operation: 16-9=7 Exploring Operation: 84-16=68, Resulting Numbers: [9, 68] Generated Node #0,0,3: 12:[9, 68] Operation: 84-16=68 Moving to Node #0,0,3 Current State: 12:[9, 68], Operations: ['61-45=16', '84-16=68'] Exploring Operation: 9*68=612, Resulting Numbers: [612] 612,12 unequal: No Solution Exploring Operation: 9+68=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[16, 75], Operations: ['61-45=16', '84-9=75'] Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,12 unequal: No Solution Exploring Operation: 16*75=1200, Resulting Numbers: [1200] 1200,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[84, 7], Operations: ['61-45=16', '16-9=7'] Exploring Operation: 84*7=588, Resulting Numbers: [588] 588,12 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[9, 45, 61, 84], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [9, 84, 16] Generated Node #0,0: 12:[9, 84, 16] Operation: 61-45=16 Moving to Node #0,0 Current State: 12:[9, 84, 16], Operations: ['61-45=16'] Exploring Operation: 16-9=7, Resulting Numbers: [84, 7] Generated Node #0,0,2: 12:[84, 7] Operation: 16-9=7 Moving to Node #0,0,2 Current State: 12:[84, 7], Operations: ['61-45=16', '16-9=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 14, 21, 4, 84 ]
72
[ "14+4=18", "84/21=4", "18*4=72" ]
Current State: 72:[14, 21, 4, 84], Operations: [] Exploring Operation: 14+4=18, Resulting Numbers: [21, 84, 18] Generated Node #2: [21, 84, 18] from Operation: 14+4=18 Current State: 72:[21, 84, 18], Operations: ['14+4=18'] Exploring Operation: 84/21=4, Resulting Numbers: [18, 4] Generated Node #3: [18, 4] from Operation: 84/21=4 Current State: 72:[18, 4], Operations: ['14+4=18', '84/21=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[14, 21, 4, 84], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [14, 21, 21] Generated Node #0,0: 72:[14, 21, 21] Operation: 84/4=21 Exploring Operation: 84-14=70, Resulting Numbers: [21, 4, 70] Generated Node #0,1: 72:[21, 4, 70] Operation: 84-14=70 Exploring Operation: 84/21=4, Resulting Numbers: [14, 4, 4] Generated Node #0,2: 72:[14, 4, 4] Operation: 84/21=4 Exploring Operation: 84/14=6, Resulting Numbers: [21, 4, 6] Generated Node #0,3: 72:[21, 4, 6] Operation: 84/14=6 Exploring Operation: 84-21=63, Resulting Numbers: [14, 4, 63] Generated Node #0,4: 72:[14, 4, 63] Operation: 84-21=63 Moving to Node #0,2 Current State: 72:[14, 4, 4], Operations: ['84/21=4'] Exploring Operation: 14-4=10, Resulting Numbers: [4, 10] Generated Node #0,2,0: 72:[4, 10] Operation: 14-4=10 Exploring Operation: 14-4=10, Resulting Numbers: [4, 10] Generated Node #0,2,1: 72:[4, 10] Operation: 14-4=10 Exploring Operation: 14+4=18, Resulting Numbers: [4, 18] Generated Node #0,2,2: 72:[4, 18] Operation: 14+4=18 Exploring Operation: 14+4=18, Resulting Numbers: [4, 18] Generated Node #0,2,3: 72:[4, 18] Operation: 14+4=18 Exploring Operation: 4+4=8, Resulting Numbers: [14, 8] Generated Node #0,2,4: 72:[14, 8] Operation: 4+4=8 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[4, 18], Operations: ['84/21=4', '14+4=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[14, 21, 4, 84], Operations: [] Exploring Operation: 84/21=4, Resulting Numbers: [14, 4, 4] Generated Node #0,2: 72:[14, 4, 4] Operation: 84/21=4 Moving to Node #0,2 Current State: 72:[14, 4, 4], Operations: ['84/21=4'] Exploring Operation: 14+4=18, Resulting Numbers: [4, 18] Generated Node #0,2,2: 72:[4, 18] Operation: 14+4=18 Moving to Node #0,2,2 Current State: 72:[4, 18], Operations: ['84/21=4', '14+4=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 64, 37, 97, 23 ]
62
[ "97-23=74", "74/37=2", "64-2=62" ]
Current State: 62:[64, 37, 97, 23], Operations: [] Exploring Operation: 97-23=74, Resulting Numbers: [64, 37, 74] Generated Node #2: [64, 37, 74] from Operation: 97-23=74 Current State: 62:[64, 37, 74], Operations: ['97-23=74'] Exploring Operation: 74/37=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 74/37=2 Current State: 62:[64, 2], Operations: ['97-23=74', '74/37=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[64, 37, 97, 23], Operations: [] Exploring Operation: 97-37=60, Resulting Numbers: [64, 23, 60] Generated Node #0,0: 62:[64, 23, 60] Operation: 97-37=60 Exploring Operation: 97-23=74, Resulting Numbers: [64, 37, 74] Generated Node #0,1: 62:[64, 37, 74] Operation: 97-23=74 Exploring Operation: 97-64=33, Resulting Numbers: [37, 23, 33] Generated Node #0,2: 62:[37, 23, 33] Operation: 97-64=33 Exploring Operation: 37+23=60, Resulting Numbers: [64, 97, 60] Generated Node #0,3: 62:[64, 97, 60] Operation: 37+23=60 Moving to Node #0,0 Current State: 62:[64, 23, 60], Operations: ['97-37=60'] Exploring Operation: 64-23=41, Resulting Numbers: [60, 41] Generated Node #0,0,0: 62:[60, 41] Operation: 64-23=41 Exploring Operation: 64-60=4, Resulting Numbers: [23, 4] Generated Node #0,0,1: 62:[23, 4] Operation: 64-60=4 Exploring Operation: 23+60=83, Resulting Numbers: [64, 83] Generated Node #0,0,2: 62:[64, 83] Operation: 23+60=83 Exploring Operation: 60-23=37, Resulting Numbers: [64, 37] Generated Node #0,0,3: 62:[64, 37] Operation: 60-23=37 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 62:[64, 37], Operations: ['97-37=60', '60-23=37'] Exploring Operation: 64-37=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 64+37=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 64*37=2368, Resulting Numbers: [2368] 2368,62 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 #0,0,1 Current State: 62:[23, 4], Operations: ['97-37=60', '64-60=4'] Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,62 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 #0,0,0 Current State: 62:[60, 41], Operations: ['97-37=60', '64-23=41'] Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 60+41=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 60*41=2460, Resulting Numbers: [2460] 2460,62 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 #0,0,2 Current State: 62:[64, 83], Operations: ['97-37=60', '23+60=83'] Exploring Operation: 64*83=5312, Resulting Numbers: [5312] 5312,62 unequal: No Solution Exploring Operation: 83-64=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 64+83=147, Resulting Numbers: [147] 147,62 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: 62:[37, 23, 33], Operations: ['97-64=33'] Exploring Operation: 37-33=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 62:[23, 4] Operation: 37-33=4 Exploring Operation: 37+23=60, Resulting Numbers: [33, 60] Generated Node #0,2,1: 62:[33, 60] Operation: 37+23=60 Exploring Operation: 23+33=56, Resulting Numbers: [37, 56] Generated Node #0,2,2: 62:[37, 56] Operation: 23+33=56 Exploring Operation: 37-23=14, Resulting Numbers: [33, 14] Generated Node #0,2,3: 62:[33, 14] Operation: 37-23=14 Moving to Node #0,1 Current State: 62:[64, 37, 74], Operations: ['97-23=74'] Exploring Operation: 74-64=10, Resulting Numbers: [37, 10] Generated Node #0,1,0: 62:[37, 10] Operation: 74-64=10 Exploring Operation: 74/37=2, Resulting Numbers: [64, 2] Generated Node #0,1,1: 62:[64, 2] Operation: 74/37=2 Exploring Operation: 64-37=27, Resulting Numbers: [74, 27] Generated Node #0,1,2: 62:[74, 27] Operation: 64-37=27 Exploring Operation: 74-37=37, Resulting Numbers: [64, 37] Generated Node #0,1,3: 62:[64, 37] Operation: 74-37=37 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[64, 2], Operations: ['97-23=74', '74/37=2'] Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,62 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[64, 37, 97, 23], Operations: [] Exploring Operation: 97-23=74, Resulting Numbers: [64, 37, 74] Generated Node #0,1: 62:[64, 37, 74] Operation: 97-23=74 Moving to Node #0,1 Current State: 62:[64, 37, 74], Operations: ['97-23=74'] Exploring Operation: 74/37=2, Resulting Numbers: [64, 2] Generated Node #0,1,1: 62:[64, 2] Operation: 74/37=2 Moving to Node #0,1,1 Current State: 62:[64, 2], Operations: ['97-23=74', '74/37=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 92, 96, 6, 10 ]
34
[ "96-92=4", "6*4=24", "10+24=34" ]
Current State: 34:[92, 96, 6, 10], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [6, 10, 4] Generated Node #2: [6, 10, 4] from Operation: 96-92=4 Current State: 34:[6, 10, 4], Operations: ['96-92=4'] Exploring Operation: 6*4=24, Resulting Numbers: [10, 24] Generated Node #3: [10, 24] from Operation: 6*4=24 Current State: 34:[10, 24], Operations: ['96-92=4', '6*4=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[92, 96, 6, 10], Operations: [] Exploring Operation: 96-10=86, Resulting Numbers: [92, 6, 86] Generated Node #0,0: 34:[92, 6, 86] Operation: 96-10=86 Exploring Operation: 92-10=82, Resulting Numbers: [96, 6, 82] Generated Node #0,1: 34:[96, 6, 82] Operation: 92-10=82 Exploring Operation: 96-92=4, Resulting Numbers: [6, 10, 4] Generated Node #0,2: 34:[6, 10, 4] Operation: 96-92=4 Exploring Operation: 92-6=86, Resulting Numbers: [96, 10, 86] Generated Node #0,3: 34:[96, 10, 86] Operation: 92-6=86 Exploring Operation: 96/6=16, Resulting Numbers: [92, 10, 16] Generated Node #0,4: 34:[92, 10, 16] Operation: 96/6=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[6, 10, 4], Operations: ['96-92=4'] Exploring Operation: 10-6=4, Resulting Numbers: [4, 4] Generated Node #0,2,0: 34:[4, 4] Operation: 10-6=4 Exploring Operation: 6+10=16, Resulting Numbers: [4, 16] Generated Node #0,2,1: 34:[4, 16] Operation: 6+10=16 Exploring Operation: 6-4=2, Resulting Numbers: [10, 2] Generated Node #0,2,2: 34:[10, 2] Operation: 6-4=2 Exploring Operation: 10+4=14, Resulting Numbers: [6, 14] Generated Node #0,2,3: 34:[6, 14] Operation: 10+4=14 Exploring Operation: 10-4=6, Resulting Numbers: [6, 6] Generated Node #0,2,4: 34:[6, 6] Operation: 10-4=6 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 34:[4, 16], Operations: ['96-92=4', '6+10=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[4, 4], Operations: ['96-92=4', '10-6=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[10, 2], Operations: ['96-92=4', '6-4=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 34:[6, 14], Operations: ['96-92=4', '10+4=14'] Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 34:[6, 6], Operations: ['96-92=4', '10-4=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 34:[92, 10, 16], Operations: ['96/6=16'] Exploring Operation: 92+10=102, Resulting Numbers: [16, 102] Generated Node #0,4,0: 34:[16, 102] Operation: 92+10=102 Exploring Operation: 92-10=82, Resulting Numbers: [16, 82] Generated Node #0,4,1: 34:[16, 82] Operation: 92-10=82 Exploring Operation: 92-16=76, Resulting Numbers: [10, 76] Generated Node #0,4,2: 34:[10, 76] Operation: 92-16=76 Exploring Operation: 10+16=26, Resulting Numbers: [92, 26] Generated Node #0,4,3: 34:[92, 26] Operation: 10+16=26 Exploring Operation: 16-10=6, Resulting Numbers: [92, 6] Generated Node #0,4,4: 34:[92, 6] Operation: 16-10=6 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 34:[16, 82], Operations: ['96/6=16', '92-10=82'] Exploring Operation: 16+82=98, Resulting Numbers: [98] 98,34 unequal: No Solution Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 16*82=1312, Resulting Numbers: [1312] 1312,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 34:[10, 76], Operations: ['96/6=16', '92-16=76'] Exploring Operation: 10*76=760, Resulting Numbers: [760] 760,34 unequal: No Solution Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 10+76=86, Resulting Numbers: [86] 86,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 34:[92, 6], Operations: ['96/6=16', '16-10=6'] Exploring Operation: 92*6=552, Resulting Numbers: [552] 552,34 unequal: No Solution Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 92+6=98, Resulting Numbers: [98] 98,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 34:[92, 26], Operations: ['96/6=16', '10+16=26'] Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,34 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 34:[16, 102], Operations: ['96/6=16', '92+10=102'] Exploring Operation: 102-16=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 16+102=118, Resulting Numbers: [118] 118,34 unequal: No Solution Exploring Operation: 16*102=1632, Resulting Numbers: [1632] 1632,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[92, 6, 86], Operations: ['96-10=86'] Exploring Operation: 92-6=86, Resulting Numbers: [86, 86] Generated Node #0,0,0: 34:[86, 86] Operation: 92-6=86 Exploring Operation: 6+86=92, Resulting Numbers: [92, 92] Generated Node #0,0,1: 34:[92, 92] Operation: 6+86=92 Exploring Operation: 92-86=6, Resulting Numbers: [6, 6] Generated Node #0,0,2: 34:[6, 6] Operation: 92-86=6 Exploring Operation: 92+6=98, Resulting Numbers: [86, 98] Generated Node #0,0,3: 34:[86, 98] Operation: 92+6=98 Exploring Operation: 86-6=80, Resulting Numbers: [92, 80] Generated Node #0,0,4: 34:[92, 80] Operation: 86-6=80 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[6, 6], Operations: ['96-10=86', '92-86=6'] Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[86, 86], Operations: ['96-10=86', '92-6=86'] Exploring Operation: 86+86=172, Resulting Numbers: [172] 172,34 unequal: No Solution Exploring Operation: 86*86=7396, Resulting Numbers: [7396] 7396,34 unequal: No Solution Exploring Operation: 86-86=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 86/86=1, Resulting Numbers: [1] 1,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 34:[92, 80], Operations: ['96-10=86', '86-6=80'] Exploring Operation: 92*80=7360, Resulting Numbers: [7360] 7360,34 unequal: No Solution Exploring Operation: 92-80=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 92+80=172, Resulting Numbers: [172] 172,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[92, 92], Operations: ['96-10=86', '6+86=92'] Exploring Operation: 92-92=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 92+92=184, Resulting Numbers: [184] 184,34 unequal: No Solution Exploring Operation: 92/92=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 92*92=8464, Resulting Numbers: [8464] 8464,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 34:[86, 98], Operations: ['96-10=86', '92+6=98'] Exploring Operation: 86+98=184, Resulting Numbers: [184] 184,34 unequal: No Solution Exploring Operation: 86*98=8428, Resulting Numbers: [8428] 8428,34 unequal: No Solution Exploring Operation: 98-86=12, Resulting Numbers: [12] 12,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[96, 6, 82], Operations: ['92-10=82'] Exploring Operation: 96+6=102, Resulting Numbers: [82, 102] Generated Node #0,1,0: 34:[82, 102] Operation: 96+6=102 Exploring Operation: 96/6=16, Resulting Numbers: [82, 16] Generated Node #0,1,1: 34:[82, 16] Operation: 96/6=16 Exploring Operation: 96-6=90, Resulting Numbers: [82, 90] Generated Node #0,1,2: 34:[82, 90] Operation: 96-6=90 Exploring Operation: 82-6=76, Resulting Numbers: [96, 76] Generated Node #0,1,3: 34:[96, 76] Operation: 82-6=76 Exploring Operation: 96-82=14, Resulting Numbers: [6, 14] Generated Node #0,1,4: 34:[6, 14] Operation: 96-82=14 Moving to Node #0,1,4 Current State: 34:[6, 14], Operations: ['92-10=82', '96-82=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[82, 16], Operations: ['92-10=82', '96/6=16'] Exploring Operation: 82*16=1312, Resulting Numbers: [1312] 1312,34 unequal: No Solution Exploring Operation: 82+16=98, Resulting Numbers: [98] 98,34 unequal: No Solution Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[82, 90], Operations: ['92-10=82', '96-6=90'] Exploring Operation: 82*90=7380, Resulting Numbers: [7380] 7380,34 unequal: No Solution Exploring Operation: 90-82=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 82+90=172, Resulting Numbers: [172] 172,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[96, 76], Operations: ['92-10=82', '82-6=76'] Exploring Operation: 96+76=172, Resulting Numbers: [172] 172,34 unequal: No Solution Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 96*76=7296, Resulting Numbers: [7296] 7296,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[82, 102], Operations: ['92-10=82', '96+6=102'] Exploring Operation: 82+102=184, Resulting Numbers: [184] 184,34 unequal: No Solution Exploring Operation: 82*102=8364, Resulting Numbers: [8364] 8364,34 unequal: No Solution Exploring Operation: 102-82=20, Resulting Numbers: [20] 20,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[96, 10, 86], Operations: ['92-6=86'] Exploring Operation: 96-86=10, Resulting Numbers: [10, 10] Generated Node #0,3,0: 34:[10, 10] Operation: 96-86=10 Exploring Operation: 86-10=76, Resulting Numbers: [96, 76] Generated Node #0,3,1: 34:[96, 76] Operation: 86-10=76 Exploring Operation: 96-10=86, Resulting Numbers: [86, 86] Generated Node #0,3,2: 34:[86, 86] Operation: 96-10=86 Exploring Operation: 96+10=106, Resulting Numbers: [86, 106] Generated Node #0,3,3: 34:[86, 106] Operation: 96+10=106 Exploring Operation: 10+86=96, Resulting Numbers: [96, 96] Generated Node #0,3,4: 34:[96, 96] Operation: 10+86=96 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 34:[10, 10], Operations: ['92-6=86', '96-86=10'] Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,34 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 34:[96, 76], Operations: ['92-6=86', '86-10=76'] Exploring Operation: 96+76=172, Resulting Numbers: [172] 172,34 unequal: No Solution Exploring Operation: 96*76=7296, Resulting Numbers: [7296] 7296,34 unequal: No Solution Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 34:[86, 86], Operations: ['92-6=86', '96-10=86'] Exploring Operation: 86/86=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 86*86=7396, Resulting Numbers: [7396] 7396,34 unequal: No Solution Exploring Operation: 86-86=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 86+86=172, Resulting Numbers: [172] 172,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 34:[86, 106], Operations: ['92-6=86', '96+10=106'] Exploring Operation: 86+106=192, Resulting Numbers: [192] 192,34 unequal: No Solution Exploring Operation: 86*106=9116, Resulting Numbers: [9116] 9116,34 unequal: No Solution Exploring Operation: 106-86=20, Resulting Numbers: [20] 20,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 34:[96, 96], Operations: ['92-6=86', '10+86=96'] Exploring Operation: 96+96=192, Resulting Numbers: [192] 192,34 unequal: No Solution Exploring Operation: 96*96=9216, Resulting Numbers: [9216] 9216,34 unequal: No Solution Exploring Operation: 96/96=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 96-96=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 49, 56, 14, 98 ]
57
[ "56*14=784", "784/98=8", "49+8=57" ]
Current State: 57:[49, 56, 14, 98], Operations: [] Exploring Operation: 56*14=784, Resulting Numbers: [49, 98, 784] Generated Node #2: [49, 98, 784] from Operation: 56*14=784 Current State: 57:[49, 98, 784], Operations: ['56*14=784'] Exploring Operation: 784/98=8, Resulting Numbers: [49, 8] Generated Node #3: [49, 8] from Operation: 784/98=8 Current State: 57:[49, 8], Operations: ['56*14=784', '784/98=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[49, 56, 14, 98], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [56, 14, 2] Generated Node #0,0: 57:[56, 14, 2] Operation: 98/49=2 Exploring Operation: 98-49=49, Resulting Numbers: [56, 14, 49] Generated Node #0,1: 57:[56, 14, 49] Operation: 98-49=49 Exploring Operation: 98/14=7, Resulting Numbers: [49, 56, 7] Generated Node #0,2: 57:[49, 56, 7] Operation: 98/14=7 Exploring Operation: 98-56=42, Resulting Numbers: [49, 14, 42] Generated Node #0,3: 57:[49, 14, 42] Operation: 98-56=42 Moving to Node #0,0 Current State: 57:[56, 14, 2], Operations: ['98/49=2'] Exploring Operation: 14+2=16, Resulting Numbers: [56, 16] Generated Node #0,0,0: 57:[56, 16] Operation: 14+2=16 Exploring Operation: 56+2=58, Resulting Numbers: [14, 58] Generated Node #0,0,1: 57:[14, 58] Operation: 56+2=58 Exploring Operation: 14/2=7, Resulting Numbers: [56, 7] Generated Node #0,0,2: 57:[56, 7] Operation: 14/2=7 Exploring Operation: 56/14=4, Resulting Numbers: [2, 4] Generated Node #0,0,3: 57:[2, 4] Operation: 56/14=4 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[2, 4], Operations: ['98/49=2', '56/14=4'] Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,57 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 #0,0,0 Current State: 57:[56, 16], Operations: ['98/49=2', '14+2=16'] Exploring Operation: 56*16=896, Resulting Numbers: [896] 896,57 unequal: No Solution Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,57 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:[56, 7], Operations: ['98/49=2', '14/2=7'] Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,57 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,57 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:[14, 58], Operations: ['98/49=2', '56+2=58'] Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,57 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,57 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: 57:[49, 56, 7], Operations: ['98/14=7'] Exploring Operation: 56-49=7, Resulting Numbers: [7, 7] Generated Node #0,2,0: 57:[7, 7] Operation: 56-49=7 Exploring Operation: 49+7=56, Resulting Numbers: [56, 56] Generated Node #0,2,1: 57:[56, 56] Operation: 49+7=56 Exploring Operation: 56/7=8, Resulting Numbers: [49, 8] Generated Node #0,2,2: 57:[49, 8] Operation: 56/7=8 Exploring Operation: 49/7=7, Resulting Numbers: [56, 7] Generated Node #0,2,3: 57:[56, 7] Operation: 49/7=7 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 57:[56, 56], Operations: ['98/14=7', '49+7=56'] Exploring Operation: 56*56=3136, Resulting Numbers: [3136] 3136,57 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 56+56=112, Resulting Numbers: [112] 112,57 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 #0,2,3 Current State: 57:[56, 7], Operations: ['98/14=7', '49/7=7'] Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,57 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 56+7=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 #0,2,0 Current State: 57:[7, 7], Operations: ['98/14=7', '56-49=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,57 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 #0,2,2 Current State: 57:[49, 8], Operations: ['98/14=7', '56/7=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[49, 56, 14, 98], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [49, 56, 7] Generated Node #0,2: 57:[49, 56, 7] Operation: 98/14=7 Moving to Node #0,2 Current State: 57:[49, 56, 7], Operations: ['98/14=7'] Exploring Operation: 56/7=8, Resulting Numbers: [49, 8] Generated Node #0,2,2: 57:[49, 8] Operation: 56/7=8 Moving to Node #0,2,2 Current State: 57:[49, 8], Operations: ['98/14=7', '56/7=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_4
sum_heuristic
[ 82, 50, 58, 99 ]
73
[ "82-50=32", "99-58=41", "32+41=73" ]
Current State: 73:[82, 50, 58, 99], Operations: [] Exploring Operation: 82-50=32, Resulting Numbers: [58, 99, 32] Generated Node #2: [58, 99, 32] from Operation: 82-50=32 Current State: 73:[58, 99, 32], Operations: ['82-50=32'] Exploring Operation: 99-58=41, Resulting Numbers: [32, 41] Generated Node #3: [32, 41] from Operation: 99-58=41 Current State: 73:[32, 41], Operations: ['82-50=32', '99-58=41'] Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[82, 50, 58, 99], Operations: [] Exploring Operation: 99-58=41, Resulting Numbers: [82, 50, 41] Generated Node #0,0: 73:[82, 50, 41] Operation: 99-58=41 Exploring Operation: 50+58=108, Resulting Numbers: [82, 99, 108] Generated Node #0,1: 73:[82, 99, 108] Operation: 50+58=108 Exploring Operation: 99-50=49, Resulting Numbers: [82, 58, 49] Generated Node #0,2: 73:[82, 58, 49] Operation: 99-50=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[82, 58, 49], Operations: ['99-50=49'] Exploring Operation: 58+49=107, Resulting Numbers: [82, 107] Generated Node #0,2,0: 73:[82, 107] Operation: 58+49=107 Exploring Operation: 82-58=24, Resulting Numbers: [49, 24] Generated Node #0,2,1: 73:[49, 24] Operation: 82-58=24 Exploring Operation: 82-49=33, Resulting Numbers: [58, 33] Generated Node #0,2,2: 73:[58, 33] Operation: 82-49=33 Moving to Node #0,2,0 Current State: 73:[82, 107], Operations: ['99-50=49', '58+49=107'] Exploring Operation: 82+107=189, Resulting Numbers: [189] 189,73 unequal: No Solution Exploring Operation: 107-82=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 82*107=8774, Resulting Numbers: [8774] 8774,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[58, 33], Operations: ['99-50=49', '82-49=33'] Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 58*33=1914, Resulting Numbers: [1914] 1914,73 unequal: No Solution Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[49, 24], Operations: ['99-50=49', '82-58=24'] Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,73 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[82, 50, 58, 99], Operations: [] Exploring Operation: 99-50=49, Resulting Numbers: [82, 58, 49] Generated Node #0,2: 73:[82, 58, 49] Operation: 99-50=49 Moving to Node #0,2 Current State: 73:[82, 58, 49], Operations: ['99-50=49'] Exploring Operation: 82-58=24, Resulting Numbers: [49, 24] Generated Node #0,2,1: 73:[49, 24] Operation: 82-58=24 Moving to Node #0,2,1 Current State: 73:[49, 24], Operations: ['99-50=49', '82-58=24'] Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 48, 28, 14, 73 ]
50
[ "73-48=25", "28/14=2", "25*2=50" ]
Current State: 50:[48, 28, 14, 73], Operations: [] Exploring Operation: 73-48=25, Resulting Numbers: [28, 14, 25] Generated Node #2: [28, 14, 25] from Operation: 73-48=25 Current State: 50:[28, 14, 25], Operations: ['73-48=25'] Exploring Operation: 28/14=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 28/14=2 Current State: 50:[25, 2], Operations: ['73-48=25', '28/14=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[48, 28, 14, 73], Operations: [] Exploring Operation: 73-48=25, Resulting Numbers: [28, 14, 25] Generated Node #0,0: 50:[28, 14, 25] Operation: 73-48=25 Exploring Operation: 73-28=45, Resulting Numbers: [48, 14, 45] Generated Node #0,1: 50:[48, 14, 45] Operation: 73-28=45 Exploring Operation: 73-14=59, Resulting Numbers: [48, 28, 59] Generated Node #0,2: 50:[48, 28, 59] Operation: 73-14=59 Exploring Operation: 28-14=14, Resulting Numbers: [48, 73, 14] Generated Node #0,3: 50:[48, 73, 14] Operation: 28-14=14 Exploring Operation: 28/14=2, Resulting Numbers: [48, 73, 2] Generated Node #0,4: 50:[48, 73, 2] Operation: 28/14=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[28, 14, 25], Operations: ['73-48=25'] Exploring Operation: 28/14=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 50:[25, 2] Operation: 28/14=2 Exploring Operation: 28+25=53, Resulting Numbers: [14, 53] Generated Node #0,0,1: 50:[14, 53] Operation: 28+25=53 Exploring Operation: 25-14=11, Resulting Numbers: [28, 11] Generated Node #0,0,2: 50:[28, 11] Operation: 25-14=11 Exploring Operation: 28-14=14, Resulting Numbers: [25, 14] Generated Node #0,0,3: 50:[25, 14] Operation: 28-14=14 Exploring Operation: 28-25=3, Resulting Numbers: [14, 3] Generated Node #0,0,4: 50:[14, 3] Operation: 28-25=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[25, 2], Operations: ['73-48=25', '28/14=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[48, 28, 14, 73], Operations: [] Exploring Operation: 73-48=25, Resulting Numbers: [28, 14, 25] Generated Node #0,0: 50:[28, 14, 25] Operation: 73-48=25 Moving to Node #0,0 Current State: 50:[28, 14, 25], Operations: ['73-48=25'] Exploring Operation: 28/14=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 50:[25, 2] Operation: 28/14=2 Moving to Node #0,0,0 Current State: 50:[25, 2], Operations: ['73-48=25', '28/14=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 86, 83, 86, 41 ]
15
[ "86-83=3", "86-41=45", "45/3=15" ]
Current State: 15:[86, 83, 86, 41], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [41, 3] Generated Node #2: [41, 3] from Operation: 86-83=3 Current State: 15:[41, 3], Operations: ['86-83=3'] Exploring Operation: 86-41=45, Resulting Numbers: [3, 45] Generated Node #3: [3, 45] from Operation: 86-41=45 Current State: 15:[3, 45], Operations: ['86-83=3', '86-41=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[86, 83, 86, 41], Operations: [] Exploring Operation: 86/86=1, Resulting Numbers: [83, 41, 1] Generated Node #0,0: 15:[83, 41, 1] Operation: 86/86=1 Exploring Operation: 86-86=0, Resulting Numbers: [83, 41, 0] Generated Node #0,1: 15:[83, 41, 0] Operation: 86-86=0 Exploring Operation: 86-83=3, Resulting Numbers: [86, 41, 3] Generated Node #0,2: 15:[86, 41, 3] Operation: 86-83=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[83, 41, 1], Operations: ['86/86=1'] Exploring Operation: 83-1=82, Resulting Numbers: [41, 82] Generated Node #0,0,0: 15:[41, 82] Operation: 83-1=82 Exploring Operation: 83-41=42, Resulting Numbers: [1, 42] Generated Node #0,0,1: 15:[1, 42] Operation: 83-41=42 Exploring Operation: 41-1=40, Resulting Numbers: [83, 40] Generated Node #0,0,2: 15:[83, 40] Operation: 41-1=40 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[1, 42], Operations: ['86/86=1', '83-41=42'] Exploring Operation: 1*42=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 42-1=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 #0,0,0 Current State: 15:[41, 82], Operations: ['86/86=1', '83-1=82'] Exploring Operation: 41+82=123, Resulting Numbers: [123] 123,15 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,15 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:[83, 40], Operations: ['86/86=1', '41-1=40'] Exploring Operation: 83*40=3320, Resulting Numbers: [3320] 3320,15 unequal: No Solution Exploring Operation: 83+40=123, Resulting Numbers: [123] 123,15 unequal: No Solution Exploring Operation: 83-40=43, Resulting Numbers: [43] 43,15 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:[83, 41, 0], Operations: ['86-86=0'] Exploring Operation: 41*0=0, Resulting Numbers: [83, 0] Generated Node #0,1,0: 15:[83, 0] Operation: 41*0=0 Exploring Operation: 83*0=0, Resulting Numbers: [41, 0] Generated Node #0,1,1: 15:[41, 0] Operation: 83*0=0 Exploring Operation: 83-41=42, Resulting Numbers: [0, 42] Generated Node #0,1,2: 15:[0, 42] Operation: 83-41=42 Moving to Node #0,1,1 Current State: 15:[41, 0], Operations: ['86-86=0', '83*0=0'] Exploring Operation: 41*0=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 41+0=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 41-0=41, Resulting Numbers: [41] 41,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[0, 42], Operations: ['86-86=0', '83-41=42'] Exploring Operation: 42-0=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 0+42=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 0*42=0, Resulting Numbers: [0] 0,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[83, 0], Operations: ['86-86=0', '41*0=0'] Exploring Operation: 83*0=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 83-0=83, Resulting Numbers: [83] 83,15 unequal: No Solution Exploring Operation: 83+0=83, Resulting Numbers: [83] 83,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[86, 41, 3], Operations: ['86-83=3'] Exploring Operation: 86-41=45, Resulting Numbers: [3, 45] Generated Node #0,2,0: 15:[3, 45] Operation: 86-41=45 Exploring Operation: 86-3=83, Resulting Numbers: [41, 83] Generated Node #0,2,1: 15:[41, 83] Operation: 86-3=83 Exploring Operation: 41-3=38, Resulting Numbers: [86, 38] Generated Node #0,2,2: 15:[86, 38] Operation: 41-3=38 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 15:[3, 45], Operations: ['86-83=3', '86-41=45'] 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:[86, 83, 86, 41], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [86, 41, 3] Generated Node #0,2: 15:[86, 41, 3] Operation: 86-83=3 Moving to Node #0,2 Current State: 15:[86, 41, 3], Operations: ['86-83=3'] Exploring Operation: 86-41=45, Resulting Numbers: [3, 45] Generated Node #0,2,0: 15:[3, 45] Operation: 86-41=45 Moving to Node #0,2,0 Current State: 15:[3, 45], Operations: ['86-83=3', '86-41=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 38, 25, 97, 1 ]
84
[ "38-25=13", "97*1=97", "97-13=84" ]
Current State: 84:[38, 25, 97, 1], Operations: [] Exploring Operation: 38-25=13, Resulting Numbers: [97, 1, 13] Generated Node #2: [97, 1, 13] from Operation: 38-25=13 Current State: 84:[97, 1, 13], Operations: ['38-25=13'] Exploring Operation: 97*1=97, Resulting Numbers: [13, 97] Generated Node #3: [13, 97] from Operation: 97*1=97 Current State: 84:[13, 97], Operations: ['38-25=13', '97*1=97'] Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[38, 25, 97, 1], Operations: [] Exploring Operation: 38+1=39, Resulting Numbers: [25, 97, 39] Generated Node #0,0: 84:[25, 97, 39] Operation: 38+1=39 Exploring Operation: 38-25=13, Resulting Numbers: [97, 1, 13] Generated Node #0,1: 84:[97, 1, 13] Operation: 38-25=13 Exploring Operation: 97-25=72, Resulting Numbers: [38, 1, 72] Generated Node #0,2: 84:[38, 1, 72] Operation: 97-25=72 Exploring Operation: 25+1=26, Resulting Numbers: [38, 97, 26] Generated Node #0,3: 84:[38, 97, 26] Operation: 25+1=26 Exploring Operation: 97-1=96, Resulting Numbers: [38, 25, 96] Generated Node #0,4: 84:[38, 25, 96] Operation: 97-1=96 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[97, 1, 13], Operations: ['38-25=13'] Exploring Operation: 97-13=84, Resulting Numbers: [1, 84] Generated Node #0,1,0: 84:[1, 84] Operation: 97-13=84 Exploring Operation: 13-1=12, Resulting Numbers: [97, 12] Generated Node #0,1,1: 84:[97, 12] Operation: 13-1=12 Exploring Operation: 97-1=96, Resulting Numbers: [13, 96] Generated Node #0,1,2: 84:[13, 96] Operation: 97-1=96 Exploring Operation: 97*1=97, Resulting Numbers: [13, 97] Generated Node #0,1,3: 84:[13, 97] Operation: 97*1=97 Exploring Operation: 1+13=14, Resulting Numbers: [97, 14] Generated Node #0,1,4: 84:[97, 14] Operation: 1+13=14 Moving to Node #0,1,0 Current State: 84:[1, 84], Operations: ['38-25=13', '97-13=84'] Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[38, 25, 97, 1], Operations: [] Exploring Operation: 38-25=13, Resulting Numbers: [97, 1, 13] Generated Node #0,1: 84:[97, 1, 13] Operation: 38-25=13 Moving to Node #0,1 Current State: 84:[97, 1, 13], Operations: ['38-25=13'] Exploring Operation: 97-13=84, Resulting Numbers: [1, 84] Generated Node #0,1,0: 84:[1, 84] Operation: 97-13=84 Moving to Node #0,1,0 Current State: 84:[1, 84], Operations: ['38-25=13', '97-13=84'] Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 4, 25, 35, 80 ]
66
[ "25-4=21", "80-35=45", "21+45=66" ]
Current State: 66:[4, 25, 35, 80], Operations: [] Exploring Operation: 25-4=21, Resulting Numbers: [35, 80, 21] Generated Node #2: [35, 80, 21] from Operation: 25-4=21 Current State: 66:[35, 80, 21], Operations: ['25-4=21'] Exploring Operation: 80-35=45, Resulting Numbers: [21, 45] Generated Node #3: [21, 45] from Operation: 80-35=45 Current State: 66:[21, 45], Operations: ['25-4=21', '80-35=45'] Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[4, 25, 35, 80], Operations: [] Exploring Operation: 80-25=55, Resulting Numbers: [4, 35, 55] Generated Node #0,0: 66:[4, 35, 55] Operation: 80-25=55 Exploring Operation: 80/4=20, Resulting Numbers: [25, 35, 20] Generated Node #0,1: 66:[25, 35, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [25, 35, 76] Generated Node #0,2: 66:[25, 35, 76] Operation: 80-4=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[25, 35, 20], Operations: ['80/4=20'] Exploring Operation: 35-20=15, Resulting Numbers: [25, 15] Generated Node #0,1,0: 66:[25, 15] Operation: 35-20=15 Exploring Operation: 25-20=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 66:[35, 5] Operation: 25-20=5 Exploring Operation: 35-25=10, Resulting Numbers: [20, 10] Generated Node #0,1,2: 66:[20, 10] Operation: 35-25=10 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[35, 5], Operations: ['80/4=20', '25-20=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,66 unequal: No Solution No 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: 66:[20, 10], Operations: ['80/4=20', '35-25=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,66 unequal: No Solution No 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: 66:[25, 15], Operations: ['80/4=20', '35-20=15'] Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,66 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,66 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[4, 35, 55], Operations: ['80-25=55'] Exploring Operation: 55-35=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 66:[4, 20] Operation: 55-35=20 Exploring Operation: 4+55=59, Resulting Numbers: [35, 59] Generated Node #0,0,1: 66:[35, 59] Operation: 4+55=59 Exploring Operation: 35-4=31, Resulting Numbers: [55, 31] Generated Node #0,0,2: 66:[55, 31] Operation: 35-4=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[4, 20], Operations: ['80-25=55', '55-35=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,66 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,66 unequal: No Solution No 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: 66:[35, 59], Operations: ['80-25=55', '4+55=59'] Exploring Operation: 35*59=2065, Resulting Numbers: [2065] 2065,66 unequal: No Solution Exploring Operation: 59-35=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 35+59=94, Resulting Numbers: [94] 94,66 unequal: No Solution No 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: 66:[55, 31], Operations: ['80-25=55', '35-4=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,66 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 55*31=1705, Resulting Numbers: [1705] 1705,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[25, 35, 76], Operations: ['80-4=76'] Exploring Operation: 25+35=60, Resulting Numbers: [76, 60] Generated Node #0,2,0: 66:[76, 60] Operation: 25+35=60 Exploring Operation: 76-35=41, Resulting Numbers: [25, 41] Generated Node #0,2,1: 66:[25, 41] Operation: 76-35=41 Exploring Operation: 35-25=10, Resulting Numbers: [76, 10] Generated Node #0,2,2: 66:[76, 10] Operation: 35-25=10 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[25, 41], Operations: ['80-4=76', '76-35=41'] Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,66 unequal: No Solution Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,66 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[4, 25, 35, 80], Operations: [] Exploring Operation: 80-4=76, Resulting Numbers: [25, 35, 76] Generated Node #0,2: 66:[25, 35, 76] Operation: 80-4=76 Moving to Node #0,2 Current State: 66:[25, 35, 76], Operations: ['80-4=76'] Exploring Operation: 76-35=41, Resulting Numbers: [25, 41] Generated Node #0,2,1: 66:[25, 41] Operation: 76-35=41 Moving to Node #0,2,1 Current State: 66:[25, 41], Operations: ['80-4=76', '76-35=41'] Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
sum_heuristic
[ 98, 92, 75, 70 ]
45
[ "98+92=190", "75+70=145", "190-145=45" ]
Current State: 45:[98, 92, 75, 70], Operations: [] Exploring Operation: 98+92=190, Resulting Numbers: [75, 70, 190] Generated Node #2: [75, 70, 190] from Operation: 98+92=190 Current State: 45:[75, 70, 190], Operations: ['98+92=190'] Exploring Operation: 75+70=145, Resulting Numbers: [190, 145] Generated Node #3: [190, 145] from Operation: 75+70=145 Current State: 45:[190, 145], Operations: ['98+92=190', '75+70=145'] Exploring Operation: 190-145=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[98, 92, 75, 70], Operations: [] Exploring Operation: 98-92=6, Resulting Numbers: [75, 70, 6] Generated Node #0,0: 45:[75, 70, 6] Operation: 98-92=6 Exploring Operation: 98-75=23, Resulting Numbers: [92, 70, 23] Generated Node #0,1: 45:[92, 70, 23] Operation: 98-75=23 Exploring Operation: 92-75=17, Resulting Numbers: [98, 70, 17] Generated Node #0,2: 45:[98, 70, 17] Operation: 92-75=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[75, 70, 6], Operations: ['98-92=6'] Exploring Operation: 70-6=64, Resulting Numbers: [75, 64] Generated Node #0,0,0: 45:[75, 64] Operation: 70-6=64 Exploring Operation: 75-70=5, Resulting Numbers: [6, 5] Generated Node #0,0,1: 45:[6, 5] Operation: 75-70=5 Exploring Operation: 75-6=69, Resulting Numbers: [70, 69] Generated Node #0,0,2: 45:[70, 69] Operation: 75-6=69 Moving to Node #0,0,1 Current State: 45:[6, 5], Operations: ['98-92=6', '75-70=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[75, 64], Operations: ['98-92=6', '70-6=64'] Exploring Operation: 75+64=139, Resulting Numbers: [139] 139,45 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 75*64=4800, Resulting Numbers: [4800] 4800,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[70, 69], Operations: ['98-92=6', '75-6=69'] Exploring Operation: 70*69=4830, Resulting Numbers: [4830] 4830,45 unequal: No Solution Exploring Operation: 70+69=139, Resulting Numbers: [139] 139,45 unequal: No Solution Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[92, 70, 23], Operations: ['98-75=23'] Exploring Operation: 92/23=4, Resulting Numbers: [70, 4] Generated Node #0,1,0: 45:[70, 4] Operation: 92/23=4 Exploring Operation: 92-23=69, Resulting Numbers: [70, 69] Generated Node #0,1,1: 45:[70, 69] Operation: 92-23=69 Exploring Operation: 92-70=22, Resulting Numbers: [23, 22] Generated Node #0,1,2: 45:[23, 22] Operation: 92-70=22 Moving to Node #0,1,2 Current State: 45:[23, 22], Operations: ['98-75=23', '92-70=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[98, 92, 75, 70], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [92, 70, 23] Generated Node #0,1: 45:[92, 70, 23] Operation: 98-75=23 Moving to Node #0,1 Current State: 45:[92, 70, 23], Operations: ['98-75=23'] Exploring Operation: 92-70=22, Resulting Numbers: [23, 22] Generated Node #0,1,2: 45:[23, 22] Operation: 92-70=22 Moving to Node #0,1,2 Current State: 45:[23, 22], Operations: ['98-75=23', '92-70=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 54, 84, 39, 18 ]
67
[ "54/18=3", "84/3=28", "39+28=67" ]
Current State: 67:[54, 84, 39, 18], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [84, 39, 3] Generated Node #2: [84, 39, 3] from Operation: 54/18=3 Current State: 67:[84, 39, 3], Operations: ['54/18=3'] Exploring Operation: 84/3=28, Resulting Numbers: [39, 28] Generated Node #3: [39, 28] from Operation: 84/3=28 Current State: 67:[39, 28], Operations: ['54/18=3', '84/3=28'] Exploring Operation: 39+28=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[54, 84, 39, 18], Operations: [] Exploring Operation: 39+18=57, Resulting Numbers: [54, 84, 57] Generated Node #0,0: 67:[54, 84, 57] Operation: 39+18=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[54, 84, 57], Operations: ['39+18=57'] Exploring Operation: 84-54=30, Resulting Numbers: [57, 30] Generated Node #0,0,0: 67:[57, 30] Operation: 84-54=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[57, 30], Operations: ['39+18=57', '84-54=30'] Exploring Operation: 57+30=87, Resulting Numbers: [87] 87,67 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
[ 61, 68, 99, 9 ]
21
[ "61+68=129", "99+9=108", "129-108=21" ]
Current State: 21:[61, 68, 99, 9], Operations: [] Exploring Operation: 61+68=129, Resulting Numbers: [99, 9, 129] Generated Node #2: [99, 9, 129] from Operation: 61+68=129 Current State: 21:[99, 9, 129], Operations: ['61+68=129'] Exploring Operation: 99+9=108, Resulting Numbers: [129, 108] Generated Node #3: [129, 108] from Operation: 99+9=108 Current State: 21:[129, 108], Operations: ['61+68=129', '99+9=108'] Exploring Operation: 129-108=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[61, 68, 99, 9], Operations: [] Exploring Operation: 99-61=38, Resulting Numbers: [68, 9, 38] Generated Node #0,0: 21:[68, 9, 38] Operation: 99-61=38 Exploring Operation: 68-61=7, Resulting Numbers: [99, 9, 7] Generated Node #0,1: 21:[99, 9, 7] Operation: 68-61=7 Exploring Operation: 99-68=31, Resulting Numbers: [61, 9, 31] Generated Node #0,2: 21:[61, 9, 31] Operation: 99-68=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[61, 9, 31], Operations: ['99-68=31'] Exploring Operation: 31-9=22, Resulting Numbers: [61, 22] Generated Node #0,2,0: 21:[61, 22] Operation: 31-9=22 Exploring Operation: 61-9=52, Resulting Numbers: [31, 52] Generated Node #0,2,1: 21:[31, 52] Operation: 61-9=52 Exploring Operation: 61-31=30, Resulting Numbers: [9, 30] Generated Node #0,2,2: 21:[9, 30] Operation: 61-31=30 Moving to Node #0,2,2 Current State: 21:[9, 30], Operations: ['99-68=31', '61-31=30'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[61, 68, 99, 9], Operations: [] Exploring Operation: 99-68=31, Resulting Numbers: [61, 9, 31] Generated Node #0,2: 21:[61, 9, 31] Operation: 99-68=31 Moving to Node #0,2 Current State: 21:[61, 9, 31], Operations: ['99-68=31'] Exploring Operation: 61-31=30, Resulting Numbers: [9, 30] Generated Node #0,2,2: 21:[9, 30] Operation: 61-31=30 Moving to Node #0,2,2 Current State: 21:[9, 30], Operations: ['99-68=31', '61-31=30'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 93, 32, 90, 47 ]
45
[ "93-90=3", "47-32=15", "3*15=45" ]
Current State: 45:[93, 32, 90, 47], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [32, 47, 3] Generated Node #2: [32, 47, 3] from Operation: 93-90=3 Current State: 45:[32, 47, 3], Operations: ['93-90=3'] Exploring Operation: 47-32=15, Resulting Numbers: [3, 15] Generated Node #3: [3, 15] from Operation: 47-32=15 Current State: 45:[3, 15], Operations: ['93-90=3', '47-32=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[93, 32, 90, 47], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [32, 47, 3] Generated Node #0,0: 45:[32, 47, 3] Operation: 93-90=3 Exploring Operation: 93-32=61, Resulting Numbers: [90, 47, 61] Generated Node #0,1: 45:[90, 47, 61] Operation: 93-32=61 Exploring Operation: 93-47=46, Resulting Numbers: [32, 90, 46] Generated Node #0,2: 45:[32, 90, 46] Operation: 93-47=46 Exploring Operation: 90-32=58, Resulting Numbers: [93, 47, 58] Generated Node #0,3: 45:[93, 47, 58] Operation: 90-32=58 Moving to Node #0,0 Current State: 45:[32, 47, 3], Operations: ['93-90=3'] Exploring Operation: 47-32=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 45:[3, 15] Operation: 47-32=15 Exploring Operation: 47-3=44, Resulting Numbers: [32, 44] Generated Node #0,0,1: 45:[32, 44] Operation: 47-3=44 Exploring Operation: 32+3=35, Resulting Numbers: [47, 35] Generated Node #0,0,2: 45:[47, 35] Operation: 32+3=35 Exploring Operation: 32-3=29, Resulting Numbers: [47, 29] Generated Node #0,0,3: 45:[47, 29] Operation: 32-3=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[3, 15], Operations: ['93-90=3', '47-32=15'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[93, 32, 90, 47], Operations: [] Exploring Operation: 93-90=3, Resulting Numbers: [32, 47, 3] Generated Node #0,0: 45:[32, 47, 3] Operation: 93-90=3 Moving to Node #0,0 Current State: 45:[32, 47, 3], Operations: ['93-90=3'] Exploring Operation: 47-32=15, Resulting Numbers: [3, 15] Generated Node #0,0,0: 45:[3, 15] Operation: 47-32=15 Moving to Node #0,0,0 Current State: 45:[3, 15], Operations: ['93-90=3', '47-32=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 24, 7, 26, 2 ]
60
[ "24-7=17", "2*17=34", "26+34=60" ]
Current State: 60:[24, 7, 26, 2], Operations: [] Exploring Operation: 24-7=17, Resulting Numbers: [26, 2, 17] Generated Node #2: [26, 2, 17] from Operation: 24-7=17 Current State: 60:[26, 2, 17], Operations: ['24-7=17'] Exploring Operation: 2*17=34, Resulting Numbers: [26, 34] Generated Node #3: [26, 34] from Operation: 2*17=34 Current State: 60:[26, 34], Operations: ['24-7=17', '2*17=34'] Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[24, 7, 26, 2], Operations: [] Exploring Operation: 24/2=12, Resulting Numbers: [7, 26, 12] Generated Node #0,0: 60:[7, 26, 12] Operation: 24/2=12 Exploring Operation: 24-7=17, Resulting Numbers: [26, 2, 17] Generated Node #0,1: 60:[26, 2, 17] Operation: 24-7=17 Exploring Operation: 26-24=2, Resulting Numbers: [7, 2, 2] Generated Node #0,2: 60:[7, 2, 2] Operation: 26-24=2 Exploring Operation: 24+7=31, Resulting Numbers: [26, 2, 31] Generated Node #0,3: 60:[26, 2, 31] Operation: 24+7=31 Exploring Operation: 26-7=19, Resulting Numbers: [24, 2, 19] Generated Node #0,4: 60:[24, 2, 19] Operation: 26-7=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[7, 2, 2], Operations: ['26-24=2'] Exploring Operation: 7+2=9, Resulting Numbers: [2, 9] Generated Node #0,2,0: 60:[2, 9] Operation: 7+2=9 Exploring Operation: 7*2=14, Resulting Numbers: [2, 14] Generated Node #0,2,1: 60:[2, 14] Operation: 7*2=14 Exploring Operation: 7+2=9, Resulting Numbers: [2, 9] Generated Node #0,2,2: 60:[2, 9] Operation: 7+2=9 Exploring Operation: 7-2=5, Resulting Numbers: [2, 5] Generated Node #0,2,3: 60:[2, 5] Operation: 7-2=5 Exploring Operation: 7-2=5, Resulting Numbers: [2, 5] Generated Node #0,2,4: 60:[2, 5] Operation: 7-2=5 Moving to Node #0,2,3 Current State: 60:[2, 5], Operations: ['26-24=2', '7-2=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,2,4 Current State: 60:[2, 5], Operations: ['26-24=2', '7-2=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[2, 9], Operations: ['26-24=2', '7+2=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[2, 14], Operations: ['26-24=2', '7*2=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,60 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[2, 9], Operations: ['26-24=2', '7+2=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,60 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 Current State: 60:[7, 26, 12], Operations: ['24/2=12'] Exploring Operation: 26-12=14, Resulting Numbers: [7, 14] Generated Node #0,0,0: 60:[7, 14] Operation: 26-12=14 Exploring Operation: 12-7=5, Resulting Numbers: [26, 5] Generated Node #0,0,1: 60:[26, 5] Operation: 12-7=5 Exploring Operation: 7+26=33, Resulting Numbers: [12, 33] Generated Node #0,0,2: 60:[12, 33] Operation: 7+26=33 Exploring Operation: 7+12=19, Resulting Numbers: [26, 19] Generated Node #0,0,3: 60:[26, 19] Operation: 7+12=19 Exploring Operation: 26-7=19, Resulting Numbers: [12, 19] Generated Node #0,0,4: 60:[12, 19] Operation: 26-7=19 Moving to Node #0,0,4 Current State: 60:[12, 19], Operations: ['24/2=12', '26-7=19'] Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,60 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,60 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[7, 14], Operations: ['24/2=12', '26-12=14'] Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,60 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,60 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,0,2 Current State: 60:[12, 33], Operations: ['24/2=12', '7+26=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,60 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[26, 5], Operations: ['24/2=12', '12-7=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,60 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,60 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,60 unequal: No Solution Moving to Node #0,0,3 Current State: 60:[26, 19], Operations: ['24/2=12', '7+12=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,60 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,60 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 Current State: 60:[26, 2, 31], Operations: ['24+7=31'] Exploring Operation: 26/2=13, Resulting Numbers: [31, 13] Generated Node #0,3,0: 60:[31, 13] Operation: 26/2=13 Exploring Operation: 31-26=5, Resulting Numbers: [2, 5] Generated Node #0,3,1: 60:[2, 5] Operation: 31-26=5 Exploring Operation: 26+2=28, Resulting Numbers: [31, 28] Generated Node #0,3,2: 60:[31, 28] Operation: 26+2=28 Exploring Operation: 26-2=24, Resulting Numbers: [31, 24] Generated Node #0,3,3: 60:[31, 24] Operation: 26-2=24 Exploring Operation: 26+31=57, Resulting Numbers: [2, 57] Generated Node #0,3,4: 60:[2, 57] Operation: 26+31=57 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 60:[2, 5], Operations: ['24+7=31', '31-26=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,60 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 #0,3,0 Current State: 60:[31, 13], Operations: ['24+7=31', '26/2=13'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,60 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 #0,3,2 Current State: 60:[31, 28], Operations: ['24+7=31', '26+2=28'] Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,60 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,60 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 #0,3,4 Current State: 60:[2, 57], Operations: ['24+7=31', '26+31=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,60 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 #0,3,3 Current State: 60:[31, 24], Operations: ['24+7=31', '26-2=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,60 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,60 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 #0,4 Current State: 60:[24, 2, 19], Operations: ['26-7=19'] Exploring Operation: 24+2=26, Resulting Numbers: [19, 26] Generated Node #0,4,0: 60:[19, 26] Operation: 24+2=26 Exploring Operation: 2+19=21, Resulting Numbers: [24, 21] Generated Node #0,4,1: 60:[24, 21] Operation: 2+19=21 Exploring Operation: 24/2=12, Resulting Numbers: [19, 12] Generated Node #0,4,2: 60:[19, 12] Operation: 24/2=12 Exploring Operation: 24-19=5, Resulting Numbers: [2, 5] Generated Node #0,4,3: 60:[2, 5] Operation: 24-19=5 Exploring Operation: 24-2=22, Resulting Numbers: [19, 22] Generated Node #0,4,4: 60:[19, 22] Operation: 24-2=22 Moving to Node #0,4,3 Current State: 60:[2, 5], Operations: ['26-7=19', '24-19=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,4,2 Current State: 60:[19, 12], Operations: ['26-7=19', '24/2=12'] Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,60 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,60 unequal: No Solution Moving to Node #0,4,4 Current State: 60:[19, 22], Operations: ['26-7=19', '24-2=22'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,60 unequal: No Solution Moving to Node #0,4,0 Current State: 60:[19, 26], Operations: ['26-7=19', '24+2=26'] Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,60 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,4,1 Current State: 60:[24, 21], Operations: ['26-7=19', '2+19=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,60 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,60 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 Current State: 60:[26, 2, 17], Operations: ['24-7=17'] Exploring Operation: 26-17=9, Resulting Numbers: [2, 9] Generated Node #0,1,0: 60:[2, 9] Operation: 26-17=9 Exploring Operation: 26/2=13, Resulting Numbers: [17, 13] Generated Node #0,1,1: 60:[17, 13] Operation: 26/2=13 Exploring Operation: 26+2=28, Resulting Numbers: [17, 28] Generated Node #0,1,2: 60:[17, 28] Operation: 26+2=28 Exploring Operation: 17-2=15, Resulting Numbers: [26, 15] Generated Node #0,1,3: 60:[26, 15] Operation: 17-2=15 Exploring Operation: 2+17=19, Resulting Numbers: [26, 19] Generated Node #0,1,4: 60:[26, 19] Operation: 2+17=19 Moving to Node #0,1,0 Current State: 60:[2, 9], Operations: ['24-7=17', '26-17=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[17, 13], Operations: ['24-7=17', '26/2=13'] Exploring Operation: 17*13=221, Resulting Numbers: [221] 221,60 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 17+13=30, Resulting Numbers: [30] 30,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[17, 28], Operations: ['24-7=17', '26+2=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 17*28=476, Resulting Numbers: [476] 476,60 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[26, 15], Operations: ['24-7=17', '17-2=15'] Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,60 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,60 unequal: No Solution Moving to Node #0,1,4 Current State: 60:[26, 19], Operations: ['24-7=17', '2+17=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,60 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,60 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,60 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
[ 3, 65, 48, 50 ]
66
[ "3+65=68", "50-48=2", "68-2=66" ]
Current State: 66:[3, 65, 48, 50], Operations: [] Exploring Operation: 3+65=68, Resulting Numbers: [48, 50, 68] Generated Node #2: [48, 50, 68] from Operation: 3+65=68 Current State: 66:[48, 50, 68], Operations: ['3+65=68'] Exploring Operation: 50-48=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 50-48=2 Current State: 66:[68, 2], Operations: ['3+65=68', '50-48=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[3, 65, 48, 50], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [3, 65, 2] Generated Node #0,0: 66:[3, 65, 2] Operation: 50-48=2 Exploring Operation: 65-50=15, Resulting Numbers: [3, 48, 15] Generated Node #0,1: 66:[3, 48, 15] Operation: 65-50=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[3, 65, 2], Operations: ['50-48=2'] Exploring Operation: 3*2=6, Resulting Numbers: [65, 6] Generated Node #0,0,0: 66:[65, 6] Operation: 3*2=6 Exploring Operation: 65+2=67, Resulting Numbers: [3, 67] Generated Node #0,0,1: 66:[3, 67] Operation: 65+2=67 Moving to Node #0,0,0 Current State: 66:[65, 6], Operations: ['50-48=2', '3*2=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,66 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[3, 67], Operations: ['50-48=2', '65+2=67'] Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,66 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[3, 48, 15], Operations: ['65-50=15'] Exploring Operation: 48-15=33, Resulting Numbers: [3, 33] Generated Node #0,1,0: 66:[3, 33] Operation: 48-15=33 Exploring Operation: 48+15=63, Resulting Numbers: [3, 63] Generated Node #0,1,1: 66:[3, 63] Operation: 48+15=63 Moving to Node #0,1,0 Current State: 66:[3, 33], Operations: ['65-50=15', '48-15=33'] Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,66 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[3, 63], Operations: ['65-50=15', '48+15=63'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,66 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[3, 65, 48, 50], Operations: [] Exploring Operation: 65-50=15, Resulting Numbers: [3, 48, 15] Generated Node #0,1: 66:[3, 48, 15] Operation: 65-50=15 Moving to Node #0,1 Current State: 66:[3, 48, 15], Operations: ['65-50=15'] Exploring Operation: 48+15=63, Resulting Numbers: [3, 63] Generated Node #0,1,1: 66:[3, 63] Operation: 48+15=63 Moving to Node #0,1,1 Current State: 66:[3, 63], Operations: ['65-50=15', '48+15=63'] Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 30, 10, 13, 90 ]
87
[ "90/10=9", "13*9=117", "117-30=87" ]
Current State: 87:[30, 10, 13, 90], Operations: [] Exploring Operation: 90/10=9, Resulting Numbers: [30, 13, 9] Generated Node #2: [30, 13, 9] from Operation: 90/10=9 Current State: 87:[30, 13, 9], Operations: ['90/10=9'] Exploring Operation: 13*9=117, Resulting Numbers: [30, 117] Generated Node #3: [30, 117] from Operation: 13*9=117 Current State: 87:[30, 117], Operations: ['90/10=9', '13*9=117'] Exploring Operation: 117-30=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[30, 10, 13, 90], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [13, 90, 3] Generated Node #0,0: 87:[13, 90, 3] Operation: 30/10=3 Exploring Operation: 13-10=3, Resulting Numbers: [30, 90, 3] Generated Node #0,1: 87:[30, 90, 3] Operation: 13-10=3 Exploring Operation: 10+13=23, Resulting Numbers: [30, 90, 23] Generated Node #0,2: 87:[30, 90, 23] Operation: 10+13=23 Exploring Operation: 90/30=3, Resulting Numbers: [10, 13, 3] Generated Node #0,3: 87:[10, 13, 3] Operation: 90/30=3 Moving to Node #0,1 Current State: 87:[30, 90, 3], Operations: ['13-10=3'] Exploring Operation: 90/3=30, Resulting Numbers: [30, 30] Generated Node #0,1,0: 87:[30, 30] Operation: 90/3=30 Exploring Operation: 90-3=87, Resulting Numbers: [30, 87] Generated Node #0,1,1: 87:[30, 87] Operation: 90-3=87 Exploring Operation: 30-3=27, Resulting Numbers: [90, 27] Generated Node #0,1,2: 87:[90, 27] Operation: 30-3=27 Exploring Operation: 90/30=3, Resulting Numbers: [3, 3] Generated Node #0,1,3: 87:[3, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[3, 3], Operations: ['13-10=3', '90/30=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,87 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,87 unequal: No Solution No 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: 87:[30, 87], Operations: ['13-10=3', '90-3=87'] Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,87 unequal: No Solution Exploring Operation: 30*87=2610, Resulting Numbers: [2610] 2610,87 unequal: No Solution Exploring Operation: 30+87=117, Resulting Numbers: [117] 117,87 unequal: No Solution No 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: 87:[30, 30], Operations: ['13-10=3', '90/3=30'] Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,87 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,87 unequal: No Solution No 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: 87:[90, 27], Operations: ['13-10=3', '30-3=27'] Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,87 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,87 unequal: No Solution Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,87 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: 87:[30, 90, 23], Operations: ['10+13=23'] Exploring Operation: 90-23=67, Resulting Numbers: [30, 67] Generated Node #0,2,0: 87:[30, 67] Operation: 90-23=67 Exploring Operation: 30+23=53, Resulting Numbers: [90, 53] Generated Node #0,2,1: 87:[90, 53] Operation: 30+23=53 Exploring Operation: 30-23=7, Resulting Numbers: [90, 7] Generated Node #0,2,2: 87:[90, 7] Operation: 30-23=7 Exploring Operation: 90/30=3, Resulting Numbers: [23, 3] Generated Node #0,2,3: 87:[23, 3] Operation: 90/30=3 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[23, 3], Operations: ['10+13=23', '90/30=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,87 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,87 unequal: No Solution No 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: 87:[90, 7], Operations: ['10+13=23', '30-23=7'] Exploring Operation: 90*7=630, Resulting Numbers: [630] 630,87 unequal: No Solution Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,87 unequal: No Solution Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,87 unequal: No Solution No 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: 87:[30, 67], Operations: ['10+13=23', '90-23=67'] Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,87 unequal: No Solution Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,87 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,87 unequal: No Solution No 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: 87:[90, 53], Operations: ['10+13=23', '30+23=53'] Exploring Operation: 90*53=4770, Resulting Numbers: [4770] 4770,87 unequal: No Solution Exploring Operation: 90-53=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 90+53=143, Resulting Numbers: [143] 143,87 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: 87:[13, 90, 3], Operations: ['30/10=3'] Exploring Operation: 90-3=87, Resulting Numbers: [13, 87] Generated Node #0,0,0: 87:[13, 87] Operation: 90-3=87 Exploring Operation: 13-3=10, Resulting Numbers: [90, 10] Generated Node #0,0,1: 87:[90, 10] Operation: 13-3=10 Exploring Operation: 90/3=30, Resulting Numbers: [13, 30] Generated Node #0,0,2: 87:[13, 30] Operation: 90/3=30 Exploring Operation: 90-13=77, Resulting Numbers: [3, 77] Generated Node #0,0,3: 87:[3, 77] Operation: 90-13=77 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[13, 87], Operations: ['30/10=3', '90-3=87'] Exploring Operation: 13*87=1131, Resulting Numbers: [1131] 1131,87 unequal: No Solution Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 13+87=100, Resulting Numbers: [100] 100,87 unequal: No Solution No 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: 87:[90, 10], Operations: ['30/10=3', '13-3=10'] Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,87 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,87 unequal: No Solution Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,87 unequal: No Solution No 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: 87:[3, 77], Operations: ['30/10=3', '90-13=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 3*77=231, Resulting Numbers: [231] 231,87 unequal: No Solution No 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: 87:[13, 30], Operations: ['30/10=3', '90/3=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,87 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: 87:[10, 13, 3], Operations: ['90/30=3'] Exploring Operation: 13-10=3, Resulting Numbers: [3, 3] Generated Node #0,3,0: 87:[3, 3] Operation: 13-10=3 Exploring Operation: 10-3=7, Resulting Numbers: [13, 7] Generated Node #0,3,1: 87:[13, 7] Operation: 10-3=7 Exploring Operation: 10*3=30, Resulting Numbers: [13, 30] Generated Node #0,3,2: 87:[13, 30] Operation: 10*3=30 Exploring Operation: 10+13=23, Resulting Numbers: [3, 23] Generated Node #0,3,3: 87:[3, 23] Operation: 10+13=23 Moving to Node #0,3,0 Current State: 87:[3, 3], Operations: ['90/30=3', '13-10=3'] Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,87 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[3, 23], Operations: ['90/30=3', '10+13=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,87 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,87 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[13, 30], Operations: ['90/30=3', '10*3=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[13, 7], Operations: ['90/30=3', '10-3=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,87 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,87 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 67, 62, 35, 75 ]
100
[ "67-62=5", "35*5=175", "175-75=100" ]
Current State: 100:[67, 62, 35, 75], Operations: [] Exploring Operation: 67-62=5, Resulting Numbers: [35, 75, 5] Generated Node #2: [35, 75, 5] from Operation: 67-62=5 Current State: 100:[35, 75, 5], Operations: ['67-62=5'] Exploring Operation: 35*5=175, Resulting Numbers: [75, 175] Generated Node #3: [75, 175] from Operation: 35*5=175 Current State: 100:[75, 175], Operations: ['67-62=5', '35*5=175'] Exploring Operation: 175-75=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[67, 62, 35, 75], Operations: [] Exploring Operation: 75-67=8, Resulting Numbers: [62, 35, 8] Generated Node #0,0: 100:[62, 35, 8] Operation: 75-67=8 Exploring Operation: 67+35=102, Resulting Numbers: [62, 75, 102] Generated Node #0,1: 100:[62, 75, 102] Operation: 67+35=102 Exploring Operation: 67-62=5, Resulting Numbers: [35, 75, 5] Generated Node #0,2: 100:[35, 75, 5] Operation: 67-62=5 Exploring Operation: 75-62=13, Resulting Numbers: [67, 35, 13] Generated Node #0,3: 100:[67, 35, 13] Operation: 75-62=13 Moving to Node #0,0 Current State: 100:[62, 35, 8], Operations: ['75-67=8'] Exploring Operation: 62+35=97, Resulting Numbers: [8, 97] Generated Node #0,0,0: 100:[8, 97] Operation: 62+35=97 Exploring Operation: 62-35=27, Resulting Numbers: [8, 27] Generated Node #0,0,1: 100:[8, 27] Operation: 62-35=27 Exploring Operation: 35-8=27, Resulting Numbers: [62, 27] Generated Node #0,0,2: 100:[62, 27] Operation: 35-8=27 Exploring Operation: 62-8=54, Resulting Numbers: [35, 54] Generated Node #0,0,3: 100:[35, 54] Operation: 62-8=54 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[8, 27], Operations: ['75-67=8', '62-35=27'] Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,100 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,100 unequal: No Solution No 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: 100:[8, 97], Operations: ['75-67=8', '62+35=97'] Exploring Operation: 8+97=105, Resulting Numbers: [105] 105,100 unequal: No Solution Exploring Operation: 8*97=776, Resulting Numbers: [776] 776,100 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,100 unequal: No Solution No 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: 100:[62, 27], Operations: ['75-67=8', '35-8=27'] Exploring Operation: 62*27=1674, Resulting Numbers: [1674] 1674,100 unequal: No Solution Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,100 unequal: No Solution No 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: 100:[35, 54], Operations: ['75-67=8', '62-8=54'] Exploring Operation: 35*54=1890, Resulting Numbers: [1890] 1890,100 unequal: No Solution Exploring Operation: 54-35=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 35+54=89, Resulting Numbers: [89] 89,100 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: 100:[67, 35, 13], Operations: ['75-62=13'] Exploring Operation: 67+35=102, Resulting Numbers: [13, 102] Generated Node #0,3,0: 100:[13, 102] Operation: 67+35=102 Exploring Operation: 67-13=54, Resulting Numbers: [35, 54] Generated Node #0,3,1: 100:[35, 54] Operation: 67-13=54 Exploring Operation: 35+13=48, Resulting Numbers: [67, 48] Generated Node #0,3,2: 100:[67, 48] Operation: 35+13=48 Exploring Operation: 67-35=32, Resulting Numbers: [13, 32] Generated Node #0,3,3: 100:[13, 32] Operation: 67-35=32 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 100:[13, 102], Operations: ['75-62=13', '67+35=102'] Exploring Operation: 102-13=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 13+102=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 13*102=1326, Resulting Numbers: [1326] 1326,100 unequal: No Solution No 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: 100:[13, 32], Operations: ['75-62=13', '67-35=32'] Exploring Operation: 13+32=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 13*32=416, Resulting Numbers: [416] 416,100 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,100 unequal: No Solution No 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: 100:[35, 54], Operations: ['75-62=13', '67-13=54'] Exploring Operation: 35+54=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 35*54=1890, Resulting Numbers: [1890] 1890,100 unequal: No Solution Exploring Operation: 54-35=19, Resulting Numbers: [19] 19,100 unequal: No Solution No 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: 100:[67, 48], Operations: ['75-62=13', '35+13=48'] Exploring Operation: 67+48=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 67*48=3216, Resulting Numbers: [3216] 3216,100 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,100 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: 100:[35, 75, 5], Operations: ['67-62=5'] Exploring Operation: 35/5=7, Resulting Numbers: [75, 7] Generated Node #0,2,0: 100:[75, 7] Operation: 35/5=7 Exploring Operation: 75-35=40, Resulting Numbers: [5, 40] Generated Node #0,2,1: 100:[5, 40] Operation: 75-35=40 Exploring Operation: 75/5=15, Resulting Numbers: [35, 15] Generated Node #0,2,2: 100:[35, 15] Operation: 75/5=15 Exploring Operation: 35+75=110, Resulting Numbers: [5, 110] Generated Node #0,2,3: 100:[5, 110] Operation: 35+75=110 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[5, 40], Operations: ['67-62=5', '75-35=40'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,100 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,100 unequal: No Solution No 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: 100:[5, 110], Operations: ['67-62=5', '35+75=110'] Exploring Operation: 5+110=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 110/5=22, Resulting Numbers: [22] 22,100 unequal: No Solution Exploring Operation: 5*110=550, Resulting Numbers: [550] 550,100 unequal: No Solution Exploring Operation: 110-5=105, Resulting Numbers: [105] 105,100 unequal: No Solution No 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: 100:[35, 15], Operations: ['67-62=5', '75/5=15'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,100 unequal: No Solution No 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: 100:[75, 7], Operations: ['67-62=5', '35/5=7'] Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,100 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,100 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: 100:[62, 75, 102], Operations: ['67+35=102'] Exploring Operation: 102-75=27, Resulting Numbers: [62, 27] Generated Node #0,1,0: 100:[62, 27] Operation: 102-75=27 Exploring Operation: 75-62=13, Resulting Numbers: [102, 13] Generated Node #0,1,1: 100:[102, 13] Operation: 75-62=13 Exploring Operation: 102-62=40, Resulting Numbers: [75, 40] Generated Node #0,1,2: 100:[75, 40] Operation: 102-62=40 Exploring Operation: 62+75=137, Resulting Numbers: [102, 137] Generated Node #0,1,3: 100:[102, 137] Operation: 62+75=137 Moving to Node #0,1,1 Current State: 100:[102, 13], Operations: ['67+35=102', '75-62=13'] Exploring Operation: 102+13=115, Resulting Numbers: [115] 115,100 unequal: No Solution Exploring Operation: 102*13=1326, Resulting Numbers: [1326] 1326,100 unequal: No Solution Exploring Operation: 102-13=89, Resulting Numbers: [89] 89,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[62, 27], Operations: ['67+35=102', '102-75=27'] Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 62*27=1674, Resulting Numbers: [1674] 1674,100 unequal: No Solution Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[75, 40], Operations: ['67+35=102', '102-62=40'] Exploring Operation: 75*40=3000, Resulting Numbers: [3000] 3000,100 unequal: No Solution Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 75+40=115, Resulting Numbers: [115] 115,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[102, 137], Operations: ['67+35=102', '62+75=137'] Exploring Operation: 102*137=13974, Resulting Numbers: [13974] 13974,100 unequal: No Solution Exploring Operation: 137-102=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 102+137=239, Resulting Numbers: [239] 239,100 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 89, 69, 98, 72 ]
77
[ "98-89=9", "72/9=8", "69+8=77" ]
Current State: 77:[89, 69, 98, 72], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [69, 72, 9] Generated Node #2: [69, 72, 9] from Operation: 98-89=9 Current State: 77:[69, 72, 9], Operations: ['98-89=9'] Exploring Operation: 72/9=8, Resulting Numbers: [69, 8] Generated Node #3: [69, 8] from Operation: 72/9=8 Current State: 77:[69, 8], Operations: ['98-89=9', '72/9=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[89, 69, 98, 72], Operations: [] Exploring Operation: 89-69=20, Resulting Numbers: [98, 72, 20] Generated Node #0,0: 77:[98, 72, 20] Operation: 89-69=20 Exploring Operation: 98-72=26, Resulting Numbers: [89, 69, 26] Generated Node #0,1: 77:[89, 69, 26] Operation: 98-72=26 Exploring Operation: 98-89=9, Resulting Numbers: [69, 72, 9] Generated Node #0,2: 77:[69, 72, 9] Operation: 98-89=9 Exploring Operation: 89-72=17, Resulting Numbers: [69, 98, 17] Generated Node #0,3: 77:[69, 98, 17] Operation: 89-72=17 Exploring Operation: 98-69=29, Resulting Numbers: [89, 72, 29] Generated Node #0,4: 77:[89, 72, 29] Operation: 98-69=29 Moving to Node #0,2 Current State: 77:[69, 72, 9], Operations: ['98-89=9'] Exploring Operation: 72+9=81, Resulting Numbers: [69, 81] Generated Node #0,2,0: 77:[69, 81] Operation: 72+9=81 Exploring Operation: 72/9=8, Resulting Numbers: [69, 8] Generated Node #0,2,1: 77:[69, 8] Operation: 72/9=8 Exploring Operation: 69-9=60, Resulting Numbers: [72, 60] Generated Node #0,2,2: 77:[72, 60] Operation: 69-9=60 Exploring Operation: 72-69=3, Resulting Numbers: [9, 3] Generated Node #0,2,3: 77:[9, 3] Operation: 72-69=3 Exploring Operation: 69+9=78, Resulting Numbers: [72, 78] Generated Node #0,2,4: 77:[72, 78] Operation: 69+9=78 Moving to Node #0,1 Current State: 77:[89, 69, 26], Operations: ['98-72=26'] Exploring Operation: 89-69=20, Resulting Numbers: [26, 20] Generated Node #0,1,0: 77:[26, 20] Operation: 89-69=20 Exploring Operation: 69+26=95, Resulting Numbers: [89, 95] Generated Node #0,1,1: 77:[89, 95] Operation: 69+26=95 Exploring Operation: 89-26=63, Resulting Numbers: [69, 63] Generated Node #0,1,2: 77:[69, 63] Operation: 89-26=63 Exploring Operation: 69-26=43, Resulting Numbers: [89, 43] Generated Node #0,1,3: 77:[89, 43] Operation: 69-26=43 Exploring Operation: 89+26=115, Resulting Numbers: [69, 115] Generated Node #0,1,4: 77:[69, 115] Operation: 89+26=115 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[69, 63], Operations: ['98-72=26', '89-26=63'] Exploring Operation: 69-63=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 69*63=4347, Resulting Numbers: [4347] 4347,77 unequal: No Solution Exploring Operation: 69+63=132, Resulting Numbers: [132] 132,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[26, 20], Operations: ['98-72=26', '89-69=20'] Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,77 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[89, 95], Operations: ['98-72=26', '69+26=95'] Exploring Operation: 95-89=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 89+95=184, Resulting Numbers: [184] 184,77 unequal: No Solution Exploring Operation: 89*95=8455, Resulting Numbers: [8455] 8455,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 77:[89, 43], Operations: ['98-72=26', '69-26=43'] Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 89+43=132, Resulting Numbers: [132] 132,77 unequal: No Solution Exploring Operation: 89*43=3827, Resulting Numbers: [3827] 3827,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 77:[69, 115], Operations: ['98-72=26', '89+26=115'] Exploring Operation: 115-69=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 69*115=7935, Resulting Numbers: [7935] 7935,77 unequal: No Solution Exploring Operation: 69+115=184, Resulting Numbers: [184] 184,77 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: 77:[89, 72, 29], Operations: ['98-69=29'] Exploring Operation: 89-72=17, Resulting Numbers: [29, 17] Generated Node #0,4,0: 77:[29, 17] Operation: 89-72=17 Exploring Operation: 89-29=60, Resulting Numbers: [72, 60] Generated Node #0,4,1: 77:[72, 60] Operation: 89-29=60 Exploring Operation: 72-29=43, Resulting Numbers: [89, 43] Generated Node #0,4,2: 77:[89, 43] Operation: 72-29=43 Exploring Operation: 72+29=101, Resulting Numbers: [89, 101] Generated Node #0,4,3: 77:[89, 101] Operation: 72+29=101 Exploring Operation: 89+29=118, Resulting Numbers: [72, 118] Generated Node #0,4,4: 77:[72, 118] Operation: 89+29=118 Moving to Node #0,0 Current State: 77:[98, 72, 20], Operations: ['89-69=20'] Exploring Operation: 98+20=118, Resulting Numbers: [72, 118] Generated Node #0,0,0: 77:[72, 118] Operation: 98+20=118 Exploring Operation: 98-72=26, Resulting Numbers: [20, 26] Generated Node #0,0,1: 77:[20, 26] Operation: 98-72=26 Exploring Operation: 72-20=52, Resulting Numbers: [98, 52] Generated Node #0,0,2: 77:[98, 52] Operation: 72-20=52 Exploring Operation: 72+20=92, Resulting Numbers: [98, 92] Generated Node #0,0,3: 77:[98, 92] Operation: 72+20=92 Exploring Operation: 98-20=78, Resulting Numbers: [72, 78] Generated Node #0,0,4: 77:[72, 78] Operation: 98-20=78 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 77:[72, 78], Operations: ['89-69=20', '98-20=78'] Exploring Operation: 72+78=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 72*78=5616, Resulting Numbers: [5616] 5616,77 unequal: No Solution Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[20, 26], Operations: ['89-69=20', '98-72=26'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[98, 92], Operations: ['89-69=20', '72+20=92'] Exploring Operation: 98+92=190, Resulting Numbers: [190] 190,77 unequal: No Solution Exploring Operation: 98-92=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 98*92=9016, Resulting Numbers: [9016] 9016,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[72, 118], Operations: ['89-69=20', '98+20=118'] Exploring Operation: 118-72=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 72*118=8496, Resulting Numbers: [8496] 8496,77 unequal: No Solution Exploring Operation: 72+118=190, Resulting Numbers: [190] 190,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 77:[98, 52], Operations: ['89-69=20', '72-20=52'] Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,77 unequal: No Solution Exploring Operation: 98*52=5096, Resulting Numbers: [5096] 5096,77 unequal: No Solution Exploring Operation: 98+52=150, Resulting Numbers: [150] 150,77 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: 77:[69, 98, 17], Operations: ['89-72=17'] Exploring Operation: 69-17=52, Resulting Numbers: [98, 52] Generated Node #0,3,0: 77:[98, 52] Operation: 69-17=52 Exploring Operation: 98+17=115, Resulting Numbers: [69, 115] Generated Node #0,3,1: 77:[69, 115] Operation: 98+17=115 Exploring Operation: 98-69=29, Resulting Numbers: [17, 29] Generated Node #0,3,2: 77:[17, 29] Operation: 98-69=29 Exploring Operation: 69+17=86, Resulting Numbers: [98, 86] Generated Node #0,3,3: 77:[98, 86] Operation: 69+17=86 Exploring Operation: 98-17=81, Resulting Numbers: [69, 81] Generated Node #0,3,4: 77:[69, 81] Operation: 98-17=81 Moving to Node #0,2,3 Current State: 77:[9, 3], Operations: ['98-89=9', '72-69=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,77 unequal: No Solution Moving to Node #0,2,4 Current State: 77:[72, 78], Operations: ['98-89=9', '69+9=78'] Exploring Operation: 78-72=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 72*78=5616, Resulting Numbers: [5616] 5616,77 unequal: No Solution Exploring Operation: 72+78=150, Resulting Numbers: [150] 150,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[69, 8], Operations: ['98-89=9', '72/9=8'] Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,77 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[89, 69, 98, 72], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [69, 72, 9] Generated Node #0,2: 77:[69, 72, 9] Operation: 98-89=9 Moving to Node #0,2 Current State: 77:[69, 72, 9], Operations: ['98-89=9'] Exploring Operation: 72/9=8, Resulting Numbers: [69, 8] Generated Node #0,2,1: 77:[69, 8] Operation: 72/9=8 Moving to Node #0,2,1 Current State: 77:[69, 8], Operations: ['98-89=9', '72/9=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.935764
hs_5
sum_heuristic
[ 26, 33, 43, 2 ]
32
[ "26+33=59", "59-43=16", "2*16=32" ]
Current State: 32:[26, 33, 43, 2], Operations: [] Exploring Operation: 26+33=59, Resulting Numbers: [43, 2, 59] Generated Node #2: [43, 2, 59] from Operation: 26+33=59 Current State: 32:[43, 2, 59], Operations: ['26+33=59'] Exploring Operation: 59-43=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 59-43=16 Current State: 32:[2, 16], Operations: ['26+33=59', '59-43=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[26, 33, 43, 2], Operations: [] Exploring Operation: 43-26=17, Resulting Numbers: [33, 2, 17] Generated Node #0,0: 32:[33, 2, 17] Operation: 43-26=17 Moving to Node #0,0 Current State: 32:[33, 2, 17], Operations: ['43-26=17'] Exploring Operation: 33-17=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 33-17=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['43-26=17', '33-17=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[26, 33, 43, 2], Operations: [] Exploring Operation: 43-26=17, Resulting Numbers: [33, 2, 17] Generated Node #0,0: 32:[33, 2, 17] Operation: 43-26=17 Moving to Node #0,0 Current State: 32:[33, 2, 17], Operations: ['43-26=17'] Exploring Operation: 33-17=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 32:[2, 16] Operation: 33-17=16 Moving to Node #0,0,0 Current State: 32:[2, 16], Operations: ['43-26=17', '33-17=16'] Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 52, 83, 46, 27 ]
41
[ "52+83=135", "135/27=5", "46-5=41" ]
Current State: 41:[52, 83, 46, 27], Operations: [] Exploring Operation: 52+83=135, Resulting Numbers: [46, 27, 135] Generated Node #2: [46, 27, 135] from Operation: 52+83=135 Current State: 41:[46, 27, 135], Operations: ['52+83=135'] Exploring Operation: 135/27=5, Resulting Numbers: [46, 5] Generated Node #3: [46, 5] from Operation: 135/27=5 Current State: 41:[46, 5], Operations: ['52+83=135', '135/27=5'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[52, 83, 46, 27], Operations: [] Exploring Operation: 83-52=31, Resulting Numbers: [46, 27, 31] Generated Node #0,0: 41:[46, 27, 31] Operation: 83-52=31 Exploring Operation: 83-46=37, Resulting Numbers: [52, 27, 37] Generated Node #0,1: 41:[52, 27, 37] Operation: 83-46=37 Exploring Operation: 83-27=56, Resulting Numbers: [52, 46, 56] Generated Node #0,2: 41:[52, 46, 56] Operation: 83-27=56 Moving to Node #0,0 Current State: 41:[46, 27, 31], Operations: ['83-52=31'] Exploring Operation: 27+31=58, Resulting Numbers: [46, 58] Generated Node #0,0,0: 41:[46, 58] Operation: 27+31=58 Exploring Operation: 46-27=19, Resulting Numbers: [31, 19] Generated Node #0,0,1: 41:[31, 19] Operation: 46-27=19 Exploring Operation: 46-31=15, Resulting Numbers: [27, 15] Generated Node #0,0,2: 41:[27, 15] Operation: 46-31=15 Moving to Node #0,1 Current State: 41:[52, 27, 37], Operations: ['83-46=37'] Exploring Operation: 52-27=25, Resulting Numbers: [37, 25] Generated Node #0,1,0: 41:[37, 25] Operation: 52-27=25 Exploring Operation: 52-37=15, Resulting Numbers: [27, 15] Generated Node #0,1,1: 41:[27, 15] Operation: 52-37=15 Exploring Operation: 27+37=64, Resulting Numbers: [52, 64] Generated Node #0,1,2: 41:[52, 64] Operation: 27+37=64 Moving to Node #0,2 Current State: 41:[52, 46, 56], Operations: ['83-27=56'] Exploring Operation: 52-46=6, Resulting Numbers: [56, 6] Generated Node #0,2,0: 41:[56, 6] Operation: 52-46=6 Exploring Operation: 56-52=4, Resulting Numbers: [46, 4] Generated Node #0,2,1: 41:[46, 4] Operation: 56-52=4 Exploring Operation: 56-46=10, Resulting Numbers: [52, 10] Generated Node #0,2,2: 41:[52, 10] Operation: 56-46=10 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 41:[46, 4], Operations: ['83-27=56', '56-52=4'] Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,41 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,41 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[52, 10], Operations: ['83-27=56', '56-46=10'] Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,41 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[56, 6], Operations: ['83-27=56', '52-46=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,41 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 41:[37, 25], Operations: ['83-46=37', '52-27=25'] Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[46, 58], Operations: ['83-52=31', '27+31=58'] Exploring Operation: 46*58=2668, Resulting Numbers: [2668] 2668,41 unequal: No Solution Exploring Operation: 58-46=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 46+58=104, Resulting Numbers: [104] 104,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[31, 19], Operations: ['83-52=31', '46-27=19'] Exploring Operation: 31*19=589, Resulting Numbers: [589] 589,41 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 31+19=50, Resulting Numbers: [50] 50,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[52, 64], Operations: ['83-46=37', '27+37=64'] Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 52*64=3328, Resulting Numbers: [3328] 3328,41 unequal: No Solution Exploring Operation: 52+64=116, Resulting Numbers: [116] 116,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[27, 15], Operations: ['83-46=37', '52-37=15'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,41 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[27, 15], Operations: ['83-52=31', '46-31=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,41 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 41, 42, 21, 15 ]
56
[ "41-21=20", "42*20=840", "840/15=56" ]
Current State: 56:[41, 42, 21, 15], Operations: [] Exploring Operation: 41-21=20, Resulting Numbers: [42, 15, 20] Generated Node #2: [42, 15, 20] from Operation: 41-21=20 Current State: 56:[42, 15, 20], Operations: ['41-21=20'] Exploring Operation: 42*20=840, Resulting Numbers: [15, 840] Generated Node #3: [15, 840] from Operation: 42*20=840 Current State: 56:[15, 840], Operations: ['41-21=20', '42*20=840'] Exploring Operation: 840/15=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[41, 42, 21, 15], Operations: [] Exploring Operation: 42-41=1, Resulting Numbers: [21, 15, 1] Generated Node #0,0: 56:[21, 15, 1] Operation: 42-41=1 Exploring Operation: 42/21=2, Resulting Numbers: [41, 15, 2] Generated Node #0,1: 56:[41, 15, 2] Operation: 42/21=2 Exploring Operation: 41+15=56, Resulting Numbers: [42, 21, 56] Generated Node #0,2: 56:[42, 21, 56] Operation: 41+15=56 Exploring Operation: 41-21=20, Resulting Numbers: [42, 15, 20] Generated Node #0,3: 56:[42, 15, 20] Operation: 41-21=20 Exploring Operation: 41+21=62, Resulting Numbers: [42, 15, 62] Generated Node #0,4: 56:[42, 15, 62] Operation: 41+21=62 Moving to Node #0,0 Current State: 56:[21, 15, 1], Operations: ['42-41=1'] Exploring Operation: 21-15=6, Resulting Numbers: [1, 6] Generated Node #0,0,0: 56:[1, 6] Operation: 21-15=6 Exploring Operation: 21*1=21, Resulting Numbers: [15, 21] Generated Node #0,0,1: 56:[15, 21] Operation: 21*1=21 Exploring Operation: 15-1=14, Resulting Numbers: [21, 14] Generated Node #0,0,2: 56:[21, 14] Operation: 15-1=14 Exploring Operation: 21+1=22, Resulting Numbers: [15, 22] Generated Node #0,0,3: 56:[15, 22] Operation: 21+1=22 Exploring Operation: 21-1=20, Resulting Numbers: [15, 20] Generated Node #0,0,4: 56:[15, 20] Operation: 21-1=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[1, 6], Operations: ['42-41=1', '21-15=6'] Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[21, 14], Operations: ['42-41=1', '15-1=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,56 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 56:[15, 22], Operations: ['42-41=1', '21+1=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,56 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 56:[15, 20], Operations: ['42-41=1', '21-1=20'] Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,56 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[15, 21], Operations: ['42-41=1', '21*1=21'] Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,56 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,56 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: 56:[41, 15, 2], Operations: ['42/21=2'] Exploring Operation: 41+2=43, Resulting Numbers: [15, 43] Generated Node #0,1,0: 56:[15, 43] Operation: 41+2=43 Exploring Operation: 15-2=13, Resulting Numbers: [41, 13] Generated Node #0,1,1: 56:[41, 13] Operation: 15-2=13 Exploring Operation: 41-2=39, Resulting Numbers: [15, 39] Generated Node #0,1,2: 56:[15, 39] Operation: 41-2=39 Exploring Operation: 41-15=26, Resulting Numbers: [2, 26] Generated Node #0,1,3: 56:[2, 26] Operation: 41-15=26 Exploring Operation: 41+15=56, Resulting Numbers: [2, 56] Generated Node #0,1,4: 56:[2, 56] Operation: 41+15=56 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 56:[2, 56], Operations: ['42/21=2', '41+15=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 2*56=112, Resulting Numbers: [112] 112,56 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[2, 26], Operations: ['42/21=2', '41-15=26'] Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,56 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[15, 39], Operations: ['42/21=2', '41-2=39'] Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,56 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[15, 43], Operations: ['42/21=2', '41+2=43'] Exploring Operation: 15*43=645, Resulting Numbers: [645] 645,56 unequal: No Solution Exploring Operation: 43-15=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 15+43=58, Resulting Numbers: [58] 58,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[41, 13], Operations: ['42/21=2', '15-2=13'] Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,56 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,56 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: 56:[42, 21, 56], Operations: ['41+15=56'] Exploring Operation: 42+21=63, Resulting Numbers: [56, 63] Generated Node #0,2,0: 56:[56, 63] Operation: 42+21=63 Exploring Operation: 42-21=21, Resulting Numbers: [56, 21] Generated Node #0,2,1: 56:[56, 21] Operation: 42-21=21 Exploring Operation: 56-21=35, Resulting Numbers: [42, 35] Generated Node #0,2,2: 56:[42, 35] Operation: 56-21=35 Exploring Operation: 42/21=2, Resulting Numbers: [56, 2] Generated Node #0,2,3: 56:[56, 2] Operation: 42/21=2 Exploring Operation: 56-42=14, Resulting Numbers: [21, 14] Generated Node #0,2,4: 56:[21, 14] Operation: 56-42=14 Moving to Node #0,3 Current State: 56:[42, 15, 20], Operations: ['41-21=20'] Exploring Operation: 42-15=27, Resulting Numbers: [20, 27] Generated Node #0,3,0: 56:[20, 27] Operation: 42-15=27 Exploring Operation: 42+20=62, Resulting Numbers: [15, 62] Generated Node #0,3,1: 56:[15, 62] Operation: 42+20=62 Exploring Operation: 20-15=5, Resulting Numbers: [42, 5] Generated Node #0,3,2: 56:[42, 5] Operation: 20-15=5 Exploring Operation: 42+15=57, Resulting Numbers: [20, 57] Generated Node #0,3,3: 56:[20, 57] Operation: 42+15=57 Exploring Operation: 42-20=22, Resulting Numbers: [15, 22] Generated Node #0,3,4: 56:[15, 22] Operation: 42-20=22 Moving to Node #0,4 Current State: 56:[42, 15, 62], Operations: ['41+21=62'] Exploring Operation: 62-15=47, Resulting Numbers: [42, 47] Generated Node #0,4,0: 56:[42, 47] Operation: 62-15=47 Exploring Operation: 62-42=20, Resulting Numbers: [15, 20] Generated Node #0,4,1: 56:[15, 20] Operation: 62-42=20 Exploring Operation: 15+62=77, Resulting Numbers: [42, 77] Generated Node #0,4,2: 56:[42, 77] Operation: 15+62=77 Exploring Operation: 42+15=57, Resulting Numbers: [62, 57] Generated Node #0,4,3: 56:[62, 57] Operation: 42+15=57 Exploring Operation: 42-15=27, Resulting Numbers: [62, 27] Generated Node #0,4,4: 56:[62, 27] Operation: 42-15=27 Moving to Node #0,2,3 Current State: 56:[56, 2], Operations: ['41+15=56', '42/21=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[56, 21], Operations: ['41+15=56', '42-21=21'] Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,56 unequal: No Solution Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[15, 62], Operations: ['41-21=20', '42+20=62'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,56 unequal: No Solution Exploring Operation: 15+62=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 15*62=930, Resulting Numbers: [930] 930,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[20, 27], Operations: ['41-21=20', '42-15=27'] Exploring Operation: 20*27=540, Resulting Numbers: [540] 540,56 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 20+27=47, Resulting Numbers: [47] 47,56 unequal: No Solution Moving to Node #0,4,4 Current State: 56:[62, 27], Operations: ['41+21=62', '42-15=27'] Exploring Operation: 62*27=1674, Resulting Numbers: [1674] 1674,56 unequal: No Solution Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 62+27=89, Resulting Numbers: [89] 89,56 unequal: No Solution Moving to Node #0,4,3 Current State: 56:[62, 57], Operations: ['41+21=62', '42+15=57'] Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 62*57=3534, Resulting Numbers: [3534] 3534,56 unequal: No Solution Exploring Operation: 62+57=119, Resulting Numbers: [119] 119,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[56, 63], Operations: ['41+15=56', '42+21=63'] Exploring Operation: 56+63=119, Resulting Numbers: [119] 119,56 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 56*63=3528, Resulting Numbers: [3528] 3528,56 unequal: No Solution Moving to Node #0,4,1 Current State: 56:[15, 20], Operations: ['41+21=62', '62-42=20'] Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,56 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,56 unequal: No Solution Moving to Node #0,2,4 Current State: 56:[21, 14], Operations: ['41+15=56', '56-42=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,56 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[20, 57], Operations: ['41-21=20', '42+15=57'] Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,56 unequal: No Solution Exploring Operation: 20*57=1140, Resulting Numbers: [1140] 1140,56 unequal: No Solution Moving to Node #0,3,4 Current State: 56:[15, 22], Operations: ['41-21=20', '42-20=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 15*22=330, Resulting Numbers: [330] 330,56 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[42, 5], Operations: ['41-21=20', '20-15=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,56 unequal: No Solution Exploring Operation: 42*5=210, Resulting Numbers: [210] 210,56 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[42, 35], Operations: ['41+15=56', '56-21=35'] Exploring Operation: 42+35=77, Resulting Numbers: [77] 77,56 unequal: No Solution Exploring Operation: 42*35=1470, Resulting Numbers: [1470] 1470,56 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,56 unequal: No Solution Moving to Node #0,4,0 Current State: 56:[42, 47], Operations: ['41+21=62', '62-15=47'] Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,56 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,56 unequal: No Solution Moving to Node #0,4,2 Current State: 56:[42, 77], Operations: ['41+21=62', '15+62=77'] Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 42+77=119, Resulting Numbers: [119] 119,56 unequal: No Solution Exploring Operation: 42*77=3234, Resulting Numbers: [3234] 3234,56 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 72, 41, 41, 24 ]
96
[ "72+41=113", "41-24=17", "113-17=96" ]
Current State: 96:[72, 41, 41, 24], Operations: [] Exploring Operation: 72+41=113, Resulting Numbers: [24, 113] Generated Node #2: [24, 113] from Operation: 72+41=113 Current State: 96:[24, 113], Operations: ['72+41=113'] Exploring Operation: 41-24=17, Resulting Numbers: [113, 17] Generated Node #3: [113, 17] from Operation: 41-24=17 Current State: 96:[113, 17], Operations: ['72+41=113', '41-24=17'] Exploring Operation: 113-17=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[72, 41, 41, 24], Operations: [] Exploring Operation: 72-41=31, Resulting Numbers: [41, 24, 31] Generated Node #0,0: 96:[41, 24, 31] Operation: 72-41=31 Moving to Node #0,0 Current State: 96:[41, 24, 31], Operations: ['72-41=31'] Exploring Operation: 41-24=17, Resulting Numbers: [31, 17] Generated Node #0,0,0: 96:[31, 17] Operation: 41-24=17 Moving to Node #0,0,0 Current State: 96:[31, 17], Operations: ['72-41=31', '41-24=17'] Exploring Operation: 31+17=48, Resulting Numbers: [48] 48,96 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 59, 1, 62, 88 ]
33
[ "59*1=59", "88-62=26", "59-26=33" ]
Current State: 33:[59, 1, 62, 88], Operations: [] Exploring Operation: 59*1=59, Resulting Numbers: [62, 88, 59] Generated Node #2: [62, 88, 59] from Operation: 59*1=59 Current State: 33:[62, 88, 59], Operations: ['59*1=59'] Exploring Operation: 88-62=26, Resulting Numbers: [59, 26] Generated Node #3: [59, 26] from Operation: 88-62=26 Current State: 33:[59, 26], Operations: ['59*1=59', '88-62=26'] Exploring Operation: 59-26=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[59, 1, 62, 88], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [1, 62, 29] Generated Node #0,0: 33:[1, 62, 29] Operation: 88-59=29 Moving to Node #0,0 Current State: 33:[1, 62, 29], Operations: ['88-59=29'] Exploring Operation: 62-29=33, Resulting Numbers: [1, 33] Generated Node #0,0,0: 33:[1, 33] Operation: 62-29=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[1, 33], Operations: ['88-59=29', '62-29=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[59, 1, 62, 88], Operations: [] Exploring Operation: 88-59=29, Resulting Numbers: [1, 62, 29] Generated Node #0,0: 33:[1, 62, 29] Operation: 88-59=29 Moving to Node #0,0 Current State: 33:[1, 62, 29], Operations: ['88-59=29'] Exploring Operation: 62-29=33, Resulting Numbers: [1, 33] Generated Node #0,0,0: 33:[1, 33] Operation: 62-29=33 Moving to Node #0,0,0 Current State: 33:[1, 33], Operations: ['88-59=29', '62-29=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 16, 6, 55, 43 ]
24
[ "55-16=39", "43-39=4", "6*4=24" ]
Current State: 24:[16, 6, 55, 43], Operations: [] Exploring Operation: 55-16=39, Resulting Numbers: [6, 43, 39] Generated Node #2: [6, 43, 39] from Operation: 55-16=39 Current State: 24:[6, 43, 39], Operations: ['55-16=39'] Exploring Operation: 43-39=4, Resulting Numbers: [6, 4] Generated Node #3: [6, 4] from Operation: 43-39=4 Current State: 24:[6, 4], Operations: ['55-16=39', '43-39=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[16, 6, 55, 43], Operations: [] Exploring Operation: 43-16=27, Resulting Numbers: [6, 55, 27] Generated Node #0,0: 24:[6, 55, 27] Operation: 43-16=27 Exploring Operation: 55-16=39, Resulting Numbers: [6, 43, 39] Generated Node #0,1: 24:[6, 43, 39] Operation: 55-16=39 Exploring Operation: 55-43=12, Resulting Numbers: [16, 6, 12] Generated Node #0,2: 24:[16, 6, 12] Operation: 55-43=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[16, 6, 12], Operations: ['55-43=12'] Exploring Operation: 16-6=10, Resulting Numbers: [12, 10] Generated Node #0,2,0: 24:[12, 10] Operation: 16-6=10 Exploring Operation: 16+6=22, Resulting Numbers: [12, 22] Generated Node #0,2,1: 24:[12, 22] Operation: 16+6=22 Exploring Operation: 16-12=4, Resulting Numbers: [6, 4] Generated Node #0,2,2: 24:[6, 4] Operation: 16-12=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[6, 4], Operations: ['55-43=12', '16-12=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[16, 6, 55, 43], Operations: [] Exploring Operation: 55-43=12, Resulting Numbers: [16, 6, 12] Generated Node #0,2: 24:[16, 6, 12] Operation: 55-43=12 Moving to Node #0,2 Current State: 24:[16, 6, 12], Operations: ['55-43=12'] Exploring Operation: 16-12=4, Resulting Numbers: [6, 4] Generated Node #0,2,2: 24:[6, 4] Operation: 16-12=4 Moving to Node #0,2,2 Current State: 24:[6, 4], Operations: ['55-43=12', '16-12=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 35, 40, 87, 45 ]
89
[ "35+45=80", "80/40=2", "87+2=89" ]
Current State: 89:[35, 40, 87, 45], Operations: [] Exploring Operation: 35+45=80, Resulting Numbers: [40, 87, 80] Generated Node #2: [40, 87, 80] from Operation: 35+45=80 Current State: 89:[40, 87, 80], Operations: ['35+45=80'] Exploring Operation: 80/40=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 80/40=2 Current State: 89:[87, 2], Operations: ['35+45=80', '80/40=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[35, 40, 87, 45], Operations: [] Exploring Operation: 35+45=80, Resulting Numbers: [40, 87, 80] Generated Node #0,0: 89:[40, 87, 80] Operation: 35+45=80 Exploring Operation: 35+40=75, Resulting Numbers: [87, 45, 75] Generated Node #0,1: 89:[87, 45, 75] Operation: 35+40=75 Exploring Operation: 40+45=85, Resulting Numbers: [35, 87, 85] Generated Node #0,2: 89:[35, 87, 85] Operation: 40+45=85 Moving to Node #0,0 Current State: 89:[40, 87, 80], Operations: ['35+45=80'] Exploring Operation: 40+80=120, Resulting Numbers: [87, 120] Generated Node #0,0,0: 89:[87, 120] Operation: 40+80=120 Exploring Operation: 87-40=47, Resulting Numbers: [80, 47] Generated Node #0,0,1: 89:[80, 47] Operation: 87-40=47 Exploring Operation: 40+87=127, Resulting Numbers: [80, 127] Generated Node #0,0,2: 89:[80, 127] Operation: 40+87=127 Moving to Node #0,1 Current State: 89:[87, 45, 75], Operations: ['35+40=75'] Exploring Operation: 87+45=132, Resulting Numbers: [75, 132] Generated Node #0,1,0: 89:[75, 132] Operation: 87+45=132 Exploring Operation: 87-45=42, Resulting Numbers: [75, 42] Generated Node #0,1,1: 89:[75, 42] Operation: 87-45=42 Exploring Operation: 45+75=120, Resulting Numbers: [87, 120] Generated Node #0,1,2: 89:[87, 120] Operation: 45+75=120 Moving to Node #0,2 Current State: 89:[35, 87, 85], Operations: ['40+45=85'] Exploring Operation: 35+87=122, Resulting Numbers: [85, 122] Generated Node #0,2,0: 89:[85, 122] Operation: 35+87=122 Exploring Operation: 87-35=52, Resulting Numbers: [85, 52] Generated Node #0,2,1: 89:[85, 52] Operation: 87-35=52 Exploring Operation: 35+85=120, Resulting Numbers: [87, 120] Generated Node #0,2,2: 89:[87, 120] Operation: 35+85=120 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[87, 120], Operations: ['40+45=85', '35+85=120'] Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,89 unequal: No Solution Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[85, 122], Operations: ['40+45=85', '35+87=122'] Exploring Operation: 85*122=10370, Resulting Numbers: [10370] 10370,89 unequal: No Solution Exploring Operation: 85+122=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 122-85=37, Resulting Numbers: [37] 37,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[85, 52], Operations: ['40+45=85', '87-35=52'] Exploring Operation: 85-52=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 85+52=137, Resulting Numbers: [137] 137,89 unequal: No Solution Exploring Operation: 85*52=4420, Resulting Numbers: [4420] 4420,89 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: 89:[87, 120], Operations: ['35+45=80', '40+80=120'] Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[87, 120], Operations: ['35+40=75', '45+75=120'] Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,89 unequal: No Solution Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[80, 127], Operations: ['35+45=80', '40+87=127'] Exploring Operation: 127-80=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 80*127=10160, Resulting Numbers: [10160] 10160,89 unequal: No Solution Exploring Operation: 80+127=207, Resulting Numbers: [207] 207,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[80, 47], Operations: ['35+45=80', '87-40=47'] Exploring Operation: 80+47=127, Resulting Numbers: [127] 127,89 unequal: No Solution Exploring Operation: 80-47=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 80*47=3760, Resulting Numbers: [3760] 3760,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[75, 132], Operations: ['35+40=75', '87+45=132'] Exploring Operation: 75+132=207, Resulting Numbers: [207] 207,89 unequal: No Solution Exploring Operation: 75*132=9900, Resulting Numbers: [9900] 9900,89 unequal: No Solution Exploring Operation: 132-75=57, Resulting Numbers: [57] 57,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[75, 42], Operations: ['35+40=75', '87-45=42'] Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,89 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,89 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 5, 36, 8, 41 ]
35
[ "5*8=40", "41-36=5", "40-5=35" ]
Current State: 35:[5, 36, 8, 41], Operations: [] Exploring Operation: 5*8=40, Resulting Numbers: [36, 41, 40] Generated Node #2: [36, 41, 40] from Operation: 5*8=40 Current State: 35:[36, 41, 40], Operations: ['5*8=40'] Exploring Operation: 41-36=5, Resulting Numbers: [40, 5] Generated Node #3: [40, 5] from Operation: 41-36=5 Current State: 35:[40, 5], Operations: ['5*8=40', '41-36=5'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[5, 36, 8, 41], Operations: [] Exploring Operation: 41-5=36, Resulting Numbers: [36, 8, 36] Generated Node #0,0: 35:[36, 8, 36] Operation: 41-5=36 Exploring Operation: 8-5=3, Resulting Numbers: [36, 41, 3] Generated Node #0,1: 35:[36, 41, 3] Operation: 8-5=3 Exploring Operation: 41-8=33, Resulting Numbers: [5, 36, 33] Generated Node #0,2: 35:[5, 36, 33] Operation: 41-8=33 Exploring Operation: 41-36=5, Resulting Numbers: [5, 8, 5] Generated Node #0,3: 35:[5, 8, 5] Operation: 41-36=5 Moving to Node #0,3 Current State: 35:[5, 8, 5], Operations: ['41-36=5'] Exploring Operation: 8-5=3, Resulting Numbers: [5, 3] Generated Node #0,3,0: 35:[5, 3] Operation: 8-5=3 Exploring Operation: 5*8=40, Resulting Numbers: [5, 40] Generated Node #0,3,1: 35:[5, 40] Operation: 5*8=40 Exploring Operation: 8-5=3, Resulting Numbers: [5, 3] Generated Node #0,3,2: 35:[5, 3] Operation: 8-5=3 Exploring Operation: 5+5=10, Resulting Numbers: [8, 10] Generated Node #0,3,3: 35:[8, 10] Operation: 5+5=10 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 35:[5, 3], Operations: ['41-36=5', '8-5=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 35:[5, 3], Operations: ['41-36=5', '8-5=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,35 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 35:[8, 10], Operations: ['41-36=5', '5+5=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,35 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 35:[5, 40], Operations: ['41-36=5', '5*8=40'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[5, 36, 8, 41], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [5, 8, 5] Generated Node #0,3: 35:[5, 8, 5] Operation: 41-36=5 Moving to Node #0,3 Current State: 35:[5, 8, 5], Operations: ['41-36=5'] Exploring Operation: 5*8=40, Resulting Numbers: [5, 40] Generated Node #0,3,1: 35:[5, 40] Operation: 5*8=40 Moving to Node #0,3,1 Current State: 35:[5, 40], Operations: ['41-36=5', '5*8=40'] Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 37, 50, 35, 60 ]
35
[ "37-35=2", "50/2=25", "60-25=35" ]
Current State: 35:[37, 50, 35, 60], Operations: [] Exploring Operation: 37-35=2, Resulting Numbers: [50, 60, 2] Generated Node #2: [50, 60, 2] from Operation: 37-35=2 Current State: 35:[50, 60, 2], Operations: ['37-35=2'] Exploring Operation: 50/2=25, Resulting Numbers: [60, 25] Generated Node #3: [60, 25] from Operation: 50/2=25 Current State: 35:[60, 25], Operations: ['37-35=2', '50/2=25'] Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[37, 50, 35, 60], Operations: [] Exploring Operation: 60-37=23, Resulting Numbers: [50, 35, 23] Generated Node #0,0: 35:[50, 35, 23] Operation: 60-37=23 Exploring Operation: 60-50=10, Resulting Numbers: [37, 35, 10] Generated Node #0,1: 35:[37, 35, 10] Operation: 60-50=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[37, 35, 10], Operations: ['60-50=10'] Exploring Operation: 37-10=27, Resulting Numbers: [35, 27] Generated Node #0,1,0: 35:[35, 27] Operation: 37-10=27 Exploring Operation: 37-35=2, Resulting Numbers: [10, 2] Generated Node #0,1,1: 35:[10, 2] Operation: 37-35=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[10, 2], Operations: ['60-50=10', '37-35=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,35 unequal: No Solution No 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: 35:[35, 27], Operations: ['60-50=10', '37-10=27'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,35 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[50, 35, 23], Operations: ['60-37=23'] Exploring Operation: 50-23=27, Resulting Numbers: [35, 27] Generated Node #0,0,0: 35:[35, 27] Operation: 50-23=27 Exploring Operation: 50-35=15, Resulting Numbers: [23, 15] Generated Node #0,0,1: 35:[23, 15] Operation: 50-35=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[35, 27], Operations: ['60-37=23', '50-23=27'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,35 unequal: No Solution No 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: 35:[23, 15], Operations: ['60-37=23', '50-35=15'] Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,35 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_2
mult_heuristic
[ 12, 7, 63, 66 ]
33
[ "66-63=3", "7*3=21", "12+21=33" ]
Current State: 33:[12, 7, 63, 66], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [12, 7, 3] Generated Node #2: [12, 7, 3] from Operation: 66-63=3 Current State: 33:[12, 7, 3], Operations: ['66-63=3'] Exploring Operation: 7*3=21, Resulting Numbers: [12, 21] Generated Node #3: [12, 21] from Operation: 7*3=21 Current State: 33:[12, 21], Operations: ['66-63=3', '7*3=21'] Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[12, 7, 63, 66], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [12, 7, 3] Generated Node #0,0: 33:[12, 7, 3] Operation: 66-63=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[12, 7, 3], Operations: ['66-63=3'] Exploring Operation: 12-7=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 33:[3, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 33:[3, 5], Operations: ['66-63=3', '12-7=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,33 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
[ 33, 62, 22, 9 ]
42
[ "62-33=29", "22-9=13", "29+13=42" ]
Current State: 42:[33, 62, 22, 9], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [22, 9, 29] Generated Node #2: [22, 9, 29] from Operation: 62-33=29 Current State: 42:[22, 9, 29], Operations: ['62-33=29'] Exploring Operation: 22-9=13, Resulting Numbers: [29, 13] Generated Node #3: [29, 13] from Operation: 22-9=13 Current State: 42:[29, 13], Operations: ['62-33=29', '22-9=13'] Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[33, 62, 22, 9], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [22, 9, 29] Generated Node #0,0: 42:[22, 9, 29] Operation: 62-33=29 Exploring Operation: 62-9=53, Resulting Numbers: [33, 22, 53] Generated Node #0,1: 42:[33, 22, 53] Operation: 62-9=53 Exploring Operation: 62-22=40, Resulting Numbers: [33, 9, 40] Generated Node #0,2: 42:[33, 9, 40] Operation: 62-22=40 Exploring Operation: 33+9=42, Resulting Numbers: [62, 22, 42] Generated Node #0,3: 42:[62, 22, 42] Operation: 33+9=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[22, 9, 29], Operations: ['62-33=29'] Exploring Operation: 29-9=20, Resulting Numbers: [22, 20] Generated Node #0,0,0: 42:[22, 20] Operation: 29-9=20 Exploring Operation: 22-9=13, Resulting Numbers: [29, 13] Generated Node #0,0,1: 42:[29, 13] Operation: 22-9=13 Exploring Operation: 9+29=38, Resulting Numbers: [22, 38] Generated Node #0,0,2: 42:[22, 38] Operation: 9+29=38 Exploring Operation: 29-22=7, Resulting Numbers: [9, 7] Generated Node #0,0,3: 42:[9, 7] Operation: 29-22=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[22, 20], Operations: ['62-33=29', '29-9=20'] Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,42 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[33, 62, 22, 9], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [22, 9, 29] Generated Node #0,0: 42:[22, 9, 29] Operation: 62-33=29 Moving to Node #0,0 Current State: 42:[22, 9, 29], Operations: ['62-33=29'] Exploring Operation: 29-9=20, Resulting Numbers: [22, 20] Generated Node #0,0,0: 42:[22, 20] Operation: 29-9=20 Moving to Node #0,0,0 Current State: 42:[22, 20], Operations: ['62-33=29', '29-9=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 82, 60, 16, 12 ]
26
[ "82-60=22", "16-12=4", "22+4=26" ]
Current State: 26:[82, 60, 16, 12], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [16, 12, 22] Generated Node #2: [16, 12, 22] from Operation: 82-60=22 Current State: 26:[16, 12, 22], Operations: ['82-60=22'] Exploring Operation: 16-12=4, Resulting Numbers: [22, 4] Generated Node #3: [22, 4] from Operation: 16-12=4 Current State: 26:[22, 4], Operations: ['82-60=22', '16-12=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[82, 60, 16, 12], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [16, 12, 22] Generated Node #0,0: 26:[16, 12, 22] Operation: 82-60=22 Moving to Node #0,0 Current State: 26:[16, 12, 22], Operations: ['82-60=22'] Exploring Operation: 22-16=6, Resulting Numbers: [12, 6] Generated Node #0,0,0: 26:[12, 6] Operation: 22-16=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[12, 6], Operations: ['82-60=22', '22-16=6'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,26 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
[ 68, 38, 73, 22 ]
72
[ "73-68=5", "22*5=110", "110-38=72" ]
Current State: 72:[68, 38, 73, 22], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [38, 22, 5] Generated Node #2: [38, 22, 5] from Operation: 73-68=5 Current State: 72:[38, 22, 5], Operations: ['73-68=5'] Exploring Operation: 22*5=110, Resulting Numbers: [38, 110] Generated Node #3: [38, 110] from Operation: 22*5=110 Current State: 72:[38, 110], Operations: ['73-68=5', '22*5=110'] Exploring Operation: 110-38=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[68, 38, 73, 22], Operations: [] Exploring Operation: 73-68=5, Resulting Numbers: [38, 22, 5] Generated Node #0,0: 72:[38, 22, 5] Operation: 73-68=5 Exploring Operation: 73-38=35, Resulting Numbers: [68, 22, 35] Generated Node #0,1: 72:[68, 22, 35] Operation: 73-38=35 Exploring Operation: 38-22=16, Resulting Numbers: [68, 73, 16] Generated Node #0,2: 72:[68, 73, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[38, 22, 5], Operations: ['73-68=5'] Exploring Operation: 22-5=17, Resulting Numbers: [38, 17] Generated Node #0,0,0: 72:[38, 17] Operation: 22-5=17 Exploring Operation: 38-22=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 72:[5, 16] Operation: 38-22=16 Exploring Operation: 38-5=33, Resulting Numbers: [22, 33] Generated Node #0,0,2: 72:[22, 33] Operation: 38-5=33 Moving to Node #0,0,0 Current State: 72:[38, 17], Operations: ['73-68=5', '22-5=17'] Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,72 unequal: No Solution Exploring Operation: 38*17=646, Resulting Numbers: [646] 646,72 unequal: No Solution Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[5, 16], Operations: ['73-68=5', '38-22=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,72 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[22, 33], Operations: ['73-68=5', '38-5=33'] Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,72 unequal: No Solution Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[68, 22, 35], Operations: ['73-38=35'] Exploring Operation: 35-22=13, Resulting Numbers: [68, 13] Generated Node #0,1,0: 72:[68, 13] Operation: 35-22=13 Exploring Operation: 68-35=33, Resulting Numbers: [22, 33] Generated Node #0,1,1: 72:[22, 33] Operation: 68-35=33 Exploring Operation: 68-22=46, Resulting Numbers: [35, 46] Generated Node #0,1,2: 72:[35, 46] Operation: 68-22=46 Moving to Node #0,1,0 Current State: 72:[68, 13], Operations: ['73-38=35', '35-22=13'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,72 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[22, 33], Operations: ['73-38=35', '68-35=33'] Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,72 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[35, 46], Operations: ['73-38=35', '68-22=46'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,72 unequal: No Solution Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[68, 73, 16], Operations: ['38-22=16'] Exploring Operation: 68+16=84, Resulting Numbers: [73, 84] Generated Node #0,2,0: 72:[73, 84] Operation: 68+16=84 Exploring Operation: 68-16=52, Resulting Numbers: [73, 52] Generated Node #0,2,1: 72:[73, 52] Operation: 68-16=52 Exploring Operation: 73-68=5, Resulting Numbers: [16, 5] Generated Node #0,2,2: 72:[16, 5] Operation: 73-68=5 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[16, 5], Operations: ['38-22=16', '73-68=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,72 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[73, 84], Operations: ['38-22=16', '68+16=84'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 73*84=6132, Resulting Numbers: [6132] 6132,72 unequal: No Solution Exploring Operation: 73+84=157, Resulting Numbers: [157] 157,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[73, 52], Operations: ['38-22=16', '68-16=52'] Exploring Operation: 73-52=21, Resulting Numbers: [21] 21,72 unequal: No Solution Exploring Operation: 73*52=3796, Resulting Numbers: [3796] 3796,72 unequal: No Solution Exploring Operation: 73+52=125, Resulting Numbers: [125] 125,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 6, 68, 36, 3 ]
100
[ "6*68=408", "408/3=136", "136-36=100" ]
Current State: 100:[6, 68, 36, 3], Operations: [] Exploring Operation: 6*68=408, Resulting Numbers: [36, 3, 408] Generated Node #2: [36, 3, 408] from Operation: 6*68=408 Current State: 100:[36, 3, 408], Operations: ['6*68=408'] Exploring Operation: 408/3=136, Resulting Numbers: [36, 136] Generated Node #3: [36, 136] from Operation: 408/3=136 Current State: 100:[36, 136], Operations: ['6*68=408', '408/3=136'] Exploring Operation: 136-36=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[6, 68, 36, 3], Operations: [] Exploring Operation: 68-36=32, Resulting Numbers: [6, 3, 32] Generated Node #0,0: 100:[6, 3, 32] Operation: 68-36=32 Exploring Operation: 68+36=104, Resulting Numbers: [6, 3, 104] Generated Node #0,1: 100:[6, 3, 104] Operation: 68+36=104 Exploring Operation: 36/6=6, Resulting Numbers: [68, 3, 6] Generated Node #0,2: 100:[68, 3, 6] Operation: 36/6=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[6, 3, 104], Operations: ['68+36=104'] Exploring Operation: 104-6=98, Resulting Numbers: [3, 98] Generated Node #0,1,0: 100:[3, 98] Operation: 104-6=98 Exploring Operation: 6/3=2, Resulting Numbers: [104, 2] Generated Node #0,1,1: 100:[104, 2] Operation: 6/3=2 Exploring Operation: 104-3=101, Resulting Numbers: [6, 101] Generated Node #0,1,2: 100:[6, 101] Operation: 104-3=101 Moving to Node #0,1,2 Current State: 100:[6, 101], Operations: ['68+36=104', '104-3=101'] Exploring Operation: 6+101=107, Resulting Numbers: [107] 107,100 unequal: No Solution Exploring Operation: 6*101=606, Resulting Numbers: [606] 606,100 unequal: No Solution Exploring Operation: 101-6=95, Resulting Numbers: [95] 95,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[3, 98], Operations: ['68+36=104', '104-6=98'] Exploring Operation: 3*98=294, Resulting Numbers: [294] 294,100 unequal: No Solution Exploring Operation: 3+98=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[104, 2], Operations: ['68+36=104', '6/3=2'] Exploring Operation: 104-2=102, Resulting Numbers: [102] 102,100 unequal: No Solution Exploring Operation: 104+2=106, Resulting Numbers: [106] 106,100 unequal: No Solution Exploring Operation: 104/2=52, Resulting Numbers: [52] 52,100 unequal: No Solution No 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: 100:[6, 3, 32], Operations: ['68-36=32'] Exploring Operation: 32-6=26, Resulting Numbers: [3, 26] Generated Node #0,0,0: 100:[3, 26] Operation: 32-6=26 Exploring Operation: 32-3=29, Resulting Numbers: [6, 29] Generated Node #0,0,1: 100:[6, 29] Operation: 32-3=29 Exploring Operation: 3*32=96, Resulting Numbers: [6, 96] Generated Node #0,0,2: 100:[6, 96] Operation: 3*32=96 Moving to Node #0,0,0 Current State: 100:[3, 26], Operations: ['68-36=32', '32-6=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,100 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[6, 29], Operations: ['68-36=32', '32-3=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,100 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[6, 96], Operations: ['68-36=32', '3*32=96'] Exploring Operation: 96/6=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 96-6=90, Resulting Numbers: [90] 90,100 unequal: No Solution Exploring Operation: 6+96=102, Resulting Numbers: [102] 102,100 unequal: No Solution No 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: 100:[68, 3, 6], Operations: ['36/6=6'] Exploring Operation: 68-6=62, Resulting Numbers: [3, 62] Generated Node #0,2,0: 100:[3, 62] Operation: 68-6=62 Exploring Operation: 6/3=2, Resulting Numbers: [68, 2] Generated Node #0,2,1: 100:[68, 2] Operation: 6/3=2 Exploring Operation: 68-3=65, Resulting Numbers: [6, 65] Generated Node #0,2,2: 100:[6, 65] Operation: 68-3=65 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 100:[3, 62], Operations: ['36/6=6', '68-6=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,100 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,100 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 100:[6, 65], Operations: ['36/6=6', '68-3=65'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,100 unequal: No Solution Exploring Operation: 6+65=71, Resulting Numbers: [71] 71,100 unequal: No Solution Exploring Operation: 6*65=390, Resulting Numbers: [390] 390,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 100:[68, 2], Operations: ['36/6=6', '6/3=2'] Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,100 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,100 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
[ 55, 86, 52, 81 ]
41
[ "86-81=5", "55/5=11", "52-11=41" ]
Current State: 41:[55, 86, 52, 81], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [55, 52, 5] Generated Node #2: [55, 52, 5] from Operation: 86-81=5 Current State: 41:[55, 52, 5], Operations: ['86-81=5'] Exploring Operation: 55/5=11, Resulting Numbers: [52, 11] Generated Node #3: [52, 11] from Operation: 55/5=11 Current State: 41:[52, 11], Operations: ['86-81=5', '55/5=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[55, 86, 52, 81], Operations: [] Exploring Operation: 86-55=31, Resulting Numbers: [52, 81, 31] Generated Node #0,0: 41:[52, 81, 31] Operation: 86-55=31 Exploring Operation: 86-52=34, Resulting Numbers: [55, 81, 34] Generated Node #0,1: 41:[55, 81, 34] Operation: 86-52=34 Exploring Operation: 86-81=5, Resulting Numbers: [55, 52, 5] Generated Node #0,2: 41:[55, 52, 5] Operation: 86-81=5 Exploring Operation: 81-55=26, Resulting Numbers: [86, 52, 26] Generated Node #0,3: 41:[86, 52, 26] Operation: 81-55=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[52, 81, 31], Operations: ['86-55=31'] Exploring Operation: 52-31=21, Resulting Numbers: [81, 21] Generated Node #0,0,0: 41:[81, 21] Operation: 52-31=21 Exploring Operation: 81-31=50, Resulting Numbers: [52, 50] Generated Node #0,0,1: 41:[52, 50] Operation: 81-31=50 Exploring Operation: 52+31=83, Resulting Numbers: [81, 83] Generated Node #0,0,2: 41:[81, 83] Operation: 52+31=83 Exploring Operation: 81-52=29, Resulting Numbers: [31, 29] Generated Node #0,0,3: 41:[31, 29] Operation: 81-52=29 Moving to Node #0,0,1 Current State: 41:[52, 50], Operations: ['86-55=31', '81-31=50'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,41 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[31, 29], Operations: ['86-55=31', '81-52=29'] Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[81, 21], Operations: ['86-55=31', '52-31=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,41 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[81, 83], Operations: ['86-55=31', '52+31=83'] Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,41 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,41 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[55, 81, 34], Operations: ['86-52=34'] Exploring Operation: 81-34=47, Resulting Numbers: [55, 47] Generated Node #0,1,0: 41:[55, 47] Operation: 81-34=47 Exploring Operation: 81-55=26, Resulting Numbers: [34, 26] Generated Node #0,1,1: 41:[34, 26] Operation: 81-55=26 Exploring Operation: 55+34=89, Resulting Numbers: [81, 89] Generated Node #0,1,2: 41:[81, 89] Operation: 55+34=89 Exploring Operation: 55-34=21, Resulting Numbers: [81, 21] Generated Node #0,1,3: 41:[81, 21] Operation: 55-34=21 Moving to Node #0,1,0 Current State: 41:[55, 47], Operations: ['86-52=34', '81-34=47'] Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,41 unequal: No Solution Exploring Operation: 55*47=2585, Resulting Numbers: [2585] 2585,41 unequal: No Solution Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[34, 26], Operations: ['86-52=34', '81-55=26'] Exploring Operation: 34*26=884, Resulting Numbers: [884] 884,41 unequal: No Solution Exploring Operation: 34+26=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,41 unequal: No Solution Moving to Node #0,1,3 Current State: 41:[81, 21], Operations: ['86-52=34', '55-34=21'] Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,41 unequal: No Solution Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,41 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[81, 89], Operations: ['86-52=34', '55+34=89'] Exploring Operation: 81*89=7209, Resulting Numbers: [7209] 7209,41 unequal: No Solution Exploring Operation: 89-81=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 81+89=170, Resulting Numbers: [170] 170,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[55, 52, 5], Operations: ['86-81=5'] Exploring Operation: 55+5=60, Resulting Numbers: [52, 60] Generated Node #0,2,0: 41:[52, 60] Operation: 55+5=60 Exploring Operation: 52+5=57, Resulting Numbers: [55, 57] Generated Node #0,2,1: 41:[55, 57] Operation: 52+5=57 Exploring Operation: 55-5=50, Resulting Numbers: [52, 50] Generated Node #0,2,2: 41:[52, 50] Operation: 55-5=50 Exploring Operation: 52-5=47, Resulting Numbers: [55, 47] Generated Node #0,2,3: 41:[55, 47] Operation: 52-5=47 Moving to Node #0,2,2 Current State: 41:[52, 50], Operations: ['86-81=5', '55-5=50'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,41 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[55, 47], Operations: ['86-81=5', '52-5=47'] Exploring Operation: 55*47=2585, Resulting Numbers: [2585] 2585,41 unequal: No Solution Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[55, 57], Operations: ['86-81=5', '52+5=57'] Exploring Operation: 55*57=3135, Resulting Numbers: [3135] 3135,41 unequal: No Solution Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 55+57=112, Resulting Numbers: [112] 112,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[52, 60], Operations: ['86-81=5', '55+5=60'] Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,41 unequal: No Solution Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[86, 52, 26], Operations: ['81-55=26'] Exploring Operation: 86-26=60, Resulting Numbers: [52, 60] Generated Node #0,3,0: 41:[52, 60] Operation: 86-26=60 Exploring Operation: 86-52=34, Resulting Numbers: [26, 34] Generated Node #0,3,1: 41:[26, 34] Operation: 86-52=34 Exploring Operation: 52-26=26, Resulting Numbers: [86, 26] Generated Node #0,3,2: 41:[86, 26] Operation: 52-26=26 Exploring Operation: 86+26=112, Resulting Numbers: [52, 112] Generated Node #0,3,3: 41:[52, 112] Operation: 86+26=112 Moving to Node #0,3,1 Current State: 41:[26, 34], Operations: ['81-55=26', '86-52=34'] Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,41 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[52, 60], Operations: ['81-55=26', '86-26=60'] Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,41 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[86, 26], Operations: ['81-55=26', '52-26=26'] Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 86*26=2236, Resulting Numbers: [2236] 2236,41 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[52, 112], Operations: ['81-55=26', '86+26=112'] Exploring Operation: 112-52=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 52+112=164, Resulting Numbers: [164] 164,41 unequal: No Solution Exploring Operation: 52*112=5824, Resulting Numbers: [5824] 5824,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 24, 45, 28, 61 ]
36
[ "24+45=69", "61-28=33", "69-33=36" ]
Current State: 36:[24, 45, 28, 61], Operations: [] Exploring Operation: 24+45=69, Resulting Numbers: [28, 61, 69] Generated Node #2: [28, 61, 69] from Operation: 24+45=69 Current State: 36:[28, 61, 69], Operations: ['24+45=69'] Exploring Operation: 61-28=33, Resulting Numbers: [69, 33] Generated Node #3: [69, 33] from Operation: 61-28=33 Current State: 36:[69, 33], Operations: ['24+45=69', '61-28=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[24, 45, 28, 61], Operations: [] Exploring Operation: 61-24=37, Resulting Numbers: [45, 28, 37] Generated Node #0,0: 36:[45, 28, 37] Operation: 61-24=37 Exploring Operation: 61-28=33, Resulting Numbers: [24, 45, 33] Generated Node #0,1: 36:[24, 45, 33] Operation: 61-28=33 Exploring Operation: 61-45=16, Resulting Numbers: [24, 28, 16] Generated Node #0,2: 36:[24, 28, 16] Operation: 61-45=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[24, 28, 16], Operations: ['61-45=16'] Exploring Operation: 28-24=4, Resulting Numbers: [16, 4] Generated Node #0,2,0: 36:[16, 4] Operation: 28-24=4 Exploring Operation: 24-16=8, Resulting Numbers: [28, 8] Generated Node #0,2,1: 36:[28, 8] Operation: 24-16=8 Exploring Operation: 28-16=12, Resulting Numbers: [24, 12] Generated Node #0,2,2: 36:[24, 12] Operation: 28-16=12 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 36:[16, 4], Operations: ['61-45=16', '28-24=4'] Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,36 unequal: No Solution No 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: 36:[24, 12], Operations: ['61-45=16', '28-16=12'] Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[24, 45, 28, 61], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [24, 28, 16] Generated Node #0,2: 36:[24, 28, 16] Operation: 61-45=16 Moving to Node #0,2 Current State: 36:[24, 28, 16], Operations: ['61-45=16'] Exploring Operation: 28-16=12, Resulting Numbers: [24, 12] Generated Node #0,2,2: 36:[24, 12] Operation: 28-16=12 Moving to Node #0,2,2 Current State: 36:[24, 12], Operations: ['61-45=16', '28-16=12'] Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic