Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files
xet
Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 49, 47, 46, 43 ]
45
[ "49+43=92", "92/46=2", "47-2=45" ]
Current State: 45:[49, 47, 46, 43], Operations: [] Exploring Operation: 49+43=92, Resulting Numbers: [47, 46, 92] Generated Node #2: [47, 46, 92] from Operation: 49+43=92 Current State: 45:[47, 46, 92], Operations: ['49+43=92'] Exploring Operation: 92/46=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 92/46=2 Current State: 45:[47, 2], Operations: ['49+43=92', '92/46=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[49, 47, 46, 43], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [46, 43, 2] Generated Node #0,0: 45:[46, 43, 2] Operation: 49-47=2 Exploring Operation: 47-43=4, Resulting Numbers: [49, 46, 4] Generated Node #0,1: 45:[49, 46, 4] Operation: 47-43=4 Exploring Operation: 49-43=6, Resulting Numbers: [47, 46, 6] Generated Node #0,2: 45:[47, 46, 6] Operation: 49-43=6 Exploring Operation: 49-46=3, Resulting Numbers: [47, 43, 3] Generated Node #0,3: 45:[47, 43, 3] Operation: 49-46=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[46, 43, 2], Operations: ['49-47=2'] Exploring Operation: 46-2=44, Resulting Numbers: [43, 44] Generated Node #0,0,0: 45:[43, 44] Operation: 46-2=44 Exploring Operation: 43+2=45, Resulting Numbers: [46, 45] Generated Node #0,0,1: 45:[46, 45] Operation: 43+2=45 Exploring Operation: 46-43=3, Resulting Numbers: [2, 3] Generated Node #0,0,2: 45:[2, 3] Operation: 46-43=3 Exploring Operation: 46+2=48, Resulting Numbers: [43, 48] Generated Node #0,0,3: 45:[43, 48] Operation: 46+2=48 Moving to Node #0,0,1 Current State: 45:[46, 45], Operations: ['49-47=2', '43+2=45'] Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,45 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[2, 3], Operations: ['49-47=2', '46-43=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[43, 44], Operations: ['49-47=2', '46-2=44'] Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,45 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,45 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[43, 48], Operations: ['49-47=2', '46+2=48'] Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 43*48=2064, Resulting Numbers: [2064] 2064,45 unequal: No Solution Exploring Operation: 43+48=91, Resulting Numbers: [91] 91,45 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 #0,2 Current State: 45:[47, 46, 6], Operations: ['49-43=6'] Exploring Operation: 47-6=41, Resulting Numbers: [46, 41] Generated Node #0,2,0: 45:[46, 41] Operation: 47-6=41 Exploring Operation: 47-46=1, Resulting Numbers: [6, 1] Generated Node #0,2,1: 45:[6, 1] Operation: 47-46=1 Exploring Operation: 46-6=40, Resulting Numbers: [47, 40] Generated Node #0,2,2: 45:[47, 40] Operation: 46-6=40 Exploring Operation: 47+6=53, Resulting Numbers: [46, 53] Generated Node #0,2,3: 45:[46, 53] Operation: 47+6=53 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[6, 1], Operations: ['49-43=6', '47-46=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[46, 41], Operations: ['49-43=6', '47-6=41'] Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,45 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 46*41=1886, Resulting Numbers: [1886] 1886,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[47, 40], Operations: ['49-43=6', '46-6=40'] Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 47*40=1880, Resulting Numbers: [1880] 1880,45 unequal: No Solution Exploring Operation: 47+40=87, Resulting Numbers: [87] 87,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 45:[46, 53], Operations: ['49-43=6', '47+6=53'] Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,45 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[47, 43, 3], Operations: ['49-46=3'] Exploring Operation: 47-3=44, Resulting Numbers: [43, 44] Generated Node #0,3,0: 45:[43, 44] Operation: 47-3=44 Exploring Operation: 47+3=50, Resulting Numbers: [43, 50] Generated Node #0,3,1: 45:[43, 50] Operation: 47+3=50 Exploring Operation: 43+3=46, Resulting Numbers: [47, 46] Generated Node #0,3,2: 45:[47, 46] Operation: 43+3=46 Exploring Operation: 47-43=4, Resulting Numbers: [3, 4] Generated Node #0,3,3: 45:[3, 4] Operation: 47-43=4 Moving to Node #0,3,3 Current State: 45:[3, 4], Operations: ['49-46=3', '47-43=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[47, 46], Operations: ['49-46=3', '43+3=46'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,45 unequal: No Solution Exploring Operation: 47*46=2162, Resulting Numbers: [2162] 2162,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[43, 44], Operations: ['49-46=3', '47-3=44'] Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,45 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[43, 50], Operations: ['49-46=3', '47+3=50'] Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 43+50=93, Resulting Numbers: [93] 93,45 unequal: No Solution Exploring Operation: 43*50=2150, Resulting Numbers: [2150] 2150,45 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:[49, 46, 4], Operations: ['47-43=4'] Exploring Operation: 49+4=53, Resulting Numbers: [46, 53] Generated Node #0,1,0: 45:[46, 53] Operation: 49+4=53 Exploring Operation: 49-46=3, Resulting Numbers: [4, 3] Generated Node #0,1,1: 45:[4, 3] Operation: 49-46=3 Exploring Operation: 46-4=42, Resulting Numbers: [49, 42] Generated Node #0,1,2: 45:[49, 42] Operation: 46-4=42 Exploring Operation: 49-4=45, Resulting Numbers: [46, 45] Generated Node #0,1,3: 45:[46, 45] Operation: 49-4=45 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[4, 3], Operations: ['47-43=4', '49-46=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,45 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 45:[46, 45], Operations: ['47-43=4', '49-4=45'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,45 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 45:[49, 42], Operations: ['47-43=4', '46-4=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,45 unequal: No Solution Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,45 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[46, 53], Operations: ['47-43=4', '49+4=53'] Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,45 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,45 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 93, 90, 52, 95 ]
97
[ "95-93=2", "90/2=45", "52+45=97" ]
Current State: 97:[93, 90, 52, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [90, 52, 2] Generated Node #2: [90, 52, 2] from Operation: 95-93=2 Current State: 97:[90, 52, 2], Operations: ['95-93=2'] Exploring Operation: 90/2=45, Resulting Numbers: [52, 45] Generated Node #3: [52, 45] from Operation: 90/2=45 Current State: 97:[52, 45], Operations: ['95-93=2', '90/2=45'] Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[93, 90, 52, 95], Operations: [] Exploring Operation: 52+95=147, Resulting Numbers: [93, 90, 147] Generated Node #0,0: 97:[93, 90, 147] Operation: 52+95=147 Exploring Operation: 93+52=145, Resulting Numbers: [90, 95, 145] Generated Node #0,1: 97:[90, 95, 145] Operation: 93+52=145 Exploring Operation: 90+52=142, Resulting Numbers: [93, 95, 142] Generated Node #0,2: 97:[93, 95, 142] Operation: 90+52=142 Exploring Operation: 93-52=41, Resulting Numbers: [90, 95, 41] Generated Node #0,3: 97:[90, 95, 41] Operation: 93-52=41 Moving to Node #0,2 Current State: 97:[93, 95, 142], Operations: ['90+52=142'] Exploring Operation: 142-95=47, Resulting Numbers: [93, 47] Generated Node #0,2,0: 97:[93, 47] Operation: 142-95=47 Exploring Operation: 142-93=49, Resulting Numbers: [95, 49] Generated Node #0,2,1: 97:[95, 49] Operation: 142-93=49 Exploring Operation: 93+95=188, Resulting Numbers: [142, 188] Generated Node #0,2,2: 97:[142, 188] Operation: 93+95=188 Exploring Operation: 95-93=2, Resulting Numbers: [142, 2] Generated Node #0,2,3: 97:[142, 2] Operation: 95-93=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[95, 49], Operations: ['90+52=142', '142-93=49'] Exploring Operation: 95*49=4655, Resulting Numbers: [4655] 4655,97 unequal: No Solution Exploring Operation: 95+49=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 95-49=46, Resulting Numbers: [46] 46,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[93, 47], Operations: ['90+52=142', '142-95=47'] Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,97 unequal: No Solution Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[142, 188], Operations: ['90+52=142', '93+95=188'] Exploring Operation: 142+188=330, Resulting Numbers: [330] 330,97 unequal: No Solution Exploring Operation: 188-142=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 142*188=26696, Resulting Numbers: [26696] 26696,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[142, 2], Operations: ['90+52=142', '95-93=2'] Exploring Operation: 142*2=284, Resulting Numbers: [284] 284,97 unequal: No Solution Exploring Operation: 142/2=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 142+2=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 142-2=140, Resulting Numbers: [140] 140,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 97:[90, 95, 145], Operations: ['93+52=145'] Exploring Operation: 90+95=185, Resulting Numbers: [145, 185] Generated Node #0,1,0: 97:[145, 185] Operation: 90+95=185 Exploring Operation: 145-95=50, Resulting Numbers: [90, 50] Generated Node #0,1,1: 97:[90, 50] Operation: 145-95=50 Exploring Operation: 95-90=5, Resulting Numbers: [145, 5] Generated Node #0,1,2: 97:[145, 5] Operation: 95-90=5 Exploring Operation: 145-90=55, Resulting Numbers: [95, 55] Generated Node #0,1,3: 97:[95, 55] Operation: 145-90=55 Moving to Node #0,0 Current State: 97:[93, 90, 147], Operations: ['52+95=147'] Exploring Operation: 147-90=57, Resulting Numbers: [93, 57] Generated Node #0,0,0: 97:[93, 57] Operation: 147-90=57 Exploring Operation: 93-90=3, Resulting Numbers: [147, 3] Generated Node #0,0,1: 97:[147, 3] Operation: 93-90=3 Exploring Operation: 93+90=183, Resulting Numbers: [147, 183] Generated Node #0,0,2: 97:[147, 183] Operation: 93+90=183 Exploring Operation: 147-93=54, Resulting Numbers: [90, 54] Generated Node #0,0,3: 97:[90, 54] Operation: 147-93=54 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[93, 57], Operations: ['52+95=147', '147-90=57'] Exploring Operation: 93+57=150, Resulting Numbers: [150] 150,97 unequal: No Solution Exploring Operation: 93*57=5301, Resulting Numbers: [5301] 5301,97 unequal: No Solution Exploring Operation: 93-57=36, Resulting Numbers: [36] 36,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 97:[90, 54], Operations: ['52+95=147', '147-93=54'] Exploring Operation: 90-54=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 90*54=4860, Resulting Numbers: [4860] 4860,97 unequal: No Solution Exploring Operation: 90+54=144, Resulting Numbers: [144] 144,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[147, 183], Operations: ['52+95=147', '93+90=183'] Exploring Operation: 147+183=330, Resulting Numbers: [330] 330,97 unequal: No Solution Exploring Operation: 147*183=26901, Resulting Numbers: [26901] 26901,97 unequal: No Solution Exploring Operation: 183-147=36, Resulting Numbers: [36] 36,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[147, 3], Operations: ['52+95=147', '93-90=3'] Exploring Operation: 147+3=150, Resulting Numbers: [150] 150,97 unequal: No Solution Exploring Operation: 147*3=441, Resulting Numbers: [441] 441,97 unequal: No Solution Exploring Operation: 147/3=49, Resulting Numbers: [49] 49,97 unequal: No Solution Exploring Operation: 147-3=144, Resulting Numbers: [144] 144,97 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: 97:[90, 95, 41], Operations: ['93-52=41'] Exploring Operation: 95+41=136, Resulting Numbers: [90, 136] Generated Node #0,3,0: 97:[90, 136] Operation: 95+41=136 Exploring Operation: 90-41=49, Resulting Numbers: [95, 49] Generated Node #0,3,1: 97:[95, 49] Operation: 90-41=49 Exploring Operation: 95-41=54, Resulting Numbers: [90, 54] Generated Node #0,3,2: 97:[90, 54] Operation: 95-41=54 Exploring Operation: 90+41=131, Resulting Numbers: [95, 131] Generated Node #0,3,3: 97:[95, 131] Operation: 90+41=131 Moving to Node #0,3,3 Current State: 97:[95, 131], Operations: ['93-52=41', '90+41=131'] Exploring Operation: 131-95=36, Resulting Numbers: [36] 36,97 unequal: No Solution Exploring Operation: 95*131=12445, Resulting Numbers: [12445] 12445,97 unequal: No Solution Exploring Operation: 95+131=226, Resulting Numbers: [226] 226,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[95, 55], Operations: ['93+52=145', '145-90=55'] Exploring Operation: 95+55=150, Resulting Numbers: [150] 150,97 unequal: No Solution Exploring Operation: 95-55=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 95*55=5225, Resulting Numbers: [5225] 5225,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[90, 136], Operations: ['93-52=41', '95+41=136'] Exploring Operation: 136-90=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 90+136=226, Resulting Numbers: [226] 226,97 unequal: No Solution Exploring Operation: 90*136=12240, Resulting Numbers: [12240] 12240,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[95, 49], Operations: ['93-52=41', '90-41=49'] Exploring Operation: 95-49=46, Resulting Numbers: [46] 46,97 unequal: No Solution Exploring Operation: 95*49=4655, Resulting Numbers: [4655] 4655,97 unequal: No Solution Exploring Operation: 95+49=144, Resulting Numbers: [144] 144,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[90, 54], Operations: ['93-52=41', '95-41=54'] Exploring Operation: 90+54=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 90*54=4860, Resulting Numbers: [4860] 4860,97 unequal: No Solution Exploring Operation: 90-54=36, Resulting Numbers: [36] 36,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[90, 50], Operations: ['93+52=145', '145-95=50'] Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 90+50=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 90*50=4500, Resulting Numbers: [4500] 4500,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[145, 185], Operations: ['93+52=145', '90+95=185'] Exploring Operation: 185-145=40, Resulting Numbers: [40] 40,97 unequal: No Solution Exploring Operation: 145+185=330, Resulting Numbers: [330] 330,97 unequal: No Solution Exploring Operation: 145*185=26825, Resulting Numbers: [26825] 26825,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[145, 5], Operations: ['93+52=145', '95-90=5'] Exploring Operation: 145*5=725, Resulting Numbers: [725] 725,97 unequal: No Solution Exploring Operation: 145/5=29, Resulting Numbers: [29] 29,97 unequal: No Solution Exploring Operation: 145+5=150, Resulting Numbers: [150] 150,97 unequal: No Solution Exploring Operation: 145-5=140, Resulting Numbers: [140] 140,97 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 2, 63, 2, 25 ]
88
[ "2+63=65", "25-2=23", "65+23=88" ]
Current State: 88:[2, 63, 2, 25], Operations: [] Exploring Operation: 2+63=65, Resulting Numbers: [25, 65] Generated Node #2: [25, 65] from Operation: 2+63=65 Current State: 88:[25, 65], Operations: ['2+63=65'] Exploring Operation: 25-2=23, Resulting Numbers: [65, 23] Generated Node #3: [65, 23] from Operation: 25-2=23 Current State: 88:[65, 23], Operations: ['2+63=65', '25-2=23'] Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[2, 63, 2, 25], Operations: [] Exploring Operation: 63-2=61, Resulting Numbers: [2, 25, 61] Generated Node #0,0: 88:[2, 25, 61] Operation: 63-2=61 Exploring Operation: 25-2=23, Resulting Numbers: [63, 2, 23] Generated Node #0,1: 88:[63, 2, 23] Operation: 25-2=23 Exploring Operation: 63-25=38, Resulting Numbers: [2, 2, 38] Generated Node #0,2: 88:[2, 2, 38] Operation: 63-25=38 Exploring Operation: 63+25=88, Resulting Numbers: [2, 2, 88] Generated Node #0,3: 88:[2, 2, 88] Operation: 63+25=88 Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[2, 2, 88], Operations: ['63+25=88'] Exploring Operation: 2*2=4, Resulting Numbers: [88, 4] Generated Node #0,3,0: 88:[88, 4] Operation: 2*2=4 Exploring Operation: 2+2=4, Resulting Numbers: [88, 4] Generated Node #0,3,1: 88:[88, 4] Operation: 2+2=4 Exploring Operation: 88/2=44, Resulting Numbers: [2, 44] Generated Node #0,3,2: 88:[2, 44] Operation: 88/2=44 Exploring Operation: 88/2=44, Resulting Numbers: [2, 44] Generated Node #0,3,3: 88:[2, 44] Operation: 88/2=44 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[88, 4], Operations: ['63+25=88', '2*2=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,88 unequal: No Solution Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,88 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,88 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[88, 4], Operations: ['63+25=88', '2+2=4'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,88 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,88 unequal: No Solution Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,88 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[2, 44], Operations: ['63+25=88', '88/2=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,88 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[2, 63, 2, 25], Operations: [] Exploring Operation: 63+25=88, Resulting Numbers: [2, 2, 88] Generated Node #0,3: 88:[2, 2, 88] Operation: 63+25=88 Moving to Node #0,3 Current State: 88:[2, 2, 88], Operations: ['63+25=88'] Exploring Operation: 88/2=44, Resulting Numbers: [2, 44] Generated Node #0,3,2: 88:[2, 44] Operation: 88/2=44 Moving to Node #0,3,2 Current State: 88:[2, 44], Operations: ['63+25=88', '88/2=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 22, 8, 92, 96 ]
21
[ "22*92=2024", "2024-8=2016", "2016/96=21" ]
Current State: 21:[22, 8, 92, 96], Operations: [] Exploring Operation: 22*92=2024, Resulting Numbers: [8, 96, 2024] Generated Node #2: [8, 96, 2024] from Operation: 22*92=2024 Current State: 21:[8, 96, 2024], Operations: ['22*92=2024'] Exploring Operation: 2024-8=2016, Resulting Numbers: [96, 2016] Generated Node #3: [96, 2016] from Operation: 2024-8=2016 Current State: 21:[96, 2016], Operations: ['22*92=2024', '2024-8=2016'] Exploring Operation: 2016/96=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[22, 8, 92, 96], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [22, 8, 4] Generated Node #0,0: 21:[22, 8, 4] Operation: 96-92=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[22, 8, 4], Operations: ['96-92=4'] Exploring Operation: 8-4=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 21:[22, 4] Operation: 8-4=4 Moving to Node #0,0,0 Current State: 21:[22, 4], Operations: ['96-92=4', '8-4=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 59, 76, 9 ]
51
[ "9-6=3", "76-59=17", "3*17=51" ]
Current State: 51:[6, 59, 76, 9], Operations: [] Exploring Operation: 9-6=3, Resulting Numbers: [59, 76, 3] Generated Node #2: [59, 76, 3] from Operation: 9-6=3 Current State: 51:[59, 76, 3], Operations: ['9-6=3'] Exploring Operation: 76-59=17, Resulting Numbers: [3, 17] Generated Node #3: [3, 17] from Operation: 76-59=17 Current State: 51:[3, 17], Operations: ['9-6=3', '76-59=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[6, 59, 76, 9], Operations: [] Exploring Operation: 76-59=17, Resulting Numbers: [6, 9, 17] Generated Node #0,0: 51:[6, 9, 17] Operation: 76-59=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[6, 9, 17], Operations: ['76-59=17'] Exploring Operation: 9-6=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 51:[17, 3] Operation: 9-6=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[17, 3], Operations: ['76-59=17', '9-6=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[6, 59, 76, 9], Operations: [] Exploring Operation: 76-59=17, Resulting Numbers: [6, 9, 17] Generated Node #0,0: 51:[6, 9, 17] Operation: 76-59=17 Moving to Node #0,0 Current State: 51:[6, 9, 17], Operations: ['76-59=17'] Exploring Operation: 9-6=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 51:[17, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 51:[17, 3], Operations: ['76-59=17', '9-6=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 87, 25, 46, 72 ]
86
[ "87+25=112", "72-46=26", "112-26=86" ]
Current State: 86:[87, 25, 46, 72], Operations: [] Exploring Operation: 87+25=112, Resulting Numbers: [46, 72, 112] Generated Node #2: [46, 72, 112] from Operation: 87+25=112 Current State: 86:[46, 72, 112], Operations: ['87+25=112'] Exploring Operation: 72-46=26, Resulting Numbers: [112, 26] Generated Node #3: [112, 26] from Operation: 72-46=26 Current State: 86:[112, 26], Operations: ['87+25=112', '72-46=26'] Exploring Operation: 112-26=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[87, 25, 46, 72], Operations: [] Exploring Operation: 72-25=47, Resulting Numbers: [87, 46, 47] Generated Node #0,0: 86:[87, 46, 47] Operation: 72-25=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[87, 46, 47], Operations: ['72-25=47'] Exploring Operation: 47-46=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 86:[87, 1] Operation: 47-46=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[87, 1], Operations: ['72-25=47', '47-46=1'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[87, 25, 46, 72], Operations: [] Exploring Operation: 72-25=47, Resulting Numbers: [87, 46, 47] Generated Node #0,0: 86:[87, 46, 47] Operation: 72-25=47 Moving to Node #0,0 Current State: 86:[87, 46, 47], Operations: ['72-25=47'] Exploring Operation: 47-46=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 86:[87, 1] Operation: 47-46=1 Moving to Node #0,0,0 Current State: 86:[87, 1], Operations: ['72-25=47', '47-46=1'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 35, 27, 82 ]
86
[ "35-27=8", "21*8=168", "168-82=86" ]
Current State: 86:[21, 35, 27, 82], Operations: [] Exploring Operation: 35-27=8, Resulting Numbers: [21, 82, 8] Generated Node #2: [21, 82, 8] from Operation: 35-27=8 Current State: 86:[21, 82, 8], Operations: ['35-27=8'] Exploring Operation: 21*8=168, Resulting Numbers: [82, 168] Generated Node #3: [82, 168] from Operation: 21*8=168 Current State: 86:[82, 168], Operations: ['35-27=8', '21*8=168'] Exploring Operation: 168-82=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[21, 35, 27, 82], Operations: [] Exploring Operation: 27-21=6, Resulting Numbers: [35, 82, 6] Generated Node #0,0: 86:[35, 82, 6] Operation: 27-21=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[35, 82, 6], Operations: ['27-21=6'] Exploring Operation: 35+6=41, Resulting Numbers: [82, 41] Generated Node #0,0,0: 86:[82, 41] Operation: 35+6=41 Moving to Node #0,0,0 Current State: 86:[82, 41], Operations: ['27-21=6', '35+6=41'] Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 91, 1, 98, 75 ]
83
[ "91-1=90", "98+75=173", "173-90=83" ]
Current State: 83:[91, 1, 98, 75], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [98, 75, 90] Generated Node #2: [98, 75, 90] from Operation: 91-1=90 Current State: 83:[98, 75, 90], Operations: ['91-1=90'] Exploring Operation: 98+75=173, Resulting Numbers: [90, 173] Generated Node #3: [90, 173] from Operation: 98+75=173 Current State: 83:[90, 173], Operations: ['91-1=90', '98+75=173'] Exploring Operation: 173-90=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[91, 1, 98, 75], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [98, 75, 90] Generated Node #0,0: 83:[98, 75, 90] Operation: 91-1=90 Exploring Operation: 98-1=97, Resulting Numbers: [91, 75, 97] Generated Node #0,1: 83:[91, 75, 97] Operation: 98-1=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[98, 75, 90], Operations: ['91-1=90'] Exploring Operation: 98-75=23, Resulting Numbers: [90, 23] Generated Node #0,0,0: 83:[90, 23] Operation: 98-75=23 Exploring Operation: 98-90=8, Resulting Numbers: [75, 8] Generated Node #0,0,1: 83:[75, 8] Operation: 98-90=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[90, 23], Operations: ['91-1=90', '98-75=23'] Exploring Operation: 90-23=67, Resulting Numbers: [67] 67,83 unequal: No Solution Exploring Operation: 90+23=113, Resulting Numbers: [113] 113,83 unequal: No Solution No 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: 83:[75, 8], Operations: ['91-1=90', '98-90=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[91, 1, 98, 75], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [98, 75, 90] Generated Node #0,0: 83:[98, 75, 90] Operation: 91-1=90 Moving to Node #0,0 Current State: 83:[98, 75, 90], Operations: ['91-1=90'] Exploring Operation: 98-90=8, Resulting Numbers: [75, 8] Generated Node #0,0,1: 83:[75, 8] Operation: 98-90=8 Moving to Node #0,0,1 Current State: 83:[75, 8], Operations: ['91-1=90', '98-90=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 3, 72, 94, 99 ]
23
[ "3*72=216", "94+99=193", "216-193=23" ]
Current State: 23:[3, 72, 94, 99], Operations: [] Exploring Operation: 3*72=216, Resulting Numbers: [94, 99, 216] Generated Node #2: [94, 99, 216] from Operation: 3*72=216 Current State: 23:[94, 99, 216], Operations: ['3*72=216'] Exploring Operation: 94+99=193, Resulting Numbers: [216, 193] Generated Node #3: [216, 193] from Operation: 94+99=193 Current State: 23:[216, 193], Operations: ['3*72=216', '94+99=193'] Exploring Operation: 216-193=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[3, 72, 94, 99], Operations: [] Exploring Operation: 99-72=27, Resulting Numbers: [3, 94, 27] Generated Node #0,0: 23:[3, 94, 27] Operation: 99-72=27 Exploring Operation: 94-72=22, Resulting Numbers: [3, 99, 22] Generated Node #0,1: 23:[3, 99, 22] Operation: 94-72=22 Exploring Operation: 72/3=24, Resulting Numbers: [94, 99, 24] Generated Node #0,2: 23:[94, 99, 24] Operation: 72/3=24 Exploring Operation: 99-94=5, Resulting Numbers: [3, 72, 5] Generated Node #0,3: 23:[3, 72, 5] Operation: 99-94=5 Exploring Operation: 99/3=33, Resulting Numbers: [72, 94, 33] Generated Node #0,4: 23:[72, 94, 33] Operation: 99/3=33 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[3, 72, 5], Operations: ['99-94=5'] Exploring Operation: 72-3=69, Resulting Numbers: [5, 69] Generated Node #0,3,0: 23:[5, 69] Operation: 72-3=69 Exploring Operation: 3*5=15, Resulting Numbers: [72, 15] Generated Node #0,3,1: 23:[72, 15] Operation: 3*5=15 Exploring Operation: 72/3=24, Resulting Numbers: [5, 24] Generated Node #0,3,2: 23:[5, 24] Operation: 72/3=24 Exploring Operation: 72-5=67, Resulting Numbers: [3, 67] Generated Node #0,3,3: 23:[3, 67] Operation: 72-5=67 Exploring Operation: 3+5=8, Resulting Numbers: [72, 8] Generated Node #0,3,4: 23:[72, 8] Operation: 3+5=8 Moving to Node #0,3,2 Current State: 23:[5, 24], Operations: ['99-94=5', '72/3=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,23 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[72, 15], Operations: ['99-94=5', '3*5=15'] Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,23 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,23 unequal: No Solution Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[5, 69], Operations: ['99-94=5', '72-3=69'] Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 5+69=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 5*69=345, Resulting Numbers: [345] 345,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[3, 67], Operations: ['99-94=5', '72-5=67'] Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,23 unequal: No Solution Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,23 unequal: No Solution Moving to Node #0,3,4 Current State: 23:[72, 8], Operations: ['99-94=5', '3+5=8'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,23 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[3, 94, 27], Operations: ['99-72=27'] Exploring Operation: 3+27=30, Resulting Numbers: [94, 30] Generated Node #0,0,0: 23:[94, 30] Operation: 3+27=30 Exploring Operation: 3+94=97, Resulting Numbers: [27, 97] Generated Node #0,0,1: 23:[27, 97] Operation: 3+94=97 Exploring Operation: 94-27=67, Resulting Numbers: [3, 67] Generated Node #0,0,2: 23:[3, 67] Operation: 94-27=67 Exploring Operation: 94-3=91, Resulting Numbers: [27, 91] Generated Node #0,0,3: 23:[27, 91] Operation: 94-3=91 Exploring Operation: 27-3=24, Resulting Numbers: [94, 24] Generated Node #0,0,4: 23:[94, 24] Operation: 27-3=24 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[3, 67], Operations: ['99-72=27', '94-27=67'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,23 unequal: No Solution Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,23 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:[27, 91], Operations: ['99-72=27', '94-3=91'] Exploring Operation: 27+91=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 91-27=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 27*91=2457, Resulting Numbers: [2457] 2457,23 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 #0,0,4 Current State: 23:[94, 24], Operations: ['99-72=27', '27-3=24'] Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 94*24=2256, Resulting Numbers: [2256] 2256,23 unequal: No Solution Exploring Operation: 94+24=118, Resulting Numbers: [118] 118,23 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 #0,0,0 Current State: 23:[94, 30], Operations: ['99-72=27', '3+27=30'] Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,23 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,23 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,23 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:[27, 97], Operations: ['99-72=27', '3+94=97'] Exploring Operation: 27*97=2619, Resulting Numbers: [2619] 2619,23 unequal: No Solution Exploring Operation: 97-27=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 27+97=124, Resulting Numbers: [124] 124,23 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:[3, 99, 22], Operations: ['94-72=22'] Exploring Operation: 99-22=77, Resulting Numbers: [3, 77] Generated Node #0,1,0: 23:[3, 77] Operation: 99-22=77 Exploring Operation: 3+22=25, Resulting Numbers: [99, 25] Generated Node #0,1,1: 23:[99, 25] Operation: 3+22=25 Exploring Operation: 99-3=96, Resulting Numbers: [22, 96] Generated Node #0,1,2: 23:[22, 96] Operation: 99-3=96 Exploring Operation: 99/3=33, Resulting Numbers: [22, 33] Generated Node #0,1,3: 23:[22, 33] Operation: 99/3=33 Exploring Operation: 3+99=102, Resulting Numbers: [22, 102] Generated Node #0,1,4: 23:[22, 102] Operation: 3+99=102 Moving to Node #0,1,3 Current State: 23:[22, 33], Operations: ['94-72=22', '99/3=33'] Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,23 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[22, 96], Operations: ['94-72=22', '99-3=96'] Exploring Operation: 96-22=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 22+96=118, Resulting Numbers: [118] 118,23 unequal: No Solution Exploring Operation: 22*96=2112, Resulting Numbers: [2112] 2112,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[3, 77], Operations: ['94-72=22', '99-22=77'] Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 3*77=231, Resulting Numbers: [231] 231,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[99, 25], Operations: ['94-72=22', '3+22=25'] Exploring Operation: 99+25=124, Resulting Numbers: [124] 124,23 unequal: No Solution Exploring Operation: 99*25=2475, Resulting Numbers: [2475] 2475,23 unequal: No Solution Exploring Operation: 99-25=74, Resulting Numbers: [74] 74,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[22, 102], Operations: ['94-72=22', '3+99=102'] Exploring Operation: 102-22=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 22+102=124, Resulting Numbers: [124] 124,23 unequal: No Solution Exploring Operation: 22*102=2244, Resulting Numbers: [2244] 2244,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[72, 94, 33], Operations: ['99/3=33'] Exploring Operation: 72+33=105, Resulting Numbers: [94, 105] Generated Node #0,4,0: 23:[94, 105] Operation: 72+33=105 Exploring Operation: 94-33=61, Resulting Numbers: [72, 61] Generated Node #0,4,1: 23:[72, 61] Operation: 94-33=61 Exploring Operation: 72-33=39, Resulting Numbers: [94, 39] Generated Node #0,4,2: 23:[94, 39] Operation: 72-33=39 Exploring Operation: 94-72=22, Resulting Numbers: [33, 22] Generated Node #0,4,3: 23:[33, 22] Operation: 94-72=22 Exploring Operation: 72+94=166, Resulting Numbers: [33, 166] Generated Node #0,4,4: 23:[33, 166] Operation: 72+94=166 Moving to Node #0,4,3 Current State: 23:[33, 22], Operations: ['99/3=33', '94-72=22'] Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,23 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[94, 39], Operations: ['99/3=33', '72-33=39'] Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,23 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,23 unequal: No Solution Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[72, 61], Operations: ['99/3=33', '94-33=61'] Exploring Operation: 72+61=133, Resulting Numbers: [133] 133,23 unequal: No Solution Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 72*61=4392, Resulting Numbers: [4392] 4392,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[94, 105], Operations: ['99/3=33', '72+33=105'] Exploring Operation: 94*105=9870, Resulting Numbers: [9870] 9870,23 unequal: No Solution Exploring Operation: 105-94=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 94+105=199, Resulting Numbers: [199] 199,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[33, 166], Operations: ['99/3=33', '72+94=166'] Exploring Operation: 33+166=199, Resulting Numbers: [199] 199,23 unequal: No Solution Exploring Operation: 166-33=133, Resulting Numbers: [133] 133,23 unequal: No Solution Exploring Operation: 33*166=5478, Resulting Numbers: [5478] 5478,23 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:[94, 99, 24], Operations: ['72/3=24'] Exploring Operation: 94+24=118, Resulting Numbers: [99, 118] Generated Node #0,2,0: 23:[99, 118] Operation: 94+24=118 Exploring Operation: 99-24=75, Resulting Numbers: [94, 75] Generated Node #0,2,1: 23:[94, 75] Operation: 99-24=75 Exploring Operation: 99-94=5, Resulting Numbers: [24, 5] Generated Node #0,2,2: 23:[24, 5] Operation: 99-94=5 Exploring Operation: 94+99=193, Resulting Numbers: [24, 193] Generated Node #0,2,3: 23:[24, 193] Operation: 94+99=193 Exploring Operation: 94-24=70, Resulting Numbers: [99, 70] Generated Node #0,2,4: 23:[99, 70] Operation: 94-24=70 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[24, 5], Operations: ['72/3=24', '99-94=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,23 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,23 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 #0,2,1 Current State: 23:[94, 75], Operations: ['72/3=24', '99-24=75'] Exploring Operation: 94+75=169, Resulting Numbers: [169] 169,23 unequal: No Solution Exploring Operation: 94*75=7050, Resulting Numbers: [7050] 7050,23 unequal: No Solution Exploring Operation: 94-75=19, Resulting Numbers: [19] 19,23 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 #0,2,4 Current State: 23:[99, 70], Operations: ['72/3=24', '94-24=70'] Exploring Operation: 99*70=6930, Resulting Numbers: [6930] 6930,23 unequal: No Solution Exploring Operation: 99+70=169, Resulting Numbers: [169] 169,23 unequal: No Solution Exploring Operation: 99-70=29, Resulting Numbers: [29] 29,23 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 #0,2,0 Current State: 23:[99, 118], Operations: ['72/3=24', '94+24=118'] Exploring Operation: 118-99=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 99*118=11682, Resulting Numbers: [11682] 11682,23 unequal: No Solution Exploring Operation: 99+118=217, Resulting Numbers: [217] 217,23 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 #0,2,3 Current State: 23:[24, 193], Operations: ['72/3=24', '94+99=193'] Exploring Operation: 24*193=4632, Resulting Numbers: [4632] 4632,23 unequal: No Solution Exploring Operation: 193-24=169, Resulting Numbers: [169] 169,23 unequal: No Solution Exploring Operation: 24+193=217, Resulting Numbers: [217] 217,23 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_5
sum_heuristic
[ 41, 22, 36, 15 ]
53
[ "41-36=5", "15*5=75", "75-22=53" ]
Current State: 53:[41, 22, 36, 15], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [22, 15, 5] Generated Node #2: [22, 15, 5] from Operation: 41-36=5 Current State: 53:[22, 15, 5], Operations: ['41-36=5'] Exploring Operation: 15*5=75, Resulting Numbers: [22, 75] Generated Node #3: [22, 75] from Operation: 15*5=75 Current State: 53:[22, 75], Operations: ['41-36=5', '15*5=75'] Exploring Operation: 75-22=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[41, 22, 36, 15], Operations: [] Exploring Operation: 36+15=51, Resulting Numbers: [41, 22, 51] Generated Node #0,0: 53:[41, 22, 51] Operation: 36+15=51 Exploring Operation: 22+15=37, Resulting Numbers: [41, 36, 37] Generated Node #0,1: 53:[41, 36, 37] Operation: 22+15=37 Exploring Operation: 41+15=56, Resulting Numbers: [22, 36, 56] Generated Node #0,2: 53:[22, 36, 56] Operation: 41+15=56 Exploring Operation: 22+36=58, Resulting Numbers: [41, 15, 58] Generated Node #0,3: 53:[41, 15, 58] Operation: 22+36=58 Moving to Node #0,0 Current State: 53:[41, 22, 51], Operations: ['36+15=51'] Exploring Operation: 41+22=63, Resulting Numbers: [51, 63] Generated Node #0,0,0: 53:[51, 63] Operation: 41+22=63 Exploring Operation: 41-22=19, Resulting Numbers: [51, 19] Generated Node #0,0,1: 53:[51, 19] Operation: 41-22=19 Exploring Operation: 22+51=73, Resulting Numbers: [41, 73] Generated Node #0,0,2: 53:[41, 73] Operation: 22+51=73 Exploring Operation: 51-22=29, Resulting Numbers: [41, 29] Generated Node #0,0,3: 53:[41, 29] Operation: 51-22=29 Moving to Node #0,1 Current State: 53:[41, 36, 37], Operations: ['22+15=37'] Exploring Operation: 41-36=5, Resulting Numbers: [37, 5] Generated Node #0,1,0: 53:[37, 5] Operation: 41-36=5 Exploring Operation: 41+36=77, Resulting Numbers: [37, 77] Generated Node #0,1,1: 53:[37, 77] Operation: 41+36=77 Exploring Operation: 41+37=78, Resulting Numbers: [36, 78] Generated Node #0,1,2: 53:[36, 78] Operation: 41+37=78 Exploring Operation: 36+37=73, Resulting Numbers: [41, 73] Generated Node #0,1,3: 53:[41, 73] Operation: 36+37=73 Moving to Node #0,2 Current State: 53:[22, 36, 56], Operations: ['41+15=56'] Exploring Operation: 22+36=58, Resulting Numbers: [56, 58] Generated Node #0,2,0: 53:[56, 58] Operation: 22+36=58 Exploring Operation: 56-22=34, Resulting Numbers: [36, 34] Generated Node #0,2,1: 53:[36, 34] Operation: 56-22=34 Exploring Operation: 36-22=14, Resulting Numbers: [56, 14] Generated Node #0,2,2: 53:[56, 14] Operation: 36-22=14 Exploring Operation: 22+56=78, Resulting Numbers: [36, 78] Generated Node #0,2,3: 53:[36, 78] Operation: 22+56=78 Moving to Node #0,3 Current State: 53:[41, 15, 58], Operations: ['22+36=58'] Exploring Operation: 15+58=73, Resulting Numbers: [41, 73] Generated Node #0,3,0: 53:[41, 73] Operation: 15+58=73 Exploring Operation: 58-15=43, Resulting Numbers: [41, 43] Generated Node #0,3,1: 53:[41, 43] Operation: 58-15=43 Exploring Operation: 41+15=56, Resulting Numbers: [58, 56] Generated Node #0,3,2: 53:[58, 56] Operation: 41+15=56 Exploring Operation: 41-15=26, Resulting Numbers: [58, 26] Generated Node #0,3,3: 53:[58, 26] Operation: 41-15=26 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[58, 56], Operations: ['22+36=58', '41+15=56'] Exploring Operation: 58+56=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 58-56=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 58*56=3248, Resulting Numbers: [3248] 3248,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[41, 43], Operations: ['22+36=58', '58-15=43'] Exploring Operation: 41+43=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,53 unequal: No Solution Exploring Operation: 41*43=1763, Resulting Numbers: [1763] 1763,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[41, 73], Operations: ['22+36=58', '15+58=73'] Exploring Operation: 41*73=2993, Resulting Numbers: [2993] 2993,53 unequal: No Solution Exploring Operation: 41+73=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 53:[58, 26], Operations: ['22+36=58', '41-15=26'] Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,53 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,53 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: 53:[56, 58], Operations: ['41+15=56', '22+36=58'] Exploring Operation: 56+58=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 56*58=3248, Resulting Numbers: [3248] 3248,53 unequal: No Solution Exploring Operation: 58-56=2, Resulting Numbers: [2] 2,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[51, 63], Operations: ['36+15=51', '41+22=63'] Exploring Operation: 51*63=3213, Resulting Numbers: [3213] 3213,53 unequal: No Solution Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 51+63=114, Resulting Numbers: [114] 114,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[41, 73], Operations: ['22+15=37', '36+37=73'] Exploring Operation: 41*73=2993, Resulting Numbers: [2993] 2993,53 unequal: No Solution Exploring Operation: 41+73=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[41, 73], Operations: ['36+15=51', '22+51=73'] Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 41*73=2993, Resulting Numbers: [2993] 2993,53 unequal: No Solution Exploring Operation: 41+73=114, Resulting Numbers: [114] 114,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[51, 19], Operations: ['36+15=51', '41-22=19'] Exploring Operation: 51+19=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 51*19=969, Resulting Numbers: [969] 969,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[36, 34], Operations: ['41+15=56', '56-22=34'] Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 36*34=1224, Resulting Numbers: [1224] 1224,53 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[41, 29], Operations: ['36+15=51', '51-22=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,53 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[37, 77], Operations: ['22+15=37', '41+36=77'] Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,53 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[56, 14], Operations: ['41+15=56', '36-22=14'] Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,53 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[36, 78], Operations: ['22+15=37', '41+37=78'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[36, 78], Operations: ['41+15=56', '22+56=78'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,53 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[37, 5], Operations: ['22+15=37', '41-36=5'] Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,53 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,53 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 76, 14, 84, 17 ]
26
[ "84/14=6", "17*6=102", "102-76=26" ]
Current State: 26:[76, 14, 84, 17], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [76, 17, 6] Generated Node #2: [76, 17, 6] from Operation: 84/14=6 Current State: 26:[76, 17, 6], Operations: ['84/14=6'] Exploring Operation: 17*6=102, Resulting Numbers: [76, 102] Generated Node #3: [76, 102] from Operation: 17*6=102 Current State: 26:[76, 102], Operations: ['84/14=6', '17*6=102'] Exploring Operation: 102-76=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[76, 14, 84, 17], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [76, 17, 6] Generated Node #0,0: 26:[76, 17, 6] Operation: 84/14=6 Exploring Operation: 76-17=59, Resulting Numbers: [14, 84, 59] Generated Node #0,1: 26:[14, 84, 59] Operation: 76-17=59 Exploring Operation: 84-76=8, Resulting Numbers: [14, 17, 8] Generated Node #0,2: 26:[14, 17, 8] Operation: 84-76=8 Moving to Node #0,2 Current State: 26:[14, 17, 8], Operations: ['84-76=8'] Exploring Operation: 17-14=3, Resulting Numbers: [8, 3] Generated Node #0,2,0: 26:[8, 3] Operation: 17-14=3 Exploring Operation: 17+8=25, Resulting Numbers: [14, 25] Generated Node #0,2,1: 26:[14, 25] Operation: 17+8=25 Exploring Operation: 17-8=9, Resulting Numbers: [14, 9] Generated Node #0,2,2: 26:[14, 9] Operation: 17-8=9 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[14, 25], Operations: ['84-76=8', '17+8=25'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,26 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 #0,2,2 Current State: 26:[14, 9], Operations: ['84-76=8', '17-8=9'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 14+9=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 14*9=126, Resulting Numbers: [126] 126,26 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 #0,2,0 Current State: 26:[8, 3], Operations: ['84-76=8', '17-14=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,26 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:[76, 17, 6], Operations: ['84/14=6'] Exploring Operation: 17-6=11, Resulting Numbers: [76, 11] Generated Node #0,0,0: 26:[76, 11] Operation: 17-6=11 Exploring Operation: 76-17=59, Resulting Numbers: [6, 59] Generated Node #0,0,1: 26:[6, 59] Operation: 76-17=59 Exploring Operation: 76-6=70, Resulting Numbers: [17, 70] Generated Node #0,0,2: 26:[17, 70] Operation: 76-6=70 Moving to Node #0,1 Current State: 26:[14, 84, 59], Operations: ['76-17=59'] Exploring Operation: 84/14=6, Resulting Numbers: [59, 6] Generated Node #0,1,0: 26:[59, 6] Operation: 84/14=6 Exploring Operation: 84-14=70, Resulting Numbers: [59, 70] Generated Node #0,1,1: 26:[59, 70] Operation: 84-14=70 Exploring Operation: 84-59=25, Resulting Numbers: [14, 25] Generated Node #0,1,2: 26:[14, 25] Operation: 84-59=25 Moving to Node #0,1,2 Current State: 26:[14, 25], Operations: ['76-17=59', '84-59=25'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[6, 59], Operations: ['84/14=6', '76-17=59'] Exploring Operation: 6*59=354, Resulting Numbers: [354] 354,26 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[59, 6], Operations: ['76-17=59', '84/14=6'] Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,26 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[17, 70], Operations: ['84/14=6', '76-6=70'] Exploring Operation: 70-17=53, Resulting Numbers: [53] 53,26 unequal: No Solution Exploring Operation: 17+70=87, Resulting Numbers: [87] 87,26 unequal: No Solution Exploring Operation: 17*70=1190, Resulting Numbers: [1190] 1190,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[76, 11], Operations: ['84/14=6', '17-6=11'] Exploring Operation: 76+11=87, Resulting Numbers: [87] 87,26 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 76*11=836, Resulting Numbers: [836] 836,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[59, 70], Operations: ['76-17=59', '84-14=70'] Exploring Operation: 59+70=129, Resulting Numbers: [129] 129,26 unequal: No Solution Exploring Operation: 59*70=4130, Resulting Numbers: [4130] 4130,26 unequal: No Solution Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,26 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 53, 50, 17, 57 ]
29
[ "53+50=103", "17+57=74", "103-74=29" ]
Current State: 29:[53, 50, 17, 57], Operations: [] Exploring Operation: 53+50=103, Resulting Numbers: [17, 57, 103] Generated Node #2: [17, 57, 103] from Operation: 53+50=103 Current State: 29:[17, 57, 103], Operations: ['53+50=103'] Exploring Operation: 17+57=74, Resulting Numbers: [103, 74] Generated Node #3: [103, 74] from Operation: 17+57=74 Current State: 29:[103, 74], Operations: ['53+50=103', '17+57=74'] Exploring Operation: 103-74=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[53, 50, 17, 57], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [50, 57, 36] Generated Node #0,0: 29:[50, 57, 36] Operation: 53-17=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[50, 57, 36], Operations: ['53-17=36'] Exploring Operation: 57-50=7, Resulting Numbers: [36, 7] Generated Node #0,0,0: 29:[36, 7] Operation: 57-50=7 Moving to Node #0,0,0 Current State: 29:[36, 7], Operations: ['53-17=36', '57-50=7'] Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[53, 50, 17, 57], Operations: [] Exploring Operation: 53-17=36, Resulting Numbers: [50, 57, 36] Generated Node #0,0: 29:[50, 57, 36] Operation: 53-17=36 Moving to Node #0,0 Current State: 29:[50, 57, 36], Operations: ['53-17=36'] Exploring Operation: 57-50=7, Resulting Numbers: [36, 7] Generated Node #0,0,0: 29:[36, 7] Operation: 57-50=7 Moving to Node #0,0,0 Current State: 29:[36, 7], Operations: ['53-17=36', '57-50=7'] Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 21, 24, 67, 15 ]
37
[ "21+24=45", "67+15=82", "82-45=37" ]
Current State: 37:[21, 24, 67, 15], Operations: [] Exploring Operation: 21+24=45, Resulting Numbers: [67, 15, 45] Generated Node #2: [67, 15, 45] from Operation: 21+24=45 Current State: 37:[67, 15, 45], Operations: ['21+24=45'] Exploring Operation: 67+15=82, Resulting Numbers: [45, 82] Generated Node #3: [45, 82] from Operation: 67+15=82 Current State: 37:[45, 82], Operations: ['21+24=45', '67+15=82'] Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[21, 24, 67, 15], Operations: [] Exploring Operation: 67-15=52, Resulting Numbers: [21, 24, 52] Generated Node #0,0: 37:[21, 24, 52] Operation: 67-15=52 Exploring Operation: 67-24=43, Resulting Numbers: [21, 15, 43] Generated Node #0,1: 37:[21, 15, 43] Operation: 67-24=43 Exploring Operation: 67-21=46, Resulting Numbers: [24, 15, 46] Generated Node #0,2: 37:[24, 15, 46] Operation: 67-21=46 Exploring Operation: 21+15=36, Resulting Numbers: [24, 67, 36] Generated Node #0,3: 37:[24, 67, 36] Operation: 21+15=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[21, 24, 52], Operations: ['67-15=52'] Exploring Operation: 52-24=28, Resulting Numbers: [21, 28] Generated Node #0,0,0: 37:[21, 28] Operation: 52-24=28 Exploring Operation: 24-21=3, Resulting Numbers: [52, 3] Generated Node #0,0,1: 37:[52, 3] Operation: 24-21=3 Exploring Operation: 21+24=45, Resulting Numbers: [52, 45] Generated Node #0,0,2: 37:[52, 45] Operation: 21+24=45 Exploring Operation: 52-21=31, Resulting Numbers: [24, 31] Generated Node #0,0,3: 37:[24, 31] Operation: 52-21=31 Moving to Node #0,0,3 Current State: 37:[24, 31], Operations: ['67-15=52', '52-21=31'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[52, 45], Operations: ['67-15=52', '21+24=45'] Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,37 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[21, 28], Operations: ['67-15=52', '52-24=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[52, 3], Operations: ['67-15=52', '24-21=3'] Exploring Operation: 52*3=156, Resulting Numbers: [156] 156,37 unequal: No Solution Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[21, 15, 43], Operations: ['67-24=43'] Exploring Operation: 43-15=28, Resulting Numbers: [21, 28] Generated Node #0,1,0: 37:[21, 28] Operation: 43-15=28 Exploring Operation: 21+15=36, Resulting Numbers: [43, 36] Generated Node #0,1,1: 37:[43, 36] Operation: 21+15=36 Exploring Operation: 21-15=6, Resulting Numbers: [43, 6] Generated Node #0,1,2: 37:[43, 6] Operation: 21-15=6 Exploring Operation: 43-21=22, Resulting Numbers: [15, 22] Generated Node #0,1,3: 37:[15, 22] Operation: 43-21=22 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[43, 36], Operations: ['67-24=43', '21+15=36'] Exploring Operation: 43*36=1548, Resulting Numbers: [1548] 1548,37 unequal: No Solution Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 43+36=79, Resulting Numbers: [79] 79,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[21, 28], Operations: ['67-24=43', '43-15=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,37 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[43, 6], Operations: ['67-24=43', '21-15=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[21, 24, 67, 15], Operations: [] Exploring Operation: 67-24=43, Resulting Numbers: [21, 15, 43] Generated Node #0,1: 37:[21, 15, 43] Operation: 67-24=43 Moving to Node #0,1 Current State: 37:[21, 15, 43], Operations: ['67-24=43'] Exploring Operation: 21-15=6, Resulting Numbers: [43, 6] Generated Node #0,1,2: 37:[43, 6] Operation: 21-15=6 Moving to Node #0,1,2 Current State: 37:[43, 6], Operations: ['67-24=43', '21-15=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 12, 72, 20, 33 ]
65
[ "72-33=39", "20*39=780", "780/12=65" ]
Current State: 65:[12, 72, 20, 33], Operations: [] Exploring Operation: 72-33=39, Resulting Numbers: [12, 20, 39] Generated Node #2: [12, 20, 39] from Operation: 72-33=39 Current State: 65:[12, 20, 39], Operations: ['72-33=39'] Exploring Operation: 20*39=780, Resulting Numbers: [12, 780] Generated Node #3: [12, 780] from Operation: 20*39=780 Current State: 65:[12, 780], Operations: ['72-33=39', '20*39=780'] Exploring Operation: 780/12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[12, 72, 20, 33], Operations: [] Exploring Operation: 33-20=13, Resulting Numbers: [12, 72, 13] Generated Node #0,0: 65:[12, 72, 13] Operation: 33-20=13 Exploring Operation: 20+33=53, Resulting Numbers: [12, 72, 53] Generated Node #0,1: 65:[12, 72, 53] Operation: 20+33=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[12, 72, 13], Operations: ['33-20=13'] Exploring Operation: 72/12=6, Resulting Numbers: [13, 6] Generated Node #0,0,0: 65:[13, 6] Operation: 72/12=6 Exploring Operation: 72-12=60, Resulting Numbers: [13, 60] Generated Node #0,0,1: 65:[13, 60] Operation: 72-12=60 Moving to Node #0,0,0 Current State: 65:[13, 6], Operations: ['33-20=13', '72/12=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[13, 60], Operations: ['33-20=13', '72-12=60'] Exploring Operation: 13+60=73, Resulting Numbers: [73] 73,65 unequal: No Solution Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[12, 72, 53], Operations: ['20+33=53'] Exploring Operation: 12+53=65, Resulting Numbers: [72, 65] Generated Node #0,1,0: 65:[72, 65] Operation: 12+53=65 Exploring Operation: 72-53=19, Resulting Numbers: [12, 19] Generated Node #0,1,1: 65:[12, 19] Operation: 72-53=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[72, 65], Operations: ['20+33=53', '12+53=65'] Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 72+65=137, Resulting Numbers: [137] 137,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 65:[12, 19], Operations: ['20+33=53', '72-53=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 76, 4, 75, 73 ]
34
[ "75-73=2", "76/2=38", "38-4=34" ]
Current State: 34:[76, 4, 75, 73], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [76, 4, 2] Generated Node #2: [76, 4, 2] from Operation: 75-73=2 Current State: 34:[76, 4, 2], Operations: ['75-73=2'] Exploring Operation: 76/2=38, Resulting Numbers: [4, 38] Generated Node #3: [4, 38] from Operation: 76/2=38 Current State: 34:[4, 38], Operations: ['75-73=2', '76/2=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[76, 4, 75, 73], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [4, 75, 3] Generated Node #0,0: 34:[4, 75, 3] Operation: 76-73=3 Exploring Operation: 76-75=1, Resulting Numbers: [4, 73, 1] Generated Node #0,1: 34:[4, 73, 1] Operation: 76-75=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[4, 73, 1], Operations: ['76-75=1'] Exploring Operation: 73-4=69, Resulting Numbers: [1, 69] Generated Node #0,1,0: 34:[1, 69] Operation: 73-4=69 Exploring Operation: 4-1=3, Resulting Numbers: [73, 3] Generated Node #0,1,1: 34:[73, 3] Operation: 4-1=3 Moving to Node #0,1,0 Current State: 34:[1, 69], Operations: ['76-75=1', '73-4=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,34 unequal: No Solution Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[73, 3], Operations: ['76-75=1', '4-1=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,34 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[4, 75, 3], Operations: ['76-73=3'] Exploring Operation: 75-4=71, Resulting Numbers: [3, 71] Generated Node #0,0,0: 34:[3, 71] Operation: 75-4=71 Exploring Operation: 75/3=25, Resulting Numbers: [4, 25] Generated Node #0,0,1: 34:[4, 25] Operation: 75/3=25 Moving to Node #0,0,1 Current State: 34:[4, 25], Operations: ['76-73=3', '75/3=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,34 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[3, 71], Operations: ['76-73=3', '75-4=71'] Exploring Operation: 3+71=74, Resulting Numbers: [74] 74,34 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 77, 9, 2, 74 ]
17
[ "77+2=79", "74+79=153", "153/9=17" ]
Current State: 17:[77, 9, 2, 74], Operations: [] Exploring Operation: 77+2=79, Resulting Numbers: [9, 74, 79] Generated Node #2: [9, 74, 79] from Operation: 77+2=79 Current State: 17:[9, 74, 79], Operations: ['77+2=79'] Exploring Operation: 74+79=153, Resulting Numbers: [9, 153] Generated Node #3: [9, 153] from Operation: 74+79=153 Current State: 17:[9, 153], Operations: ['77+2=79', '74+79=153'] Exploring Operation: 153/9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[77, 9, 2, 74], Operations: [] Exploring Operation: 9*2=18, Resulting Numbers: [77, 74, 18] Generated Node #0,0: 17:[77, 74, 18] Operation: 9*2=18 Exploring Operation: 74/2=37, Resulting Numbers: [77, 9, 37] Generated Node #0,1: 17:[77, 9, 37] Operation: 74/2=37 Exploring Operation: 77-74=3, Resulting Numbers: [9, 2, 3] Generated Node #0,2: 17:[9, 2, 3] Operation: 77-74=3 Exploring Operation: 77-9=68, Resulting Numbers: [2, 74, 68] Generated Node #0,3: 17:[2, 74, 68] Operation: 77-9=68 Moving to Node #0,2 Current State: 17:[9, 2, 3], Operations: ['77-74=3'] Exploring Operation: 9+3=12, Resulting Numbers: [2, 12] Generated Node #0,2,0: 17:[2, 12] Operation: 9+3=12 Exploring Operation: 2*3=6, Resulting Numbers: [9, 6] Generated Node #0,2,1: 17:[9, 6] Operation: 2*3=6 Exploring Operation: 9*2=18, Resulting Numbers: [3, 18] Generated Node #0,2,2: 17:[3, 18] Operation: 9*2=18 Exploring Operation: 9+2=11, Resulting Numbers: [3, 11] Generated Node #0,2,3: 17:[3, 11] Operation: 9+2=11 Moving to Node #0,1 Current State: 17:[77, 9, 37], Operations: ['74/2=37'] Exploring Operation: 77-37=40, Resulting Numbers: [9, 40] Generated Node #0,1,0: 17:[9, 40] Operation: 77-37=40 Exploring Operation: 77-9=68, Resulting Numbers: [37, 68] Generated Node #0,1,1: 17:[37, 68] Operation: 77-9=68 Exploring Operation: 37-9=28, Resulting Numbers: [77, 28] Generated Node #0,1,2: 17:[77, 28] Operation: 37-9=28 Exploring Operation: 77+9=86, Resulting Numbers: [37, 86] Generated Node #0,1,3: 17:[37, 86] Operation: 77+9=86 Moving to Node #0,0 Current State: 17:[77, 74, 18], Operations: ['9*2=18'] Exploring Operation: 77-18=59, Resulting Numbers: [74, 59] Generated Node #0,0,0: 17:[74, 59] Operation: 77-18=59 Exploring Operation: 77+74=151, Resulting Numbers: [18, 151] Generated Node #0,0,1: 17:[18, 151] Operation: 77+74=151 Exploring Operation: 77-74=3, Resulting Numbers: [18, 3] Generated Node #0,0,2: 17:[18, 3] Operation: 77-74=3 Exploring Operation: 74-18=56, Resulting Numbers: [77, 56] Generated Node #0,0,3: 17:[77, 56] Operation: 74-18=56 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 17:[18, 3], Operations: ['9*2=18', '77-74=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,17 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 #0,0,0 Current State: 17:[74, 59], Operations: ['9*2=18', '77-18=59'] Exploring Operation: 74*59=4366, Resulting Numbers: [4366] 4366,17 unequal: No Solution Exploring Operation: 74-59=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 74+59=133, Resulting Numbers: [133] 133,17 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 #0,0,3 Current State: 17:[77, 56], Operations: ['9*2=18', '74-18=56'] Exploring Operation: 77*56=4312, Resulting Numbers: [4312] 4312,17 unequal: No Solution Exploring Operation: 77+56=133, Resulting Numbers: [133] 133,17 unequal: No Solution Exploring Operation: 77-56=21, Resulting Numbers: [21] 21,17 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 #0,0,1 Current State: 17:[18, 151], Operations: ['9*2=18', '77+74=151'] Exploring Operation: 151-18=133, Resulting Numbers: [133] 133,17 unequal: No Solution Exploring Operation: 18*151=2718, Resulting Numbers: [2718] 2718,17 unequal: No Solution Exploring Operation: 18+151=169, Resulting Numbers: [169] 169,17 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: 17:[2, 74, 68], Operations: ['77-9=68'] Exploring Operation: 74-68=6, Resulting Numbers: [2, 6] Generated Node #0,3,0: 17:[2, 6] Operation: 74-68=6 Exploring Operation: 68/2=34, Resulting Numbers: [74, 34] Generated Node #0,3,1: 17:[74, 34] Operation: 68/2=34 Exploring Operation: 74-2=72, Resulting Numbers: [68, 72] Generated Node #0,3,2: 17:[68, 72] Operation: 74-2=72 Exploring Operation: 74/2=37, Resulting Numbers: [68, 37] Generated Node #0,3,3: 17:[68, 37] Operation: 74/2=37 Moving to Node #0,2,2 Current State: 17:[3, 18], Operations: ['77-74=3', '9*2=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[9, 6], Operations: ['77-74=3', '2*3=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,17 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[2, 12], Operations: ['77-74=3', '9+3=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,17 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[3, 11], Operations: ['77-74=3', '9+2=11'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,17 unequal: No Solution Moving to Node #0,3,0 Current State: 17:[2, 6], Operations: ['77-9=68', '74-68=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[9, 40], Operations: ['74/2=37', '77-37=40'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 9*40=360, Resulting Numbers: [360] 360,17 unequal: No Solution Exploring Operation: 9+40=49, Resulting Numbers: [49] 49,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[77, 28], Operations: ['74/2=37', '37-9=28'] Exploring Operation: 77*28=2156, Resulting Numbers: [2156] 2156,17 unequal: No Solution Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 77+28=105, Resulting Numbers: [105] 105,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[37, 68], Operations: ['74/2=37', '77-9=68'] Exploring Operation: 37+68=105, Resulting Numbers: [105] 105,17 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 37*68=2516, Resulting Numbers: [2516] 2516,17 unequal: No Solution Moving to Node #0,3,3 Current State: 17:[68, 37], Operations: ['77-9=68', '74/2=37'] Exploring Operation: 68+37=105, Resulting Numbers: [105] 105,17 unequal: No Solution Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 68*37=2516, Resulting Numbers: [2516] 2516,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[74, 34], Operations: ['77-9=68', '68/2=34'] Exploring Operation: 74*34=2516, Resulting Numbers: [2516] 2516,17 unequal: No Solution Exploring Operation: 74+34=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[37, 86], Operations: ['74/2=37', '77+9=86'] Exploring Operation: 37*86=3182, Resulting Numbers: [3182] 3182,17 unequal: No Solution Exploring Operation: 37+86=123, Resulting Numbers: [123] 123,17 unequal: No Solution Exploring Operation: 86-37=49, Resulting Numbers: [49] 49,17 unequal: No Solution Moving to Node #0,3,2 Current State: 17:[68, 72], Operations: ['77-9=68', '74-2=72'] Exploring Operation: 68*72=4896, Resulting Numbers: [4896] 4896,17 unequal: No Solution Exploring Operation: 72-68=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 68+72=140, Resulting Numbers: [140] 140,17 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 69, 65, 38, 16 ]
18
[ "69-65=4", "38-16=22", "22-4=18" ]
Current State: 18:[69, 65, 38, 16], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [38, 16, 4] Generated Node #2: [38, 16, 4] from Operation: 69-65=4 Current State: 18:[38, 16, 4], Operations: ['69-65=4'] Exploring Operation: 38-16=22, Resulting Numbers: [4, 22] Generated Node #3: [4, 22] from Operation: 38-16=22 Current State: 18:[4, 22], Operations: ['69-65=4', '38-16=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[69, 65, 38, 16], Operations: [] Exploring Operation: 65-16=49, Resulting Numbers: [69, 38, 49] Generated Node #0,0: 18:[69, 38, 49] Operation: 65-16=49 Exploring Operation: 69-16=53, Resulting Numbers: [65, 38, 53] Generated Node #0,1: 18:[65, 38, 53] Operation: 69-16=53 Exploring Operation: 65-38=27, Resulting Numbers: [69, 16, 27] Generated Node #0,2: 18:[69, 16, 27] Operation: 65-38=27 Exploring Operation: 69-65=4, Resulting Numbers: [38, 16, 4] Generated Node #0,3: 18:[38, 16, 4] Operation: 69-65=4 Exploring Operation: 69-38=31, Resulting Numbers: [65, 16, 31] Generated Node #0,4: 18:[65, 16, 31] Operation: 69-38=31 Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[38, 16, 4], Operations: ['69-65=4'] Exploring Operation: 16-4=12, Resulting Numbers: [38, 12] Generated Node #0,3,0: 18:[38, 12] Operation: 16-4=12 Exploring Operation: 16+4=20, Resulting Numbers: [38, 20] Generated Node #0,3,1: 18:[38, 20] Operation: 16+4=20 Exploring Operation: 38-16=22, Resulting Numbers: [4, 22] Generated Node #0,3,2: 18:[4, 22] Operation: 38-16=22 Exploring Operation: 16/4=4, Resulting Numbers: [38, 4] Generated Node #0,3,3: 18:[38, 4] Operation: 16/4=4 Exploring Operation: 38-4=34, Resulting Numbers: [16, 34] Generated Node #0,3,4: 18:[16, 34] Operation: 38-4=34 Moving to Node #0,3,2 Current State: 18:[4, 22], Operations: ['69-65=4', '38-16=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[69, 65, 38, 16], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [38, 16, 4] Generated Node #0,3: 18:[38, 16, 4] Operation: 69-65=4 Moving to Node #0,3 Current State: 18:[38, 16, 4], Operations: ['69-65=4'] Exploring Operation: 38-16=22, Resulting Numbers: [4, 22] Generated Node #0,3,2: 18:[4, 22] Operation: 38-16=22 Moving to Node #0,3,2 Current State: 18:[4, 22], Operations: ['69-65=4', '38-16=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 15, 94, 53, 29 ]
27
[ "15+94=109", "53+29=82", "109-82=27" ]
Current State: 27:[15, 94, 53, 29], Operations: [] Exploring Operation: 15+94=109, Resulting Numbers: [53, 29, 109] Generated Node #2: [53, 29, 109] from Operation: 15+94=109 Current State: 27:[53, 29, 109], Operations: ['15+94=109'] Exploring Operation: 53+29=82, Resulting Numbers: [109, 82] Generated Node #3: [109, 82] from Operation: 53+29=82 Current State: 27:[109, 82], Operations: ['15+94=109', '53+29=82'] Exploring Operation: 109-82=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[15, 94, 53, 29], Operations: [] Exploring Operation: 53-15=38, Resulting Numbers: [94, 29, 38] Generated Node #0,0: 27:[94, 29, 38] Operation: 53-15=38 Exploring Operation: 53-29=24, Resulting Numbers: [15, 94, 24] Generated Node #0,1: 27:[15, 94, 24] Operation: 53-29=24 Exploring Operation: 94-29=65, Resulting Numbers: [15, 53, 65] Generated Node #0,2: 27:[15, 53, 65] Operation: 94-29=65 Exploring Operation: 94-53=41, Resulting Numbers: [15, 29, 41] Generated Node #0,3: 27:[15, 29, 41] Operation: 94-53=41 Exploring Operation: 94-15=79, Resulting Numbers: [53, 29, 79] Generated Node #0,4: 27:[53, 29, 79] Operation: 94-15=79 Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[15, 29, 41], Operations: ['94-53=41'] Exploring Operation: 15+41=56, Resulting Numbers: [29, 56] Generated Node #0,3,0: 27:[29, 56] Operation: 15+41=56 Exploring Operation: 29-15=14, Resulting Numbers: [41, 14] Generated Node #0,3,1: 27:[41, 14] Operation: 29-15=14 Exploring Operation: 15+29=44, Resulting Numbers: [41, 44] Generated Node #0,3,2: 27:[41, 44] Operation: 15+29=44 Exploring Operation: 41-15=26, Resulting Numbers: [29, 26] Generated Node #0,3,3: 27:[29, 26] Operation: 41-15=26 Exploring Operation: 41-29=12, Resulting Numbers: [15, 12] Generated Node #0,3,4: 27:[15, 12] Operation: 41-29=12 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 27:[29, 26], Operations: ['94-53=41', '41-15=26'] Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,27 unequal: No Solution Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,27 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,27 unequal: No Solution No 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: 27:[15, 12], Operations: ['94-53=41', '41-29=12'] Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,27 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[15, 94, 53, 29], Operations: [] Exploring Operation: 94-53=41, Resulting Numbers: [15, 29, 41] Generated Node #0,3: 27:[15, 29, 41] Operation: 94-53=41 Moving to Node #0,3 Current State: 27:[15, 29, 41], Operations: ['94-53=41'] Exploring Operation: 41-29=12, Resulting Numbers: [15, 12] Generated Node #0,3,4: 27:[15, 12] Operation: 41-29=12 Moving to Node #0,3,4 Current State: 27:[15, 12], Operations: ['94-53=41', '41-29=12'] Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 22, 28, 10, 28 ]
14
[ "28*10=280", "28+280=308", "308/22=14" ]
Current State: 14:[22, 28, 10, 28], Operations: [] Exploring Operation: 28*10=280, Resulting Numbers: [22, 280] Generated Node #2: [22, 280] from Operation: 28*10=280 Current State: 14:[22, 280], Operations: ['28*10=280'] Exploring Operation: 28+280=308, Resulting Numbers: [22, 308] Generated Node #3: [22, 308] from Operation: 28+280=308 Current State: 14:[22, 308], Operations: ['28*10=280', '28+280=308'] Exploring Operation: 308/22=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[22, 28, 10, 28], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [10, 28, 6] Generated Node #0,0: 14:[10, 28, 6] Operation: 28-22=6 Exploring Operation: 28/28=1, Resulting Numbers: [22, 10, 1] Generated Node #0,1: 14:[22, 10, 1] Operation: 28/28=1 Exploring Operation: 28-22=6, Resulting Numbers: [28, 10, 6] Generated Node #0,2: 14:[28, 10, 6] Operation: 28-22=6 Exploring Operation: 28-28=0, Resulting Numbers: [22, 10, 0] Generated Node #0,3: 14:[22, 10, 0] Operation: 28-28=0 Moving to Node #0,1 Current State: 14:[22, 10, 1], Operations: ['28/28=1'] Exploring Operation: 22-10=12, Resulting Numbers: [1, 12] Generated Node #0,1,0: 14:[1, 12] Operation: 22-10=12 Exploring Operation: 22*1=22, Resulting Numbers: [10, 22] Generated Node #0,1,1: 14:[10, 22] Operation: 22*1=22 Exploring Operation: 10-1=9, Resulting Numbers: [22, 9] Generated Node #0,1,2: 14:[22, 9] Operation: 10-1=9 Exploring Operation: 22-1=21, Resulting Numbers: [10, 21] Generated Node #0,1,3: 14:[10, 21] Operation: 22-1=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[1, 12], Operations: ['28/28=1', '22-10=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,14 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:[22, 9], Operations: ['28/28=1', '10-1=9'] Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,14 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 #0,1,3 Current State: 14:[10, 21], Operations: ['28/28=1', '22-1=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,14 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,14 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,14 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:[10, 22], Operations: ['28/28=1', '22*1=22'] Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,14 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: 14:[22, 10, 0], Operations: ['28-28=0'] Exploring Operation: 22+0=22, Resulting Numbers: [10, 22] Generated Node #0,3,0: 14:[10, 22] Operation: 22+0=22 Exploring Operation: 22*0=0, Resulting Numbers: [10, 0] Generated Node #0,3,1: 14:[10, 0] Operation: 22*0=0 Exploring Operation: 22-10=12, Resulting Numbers: [0, 12] Generated Node #0,3,2: 14:[0, 12] Operation: 22-10=12 Exploring Operation: 10*0=0, Resulting Numbers: [22, 0] Generated Node #0,3,3: 14:[22, 0] Operation: 10*0=0 Moving to Node #0,2 Current State: 14:[28, 10, 6], Operations: ['28-22=6'] Exploring Operation: 10-6=4, Resulting Numbers: [28, 4] Generated Node #0,2,0: 14:[28, 4] Operation: 10-6=4 Exploring Operation: 28-10=18, Resulting Numbers: [6, 18] Generated Node #0,2,1: 14:[6, 18] Operation: 28-10=18 Exploring Operation: 10+6=16, Resulting Numbers: [28, 16] Generated Node #0,2,2: 14:[28, 16] Operation: 10+6=16 Exploring Operation: 28-6=22, Resulting Numbers: [10, 22] Generated Node #0,2,3: 14:[10, 22] Operation: 28-6=22 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[6, 18], Operations: ['28-22=6', '28-10=18'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,14 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 14:[10, 22], Operations: ['28-22=6', '28-6=22'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[28, 4], Operations: ['28-22=6', '10-6=4'] Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,14 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[28, 16], Operations: ['28-22=6', '10+6=16'] Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,14 unequal: No Solution Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,14 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,14 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:[10, 28, 6], Operations: ['28-22=6'] Exploring Operation: 28-10=18, Resulting Numbers: [6, 18] Generated Node #0,0,0: 14:[6, 18] Operation: 28-10=18 Exploring Operation: 10-6=4, Resulting Numbers: [28, 4] Generated Node #0,0,1: 14:[28, 4] Operation: 10-6=4 Exploring Operation: 28-6=22, Resulting Numbers: [10, 22] Generated Node #0,0,2: 14:[10, 22] Operation: 28-6=22 Exploring Operation: 10+6=16, Resulting Numbers: [28, 16] Generated Node #0,0,3: 14:[28, 16] Operation: 10+6=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[6, 18], Operations: ['28-22=6', '28-10=18'] Exploring Operation: 6*18=108, Resulting Numbers: [108] 108,14 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,14 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 #0,0,2 Current State: 14:[10, 22], Operations: ['28-22=6', '28-6=22'] Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,14 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,14 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 #0,0,1 Current State: 14:[28, 4], Operations: ['28-22=6', '10-6=4'] Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,14 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,14 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 #0,0,3 Current State: 14:[28, 16], Operations: ['28-22=6', '10+6=16'] Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,14 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 14:[0, 12], Operations: ['28-28=0', '22-10=12'] Exploring Operation: 0*12=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 12-0=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 0+12=12, Resulting Numbers: [12] 12,14 unequal: No Solution Moving to Node #0,3,1 Current State: 14:[10, 0], Operations: ['28-28=0', '22*0=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,14 unequal: No Solution Moving to Node #0,3,3 Current State: 14:[22, 0], Operations: ['28-28=0', '10*0=0'] Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 22*0=0, Resulting Numbers: [0] 0,14 unequal: No Solution Moving to Node #0,3,0 Current State: 14:[10, 22], Operations: ['28-28=0', '22+0=22'] Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,14 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,14 unequal: No Solution Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,14 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 99, 99, 73, 65 ]
65
[ "99-99=0", "73*0=0", "65+0=65" ]
Current State: 65:[99, 99, 73, 65], Operations: [] Exploring Operation: 99-99=0, Resulting Numbers: [73, 65, 0] Generated Node #2: [73, 65, 0] from Operation: 99-99=0 Current State: 65:[73, 65, 0], Operations: ['99-99=0'] Exploring Operation: 73*0=0, Resulting Numbers: [65, 0] Generated Node #3: [65, 0] from Operation: 73*0=0 Current State: 65:[65, 0], Operations: ['99-99=0', '73*0=0'] Exploring Operation: 65+0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[99, 99, 73, 65], Operations: [] Exploring Operation: 99-73=26, Resulting Numbers: [99, 65, 26] Generated Node #0,0: 65:[99, 65, 26] Operation: 99-73=26 Exploring Operation: 99/99=1, Resulting Numbers: [73, 65, 1] Generated Node #0,1: 65:[73, 65, 1] Operation: 99/99=1 Exploring Operation: 99-99=0, Resulting Numbers: [73, 65, 0] Generated Node #0,2: 65:[73, 65, 0] Operation: 99-99=0 Moving to Node #0,1 Current State: 65:[73, 65, 1], Operations: ['99/99=1'] Exploring Operation: 73*1=73, Resulting Numbers: [65, 73] Generated Node #0,1,0: 65:[65, 73] Operation: 73*1=73 Exploring Operation: 73-1=72, Resulting Numbers: [65, 72] Generated Node #0,1,1: 65:[65, 72] Operation: 73-1=72 Exploring Operation: 73-65=8, Resulting Numbers: [1, 8] Generated Node #0,1,2: 65:[1, 8] Operation: 73-65=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[65, 72], Operations: ['99/99=1', '73-1=72'] Exploring Operation: 65+72=137, Resulting Numbers: [137] 137,65 unequal: No Solution Exploring Operation: 65*72=4680, Resulting Numbers: [4680] 4680,65 unequal: No Solution Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,65 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:[1, 8], Operations: ['99/99=1', '73-65=8'] Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,65 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 #0,1,0 Current State: 65:[65, 73], Operations: ['99/99=1', '73*1=73'] Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 65*73=4745, Resulting Numbers: [4745] 4745,65 unequal: No Solution Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,65 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: 65:[73, 65, 0], Operations: ['99-99=0'] Exploring Operation: 73-65=8, Resulting Numbers: [0, 8] Generated Node #0,2,0: 65:[0, 8] Operation: 73-65=8 Exploring Operation: 73+0=73, Resulting Numbers: [65, 73] Generated Node #0,2,1: 65:[65, 73] Operation: 73+0=73 Exploring Operation: 73*0=0, Resulting Numbers: [65, 0] Generated Node #0,2,2: 65:[65, 0] Operation: 73*0=0 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[65, 0], Operations: ['99-99=0', '73*0=0'] Exploring Operation: 65+0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[99, 99, 73, 65], Operations: [] Exploring Operation: 99-99=0, Resulting Numbers: [73, 65, 0] Generated Node #0,2: 65:[73, 65, 0] Operation: 99-99=0 Moving to Node #0,2 Current State: 65:[73, 65, 0], Operations: ['99-99=0'] Exploring Operation: 73*0=0, Resulting Numbers: [65, 0] Generated Node #0,2,2: 65:[65, 0] Operation: 73*0=0 Moving to Node #0,2,2 Current State: 65:[65, 0], Operations: ['99-99=0', '73*0=0'] Exploring Operation: 65+0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 40, 86, 57, 98 ]
87
[ "86-40=46", "98-57=41", "46+41=87" ]
Current State: 87:[40, 86, 57, 98], Operations: [] Exploring Operation: 86-40=46, Resulting Numbers: [57, 98, 46] Generated Node #2: [57, 98, 46] from Operation: 86-40=46 Current State: 87:[57, 98, 46], Operations: ['86-40=46'] Exploring Operation: 98-57=41, Resulting Numbers: [46, 41] Generated Node #3: [46, 41] from Operation: 98-57=41 Current State: 87:[46, 41], Operations: ['86-40=46', '98-57=41'] Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[40, 86, 57, 98], Operations: [] Exploring Operation: 57-40=17, Resulting Numbers: [86, 98, 17] Generated Node #0,0: 87:[86, 98, 17] Operation: 57-40=17 Exploring Operation: 86-57=29, Resulting Numbers: [40, 98, 29] Generated Node #0,1: 87:[40, 98, 29] Operation: 86-57=29 Exploring Operation: 40+57=97, Resulting Numbers: [86, 98, 97] Generated Node #0,2: 87:[86, 98, 97] Operation: 40+57=97 Moving to Node #0,1 Current State: 87:[40, 98, 29], Operations: ['86-57=29'] Exploring Operation: 98-40=58, Resulting Numbers: [29, 58] Generated Node #0,1,0: 87:[29, 58] Operation: 98-40=58 Exploring Operation: 40-29=11, Resulting Numbers: [98, 11] Generated Node #0,1,1: 87:[98, 11] Operation: 40-29=11 Exploring Operation: 40+29=69, Resulting Numbers: [98, 69] Generated Node #0,1,2: 87:[98, 69] Operation: 40+29=69 Moving to Node #0,2 Current State: 87:[86, 98, 97], Operations: ['40+57=97'] Exploring Operation: 98-86=12, Resulting Numbers: [97, 12] Generated Node #0,2,0: 87:[97, 12] Operation: 98-86=12 Exploring Operation: 97-86=11, Resulting Numbers: [98, 11] Generated Node #0,2,1: 87:[98, 11] Operation: 97-86=11 Exploring Operation: 98-97=1, Resulting Numbers: [86, 1] Generated Node #0,2,2: 87:[86, 1] Operation: 98-97=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[86, 1], Operations: ['40+57=97', '98-97=1'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,87 unequal: No Solution Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[40, 86, 57, 98], Operations: [] Exploring Operation: 40+57=97, Resulting Numbers: [86, 98, 97] Generated Node #0,2: 87:[86, 98, 97] Operation: 40+57=97 Moving to Node #0,2 Current State: 87:[86, 98, 97], Operations: ['40+57=97'] Exploring Operation: 98-97=1, Resulting Numbers: [86, 1] Generated Node #0,2,2: 87:[86, 1] Operation: 98-97=1 Moving to Node #0,2,2 Current State: 87:[86, 1], Operations: ['40+57=97', '98-97=1'] Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 10, 50, 90, 28 ]
67
[ "50/10=5", "90-28=62", "5+62=67" ]
Current State: 67:[10, 50, 90, 28], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [90, 28, 5] Generated Node #2: [90, 28, 5] from Operation: 50/10=5 Current State: 67:[90, 28, 5], Operations: ['50/10=5'] Exploring Operation: 90-28=62, Resulting Numbers: [5, 62] Generated Node #3: [5, 62] from Operation: 90-28=62 Current State: 67:[5, 62], Operations: ['50/10=5', '90-28=62'] Exploring Operation: 5+62=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[10, 50, 90, 28], Operations: [] Exploring Operation: 10+28=38, Resulting Numbers: [50, 90, 38] Generated Node #0,0: 67:[50, 90, 38] Operation: 10+28=38 Exploring Operation: 90-28=62, Resulting Numbers: [10, 50, 62] Generated Node #0,1: 67:[10, 50, 62] Operation: 90-28=62 Exploring Operation: 10+50=60, Resulting Numbers: [90, 28, 60] Generated Node #0,2: 67:[90, 28, 60] Operation: 10+50=60 Exploring Operation: 90-10=80, Resulting Numbers: [50, 28, 80] Generated Node #0,3: 67:[50, 28, 80] Operation: 90-10=80 Exploring Operation: 50-10=40, Resulting Numbers: [90, 28, 40] Generated Node #0,4: 67:[90, 28, 40] Operation: 50-10=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[50, 90, 38], Operations: ['10+28=38'] Exploring Operation: 50+38=88, Resulting Numbers: [90, 88] Generated Node #0,0,0: 67:[90, 88] Operation: 50+38=88 Exploring Operation: 90+38=128, Resulting Numbers: [50, 128] Generated Node #0,0,1: 67:[50, 128] Operation: 90+38=128 Exploring Operation: 50-38=12, Resulting Numbers: [90, 12] Generated Node #0,0,2: 67:[90, 12] Operation: 50-38=12 Exploring Operation: 90-38=52, Resulting Numbers: [50, 52] Generated Node #0,0,3: 67:[50, 52] Operation: 90-38=52 Exploring Operation: 90-50=40, Resulting Numbers: [38, 40] Generated Node #0,0,4: 67:[38, 40] Operation: 90-50=40 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 67:[50, 52], Operations: ['10+28=38', '90-38=52'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[90, 88], Operations: ['10+28=38', '50+38=88'] Exploring Operation: 90+88=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 90*88=7920, Resulting Numbers: [7920] 7920,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 67:[38, 40], Operations: ['10+28=38', '90-50=40'] Exploring Operation: 38+40=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 38*40=1520, Resulting Numbers: [1520] 1520,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[50, 128], Operations: ['10+28=38', '90+38=128'] Exploring Operation: 50+128=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 50*128=6400, Resulting Numbers: [6400] 6400,67 unequal: No Solution Exploring Operation: 128-50=78, Resulting Numbers: [78] 78,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 67:[90, 12], Operations: ['10+28=38', '50-38=12'] Exploring Operation: 90+12=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 90*12=1080, Resulting Numbers: [1080] 1080,67 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 67:[90, 28, 60], Operations: ['10+50=60'] Exploring Operation: 90-60=30, Resulting Numbers: [28, 30] Generated Node #0,2,0: 67:[28, 30] Operation: 90-60=30 Exploring Operation: 90+28=118, Resulting Numbers: [60, 118] Generated Node #0,2,1: 67:[60, 118] Operation: 90+28=118 Exploring Operation: 60-28=32, Resulting Numbers: [90, 32] Generated Node #0,2,2: 67:[90, 32] Operation: 60-28=32 Exploring Operation: 90-28=62, Resulting Numbers: [60, 62] Generated Node #0,2,3: 67:[60, 62] Operation: 90-28=62 Exploring Operation: 28+60=88, Resulting Numbers: [90, 88] Generated Node #0,2,4: 67:[90, 88] Operation: 28+60=88 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 67:[60, 62], Operations: ['10+50=60', '90-28=62'] Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,67 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 67:[90, 88], Operations: ['10+50=60', '28+60=88'] Exploring Operation: 90+88=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 90*88=7920, Resulting Numbers: [7920] 7920,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 67:[60, 118], Operations: ['10+50=60', '90+28=118'] Exploring Operation: 60*118=7080, Resulting Numbers: [7080] 7080,67 unequal: No Solution Exploring Operation: 118-60=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 60+118=178, Resulting Numbers: [178] 178,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 67:[90, 32], Operations: ['10+50=60', '60-28=32'] Exploring Operation: 90+32=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 90*32=2880, Resulting Numbers: [2880] 2880,67 unequal: No Solution Exploring Operation: 90-32=58, Resulting Numbers: [58] 58,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 67:[28, 30], Operations: ['10+50=60', '90-60=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,67 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,67 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[50, 28, 80], Operations: ['90-10=80'] Exploring Operation: 50-28=22, Resulting Numbers: [80, 22] Generated Node #0,3,0: 67:[80, 22] Operation: 50-28=22 Exploring Operation: 80-28=52, Resulting Numbers: [50, 52] Generated Node #0,3,1: 67:[50, 52] Operation: 80-28=52 Exploring Operation: 80-50=30, Resulting Numbers: [28, 30] Generated Node #0,3,2: 67:[28, 30] Operation: 80-50=30 Exploring Operation: 28+80=108, Resulting Numbers: [50, 108] Generated Node #0,3,3: 67:[50, 108] Operation: 28+80=108 Exploring Operation: 50+28=78, Resulting Numbers: [80, 78] Generated Node #0,3,4: 67:[80, 78] Operation: 50+28=78 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 67:[80, 78], Operations: ['90-10=80', '50+28=78'] Exploring Operation: 80+78=158, Resulting Numbers: [158] 158,67 unequal: No Solution Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 80*78=6240, Resulting Numbers: [6240] 6240,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 67:[50, 52], Operations: ['90-10=80', '80-28=52'] Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,67 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 67:[80, 22], Operations: ['90-10=80', '50-28=22'] Exploring Operation: 80*22=1760, Resulting Numbers: [1760] 1760,67 unequal: No Solution Exploring Operation: 80+22=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 80-22=58, Resulting Numbers: [58] 58,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 67:[50, 108], Operations: ['90-10=80', '28+80=108'] Exploring Operation: 50+108=158, Resulting Numbers: [158] 158,67 unequal: No Solution Exploring Operation: 50*108=5400, Resulting Numbers: [5400] 5400,67 unequal: No Solution Exploring Operation: 108-50=58, Resulting Numbers: [58] 58,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 67:[28, 30], Operations: ['90-10=80', '80-50=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,67 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,67 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[10, 50, 62], Operations: ['90-28=62'] Exploring Operation: 50/10=5, Resulting Numbers: [62, 5] Generated Node #0,1,0: 67:[62, 5] Operation: 50/10=5 Exploring Operation: 62-10=52, Resulting Numbers: [50, 52] Generated Node #0,1,1: 67:[50, 52] Operation: 62-10=52 Exploring Operation: 10+62=72, Resulting Numbers: [50, 72] Generated Node #0,1,2: 67:[50, 72] Operation: 10+62=72 Exploring Operation: 10+50=60, Resulting Numbers: [62, 60] Generated Node #0,1,3: 67:[62, 60] Operation: 10+50=60 Exploring Operation: 50-10=40, Resulting Numbers: [62, 40] Generated Node #0,1,4: 67:[62, 40] Operation: 50-10=40 Moving to Node #0,1,3 Current State: 67:[62, 60], Operations: ['90-28=62', '10+50=60'] Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[50, 72], Operations: ['90-28=62', '10+62=72'] Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 50*72=3600, Resulting Numbers: [3600] 3600,67 unequal: No Solution Exploring Operation: 50+72=122, Resulting Numbers: [122] 122,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[50, 52], Operations: ['90-28=62', '62-10=52'] Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,67 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[62, 40], Operations: ['90-28=62', '50-10=40'] Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 62+40=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 62*40=2480, Resulting Numbers: [2480] 2480,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[62, 5], Operations: ['90-28=62', '50/10=5'] Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,67 unequal: No Solution Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,67 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[10, 50, 90, 28], Operations: [] Exploring Operation: 90-28=62, Resulting Numbers: [10, 50, 62] Generated Node #0,1: 67:[10, 50, 62] Operation: 90-28=62 Moving to Node #0,1 Current State: 67:[10, 50, 62], Operations: ['90-28=62'] Exploring Operation: 50/10=5, Resulting Numbers: [62, 5] Generated Node #0,1,0: 67:[62, 5] Operation: 50/10=5 Moving to Node #0,1,0 Current State: 67:[62, 5], Operations: ['90-28=62', '50/10=5'] Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.922743
hs_5
sum_heuristic
[ 64, 62, 6, 47 ]
35
[ "64-62=2", "6*2=12", "47-12=35" ]
Current State: 35:[64, 62, 6, 47], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [6, 47, 2] Generated Node #2: [6, 47, 2] from Operation: 64-62=2 Current State: 35:[6, 47, 2], Operations: ['64-62=2'] Exploring Operation: 6*2=12, Resulting Numbers: [47, 12] Generated Node #3: [47, 12] from Operation: 6*2=12 Current State: 35:[47, 12], Operations: ['64-62=2', '6*2=12'] Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[64, 62, 6, 47], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [6, 47, 2] Generated Node #0,0: 35:[6, 47, 2] Operation: 64-62=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[6, 47, 2], Operations: ['64-62=2'] Exploring Operation: 47-6=41, Resulting Numbers: [2, 41] Generated Node #0,0,0: 35:[2, 41] Operation: 47-6=41 Moving to Node #0,0,0 Current State: 35:[2, 41], Operations: ['64-62=2', '47-6=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 53, 69, 3, 39 ]
52
[ "69-53=16", "39-3=36", "16+36=52" ]
Current State: 52:[53, 69, 3, 39], Operations: [] Exploring Operation: 69-53=16, Resulting Numbers: [3, 39, 16] Generated Node #2: [3, 39, 16] from Operation: 69-53=16 Current State: 52:[3, 39, 16], Operations: ['69-53=16'] Exploring Operation: 39-3=36, Resulting Numbers: [16, 36] Generated Node #3: [16, 36] from Operation: 39-3=36 Current State: 52:[16, 36], Operations: ['69-53=16', '39-3=36'] Exploring Operation: 16+36=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[53, 69, 3, 39], Operations: [] Exploring Operation: 69-39=30, Resulting Numbers: [53, 3, 30] Generated Node #0,0: 52:[53, 3, 30] Operation: 69-39=30 Moving to Node #0,0 Current State: 52:[53, 3, 30], Operations: ['69-39=30'] Exploring Operation: 30-3=27, Resulting Numbers: [53, 27] Generated Node #0,0,0: 52:[53, 27] Operation: 30-3=27 Moving to Node #0,0,0 Current State: 52:[53, 27], Operations: ['69-39=30', '30-3=27'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,52 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 15, 5, 5, 53 ]
93
[ "15+53=68", "5*5=25", "68+25=93" ]
Current State: 93:[15, 5, 5, 53], Operations: [] Exploring Operation: 15+53=68, Resulting Numbers: [5, 5, 68] Generated Node #2: [5, 5, 68] from Operation: 15+53=68 Current State: 93:[5, 5, 68], Operations: ['15+53=68'] Exploring Operation: 5*5=25, Resulting Numbers: [68, 25] Generated Node #3: [68, 25] from Operation: 5*5=25 Current State: 93:[68, 25], Operations: ['15+53=68', '5*5=25'] Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[15, 5, 5, 53], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [5, 53, 3] Generated Node #0,0: 93:[5, 53, 3] Operation: 15/5=3 Exploring Operation: 53-15=38, Resulting Numbers: [5, 5, 38] Generated Node #0,1: 93:[5, 5, 38] Operation: 53-15=38 Exploring Operation: 15/5=3, Resulting Numbers: [5, 53, 3] Generated Node #0,2: 93:[5, 53, 3] Operation: 15/5=3 Moving to Node #0,1 Current State: 93:[5, 5, 38], Operations: ['53-15=38'] Exploring Operation: 5/5=1, Resulting Numbers: [38, 1] Generated Node #0,1,0: 93:[38, 1] Operation: 5/5=1 Exploring Operation: 38-5=33, Resulting Numbers: [5, 33] Generated Node #0,1,1: 93:[5, 33] Operation: 38-5=33 Exploring Operation: 38-5=33, Resulting Numbers: [5, 33] Generated Node #0,1,2: 93:[5, 33] Operation: 38-5=33 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[5, 33], Operations: ['53-15=38', '38-5=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,93 unequal: No Solution Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,93 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,93 unequal: No Solution No 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: 93:[5, 33], Operations: ['53-15=38', '38-5=33'] Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,93 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,93 unequal: No Solution Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,93 unequal: No Solution No 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: 93:[38, 1], Operations: ['53-15=38', '5/5=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,93 unequal: No Solution Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,93 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: 93:[5, 53, 3], Operations: ['15/5=3'] Exploring Operation: 5-3=2, Resulting Numbers: [53, 2] Generated Node #0,0,0: 93:[53, 2] Operation: 5-3=2 Exploring Operation: 53-3=50, Resulting Numbers: [5, 50] Generated Node #0,0,1: 93:[5, 50] Operation: 53-3=50 Exploring Operation: 53-5=48, Resulting Numbers: [3, 48] Generated Node #0,0,2: 93:[3, 48] Operation: 53-5=48 Moving to Node #0,2 Current State: 93:[5, 53, 3], Operations: ['15/5=3'] Exploring Operation: 53-3=50, Resulting Numbers: [5, 50] Generated Node #0,2,0: 93:[5, 50] Operation: 53-3=50 Exploring Operation: 53-5=48, Resulting Numbers: [3, 48] Generated Node #0,2,1: 93:[3, 48] Operation: 53-5=48 Exploring Operation: 5-3=2, Resulting Numbers: [53, 2] Generated Node #0,2,2: 93:[53, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[3, 48], Operations: ['15/5=3', '53-5=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,93 unequal: No Solution No 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: 93:[5, 50], Operations: ['15/5=3', '53-3=50'] Exploring Operation: 5+50=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,93 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,93 unequal: No Solution No 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: 93:[53, 2], Operations: ['15/5=3', '5-3=2'] Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,93 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: 93:[3, 48], Operations: ['15/5=3', '53-5=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[5, 50], Operations: ['15/5=3', '53-3=50'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 5+50=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[53, 2], Operations: ['15/5=3', '5-3=2'] Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,93 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 69, 69, 91, 94 ]
92
[ "94-91=3", "69/3=23", "69+23=92" ]
Current State: 92:[69, 69, 91, 94], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [69, 69, 3] Generated Node #2: [69, 69, 3] from Operation: 94-91=3 Current State: 92:[69, 69, 3], Operations: ['94-91=3'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,92 equal: Goal Reached Exploring Operation: 69+23=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[69, 69, 91, 94], Operations: [] Exploring Operation: 91-69=22, Resulting Numbers: [69, 94, 22] Generated Node #0,0: 92:[69, 94, 22] Operation: 91-69=22 Exploring Operation: 69/69=1, Resulting Numbers: [91, 94, 1] Generated Node #0,1: 92:[91, 94, 1] Operation: 69/69=1 Exploring Operation: 69-69=0, Resulting Numbers: [91, 94, 0] Generated Node #0,2: 92:[91, 94, 0] Operation: 69-69=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[91, 94, 1], Operations: ['69/69=1'] Exploring Operation: 94-1=93, Resulting Numbers: [91, 93] Generated Node #0,1,0: 92:[91, 93] Operation: 94-1=93 Exploring Operation: 94-91=3, Resulting Numbers: [1, 3] Generated Node #0,1,1: 92:[1, 3] Operation: 94-91=3 Exploring Operation: 91+1=92, Resulting Numbers: [94, 92] Generated Node #0,1,2: 92:[94, 92] Operation: 91+1=92 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 92:[91, 93], Operations: ['69/69=1', '94-1=93'] Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,92 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,92 unequal: No Solution Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 92:[1, 3], Operations: ['69/69=1', '94-91=3'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 92:[94, 92], Operations: ['69/69=1', '91+1=92'] Exploring Operation: 94+92=186, Resulting Numbers: [186] 186,92 unequal: No Solution Exploring Operation: 94*92=8648, Resulting Numbers: [8648] 8648,92 unequal: No Solution Exploring Operation: 94-92=2, Resulting Numbers: [2] 2,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[91, 94, 0], Operations: ['69-69=0'] Exploring Operation: 91-0=91, Resulting Numbers: [94, 91] Generated Node #0,2,0: 92:[94, 91] Operation: 91-0=91 Exploring Operation: 91+0=91, Resulting Numbers: [94, 91] Generated Node #0,2,1: 92:[94, 91] Operation: 91+0=91 Exploring Operation: 94-91=3, Resulting Numbers: [0, 3] Generated Node #0,2,2: 92:[0, 3] Operation: 94-91=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 92:[94, 91], Operations: ['69-69=0', '91-0=91'] Exploring Operation: 94-91=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 94+91=185, Resulting Numbers: [185] 185,92 unequal: No Solution Exploring Operation: 94*91=8554, Resulting Numbers: [8554] 8554,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 92:[94, 91], Operations: ['69-69=0', '91+0=91'] Exploring Operation: 94+91=185, Resulting Numbers: [185] 185,92 unequal: No Solution Exploring Operation: 94-91=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 94*91=8554, Resulting Numbers: [8554] 8554,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 92:[0, 3], Operations: ['69-69=0', '94-91=3'] Exploring Operation: 0*3=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 0+3=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 3-0=3, Resulting Numbers: [3] 3,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[69, 94, 22], Operations: ['91-69=22'] Exploring Operation: 69+22=91, Resulting Numbers: [94, 91] Generated Node #0,0,0: 92:[94, 91] Operation: 69+22=91 Exploring Operation: 69-22=47, Resulting Numbers: [94, 47] Generated Node #0,0,1: 92:[94, 47] Operation: 69-22=47 Exploring Operation: 94-69=25, Resulting Numbers: [22, 25] Generated Node #0,0,2: 92:[22, 25] Operation: 94-69=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[94, 91], Operations: ['91-69=22', '69+22=91'] Exploring Operation: 94+91=185, Resulting Numbers: [185] 185,92 unequal: No Solution Exploring Operation: 94-91=3, Resulting Numbers: [3] 3,92 unequal: No Solution Exploring Operation: 94*91=8554, Resulting Numbers: [8554] 8554,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 92:[94, 47], Operations: ['91-69=22', '69-22=47'] Exploring Operation: 94+47=141, Resulting Numbers: [141] 141,92 unequal: No Solution Exploring Operation: 94/47=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 94-47=47, Resulting Numbers: [47] 47,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 92:[22, 25], Operations: ['91-69=22', '94-69=25'] Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,92 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 25, 85, 8, 1 ]
90
[ "8-1=7", "25*7=175", "175-85=90" ]
Current State: 90:[25, 85, 8, 1], Operations: [] Exploring Operation: 8-1=7, Resulting Numbers: [25, 85, 7] Generated Node #2: [25, 85, 7] from Operation: 8-1=7 Current State: 90:[25, 85, 7], Operations: ['8-1=7'] Exploring Operation: 25*7=175, Resulting Numbers: [85, 175] Generated Node #3: [85, 175] from Operation: 25*7=175 Current State: 90:[85, 175], Operations: ['8-1=7', '25*7=175'] Exploring Operation: 175-85=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[25, 85, 8, 1], Operations: [] Exploring Operation: 25+8=33, Resulting Numbers: [85, 1, 33] Generated Node #0,0: 90:[85, 1, 33] Operation: 25+8=33 Exploring Operation: 25-8=17, Resulting Numbers: [85, 1, 17] Generated Node #0,1: 90:[85, 1, 17] Operation: 25-8=17 Exploring Operation: 85+8=93, Resulting Numbers: [25, 1, 93] Generated Node #0,2: 90:[25, 1, 93] Operation: 85+8=93 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[85, 1, 17], Operations: ['25-8=17'] Exploring Operation: 85/17=5, Resulting Numbers: [1, 5] Generated Node #0,1,0: 90:[1, 5] Operation: 85/17=5 Exploring Operation: 1+17=18, Resulting Numbers: [85, 18] Generated Node #0,1,1: 90:[85, 18] Operation: 1+17=18 Exploring Operation: 85+1=86, Resulting Numbers: [17, 86] Generated Node #0,1,2: 90:[17, 86] Operation: 85+1=86 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[1, 5], Operations: ['25-8=17', '85/17=5'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[85, 18], Operations: ['25-8=17', '1+17=18'] Exploring Operation: 85*18=1530, Resulting Numbers: [1530] 1530,90 unequal: No Solution Exploring Operation: 85+18=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,90 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:[17, 86], Operations: ['25-8=17', '85+1=86'] Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 17+86=103, Resulting Numbers: [103] 103,90 unequal: No Solution Exploring Operation: 17*86=1462, Resulting Numbers: [1462] 1462,90 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:[85, 1, 33], Operations: ['25+8=33'] Exploring Operation: 33-1=32, Resulting Numbers: [85, 32] Generated Node #0,0,0: 90:[85, 32] Operation: 33-1=32 Exploring Operation: 85+1=86, Resulting Numbers: [33, 86] Generated Node #0,0,1: 90:[33, 86] Operation: 85+1=86 Exploring Operation: 85*1=85, Resulting Numbers: [33, 85] Generated Node #0,0,2: 90:[33, 85] Operation: 85*1=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[85, 32], Operations: ['25+8=33', '33-1=32'] Exploring Operation: 85*32=2720, Resulting Numbers: [2720] 2720,90 unequal: No Solution Exploring Operation: 85+32=117, Resulting Numbers: [117] 117,90 unequal: No Solution Exploring Operation: 85-32=53, Resulting Numbers: [53] 53,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[33, 86], Operations: ['25+8=33', '85+1=86'] Exploring Operation: 33+86=119, Resulting Numbers: [119] 119,90 unequal: No Solution Exploring Operation: 33*86=2838, Resulting Numbers: [2838] 2838,90 unequal: No Solution Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[33, 85], Operations: ['25+8=33', '85*1=85'] Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,90 unequal: No Solution Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,90 unequal: No Solution Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[25, 1, 93], Operations: ['85+8=93'] Exploring Operation: 25+1=26, Resulting Numbers: [93, 26] Generated Node #0,2,0: 90:[93, 26] Operation: 25+1=26 Exploring Operation: 93-1=92, Resulting Numbers: [25, 92] Generated Node #0,2,1: 90:[25, 92] Operation: 93-1=92 Exploring Operation: 25*1=25, Resulting Numbers: [93, 25] Generated Node #0,2,2: 90:[93, 25] Operation: 25*1=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[93, 26], Operations: ['85+8=93', '25+1=26'] Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,90 unequal: No Solution Exploring Operation: 93*26=2418, Resulting Numbers: [2418] 2418,90 unequal: No Solution Exploring Operation: 93+26=119, Resulting Numbers: [119] 119,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[25, 92], Operations: ['85+8=93', '93-1=92'] Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,90 unequal: No Solution Exploring Operation: 25*92=2300, Resulting Numbers: [2300] 2300,90 unequal: No Solution Exploring Operation: 25+92=117, Resulting Numbers: [117] 117,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[93, 25], Operations: ['85+8=93', '25*1=25'] Exploring Operation: 93-25=68, Resulting Numbers: [68] 68,90 unequal: No Solution Exploring Operation: 93*25=2325, Resulting Numbers: [2325] 2325,90 unequal: No Solution Exploring Operation: 93+25=118, Resulting Numbers: [118] 118,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 71, 67, 27, 61 ]
91
[ "67-61=6", "27*6=162", "162-71=91" ]
Current State: 91:[71, 67, 27, 61], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [71, 27, 6] Generated Node #2: [71, 27, 6] from Operation: 67-61=6 Current State: 91:[71, 27, 6], Operations: ['67-61=6'] Exploring Operation: 27*6=162, Resulting Numbers: [71, 162] Generated Node #3: [71, 162] from Operation: 27*6=162 Current State: 91:[71, 162], Operations: ['67-61=6', '27*6=162'] Exploring Operation: 162-71=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[71, 67, 27, 61], Operations: [] Exploring Operation: 71-67=4, Resulting Numbers: [27, 61, 4] Generated Node #0,0: 91:[27, 61, 4] Operation: 71-67=4 Exploring Operation: 67-61=6, Resulting Numbers: [71, 27, 6] Generated Node #0,1: 91:[71, 27, 6] Operation: 67-61=6 Exploring Operation: 71-61=10, Resulting Numbers: [67, 27, 10] Generated Node #0,2: 91:[67, 27, 10] Operation: 71-61=10 Exploring Operation: 27+61=88, Resulting Numbers: [71, 67, 88] Generated Node #0,3: 91:[71, 67, 88] Operation: 27+61=88 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[71, 27, 6], Operations: ['67-61=6'] Exploring Operation: 71+6=77, Resulting Numbers: [27, 77] Generated Node #0,1,0: 91:[27, 77] Operation: 71+6=77 Exploring Operation: 71-27=44, Resulting Numbers: [6, 44] Generated Node #0,1,1: 91:[6, 44] Operation: 71-27=44 Exploring Operation: 27-6=21, Resulting Numbers: [71, 21] Generated Node #0,1,2: 91:[71, 21] Operation: 27-6=21 Exploring Operation: 71+27=98, Resulting Numbers: [6, 98] Generated Node #0,1,3: 91:[6, 98] Operation: 71+27=98 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 91:[6, 98], Operations: ['67-61=6', '71+27=98'] Exploring Operation: 6+98=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 6*98=588, Resulting Numbers: [588] 588,91 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[27, 77], Operations: ['67-61=6', '71+6=77'] Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 27+77=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 27*77=2079, Resulting Numbers: [2079] 2079,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[71, 21], Operations: ['67-61=6', '27-6=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[6, 44], Operations: ['67-61=6', '71-27=44'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,91 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[67, 27, 10], Operations: ['71-61=10'] Exploring Operation: 67+27=94, Resulting Numbers: [10, 94] Generated Node #0,2,0: 91:[10, 94] Operation: 67+27=94 Exploring Operation: 27-10=17, Resulting Numbers: [67, 17] Generated Node #0,2,1: 91:[67, 17] Operation: 27-10=17 Exploring Operation: 67-27=40, Resulting Numbers: [10, 40] Generated Node #0,2,2: 91:[10, 40] Operation: 67-27=40 Exploring Operation: 67+10=77, Resulting Numbers: [27, 77] Generated Node #0,2,3: 91:[27, 77] Operation: 67+10=77 Moving to Node #0,2,0 Current State: 91:[10, 94], Operations: ['71-61=10', '67+27=94'] Exploring Operation: 10+94=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 10*94=940, Resulting Numbers: [940] 940,91 unequal: No Solution Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[27, 77], Operations: ['71-61=10', '67+10=77'] Exploring Operation: 27+77=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 27*77=2079, Resulting Numbers: [2079] 2079,91 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[67, 17], Operations: ['71-61=10', '27-10=17'] Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,91 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[10, 40], Operations: ['71-61=10', '67-27=40'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,91 unequal: No Solution Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[27, 61, 4], Operations: ['71-67=4'] Exploring Operation: 61+4=65, Resulting Numbers: [27, 65] Generated Node #0,0,0: 91:[27, 65] Operation: 61+4=65 Exploring Operation: 27+61=88, Resulting Numbers: [4, 88] Generated Node #0,0,1: 91:[4, 88] Operation: 27+61=88 Exploring Operation: 27-4=23, Resulting Numbers: [61, 23] Generated Node #0,0,2: 91:[61, 23] Operation: 27-4=23 Exploring Operation: 61-27=34, Resulting Numbers: [4, 34] Generated Node #0,0,3: 91:[4, 34] Operation: 61-27=34 Moving to Node #0,0,1 Current State: 91:[4, 88], Operations: ['71-67=4', '27+61=88'] Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 4*88=352, Resulting Numbers: [352] 352,91 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[4, 34], Operations: ['71-67=4', '61-27=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,91 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,91 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[61, 23], Operations: ['71-67=4', '27-4=23'] Exploring Operation: 61+23=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 61*23=1403, Resulting Numbers: [1403] 1403,91 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[27, 65], Operations: ['71-67=4', '61+4=65'] Exploring Operation: 27+65=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 27*65=1755, Resulting Numbers: [1755] 1755,91 unequal: No Solution Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[71, 67, 88], Operations: ['27+61=88'] Exploring Operation: 71-67=4, Resulting Numbers: [88, 4] Generated Node #0,3,0: 91:[88, 4] Operation: 71-67=4 Exploring Operation: 88-67=21, Resulting Numbers: [71, 21] Generated Node #0,3,1: 91:[71, 21] Operation: 88-67=21 Exploring Operation: 88-71=17, Resulting Numbers: [67, 17] Generated Node #0,3,2: 91:[67, 17] Operation: 88-71=17 Exploring Operation: 71+67=138, Resulting Numbers: [88, 138] Generated Node #0,3,3: 91:[88, 138] Operation: 71+67=138 Moving to Node #0,3,0 Current State: 91:[88, 4], Operations: ['27+61=88', '71-67=4'] Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,91 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[67, 17], Operations: ['27+61=88', '88-71=17'] Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,91 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[71, 21], Operations: ['27+61=88', '88-67=21'] Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,91 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[88, 138], Operations: ['27+61=88', '71+67=138'] Exploring Operation: 88+138=226, Resulting Numbers: [226] 226,91 unequal: No Solution Exploring Operation: 138-88=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 88*138=12144, Resulting Numbers: [12144] 12144,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 56, 92, 4, 42 ]
75
[ "56+42=98", "92/4=23", "98-23=75" ]
Current State: 75:[56, 92, 4, 42], Operations: [] Exploring Operation: 56+42=98, Resulting Numbers: [92, 4, 98] Generated Node #2: [92, 4, 98] from Operation: 56+42=98 Current State: 75:[92, 4, 98], Operations: ['56+42=98'] Exploring Operation: 92/4=23, Resulting Numbers: [98, 23] Generated Node #3: [98, 23] from Operation: 92/4=23 Current State: 75:[98, 23], Operations: ['56+42=98', '92/4=23'] Exploring Operation: 98-23=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[56, 92, 4, 42], Operations: [] Exploring Operation: 92-56=36, Resulting Numbers: [4, 42, 36] Generated Node #0,0: 75:[4, 42, 36] Operation: 92-56=36 Exploring Operation: 56-42=14, Resulting Numbers: [92, 4, 14] Generated Node #0,1: 75:[92, 4, 14] Operation: 56-42=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[92, 4, 14], Operations: ['56-42=14'] Exploring Operation: 92-14=78, Resulting Numbers: [4, 78] Generated Node #0,1,0: 75:[4, 78] Operation: 92-14=78 Exploring Operation: 92/4=23, Resulting Numbers: [14, 23] Generated Node #0,1,1: 75:[14, 23] Operation: 92/4=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[14, 23], Operations: ['56-42=14', '92/4=23'] Exploring Operation: 14+23=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[4, 78], Operations: ['56-42=14', '92-14=78'] Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,75 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[4, 42, 36], Operations: ['92-56=36'] Exploring Operation: 42-36=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 75:[4, 6] Operation: 42-36=6 Exploring Operation: 42+36=78, Resulting Numbers: [4, 78] Generated Node #0,0,1: 75:[4, 78] Operation: 42+36=78 Moving to Node #0,0,0 Current State: 75:[4, 6], Operations: ['92-56=36', '42-36=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[4, 78], Operations: ['92-56=36', '42+36=78'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,75 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
[ 21, 87, 28, 54 ]
40
[ "87-21=66", "54-28=26", "66-26=40" ]
Current State: 40:[21, 87, 28, 54], Operations: [] Exploring Operation: 87-21=66, Resulting Numbers: [28, 54, 66] Generated Node #2: [28, 54, 66] from Operation: 87-21=66 Current State: 40:[28, 54, 66], Operations: ['87-21=66'] Exploring Operation: 54-28=26, Resulting Numbers: [66, 26] Generated Node #3: [66, 26] from Operation: 54-28=26 Current State: 40:[66, 26], Operations: ['87-21=66', '54-28=26'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[21, 87, 28, 54], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [21, 28, 33] Generated Node #0,0: 40:[21, 28, 33] Operation: 87-54=33 Exploring Operation: 87-28=59, Resulting Numbers: [21, 54, 59] Generated Node #0,1: 40:[21, 54, 59] Operation: 87-28=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[21, 28, 33], Operations: ['87-54=33'] Exploring Operation: 28-21=7, Resulting Numbers: [33, 7] Generated Node #0,0,0: 40:[33, 7] Operation: 28-21=7 Exploring Operation: 33-28=5, Resulting Numbers: [21, 5] Generated Node #0,0,1: 40:[21, 5] Operation: 33-28=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 40:[21, 5], Operations: ['87-54=33', '33-28=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,40 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,40 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 #0,0,0 Current State: 40:[33, 7], Operations: ['87-54=33', '28-21=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[21, 87, 28, 54], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [21, 28, 33] Generated Node #0,0: 40:[21, 28, 33] Operation: 87-54=33 Moving to Node #0,0 Current State: 40:[21, 28, 33], Operations: ['87-54=33'] Exploring Operation: 28-21=7, Resulting Numbers: [33, 7] Generated Node #0,0,0: 40:[33, 7] Operation: 28-21=7 Moving to Node #0,0,0 Current State: 40:[33, 7], Operations: ['87-54=33', '28-21=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 18, 52, 39, 11 ]
16
[ "52-18=34", "39+11=50", "50-34=16" ]
Current State: 16:[18, 52, 39, 11], Operations: [] Exploring Operation: 52-18=34, Resulting Numbers: [39, 11, 34] Generated Node #2: [39, 11, 34] from Operation: 52-18=34 Current State: 16:[39, 11, 34], Operations: ['52-18=34'] Exploring Operation: 39+11=50, Resulting Numbers: [34, 50] Generated Node #3: [34, 50] from Operation: 39+11=50 Current State: 16:[34, 50], Operations: ['52-18=34', '39+11=50'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[18, 52, 39, 11], Operations: [] Exploring Operation: 52-39=13, Resulting Numbers: [18, 11, 13] Generated Node #0,0: 16:[18, 11, 13] Operation: 52-39=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[18, 11, 13], Operations: ['52-39=13'] Exploring Operation: 13-11=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 16:[18, 2] Operation: 13-11=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[18, 2], Operations: ['52-39=13', '13-11=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[18, 52, 39, 11], Operations: [] Exploring Operation: 52-39=13, Resulting Numbers: [18, 11, 13] Generated Node #0,0: 16:[18, 11, 13] Operation: 52-39=13 Moving to Node #0,0 Current State: 16:[18, 11, 13], Operations: ['52-39=13'] Exploring Operation: 13-11=2, Resulting Numbers: [18, 2] Generated Node #0,0,0: 16:[18, 2] Operation: 13-11=2 Moving to Node #0,0,0 Current State: 16:[18, 2], Operations: ['52-39=13', '13-11=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 72, 94, 79, 87 ]
30
[ "94-72=22", "87-79=8", "22+8=30" ]
Current State: 30:[72, 94, 79, 87], Operations: [] Exploring Operation: 94-72=22, Resulting Numbers: [79, 87, 22] Generated Node #2: [79, 87, 22] from Operation: 94-72=22 Current State: 30:[79, 87, 22], Operations: ['94-72=22'] Exploring Operation: 87-79=8, Resulting Numbers: [22, 8] Generated Node #3: [22, 8] from Operation: 87-79=8 Current State: 30:[22, 8], Operations: ['94-72=22', '87-79=8'] Exploring Operation: 22+8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[72, 94, 79, 87], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [72, 79, 7] Generated Node #0,0: 30:[72, 79, 7] Operation: 94-87=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[72, 79, 7], Operations: ['94-87=7'] Exploring Operation: 79-72=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 30:[7, 7] Operation: 79-72=7 Moving to Node #0,0,0 Current State: 30:[7, 7], Operations: ['94-87=7', '79-72=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,30 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
[ 8, 64, 91, 29 ]
77
[ "8*29=232", "64+91=155", "232-155=77" ]
Current State: 77:[8, 64, 91, 29], Operations: [] Exploring Operation: 8*29=232, Resulting Numbers: [64, 91, 232] Generated Node #2: [64, 91, 232] from Operation: 8*29=232 Current State: 77:[64, 91, 232], Operations: ['8*29=232'] Exploring Operation: 64+91=155, Resulting Numbers: [232, 155] Generated Node #3: [232, 155] from Operation: 64+91=155 Current State: 77:[232, 155], Operations: ['8*29=232', '64+91=155'] Exploring Operation: 232-155=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[8, 64, 91, 29], Operations: [] Exploring Operation: 8+64=72, Resulting Numbers: [91, 29, 72] Generated Node #0,0: 77:[91, 29, 72] Operation: 8+64=72 Exploring Operation: 91-64=27, Resulting Numbers: [8, 29, 27] Generated Node #0,1: 77:[8, 29, 27] Operation: 91-64=27 Exploring Operation: 91-29=62, Resulting Numbers: [8, 64, 62] Generated Node #0,2: 77:[8, 64, 62] Operation: 91-29=62 Exploring Operation: 64+29=93, Resulting Numbers: [8, 91, 93] Generated Node #0,3: 77:[8, 91, 93] Operation: 64+29=93 Exploring Operation: 64/8=8, Resulting Numbers: [91, 29, 8] Generated Node #0,4: 77:[91, 29, 8] Operation: 64/8=8 Moving to Node #0,2 Current State: 77:[8, 64, 62], Operations: ['91-29=62'] Exploring Operation: 64-62=2, Resulting Numbers: [8, 2] Generated Node #0,2,0: 77:[8, 2] Operation: 64-62=2 Exploring Operation: 8+64=72, Resulting Numbers: [62, 72] Generated Node #0,2,1: 77:[62, 72] Operation: 8+64=72 Exploring Operation: 8+62=70, Resulting Numbers: [64, 70] Generated Node #0,2,2: 77:[64, 70] Operation: 8+62=70 Exploring Operation: 64-8=56, Resulting Numbers: [62, 56] Generated Node #0,2,3: 77:[62, 56] Operation: 64-8=56 Exploring Operation: 64/8=8, Resulting Numbers: [62, 8] Generated Node #0,2,4: 77:[62, 8] Operation: 64/8=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 77:[8, 2], Operations: ['91-29=62', '64-62=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 77:[62, 8], Operations: ['91-29=62', '64/8=8'] Exploring Operation: 62*8=496, Resulting Numbers: [496] 496,77 unequal: No Solution Exploring Operation: 62+8=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 77:[62, 72], Operations: ['91-29=62', '8+64=72'] Exploring Operation: 62*72=4464, Resulting Numbers: [4464] 4464,77 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 62+72=134, Resulting Numbers: [134] 134,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 77:[64, 70], Operations: ['91-29=62', '8+62=70'] Exploring Operation: 64+70=134, Resulting Numbers: [134] 134,77 unequal: No Solution Exploring Operation: 64*70=4480, Resulting Numbers: [4480] 4480,77 unequal: No Solution Exploring Operation: 70-64=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 #0,2,3 Current State: 77:[62, 56], Operations: ['91-29=62', '64-8=56'] Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,77 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,77 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:[8, 91, 93], Operations: ['64+29=93'] Exploring Operation: 91-8=83, Resulting Numbers: [93, 83] Generated Node #0,3,0: 77:[93, 83] Operation: 91-8=83 Exploring Operation: 8+93=101, Resulting Numbers: [91, 101] Generated Node #0,3,1: 77:[91, 101] Operation: 8+93=101 Exploring Operation: 93-8=85, Resulting Numbers: [91, 85] Generated Node #0,3,2: 77:[91, 85] Operation: 93-8=85 Exploring Operation: 8+91=99, Resulting Numbers: [93, 99] Generated Node #0,3,3: 77:[93, 99] Operation: 8+91=99 Exploring Operation: 93-91=2, Resulting Numbers: [8, 2] Generated Node #0,3,4: 77:[8, 2] Operation: 93-91=2 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 77:[8, 2], Operations: ['64+29=93', '93-91=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 8-2=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 #0,3,0 Current State: 77:[93, 83], Operations: ['64+29=93', '91-8=83'] Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,77 unequal: No Solution Exploring Operation: 93*83=7719, Resulting Numbers: [7719] 7719,77 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,77 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 #0,3,2 Current State: 77:[91, 85], Operations: ['64+29=93', '93-8=85'] Exploring Operation: 91-85=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 91+85=176, Resulting Numbers: [176] 176,77 unequal: No Solution Exploring Operation: 91*85=7735, Resulting Numbers: [7735] 7735,77 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 #0,3,1 Current State: 77:[91, 101], Operations: ['64+29=93', '8+93=101'] Exploring Operation: 101-91=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 91+101=192, Resulting Numbers: [192] 192,77 unequal: No Solution Exploring Operation: 91*101=9191, Resulting Numbers: [9191] 9191,77 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 #0,3,3 Current State: 77:[93, 99], Operations: ['64+29=93', '8+91=99'] Exploring Operation: 93*99=9207, Resulting Numbers: [9207] 9207,77 unequal: No Solution Exploring Operation: 93+99=192, Resulting Numbers: [192] 192,77 unequal: No Solution Exploring Operation: 99-93=6, Resulting Numbers: [6] 6,77 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:[91, 29, 8], Operations: ['64/8=8'] Exploring Operation: 91+8=99, Resulting Numbers: [29, 99] Generated Node #0,4,0: 77:[29, 99] Operation: 91+8=99 Exploring Operation: 29-8=21, Resulting Numbers: [91, 21] Generated Node #0,4,1: 77:[91, 21] Operation: 29-8=21 Exploring Operation: 29+8=37, Resulting Numbers: [91, 37] Generated Node #0,4,2: 77:[91, 37] Operation: 29+8=37 Exploring Operation: 91-29=62, Resulting Numbers: [8, 62] Generated Node #0,4,3: 77:[8, 62] Operation: 91-29=62 Exploring Operation: 91-8=83, Resulting Numbers: [29, 83] Generated Node #0,4,4: 77:[29, 83] Operation: 91-8=83 Moving to Node #0,1 Current State: 77:[8, 29, 27], Operations: ['91-64=27'] Exploring Operation: 29-8=21, Resulting Numbers: [27, 21] Generated Node #0,1,0: 77:[27, 21] Operation: 29-8=21 Exploring Operation: 29+27=56, Resulting Numbers: [8, 56] Generated Node #0,1,1: 77:[8, 56] Operation: 29+27=56 Exploring Operation: 8+29=37, Resulting Numbers: [27, 37] Generated Node #0,1,2: 77:[27, 37] Operation: 8+29=37 Exploring Operation: 27-8=19, Resulting Numbers: [29, 19] Generated Node #0,1,3: 77:[29, 19] Operation: 27-8=19 Exploring Operation: 29-27=2, Resulting Numbers: [8, 2] Generated Node #0,1,4: 77:[8, 2] Operation: 29-27=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 77:[8, 2], Operations: ['91-64=27', '29-27=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 8-2=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:[8, 56], Operations: ['91-64=27', '29+27=56'] Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 8*56=448, Resulting Numbers: [448] 448,77 unequal: No Solution Exploring Operation: 8+56=64, Resulting Numbers: [64] 64,77 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:[27, 21], Operations: ['91-64=27', '29-8=21'] Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,77 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 27-21=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 #0,1,3 Current State: 77:[29, 19], Operations: ['91-64=27', '27-8=19'] Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,77 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,77 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 #0,1,2 Current State: 77:[27, 37], Operations: ['91-64=27', '8+29=37'] Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,77 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,77 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:[91, 29, 72], Operations: ['8+64=72'] Exploring Operation: 29+72=101, Resulting Numbers: [91, 101] Generated Node #0,0,0: 77:[91, 101] Operation: 29+72=101 Exploring Operation: 91+29=120, Resulting Numbers: [72, 120] Generated Node #0,0,1: 77:[72, 120] Operation: 91+29=120 Exploring Operation: 72-29=43, Resulting Numbers: [91, 43] Generated Node #0,0,2: 77:[91, 43] Operation: 72-29=43 Exploring Operation: 91-72=19, Resulting Numbers: [29, 19] Generated Node #0,0,3: 77:[29, 19] Operation: 91-72=19 Exploring Operation: 91-29=62, Resulting Numbers: [72, 62] Generated Node #0,0,4: 77:[72, 62] Operation: 91-29=62 Moving to Node #0,4,3 Current State: 77:[8, 62], Operations: ['64/8=8', '91-29=62'] Exploring Operation: 8*62=496, Resulting Numbers: [496] 496,77 unequal: No Solution Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 8+62=70, Resulting Numbers: [70] 70,77 unequal: No Solution Moving to Node #0,0,4 Current State: 77:[72, 62], Operations: ['8+64=72', '91-29=62'] Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,77 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,77 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,77 unequal: No Solution Moving to Node #0,4,4 Current State: 77:[29, 83], Operations: ['64/8=8', '91-8=83'] Exploring Operation: 29*83=2407, Resulting Numbers: [2407] 2407,77 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 29+83=112, Resulting Numbers: [112] 112,77 unequal: No Solution Moving to Node #0,4,1 Current State: 77:[91, 21], Operations: ['64/8=8', '29-8=21'] Exploring Operation: 91+21=112, Resulting Numbers: [112] 112,77 unequal: No Solution Exploring Operation: 91-21=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 91*21=1911, Resulting Numbers: [1911] 1911,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[29, 19], Operations: ['8+64=72', '91-72=19'] Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,77 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[91, 101], Operations: ['8+64=72', '29+72=101'] Exploring Operation: 101-91=10, Resulting Numbers: [10] 10,77 unequal: No Solution Exploring Operation: 91*101=9191, Resulting Numbers: [9191] 9191,77 unequal: No Solution Exploring Operation: 91+101=192, Resulting Numbers: [192] 192,77 unequal: No Solution Moving to Node #0,4,2 Current State: 77:[91, 37], Operations: ['64/8=8', '29+8=37'] Exploring Operation: 91*37=3367, Resulting Numbers: [3367] 3367,77 unequal: No Solution Exploring Operation: 91+37=128, Resulting Numbers: [128] 128,77 unequal: No Solution Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,77 unequal: No Solution Moving to Node #0,4,0 Current State: 77:[29, 99], Operations: ['64/8=8', '91+8=99'] Exploring Operation: 29*99=2871, Resulting Numbers: [2871] 2871,77 unequal: No Solution Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 29+99=128, Resulting Numbers: [128] 128,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[91, 43], Operations: ['8+64=72', '72-29=43'] Exploring Operation: 91*43=3913, Resulting Numbers: [3913] 3913,77 unequal: No Solution Exploring Operation: 91-43=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 91+43=134, Resulting Numbers: [134] 134,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[72, 120], Operations: ['8+64=72', '91+29=120'] Exploring Operation: 120-72=48, Resulting Numbers: [48] 48,77 unequal: No Solution Exploring Operation: 72*120=8640, Resulting Numbers: [8640] 8640,77 unequal: No Solution Exploring Operation: 72+120=192, Resulting Numbers: [192] 192,77 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 36, 76, 37, 26 ]
23
[ "76-36=40", "37+26=63", "63-40=23" ]
Current State: 23:[36, 76, 37, 26], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [37, 26, 40] Generated Node #2: [37, 26, 40] from Operation: 76-36=40 Current State: 23:[37, 26, 40], Operations: ['76-36=40'] Exploring Operation: 37+26=63, Resulting Numbers: [40, 63] Generated Node #3: [40, 63] from Operation: 37+26=63 Current State: 23:[40, 63], Operations: ['76-36=40', '37+26=63'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[36, 76, 37, 26], Operations: [] Exploring Operation: 76-37=39, Resulting Numbers: [36, 26, 39] Generated Node #0,0: 23:[36, 26, 39] Operation: 76-37=39 Exploring Operation: 76-36=40, Resulting Numbers: [37, 26, 40] Generated Node #0,1: 23:[37, 26, 40] Operation: 76-36=40 Moving to Node #0,0 Current State: 23:[36, 26, 39], Operations: ['76-37=39'] Exploring Operation: 39-26=13, Resulting Numbers: [36, 13] Generated Node #0,0,0: 23:[36, 13] Operation: 39-26=13 Exploring Operation: 39-36=3, Resulting Numbers: [26, 3] Generated Node #0,0,1: 23:[26, 3] Operation: 39-36=3 Moving to Node #0,1 Current State: 23:[37, 26, 40], Operations: ['76-36=40'] Exploring Operation: 40-26=14, Resulting Numbers: [37, 14] Generated Node #0,1,0: 23:[37, 14] Operation: 40-26=14 Exploring Operation: 40-37=3, Resulting Numbers: [26, 3] Generated Node #0,1,1: 23:[26, 3] Operation: 40-37=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[37, 14], Operations: ['76-36=40', '40-26=14'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[36, 76, 37, 26], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [37, 26, 40] Generated Node #0,1: 23:[37, 26, 40] Operation: 76-36=40 Moving to Node #0,1 Current State: 23:[37, 26, 40], Operations: ['76-36=40'] Exploring Operation: 40-26=14, Resulting Numbers: [37, 14] Generated Node #0,1,0: 23:[37, 14] Operation: 40-26=14 Moving to Node #0,1,0 Current State: 23:[37, 14], Operations: ['76-36=40', '40-26=14'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 6, 64, 23, 69 ]
46
[ "6*69=414", "414/23=18", "64-18=46" ]
Current State: 46:[6, 64, 23, 69], Operations: [] Exploring Operation: 6*69=414, Resulting Numbers: [64, 23, 414] Generated Node #2: [64, 23, 414] from Operation: 6*69=414 Current State: 46:[64, 23, 414], Operations: ['6*69=414'] Exploring Operation: 414/23=18, Resulting Numbers: [64, 18] Generated Node #3: [64, 18] from Operation: 414/23=18 Current State: 46:[64, 18], Operations: ['6*69=414', '414/23=18'] Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[6, 64, 23, 69], Operations: [] Exploring Operation: 69-23=46, Resulting Numbers: [6, 64, 46] Generated Node #0,0: 46:[6, 64, 46] Operation: 69-23=46 Exploring Operation: 69-64=5, Resulting Numbers: [6, 23, 5] Generated Node #0,1: 46:[6, 23, 5] Operation: 69-64=5 Moving to Node #0,1 Current State: 46:[6, 23, 5], Operations: ['69-64=5'] Exploring Operation: 6-5=1, Resulting Numbers: [23, 1] Generated Node #0,1,0: 46:[23, 1] Operation: 6-5=1 Exploring Operation: 6*5=30, Resulting Numbers: [23, 30] Generated Node #0,1,1: 46:[23, 30] Operation: 6*5=30 Moving to Node #0,0 Current State: 46:[6, 64, 46], Operations: ['69-23=46'] Exploring Operation: 64-46=18, Resulting Numbers: [6, 18] Generated Node #0,0,0: 46:[6, 18] Operation: 64-46=18 Exploring Operation: 64-6=58, Resulting Numbers: [46, 58] Generated Node #0,0,1: 46:[46, 58] Operation: 64-6=58 Moving to Node #0,1,0 Current State: 46:[23, 1], Operations: ['69-64=5', '6-5=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[23, 30], Operations: ['69-64=5', '6*5=30'] Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[6, 18], Operations: ['69-23=46', '64-46=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[46, 58], Operations: ['69-23=46', '64-6=58'] Exploring Operation: 58-46=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 46+58=104, Resulting Numbers: [104] 104,46 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 84, 5, 77, 95 ]
12
[ "84-77=7", "95/5=19", "19-7=12" ]
Current State: 12:[84, 5, 77, 95], Operations: [] Exploring Operation: 84-77=7, Resulting Numbers: [5, 95, 7] Generated Node #2: [5, 95, 7] from Operation: 84-77=7 Current State: 12:[5, 95, 7], Operations: ['84-77=7'] Exploring Operation: 95/5=19, Resulting Numbers: [7, 19] Generated Node #3: [7, 19] from Operation: 95/5=19 Current State: 12:[7, 19], Operations: ['84-77=7', '95/5=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[84, 5, 77, 95], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [5, 77, 11] Generated Node #0,0: 12:[5, 77, 11] Operation: 95-84=11 Moving to Node #0,0 Current State: 12:[5, 77, 11], Operations: ['95-84=11'] Exploring Operation: 77/11=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 77/11=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['95-84=11', '77/11=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[84, 5, 77, 95], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [5, 77, 11] Generated Node #0,0: 12:[5, 77, 11] Operation: 95-84=11 Moving to Node #0,0 Current State: 12:[5, 77, 11], Operations: ['95-84=11'] Exploring Operation: 77/11=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 12:[5, 7] Operation: 77/11=7 Moving to Node #0,0,0 Current State: 12:[5, 7], Operations: ['95-84=11', '77/11=7'] Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 8, 25, 47, 26 ]
90
[ "25-8=17", "47+26=73", "17+73=90" ]
Current State: 90:[8, 25, 47, 26], Operations: [] Exploring Operation: 25-8=17, Resulting Numbers: [47, 26, 17] Generated Node #2: [47, 26, 17] from Operation: 25-8=17 Current State: 90:[47, 26, 17], Operations: ['25-8=17'] Exploring Operation: 47+26=73, Resulting Numbers: [17, 73] Generated Node #3: [17, 73] from Operation: 47+26=73 Current State: 90:[17, 73], Operations: ['25-8=17', '47+26=73'] Exploring Operation: 17+73=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[8, 25, 47, 26], Operations: [] Exploring Operation: 8+25=33, Resulting Numbers: [47, 26, 33] Generated Node #0,0: 90:[47, 26, 33] Operation: 8+25=33 Exploring Operation: 25-8=17, Resulting Numbers: [47, 26, 17] Generated Node #0,1: 90:[47, 26, 17] Operation: 25-8=17 Exploring Operation: 26-8=18, Resulting Numbers: [25, 47, 18] Generated Node #0,2: 90:[25, 47, 18] Operation: 26-8=18 Exploring Operation: 26-25=1, Resulting Numbers: [8, 47, 1] Generated Node #0,3: 90:[8, 47, 1] Operation: 26-25=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[8, 47, 1], Operations: ['26-25=1'] Exploring Operation: 8-1=7, Resulting Numbers: [47, 7] Generated Node #0,3,0: 90:[47, 7] Operation: 8-1=7 Exploring Operation: 47-1=46, Resulting Numbers: [8, 46] Generated Node #0,3,1: 90:[8, 46] Operation: 47-1=46 Exploring Operation: 8*1=8, Resulting Numbers: [47, 8] Generated Node #0,3,2: 90:[47, 8] Operation: 8*1=8 Exploring Operation: 8+1=9, Resulting Numbers: [47, 9] Generated Node #0,3,3: 90:[47, 9] Operation: 8+1=9 Moving to Node #0,3,1 Current State: 90:[8, 46], Operations: ['26-25=1', '47-1=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,90 unequal: No Solution Exploring Operation: 8*46=368, Resulting Numbers: [368] 368,90 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[47, 9], Operations: ['26-25=1', '8+1=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,90 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[47, 8], Operations: ['26-25=1', '8*1=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,90 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,90 unequal: No Solution Moving to Node #0,3,0 Current State: 90:[47, 7], Operations: ['26-25=1', '8-1=7'] Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,90 unequal: No Solution Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,90 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,90 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 #0,1 Current State: 90:[47, 26, 17], Operations: ['25-8=17'] Exploring Operation: 26+17=43, Resulting Numbers: [47, 43] Generated Node #0,1,0: 90:[47, 43] Operation: 26+17=43 Exploring Operation: 47-26=21, Resulting Numbers: [17, 21] Generated Node #0,1,1: 90:[17, 21] Operation: 47-26=21 Exploring Operation: 26-17=9, Resulting Numbers: [47, 9] Generated Node #0,1,2: 90:[47, 9] Operation: 26-17=9 Exploring Operation: 47-17=30, Resulting Numbers: [26, 30] Generated Node #0,1,3: 90:[26, 30] Operation: 47-17=30 Moving to Node #0,1,2 Current State: 90:[47, 9], Operations: ['25-8=17', '26-17=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 47*9=423, Resulting Numbers: [423] 423,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[17, 21], Operations: ['25-8=17', '47-26=21'] Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,90 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[47, 43], Operations: ['25-8=17', '26+17=43'] Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,90 unequal: No Solution Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[8, 25, 47, 26], Operations: [] Exploring Operation: 25-8=17, Resulting Numbers: [47, 26, 17] Generated Node #0,1: 90:[47, 26, 17] Operation: 25-8=17 Moving to Node #0,1 Current State: 90:[47, 26, 17], Operations: ['25-8=17'] Exploring Operation: 26+17=43, Resulting Numbers: [47, 43] Generated Node #0,1,0: 90:[47, 43] Operation: 26+17=43 Moving to Node #0,1,0 Current State: 90:[47, 43], Operations: ['25-8=17', '26+17=43'] Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 61, 4, 3, 29 ]
13
[ "61+3=64", "64/4=16", "29-16=13" ]
Current State: 13:[61, 4, 3, 29], Operations: [] Exploring Operation: 61+3=64, Resulting Numbers: [4, 29, 64] Generated Node #2: [4, 29, 64] from Operation: 61+3=64 Current State: 13:[4, 29, 64], Operations: ['61+3=64'] Exploring Operation: 64/4=16, Resulting Numbers: [29, 16] Generated Node #3: [29, 16] from Operation: 64/4=16 Current State: 13:[29, 16], Operations: ['61+3=64', '64/4=16'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[61, 4, 3, 29], Operations: [] Exploring Operation: 61-4=57, Resulting Numbers: [3, 29, 57] Generated Node #0,0: 13:[3, 29, 57] Operation: 61-4=57 Exploring Operation: 4*3=12, Resulting Numbers: [61, 29, 12] Generated Node #0,1: 13:[61, 29, 12] Operation: 4*3=12 Exploring Operation: 61-29=32, Resulting Numbers: [4, 3, 32] Generated Node #0,2: 13:[4, 3, 32] Operation: 61-29=32 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[4, 3, 32], Operations: ['61-29=32'] Exploring Operation: 4+3=7, Resulting Numbers: [32, 7] Generated Node #0,2,0: 13:[32, 7] Operation: 4+3=7 Exploring Operation: 32/4=8, Resulting Numbers: [3, 8] Generated Node #0,2,1: 13:[3, 8] Operation: 32/4=8 Exploring Operation: 4*3=12, Resulting Numbers: [32, 12] Generated Node #0,2,2: 13:[32, 12] Operation: 4*3=12 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[3, 8], Operations: ['61-29=32', '32/4=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,13 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,13 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[32, 12], Operations: ['61-29=32', '4*3=12'] Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,13 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[32, 7], Operations: ['61-29=32', '4+3=7'] Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,13 unequal: No Solution Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[61, 29, 12], Operations: ['4*3=12'] Exploring Operation: 61-12=49, Resulting Numbers: [29, 49] Generated Node #0,1,0: 13:[29, 49] Operation: 61-12=49 Exploring Operation: 29-12=17, Resulting Numbers: [61, 17] Generated Node #0,1,1: 13:[61, 17] Operation: 29-12=17 Exploring Operation: 61-29=32, Resulting Numbers: [12, 32] Generated Node #0,1,2: 13:[12, 32] Operation: 61-29=32 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[12, 32], Operations: ['4*3=12', '61-29=32'] Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,13 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[29, 49], Operations: ['4*3=12', '61-12=49'] Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 29*49=1421, Resulting Numbers: [1421] 1421,13 unequal: No Solution Exploring Operation: 29+49=78, Resulting Numbers: [78] 78,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[61, 17], Operations: ['4*3=12', '29-12=17'] Exploring Operation: 61*17=1037, Resulting Numbers: [1037] 1037,13 unequal: No Solution Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,13 unequal: No Solution Exploring Operation: 61+17=78, Resulting Numbers: [78] 78,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[3, 29, 57], Operations: ['61-4=57'] Exploring Operation: 57/3=19, Resulting Numbers: [29, 19] Generated Node #0,0,0: 13:[29, 19] Operation: 57/3=19 Exploring Operation: 29-3=26, Resulting Numbers: [57, 26] Generated Node #0,0,1: 13:[57, 26] Operation: 29-3=26 Exploring Operation: 57-29=28, Resulting Numbers: [3, 28] Generated Node #0,0,2: 13:[3, 28] Operation: 57-29=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[29, 19], Operations: ['61-4=57', '57/3=19'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 13:[3, 28], Operations: ['61-4=57', '57-29=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,13 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[57, 26], Operations: ['61-4=57', '29-3=26'] Exploring Operation: 57*26=1482, Resulting Numbers: [1482] 1482,13 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 57+26=83, Resulting Numbers: [83] 83,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 26, 2, 42, 76 ]
66
[ "26*2=52", "42+76=118", "118-52=66" ]
Current State: 66:[26, 2, 42, 76], Operations: [] Exploring Operation: 26*2=52, Resulting Numbers: [42, 76, 52] Generated Node #2: [42, 76, 52] from Operation: 26*2=52 Current State: 66:[42, 76, 52], Operations: ['26*2=52'] Exploring Operation: 42+76=118, Resulting Numbers: [52, 118] Generated Node #3: [52, 118] from Operation: 42+76=118 Current State: 66:[52, 118], Operations: ['26*2=52', '42+76=118'] Exploring Operation: 118-52=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[26, 2, 42, 76], Operations: [] Exploring Operation: 42-26=16, Resulting Numbers: [2, 76, 16] Generated Node #0,0: 66:[2, 76, 16] Operation: 42-26=16 Exploring Operation: 26+42=68, Resulting Numbers: [2, 76, 68] Generated Node #0,1: 66:[2, 76, 68] Operation: 26+42=68 Exploring Operation: 76-42=34, Resulting Numbers: [26, 2, 34] Generated Node #0,2: 66:[26, 2, 34] Operation: 76-42=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[26, 2, 34], Operations: ['76-42=34'] Exploring Operation: 34-26=8, Resulting Numbers: [2, 8] Generated Node #0,2,0: 66:[2, 8] Operation: 34-26=8 Exploring Operation: 26/2=13, Resulting Numbers: [34, 13] Generated Node #0,2,1: 66:[34, 13] Operation: 26/2=13 Exploring Operation: 26-2=24, Resulting Numbers: [34, 24] Generated Node #0,2,2: 66:[34, 24] Operation: 26-2=24 Moving to Node #0,2,0 Current State: 66:[2, 8], Operations: ['76-42=34', '34-26=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,66 unequal: No Solution Moving to Node #0,2,1 Current State: 66:[34, 13], Operations: ['76-42=34', '26/2=13'] Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,66 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,66 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[34, 24], Operations: ['76-42=34', '26-2=24'] Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,66 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,66 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:[2, 76, 68], Operations: ['26+42=68'] Exploring Operation: 76/2=38, Resulting Numbers: [68, 38] Generated Node #0,1,0: 66:[68, 38] Operation: 76/2=38 Exploring Operation: 76-68=8, Resulting Numbers: [2, 8] Generated Node #0,1,1: 66:[2, 8] Operation: 76-68=8 Exploring Operation: 76-2=74, Resulting Numbers: [68, 74] Generated Node #0,1,2: 66:[68, 74] Operation: 76-2=74 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[2, 8], Operations: ['26+42=68', '76-68=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,66 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,66 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:[68, 38], Operations: ['26+42=68', '76/2=38'] Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,66 unequal: No Solution Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,66 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:[68, 74], Operations: ['26+42=68', '76-2=74'] Exploring Operation: 68*74=5032, Resulting Numbers: [5032] 5032,66 unequal: No Solution Exploring Operation: 68+74=142, Resulting Numbers: [142] 142,66 unequal: No Solution Exploring Operation: 74-68=6, Resulting Numbers: [6] 6,66 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:[2, 76, 16], Operations: ['42-26=16'] Exploring Operation: 76/2=38, Resulting Numbers: [16, 38] Generated Node #0,0,0: 66:[16, 38] Operation: 76/2=38 Exploring Operation: 2*16=32, Resulting Numbers: [76, 32] Generated Node #0,0,1: 66:[76, 32] Operation: 2*16=32 Exploring Operation: 76-16=60, Resulting Numbers: [2, 60] Generated Node #0,0,2: 66:[2, 60] Operation: 76-16=60 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 66:[2, 60], Operations: ['42-26=16', '76-16=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,66 unequal: No Solution Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,66 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 #0,0,0 Current State: 66:[16, 38], Operations: ['42-26=16', '76/2=38'] Exploring Operation: 16*38=608, Resulting Numbers: [608] 608,66 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,66 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:[76, 32], Operations: ['42-26=16', '2*16=32'] Exploring Operation: 76*32=2432, Resulting Numbers: [2432] 2432,66 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 76+32=108, Resulting Numbers: [108] 108,66 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 93, 26, 89, 50 ]
57
[ "93+89=182", "182/26=7", "50+7=57" ]
Current State: 57:[93, 26, 89, 50], Operations: [] Exploring Operation: 93+89=182, Resulting Numbers: [26, 50, 182] Generated Node #2: [26, 50, 182] from Operation: 93+89=182 Current State: 57:[26, 50, 182], Operations: ['93+89=182'] Exploring Operation: 182/26=7, Resulting Numbers: [50, 7] Generated Node #3: [50, 7] from Operation: 182/26=7 Current State: 57:[50, 7], Operations: ['93+89=182', '182/26=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[93, 26, 89, 50], Operations: [] Exploring Operation: 93-26=67, Resulting Numbers: [89, 50, 67] Generated Node #0,0: 57:[89, 50, 67] Operation: 93-26=67 Exploring Operation: 89-26=63, Resulting Numbers: [93, 50, 63] Generated Node #0,1: 57:[93, 50, 63] Operation: 89-26=63 Exploring Operation: 93-89=4, Resulting Numbers: [26, 50, 4] Generated Node #0,2: 57:[26, 50, 4] Operation: 93-89=4 Exploring Operation: 93-50=43, Resulting Numbers: [26, 89, 43] Generated Node #0,3: 57:[26, 89, 43] Operation: 93-50=43 Exploring Operation: 89-50=39, Resulting Numbers: [93, 26, 39] Generated Node #0,4: 57:[93, 26, 39] Operation: 89-50=39 Moving to Node #0,2 Current State: 57:[26, 50, 4], Operations: ['93-89=4'] Exploring Operation: 50+4=54, Resulting Numbers: [26, 54] Generated Node #0,2,0: 57:[26, 54] Operation: 50+4=54 Exploring Operation: 50-26=24, Resulting Numbers: [4, 24] Generated Node #0,2,1: 57:[4, 24] Operation: 50-26=24 Exploring Operation: 50-4=46, Resulting Numbers: [26, 46] Generated Node #0,2,2: 57:[26, 46] Operation: 50-4=46 Exploring Operation: 26-4=22, Resulting Numbers: [50, 22] Generated Node #0,2,3: 57:[50, 22] Operation: 26-4=22 Exploring Operation: 26+4=30, Resulting Numbers: [50, 30] Generated Node #0,2,4: 57:[50, 30] Operation: 26+4=30 Moving to Node #0,1 Current State: 57:[93, 50, 63], Operations: ['89-26=63'] Exploring Operation: 93-50=43, Resulting Numbers: [63, 43] Generated Node #0,1,0: 57:[63, 43] Operation: 93-50=43 Exploring Operation: 63-50=13, Resulting Numbers: [93, 13] Generated Node #0,1,1: 57:[93, 13] Operation: 63-50=13 Exploring Operation: 93+50=143, Resulting Numbers: [63, 143] Generated Node #0,1,2: 57:[63, 143] Operation: 93+50=143 Exploring Operation: 93-63=30, Resulting Numbers: [50, 30] Generated Node #0,1,3: 57:[50, 30] Operation: 93-63=30 Exploring Operation: 50+63=113, Resulting Numbers: [93, 113] Generated Node #0,1,4: 57:[93, 113] Operation: 50+63=113 Moving to Node #0,0 Current State: 57:[89, 50, 67], Operations: ['93-26=67'] Exploring Operation: 89-67=22, Resulting Numbers: [50, 22] Generated Node #0,0,0: 57:[50, 22] Operation: 89-67=22 Exploring Operation: 50+67=117, Resulting Numbers: [89, 117] Generated Node #0,0,1: 57:[89, 117] Operation: 50+67=117 Exploring Operation: 89-50=39, Resulting Numbers: [67, 39] Generated Node #0,0,2: 57:[67, 39] Operation: 89-50=39 Exploring Operation: 67-50=17, Resulting Numbers: [89, 17] Generated Node #0,0,3: 57:[89, 17] Operation: 67-50=17 Exploring Operation: 89+50=139, Resulting Numbers: [67, 139] Generated Node #0,0,4: 57:[67, 139] Operation: 89+50=139 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[50, 22], Operations: ['93-26=67', '89-67=22'] Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,57 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:[67, 39], Operations: ['93-26=67', '89-50=39'] Exploring Operation: 67+39=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 67*39=2613, Resulting Numbers: [2613] 2613,57 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[89, 17], Operations: ['93-26=67', '67-50=17'] Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 89+17=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 89*17=1513, Resulting Numbers: [1513] 1513,57 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:[89, 117], Operations: ['93-26=67', '50+67=117'] Exploring Operation: 117-89=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 89*117=10413, Resulting Numbers: [10413] 10413,57 unequal: No Solution Exploring Operation: 89+117=206, Resulting Numbers: [206] 206,57 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 #0,0,4 Current State: 57:[67, 139], Operations: ['93-26=67', '89+50=139'] Exploring Operation: 67*139=9313, Resulting Numbers: [9313] 9313,57 unequal: No Solution Exploring Operation: 139-67=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 67+139=206, Resulting Numbers: [206] 206,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 57:[26, 89, 43], Operations: ['93-50=43'] Exploring Operation: 26+89=115, Resulting Numbers: [43, 115] Generated Node #0,3,0: 57:[43, 115] Operation: 26+89=115 Exploring Operation: 89-26=63, Resulting Numbers: [43, 63] Generated Node #0,3,1: 57:[43, 63] Operation: 89-26=63 Exploring Operation: 43-26=17, Resulting Numbers: [89, 17] Generated Node #0,3,2: 57:[89, 17] Operation: 43-26=17 Exploring Operation: 26+43=69, Resulting Numbers: [89, 69] Generated Node #0,3,3: 57:[89, 69] Operation: 26+43=69 Exploring Operation: 89-43=46, Resulting Numbers: [26, 46] Generated Node #0,3,4: 57:[26, 46] Operation: 89-43=46 Moving to Node #0,4 Current State: 57:[93, 26, 39], Operations: ['89-50=39'] Exploring Operation: 93+26=119, Resulting Numbers: [39, 119] Generated Node #0,4,0: 57:[39, 119] Operation: 93+26=119 Exploring Operation: 39-26=13, Resulting Numbers: [93, 13] Generated Node #0,4,1: 57:[93, 13] Operation: 39-26=13 Exploring Operation: 26+39=65, Resulting Numbers: [93, 65] Generated Node #0,4,2: 57:[93, 65] Operation: 26+39=65 Exploring Operation: 93-26=67, Resulting Numbers: [39, 67] Generated Node #0,4,3: 57:[39, 67] Operation: 93-26=67 Exploring Operation: 93-39=54, Resulting Numbers: [26, 54] Generated Node #0,4,4: 57:[26, 54] Operation: 93-39=54 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[26, 54], Operations: ['89-50=39', '93-39=54'] Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 26*54=1404, Resulting Numbers: [1404] 1404,57 unequal: No Solution Exploring Operation: 26+54=80, Resulting Numbers: [80] 80,57 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 #0,4,3 Current State: 57:[39, 67], Operations: ['89-50=39', '93-26=67'] Exploring Operation: 39+67=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 39*67=2613, Resulting Numbers: [2613] 2613,57 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,57 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 #0,4,1 Current State: 57:[93, 13], Operations: ['89-50=39', '39-26=13'] Exploring Operation: 93+13=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 93*13=1209, Resulting Numbers: [1209] 1209,57 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 #0,4,2 Current State: 57:[93, 65], Operations: ['89-50=39', '26+39=65'] Exploring Operation: 93+65=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 93-65=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 93*65=6045, Resulting Numbers: [6045] 6045,57 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 #0,4,0 Current State: 57:[39, 119], Operations: ['89-50=39', '93+26=119'] Exploring Operation: 119-39=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 39+119=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 39*119=4641, Resulting Numbers: [4641] 4641,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 57:[4, 24], Operations: ['93-89=4', '50-26=24'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,57 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[50, 22], Operations: ['93-89=4', '26-4=22'] Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,57 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[26, 54], Operations: ['93-89=4', '50+4=54'] Exploring Operation: 26*54=1404, Resulting Numbers: [1404] 1404,57 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 26+54=80, Resulting Numbers: [80] 80,57 unequal: No Solution Moving to Node #0,1,3 Current State: 57:[50, 30], Operations: ['89-26=63', '93-63=30'] Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,57 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,2,4 Current State: 57:[50, 30], Operations: ['93-89=4', '26+4=30'] Exploring Operation: 50+30=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 50*30=1500, Resulting Numbers: [1500] 1500,57 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,3,4 Current State: 57:[26, 46], Operations: ['93-50=43', '89-43=46'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,57 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[26, 46], Operations: ['93-89=4', '50-4=46'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[63, 43], Operations: ['89-26=63', '93-50=43'] Exploring Operation: 63+43=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 63*43=2709, Resulting Numbers: [2709] 2709,57 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[43, 63], Operations: ['93-50=43', '89-26=63'] Exploring Operation: 43+63=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 43*63=2709, Resulting Numbers: [2709] 2709,57 unequal: No Solution Moving to Node #0,3,2 Current State: 57:[89, 17], Operations: ['93-50=43', '43-26=17'] Exploring Operation: 89+17=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 89*17=1513, Resulting Numbers: [1513] 1513,57 unequal: No Solution Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[93, 13], Operations: ['89-26=63', '63-50=13'] Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 93*13=1209, Resulting Numbers: [1209] 1209,57 unequal: No Solution Exploring Operation: 93+13=106, Resulting Numbers: [106] 106,57 unequal: No Solution Moving to Node #0,3,3 Current State: 57:[89, 69], Operations: ['93-50=43', '26+43=69'] Exploring Operation: 89+69=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 89*69=6141, Resulting Numbers: [6141] 6141,57 unequal: No Solution Exploring Operation: 89-69=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[43, 115], Operations: ['93-50=43', '26+89=115'] Exploring Operation: 43+115=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 115-43=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 43*115=4945, Resulting Numbers: [4945] 4945,57 unequal: No Solution Moving to Node #0,1,4 Current State: 57:[93, 113], Operations: ['89-26=63', '50+63=113'] Exploring Operation: 113-93=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 93+113=206, Resulting Numbers: [206] 206,57 unequal: No Solution Exploring Operation: 93*113=10509, Resulting Numbers: [10509] 10509,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[63, 143], Operations: ['89-26=63', '93+50=143'] Exploring Operation: 63*143=9009, Resulting Numbers: [9009] 9009,57 unequal: No Solution Exploring Operation: 143-63=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 63+143=206, Resulting Numbers: [206] 206,57 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 12, 6, 39, 90 ]
20
[ "39-12=27", "6*90=540", "540/27=20" ]
Current State: 20:[12, 6, 39, 90], Operations: [] Exploring Operation: 39-12=27, Resulting Numbers: [6, 90, 27] Generated Node #2: [6, 90, 27] from Operation: 39-12=27 Current State: 20:[6, 90, 27], Operations: ['39-12=27'] Exploring Operation: 6*90=540, Resulting Numbers: [27, 540] Generated Node #3: [27, 540] from Operation: 6*90=540 Current State: 20:[27, 540], Operations: ['39-12=27', '6*90=540'] Exploring Operation: 540/27=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[12, 6, 39, 90], Operations: [] Exploring Operation: 90-39=51, Resulting Numbers: [12, 6, 51] Generated Node #0,0: 20:[12, 6, 51] Operation: 90-39=51 Exploring Operation: 39-12=27, Resulting Numbers: [6, 90, 27] Generated Node #0,1: 20:[6, 90, 27] Operation: 39-12=27 Exploring Operation: 90/6=15, Resulting Numbers: [12, 39, 15] Generated Node #0,2: 20:[12, 39, 15] Operation: 90/6=15 Moving to Node #0,2 Current State: 20:[12, 39, 15], Operations: ['90/6=15'] Exploring Operation: 15-12=3, Resulting Numbers: [39, 3] Generated Node #0,2,0: 20:[39, 3] Operation: 15-12=3 Exploring Operation: 39-12=27, Resulting Numbers: [15, 27] Generated Node #0,2,1: 20:[15, 27] Operation: 39-12=27 Exploring Operation: 39-15=24, Resulting Numbers: [12, 24] Generated Node #0,2,2: 20:[12, 24] Operation: 39-15=24 Moving to Node #0,0 Current State: 20:[12, 6, 51], Operations: ['90-39=51'] Exploring Operation: 12/6=2, Resulting Numbers: [51, 2] Generated Node #0,0,0: 20:[51, 2] Operation: 12/6=2 Exploring Operation: 51-12=39, Resulting Numbers: [6, 39] Generated Node #0,0,1: 20:[6, 39] Operation: 51-12=39 Exploring Operation: 51-6=45, Resulting Numbers: [12, 45] Generated Node #0,0,2: 20:[12, 45] Operation: 51-6=45 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[6, 39], Operations: ['90-39=51', '51-12=39'] Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,20 unequal: No Solution Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,20 unequal: No Solution Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 20:[12, 45], Operations: ['90-39=51', '51-6=45'] Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 12*45=540, Resulting Numbers: [540] 540,20 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[51, 2], Operations: ['90-39=51', '12/6=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,20 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,20 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,20 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: 20:[6, 90, 27], Operations: ['39-12=27'] Exploring Operation: 90/6=15, Resulting Numbers: [27, 15] Generated Node #0,1,0: 20:[27, 15] Operation: 90/6=15 Exploring Operation: 90-6=84, Resulting Numbers: [27, 84] Generated Node #0,1,1: 20:[27, 84] Operation: 90-6=84 Exploring Operation: 90-27=63, Resulting Numbers: [6, 63] Generated Node #0,1,2: 20:[6, 63] Operation: 90-27=63 Moving to Node #0,2,2 Current State: 20:[12, 24], Operations: ['90/6=15', '39-15=24'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 12+24=36, Resulting Numbers: [36] 36,20 unequal: No Solution Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[15, 27], Operations: ['90/6=15', '39-12=27'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 15*27=405, Resulting Numbers: [405] 405,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[27, 15], Operations: ['39-12=27', '90/6=15'] Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,20 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[39, 3], Operations: ['90/6=15', '15-12=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,20 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[6, 63], Operations: ['39-12=27', '90-27=63'] Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,20 unequal: No Solution Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,20 unequal: No Solution Exploring Operation: 6*63=378, Resulting Numbers: [378] 378,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[27, 84], Operations: ['39-12=27', '90-6=84'] Exploring Operation: 27*84=2268, Resulting Numbers: [2268] 2268,20 unequal: No Solution Exploring Operation: 27+84=111, Resulting Numbers: [111] 111,20 unequal: No Solution Exploring Operation: 84-27=57, Resulting Numbers: [57] 57,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 76, 10, 6, 67 ]
30
[ "76-6=70", "70-67=3", "10*3=30" ]
Current State: 30:[76, 10, 6, 67], Operations: [] Exploring Operation: 76-6=70, Resulting Numbers: [10, 67, 70] Generated Node #2: [10, 67, 70] from Operation: 76-6=70 Current State: 30:[10, 67, 70], Operations: ['76-6=70'] Exploring Operation: 70-67=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 70-67=3 Current State: 30:[10, 3], Operations: ['76-6=70', '70-67=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[76, 10, 6, 67], Operations: [] Exploring Operation: 76-6=70, Resulting Numbers: [10, 67, 70] Generated Node #0,0: 30:[10, 67, 70] Operation: 76-6=70 Exploring Operation: 76-10=66, Resulting Numbers: [6, 67, 66] Generated Node #0,1: 30:[6, 67, 66] Operation: 76-10=66 Exploring Operation: 67-6=61, Resulting Numbers: [76, 10, 61] Generated Node #0,2: 30:[76, 10, 61] Operation: 67-6=61 Exploring Operation: 67-10=57, Resulting Numbers: [76, 6, 57] Generated Node #0,3: 30:[76, 6, 57] Operation: 67-10=57 Exploring Operation: 76-67=9, Resulting Numbers: [10, 6, 9] Generated Node #0,4: 30:[10, 6, 9] Operation: 76-67=9 Moving to Node #0,4 Current State: 30:[10, 6, 9], Operations: ['76-67=9'] Exploring Operation: 10+6=16, Resulting Numbers: [9, 16] Generated Node #0,4,0: 30:[9, 16] Operation: 10+6=16 Exploring Operation: 6+9=15, Resulting Numbers: [10, 15] Generated Node #0,4,1: 30:[10, 15] Operation: 6+9=15 Exploring Operation: 10-9=1, Resulting Numbers: [6, 1] Generated Node #0,4,2: 30:[6, 1] Operation: 10-9=1 Exploring Operation: 10-6=4, Resulting Numbers: [9, 4] Generated Node #0,4,3: 30:[9, 4] Operation: 10-6=4 Exploring Operation: 9-6=3, Resulting Numbers: [10, 3] Generated Node #0,4,4: 30:[10, 3] Operation: 9-6=3 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 30:[10, 15], Operations: ['76-67=9', '6+9=15'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,30 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 30:[10, 3], Operations: ['76-67=9', '9-6=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[76, 10, 6, 67], Operations: [] Exploring Operation: 76-67=9, Resulting Numbers: [10, 6, 9] Generated Node #0,4: 30:[10, 6, 9] Operation: 76-67=9 Moving to Node #0,4 Current State: 30:[10, 6, 9], Operations: ['76-67=9'] Exploring Operation: 9-6=3, Resulting Numbers: [10, 3] Generated Node #0,4,4: 30:[10, 3] Operation: 9-6=3 Moving to Node #0,4,4 Current State: 30:[10, 3], Operations: ['76-67=9', '9-6=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 37, 40, 74, 37 ]
41
[ "74-37=37", "37/37=1", "40+1=41" ]
Current State: 41:[37, 40, 74, 37], Operations: [] Exploring Operation: 74-37=37, Resulting Numbers: [40, 37] Generated Node #2: [40, 37] from Operation: 74-37=37 Current State: 41:[40, 37], Operations: ['74-37=37'] Exploring Operation: 37/37=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 37/37=1 Current State: 41:[40, 1], Operations: ['74-37=37', '37/37=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[37, 40, 74, 37], Operations: [] Exploring Operation: 74-40=34, Resulting Numbers: [37, 37, 34] Generated Node #0,0: 41:[37, 37, 34] Operation: 74-40=34 Exploring Operation: 74-37=37, Resulting Numbers: [37, 40, 37] Generated Node #0,1: 41:[37, 40, 37] Operation: 74-37=37 Exploring Operation: 74-37=37, Resulting Numbers: [40, 37, 37] Generated Node #0,2: 41:[40, 37, 37] Operation: 74-37=37 Moving to Node #0,1 Current State: 41:[37, 40, 37], Operations: ['74-37=37'] Exploring Operation: 40+37=77, Resulting Numbers: [37, 77] Generated Node #0,1,0: 41:[37, 77] Operation: 40+37=77 Exploring Operation: 37+40=77, Resulting Numbers: [37, 77] Generated Node #0,1,1: 41:[37, 77] Operation: 37+40=77 Exploring Operation: 37+37=74, Resulting Numbers: [40, 74] Generated Node #0,1,2: 41:[40, 74] Operation: 37+37=74 Moving to Node #0,2 Current State: 41:[40, 37, 37], Operations: ['74-37=37'] Exploring Operation: 37+37=74, Resulting Numbers: [40, 74] Generated Node #0,2,0: 41:[40, 74] Operation: 37+37=74 Exploring Operation: 40+37=77, Resulting Numbers: [37, 77] Generated Node #0,2,1: 41:[37, 77] Operation: 40+37=77 Exploring Operation: 40+37=77, Resulting Numbers: [37, 77] Generated Node #0,2,2: 41:[37, 77] Operation: 40+37=77 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[40, 74], Operations: ['74-37=37', '37+37=74'] Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,41 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 #0,2,1 Current State: 41:[37, 77], Operations: ['74-37=37', '40+37=77'] Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,41 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:[37, 77], Operations: ['74-37=37', '40+37=77'] Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,41 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,41 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: 41:[37, 37, 34], Operations: ['74-40=34'] Exploring Operation: 37+34=71, Resulting Numbers: [37, 71] Generated Node #0,0,0: 41:[37, 71] Operation: 37+34=71 Exploring Operation: 37+34=71, Resulting Numbers: [37, 71] Generated Node #0,0,1: 41:[37, 71] Operation: 37+34=71 Exploring Operation: 37+37=74, Resulting Numbers: [34, 74] Generated Node #0,0,2: 41:[34, 74] Operation: 37+37=74 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[37, 71], Operations: ['74-40=34', '37+34=71'] Exploring Operation: 37*71=2627, Resulting Numbers: [2627] 2627,41 unequal: No Solution Exploring Operation: 37+71=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[37, 71], Operations: ['74-40=34', '37+34=71'] Exploring Operation: 37+71=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 37*71=2627, Resulting Numbers: [2627] 2627,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[34, 74], Operations: ['74-40=34', '37+37=74'] Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 41:[40, 74], Operations: ['74-37=37', '37+37=74'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,41 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[37, 77], Operations: ['74-37=37', '40+37=77'] Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[37, 77], Operations: ['74-37=37', '37+40=77'] Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,41 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 66, 67, 33, 32 ]
34
[ "66*33=2178", "67*32=2144", "2178-2144=34" ]
Current State: 34:[66, 67, 33, 32], Operations: [] Exploring Operation: 66*33=2178, Resulting Numbers: [67, 32, 2178] Generated Node #2: [67, 32, 2178] from Operation: 66*33=2178 Current State: 34:[67, 32, 2178], Operations: ['66*33=2178'] Exploring Operation: 67*32=2144, Resulting Numbers: [2178, 2144] Generated Node #3: [2178, 2144] from Operation: 67*32=2144 Current State: 34:[2178, 2144], Operations: ['66*33=2178', '67*32=2144'] Exploring Operation: 2178-2144=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[66, 67, 33, 32], Operations: [] Exploring Operation: 67-66=1, Resulting Numbers: [33, 32, 1] Generated Node #0,0: 34:[33, 32, 1] Operation: 67-66=1 Exploring Operation: 66-32=34, Resulting Numbers: [67, 33, 34] Generated Node #0,1: 34:[67, 33, 34] Operation: 66-32=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[33, 32, 1], Operations: ['67-66=1'] Exploring Operation: 33-32=1, Resulting Numbers: [1, 1] Generated Node #0,0,0: 34:[1, 1] Operation: 33-32=1 Exploring Operation: 33+1=34, Resulting Numbers: [32, 34] Generated Node #0,0,1: 34:[32, 34] Operation: 33+1=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[1, 1], Operations: ['67-66=1', '33-32=1'] Exploring Operation: 1*1=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 1+1=2, Resulting Numbers: [2] 2,34 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:[32, 34], Operations: ['67-66=1', '33+1=34'] Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,34 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,34 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:[67, 33, 34], Operations: ['66-32=34'] Exploring Operation: 67-34=33, Resulting Numbers: [33, 33] Generated Node #0,1,0: 34:[33, 33] Operation: 67-34=33 Exploring Operation: 67-33=34, Resulting Numbers: [34, 34] Generated Node #0,1,1: 34:[34, 34] Operation: 67-33=34 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[34, 34], Operations: ['66-32=34', '67-33=34'] Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 34/34=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 #0,1,0 Current State: 34:[33, 33], Operations: ['66-32=34', '67-34=33'] Exploring Operation: 33-33=0, Resulting Numbers: [0] 0,34 unequal: No Solution Exploring Operation: 33/33=1, Resulting Numbers: [1] 1,34 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_2
mult_heuristic
[ 77, 32, 4, 24 ]
75
[ "77-24=53", "32*4=128", "128-53=75" ]
Current State: 75:[77, 32, 4, 24], Operations: [] Exploring Operation: 77-24=53, Resulting Numbers: [32, 4, 53] Generated Node #2: [32, 4, 53] from Operation: 77-24=53 Current State: 75:[32, 4, 53], Operations: ['77-24=53'] Exploring Operation: 32*4=128, Resulting Numbers: [53, 128] Generated Node #3: [53, 128] from Operation: 32*4=128 Current State: 75:[53, 128], Operations: ['77-24=53', '32*4=128'] Exploring Operation: 128-53=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[77, 32, 4, 24], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [77, 24, 8] Generated Node #0,0: 75:[77, 24, 8] Operation: 32/4=8 Exploring Operation: 32-4=28, Resulting Numbers: [77, 24, 28] Generated Node #0,1: 75:[77, 24, 28] Operation: 32-4=28 Exploring Operation: 32-24=8, Resulting Numbers: [77, 4, 8] Generated Node #0,2: 75:[77, 4, 8] Operation: 32-24=8 Moving to Node #0,0 Current State: 75:[77, 24, 8], Operations: ['32/4=8'] Exploring Operation: 77-8=69, Resulting Numbers: [24, 69] Generated Node #0,0,0: 75:[24, 69] Operation: 77-8=69 Exploring Operation: 24-8=16, Resulting Numbers: [77, 16] Generated Node #0,0,1: 75:[77, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [77, 3] Generated Node #0,0,2: 75:[77, 3] Operation: 24/8=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[77, 3], Operations: ['32/4=8', '24/8=3'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,75 unequal: No Solution Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[77, 16], Operations: ['32/4=8', '24-8=16'] Exploring Operation: 77*16=1232, Resulting Numbers: [1232] 1232,75 unequal: No Solution Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,75 unequal: No Solution Exploring Operation: 77+16=93, Resulting Numbers: [93] 93,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[24, 69], Operations: ['32/4=8', '77-8=69'] Exploring Operation: 24+69=93, Resulting Numbers: [93] 93,75 unequal: No Solution Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,75 unequal: No Solution Exploring Operation: 24*69=1656, Resulting Numbers: [1656] 1656,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 75:[77, 24, 28], Operations: ['32-4=28'] Exploring Operation: 77-24=53, Resulting Numbers: [28, 53] Generated Node #0,1,0: 75:[28, 53] Operation: 77-24=53 Exploring Operation: 28-24=4, Resulting Numbers: [77, 4] Generated Node #0,1,1: 75:[77, 4] Operation: 28-24=4 Exploring Operation: 77-28=49, Resulting Numbers: [24, 49] Generated Node #0,1,2: 75:[24, 49] Operation: 77-28=49 Moving to Node #0,2 Current State: 75:[77, 4, 8], Operations: ['32-24=8'] Exploring Operation: 8-4=4, Resulting Numbers: [77, 4] Generated Node #0,2,0: 75:[77, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [77, 2] Generated Node #0,2,1: 75:[77, 2] Operation: 8/4=2 Exploring Operation: 77-4=73, Resulting Numbers: [8, 73] Generated Node #0,2,2: 75:[8, 73] Operation: 77-4=73 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 75:[77, 4], Operations: ['32-24=8', '8-4=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,75 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 75:[77, 2], Operations: ['32-24=8', '8/4=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[77, 32, 4, 24], Operations: [] Exploring Operation: 32-24=8, Resulting Numbers: [77, 4, 8] Generated Node #0,2: 75:[77, 4, 8] Operation: 32-24=8 Moving to Node #0,2 Current State: 75:[77, 4, 8], Operations: ['32-24=8'] Exploring Operation: 8/4=2, Resulting Numbers: [77, 2] Generated Node #0,2,1: 75:[77, 2] Operation: 8/4=2 Moving to Node #0,2,1 Current State: 75:[77, 2], Operations: ['32-24=8', '8/4=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 56, 52, 37, 8 ]
41
[ "56-52=4", "37+8=45", "45-4=41" ]
Current State: 41:[56, 52, 37, 8], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [37, 8, 4] Generated Node #2: [37, 8, 4] from Operation: 56-52=4 Current State: 41:[37, 8, 4], Operations: ['56-52=4'] Exploring Operation: 37+8=45, Resulting Numbers: [4, 45] Generated Node #3: [4, 45] from Operation: 37+8=45 Current State: 41:[4, 45], Operations: ['56-52=4', '37+8=45'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[56, 52, 37, 8], Operations: [] Exploring Operation: 56-8=48, Resulting Numbers: [52, 37, 48] Generated Node #0,0: 41:[52, 37, 48] Operation: 56-8=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[52, 37, 48], Operations: ['56-8=48'] Exploring Operation: 52-37=15, Resulting Numbers: [48, 15] Generated Node #0,0,0: 41:[48, 15] Operation: 52-37=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[48, 15], Operations: ['56-8=48', '52-37=15'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 12, 55, 3, 30 ]
29
[ "12/3=4", "55-30=25", "4+25=29" ]
Current State: 29:[12, 55, 3, 30], Operations: [] Exploring Operation: 12/3=4, Resulting Numbers: [55, 30, 4] Generated Node #2: [55, 30, 4] from Operation: 12/3=4 Current State: 29:[55, 30, 4], Operations: ['12/3=4'] Exploring Operation: 55-30=25, Resulting Numbers: [4, 25] Generated Node #3: [4, 25] from Operation: 55-30=25 Current State: 29:[4, 25], Operations: ['12/3=4', '55-30=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[12, 55, 3, 30], Operations: [] Exploring Operation: 12*3=36, Resulting Numbers: [55, 30, 36] Generated Node #0,0: 29:[55, 30, 36] Operation: 12*3=36 Exploring Operation: 55-12=43, Resulting Numbers: [3, 30, 43] Generated Node #0,1: 29:[3, 30, 43] Operation: 55-12=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[55, 30, 36], Operations: ['12*3=36'] Exploring Operation: 55-30=25, Resulting Numbers: [36, 25] Generated Node #0,0,0: 29:[36, 25] Operation: 55-30=25 Exploring Operation: 55-36=19, Resulting Numbers: [30, 19] Generated Node #0,0,1: 29:[30, 19] Operation: 55-36=19 Moving to Node #0,0,0 Current State: 29:[36, 25], Operations: ['12*3=36', '55-30=25'] Exploring Operation: 36+25=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[30, 19], Operations: ['12*3=36', '55-36=19'] Exploring Operation: 30+19=49, Resulting Numbers: [49] 49,29 unequal: No Solution Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,29 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 #0,1 Current State: 29:[3, 30, 43], Operations: ['55-12=43'] Exploring Operation: 43-3=40, Resulting Numbers: [30, 40] Generated Node #0,1,0: 29:[30, 40] Operation: 43-3=40 Exploring Operation: 30-3=27, Resulting Numbers: [43, 27] Generated Node #0,1,1: 29:[43, 27] Operation: 30-3=27 Moving to Node #0,1,0 Current State: 29:[30, 40], Operations: ['55-12=43', '43-3=40'] Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,29 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[43, 27], Operations: ['55-12=43', '30-3=27'] Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,29 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
[ 62, 36, 2, 4 ]
52
[ "62-36=26", "4-2=2", "26*2=52" ]
Current State: 52:[62, 36, 2, 4], Operations: [] Exploring Operation: 62-36=26, Resulting Numbers: [2, 4, 26] Generated Node #2: [2, 4, 26] from Operation: 62-36=26 Current State: 52:[2, 4, 26], Operations: ['62-36=26'] Exploring Operation: 4-2=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 4-2=2 Current State: 52:[26, 2], Operations: ['62-36=26', '4-2=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[62, 36, 2, 4], Operations: [] Exploring Operation: 36/2=18, Resulting Numbers: [62, 4, 18] Generated Node #0,0: 52:[62, 4, 18] Operation: 36/2=18 Exploring Operation: 62/2=31, Resulting Numbers: [36, 4, 31] Generated Node #0,1: 52:[36, 4, 31] Operation: 62/2=31 Exploring Operation: 36/4=9, Resulting Numbers: [62, 2, 9] Generated Node #0,2: 52:[62, 2, 9] Operation: 36/4=9 Exploring Operation: 62-36=26, Resulting Numbers: [2, 4, 26] Generated Node #0,3: 52:[2, 4, 26] Operation: 62-36=26 Exploring Operation: 62-4=58, Resulting Numbers: [36, 2, 58] Generated Node #0,4: 52:[36, 2, 58] Operation: 62-4=58 Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[2, 4, 26], Operations: ['62-36=26'] Exploring Operation: 2*26=52, Resulting Numbers: [4, 52] Generated Node #0,3,0: 52:[4, 52] Operation: 2*26=52 Exploring Operation: 4-2=2, Resulting Numbers: [26, 2] Generated Node #0,3,1: 52:[26, 2] Operation: 4-2=2 Exploring Operation: 2+4=6, Resulting Numbers: [26, 6] Generated Node #0,3,2: 52:[26, 6] Operation: 2+4=6 Exploring Operation: 4/2=2, Resulting Numbers: [26, 2] Generated Node #0,3,3: 52:[26, 2] Operation: 4/2=2 Exploring Operation: 26/2=13, Resulting Numbers: [4, 13] Generated Node #0,3,4: 52:[4, 13] Operation: 26/2=13 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[4, 52], Operations: ['62-36=26', '2*26=52'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,52 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,52 unequal: No Solution No 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: 52:[26, 2], Operations: ['62-36=26', '4-2=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[62, 36, 2, 4], Operations: [] Exploring Operation: 62-36=26, Resulting Numbers: [2, 4, 26] Generated Node #0,3: 52:[2, 4, 26] Operation: 62-36=26 Moving to Node #0,3 Current State: 52:[2, 4, 26], Operations: ['62-36=26'] Exploring Operation: 4-2=2, Resulting Numbers: [26, 2] Generated Node #0,3,1: 52:[26, 2] Operation: 4-2=2 Moving to Node #0,3,1 Current State: 52:[26, 2], Operations: ['62-36=26', '4-2=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 28, 10, 10, 40 ]
12
[ "28+10=38", "10+40=50", "50-38=12" ]
Current State: 12:[28, 10, 10, 40], Operations: [] Exploring Operation: 28+10=38, Resulting Numbers: [40, 38] Generated Node #2: [40, 38] from Operation: 28+10=38 Current State: 12:[40, 38], Operations: ['28+10=38'] Exploring Operation: 10+40=50, Resulting Numbers: [38, 50] Generated Node #3: [38, 50] from Operation: 10+40=50 Current State: 12:[38, 50], Operations: ['28+10=38', '10+40=50'] Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[28, 10, 10, 40], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [28, 10, 4] Generated Node #0,0: 12:[28, 10, 4] Operation: 40/10=4 Exploring Operation: 40-28=12, Resulting Numbers: [10, 10, 12] Generated Node #0,1: 12:[10, 10, 12] Operation: 40-28=12 Moving to Node #0,1 Current State: 12:[10, 10, 12], Operations: ['40-28=12'] Exploring Operation: 10/10=1, Resulting Numbers: [12, 1] Generated Node #0,1,0: 12:[12, 1] Operation: 10/10=1 Exploring Operation: 10-10=0, Resulting Numbers: [12, 0] Generated Node #0,1,1: 12:[12, 0] Operation: 10-10=0 Moving to Node #0,0 Current State: 12:[28, 10, 4], Operations: ['40/10=4'] Exploring Operation: 28-10=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 12:[4, 18] Operation: 28-10=18 Exploring Operation: 28/4=7, Resulting Numbers: [10, 7] Generated Node #0,0,1: 12:[10, 7] Operation: 28/4=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[10, 7], Operations: ['40/10=4', '28/4=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,12 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[4, 18], Operations: ['40/10=4', '28-10=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,12 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: 12:[12, 1], Operations: ['40-28=12', '10/10=1'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[28, 10, 10, 40], Operations: [] Exploring Operation: 40-28=12, Resulting Numbers: [10, 10, 12] Generated Node #0,1: 12:[10, 10, 12] Operation: 40-28=12 Moving to Node #0,1 Current State: 12:[10, 10, 12], Operations: ['40-28=12'] Exploring Operation: 10/10=1, Resulting Numbers: [12, 1] Generated Node #0,1,0: 12:[12, 1] Operation: 10/10=1 Moving to Node #0,1,0 Current State: 12:[12, 1], Operations: ['40-28=12', '10/10=1'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 51, 46, 57, 56 ]
97
[ "51+46=97", "57-56=1", "97*1=97" ]
Current State: 97:[51, 46, 57, 56], Operations: [] Exploring Operation: 51+46=97, Resulting Numbers: [57, 56, 97] Generated Node #2: [57, 56, 97] from Operation: 51+46=97 Current State: 97:[57, 56, 97], Operations: ['51+46=97'] Exploring Operation: 57-56=1, Resulting Numbers: [97, 1] Generated Node #3: [97, 1] from Operation: 57-56=1 Current State: 97:[97, 1], Operations: ['51+46=97', '57-56=1'] Exploring Operation: 97*1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[51, 46, 57, 56], Operations: [] Exploring Operation: 51+56=107, Resulting Numbers: [46, 57, 107] Generated Node #0,0: 97:[46, 57, 107] Operation: 51+56=107 Exploring Operation: 46+57=103, Resulting Numbers: [51, 56, 103] Generated Node #0,1: 97:[51, 56, 103] Operation: 46+57=103 Exploring Operation: 46+56=102, Resulting Numbers: [51, 57, 102] Generated Node #0,2: 97:[51, 57, 102] Operation: 46+56=102 Exploring Operation: 51+46=97, Resulting Numbers: [57, 56, 97] Generated Node #0,3: 97:[57, 56, 97] Operation: 51+46=97 Moving to Node #0,3 Current State: 97:[57, 56, 97], Operations: ['51+46=97'] Exploring Operation: 57+56=113, Resulting Numbers: [97, 113] Generated Node #0,3,0: 97:[97, 113] Operation: 57+56=113 Exploring Operation: 57-56=1, Resulting Numbers: [97, 1] Generated Node #0,3,1: 97:[97, 1] Operation: 57-56=1 Exploring Operation: 56+97=153, Resulting Numbers: [57, 153] Generated Node #0,3,2: 97:[57, 153] Operation: 56+97=153 Exploring Operation: 97-56=41, Resulting Numbers: [57, 41] Generated Node #0,3,3: 97:[57, 41] Operation: 97-56=41 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 97:[97, 113], Operations: ['51+46=97', '57+56=113'] Exploring Operation: 97+113=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 113-97=16, Resulting Numbers: [16] 16,97 unequal: No Solution Exploring Operation: 97*113=10961, Resulting Numbers: [10961] 10961,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 97:[97, 1], Operations: ['51+46=97', '57-56=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,97 unequal: No Solution Exploring Operation: 97/1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[51, 46, 57, 56], Operations: [] Exploring Operation: 51+46=97, Resulting Numbers: [57, 56, 97] Generated Node #0,3: 97:[57, 56, 97] Operation: 51+46=97 Moving to Node #0,3 Current State: 97:[57, 56, 97], Operations: ['51+46=97'] Exploring Operation: 57-56=1, Resulting Numbers: [97, 1] Generated Node #0,3,1: 97:[97, 1] Operation: 57-56=1 Moving to Node #0,3,1 Current State: 97:[97, 1], Operations: ['51+46=97', '57-56=1'] Exploring Operation: 97/1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 15, 72, 21, 15 ]
93
[ "15+72=87", "21-15=6", "87+6=93" ]
Current State: 93:[15, 72, 21, 15], Operations: [] Exploring Operation: 15+72=87, Resulting Numbers: [21, 87] Generated Node #2: [21, 87] from Operation: 15+72=87 Current State: 93:[21, 87], Operations: ['15+72=87'] Exploring Operation: 21-15=6, Resulting Numbers: [87, 6] Generated Node #3: [87, 6] from Operation: 21-15=6 Current State: 93:[87, 6], Operations: ['15+72=87', '21-15=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[15, 72, 21, 15], Operations: [] Exploring Operation: 72+21=93, Resulting Numbers: [15, 15, 93] Generated Node #0,0: 93:[15, 15, 93] Operation: 72+21=93 Moving to Node #0,0 Current State: 93:[15, 15, 93], Operations: ['72+21=93'] Exploring Operation: 15+15=30, Resulting Numbers: [93, 30] Generated Node #0,0,0: 93:[93, 30] Operation: 15+15=30 Moving to Node #0,0,0 Current State: 93:[93, 30], Operations: ['72+21=93', '15+15=30'] Exploring Operation: 93+30=123, Resulting Numbers: [123] 123,93 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 8, 72, 32, 91 ]
21
[ "8+72=80", "91-32=59", "80-59=21" ]
Current State: 21:[8, 72, 32, 91], Operations: [] Exploring Operation: 8+72=80, Resulting Numbers: [32, 91, 80] Generated Node #2: [32, 91, 80] from Operation: 8+72=80 Current State: 21:[32, 91, 80], Operations: ['8+72=80'] Exploring Operation: 91-32=59, Resulting Numbers: [80, 59] Generated Node #3: [80, 59] from Operation: 91-32=59 Current State: 21:[80, 59], Operations: ['8+72=80', '91-32=59'] Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[8, 72, 32, 91], Operations: [] Exploring Operation: 72-32=40, Resulting Numbers: [8, 91, 40] Generated Node #0,0: 21:[8, 91, 40] Operation: 72-32=40 Exploring Operation: 91-72=19, Resulting Numbers: [8, 32, 19] Generated Node #0,1: 21:[8, 32, 19] Operation: 91-72=19 Exploring Operation: 91-32=59, Resulting Numbers: [8, 72, 59] Generated Node #0,2: 21:[8, 72, 59] Operation: 91-32=59 Exploring Operation: 72/8=9, Resulting Numbers: [32, 91, 9] Generated Node #0,3: 21:[32, 91, 9] Operation: 72/8=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[8, 32, 19], Operations: ['91-72=19'] Exploring Operation: 32/8=4, Resulting Numbers: [19, 4] Generated Node #0,1,0: 21:[19, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [19, 24] Generated Node #0,1,1: 21:[19, 24] Operation: 32-8=24 Exploring Operation: 32-19=13, Resulting Numbers: [8, 13] Generated Node #0,1,2: 21:[8, 13] Operation: 32-19=13 Exploring Operation: 19-8=11, Resulting Numbers: [32, 11] Generated Node #0,1,3: 21:[32, 11] Operation: 19-8=11 Moving to Node #0,1,0 Current State: 21:[19, 4], Operations: ['91-72=19', '32/8=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[19, 24], Operations: ['91-72=19', '32-8=24'] Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[8, 13], Operations: ['91-72=19', '32-19=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,21 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[8, 72, 32, 91], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [8, 32, 19] Generated Node #0,1: 21:[8, 32, 19] Operation: 91-72=19 Moving to Node #0,1 Current State: 21:[8, 32, 19], Operations: ['91-72=19'] Exploring Operation: 32-19=13, Resulting Numbers: [8, 13] Generated Node #0,1,2: 21:[8, 13] Operation: 32-19=13 Moving to Node #0,1,2 Current State: 21:[8, 13], Operations: ['91-72=19', '32-19=13'] Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 59, 72, 33, 5 ]
15
[ "72-59=13", "33-5=28", "28-13=15" ]
Current State: 15:[59, 72, 33, 5], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [33, 5, 13] Generated Node #2: [33, 5, 13] from Operation: 72-59=13 Current State: 15:[33, 5, 13], Operations: ['72-59=13'] Exploring Operation: 33-5=28, Resulting Numbers: [13, 28] Generated Node #3: [13, 28] from Operation: 33-5=28 Current State: 15:[13, 28], Operations: ['72-59=13', '33-5=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[59, 72, 33, 5], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [33, 5, 13] Generated Node #0,0: 15:[33, 5, 13] Operation: 72-59=13 Moving to Node #0,0 Current State: 15:[33, 5, 13], Operations: ['72-59=13'] Exploring Operation: 33-13=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 15:[5, 20] Operation: 33-13=20 Moving to Node #0,0,0 Current State: 15:[5, 20], Operations: ['72-59=13', '33-13=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[59, 72, 33, 5], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [33, 5, 13] Generated Node #0,0: 15:[33, 5, 13] Operation: 72-59=13 Moving to Node #0,0 Current State: 15:[33, 5, 13], Operations: ['72-59=13'] Exploring Operation: 33-13=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 15:[5, 20] Operation: 33-13=20 Moving to Node #0,0,0 Current State: 15:[5, 20], Operations: ['72-59=13', '33-13=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 18, 23, 26, 9 ]
22
[ "23-18=5", "26-9=17", "5+17=22" ]
Current State: 22:[18, 23, 26, 9], Operations: [] Exploring Operation: 23-18=5, Resulting Numbers: [26, 9, 5] Generated Node #2: [26, 9, 5] from Operation: 23-18=5 Current State: 22:[26, 9, 5], Operations: ['23-18=5'] Exploring Operation: 26-9=17, Resulting Numbers: [5, 17] Generated Node #3: [5, 17] from Operation: 26-9=17 Current State: 22:[5, 17], Operations: ['23-18=5', '26-9=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[18, 23, 26, 9], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [23, 26, 2] Generated Node #0,0: 22:[23, 26, 2] Operation: 18/9=2 Moving to Node #0,0 Current State: 22:[23, 26, 2], Operations: ['18/9=2'] Exploring Operation: 26-23=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 22:[2, 3] Operation: 26-23=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[2, 3], Operations: ['18/9=2', '26-23=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 26, 42, 40, 68 ]
88
[ "26*68=1768", "42*40=1680", "1768-1680=88" ]
Current State: 88:[26, 42, 40, 68], Operations: [] Exploring Operation: 26*68=1768, Resulting Numbers: [42, 40, 1768] Generated Node #2: [42, 40, 1768] from Operation: 26*68=1768 Current State: 88:[42, 40, 1768], Operations: ['26*68=1768'] Exploring Operation: 42*40=1680, Resulting Numbers: [1768, 1680] Generated Node #3: [1768, 1680] from Operation: 42*40=1680 Current State: 88:[1768, 1680], Operations: ['26*68=1768', '42*40=1680'] Exploring Operation: 1768-1680=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[26, 42, 40, 68], Operations: [] Exploring Operation: 68-42=26, Resulting Numbers: [26, 40, 26] Generated Node #0,0: 88:[26, 40, 26] Operation: 68-42=26 Exploring Operation: 68-26=42, Resulting Numbers: [42, 40, 42] Generated Node #0,1: 88:[42, 40, 42] Operation: 68-26=42 Exploring Operation: 26+68=94, Resulting Numbers: [42, 40, 94] Generated Node #0,2: 88:[42, 40, 94] Operation: 26+68=94 Exploring Operation: 42-40=2, Resulting Numbers: [26, 68, 2] Generated Node #0,3: 88:[26, 68, 2] Operation: 42-40=2 Exploring Operation: 68-40=28, Resulting Numbers: [26, 42, 28] Generated Node #0,4: 88:[26, 42, 28] Operation: 68-40=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[42, 40, 42], Operations: ['68-26=42'] Exploring Operation: 42-40=2, Resulting Numbers: [42, 2] Generated Node #0,1,0: 88:[42, 2] Operation: 42-40=2 Exploring Operation: 42-40=2, Resulting Numbers: [42, 2] Generated Node #0,1,1: 88:[42, 2] Operation: 42-40=2 Exploring Operation: 42+40=82, Resulting Numbers: [42, 82] Generated Node #0,1,2: 88:[42, 82] Operation: 42+40=82 Exploring Operation: 42/42=1, Resulting Numbers: [40, 1] Generated Node #0,1,3: 88:[40, 1] Operation: 42/42=1 Exploring Operation: 42-42=0, Resulting Numbers: [40, 0] Generated Node #0,1,4: 88:[40, 0] Operation: 42-42=0 Moving to Node #0,1,0 Current State: 88:[42, 2], Operations: ['68-26=42', '42-40=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,88 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[42, 2], Operations: ['68-26=42', '42-40=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,88 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[40, 1], Operations: ['68-26=42', '42/42=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,88 unequal: No Solution Moving to Node #0,1,4 Current State: 88:[40, 0], Operations: ['68-26=42', '42-42=0'] Exploring Operation: 40-0=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40*0=0, Resulting Numbers: [0] 0,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[42, 82], Operations: ['68-26=42', '42+40=82'] Exploring Operation: 42*82=3444, Resulting Numbers: [3444] 3444,88 unequal: No Solution Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 42+82=124, Resulting Numbers: [124] 124,88 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 #0,0 Current State: 88:[26, 40, 26], Operations: ['68-42=26'] Exploring Operation: 26/26=1, Resulting Numbers: [40, 1] Generated Node #0,0,0: 88:[40, 1] Operation: 26/26=1 Exploring Operation: 26+26=52, Resulting Numbers: [40, 52] Generated Node #0,0,1: 88:[40, 52] Operation: 26+26=52 Exploring Operation: 40-26=14, Resulting Numbers: [26, 14] Generated Node #0,0,2: 88:[26, 14] Operation: 40-26=14 Exploring Operation: 40-26=14, Resulting Numbers: [26, 14] Generated Node #0,0,3: 88:[26, 14] Operation: 40-26=14 Exploring Operation: 26-26=0, Resulting Numbers: [40, 0] Generated Node #0,0,4: 88:[40, 0] Operation: 26-26=0 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[40, 1], Operations: ['68-42=26', '26/26=1'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 88:[40, 0], Operations: ['68-42=26', '26-26=0'] Exploring Operation: 40*0=0, Resulting Numbers: [0] 0,88 unequal: No Solution Exploring Operation: 40-0=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[26, 14], Operations: ['68-42=26', '40-26=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,88 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[26, 14], Operations: ['68-42=26', '40-26=14'] Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,88 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[40, 52], Operations: ['68-42=26', '26+26=52'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,88 unequal: No Solution Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[42, 40, 94], Operations: ['26+68=94'] Exploring Operation: 42+40=82, Resulting Numbers: [94, 82] Generated Node #0,2,0: 88:[94, 82] Operation: 42+40=82 Exploring Operation: 40+94=134, Resulting Numbers: [42, 134] Generated Node #0,2,1: 88:[42, 134] Operation: 40+94=134 Exploring Operation: 42-40=2, Resulting Numbers: [94, 2] Generated Node #0,2,2: 88:[94, 2] Operation: 42-40=2 Exploring Operation: 94-40=54, Resulting Numbers: [42, 54] Generated Node #0,2,3: 88:[42, 54] Operation: 94-40=54 Exploring Operation: 94-42=52, Resulting Numbers: [40, 52] Generated Node #0,2,4: 88:[40, 52] Operation: 94-42=52 Moving to Node #0,2,2 Current State: 88:[94, 2], Operations: ['26+68=94', '42-40=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,88 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[42, 54], Operations: ['26+68=94', '94-40=54'] Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[94, 82], Operations: ['26+68=94', '42+40=82'] Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,88 unequal: No Solution Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,88 unequal: No Solution Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[40, 52], Operations: ['26+68=94', '94-42=52'] Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[42, 134], Operations: ['26+68=94', '40+94=134'] Exploring Operation: 42+134=176, Resulting Numbers: [176] 176,88 unequal: No Solution Exploring Operation: 134-42=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 42*134=5628, Resulting Numbers: [5628] 5628,88 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 #0,4 Current State: 88:[26, 42, 28], Operations: ['68-40=28'] Exploring Operation: 42-28=14, Resulting Numbers: [26, 14] Generated Node #0,4,0: 88:[26, 14] Operation: 42-28=14 Exploring Operation: 42+28=70, Resulting Numbers: [26, 70] Generated Node #0,4,1: 88:[26, 70] Operation: 42+28=70 Exploring Operation: 26+28=54, Resulting Numbers: [42, 54] Generated Node #0,4,2: 88:[42, 54] Operation: 26+28=54 Exploring Operation: 28-26=2, Resulting Numbers: [42, 2] Generated Node #0,4,3: 88:[42, 2] Operation: 28-26=2 Exploring Operation: 42-26=16, Resulting Numbers: [28, 16] Generated Node #0,4,4: 88:[28, 16] Operation: 42-26=16 Moving to Node #0,4,3 Current State: 88:[42, 2], Operations: ['68-40=28', '28-26=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[26, 14], Operations: ['68-40=28', '42-28=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[28, 16], Operations: ['68-40=28', '42-26=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,88 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[42, 54], Operations: ['68-40=28', '26+28=54'] Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,88 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[26, 70], Operations: ['68-40=28', '42+28=70'] Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,88 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[26, 68, 2], Operations: ['42-40=2'] Exploring Operation: 26-2=24, Resulting Numbers: [68, 24] Generated Node #0,3,0: 88:[68, 24] Operation: 26-2=24 Exploring Operation: 68-26=42, Resulting Numbers: [2, 42] Generated Node #0,3,1: 88:[2, 42] Operation: 68-26=42 Exploring Operation: 68/2=34, Resulting Numbers: [26, 34] Generated Node #0,3,2: 88:[26, 34] Operation: 68/2=34 Exploring Operation: 26/2=13, Resulting Numbers: [68, 13] Generated Node #0,3,3: 88:[68, 13] Operation: 26/2=13 Exploring Operation: 26+68=94, Resulting Numbers: [2, 94] Generated Node #0,3,4: 88:[2, 94] Operation: 26+68=94 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[2, 42], Operations: ['42-40=2', '68-26=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,88 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 88:[2, 94], Operations: ['42-40=2', '26+68=94'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,88 unequal: No Solution Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 2*94=188, Resulting Numbers: [188] 188,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[26, 34], Operations: ['42-40=2', '68/2=34'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,88 unequal: No Solution Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[68, 24], Operations: ['42-40=2', '26-2=24'] Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,88 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[68, 13], Operations: ['42-40=2', '26/2=13'] Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 99, 41, 60, 16 ]
21
[ "60*16=960", "960-99=861", "861/41=21" ]
Current State: 21:[99, 41, 60, 16], Operations: [] Exploring Operation: 60*16=960, Resulting Numbers: [99, 41, 960] Generated Node #2: [99, 41, 960] from Operation: 60*16=960 Current State: 21:[99, 41, 960], Operations: ['60*16=960'] Exploring Operation: 960-99=861, Resulting Numbers: [41, 861] Generated Node #3: [41, 861] from Operation: 960-99=861 Current State: 21:[41, 861], Operations: ['60*16=960', '960-99=861'] Exploring Operation: 861/41=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[99, 41, 60, 16], Operations: [] Exploring Operation: 99-41=58, Resulting Numbers: [60, 16, 58] Generated Node #0,0: 21:[60, 16, 58] Operation: 99-41=58 Exploring Operation: 99-60=39, Resulting Numbers: [41, 16, 39] Generated Node #0,1: 21:[41, 16, 39] Operation: 99-60=39 Exploring Operation: 60-41=19, Resulting Numbers: [99, 16, 19] Generated Node #0,2: 21:[99, 16, 19] Operation: 60-41=19 Moving to Node #0,1 Current State: 21:[41, 16, 39], Operations: ['99-60=39'] Exploring Operation: 39-16=23, Resulting Numbers: [41, 23] Generated Node #0,1,0: 21:[41, 23] Operation: 39-16=23 Exploring Operation: 41-16=25, Resulting Numbers: [39, 25] Generated Node #0,1,1: 21:[39, 25] Operation: 41-16=25 Exploring Operation: 41-39=2, Resulting Numbers: [16, 2] Generated Node #0,1,2: 21:[16, 2] Operation: 41-39=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[16, 2], Operations: ['99-60=39', '41-39=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[41, 23], Operations: ['99-60=39', '39-16=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,21 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[39, 25], Operations: ['99-60=39', '41-16=25'] Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,21 unequal: No Solution Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,21 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: 21:[60, 16, 58], Operations: ['99-41=58'] Exploring Operation: 60-58=2, Resulting Numbers: [16, 2] Generated Node #0,0,0: 21:[16, 2] Operation: 60-58=2 Exploring Operation: 60-16=44, Resulting Numbers: [58, 44] Generated Node #0,0,1: 21:[58, 44] Operation: 60-16=44 Exploring Operation: 58-16=42, Resulting Numbers: [60, 42] Generated Node #0,0,2: 21:[60, 42] Operation: 58-16=42 Moving to Node #0,2 Current State: 21:[99, 16, 19], Operations: ['60-41=19'] Exploring Operation: 19-16=3, Resulting Numbers: [99, 3] Generated Node #0,2,0: 21:[99, 3] Operation: 19-16=3 Exploring Operation: 99-16=83, Resulting Numbers: [19, 83] Generated Node #0,2,1: 21:[19, 83] Operation: 99-16=83 Exploring Operation: 99-19=80, Resulting Numbers: [16, 80] Generated Node #0,2,2: 21:[16, 80] Operation: 99-19=80 Moving to Node #0,0,0 Current State: 21:[16, 2], Operations: ['99-41=58', '60-58=2'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[60, 42], Operations: ['99-41=58', '58-16=42'] Exploring Operation: 60*42=2520, Resulting Numbers: [2520] 2520,21 unequal: No Solution Exploring Operation: 60+42=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[58, 44], Operations: ['99-41=58', '60-16=44'] Exploring Operation: 58*44=2552, Resulting Numbers: [2552] 2552,21 unequal: No Solution Exploring Operation: 58+44=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 58-44=14, Resulting Numbers: [14] 14,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[19, 83], Operations: ['60-41=19', '99-16=83'] Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 19*83=1577, Resulting Numbers: [1577] 1577,21 unequal: No Solution Exploring Operation: 19+83=102, Resulting Numbers: [102] 102,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[16, 80], Operations: ['60-41=19', '99-19=80'] Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 16+80=96, Resulting Numbers: [96] 96,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[99, 3], Operations: ['60-41=19', '19-16=3'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 99+3=102, Resulting Numbers: [102] 102,21 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 17, 10, 7, 71 ]
58
[ "17*7=119", "71-10=61", "119-61=58" ]
Current State: 58:[17, 10, 7, 71], Operations: [] Exploring Operation: 17*7=119, Resulting Numbers: [10, 71, 119] Generated Node #2: [10, 71, 119] from Operation: 17*7=119 Current State: 58:[10, 71, 119], Operations: ['17*7=119'] Exploring Operation: 71-10=61, Resulting Numbers: [119, 61] Generated Node #3: [119, 61] from Operation: 71-10=61 Current State: 58:[119, 61], Operations: ['17*7=119', '71-10=61'] Exploring Operation: 119-61=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[17, 10, 7, 71], Operations: [] Exploring Operation: 71-17=54, Resulting Numbers: [10, 7, 54] Generated Node #0,0: 58:[10, 7, 54] Operation: 71-17=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[10, 7, 54], Operations: ['71-17=54'] Exploring Operation: 10-7=3, Resulting Numbers: [54, 3] Generated Node #0,0,0: 58:[54, 3] Operation: 10-7=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[54, 3], Operations: ['71-17=54', '10-7=3'] Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,58 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
[ 62, 60, 29, 27 ]
85
[ "62-60=2", "29*2=58", "27+58=85" ]
Current State: 85:[62, 60, 29, 27], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [29, 27, 2] Generated Node #2: [29, 27, 2] from Operation: 62-60=2 Current State: 85:[29, 27, 2], Operations: ['62-60=2'] Exploring Operation: 29*2=58, Resulting Numbers: [27, 58] Generated Node #3: [27, 58] from Operation: 29*2=58 Current State: 85:[27, 58], Operations: ['62-60=2', '29*2=58'] Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[62, 60, 29, 27], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [29, 27, 2] Generated Node #0,0: 85:[29, 27, 2] Operation: 62-60=2 Exploring Operation: 62+29=91, Resulting Numbers: [60, 27, 91] Generated Node #0,1: 85:[60, 27, 91] Operation: 62+29=91 Exploring Operation: 60+27=87, Resulting Numbers: [62, 29, 87] Generated Node #0,2: 85:[62, 29, 87] Operation: 60+27=87 Exploring Operation: 62+27=89, Resulting Numbers: [60, 29, 89] Generated Node #0,3: 85:[60, 29, 89] Operation: 62+27=89 Exploring Operation: 60+29=89, Resulting Numbers: [62, 27, 89] Generated Node #0,4: 85:[62, 27, 89] Operation: 60+29=89 Moving to Node #0,0 Current State: 85:[29, 27, 2], Operations: ['62-60=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27, 27] Generated Node #0,0,0: 85:[27, 27] Operation: 29-2=27 Exploring Operation: 29+2=31, Resulting Numbers: [27, 31] Generated Node #0,0,1: 85:[27, 31] Operation: 29+2=31 Exploring Operation: 29-27=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 85:[2, 2] Operation: 29-27=2 Exploring Operation: 27+2=29, Resulting Numbers: [29, 29] Generated Node #0,0,3: 85:[29, 29] Operation: 27+2=29 Exploring Operation: 27-2=25, Resulting Numbers: [29, 25] Generated Node #0,0,4: 85:[29, 25] Operation: 27-2=25 Moving to Node #0,4 Current State: 85:[62, 27, 89], Operations: ['60+29=89'] Exploring Operation: 62-27=35, Resulting Numbers: [89, 35] Generated Node #0,4,0: 85:[89, 35] Operation: 62-27=35 Exploring Operation: 62+27=89, Resulting Numbers: [89, 89] Generated Node #0,4,1: 85:[89, 89] Operation: 62+27=89 Exploring Operation: 27+89=116, Resulting Numbers: [62, 116] Generated Node #0,4,2: 85:[62, 116] Operation: 27+89=116 Exploring Operation: 89-27=62, Resulting Numbers: [62, 62] Generated Node #0,4,3: 85:[62, 62] Operation: 89-27=62 Exploring Operation: 89-62=27, Resulting Numbers: [27, 27] Generated Node #0,4,4: 85:[27, 27] Operation: 89-62=27 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 85:[89, 89], Operations: ['60+29=89', '62+27=89'] Exploring Operation: 89-89=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 89+89=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 89/89=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 89*89=7921, Resulting Numbers: [7921] 7921,85 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 #0,4,4 Current State: 85:[27, 27], Operations: ['60+29=89', '89-62=27'] Exploring Operation: 27-27=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 27/27=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 27*27=729, Resulting Numbers: [729] 729,85 unequal: No Solution Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,85 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 #0,4,0 Current State: 85:[89, 35], Operations: ['60+29=89', '62-27=35'] Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,85 unequal: No Solution Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,85 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 #0,4,3 Current State: 85:[62, 62], Operations: ['60+29=89', '89-27=62'] Exploring Operation: 62+62=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 62-62=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 62*62=3844, Resulting Numbers: [3844] 3844,85 unequal: No Solution Exploring Operation: 62/62=1, Resulting Numbers: [1] 1,85 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 #0,4,2 Current State: 85:[62, 116], Operations: ['60+29=89', '27+89=116'] Exploring Operation: 62+116=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 62*116=7192, Resulting Numbers: [7192] 7192,85 unequal: No Solution Exploring Operation: 116-62=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 85:[62, 29, 87], Operations: ['60+27=87'] Exploring Operation: 87-62=25, Resulting Numbers: [29, 25] Generated Node #0,2,0: 85:[29, 25] Operation: 87-62=25 Exploring Operation: 62-29=33, Resulting Numbers: [87, 33] Generated Node #0,2,1: 85:[87, 33] Operation: 62-29=33 Exploring Operation: 62+29=91, Resulting Numbers: [87, 91] Generated Node #0,2,2: 85:[87, 91] Operation: 62+29=91 Exploring Operation: 87/29=3, Resulting Numbers: [62, 3] Generated Node #0,2,3: 85:[62, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [62, 58] Generated Node #0,2,4: 85:[62, 58] Operation: 87-29=58 Moving to Node #0,1 Current State: 85:[60, 27, 91], Operations: ['62+29=91'] Exploring Operation: 27+91=118, Resulting Numbers: [60, 118] Generated Node #0,1,0: 85:[60, 118] Operation: 27+91=118 Exploring Operation: 60-27=33, Resulting Numbers: [91, 33] Generated Node #0,1,1: 85:[91, 33] Operation: 60-27=33 Exploring Operation: 91-60=31, Resulting Numbers: [27, 31] Generated Node #0,1,2: 85:[27, 31] Operation: 91-60=31 Exploring Operation: 91-27=64, Resulting Numbers: [60, 64] Generated Node #0,1,3: 85:[60, 64] Operation: 91-27=64 Exploring Operation: 60+27=87, Resulting Numbers: [91, 87] Generated Node #0,1,4: 85:[91, 87] Operation: 60+27=87 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 85:[91, 87], Operations: ['62+29=91', '60+27=87'] Exploring Operation: 91-87=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 91+87=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 91*87=7917, Resulting Numbers: [7917] 7917,85 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 #0,1,1 Current State: 85:[91, 33], Operations: ['62+29=91', '60-27=33'] Exploring Operation: 91+33=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 91-33=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 91*33=3003, Resulting Numbers: [3003] 3003,85 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 #0,1,2 Current State: 85:[27, 31], Operations: ['62+29=91', '91-60=31'] Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,85 unequal: No Solution Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,85 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 #0,1,3 Current State: 85:[60, 64], Operations: ['62+29=91', '91-27=64'] Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,85 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 #0,1,0 Current State: 85:[60, 118], Operations: ['62+29=91', '27+91=118'] Exploring Operation: 60*118=7080, Resulting Numbers: [7080] 7080,85 unequal: No Solution Exploring Operation: 118-60=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 60+118=178, Resulting Numbers: [178] 178,85 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: 85:[60, 29, 89], Operations: ['62+27=89'] Exploring Operation: 60-29=31, Resulting Numbers: [89, 31] Generated Node #0,3,0: 85:[89, 31] Operation: 60-29=31 Exploring Operation: 29+89=118, Resulting Numbers: [60, 118] Generated Node #0,3,1: 85:[60, 118] Operation: 29+89=118 Exploring Operation: 60+29=89, Resulting Numbers: [89, 89] Generated Node #0,3,2: 85:[89, 89] Operation: 60+29=89 Exploring Operation: 89-29=60, Resulting Numbers: [60, 60] Generated Node #0,3,3: 85:[60, 60] Operation: 89-29=60 Exploring Operation: 89-60=29, Resulting Numbers: [29, 29] Generated Node #0,3,4: 85:[29, 29] Operation: 89-60=29 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[89, 89], Operations: ['62+27=89', '60+29=89'] Exploring Operation: 89-89=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 89+89=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 89*89=7921, Resulting Numbers: [7921] 7921,85 unequal: No Solution Exploring Operation: 89/89=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[89, 31], Operations: ['62+27=89', '60-29=31'] Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,85 unequal: No Solution Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 85:[29, 29], Operations: ['62+27=89', '89-60=29'] Exploring Operation: 29-29=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 29*29=841, Resulting Numbers: [841] 841,85 unequal: No Solution Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 29/29=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 85:[60, 60], Operations: ['62+27=89', '89-29=60'] Exploring Operation: 60-60=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 60/60=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 60*60=3600, Resulting Numbers: [3600] 3600,85 unequal: No Solution Exploring Operation: 60+60=120, Resulting Numbers: [120] 120,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 85:[60, 118], Operations: ['62+27=89', '29+89=118'] Exploring Operation: 60+118=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 118-60=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 60*118=7080, Resulting Numbers: [7080] 7080,85 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: 85:[2, 2], Operations: ['62-60=2', '29-27=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[87, 91], Operations: ['60+27=87', '62+29=91'] Exploring Operation: 87+91=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 91-87=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 87*91=7917, Resulting Numbers: [7917] 7917,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[87, 33], Operations: ['60+27=87', '62-29=33'] Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 87*33=2871, Resulting Numbers: [2871] 2871,85 unequal: No Solution Exploring Operation: 87+33=120, Resulting Numbers: [120] 120,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[29, 25], Operations: ['62-60=2', '27-2=25'] Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[27, 27], Operations: ['62-60=2', '29-2=27'] Exploring Operation: 27/27=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 27+27=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 27-27=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 27*27=729, Resulting Numbers: [729] 729,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[29, 25], Operations: ['60+27=87', '87-62=25'] Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[27, 31], Operations: ['62-60=2', '29+2=31'] Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,85 unequal: No Solution Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[29, 29], Operations: ['62-60=2', '27+2=29'] Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 29/29=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 29*29=841, Resulting Numbers: [841] 841,85 unequal: No Solution Exploring Operation: 29-29=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[62, 3], Operations: ['60+27=87', '87/29=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,85 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,85 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[62, 58], Operations: ['60+27=87', '87-29=58'] Exploring Operation: 62-58=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 62*58=3596, Resulting Numbers: [3596] 3596,85 unequal: No Solution Exploring Operation: 62+58=120, Resulting Numbers: [120] 120,85 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 55, 37, 74, 43 ]
61
[ "55+37=92", "74-43=31", "92-31=61" ]
Current State: 61:[55, 37, 74, 43], Operations: [] Exploring Operation: 55+37=92, Resulting Numbers: [74, 43, 92] Generated Node #2: [74, 43, 92] from Operation: 55+37=92 Current State: 61:[74, 43, 92], Operations: ['55+37=92'] Exploring Operation: 74-43=31, Resulting Numbers: [92, 31] Generated Node #3: [92, 31] from Operation: 74-43=31 Current State: 61:[92, 31], Operations: ['55+37=92', '74-43=31'] Exploring Operation: 92-31=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[55, 37, 74, 43], Operations: [] Exploring Operation: 74-37=37, Resulting Numbers: [55, 43, 37] Generated Node #0,0: 61:[55, 43, 37] Operation: 74-37=37 Exploring Operation: 74-43=31, Resulting Numbers: [55, 37, 31] Generated Node #0,1: 61:[55, 37, 31] Operation: 74-43=31 Exploring Operation: 37+43=80, Resulting Numbers: [55, 74, 80] Generated Node #0,2: 61:[55, 74, 80] Operation: 37+43=80 Exploring Operation: 55+37=92, Resulting Numbers: [74, 43, 92] Generated Node #0,3: 61:[74, 43, 92] Operation: 55+37=92 Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[55, 74, 80], Operations: ['37+43=80'] Exploring Operation: 80-74=6, Resulting Numbers: [55, 6] Generated Node #0,2,0: 61:[55, 6] Operation: 80-74=6 Exploring Operation: 74-55=19, Resulting Numbers: [80, 19] Generated Node #0,2,1: 61:[80, 19] Operation: 74-55=19 Exploring Operation: 55+74=129, Resulting Numbers: [80, 129] Generated Node #0,2,2: 61:[80, 129] Operation: 55+74=129 Exploring Operation: 80-55=25, Resulting Numbers: [74, 25] Generated Node #0,2,3: 61:[74, 25] Operation: 80-55=25 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 61:[74, 25], Operations: ['37+43=80', '80-55=25'] Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 74+25=99, Resulting Numbers: [99] 99,61 unequal: No Solution Exploring Operation: 74*25=1850, Resulting Numbers: [1850] 1850,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[55, 6], Operations: ['37+43=80', '80-74=6'] Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 55*6=330, Resulting Numbers: [330] 330,61 unequal: No Solution Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[55, 37, 74, 43], Operations: [] Exploring Operation: 37+43=80, Resulting Numbers: [55, 74, 80] Generated Node #0,2: 61:[55, 74, 80] Operation: 37+43=80 Moving to Node #0,2 Current State: 61:[55, 74, 80], Operations: ['37+43=80'] Exploring Operation: 80-74=6, Resulting Numbers: [55, 6] Generated Node #0,2,0: 61:[55, 6] Operation: 80-74=6 Moving to Node #0,2,0 Current State: 61:[55, 6], Operations: ['37+43=80', '80-74=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 74, 47, 75, 80 ]
22
[ "74-47=27", "80-75=5", "27-5=22" ]
Current State: 22:[74, 47, 75, 80], Operations: [] Exploring Operation: 74-47=27, Resulting Numbers: [75, 80, 27] Generated Node #2: [75, 80, 27] from Operation: 74-47=27 Current State: 22:[75, 80, 27], Operations: ['74-47=27'] Exploring Operation: 80-75=5, Resulting Numbers: [27, 5] Generated Node #3: [27, 5] from Operation: 80-75=5 Current State: 22:[27, 5], Operations: ['74-47=27', '80-75=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[74, 47, 75, 80], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [74, 47, 5] Generated Node #0,0: 22:[74, 47, 5] Operation: 80-75=5 Exploring Operation: 74-47=27, Resulting Numbers: [75, 80, 27] Generated Node #0,1: 22:[75, 80, 27] Operation: 74-47=27 Exploring Operation: 80-74=6, Resulting Numbers: [47, 75, 6] Generated Node #0,2: 22:[47, 75, 6] Operation: 80-74=6 Exploring Operation: 75-74=1, Resulting Numbers: [47, 80, 1] Generated Node #0,3: 22:[47, 80, 1] Operation: 75-74=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[74, 47, 5], Operations: ['80-75=5'] Exploring Operation: 74+5=79, Resulting Numbers: [47, 79] Generated Node #0,0,0: 22:[47, 79] Operation: 74+5=79 Exploring Operation: 74-5=69, Resulting Numbers: [47, 69] Generated Node #0,0,1: 22:[47, 69] Operation: 74-5=69 Exploring Operation: 47-5=42, Resulting Numbers: [74, 42] Generated Node #0,0,2: 22:[74, 42] Operation: 47-5=42 Exploring Operation: 74-47=27, Resulting Numbers: [5, 27] Generated Node #0,0,3: 22:[5, 27] Operation: 74-47=27 Moving to Node #0,0,3 Current State: 22:[5, 27], Operations: ['80-75=5', '74-47=27'] Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,22 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,22 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[74, 47, 75, 80], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [74, 47, 5] Generated Node #0,0: 22:[74, 47, 5] Operation: 80-75=5 Moving to Node #0,0 Current State: 22:[74, 47, 5], Operations: ['80-75=5'] Exploring Operation: 74-47=27, Resulting Numbers: [5, 27] Generated Node #0,0,3: 22:[5, 27] Operation: 74-47=27 Moving to Node #0,0,3 Current State: 22:[5, 27], Operations: ['80-75=5', '74-47=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 58, 51, 35, 48 ]
26
[ "58+51=109", "35+48=83", "109-83=26" ]
Current State: 26:[58, 51, 35, 48], Operations: [] Exploring Operation: 58+51=109, Resulting Numbers: [35, 48, 109] Generated Node #2: [35, 48, 109] from Operation: 58+51=109 Current State: 26:[35, 48, 109], Operations: ['58+51=109'] Exploring Operation: 35+48=83, Resulting Numbers: [109, 83] Generated Node #3: [109, 83] from Operation: 35+48=83 Current State: 26:[109, 83], Operations: ['58+51=109', '35+48=83'] Exploring Operation: 109-83=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[58, 51, 35, 48], Operations: [] Exploring Operation: 58-51=7, Resulting Numbers: [35, 48, 7] Generated Node #0,0: 26:[35, 48, 7] Operation: 58-51=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[35, 48, 7], Operations: ['58-51=7'] Exploring Operation: 48-35=13, Resulting Numbers: [7, 13] Generated Node #0,0,0: 26:[7, 13] Operation: 48-35=13 Moving to Node #0,0,0 Current State: 26:[7, 13], Operations: ['58-51=7', '48-35=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,26 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
[ 16, 72, 30, 75 ]
49
[ "72-16=56", "30+75=105", "105-56=49" ]
Current State: 49:[16, 72, 30, 75], Operations: [] Exploring Operation: 72-16=56, Resulting Numbers: [30, 75, 56] Generated Node #2: [30, 75, 56] from Operation: 72-16=56 Current State: 49:[30, 75, 56], Operations: ['72-16=56'] Exploring Operation: 30+75=105, Resulting Numbers: [56, 105] Generated Node #3: [56, 105] from Operation: 30+75=105 Current State: 49:[56, 105], Operations: ['72-16=56', '30+75=105'] Exploring Operation: 105-56=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[16, 72, 30, 75], Operations: [] Exploring Operation: 72-30=42, Resulting Numbers: [16, 75, 42] Generated Node #0,0: 49:[16, 75, 42] Operation: 72-30=42 Exploring Operation: 72-16=56, Resulting Numbers: [30, 75, 56] Generated Node #0,1: 49:[30, 75, 56] Operation: 72-16=56 Exploring Operation: 75-30=45, Resulting Numbers: [16, 72, 45] Generated Node #0,2: 49:[16, 72, 45] Operation: 75-30=45 Exploring Operation: 75-72=3, Resulting Numbers: [16, 30, 3] Generated Node #0,3: 49:[16, 30, 3] Operation: 75-72=3 Exploring Operation: 16+30=46, Resulting Numbers: [72, 75, 46] Generated Node #0,4: 49:[72, 75, 46] Operation: 16+30=46 Moving to Node #0,3 Current State: 49:[16, 30, 3], Operations: ['75-72=3'] Exploring Operation: 30-16=14, Resulting Numbers: [3, 14] Generated Node #0,3,0: 49:[3, 14] Operation: 30-16=14 Exploring Operation: 16+30=46, Resulting Numbers: [3, 46] Generated Node #0,3,1: 49:[3, 46] Operation: 16+30=46 Exploring Operation: 30/3=10, Resulting Numbers: [16, 10] Generated Node #0,3,2: 49:[16, 10] Operation: 30/3=10 Exploring Operation: 16-3=13, Resulting Numbers: [30, 13] Generated Node #0,3,3: 49:[30, 13] Operation: 16-3=13 Exploring Operation: 16*3=48, Resulting Numbers: [30, 48] Generated Node #0,3,4: 49:[30, 48] Operation: 16*3=48 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 49:[3, 46], Operations: ['75-72=3', '16+30=46'] Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[16, 72, 30, 75], Operations: [] Exploring Operation: 75-72=3, Resulting Numbers: [16, 30, 3] Generated Node #0,3: 49:[16, 30, 3] Operation: 75-72=3 Moving to Node #0,3 Current State: 49:[16, 30, 3], Operations: ['75-72=3'] Exploring Operation: 16+30=46, Resulting Numbers: [3, 46] Generated Node #0,3,1: 49:[3, 46] Operation: 16+30=46 Moving to Node #0,3,1 Current State: 49:[3, 46], Operations: ['75-72=3', '16+30=46'] Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 61, 58, 26, 31 ]
15
[ "61-58=3", "31-26=5", "3*5=15" ]
Current State: 15:[61, 58, 26, 31], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [26, 31, 3] Generated Node #2: [26, 31, 3] from Operation: 61-58=3 Current State: 15:[26, 31, 3], Operations: ['61-58=3'] Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #3: [3, 5] from Operation: 31-26=5 Current State: 15:[3, 5], Operations: ['61-58=3', '31-26=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[61, 58, 26, 31], Operations: [] Exploring Operation: 61-31=30, Resulting Numbers: [58, 26, 30] Generated Node #0,0: 15:[58, 26, 30] Operation: 61-31=30 Exploring Operation: 61-58=3, Resulting Numbers: [26, 31, 3] Generated Node #0,1: 15:[26, 31, 3] Operation: 61-58=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[26, 31, 3], Operations: ['61-58=3'] Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 15:[3, 5] Operation: 31-26=5 Exploring Operation: 26-3=23, Resulting Numbers: [31, 23] Generated Node #0,1,1: 15:[31, 23] Operation: 26-3=23 Moving to Node #0,1,0 Current State: 15:[3, 5], Operations: ['61-58=3', '31-26=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[61, 58, 26, 31], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [26, 31, 3] Generated Node #0,1: 15:[26, 31, 3] Operation: 61-58=3 Moving to Node #0,1 Current State: 15:[26, 31, 3], Operations: ['61-58=3'] Exploring Operation: 31-26=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 15:[3, 5] Operation: 31-26=5 Moving to Node #0,1,0 Current State: 15:[3, 5], Operations: ['61-58=3', '31-26=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 69, 35, 38, 1 ]
22
[ "38-35=3", "69/3=23", "23-1=22" ]
Current State: 22:[69, 35, 38, 1], Operations: [] Exploring Operation: 38-35=3, Resulting Numbers: [69, 1, 3] Generated Node #2: [69, 1, 3] from Operation: 38-35=3 Current State: 22:[69, 1, 3], Operations: ['38-35=3'] Exploring Operation: 69/3=23, Resulting Numbers: [1, 23] Generated Node #3: [1, 23] from Operation: 69/3=23 Current State: 22:[1, 23], Operations: ['38-35=3', '69/3=23'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[69, 35, 38, 1], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [35, 1, 31] Generated Node #0,0: 22:[35, 1, 31] Operation: 69-38=31 Moving to Node #0,0 Current State: 22:[35, 1, 31], Operations: ['69-38=31'] Exploring Operation: 35-31=4, Resulting Numbers: [1, 4] Generated Node #0,0,0: 22:[1, 4] Operation: 35-31=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[1, 4], Operations: ['69-38=31', '35-31=4'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 41, 80, 40, 44 ]
21
[ "44-40=4", "80/4=20", "41-20=21" ]
Current State: 21:[41, 80, 40, 44], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [41, 80, 4] Generated Node #2: [41, 80, 4] from Operation: 44-40=4 Current State: 21:[41, 80, 4], Operations: ['44-40=4'] Exploring Operation: 80/4=20, Resulting Numbers: [41, 20] Generated Node #3: [41, 20] from Operation: 80/4=20 Current State: 21:[41, 20], Operations: ['44-40=4', '80/4=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[41, 80, 40, 44], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [41, 44, 2] Generated Node #0,0: 21:[41, 44, 2] Operation: 80/40=2 Exploring Operation: 80-41=39, Resulting Numbers: [40, 44, 39] Generated Node #0,1: 21:[40, 44, 39] Operation: 80-41=39 Exploring Operation: 80-44=36, Resulting Numbers: [41, 40, 36] Generated Node #0,2: 21:[41, 40, 36] Operation: 80-44=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[41, 44, 2], Operations: ['80/40=2'] Exploring Operation: 41-2=39, Resulting Numbers: [44, 39] Generated Node #0,0,0: 21:[44, 39] Operation: 41-2=39 Exploring Operation: 44/2=22, Resulting Numbers: [41, 22] Generated Node #0,0,1: 21:[41, 22] Operation: 44/2=22 Exploring Operation: 44-41=3, Resulting Numbers: [2, 3] Generated Node #0,0,2: 21:[2, 3] Operation: 44-41=3 Moving to Node #0,0,2 Current State: 21:[2, 3], Operations: ['80/40=2', '44-41=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[41, 22], Operations: ['80/40=2', '44/2=22'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,21 unequal: No Solution Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[44, 39], Operations: ['80/40=2', '41-2=39'] Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,21 unequal: No Solution Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[41, 40, 36], Operations: ['80-44=36'] Exploring Operation: 41-40=1, Resulting Numbers: [36, 1] Generated Node #0,2,0: 21:[36, 1] Operation: 41-40=1 Exploring Operation: 41-36=5, Resulting Numbers: [40, 5] Generated Node #0,2,1: 21:[40, 5] Operation: 41-36=5 Exploring Operation: 40-36=4, Resulting Numbers: [41, 4] Generated Node #0,2,2: 21:[41, 4] Operation: 40-36=4 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[36, 1], Operations: ['80-44=36', '41-40=1'] Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,21 unequal: No Solution No 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: 21:[40, 5], Operations: ['80-44=36', '41-36=5'] Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,21 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,21 unequal: No Solution No 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: 21:[41, 4], Operations: ['80-44=36', '40-36=4'] Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,21 unequal: No Solution Exploring Operation: 41*4=164, Resulting Numbers: [164] 164,21 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,21 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: 21:[40, 44, 39], Operations: ['80-41=39'] Exploring Operation: 44-40=4, Resulting Numbers: [39, 4] Generated Node #0,1,0: 21:[39, 4] Operation: 44-40=4 Exploring Operation: 44-39=5, Resulting Numbers: [40, 5] Generated Node #0,1,1: 21:[40, 5] Operation: 44-39=5 Exploring Operation: 40-39=1, Resulting Numbers: [44, 1] Generated Node #0,1,2: 21:[44, 1] Operation: 40-39=1 Moving to Node #0,1,0 Current State: 21:[39, 4], Operations: ['80-41=39', '44-40=4'] Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,21 unequal: No Solution Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[40, 5], Operations: ['80-41=39', '44-39=5'] Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,21 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[44, 1], Operations: ['80-41=39', '40-39=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,21 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,21 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
[ 95, 99, 32, 70 ]
62
[ "99-95=4", "32/4=8", "70-8=62" ]
Current State: 62:[95, 99, 32, 70], Operations: [] Exploring Operation: 99-95=4, Resulting Numbers: [32, 70, 4] Generated Node #2: [32, 70, 4] from Operation: 99-95=4 Current State: 62:[32, 70, 4], Operations: ['99-95=4'] Exploring Operation: 32/4=8, Resulting Numbers: [70, 8] Generated Node #3: [70, 8] from Operation: 32/4=8 Current State: 62:[70, 8], Operations: ['99-95=4', '32/4=8'] Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[95, 99, 32, 70], Operations: [] Exploring Operation: 95-70=25, Resulting Numbers: [99, 32, 25] Generated Node #0,0: 62:[99, 32, 25] Operation: 95-70=25 Exploring Operation: 95-32=63, Resulting Numbers: [99, 70, 63] Generated Node #0,1: 62:[99, 70, 63] Operation: 95-32=63 Exploring Operation: 99-70=29, Resulting Numbers: [95, 32, 29] Generated Node #0,2: 62:[95, 32, 29] Operation: 99-70=29 Exploring Operation: 99-95=4, Resulting Numbers: [32, 70, 4] Generated Node #0,3: 62:[32, 70, 4] Operation: 99-95=4 Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[32, 70, 4], Operations: ['99-95=4'] Exploring Operation: 32-4=28, Resulting Numbers: [70, 28] Generated Node #0,3,0: 62:[70, 28] Operation: 32-4=28 Exploring Operation: 70-32=38, Resulting Numbers: [4, 38] Generated Node #0,3,1: 62:[4, 38] Operation: 70-32=38 Exploring Operation: 70-4=66, Resulting Numbers: [32, 66] Generated Node #0,3,2: 62:[32, 66] Operation: 70-4=66 Exploring Operation: 32+4=36, Resulting Numbers: [70, 36] Generated Node #0,3,3: 62:[70, 36] Operation: 32+4=36 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 62:[32, 66], Operations: ['99-95=4', '70-4=66'] Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 32+66=98, Resulting Numbers: [98] 98,62 unequal: No Solution Exploring Operation: 32*66=2112, Resulting Numbers: [2112] 2112,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[4, 38], Operations: ['99-95=4', '70-32=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,62 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[70, 28], Operations: ['99-95=4', '32-4=28'] Exploring Operation: 70+28=98, Resulting Numbers: [98] 98,62 unequal: No Solution Exploring Operation: 70*28=1960, Resulting Numbers: [1960] 1960,62 unequal: No Solution Exploring Operation: 70-28=42, Resulting Numbers: [42] 42,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 62:[70, 36], Operations: ['99-95=4', '32+4=36'] Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,62 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[95, 32, 29], Operations: ['99-70=29'] Exploring Operation: 95-32=63, Resulting Numbers: [29, 63] Generated Node #0,2,0: 62:[29, 63] Operation: 95-32=63 Exploring Operation: 95-29=66, Resulting Numbers: [32, 66] Generated Node #0,2,1: 62:[32, 66] Operation: 95-29=66 Exploring Operation: 32+29=61, Resulting Numbers: [95, 61] Generated Node #0,2,2: 62:[95, 61] Operation: 32+29=61 Exploring Operation: 32-29=3, Resulting Numbers: [95, 3] Generated Node #0,2,3: 62:[95, 3] Operation: 32-29=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[29, 63], Operations: ['99-70=29', '95-32=63'] Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,62 unequal: No Solution Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[32, 66], Operations: ['99-70=29', '95-29=66'] Exploring Operation: 32*66=2112, Resulting Numbers: [2112] 2112,62 unequal: No Solution Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 32+66=98, Resulting Numbers: [98] 98,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[95, 61], Operations: ['99-70=29', '32+29=61'] Exploring Operation: 95-61=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 95+61=156, Resulting Numbers: [156] 156,62 unequal: No Solution Exploring Operation: 95*61=5795, Resulting Numbers: [5795] 5795,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 62:[95, 3], Operations: ['99-70=29', '32-29=3'] Exploring Operation: 95*3=285, Resulting Numbers: [285] 285,62 unequal: No Solution Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,62 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[99, 32, 25], Operations: ['95-70=25'] Exploring Operation: 32+25=57, Resulting Numbers: [99, 57] Generated Node #0,0,0: 62:[99, 57] Operation: 32+25=57 Exploring Operation: 99-32=67, Resulting Numbers: [25, 67] Generated Node #0,0,1: 62:[25, 67] Operation: 99-32=67 Exploring Operation: 32-25=7, Resulting Numbers: [99, 7] Generated Node #0,0,2: 62:[99, 7] Operation: 32-25=7 Exploring Operation: 99-25=74, Resulting Numbers: [32, 74] Generated Node #0,0,3: 62:[32, 74] Operation: 99-25=74 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[25, 67], Operations: ['95-70=25', '99-32=67'] Exploring Operation: 25+67=92, Resulting Numbers: [92] 92,62 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 25*67=1675, Resulting Numbers: [1675] 1675,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 62:[32, 74], Operations: ['95-70=25', '99-25=74'] Exploring Operation: 32+74=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 32*74=2368, Resulting Numbers: [2368] 2368,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[99, 57], Operations: ['95-70=25', '32+25=57'] Exploring Operation: 99-57=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 99*57=5643, Resulting Numbers: [5643] 5643,62 unequal: No Solution Exploring Operation: 99+57=156, Resulting Numbers: [156] 156,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[99, 7], Operations: ['95-70=25', '32-25=7'] Exploring Operation: 99*7=693, Resulting Numbers: [693] 693,62 unequal: No Solution Exploring Operation: 99+7=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[99, 70, 63], Operations: ['95-32=63'] Exploring Operation: 99+70=169, Resulting Numbers: [63, 169] Generated Node #0,1,0: 62:[63, 169] Operation: 99+70=169 Exploring Operation: 70-63=7, Resulting Numbers: [99, 7] Generated Node #0,1,1: 62:[99, 7] Operation: 70-63=7 Exploring Operation: 99-70=29, Resulting Numbers: [63, 29] Generated Node #0,1,2: 62:[63, 29] Operation: 99-70=29 Exploring Operation: 99-63=36, Resulting Numbers: [70, 36] Generated Node #0,1,3: 62:[70, 36] Operation: 99-63=36 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[63, 29], Operations: ['95-32=63', '99-70=29'] Exploring Operation: 63*29=1827, Resulting Numbers: [1827] 1827,62 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 63+29=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 62:[70, 36], Operations: ['95-32=63', '99-63=36'] Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[99, 7], Operations: ['95-32=63', '70-63=7'] Exploring Operation: 99+7=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 99*7=693, Resulting Numbers: [693] 693,62 unequal: No Solution Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[63, 169], Operations: ['95-32=63', '99+70=169'] Exploring Operation: 63*169=10647, Resulting Numbers: [10647] 10647,62 unequal: No Solution Exploring Operation: 169-63=106, Resulting Numbers: [106] 106,62 unequal: No Solution Exploring Operation: 63+169=232, Resulting Numbers: [232] 232,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 14, 20, 50, 68 ]
52
[ "14+20=34", "68-50=18", "34+18=52" ]
Current State: 52:[14, 20, 50, 68], Operations: [] Exploring Operation: 14+20=34, Resulting Numbers: [50, 68, 34] Generated Node #2: [50, 68, 34] from Operation: 14+20=34 Current State: 52:[50, 68, 34], Operations: ['14+20=34'] Exploring Operation: 68-50=18, Resulting Numbers: [34, 18] Generated Node #3: [34, 18] from Operation: 68-50=18 Current State: 52:[34, 18], Operations: ['14+20=34', '68-50=18'] Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[14, 20, 50, 68], Operations: [] Exploring Operation: 68-14=54, Resulting Numbers: [20, 50, 54] Generated Node #0,0: 52:[20, 50, 54] Operation: 68-14=54 Exploring Operation: 68-50=18, Resulting Numbers: [14, 20, 18] Generated Node #0,1: 52:[14, 20, 18] Operation: 68-50=18 Exploring Operation: 20-14=6, Resulting Numbers: [50, 68, 6] Generated Node #0,2: 52:[50, 68, 6] Operation: 20-14=6 Exploring Operation: 68-20=48, Resulting Numbers: [14, 50, 48] Generated Node #0,3: 52:[14, 50, 48] Operation: 68-20=48 Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[14, 50, 48], Operations: ['68-20=48'] Exploring Operation: 50-48=2, Resulting Numbers: [14, 2] Generated Node #0,3,0: 52:[14, 2] Operation: 50-48=2 Exploring Operation: 50-14=36, Resulting Numbers: [48, 36] Generated Node #0,3,1: 52:[48, 36] Operation: 50-14=36 Exploring Operation: 48-14=34, Resulting Numbers: [50, 34] Generated Node #0,3,2: 52:[50, 34] Operation: 48-14=34 Exploring Operation: 14+48=62, Resulting Numbers: [50, 62] Generated Node #0,3,3: 52:[50, 62] Operation: 14+48=62 Moving to Node #0,3,0 Current State: 52:[14, 2], Operations: ['68-20=48', '50-48=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[50, 34], Operations: ['68-20=48', '48-14=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,52 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[50, 62], Operations: ['68-20=48', '14+48=62'] Exploring Operation: 50+62=112, Resulting Numbers: [112] 112,52 unequal: No Solution Exploring Operation: 50*62=3100, Resulting Numbers: [3100] 3100,52 unequal: No Solution Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[48, 36], Operations: ['68-20=48', '50-14=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[20, 50, 54], Operations: ['68-14=54'] Exploring Operation: 50-20=30, Resulting Numbers: [54, 30] Generated Node #0,0,0: 52:[54, 30] Operation: 50-20=30 Exploring Operation: 54-20=34, Resulting Numbers: [50, 34] Generated Node #0,0,1: 52:[50, 34] Operation: 54-20=34 Exploring Operation: 20+50=70, Resulting Numbers: [54, 70] Generated Node #0,0,2: 52:[54, 70] Operation: 20+50=70 Exploring Operation: 54-50=4, Resulting Numbers: [20, 4] Generated Node #0,0,3: 52:[20, 4] Operation: 54-50=4 Moving to Node #0,0,0 Current State: 52:[54, 30], Operations: ['68-14=54', '50-20=30'] Exploring Operation: 54+30=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 54*30=1620, Resulting Numbers: [1620] 1620,52 unequal: No Solution Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[20, 4], Operations: ['68-14=54', '54-50=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[50, 34], Operations: ['68-14=54', '54-20=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,52 unequal: No Solution Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[54, 70], Operations: ['68-14=54', '20+50=70'] Exploring Operation: 54*70=3780, Resulting Numbers: [3780] 3780,52 unequal: No Solution Exploring Operation: 54+70=124, Resulting Numbers: [124] 124,52 unequal: No Solution Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[14, 20, 18], Operations: ['68-50=18'] Exploring Operation: 14+18=32, Resulting Numbers: [20, 32] Generated Node #0,1,0: 52:[20, 32] Operation: 14+18=32 Exploring Operation: 20-18=2, Resulting Numbers: [14, 2] Generated Node #0,1,1: 52:[14, 2] Operation: 20-18=2 Exploring Operation: 20-14=6, Resulting Numbers: [18, 6] Generated Node #0,1,2: 52:[18, 6] Operation: 20-14=6 Exploring Operation: 18-14=4, Resulting Numbers: [20, 4] Generated Node #0,1,3: 52:[20, 4] Operation: 18-14=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[14, 2], Operations: ['68-50=18', '20-18=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,52 unequal: No Solution No 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: 52:[20, 4], Operations: ['68-50=18', '18-14=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,52 unequal: No Solution No 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: 52:[18, 6], Operations: ['68-50=18', '20-14=6'] Exploring Operation: 18*6=108, Resulting Numbers: [108] 108,52 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,52 unequal: No Solution Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,52 unequal: No Solution No 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: 52:[20, 32], Operations: ['68-50=18', '14+18=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[14, 20, 50, 68], Operations: [] Exploring Operation: 68-50=18, Resulting Numbers: [14, 20, 18] Generated Node #0,1: 52:[14, 20, 18] Operation: 68-50=18 Moving to Node #0,1 Current State: 52:[14, 20, 18], Operations: ['68-50=18'] Exploring Operation: 14+18=32, Resulting Numbers: [20, 32] Generated Node #0,1,0: 52:[20, 32] Operation: 14+18=32 Moving to Node #0,1,0 Current State: 52:[20, 32], Operations: ['68-50=18', '14+18=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.948785
hs_4
mult_heuristic
[ 83, 40, 95, 3 ]
97
[ "83-3=80", "80/40=2", "95+2=97" ]
Current State: 97:[83, 40, 95, 3], Operations: [] Exploring Operation: 83-3=80, Resulting Numbers: [40, 95, 80] Generated Node #2: [40, 95, 80] from Operation: 83-3=80 Current State: 97:[40, 95, 80], Operations: ['83-3=80'] Exploring Operation: 80/40=2, Resulting Numbers: [95, 2] Generated Node #3: [95, 2] from Operation: 80/40=2 Current State: 97:[95, 2], Operations: ['83-3=80', '80/40=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[83, 40, 95, 3], Operations: [] Exploring Operation: 83+3=86, Resulting Numbers: [40, 95, 86] Generated Node #0,0: 97:[40, 95, 86] Operation: 83+3=86 Exploring Operation: 40*3=120, Resulting Numbers: [83, 95, 120] Generated Node #0,1: 97:[83, 95, 120] Operation: 40*3=120 Exploring Operation: 40+3=43, Resulting Numbers: [83, 95, 43] Generated Node #0,2: 97:[83, 95, 43] Operation: 40+3=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[83, 95, 120], Operations: ['40*3=120'] Exploring Operation: 83+95=178, Resulting Numbers: [120, 178] Generated Node #0,1,0: 97:[120, 178] Operation: 83+95=178 Exploring Operation: 120-83=37, Resulting Numbers: [95, 37] Generated Node #0,1,1: 97:[95, 37] Operation: 120-83=37 Exploring Operation: 120-95=25, Resulting Numbers: [83, 25] Generated Node #0,1,2: 97:[83, 25] Operation: 120-95=25 Moving to Node #0,1,1 Current State: 97:[95, 37], Operations: ['40*3=120', '120-83=37'] Exploring Operation: 95-37=58, Resulting Numbers: [58] 58,97 unequal: No Solution Exploring Operation: 95*37=3515, Resulting Numbers: [3515] 3515,97 unequal: No Solution Exploring Operation: 95+37=132, Resulting Numbers: [132] 132,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[83, 25], Operations: ['40*3=120', '120-95=25'] Exploring Operation: 83+25=108, Resulting Numbers: [108] 108,97 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,97 unequal: No Solution Exploring Operation: 83*25=2075, Resulting Numbers: [2075] 2075,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[120, 178], Operations: ['40*3=120', '83+95=178'] Exploring Operation: 120*178=21360, Resulting Numbers: [21360] 21360,97 unequal: No Solution Exploring Operation: 120+178=298, Resulting Numbers: [298] 298,97 unequal: No Solution Exploring Operation: 178-120=58, Resulting Numbers: [58] 58,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[40, 95, 86], Operations: ['83+3=86'] Exploring Operation: 40+95=135, Resulting Numbers: [86, 135] Generated Node #0,0,0: 97:[86, 135] Operation: 40+95=135 Exploring Operation: 95-40=55, Resulting Numbers: [86, 55] Generated Node #0,0,1: 97:[86, 55] Operation: 95-40=55 Exploring Operation: 40+86=126, Resulting Numbers: [95, 126] Generated Node #0,0,2: 97:[95, 126] Operation: 40+86=126 Moving to Node #0,0,2 Current State: 97:[95, 126], Operations: ['83+3=86', '40+86=126'] Exploring Operation: 126-95=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 95+126=221, Resulting Numbers: [221] 221,97 unequal: No Solution Exploring Operation: 95*126=11970, Resulting Numbers: [11970] 11970,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[86, 135], Operations: ['83+3=86', '40+95=135'] Exploring Operation: 86*135=11610, Resulting Numbers: [11610] 11610,97 unequal: No Solution Exploring Operation: 135-86=49, Resulting Numbers: [49] 49,97 unequal: No Solution Exploring Operation: 86+135=221, Resulting Numbers: [221] 221,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[86, 55], Operations: ['83+3=86', '95-40=55'] Exploring Operation: 86-55=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 86+55=141, Resulting Numbers: [141] 141,97 unequal: No Solution Exploring Operation: 86*55=4730, Resulting Numbers: [4730] 4730,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[83, 95, 43], Operations: ['40+3=43'] Exploring Operation: 95+43=138, Resulting Numbers: [83, 138] Generated Node #0,2,0: 97:[83, 138] Operation: 95+43=138 Exploring Operation: 83-43=40, Resulting Numbers: [95, 40] Generated Node #0,2,1: 97:[95, 40] Operation: 83-43=40 Exploring Operation: 83+43=126, Resulting Numbers: [95, 126] Generated Node #0,2,2: 97:[95, 126] Operation: 83+43=126 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[95, 126], Operations: ['40+3=43', '83+43=126'] Exploring Operation: 126-95=31, Resulting Numbers: [31] 31,97 unequal: No Solution Exploring Operation: 95*126=11970, Resulting Numbers: [11970] 11970,97 unequal: No Solution Exploring Operation: 95+126=221, Resulting Numbers: [221] 221,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[83, 138], Operations: ['40+3=43', '95+43=138'] Exploring Operation: 83*138=11454, Resulting Numbers: [11454] 11454,97 unequal: No Solution Exploring Operation: 83+138=221, Resulting Numbers: [221] 221,97 unequal: No Solution Exploring Operation: 138-83=55, Resulting Numbers: [55] 55,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[95, 40], Operations: ['40+3=43', '83-43=40'] Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 95+40=135, Resulting Numbers: [135] 135,97 unequal: No Solution Exploring Operation: 95*40=3800, Resulting Numbers: [3800] 3800,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 70, 59, 87, 2 ]
40
[ "70+59=129", "87+2=89", "129-89=40" ]
Current State: 40:[70, 59, 87, 2], Operations: [] Exploring Operation: 70+59=129, Resulting Numbers: [87, 2, 129] Generated Node #2: [87, 2, 129] from Operation: 70+59=129 Current State: 40:[87, 2, 129], Operations: ['70+59=129'] Exploring Operation: 87+2=89, Resulting Numbers: [129, 89] Generated Node #3: [129, 89] from Operation: 87+2=89 Current State: 40:[129, 89], Operations: ['70+59=129', '87+2=89'] Exploring Operation: 129-89=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[70, 59, 87, 2], Operations: [] Exploring Operation: 87-59=28, Resulting Numbers: [70, 2, 28] Generated Node #0,0: 40:[70, 2, 28] Operation: 87-59=28 Exploring Operation: 87-70=17, Resulting Numbers: [59, 2, 17] Generated Node #0,1: 40:[59, 2, 17] Operation: 87-70=17 Exploring Operation: 70/2=35, Resulting Numbers: [59, 87, 35] Generated Node #0,2: 40:[59, 87, 35] Operation: 70/2=35 Exploring Operation: 70-59=11, Resulting Numbers: [87, 2, 11] Generated Node #0,3: 40:[87, 2, 11] Operation: 70-59=11 Moving to Node #0,1 Current State: 40:[59, 2, 17], Operations: ['87-70=17'] Exploring Operation: 2+17=19, Resulting Numbers: [59, 19] Generated Node #0,1,0: 40:[59, 19] Operation: 2+17=19 Exploring Operation: 59-17=42, Resulting Numbers: [2, 42] Generated Node #0,1,1: 40:[2, 42] Operation: 59-17=42 Exploring Operation: 59-2=57, Resulting Numbers: [17, 57] Generated Node #0,1,2: 40:[17, 57] Operation: 59-2=57 Exploring Operation: 59+2=61, Resulting Numbers: [17, 61] Generated Node #0,1,3: 40:[17, 61] Operation: 59+2=61 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[2, 42], Operations: ['87-70=17', '59-17=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,40 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,40 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[70, 59, 87, 2], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [59, 2, 17] Generated Node #0,1: 40:[59, 2, 17] Operation: 87-70=17 Moving to Node #0,1 Current State: 40:[59, 2, 17], Operations: ['87-70=17'] Exploring Operation: 59-17=42, Resulting Numbers: [2, 42] Generated Node #0,1,1: 40:[2, 42] Operation: 59-17=42 Moving to Node #0,1,1 Current State: 40:[2, 42], Operations: ['87-70=17', '59-17=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 3, 8, 33, 50 ]
57
[ "3*33=99", "50-8=42", "99-42=57" ]
Current State: 57:[3, 8, 33, 50], Operations: [] Exploring Operation: 3*33=99, Resulting Numbers: [8, 50, 99] Generated Node #2: [8, 50, 99] from Operation: 3*33=99 Current State: 57:[8, 50, 99], Operations: ['3*33=99'] Exploring Operation: 50-8=42, Resulting Numbers: [99, 42] Generated Node #3: [99, 42] from Operation: 50-8=42 Current State: 57:[99, 42], Operations: ['3*33=99', '50-8=42'] Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[3, 8, 33, 50], Operations: [] Exploring Operation: 50-33=17, Resulting Numbers: [3, 8, 17] Generated Node #0,0: 57:[3, 8, 17] Operation: 50-33=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[3, 8, 17], Operations: ['50-33=17'] Exploring Operation: 8-3=5, Resulting Numbers: [17, 5] Generated Node #0,0,0: 57:[17, 5] Operation: 8-3=5 Moving to Node #0,0,0 Current State: 57:[17, 5], Operations: ['50-33=17', '8-3=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,57 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, 11, 12 ]
53
[ "33/11=3", "62-12=50", "3+50=53" ]
Current State: 53:[33, 62, 11, 12], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [62, 12, 3] Generated Node #2: [62, 12, 3] from Operation: 33/11=3 Current State: 53:[62, 12, 3], Operations: ['33/11=3'] Exploring Operation: 62-12=50, Resulting Numbers: [3, 50] Generated Node #3: [3, 50] from Operation: 62-12=50 Current State: 53:[3, 50], Operations: ['33/11=3', '62-12=50'] Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[33, 62, 11, 12], Operations: [] Exploring Operation: 62-11=51, Resulting Numbers: [33, 12, 51] Generated Node #0,0: 53:[33, 12, 51] Operation: 62-11=51 Exploring Operation: 33+12=45, Resulting Numbers: [62, 11, 45] Generated Node #0,1: 53:[62, 11, 45] Operation: 33+12=45 Exploring Operation: 62-12=50, Resulting Numbers: [33, 11, 50] Generated Node #0,2: 53:[33, 11, 50] Operation: 62-12=50 Exploring Operation: 33+11=44, Resulting Numbers: [62, 12, 44] Generated Node #0,3: 53:[62, 12, 44] Operation: 33+11=44 Exploring Operation: 11+12=23, Resulting Numbers: [33, 62, 23] Generated Node #0,4: 53:[33, 62, 23] Operation: 11+12=23 Moving to Node #0,1 Current State: 53:[62, 11, 45], Operations: ['33+12=45'] Exploring Operation: 45-11=34, Resulting Numbers: [62, 34] Generated Node #0,1,0: 53:[62, 34] Operation: 45-11=34 Exploring Operation: 62+11=73, Resulting Numbers: [45, 73] Generated Node #0,1,1: 53:[45, 73] Operation: 62+11=73 Exploring Operation: 11+45=56, Resulting Numbers: [62, 56] Generated Node #0,1,2: 53:[62, 56] Operation: 11+45=56 Exploring Operation: 62-45=17, Resulting Numbers: [11, 17] Generated Node #0,1,3: 53:[11, 17] Operation: 62-45=17 Exploring Operation: 62-11=51, Resulting Numbers: [45, 51] Generated Node #0,1,4: 53:[45, 51] Operation: 62-11=51 Moving to Node #0,4 Current State: 53:[33, 62, 23], Operations: ['11+12=23'] Exploring Operation: 33-23=10, Resulting Numbers: [62, 10] Generated Node #0,4,0: 53:[62, 10] Operation: 33-23=10 Exploring Operation: 33+23=56, Resulting Numbers: [62, 56] Generated Node #0,4,1: 53:[62, 56] Operation: 33+23=56 Exploring Operation: 62-33=29, Resulting Numbers: [23, 29] Generated Node #0,4,2: 53:[23, 29] Operation: 62-33=29 Exploring Operation: 62-23=39, Resulting Numbers: [33, 39] Generated Node #0,4,3: 53:[33, 39] Operation: 62-23=39 Exploring Operation: 62+23=85, Resulting Numbers: [33, 85] Generated Node #0,4,4: 53:[33, 85] Operation: 62+23=85 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 53:[62, 56], Operations: ['11+12=23', '33+23=56'] Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,53 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 53:[33, 39], Operations: ['11+12=23', '62-23=39'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,53 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 53:[62, 10], Operations: ['11+12=23', '33-23=10'] Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,53 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,53 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 53:[33, 85], Operations: ['11+12=23', '62+23=85'] Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,53 unequal: No Solution Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,53 unequal: No Solution Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 53:[23, 29], Operations: ['11+12=23', '62-33=29'] Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,53 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,53 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,53 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: 53:[62, 12, 44], Operations: ['33+11=44'] Exploring Operation: 62+12=74, Resulting Numbers: [44, 74] Generated Node #0,3,0: 53:[44, 74] Operation: 62+12=74 Exploring Operation: 62-12=50, Resulting Numbers: [44, 50] Generated Node #0,3,1: 53:[44, 50] Operation: 62-12=50 Exploring Operation: 44-12=32, Resulting Numbers: [62, 32] Generated Node #0,3,2: 53:[62, 32] Operation: 44-12=32 Exploring Operation: 62-44=18, Resulting Numbers: [12, 18] Generated Node #0,3,3: 53:[12, 18] Operation: 62-44=18 Exploring Operation: 12+44=56, Resulting Numbers: [62, 56] Generated Node #0,3,4: 53:[62, 56] Operation: 12+44=56 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[44, 50], Operations: ['33+11=44', '62-12=50'] Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,53 unequal: No Solution Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,53 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 53:[62, 56], Operations: ['33+11=44', '12+44=56'] Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[44, 74], Operations: ['33+11=44', '62+12=74'] Exploring Operation: 44*74=3256, Resulting Numbers: [3256] 3256,53 unequal: No Solution Exploring Operation: 44+74=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[62, 32], Operations: ['33+11=44', '44-12=32'] Exploring Operation: 62*32=1984, Resulting Numbers: [1984] 1984,53 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 62+32=94, Resulting Numbers: [94] 94,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 53:[12, 18], Operations: ['33+11=44', '62-44=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,53 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,53 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: 53:[33, 12, 51], Operations: ['62-11=51'] Exploring Operation: 33+51=84, Resulting Numbers: [12, 84] Generated Node #0,0,0: 53:[12, 84] Operation: 33+51=84 Exploring Operation: 33+12=45, Resulting Numbers: [51, 45] Generated Node #0,0,1: 53:[51, 45] Operation: 33+12=45 Exploring Operation: 33-12=21, Resulting Numbers: [51, 21] Generated Node #0,0,2: 53:[51, 21] Operation: 33-12=21 Exploring Operation: 12+51=63, Resulting Numbers: [33, 63] Generated Node #0,0,3: 53:[33, 63] Operation: 12+51=63 Exploring Operation: 51-12=39, Resulting Numbers: [33, 39] Generated Node #0,0,4: 53:[33, 39] Operation: 51-12=39 Moving to Node #0,2 Current State: 53:[33, 11, 50], Operations: ['62-12=50'] Exploring Operation: 33+11=44, Resulting Numbers: [50, 44] Generated Node #0,2,0: 53:[50, 44] Operation: 33+11=44 Exploring Operation: 33/11=3, Resulting Numbers: [50, 3] Generated Node #0,2,1: 53:[50, 3] Operation: 33/11=3 Exploring Operation: 11+50=61, Resulting Numbers: [33, 61] Generated Node #0,2,2: 53:[33, 61] Operation: 11+50=61 Exploring Operation: 50-11=39, Resulting Numbers: [33, 39] Generated Node #0,2,3: 53:[33, 39] Operation: 50-11=39 Exploring Operation: 33-11=22, Resulting Numbers: [50, 22] Generated Node #0,2,4: 53:[50, 22] Operation: 33-11=22 Moving to Node #0,1,4 Current State: 53:[45, 51], Operations: ['33+12=45', '62-11=51'] Exploring Operation: 45*51=2295, Resulting Numbers: [2295] 2295,53 unequal: No Solution Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,53 unequal: No Solution Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[51, 45], Operations: ['62-11=51', '33+12=45'] Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 51*45=2295, Resulting Numbers: [2295] 2295,53 unequal: No Solution Exploring Operation: 51+45=96, Resulting Numbers: [96] 96,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[62, 56], Operations: ['33+12=45', '11+45=56'] Exploring Operation: 62+56=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 62*56=3472, Resulting Numbers: [3472] 3472,53 unequal: No Solution Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[50, 44], Operations: ['62-12=50', '33+11=44'] Exploring Operation: 50*44=2200, Resulting Numbers: [2200] 2200,53 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[62, 34], Operations: ['33+12=45', '45-11=34'] Exploring Operation: 62*34=2108, Resulting Numbers: [2108] 2108,53 unequal: No Solution Exploring Operation: 62-34=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 62+34=96, Resulting Numbers: [96] 96,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[33, 61], Operations: ['62-12=50', '11+50=61'] Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,53 unequal: No Solution Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,53 unequal: No Solution Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[45, 73], Operations: ['33+12=45', '62+11=73'] Exploring Operation: 45*73=3285, Resulting Numbers: [3285] 3285,53 unequal: No Solution Exploring Operation: 45+73=118, Resulting Numbers: [118] 118,53 unequal: No Solution Exploring Operation: 73-45=28, Resulting Numbers: [28] 28,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[33, 63], Operations: ['62-11=51', '12+51=63'] Exploring Operation: 33*63=2079, Resulting Numbers: [2079] 2079,53 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 33+63=96, Resulting Numbers: [96] 96,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[33, 39], Operations: ['62-12=50', '50-11=39'] Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,53 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,53 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[51, 21], Operations: ['62-11=51', '33-12=21'] Exploring Operation: 51+21=72, Resulting Numbers: [72] 72,53 unequal: No Solution Exploring Operation: 51*21=1071, Resulting Numbers: [1071] 1071,53 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[50, 22], Operations: ['62-12=50', '33-11=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,53 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[33, 39], Operations: ['62-11=51', '51-12=39'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,53 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,53 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[50, 3], Operations: ['62-12=50', '33/11=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,53 unequal: No Solution Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[33, 62, 11, 12], Operations: [] Exploring Operation: 62-12=50, Resulting Numbers: [33, 11, 50] Generated Node #0,2: 53:[33, 11, 50] Operation: 62-12=50 Moving to Node #0,2 Current State: 53:[33, 11, 50], Operations: ['62-12=50'] Exploring Operation: 33/11=3, Resulting Numbers: [50, 3] Generated Node #0,2,1: 53:[50, 3] Operation: 33/11=3 Moving to Node #0,2,1 Current State: 53:[50, 3], Operations: ['62-12=50', '33/11=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
0.91059
hs_5
mult_heuristic
[ 87, 49, 45, 5 ]
87
[ "49-45=4", "5-4=1", "87*1=87" ]
Current State: 87:[87, 49, 45, 5], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [87, 5, 4] Generated Node #2: [87, 5, 4] from Operation: 49-45=4 Current State: 87:[87, 5, 4], Operations: ['49-45=4'] Exploring Operation: 5-4=1, Resulting Numbers: [87, 1] Generated Node #3: [87, 1] from Operation: 5-4=1 Current State: 87:[87, 1], Operations: ['49-45=4', '5-4=1'] Exploring Operation: 87*1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[87, 49, 45, 5], Operations: [] Exploring Operation: 87-49=38, Resulting Numbers: [45, 5, 38] Generated Node #0,0: 87:[45, 5, 38] Operation: 87-49=38 Exploring Operation: 45/5=9, Resulting Numbers: [87, 49, 9] Generated Node #0,1: 87:[87, 49, 9] Operation: 45/5=9 Exploring Operation: 49-45=4, Resulting Numbers: [87, 5, 4] Generated Node #0,2: 87:[87, 5, 4] Operation: 49-45=4 Exploring Operation: 49+45=94, Resulting Numbers: [87, 5, 94] Generated Node #0,3: 87:[87, 5, 94] Operation: 49+45=94 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[87, 5, 4], Operations: ['49-45=4'] Exploring Operation: 87-5=82, Resulting Numbers: [4, 82] Generated Node #0,2,0: 87:[4, 82] Operation: 87-5=82 Exploring Operation: 87+5=92, Resulting Numbers: [4, 92] Generated Node #0,2,1: 87:[4, 92] Operation: 87+5=92 Exploring Operation: 5-4=1, Resulting Numbers: [87, 1] Generated Node #0,2,2: 87:[87, 1] Operation: 5-4=1 Exploring Operation: 87+4=91, Resulting Numbers: [5, 91] Generated Node #0,2,3: 87:[5, 91] Operation: 87+4=91 Moving to Node #0,2,2 Current State: 87:[87, 1], Operations: ['49-45=4', '5-4=1'] Exploring Operation: 87/1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[87, 49, 45, 5], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [87, 5, 4] Generated Node #0,2: 87:[87, 5, 4] Operation: 49-45=4 Moving to Node #0,2 Current State: 87:[87, 5, 4], Operations: ['49-45=4'] Exploring Operation: 5-4=1, Resulting Numbers: [87, 1] Generated Node #0,2,2: 87:[87, 1] Operation: 5-4=1 Moving to Node #0,2,2 Current State: 87:[87, 1], Operations: ['49-45=4', '5-4=1'] Exploring Operation: 87/1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 49, 12, 23, 20 ]
80
[ "49-12=37", "23+20=43", "37+43=80" ]
Current State: 80:[49, 12, 23, 20], Operations: [] Exploring Operation: 49-12=37, Resulting Numbers: [23, 20, 37] Generated Node #2: [23, 20, 37] from Operation: 49-12=37 Current State: 80:[23, 20, 37], Operations: ['49-12=37'] Exploring Operation: 23+20=43, Resulting Numbers: [37, 43] Generated Node #3: [37, 43] from Operation: 23+20=43 Current State: 80:[37, 43], Operations: ['49-12=37', '23+20=43'] Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[49, 12, 23, 20], Operations: [] Exploring Operation: 49-12=37, Resulting Numbers: [23, 20, 37] Generated Node #0,0: 80:[23, 20, 37] Operation: 49-12=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[23, 20, 37], Operations: ['49-12=37'] Exploring Operation: 37-23=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 80:[20, 14] Operation: 37-23=14 Moving to Node #0,0,0 Current State: 80:[20, 14], Operations: ['49-12=37', '37-23=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,80 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
[ 1, 49, 47, 51 ]
25
[ "51-1=50", "49-47=2", "50/2=25" ]
Current State: 25:[1, 49, 47, 51], Operations: [] Exploring Operation: 51-1=50, Resulting Numbers: [49, 47, 50] Generated Node #2: [49, 47, 50] from Operation: 51-1=50 Current State: 25:[49, 47, 50], Operations: ['51-1=50'] Exploring Operation: 49-47=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 49-47=2 Current State: 25:[50, 2], Operations: ['51-1=50', '49-47=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[1, 49, 47, 51], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [1, 47, 2] Generated Node #0,0: 25:[1, 47, 2] Operation: 51-49=2 Exploring Operation: 49-1=48, Resulting Numbers: [47, 51, 48] Generated Node #0,1: 25:[47, 51, 48] Operation: 49-1=48 Exploring Operation: 49-47=2, Resulting Numbers: [1, 51, 2] Generated Node #0,2: 25:[1, 51, 2] Operation: 49-47=2 Exploring Operation: 51-47=4, Resulting Numbers: [1, 49, 4] Generated Node #0,3: 25:[1, 49, 4] Operation: 51-47=4 Exploring Operation: 47-1=46, Resulting Numbers: [49, 51, 46] Generated Node #0,4: 25:[49, 51, 46] Operation: 47-1=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[1, 47, 2], Operations: ['51-49=2'] Exploring Operation: 1*47=47, Resulting Numbers: [2, 47] Generated Node #0,0,0: 25:[2, 47] Operation: 1*47=47 Exploring Operation: 47/1=47, Resulting Numbers: [2, 47] Generated Node #0,0,1: 25:[2, 47] Operation: 47/1=47 Exploring Operation: 47-2=45, Resulting Numbers: [1, 45] Generated Node #0,0,2: 25:[1, 45] Operation: 47-2=45 Exploring Operation: 1+2=3, Resulting Numbers: [47, 3] Generated Node #0,0,3: 25:[47, 3] Operation: 1+2=3 Exploring Operation: 47-1=46, Resulting Numbers: [2, 46] Generated Node #0,0,4: 25:[2, 46] Operation: 47-1=46 Moving to Node #0,0,2 Current State: 25:[1, 45], Operations: ['51-49=2', '47-2=45'] Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,25 unequal: No Solution Exploring Operation: 1*45=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,25 unequal: No Solution Moving to Node #0,0,4 Current State: 25:[2, 46], Operations: ['51-49=2', '47-1=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,25 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,25 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[47, 3], Operations: ['51-49=2', '1+2=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 47*3=141, Resulting Numbers: [141] 141,25 unequal: No Solution Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[2, 47], Operations: ['51-49=2', '1*47=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[2, 47], Operations: ['51-49=2', '47/1=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,25 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,25 unequal: No Solution No 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: 25:[1, 49, 4], Operations: ['51-47=4'] Exploring Operation: 49-4=45, Resulting Numbers: [1, 45] Generated Node #0,3,0: 25:[1, 45] Operation: 49-4=45 Exploring Operation: 49-1=48, Resulting Numbers: [4, 48] Generated Node #0,3,1: 25:[4, 48] Operation: 49-1=48 Exploring Operation: 1*49=49, Resulting Numbers: [4, 49] Generated Node #0,3,2: 25:[4, 49] Operation: 1*49=49 Exploring Operation: 1+4=5, Resulting Numbers: [49, 5] Generated Node #0,3,3: 25:[49, 5] Operation: 1+4=5 Exploring Operation: 49/1=49, Resulting Numbers: [4, 49] Generated Node #0,3,4: 25:[4, 49] Operation: 49/1=49 Moving to Node #0,3,0 Current State: 25:[1, 45], Operations: ['51-47=4', '49-4=45'] Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,25 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 1*45=45, Resulting Numbers: [45] 45,25 unequal: No Solution Moving to Node #0,3,3 Current State: 25:[49, 5], Operations: ['51-47=4', '1+4=5'] Exploring Operation: 49*5=245, Resulting Numbers: [245] 245,25 unequal: No Solution Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[4, 48], Operations: ['51-47=4', '49-1=48'] Exploring Operation: 4+48=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,25 unequal: No Solution Exploring Operation: 4*48=192, Resulting Numbers: [192] 192,25 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[4, 49], Operations: ['51-47=4', '1*49=49'] Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,25 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,25 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,25 unequal: No Solution Moving to Node #0,3,4 Current State: 25:[4, 49], Operations: ['51-47=4', '49/1=49'] Exploring Operation: 4*49=196, Resulting Numbers: [196] 196,25 unequal: No Solution Exploring Operation: 4+49=53, Resulting Numbers: [53] 53,25 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,25 unequal: No Solution No 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: 25:[1, 51, 2], Operations: ['49-47=2'] Exploring Operation: 51-2=49, Resulting Numbers: [1, 49] Generated Node #0,2,0: 25:[1, 49] Operation: 51-2=49 Exploring Operation: 1+2=3, Resulting Numbers: [51, 3] Generated Node #0,2,1: 25:[51, 3] Operation: 1+2=3 Exploring Operation: 51-1=50, Resulting Numbers: [2, 50] Generated Node #0,2,2: 25:[2, 50] Operation: 51-1=50 Exploring Operation: 1*51=51, Resulting Numbers: [2, 51] Generated Node #0,2,3: 25:[2, 51] Operation: 1*51=51 Exploring Operation: 51/1=51, Resulting Numbers: [2, 51] Generated Node #0,2,4: 25:[2, 51] Operation: 51/1=51 Moving to Node #0,2,0 Current State: 25:[1, 49], Operations: ['49-47=2', '51-2=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,25 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[2, 50], Operations: ['49-47=2', '51-1=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,25 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[1, 49, 47, 51], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [1, 51, 2] Generated Node #0,2: 25:[1, 51, 2] Operation: 49-47=2 Moving to Node #0,2 Current State: 25:[1, 51, 2], Operations: ['49-47=2'] Exploring Operation: 51-1=50, Resulting Numbers: [2, 50] Generated Node #0,2,2: 25:[2, 50] Operation: 51-1=50 Moving to Node #0,2,2 Current State: 25:[2, 50], Operations: ['49-47=2', '51-1=50'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.943576
hs_5
sum_heuristic
[ 30, 46, 18, 49 ]
47
[ "46-30=16", "49-18=31", "16+31=47" ]
Current State: 47:[30, 46, 18, 49], Operations: [] Exploring Operation: 46-30=16, Resulting Numbers: [18, 49, 16] Generated Node #2: [18, 49, 16] from Operation: 46-30=16 Current State: 47:[18, 49, 16], Operations: ['46-30=16'] Exploring Operation: 49-18=31, Resulting Numbers: [16, 31] Generated Node #3: [16, 31] from Operation: 49-18=31 Current State: 47:[16, 31], Operations: ['46-30=16', '49-18=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[30, 46, 18, 49], Operations: [] Exploring Operation: 30+18=48, Resulting Numbers: [46, 49, 48] Generated Node #0,0: 47:[46, 49, 48] Operation: 30+18=48 Exploring Operation: 49-18=31, Resulting Numbers: [30, 46, 31] Generated Node #0,1: 47:[30, 46, 31] Operation: 49-18=31 Exploring Operation: 46+18=64, Resulting Numbers: [30, 49, 64] Generated Node #0,2: 47:[30, 49, 64] Operation: 46+18=64 Moving to Node #0,0 Current State: 47:[46, 49, 48], Operations: ['30+18=48'] Exploring Operation: 49-48=1, Resulting Numbers: [46, 1] Generated Node #0,0,0: 47:[46, 1] Operation: 49-48=1 Exploring Operation: 48-46=2, Resulting Numbers: [49, 2] Generated Node #0,0,1: 47:[49, 2] Operation: 48-46=2 Exploring Operation: 49-46=3, Resulting Numbers: [48, 3] Generated Node #0,0,2: 47:[48, 3] Operation: 49-46=3 Moving to Node #0,1 Current State: 47:[30, 46, 31], Operations: ['49-18=31'] Exploring Operation: 30+46=76, Resulting Numbers: [31, 76] Generated Node #0,1,0: 47:[31, 76] Operation: 30+46=76 Exploring Operation: 46-30=16, Resulting Numbers: [31, 16] Generated Node #0,1,1: 47:[31, 16] Operation: 46-30=16 Exploring Operation: 30+31=61, Resulting Numbers: [46, 61] Generated Node #0,1,2: 47:[46, 61] Operation: 30+31=61 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[46, 61], Operations: ['49-18=31', '30+31=61'] Exploring Operation: 46+61=107, Resulting Numbers: [107] 107,47 unequal: No Solution Exploring Operation: 61-46=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 46*61=2806, Resulting Numbers: [2806] 2806,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[31, 76], Operations: ['49-18=31', '30+46=76'] Exploring Operation: 31+76=107, Resulting Numbers: [107] 107,47 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,47 unequal: No Solution Exploring Operation: 31*76=2356, Resulting Numbers: [2356] 2356,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[31, 16], Operations: ['49-18=31', '46-30=16'] Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[30, 46, 18, 49], Operations: [] Exploring Operation: 49-18=31, Resulting Numbers: [30, 46, 31] Generated Node #0,1: 47:[30, 46, 31] Operation: 49-18=31 Moving to Node #0,1 Current State: 47:[30, 46, 31], Operations: ['49-18=31'] Exploring Operation: 46-30=16, Resulting Numbers: [31, 16] Generated Node #0,1,1: 47:[31, 16] Operation: 46-30=16 Moving to Node #0,1,1 Current State: 47:[31, 16], Operations: ['49-18=31', '46-30=16'] Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
sum_heuristic
[ 26, 82, 21, 14 ]
73
[ "26+82=108", "21+14=35", "108-35=73" ]
Current State: 73:[26, 82, 21, 14], Operations: [] Exploring Operation: 26+82=108, Resulting Numbers: [21, 14, 108] Generated Node #2: [21, 14, 108] from Operation: 26+82=108 Current State: 73:[21, 14, 108], Operations: ['26+82=108'] Exploring Operation: 21+14=35, Resulting Numbers: [108, 35] Generated Node #3: [108, 35] from Operation: 21+14=35 Current State: 73:[108, 35], Operations: ['26+82=108', '21+14=35'] Exploring Operation: 108-35=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[26, 82, 21, 14], Operations: [] Exploring Operation: 21+14=35, Resulting Numbers: [26, 82, 35] Generated Node #0,0: 73:[26, 82, 35] Operation: 21+14=35 Exploring Operation: 26+21=47, Resulting Numbers: [82, 14, 47] Generated Node #0,1: 73:[82, 14, 47] Operation: 26+21=47 Exploring Operation: 26+14=40, Resulting Numbers: [82, 21, 40] Generated Node #0,2: 73:[82, 21, 40] Operation: 26+14=40 Moving to Node #0,0 Current State: 73:[26, 82, 35], Operations: ['21+14=35'] Exploring Operation: 26+35=61, Resulting Numbers: [82, 61] Generated Node #0,0,0: 73:[82, 61] Operation: 26+35=61 Exploring Operation: 26+82=108, Resulting Numbers: [35, 108] Generated Node #0,0,1: 73:[35, 108] Operation: 26+82=108 Exploring Operation: 82-26=56, Resulting Numbers: [35, 56] Generated Node #0,0,2: 73:[35, 56] Operation: 82-26=56 Moving to Node #0,1 Current State: 73:[82, 14, 47], Operations: ['26+21=47'] Exploring Operation: 82-14=68, Resulting Numbers: [47, 68] Generated Node #0,1,0: 73:[47, 68] Operation: 82-14=68 Exploring Operation: 82+14=96, Resulting Numbers: [47, 96] Generated Node #0,1,1: 73:[47, 96] Operation: 82+14=96 Exploring Operation: 14+47=61, Resulting Numbers: [82, 61] Generated Node #0,1,2: 73:[82, 61] Operation: 14+47=61 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[82, 61], Operations: ['26+21=47', '14+47=61'] Exploring Operation: 82*61=5002, Resulting Numbers: [5002] 5002,73 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 82+61=143, Resulting Numbers: [143] 143,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[47, 68], Operations: ['26+21=47', '82-14=68'] Exploring Operation: 47*68=3196, Resulting Numbers: [3196] 3196,73 unequal: No Solution Exploring Operation: 47+68=115, Resulting Numbers: [115] 115,73 unequal: No Solution Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[47, 96], Operations: ['26+21=47', '82+14=96'] Exploring Operation: 47*96=4512, Resulting Numbers: [4512] 4512,73 unequal: No Solution Exploring Operation: 47+96=143, Resulting Numbers: [143] 143,73 unequal: No Solution Exploring Operation: 96-47=49, Resulting Numbers: [49] 49,73 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: 73:[82, 21, 40], Operations: ['26+14=40'] Exploring Operation: 82-21=61, Resulting Numbers: [40, 61] Generated Node #0,2,0: 73:[40, 61] Operation: 82-21=61 Exploring Operation: 82+21=103, Resulting Numbers: [40, 103] Generated Node #0,2,1: 73:[40, 103] Operation: 82+21=103 Exploring Operation: 21+40=61, Resulting Numbers: [82, 61] Generated Node #0,2,2: 73:[82, 61] Operation: 21+40=61 Moving to Node #0,0,0 Current State: 73:[82, 61], Operations: ['21+14=35', '26+35=61'] Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 82+61=143, Resulting Numbers: [143] 143,73 unequal: No Solution Exploring Operation: 82*61=5002, Resulting Numbers: [5002] 5002,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[82, 61], Operations: ['26+14=40', '21+40=61'] Exploring Operation: 82*61=5002, Resulting Numbers: [5002] 5002,73 unequal: No Solution Exploring Operation: 82+61=143, Resulting Numbers: [143] 143,73 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[40, 61], Operations: ['26+14=40', '82-21=61'] Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 40+61=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 40*61=2440, Resulting Numbers: [2440] 2440,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[35, 56], Operations: ['21+14=35', '82-26=56'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 35+56=91, Resulting Numbers: [91] 91,73 unequal: No Solution Exploring Operation: 35*56=1960, Resulting Numbers: [1960] 1960,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[40, 103], Operations: ['26+14=40', '82+21=103'] Exploring Operation: 40+103=143, Resulting Numbers: [143] 143,73 unequal: No Solution Exploring Operation: 103-40=63, Resulting Numbers: [63] 63,73 unequal: No Solution Exploring Operation: 40*103=4120, Resulting Numbers: [4120] 4120,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[35, 108], Operations: ['21+14=35', '26+82=108'] Exploring Operation: 108-35=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[26, 82, 21, 14], Operations: [] Exploring Operation: 21+14=35, Resulting Numbers: [26, 82, 35] Generated Node #0,0: 73:[26, 82, 35] Operation: 21+14=35 Moving to Node #0,0 Current State: 73:[26, 82, 35], Operations: ['21+14=35'] Exploring Operation: 26+82=108, Resulting Numbers: [35, 108] Generated Node #0,0,1: 73:[35, 108] Operation: 26+82=108 Moving to Node #0,0,1 Current State: 73:[35, 108], Operations: ['21+14=35', '26+82=108'] Exploring Operation: 108-35=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
0.96441
hs_3
sum_heuristic
[ 7, 92, 26, 50 ]
20
[ "92-50=42", "42/7=6", "26-6=20" ]
Current State: 20:[7, 92, 26, 50], Operations: [] Exploring Operation: 92-50=42, Resulting Numbers: [7, 26, 42] Generated Node #2: [7, 26, 42] from Operation: 92-50=42 Current State: 20:[7, 26, 42], Operations: ['92-50=42'] Exploring Operation: 42/7=6, Resulting Numbers: [26, 6] Generated Node #3: [26, 6] from Operation: 42/7=6 Current State: 20:[26, 6], Operations: ['92-50=42', '42/7=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 92, 26, 50], Operations: [] Exploring Operation: 92-7=85, Resulting Numbers: [26, 50, 85] Generated Node #0,0: 20:[26, 50, 85] Operation: 92-7=85 Exploring Operation: 50-26=24, Resulting Numbers: [7, 92, 24] Generated Node #0,1: 20:[7, 92, 24] Operation: 50-26=24 Exploring Operation: 92-26=66, Resulting Numbers: [7, 50, 66] Generated Node #0,2: 20:[7, 50, 66] Operation: 92-26=66 Exploring Operation: 50-7=43, Resulting Numbers: [92, 26, 43] Generated Node #0,3: 20:[92, 26, 43] Operation: 50-7=43 Exploring Operation: 92-50=42, Resulting Numbers: [7, 26, 42] Generated Node #0,4: 20:[7, 26, 42] Operation: 92-50=42 Moving to Node #0,4 Current State: 20:[7, 26, 42], Operations: ['92-50=42'] Exploring Operation: 26-7=19, Resulting Numbers: [42, 19] Generated Node #0,4,0: 20:[42, 19] Operation: 26-7=19 Exploring Operation: 42-7=35, Resulting Numbers: [26, 35] Generated Node #0,4,1: 20:[26, 35] Operation: 42-7=35 Exploring Operation: 7+26=33, Resulting Numbers: [42, 33] Generated Node #0,4,2: 20:[42, 33] Operation: 7+26=33 Exploring Operation: 42-26=16, Resulting Numbers: [7, 16] Generated Node #0,4,3: 20:[7, 16] Operation: 42-26=16 Exploring Operation: 42/7=6, Resulting Numbers: [26, 6] Generated Node #0,4,4: 20:[26, 6] Operation: 42/7=6 Moving to Node #0,2 Current State: 20:[7, 50, 66], Operations: ['92-26=66'] Exploring Operation: 50-7=43, Resulting Numbers: [66, 43] Generated Node #0,2,0: 20:[66, 43] Operation: 50-7=43 Exploring Operation: 66-7=59, Resulting Numbers: [50, 59] Generated Node #0,2,1: 20:[50, 59] Operation: 66-7=59 Exploring Operation: 66-50=16, Resulting Numbers: [7, 16] Generated Node #0,2,2: 20:[7, 16] Operation: 66-50=16 Exploring Operation: 7+66=73, Resulting Numbers: [50, 73] Generated Node #0,2,3: 20:[50, 73] Operation: 7+66=73 Exploring Operation: 7+50=57, Resulting Numbers: [66, 57] Generated Node #0,2,4: 20:[66, 57] Operation: 7+50=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 20:[7, 16], Operations: ['92-26=66', '66-50=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,20 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[66, 43], Operations: ['92-26=66', '50-7=43'] Exploring Operation: 66+43=109, Resulting Numbers: [109] 109,20 unequal: No Solution Exploring Operation: 66*43=2838, Resulting Numbers: [2838] 2838,20 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[50, 59], Operations: ['92-26=66', '66-7=59'] Exploring Operation: 50*59=2950, Resulting Numbers: [2950] 2950,20 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 50+59=109, Resulting Numbers: [109] 109,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 20:[50, 73], Operations: ['92-26=66', '7+66=73'] Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,20 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,20 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 20:[66, 57], Operations: ['92-26=66', '7+50=57'] Exploring Operation: 66+57=123, Resulting Numbers: [123] 123,20 unequal: No Solution Exploring Operation: 66*57=3762, Resulting Numbers: [3762] 3762,20 unequal: No Solution Exploring Operation: 66-57=9, Resulting Numbers: [9] 9,20 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: 20:[7, 92, 24], Operations: ['50-26=24'] Exploring Operation: 24-7=17, Resulting Numbers: [92, 17] Generated Node #0,1,0: 20:[92, 17] Operation: 24-7=17 Exploring Operation: 92-24=68, Resulting Numbers: [7, 68] Generated Node #0,1,1: 20:[7, 68] Operation: 92-24=68 Exploring Operation: 92-7=85, Resulting Numbers: [24, 85] Generated Node #0,1,2: 20:[24, 85] Operation: 92-7=85 Exploring Operation: 7+92=99, Resulting Numbers: [24, 99] Generated Node #0,1,3: 20:[24, 99] Operation: 7+92=99 Exploring Operation: 7+24=31, Resulting Numbers: [92, 31] Generated Node #0,1,4: 20:[92, 31] Operation: 7+24=31 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[7, 68], Operations: ['50-26=24', '92-24=68'] Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 7*68=476, Resulting Numbers: [476] 476,20 unequal: No Solution Exploring Operation: 7+68=75, Resulting Numbers: [75] 75,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[24, 85], Operations: ['50-26=24', '92-7=85'] Exploring Operation: 24*85=2040, Resulting Numbers: [2040] 2040,20 unequal: No Solution Exploring Operation: 24+85=109, Resulting Numbers: [109] 109,20 unequal: No Solution Exploring Operation: 85-24=61, Resulting Numbers: [61] 61,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[92, 17], Operations: ['50-26=24', '24-7=17'] Exploring Operation: 92+17=109, Resulting Numbers: [109] 109,20 unequal: No Solution Exploring Operation: 92-17=75, Resulting Numbers: [75] 75,20 unequal: No Solution Exploring Operation: 92*17=1564, Resulting Numbers: [1564] 1564,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 20:[24, 99], Operations: ['50-26=24', '7+92=99'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,20 unequal: No Solution Exploring Operation: 24+99=123, Resulting Numbers: [123] 123,20 unequal: No Solution Exploring Operation: 24*99=2376, Resulting Numbers: [2376] 2376,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 20:[92, 31], Operations: ['50-26=24', '7+24=31'] Exploring Operation: 92+31=123, Resulting Numbers: [123] 123,20 unequal: No Solution Exploring Operation: 92*31=2852, Resulting Numbers: [2852] 2852,20 unequal: No Solution Exploring Operation: 92-31=61, Resulting Numbers: [61] 61,20 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: 20:[26, 50, 85], Operations: ['92-7=85'] Exploring Operation: 85-26=59, Resulting Numbers: [50, 59] Generated Node #0,0,0: 20:[50, 59] Operation: 85-26=59 Exploring Operation: 85-50=35, Resulting Numbers: [26, 35] Generated Node #0,0,1: 20:[26, 35] Operation: 85-50=35 Exploring Operation: 26+50=76, Resulting Numbers: [85, 76] Generated Node #0,0,2: 20:[85, 76] Operation: 26+50=76 Exploring Operation: 50-26=24, Resulting Numbers: [85, 24] Generated Node #0,0,3: 20:[85, 24] Operation: 50-26=24 Exploring Operation: 26+85=111, Resulting Numbers: [50, 111] Generated Node #0,0,4: 20:[50, 111] Operation: 26+85=111 Moving to Node #0,3 Current State: 20:[92, 26, 43], Operations: ['50-7=43'] Exploring Operation: 92+43=135, Resulting Numbers: [26, 135] Generated Node #0,3,0: 20:[26, 135] Operation: 92+43=135 Exploring Operation: 92-43=49, Resulting Numbers: [26, 49] Generated Node #0,3,1: 20:[26, 49] Operation: 92-43=49 Exploring Operation: 92+26=118, Resulting Numbers: [43, 118] Generated Node #0,3,2: 20:[43, 118] Operation: 92+26=118 Exploring Operation: 43-26=17, Resulting Numbers: [92, 17] Generated Node #0,3,3: 20:[92, 17] Operation: 43-26=17 Exploring Operation: 92-26=66, Resulting Numbers: [43, 66] Generated Node #0,3,4: 20:[43, 66] Operation: 92-26=66 Moving to Node #0,4,3 Current State: 20:[7, 16], Operations: ['92-50=42', '42-26=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,20 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,20 unequal: No Solution Moving to Node #0,4,4 Current State: 20:[26, 6], Operations: ['92-50=42', '42/7=6'] Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[7, 92, 26, 50], Operations: [] Exploring Operation: 92-50=42, Resulting Numbers: [7, 26, 42] Generated Node #0,4: 20:[7, 26, 42] Operation: 92-50=42 Moving to Node #0,4 Current State: 20:[7, 26, 42], Operations: ['92-50=42'] Exploring Operation: 42/7=6, Resulting Numbers: [26, 6] Generated Node #0,4,4: 20:[26, 6] Operation: 42/7=6 Moving to Node #0,4,4 Current State: 20:[26, 6], Operations: ['92-50=42', '42/7=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.939236
hs_5
sum_heuristic
[ 68, 54, 88, 86 ]
40
[ "88-86=2", "54*2=108", "108-68=40" ]
Current State: 40:[68, 54, 88, 86], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [68, 54, 2] Generated Node #2: [68, 54, 2] from Operation: 88-86=2 Current State: 40:[68, 54, 2], Operations: ['88-86=2'] Exploring Operation: 54*2=108, Resulting Numbers: [68, 108] Generated Node #3: [68, 108] from Operation: 54*2=108 Current State: 40:[68, 108], Operations: ['88-86=2', '54*2=108'] Exploring Operation: 108-68=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[68, 54, 88, 86], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [68, 54, 2] Generated Node #0,0: 40:[68, 54, 2] Operation: 88-86=2 Exploring Operation: 88-68=20, Resulting Numbers: [54, 86, 20] Generated Node #0,1: 40:[54, 86, 20] Operation: 88-68=20 Moving to Node #0,0 Current State: 40:[68, 54, 2], Operations: ['88-86=2'] Exploring Operation: 68/2=34, Resulting Numbers: [54, 34] Generated Node #0,0,0: 40:[54, 34] Operation: 68/2=34 Exploring Operation: 68-54=14, Resulting Numbers: [2, 14] Generated Node #0,0,1: 40:[2, 14] Operation: 68-54=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[2, 14], Operations: ['88-86=2', '68-54=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[54, 34], Operations: ['88-86=2', '68/2=34'] Exploring Operation: 54+34=88, Resulting Numbers: [88] 88,40 unequal: No Solution Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,40 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: 40:[54, 86, 20], Operations: ['88-68=20'] Exploring Operation: 86-54=32, Resulting Numbers: [20, 32] Generated Node #0,1,0: 40:[20, 32] Operation: 86-54=32 Exploring Operation: 86-20=66, Resulting Numbers: [54, 66] Generated Node #0,1,1: 40:[54, 66] Operation: 86-20=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[20, 32], Operations: ['88-68=20', '86-54=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,40 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[54, 66], Operations: ['88-68=20', '86-20=66'] Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,40 unequal: No Solution Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,40 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, 30, 50, 73 ]
99
[ "73-50=23", "3*23=69", "30+69=99" ]
Current State: 99:[3, 30, 50, 73], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [3, 30, 23] Generated Node #2: [3, 30, 23] from Operation: 73-50=23 Current State: 99:[3, 30, 23], Operations: ['73-50=23'] Exploring Operation: 3*23=69, Resulting Numbers: [30, 69] Generated Node #3: [30, 69] from Operation: 3*23=69 Current State: 99:[30, 69], Operations: ['73-50=23', '3*23=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[3, 30, 50, 73], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [3, 30, 23] Generated Node #0,0: 99:[3, 30, 23] Operation: 73-50=23 Moving to Node #0,0 Current State: 99:[3, 30, 23], Operations: ['73-50=23'] Exploring Operation: 30-23=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 99:[3, 7] Operation: 30-23=7 Moving to Node #0,0,0 Current State: 99:[3, 7], Operations: ['73-50=23', '30-23=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,99 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 26, 88, 11, 66 ]
44
[ "88-26=62", "66-62=4", "11*4=44" ]
Current State: 44:[26, 88, 11, 66], Operations: [] Exploring Operation: 88-26=62, Resulting Numbers: [11, 66, 62] Generated Node #2: [11, 66, 62] from Operation: 88-26=62 Current State: 44:[11, 66, 62], Operations: ['88-26=62'] Exploring Operation: 66-62=4, Resulting Numbers: [11, 4] Generated Node #3: [11, 4] from Operation: 66-62=4 Current State: 44:[11, 4], Operations: ['88-26=62', '66-62=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[26, 88, 11, 66], Operations: [] Exploring Operation: 88/11=8, Resulting Numbers: [26, 66, 8] Generated Node #0,0: 44:[26, 66, 8] Operation: 88/11=8 Exploring Operation: 88-26=62, Resulting Numbers: [11, 66, 62] Generated Node #0,1: 44:[11, 66, 62] Operation: 88-26=62 Exploring Operation: 88-66=22, Resulting Numbers: [26, 11, 22] Generated Node #0,2: 44:[26, 11, 22] Operation: 88-66=22 Moving to Node #0,2 Current State: 44:[26, 11, 22], Operations: ['88-66=22'] Exploring Operation: 26-22=4, Resulting Numbers: [11, 4] Generated Node #0,2,0: 44:[11, 4] Operation: 26-22=4 Exploring Operation: 26+22=48, Resulting Numbers: [11, 48] Generated Node #0,2,1: 44:[11, 48] Operation: 26+22=48 Exploring Operation: 26-11=15, Resulting Numbers: [22, 15] Generated Node #0,2,2: 44:[22, 15] Operation: 26-11=15 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[11, 4], Operations: ['88-66=22', '26-22=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[26, 88, 11, 66], Operations: [] Exploring Operation: 88-66=22, Resulting Numbers: [26, 11, 22] Generated Node #0,2: 44:[26, 11, 22] Operation: 88-66=22 Moving to Node #0,2 Current State: 44:[26, 11, 22], Operations: ['88-66=22'] Exploring Operation: 26-22=4, Resulting Numbers: [11, 4] Generated Node #0,2,0: 44:[11, 4] Operation: 26-22=4 Moving to Node #0,2,0 Current State: 44:[11, 4], Operations: ['88-66=22', '26-22=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 23, 17, 80, 34 ]
68
[ "23+17=40", "80*34=2720", "2720/40=68" ]
Current State: 68:[23, 17, 80, 34], Operations: [] Exploring Operation: 23+17=40, Resulting Numbers: [80, 34, 40] Generated Node #2: [80, 34, 40] from Operation: 23+17=40 Current State: 68:[80, 34, 40], Operations: ['23+17=40'] Exploring Operation: 80*34=2720, Resulting Numbers: [40, 2720] Generated Node #3: [40, 2720] from Operation: 80*34=2720 Current State: 68:[40, 2720], Operations: ['23+17=40', '80*34=2720'] Exploring Operation: 2720/40=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[23, 17, 80, 34], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [80, 34, 6] Generated Node #0,0: 68:[80, 34, 6] Operation: 23-17=6 Exploring Operation: 34-23=11, Resulting Numbers: [17, 80, 11] Generated Node #0,1: 68:[17, 80, 11] Operation: 34-23=11 Exploring Operation: 23+17=40, Resulting Numbers: [80, 34, 40] Generated Node #0,2: 68:[80, 34, 40] Operation: 23+17=40 Exploring Operation: 80-23=57, Resulting Numbers: [17, 34, 57] Generated Node #0,3: 68:[17, 34, 57] Operation: 80-23=57 Exploring Operation: 80-17=63, Resulting Numbers: [23, 34, 63] Generated Node #0,4: 68:[23, 34, 63] Operation: 80-17=63 Moving to Node #0,3 Current State: 68:[17, 34, 57], Operations: ['80-23=57'] Exploring Operation: 57-17=40, Resulting Numbers: [34, 40] Generated Node #0,3,0: 68:[34, 40] Operation: 57-17=40 Exploring Operation: 34/17=2, Resulting Numbers: [57, 2] Generated Node #0,3,1: 68:[57, 2] Operation: 34/17=2 Exploring Operation: 57-34=23, Resulting Numbers: [17, 23] Generated Node #0,3,2: 68:[17, 23] Operation: 57-34=23 Exploring Operation: 34-17=17, Resulting Numbers: [57, 17] Generated Node #0,3,3: 68:[57, 17] Operation: 34-17=17 Exploring Operation: 17+57=74, Resulting Numbers: [34, 74] Generated Node #0,3,4: 68:[34, 74] Operation: 17+57=74 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[34, 40], Operations: ['80-23=57', '57-17=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,68 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,68 unequal: No Solution No 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: 68:[17, 23], Operations: ['80-23=57', '57-34=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,68 unequal: No Solution No 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: 68:[34, 74], Operations: ['80-23=57', '17+57=74'] Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,68 unequal: No Solution No 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: 68:[57, 2], Operations: ['80-23=57', '34/17=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,68 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,68 unequal: No Solution No 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: 68:[57, 17], Operations: ['80-23=57', '34-17=17'] Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 57*17=969, Resulting Numbers: [969] 969,68 unequal: No Solution Exploring Operation: 57+17=74, Resulting Numbers: [74] 74,68 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: 68:[23, 34, 63], Operations: ['80-17=63'] Exploring Operation: 63-23=40, Resulting Numbers: [34, 40] Generated Node #0,4,0: 68:[34, 40] Operation: 63-23=40 Exploring Operation: 63-34=29, Resulting Numbers: [23, 29] Generated Node #0,4,1: 68:[23, 29] Operation: 63-34=29 Exploring Operation: 34-23=11, Resulting Numbers: [63, 11] Generated Node #0,4,2: 68:[63, 11] Operation: 34-23=11 Exploring Operation: 23+34=57, Resulting Numbers: [63, 57] Generated Node #0,4,3: 68:[63, 57] Operation: 23+34=57 Exploring Operation: 23+63=86, Resulting Numbers: [34, 86] Generated Node #0,4,4: 68:[34, 86] Operation: 23+63=86 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 68:[34, 40], Operations: ['80-17=63', '63-23=40'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,68 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,68 unequal: No Solution No 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: 68:[23, 29], Operations: ['80-17=63', '63-34=29'] Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,68 unequal: No Solution No 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: 68:[63, 11], Operations: ['80-17=63', '34-23=11'] Exploring Operation: 63+11=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 63*11=693, Resulting Numbers: [693] 693,68 unequal: No Solution Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,68 unequal: No Solution No 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: 68:[63, 57], Operations: ['80-17=63', '23+34=57'] Exploring Operation: 63*57=3591, Resulting Numbers: [3591] 3591,68 unequal: No Solution Exploring Operation: 63-57=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 63+57=120, Resulting Numbers: [120] 120,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 68:[34, 86], Operations: ['80-17=63', '23+63=86'] Exploring Operation: 34+86=120, Resulting Numbers: [120] 120,68 unequal: No Solution Exploring Operation: 34*86=2924, Resulting Numbers: [2924] 2924,68 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,68 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: 68:[80, 34, 6], Operations: ['23-17=6'] Exploring Operation: 34-6=28, Resulting Numbers: [80, 28] Generated Node #0,0,0: 68:[80, 28] Operation: 34-6=28 Exploring Operation: 80-6=74, Resulting Numbers: [34, 74] Generated Node #0,0,1: 68:[34, 74] Operation: 80-6=74 Exploring Operation: 34+6=40, Resulting Numbers: [80, 40] Generated Node #0,0,2: 68:[80, 40] Operation: 34+6=40 Exploring Operation: 80-34=46, Resulting Numbers: [6, 46] Generated Node #0,0,3: 68:[6, 46] Operation: 80-34=46 Exploring Operation: 80+6=86, Resulting Numbers: [34, 86] Generated Node #0,0,4: 68:[34, 86] Operation: 80+6=86 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[34, 74], Operations: ['23-17=6', '80-6=74'] Exploring Operation: 34+74=108, Resulting Numbers: [108] 108,68 unequal: No Solution Exploring Operation: 34*74=2516, Resulting Numbers: [2516] 2516,68 unequal: No Solution Exploring Operation: 74-34=40, Resulting Numbers: [40] 40,68 unequal: No Solution No 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: 68:[6, 46], Operations: ['23-17=6', '80-34=46'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 6+46=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 6*46=276, Resulting Numbers: [276] 276,68 unequal: No Solution No 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: 68:[80, 28], Operations: ['23-17=6', '34-6=28'] Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,68 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,68 unequal: No Solution No 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: 68:[80, 40], Operations: ['23-17=6', '34+6=40'] Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 80*40=3200, Resulting Numbers: [3200] 3200,68 unequal: No Solution Exploring Operation: 80+40=120, Resulting Numbers: [120] 120,68 unequal: No Solution Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,68 unequal: No Solution No 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: 68:[34, 86], Operations: ['23-17=6', '80+6=86'] Exploring Operation: 34+86=120, Resulting Numbers: [120] 120,68 unequal: No Solution Exploring Operation: 34*86=2924, Resulting Numbers: [2924] 2924,68 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,68 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: 68:[17, 80, 11], Operations: ['34-23=11'] Exploring Operation: 17+11=28, Resulting Numbers: [80, 28] Generated Node #0,1,0: 68:[80, 28] Operation: 17+11=28 Exploring Operation: 17-11=6, Resulting Numbers: [80, 6] Generated Node #0,1,1: 68:[80, 6] Operation: 17-11=6 Exploring Operation: 80-17=63, Resulting Numbers: [11, 63] Generated Node #0,1,2: 68:[11, 63] Operation: 80-17=63 Exploring Operation: 80+11=91, Resulting Numbers: [17, 91] Generated Node #0,1,3: 68:[17, 91] Operation: 80+11=91 Exploring Operation: 80-11=69, Resulting Numbers: [17, 69] Generated Node #0,1,4: 68:[17, 69] Operation: 80-11=69 Moving to Node #0,2 Current State: 68:[80, 34, 40], Operations: ['23+17=40'] Exploring Operation: 80-34=46, Resulting Numbers: [40, 46] Generated Node #0,2,0: 68:[40, 46] Operation: 80-34=46 Exploring Operation: 80-40=40, Resulting Numbers: [34, 40] Generated Node #0,2,1: 68:[34, 40] Operation: 80-40=40 Exploring Operation: 80/40=2, Resulting Numbers: [34, 2] Generated Node #0,2,2: 68:[34, 2] Operation: 80/40=2 Exploring Operation: 40-34=6, Resulting Numbers: [80, 6] Generated Node #0,2,3: 68:[80, 6] Operation: 40-34=6 Exploring Operation: 34+40=74, Resulting Numbers: [80, 74] Generated Node #0,2,4: 68:[80, 74] Operation: 34+40=74 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[34, 2], Operations: ['23+17=40', '80/40=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[23, 17, 80, 34], Operations: [] Exploring Operation: 23+17=40, Resulting Numbers: [80, 34, 40] Generated Node #0,2: 68:[80, 34, 40] Operation: 23+17=40 Moving to Node #0,2 Current State: 68:[80, 34, 40], Operations: ['23+17=40'] Exploring Operation: 80/40=2, Resulting Numbers: [34, 2] Generated Node #0,2,2: 68:[34, 2] Operation: 80/40=2 Moving to Node #0,2,2 Current State: 68:[34, 2], Operations: ['23+17=40', '80/40=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.927083
hs_5
mult_heuristic
[ 6, 28, 27, 3 ]
37
[ "6*3=18", "28+27=55", "55-18=37" ]
Current State: 37:[6, 28, 27, 3], Operations: [] Exploring Operation: 6*3=18, Resulting Numbers: [28, 27, 18] Generated Node #2: [28, 27, 18] from Operation: 6*3=18 Current State: 37:[28, 27, 18], Operations: ['6*3=18'] Exploring Operation: 28+27=55, Resulting Numbers: [18, 55] Generated Node #3: [18, 55] from Operation: 28+27=55 Current State: 37:[18, 55], Operations: ['6*3=18', '28+27=55'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[6, 28, 27, 3], Operations: [] Exploring Operation: 6+3=9, Resulting Numbers: [28, 27, 9] Generated Node #0,0: 37:[28, 27, 9] Operation: 6+3=9 Exploring Operation: 6*3=18, Resulting Numbers: [28, 27, 18] Generated Node #0,1: 37:[28, 27, 18] Operation: 6*3=18 Exploring Operation: 6+28=34, Resulting Numbers: [27, 3, 34] Generated Node #0,2: 37:[27, 3, 34] Operation: 6+28=34 Exploring Operation: 6+27=33, Resulting Numbers: [28, 3, 33] Generated Node #0,3: 37:[28, 3, 33] Operation: 6+27=33 Moving to Node #0,1 Current State: 37:[28, 27, 18], Operations: ['6*3=18'] Exploring Operation: 28+18=46, Resulting Numbers: [27, 46] Generated Node #0,1,0: 37:[27, 46] Operation: 28+18=46 Exploring Operation: 28-18=10, Resulting Numbers: [27, 10] Generated Node #0,1,1: 37:[27, 10] Operation: 28-18=10 Exploring Operation: 27+18=45, Resulting Numbers: [28, 45] Generated Node #0,1,2: 37:[28, 45] Operation: 27+18=45 Exploring Operation: 28+27=55, Resulting Numbers: [18, 55] Generated Node #0,1,3: 37:[18, 55] Operation: 28+27=55 Moving to Node #0,2 Current State: 37:[27, 3, 34], Operations: ['6+28=34'] Exploring Operation: 27-3=24, Resulting Numbers: [34, 24] Generated Node #0,2,0: 37:[34, 24] Operation: 27-3=24 Exploring Operation: 34-3=31, Resulting Numbers: [27, 31] Generated Node #0,2,1: 37:[27, 31] Operation: 34-3=31 Exploring Operation: 3+34=37, Resulting Numbers: [27, 37] Generated Node #0,2,2: 37:[27, 37] Operation: 3+34=37 Exploring Operation: 27+3=30, Resulting Numbers: [34, 30] Generated Node #0,2,3: 37:[34, 30] Operation: 27+3=30 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 37:[27, 37], Operations: ['6+28=34', '3+34=37'] Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,37 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 37:[34, 30], Operations: ['6+28=34', '27+3=30'] Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,37 unequal: No Solution Exploring Operation: 34*30=1020, Resulting Numbers: [1020] 1020,37 unequal: No Solution Exploring Operation: 34+30=64, Resulting Numbers: [64] 64,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 37:[34, 24], Operations: ['6+28=34', '27-3=24'] Exploring Operation: 34*24=816, Resulting Numbers: [816] 816,37 unequal: No Solution Exploring Operation: 34+24=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 37:[27, 31], Operations: ['6+28=34', '34-3=31'] Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,37 unequal: No Solution Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,37 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: 37:[28, 27, 9], Operations: ['6+3=9'] Exploring Operation: 28-9=19, Resulting Numbers: [27, 19] Generated Node #0,0,0: 37:[27, 19] Operation: 28-9=19 Exploring Operation: 27+9=36, Resulting Numbers: [28, 36] Generated Node #0,0,1: 37:[28, 36] Operation: 27+9=36 Exploring Operation: 27-9=18, Resulting Numbers: [28, 18] Generated Node #0,0,2: 37:[28, 18] Operation: 27-9=18 Exploring Operation: 28+9=37, Resulting Numbers: [27, 37] Generated Node #0,0,3: 37:[27, 37] Operation: 28+9=37 Moving to Node #0,3 Current State: 37:[28, 3, 33], Operations: ['6+27=33'] Exploring Operation: 28+3=31, Resulting Numbers: [33, 31] Generated Node #0,3,0: 37:[33, 31] Operation: 28+3=31 Exploring Operation: 3+33=36, Resulting Numbers: [28, 36] Generated Node #0,3,1: 37:[28, 36] Operation: 3+33=36 Exploring Operation: 33-3=30, Resulting Numbers: [28, 30] Generated Node #0,3,2: 37:[28, 30] Operation: 33-3=30 Exploring Operation: 28-3=25, Resulting Numbers: [33, 25] Generated Node #0,3,3: 37:[33, 25] Operation: 28-3=25 Moving to Node #0,0,1 Current State: 37:[28, 36], Operations: ['6+3=9', '27+9=36'] Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,37 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[27, 37], Operations: ['6+3=9', '28+9=37'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,37 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[33, 31], Operations: ['6+27=33', '28+3=31'] Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[28, 36], Operations: ['6+27=33', '3+33=36'] Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,37 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,37 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[33, 25], Operations: ['6+27=33', '28-3=25'] Exploring Operation: 33*25=825, Resulting Numbers: [825] 825,37 unequal: No Solution Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,37 unequal: No Solution Exploring Operation: 33+25=58, Resulting Numbers: [58] 58,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[28, 30], Operations: ['6+27=33', '33-3=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,37 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[28, 45], Operations: ['6*3=18', '27+18=45'] Exploring Operation: 28+45=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 28*45=1260, Resulting Numbers: [1260] 1260,37 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[27, 46], Operations: ['6*3=18', '28+18=46'] Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 27*46=1242, Resulting Numbers: [1242] 1242,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[27, 19], Operations: ['6+3=9', '28-9=19'] Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,37 unequal: No Solution Exploring Operation: 27+19=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 27*19=513, Resulting Numbers: [513] 513,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[28, 18], Operations: ['6+3=9', '27-9=18'] Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,37 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[18, 55], Operations: ['6*3=18', '28+27=55'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[6, 28, 27, 3], Operations: [] Exploring Operation: 6*3=18, Resulting Numbers: [28, 27, 18] Generated Node #0,1: 37:[28, 27, 18] Operation: 6*3=18 Moving to Node #0,1 Current State: 37:[28, 27, 18], Operations: ['6*3=18'] Exploring Operation: 28+27=55, Resulting Numbers: [18, 55] Generated Node #0,1,3: 37:[18, 55] Operation: 28+27=55 Moving to Node #0,1,3 Current State: 37:[18, 55], Operations: ['6*3=18', '28+27=55'] Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.94184
hs_4
mult_heuristic
[ 14, 54, 69, 76 ]
27
[ "76-69=7", "14/7=2", "54/2=27" ]
Current State: 27:[14, 54, 69, 76], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [14, 54, 7] Generated Node #2: [14, 54, 7] from Operation: 76-69=7 Current State: 27:[14, 54, 7], Operations: ['76-69=7'] Exploring Operation: 14/7=2, Resulting Numbers: [54, 2] Generated Node #3: [54, 2] from Operation: 14/7=2 Current State: 27:[54, 2], Operations: ['76-69=7', '14/7=2'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[14, 54, 69, 76], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [14, 54, 7] Generated Node #0,0: 27:[14, 54, 7] Operation: 76-69=7 Moving to Node #0,0 Current State: 27:[14, 54, 7], Operations: ['76-69=7'] Exploring Operation: 54-14=40, Resulting Numbers: [7, 40] Generated Node #0,0,0: 27:[7, 40] Operation: 54-14=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[7, 40], Operations: ['76-69=7', '54-14=40'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 80, 16, 92, 97 ]
16
[ "16*92=1472", "80+1472=1552", "1552/97=16" ]
Current State: 16:[80, 16, 92, 97], Operations: [] Exploring Operation: 16*92=1472, Resulting Numbers: [80, 97, 1472] Generated Node #2: [80, 97, 1472] from Operation: 16*92=1472 Current State: 16:[80, 97, 1472], Operations: ['16*92=1472'] Exploring Operation: 80+1472=1552, Resulting Numbers: [97, 1552] Generated Node #3: [97, 1552] from Operation: 80+1472=1552 Current State: 16:[97, 1552], Operations: ['16*92=1472', '80+1472=1552'] Exploring Operation: 1552/97=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[80, 16, 92, 97], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [16, 92, 17] Generated Node #0,0: 16:[16, 92, 17] Operation: 97-80=17 Exploring Operation: 92-80=12, Resulting Numbers: [16, 97, 12] Generated Node #0,1: 16:[16, 97, 12] Operation: 92-80=12 Exploring Operation: 97-92=5, Resulting Numbers: [80, 16, 5] Generated Node #0,2: 16:[80, 16, 5] Operation: 97-92=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[80, 16, 5], Operations: ['97-92=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16, 16] Generated Node #0,2,0: 16:[16, 16] Operation: 80/5=16 Exploring Operation: 80-16=64, Resulting Numbers: [5, 64] Generated Node #0,2,1: 16:[5, 64] Operation: 80-16=64 Exploring Operation: 80/16=5, Resulting Numbers: [5, 5] Generated Node #0,2,2: 16:[5, 5] Operation: 80/16=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 16:[16, 16], Operations: ['97-92=5', '80/5=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,16 unequal: No Solution No 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: 16:[5, 5], Operations: ['97-92=5', '80/16=5'] Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,16 unequal: No Solution No 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: 16:[5, 64], Operations: ['97-92=5', '80-16=64'] Exploring Operation: 5+64=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 5*64=320, Resulting Numbers: [320] 320,16 unequal: No Solution Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,16 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: 16:[16, 92, 17], Operations: ['97-80=17'] Exploring Operation: 17-16=1, Resulting Numbers: [92, 1] Generated Node #0,0,0: 16:[92, 1] Operation: 17-16=1 Exploring Operation: 92-16=76, Resulting Numbers: [17, 76] Generated Node #0,0,1: 16:[17, 76] Operation: 92-16=76 Exploring Operation: 92-17=75, Resulting Numbers: [16, 75] Generated Node #0,0,2: 16:[16, 75] Operation: 92-17=75 Moving to Node #0,0,2 Current State: 16:[16, 75], Operations: ['97-80=17', '92-17=75'] Exploring Operation: 16+75=91, Resulting Numbers: [91] 91,16 unequal: No Solution Exploring Operation: 16*75=1200, Resulting Numbers: [1200] 1200,16 unequal: No Solution Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[17, 76], Operations: ['97-80=17', '92-16=76'] Exploring Operation: 17+76=93, Resulting Numbers: [93] 93,16 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,16 unequal: No Solution Exploring Operation: 17*76=1292, Resulting Numbers: [1292] 1292,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[92, 1], Operations: ['97-80=17', '17-16=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,16 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,16 unequal: No Solution Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[16, 97, 12], Operations: ['92-80=12'] Exploring Operation: 97-16=81, Resulting Numbers: [12, 81] Generated Node #0,1,0: 16:[12, 81] Operation: 97-16=81 Exploring Operation: 16-12=4, Resulting Numbers: [97, 4] Generated Node #0,1,1: 16:[97, 4] Operation: 16-12=4 Exploring Operation: 97-12=85, Resulting Numbers: [16, 85] Generated Node #0,1,2: 16:[16, 85] Operation: 97-12=85 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[12, 81], Operations: ['92-80=12', '97-16=81'] Exploring Operation: 12*81=972, Resulting Numbers: [972] 972,16 unequal: No Solution Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,16 unequal: No Solution No 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: 16:[16, 85], Operations: ['92-80=12', '97-12=85'] Exploring Operation: 16*85=1360, Resulting Numbers: [1360] 1360,16 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 16+85=101, Resulting Numbers: [101] 101,16 unequal: No Solution No 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: 16:[97, 4], Operations: ['92-80=12', '16-12=4'] Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,16 unequal: No Solution Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,16 unequal: No Solution Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,16 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
[ 9, 57, 60, 43 ]
49
[ "9+57=66", "60-43=17", "66-17=49" ]
Current State: 49:[9, 57, 60, 43], Operations: [] Exploring Operation: 9+57=66, Resulting Numbers: [60, 43, 66] Generated Node #2: [60, 43, 66] from Operation: 9+57=66 Current State: 49:[60, 43, 66], Operations: ['9+57=66'] Exploring Operation: 60-43=17, Resulting Numbers: [66, 17] Generated Node #3: [66, 17] from Operation: 60-43=17 Current State: 49:[66, 17], Operations: ['9+57=66', '60-43=17'] Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[9, 57, 60, 43], Operations: [] Exploring Operation: 60-57=3, Resulting Numbers: [9, 43, 3] Generated Node #0,0: 49:[9, 43, 3] Operation: 60-57=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[9, 43, 3], Operations: ['60-57=3'] Exploring Operation: 43+3=46, Resulting Numbers: [9, 46] Generated Node #0,0,0: 49:[9, 46] Operation: 43+3=46 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[9, 46], Operations: ['60-57=3', '43+3=46'] Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,49 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
mult_heuristic
[ 38, 65, 4, 36 ]
63
[ "38+65=103", "4+36=40", "103-40=63" ]
Current State: 63:[38, 65, 4, 36], Operations: [] Exploring Operation: 38+65=103, Resulting Numbers: [4, 36, 103] Generated Node #2: [4, 36, 103] from Operation: 38+65=103 Current State: 63:[4, 36, 103], Operations: ['38+65=103'] Exploring Operation: 4+36=40, Resulting Numbers: [103, 40] Generated Node #3: [103, 40] from Operation: 4+36=40 Current State: 63:[103, 40], Operations: ['38+65=103', '4+36=40'] Exploring Operation: 103-40=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[38, 65, 4, 36], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [65, 4, 2] Generated Node #0,0: 63:[65, 4, 2] Operation: 38-36=2 Exploring Operation: 36/4=9, Resulting Numbers: [38, 65, 9] Generated Node #0,1: 63:[38, 65, 9] Operation: 36/4=9 Exploring Operation: 38+36=74, Resulting Numbers: [65, 4, 74] Generated Node #0,2: 63:[65, 4, 74] Operation: 38+36=74 Exploring Operation: 65-36=29, Resulting Numbers: [38, 4, 29] Generated Node #0,3: 63:[38, 4, 29] Operation: 65-36=29 Exploring Operation: 65-38=27, Resulting Numbers: [4, 36, 27] Generated Node #0,4: 63:[4, 36, 27] Operation: 65-38=27 Moving to Node #0,0 Current State: 63:[65, 4, 2], Operations: ['38-36=2'] Exploring Operation: 65-4=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 63:[2, 61] Operation: 65-4=61 Exploring Operation: 4*2=8, Resulting Numbers: [65, 8] Generated Node #0,0,1: 63:[65, 8] Operation: 4*2=8 Exploring Operation: 4-2=2, Resulting Numbers: [65, 2] Generated Node #0,0,2: 63:[65, 2] Operation: 4-2=2 Exploring Operation: 65-2=63, Resulting Numbers: [4, 63] Generated Node #0,0,3: 63:[4, 63] Operation: 65-2=63 Exploring Operation: 4+2=6, Resulting Numbers: [65, 6] Generated Node #0,0,4: 63:[65, 6] Operation: 4+2=6 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[4, 63], Operations: ['38-36=2', '65-2=63'] Exploring Operation: 4*63=252, Resulting Numbers: [252] 252,63 unequal: No Solution Exploring Operation: 4+63=67, Resulting Numbers: [67] 67,63 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[2, 61], Operations: ['38-36=2', '65-4=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,63 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[38, 65, 4, 36], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [65, 4, 2] Generated Node #0,0: 63:[65, 4, 2] Operation: 38-36=2 Moving to Node #0,0 Current State: 63:[65, 4, 2], Operations: ['38-36=2'] Exploring Operation: 65-4=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 63:[2, 61] Operation: 65-4=61 Moving to Node #0,0,0 Current State: 63:[2, 61], Operations: ['38-36=2', '65-4=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 68, 63, 53, 33 ]
45
[ "68+63=131", "53+33=86", "131-86=45" ]
Current State: 45:[68, 63, 53, 33], Operations: [] Exploring Operation: 68+63=131, Resulting Numbers: [53, 33, 131] Generated Node #2: [53, 33, 131] from Operation: 68+63=131 Current State: 45:[53, 33, 131], Operations: ['68+63=131'] Exploring Operation: 53+33=86, Resulting Numbers: [131, 86] Generated Node #3: [131, 86] from Operation: 53+33=86 Current State: 45:[131, 86], Operations: ['68+63=131', '53+33=86'] Exploring Operation: 131-86=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[68, 63, 53, 33], Operations: [] Exploring Operation: 68-63=5, Resulting Numbers: [53, 33, 5] Generated Node #0,0: 45:[53, 33, 5] Operation: 68-63=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[53, 33, 5], Operations: ['68-63=5'] Exploring Operation: 53-33=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 45:[5, 20] Operation: 53-33=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[5, 20], Operations: ['68-63=5', '53-33=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 59, 50, 31, 31 ]
53
[ "59-50=9", "31+31=62", "62-9=53" ]
Current State: 53:[59, 50, 31, 31], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [31, 31, 9] Generated Node #2: [31, 31, 9] from Operation: 59-50=9 Current State: 53:[31, 31, 9], Operations: ['59-50=9'] Exploring Operation: 31+31=62, Resulting Numbers: [9, 62] Generated Node #3: [9, 62] from Operation: 31+31=62 Current State: 53:[9, 62], Operations: ['59-50=9', '31+31=62'] Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[59, 50, 31, 31], Operations: [] Exploring Operation: 59-31=28, Resulting Numbers: [50, 31, 28] Generated Node #0,0: 53:[50, 31, 28] Operation: 59-31=28 Exploring Operation: 31+31=62, Resulting Numbers: [59, 50, 62] Generated Node #0,1: 53:[59, 50, 62] Operation: 31+31=62 Exploring Operation: 50+31=81, Resulting Numbers: [59, 31, 81] Generated Node #0,2: 53:[59, 31, 81] Operation: 50+31=81 Exploring Operation: 59-31=28, Resulting Numbers: [50, 31, 28] Generated Node #0,3: 53:[50, 31, 28] Operation: 59-31=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[59, 50, 62], Operations: ['31+31=62'] Exploring Operation: 59-50=9, Resulting Numbers: [62, 9] Generated Node #0,1,0: 53:[62, 9] Operation: 59-50=9 Exploring Operation: 62-50=12, Resulting Numbers: [59, 12] Generated Node #0,1,1: 53:[59, 12] Operation: 62-50=12 Exploring Operation: 59+50=109, Resulting Numbers: [62, 109] Generated Node #0,1,2: 53:[62, 109] Operation: 59+50=109 Exploring Operation: 62-59=3, Resulting Numbers: [50, 3] Generated Node #0,1,3: 53:[50, 3] Operation: 62-59=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[59, 12], Operations: ['31+31=62', '62-50=12'] Exploring Operation: 59+12=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 59*12=708, Resulting Numbers: [708] 708,53 unequal: No Solution Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[62, 9], Operations: ['31+31=62', '59-50=9'] Exploring Operation: 62*9=558, Resulting Numbers: [558] 558,53 unequal: No Solution Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[59, 50, 31, 31], Operations: [] Exploring Operation: 31+31=62, Resulting Numbers: [59, 50, 62] Generated Node #0,1: 53:[59, 50, 62] Operation: 31+31=62 Moving to Node #0,1 Current State: 53:[59, 50, 62], Operations: ['31+31=62'] Exploring Operation: 59-50=9, Resulting Numbers: [62, 9] Generated Node #0,1,0: 53:[62, 9] Operation: 59-50=9 Moving to Node #0,1,0 Current State: 53:[62, 9], Operations: ['31+31=62', '59-50=9'] Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 52, 74, 8, 72 ]
14
[ "52+74=126", "72/8=9", "126/9=14" ]
Current State: 14:[52, 74, 8, 72], Operations: [] Exploring Operation: 52+74=126, Resulting Numbers: [8, 72, 126] Generated Node #2: [8, 72, 126] from Operation: 52+74=126 Current State: 14:[8, 72, 126], Operations: ['52+74=126'] Exploring Operation: 72/8=9, Resulting Numbers: [126, 9] Generated Node #3: [126, 9] from Operation: 72/8=9 Current State: 14:[126, 9], Operations: ['52+74=126', '72/8=9'] Exploring Operation: 126/9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[52, 74, 8, 72], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [52, 8, 2] Generated Node #0,0: 14:[52, 8, 2] Operation: 74-72=2 Exploring Operation: 74-52=22, Resulting Numbers: [8, 72, 22] Generated Node #0,1: 14:[8, 72, 22] Operation: 74-52=22 Moving to Node #0,0 Current State: 14:[52, 8, 2], Operations: ['74-72=2'] Exploring Operation: 52/2=26, Resulting Numbers: [8, 26] Generated Node #0,0,0: 14:[8, 26] Operation: 52/2=26 Exploring Operation: 52-8=44, Resulting Numbers: [2, 44] Generated Node #0,0,1: 14:[2, 44] Operation: 52-8=44 Moving to Node #0,1 Current State: 14:[8, 72, 22], Operations: ['74-52=22'] Exploring Operation: 72/8=9, Resulting Numbers: [22, 9] Generated Node #0,1,0: 14:[22, 9] Operation: 72/8=9 Exploring Operation: 72-22=50, Resulting Numbers: [8, 50] Generated Node #0,1,1: 14:[8, 50] Operation: 72-22=50 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[22, 9], Operations: ['74-52=22', '72/8=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,14 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:[8, 50], Operations: ['74-52=22', '72-22=50'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,14 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: 14:[8, 26], Operations: ['74-72=2', '52/2=26'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[2, 44], Operations: ['74-72=2', '52-8=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,14 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 6, 20, 42 ]
33
[ "11*42=462", "20-6=14", "462/14=33" ]
Current State: 33:[11, 6, 20, 42], Operations: [] Exploring Operation: 11*42=462, Resulting Numbers: [6, 20, 462] Generated Node #2: [6, 20, 462] from Operation: 11*42=462 Current State: 33:[6, 20, 462], Operations: ['11*42=462'] Exploring Operation: 20-6=14, Resulting Numbers: [462, 14] Generated Node #3: [462, 14] from Operation: 20-6=14 Current State: 33:[462, 14], Operations: ['11*42=462', '20-6=14'] Exploring Operation: 462/14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[11, 6, 20, 42], Operations: [] Exploring Operation: 20-6=14, Resulting Numbers: [11, 42, 14] Generated Node #0,0: 33:[11, 42, 14] Operation: 20-6=14 Exploring Operation: 42-6=36, Resulting Numbers: [11, 20, 36] Generated Node #0,1: 33:[11, 20, 36] Operation: 42-6=36 Exploring Operation: 42/6=7, Resulting Numbers: [11, 20, 7] Generated Node #0,2: 33:[11, 20, 7] Operation: 42/6=7 Exploring Operation: 20-11=9, Resulting Numbers: [6, 42, 9] Generated Node #0,3: 33:[6, 42, 9] Operation: 20-11=9 Exploring Operation: 11+20=31, Resulting Numbers: [6, 42, 31] Generated Node #0,4: 33:[6, 42, 31] Operation: 11+20=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[11, 42, 14], Operations: ['20-6=14'] Exploring Operation: 42-11=31, Resulting Numbers: [14, 31] Generated Node #0,0,0: 33:[14, 31] Operation: 42-11=31 Exploring Operation: 14-11=3, Resulting Numbers: [42, 3] Generated Node #0,0,1: 33:[42, 3] Operation: 14-11=3 Exploring Operation: 42/14=3, Resulting Numbers: [11, 3] Generated Node #0,0,2: 33:[11, 3] Operation: 42/14=3 Exploring Operation: 42-14=28, Resulting Numbers: [11, 28] Generated Node #0,0,3: 33:[11, 28] Operation: 42-14=28 Exploring Operation: 11+14=25, Resulting Numbers: [42, 25] Generated Node #0,0,4: 33:[42, 25] Operation: 11+14=25 Moving to Node #0,0,2 Current State: 33:[11, 3], Operations: ['20-6=14', '42/14=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[11, 6, 20, 42], Operations: [] Exploring Operation: 20-6=14, Resulting Numbers: [11, 42, 14] Generated Node #0,0: 33:[11, 42, 14] Operation: 20-6=14 Moving to Node #0,0 Current State: 33:[11, 42, 14], Operations: ['20-6=14'] Exploring Operation: 42/14=3, Resulting Numbers: [11, 3] Generated Node #0,0,2: 33:[11, 3] Operation: 42/14=3 Moving to Node #0,0,2 Current State: 33:[11, 3], Operations: ['20-6=14', '42/14=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 31, 4, 27, 63 ]
34
[ "31*4=124", "27+63=90", "124-90=34" ]
Current State: 34:[31, 4, 27, 63], Operations: [] Exploring Operation: 31*4=124, Resulting Numbers: [27, 63, 124] Generated Node #2: [27, 63, 124] from Operation: 31*4=124 Current State: 34:[27, 63, 124], Operations: ['31*4=124'] Exploring Operation: 27+63=90, Resulting Numbers: [124, 90] Generated Node #3: [124, 90] from Operation: 27+63=90 Current State: 34:[124, 90], Operations: ['31*4=124', '27+63=90'] Exploring Operation: 124-90=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[31, 4, 27, 63], Operations: [] Exploring Operation: 63-31=32, Resulting Numbers: [4, 27, 32] Generated Node #0,0: 34:[4, 27, 32] Operation: 63-31=32 Exploring Operation: 31-27=4, Resulting Numbers: [4, 63, 4] Generated Node #0,1: 34:[4, 63, 4] Operation: 31-27=4 Exploring Operation: 63-27=36, Resulting Numbers: [31, 4, 36] Generated Node #0,2: 34:[31, 4, 36] Operation: 63-27=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[31, 4, 36], Operations: ['63-27=36'] Exploring Operation: 36-31=5, Resulting Numbers: [4, 5] Generated Node #0,2,0: 34:[4, 5] Operation: 36-31=5 Exploring Operation: 31+4=35, Resulting Numbers: [36, 35] Generated Node #0,2,1: 34:[36, 35] Operation: 31+4=35 Exploring Operation: 36-4=32, Resulting Numbers: [31, 32] Generated Node #0,2,2: 34:[31, 32] Operation: 36-4=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 34:[36, 35], Operations: ['63-27=36', '31+4=35'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,34 unequal: No Solution Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,34 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, 5], Operations: ['63-27=36', '36-31=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 4*5=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 #0,2,2 Current State: 34:[31, 32], Operations: ['63-27=36', '36-4=32'] Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,34 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,34 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:[4, 27, 32], Operations: ['63-31=32'] Exploring Operation: 4+27=31, Resulting Numbers: [32, 31] Generated Node #0,0,0: 34:[32, 31] Operation: 4+27=31 Exploring Operation: 32-27=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 34:[4, 5] Operation: 32-27=5 Exploring Operation: 27-4=23, Resulting Numbers: [32, 23] Generated Node #0,0,2: 34:[32, 23] Operation: 27-4=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[32, 31], Operations: ['63-31=32', '4+27=31'] Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,34 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,34 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:[4, 5], Operations: ['63-31=32', '32-27=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 4*5=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 #0,0,2 Current State: 34:[32, 23], Operations: ['63-31=32', '27-4=23'] Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,34 unequal: No Solution Exploring Operation: 32+23=55, Resulting Numbers: [55] 55,34 unequal: No Solution Exploring Operation: 32*23=736, Resulting Numbers: [736] 736,34 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:[4, 63, 4], Operations: ['31-27=4'] Exploring Operation: 4*4=16, Resulting Numbers: [63, 16] Generated Node #0,1,0: 34:[63, 16] Operation: 4*4=16 Exploring Operation: 63-4=59, Resulting Numbers: [4, 59] Generated Node #0,1,1: 34:[4, 59] Operation: 63-4=59 Exploring Operation: 63-4=59, Resulting Numbers: [4, 59] Generated Node #0,1,2: 34:[4, 59] Operation: 63-4=59 Moving to Node #0,1,1 Current State: 34:[4, 59], Operations: ['31-27=4', '63-4=59'] Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,34 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,34 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[4, 59], Operations: ['31-27=4', '63-4=59'] Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,34 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,34 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[63, 16], Operations: ['31-27=4', '4*4=16'] Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,34 unequal: No Solution Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,34 unequal: No Solution Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,34 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
[ 26, 39, 13, 43 ]
47
[ "26/13=2", "43*2=86", "86-39=47" ]
Current State: 47:[26, 39, 13, 43], Operations: [] Exploring Operation: 26/13=2, Resulting Numbers: [39, 43, 2] Generated Node #2: [39, 43, 2] from Operation: 26/13=2 Current State: 47:[39, 43, 2], Operations: ['26/13=2'] Exploring Operation: 43*2=86, Resulting Numbers: [39, 86] Generated Node #3: [39, 86] from Operation: 43*2=86 Current State: 47:[39, 86], Operations: ['26/13=2', '43*2=86'] Exploring Operation: 86-39=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[26, 39, 13, 43], Operations: [] Exploring Operation: 39+13=52, Resulting Numbers: [26, 43, 52] Generated Node #0,0: 47:[26, 43, 52] Operation: 39+13=52 Exploring Operation: 13+43=56, Resulting Numbers: [26, 39, 56] Generated Node #0,1: 47:[26, 39, 56] Operation: 13+43=56 Exploring Operation: 26+13=39, Resulting Numbers: [39, 43, 39] Generated Node #0,2: 47:[39, 43, 39] Operation: 26+13=39 Exploring Operation: 26-13=13, Resulting Numbers: [39, 43, 13] Generated Node #0,3: 47:[39, 43, 13] Operation: 26-13=13 Moving to Node #0,2 Current State: 47:[39, 43, 39], Operations: ['26+13=39'] Exploring Operation: 39+39=78, Resulting Numbers: [43, 78] Generated Node #0,2,0: 47:[43, 78] Operation: 39+39=78 Exploring Operation: 39+43=82, Resulting Numbers: [39, 82] Generated Node #0,2,1: 47:[39, 82] Operation: 39+43=82 Exploring Operation: 39/39=1, Resulting Numbers: [43, 1] Generated Node #0,2,2: 47:[43, 1] Operation: 39/39=1 Exploring Operation: 43+39=82, Resulting Numbers: [39, 82] Generated Node #0,2,3: 47:[39, 82] Operation: 43+39=82 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[43, 78], Operations: ['26+13=39', '39+39=78'] Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,47 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[39, 82], Operations: ['26+13=39', '39+43=82'] Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 47:[39, 82], Operations: ['26+13=39', '43+39=82'] Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,47 unequal: No Solution Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[43, 1], Operations: ['26+13=39', '39/39=1'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,47 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,47 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: 47:[26, 43, 52], Operations: ['39+13=52'] Exploring Operation: 26+52=78, Resulting Numbers: [43, 78] Generated Node #0,0,0: 47:[43, 78] Operation: 26+52=78 Exploring Operation: 43-26=17, Resulting Numbers: [52, 17] Generated Node #0,0,1: 47:[52, 17] Operation: 43-26=17 Exploring Operation: 26+43=69, Resulting Numbers: [52, 69] Generated Node #0,0,2: 47:[52, 69] Operation: 26+43=69 Exploring Operation: 52-26=26, Resulting Numbers: [43, 26] Generated Node #0,0,3: 47:[43, 26] Operation: 52-26=26 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[43, 26], Operations: ['39+13=52', '52-26=26'] Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,47 unequal: No Solution Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,47 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[52, 69], Operations: ['39+13=52', '26+43=69'] Exploring Operation: 52+69=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 52*69=3588, Resulting Numbers: [3588] 3588,47 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[43, 78], Operations: ['39+13=52', '26+52=78'] Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[52, 17], Operations: ['39+13=52', '43-26=17'] Exploring Operation: 52*17=884, Resulting Numbers: [884] 884,47 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,47 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: 47:[26, 39, 56], Operations: ['13+43=56'] Exploring Operation: 39-26=13, Resulting Numbers: [56, 13] Generated Node #0,1,0: 47:[56, 13] Operation: 39-26=13 Exploring Operation: 56-26=30, Resulting Numbers: [39, 30] Generated Node #0,1,1: 47:[39, 30] Operation: 56-26=30 Exploring Operation: 26+39=65, Resulting Numbers: [56, 65] Generated Node #0,1,2: 47:[56, 65] Operation: 26+39=65 Exploring Operation: 26+56=82, Resulting Numbers: [39, 82] Generated Node #0,1,3: 47:[39, 82] Operation: 26+56=82 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[39, 30], Operations: ['13+43=56', '56-26=30'] Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,47 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[56, 65], Operations: ['13+43=56', '26+39=65'] Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,47 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[56, 13], Operations: ['13+43=56', '39-26=13'] Exploring Operation: 56+13=69, Resulting Numbers: [69] 69,47 unequal: No Solution Exploring Operation: 56-13=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 56*13=728, Resulting Numbers: [728] 728,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 47:[39, 82], Operations: ['13+43=56', '26+56=82'] Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,47 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: 47:[39, 43, 13], Operations: ['26-13=13'] Exploring Operation: 39-13=26, Resulting Numbers: [43, 26] Generated Node #0,3,0: 47:[43, 26] Operation: 39-13=26 Exploring Operation: 43+13=56, Resulting Numbers: [39, 56] Generated Node #0,3,1: 47:[39, 56] Operation: 43+13=56 Exploring Operation: 39+13=52, Resulting Numbers: [43, 52] Generated Node #0,3,2: 47:[43, 52] Operation: 39+13=52 Exploring Operation: 43-13=30, Resulting Numbers: [39, 30] Generated Node #0,3,3: 47:[39, 30] Operation: 43-13=30 Moving to Node #0,3,2 Current State: 47:[43, 52], Operations: ['26-13=13', '39+13=52'] Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 43*52=2236, Resulting Numbers: [2236] 2236,47 unequal: No Solution Exploring Operation: 43+52=95, Resulting Numbers: [95] 95,47 unequal: No Solution Moving to Node #0,3,1 Current State: 47:[39, 56], Operations: ['26-13=13', '43+13=56'] Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 39*56=2184, Resulting Numbers: [2184] 2184,47 unequal: No Solution Exploring Operation: 39+56=95, Resulting Numbers: [95] 95,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[39, 30], Operations: ['26-13=13', '43-13=30'] Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,47 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[43, 26], Operations: ['26-13=13', '39-13=26'] Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,47 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,47 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 50, 56, 43 ]
56
[ "50-7=43", "56+43=99", "99-43=56" ]
Current State: 56:[7, 50, 56, 43], Operations: [] Exploring Operation: 50-7=43, Resulting Numbers: [56, 43, 43] Generated Node #2: [56, 43, 43] from Operation: 50-7=43 Current State: 56:[56, 43, 43], Operations: ['50-7=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,56 equal: Goal Reached Exploring Operation: 99-43=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[7, 50, 56, 43], Operations: [] Exploring Operation: 50-43=7, Resulting Numbers: [7, 56, 7] Generated Node #0,0: 56:[7, 56, 7] Operation: 50-43=7 Moving to Node #0,0 Current State: 56:[7, 56, 7], Operations: ['50-43=7'] Exploring Operation: 56/7=8, Resulting Numbers: [7, 8] Generated Node #0,0,0: 56:[7, 8] Operation: 56/7=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[7, 8], Operations: ['50-43=7', '56/7=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[7, 50, 56, 43], Operations: [] Exploring Operation: 50-43=7, Resulting Numbers: [7, 56, 7] Generated Node #0,0: 56:[7, 56, 7] Operation: 50-43=7 Moving to Node #0,0 Current State: 56:[7, 56, 7], Operations: ['50-43=7'] Exploring Operation: 56/7=8, Resulting Numbers: [7, 8] Generated Node #0,0,0: 56:[7, 8] Operation: 56/7=8 Moving to Node #0,0,0 Current State: 56:[7, 8], Operations: ['50-43=7', '56/7=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 86, 22, 72, 6 ]
62
[ "86-72=14", "6*14=84", "84-22=62" ]
Current State: 62:[86, 22, 72, 6], Operations: [] Exploring Operation: 86-72=14, Resulting Numbers: [22, 6, 14] Generated Node #2: [22, 6, 14] from Operation: 86-72=14 Current State: 62:[22, 6, 14], Operations: ['86-72=14'] Exploring Operation: 6*14=84, Resulting Numbers: [22, 84] Generated Node #3: [22, 84] from Operation: 6*14=84 Current State: 62:[22, 84], Operations: ['86-72=14', '6*14=84'] Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[86, 22, 72, 6], Operations: [] Exploring Operation: 86-6=80, Resulting Numbers: [22, 72, 80] Generated Node #0,0: 62:[22, 72, 80] Operation: 86-6=80 Exploring Operation: 86-72=14, Resulting Numbers: [22, 6, 14] Generated Node #0,1: 62:[22, 6, 14] Operation: 86-72=14 Exploring Operation: 22+6=28, Resulting Numbers: [86, 72, 28] Generated Node #0,2: 62:[86, 72, 28] Operation: 22+6=28 Exploring Operation: 86-22=64, Resulting Numbers: [72, 6, 64] Generated Node #0,3: 62:[72, 6, 64] Operation: 86-22=64 Moving to Node #0,3 Current State: 62:[72, 6, 64], Operations: ['86-22=64'] Exploring Operation: 64-6=58, Resulting Numbers: [72, 58] Generated Node #0,3,0: 62:[72, 58] Operation: 64-6=58 Exploring Operation: 72/6=12, Resulting Numbers: [64, 12] Generated Node #0,3,1: 62:[64, 12] Operation: 72/6=12 Exploring Operation: 72-6=66, Resulting Numbers: [64, 66] Generated Node #0,3,2: 62:[64, 66] Operation: 72-6=66 Exploring Operation: 72-64=8, Resulting Numbers: [6, 8] Generated Node #0,3,3: 62:[6, 8] Operation: 72-64=8 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[64, 66], Operations: ['86-22=64', '72-6=66'] Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 64*66=4224, Resulting Numbers: [4224] 4224,62 unequal: No Solution Exploring Operation: 64+66=130, Resulting Numbers: [130] 130,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 62:[6, 8], Operations: ['86-22=64', '72-64=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,62 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 62:[64, 12], Operations: ['86-22=64', '72/6=12'] Exploring Operation: 64+12=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 64*12=768, Resulting Numbers: [768] 768,62 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[72, 58], Operations: ['86-22=64', '64-6=58'] Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,62 unequal: No Solution Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,62 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: 62:[22, 6, 14], Operations: ['86-72=14'] Exploring Operation: 22+6=28, Resulting Numbers: [14, 28] Generated Node #0,1,0: 62:[14, 28] Operation: 22+6=28 Exploring Operation: 14-6=8, Resulting Numbers: [22, 8] Generated Node #0,1,1: 62:[22, 8] Operation: 14-6=8 Exploring Operation: 22-14=8, Resulting Numbers: [6, 8] Generated Node #0,1,2: 62:[6, 8] Operation: 22-14=8 Exploring Operation: 22+14=36, Resulting Numbers: [6, 36] Generated Node #0,1,3: 62:[6, 36] Operation: 22+14=36 Moving to Node #0,2 Current State: 62:[86, 72, 28], Operations: ['22+6=28'] Exploring Operation: 86-28=58, Resulting Numbers: [72, 58] Generated Node #0,2,0: 62:[72, 58] Operation: 86-28=58 Exploring Operation: 86+28=114, Resulting Numbers: [72, 114] Generated Node #0,2,1: 62:[72, 114] Operation: 86+28=114 Exploring Operation: 72-28=44, Resulting Numbers: [86, 44] Generated Node #0,2,2: 62:[86, 44] Operation: 72-28=44 Exploring Operation: 86-72=14, Resulting Numbers: [28, 14] Generated Node #0,2,3: 62:[28, 14] Operation: 86-72=14 Moving to Node #0,0 Current State: 62:[22, 72, 80], Operations: ['86-6=80'] Exploring Operation: 80-22=58, Resulting Numbers: [72, 58] Generated Node #0,0,0: 62:[72, 58] Operation: 80-22=58 Exploring Operation: 72-22=50, Resulting Numbers: [80, 50] Generated Node #0,0,1: 62:[80, 50] Operation: 72-22=50 Exploring Operation: 22+72=94, Resulting Numbers: [80, 94] Generated Node #0,0,2: 62:[80, 94] Operation: 22+72=94 Exploring Operation: 80-72=8, Resulting Numbers: [22, 8] Generated Node #0,0,3: 62:[22, 8] Operation: 80-72=8 Moving to Node #0,1,3 Current State: 62:[6, 36], Operations: ['86-72=14', '22+14=36'] Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,62 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,62 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[6, 8], Operations: ['86-72=14', '22-14=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[72, 58], Operations: ['22+6=28', '86-28=58'] Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,62 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[72, 58], Operations: ['86-6=80', '80-22=58'] Exploring Operation: 72-58=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 72*58=4176, Resulting Numbers: [4176] 4176,62 unequal: No Solution Exploring Operation: 72+58=130, Resulting Numbers: [130] 130,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[14, 28], Operations: ['86-72=14', '22+6=28'] Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,62 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[28, 14], Operations: ['22+6=28', '86-72=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,62 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,62 unequal: No Solution Moving to Node #0,0,3 Current State: 62:[22, 8], Operations: ['86-6=80', '80-72=8'] Exploring Operation: 22+8=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 22*8=176, Resulting Numbers: [176] 176,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[22, 8], Operations: ['86-72=14', '14-6=8'] Exploring Operation: 22+8=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 22*8=176, Resulting Numbers: [176] 176,62 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[80, 50], Operations: ['86-6=80', '72-22=50'] Exploring Operation: 80+50=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 80*50=4000, Resulting Numbers: [4000] 4000,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[86, 44], Operations: ['22+6=28', '72-28=44'] Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 86+44=130, Resulting Numbers: [130] 130,62 unequal: No Solution Exploring Operation: 86*44=3784, Resulting Numbers: [3784] 3784,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[80, 94], Operations: ['86-6=80', '22+72=94'] Exploring Operation: 80*94=7520, Resulting Numbers: [7520] 7520,62 unequal: No Solution Exploring Operation: 94-80=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 80+94=174, Resulting Numbers: [174] 174,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[72, 114], Operations: ['22+6=28', '86+28=114'] Exploring Operation: 114-72=42, Resulting Numbers: [42] 42,62 unequal: No Solution Exploring Operation: 72*114=8208, Resulting Numbers: [8208] 8208,62 unequal: No Solution Exploring Operation: 72+114=186, Resulting Numbers: [186] 186,62 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 72, 57, 67, 69 ]
73
[ "69-57=12", "72/12=6", "67+6=73" ]
Current State: 73:[72, 57, 67, 69], Operations: [] Exploring Operation: 69-57=12, Resulting Numbers: [72, 67, 12] Generated Node #2: [72, 67, 12] from Operation: 69-57=12 Current State: 73:[72, 67, 12], Operations: ['69-57=12'] Exploring Operation: 72/12=6, Resulting Numbers: [67, 6] Generated Node #3: [67, 6] from Operation: 72/12=6 Current State: 73:[67, 6], Operations: ['69-57=12', '72/12=6'] Exploring Operation: 67+6=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[72, 57, 67, 69], Operations: [] Exploring Operation: 57+67=124, Resulting Numbers: [72, 69, 124] Generated Node #0,0: 73:[72, 69, 124] Operation: 57+67=124 Exploring Operation: 72+57=129, Resulting Numbers: [67, 69, 129] Generated Node #0,1: 73:[67, 69, 129] Operation: 72+57=129 Exploring Operation: 57+69=126, Resulting Numbers: [72, 67, 126] Generated Node #0,2: 73:[72, 67, 126] Operation: 57+69=126 Moving to Node #0,0 Current State: 73:[72, 69, 124], Operations: ['57+67=124'] Exploring Operation: 124-72=52, Resulting Numbers: [69, 52] Generated Node #0,0,0: 73:[69, 52] Operation: 124-72=52 Exploring Operation: 124-69=55, Resulting Numbers: [72, 55] Generated Node #0,0,1: 73:[72, 55] Operation: 124-69=55 Exploring Operation: 72+69=141, Resulting Numbers: [124, 141] Generated Node #0,0,2: 73:[124, 141] Operation: 72+69=141 Moving to Node #0,2 Current State: 73:[72, 67, 126], Operations: ['57+69=126'] Exploring Operation: 72+67=139, Resulting Numbers: [126, 139] Generated Node #0,2,0: 73:[126, 139] Operation: 72+67=139 Exploring Operation: 126-72=54, Resulting Numbers: [67, 54] Generated Node #0,2,1: 73:[67, 54] Operation: 126-72=54 Exploring Operation: 126-67=59, Resulting Numbers: [72, 59] Generated Node #0,2,2: 73:[72, 59] Operation: 126-67=59 Moving to Node #0,1 Current State: 73:[67, 69, 129], Operations: ['72+57=129'] Exploring Operation: 129-69=60, Resulting Numbers: [67, 60] Generated Node #0,1,0: 73:[67, 60] Operation: 129-69=60 Exploring Operation: 67+69=136, Resulting Numbers: [129, 136] Generated Node #0,1,1: 73:[129, 136] Operation: 67+69=136 Exploring Operation: 129-67=62, Resulting Numbers: [69, 62] Generated Node #0,1,2: 73:[69, 62] Operation: 129-67=62 Moving to Node #0,2,2 Current State: 73:[72, 59], Operations: ['57+69=126', '126-67=59'] Exploring Operation: 72+59=131, Resulting Numbers: [131] 131,73 unequal: No Solution Exploring Operation: 72-59=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 72*59=4248, Resulting Numbers: [4248] 4248,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[69, 62], Operations: ['72+57=129', '129-67=62'] Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,73 unequal: No Solution Exploring Operation: 69*62=4278, Resulting Numbers: [4278] 4278,73 unequal: No Solution Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[72, 55], Operations: ['57+67=124', '124-69=55'] Exploring Operation: 72+55=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 72*55=3960, Resulting Numbers: [3960] 3960,73 unequal: No Solution Exploring Operation: 72-55=17, Resulting Numbers: [17] 17,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[67, 60], Operations: ['72+57=129', '129-69=60'] Exploring Operation: 67*60=4020, Resulting Numbers: [4020] 4020,73 unequal: No Solution Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 67+60=127, Resulting Numbers: [127] 127,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[67, 54], Operations: ['57+69=126', '126-72=54'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,73 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[69, 52], Operations: ['57+67=124', '124-72=52'] Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,73 unequal: No Solution Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,73 unequal: No Solution Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[124, 141], Operations: ['57+67=124', '72+69=141'] Exploring Operation: 141-124=17, Resulting Numbers: [17] 17,73 unequal: No Solution Exploring Operation: 124+141=265, Resulting Numbers: [265] 265,73 unequal: No Solution Exploring Operation: 124*141=17484, Resulting Numbers: [17484] 17484,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[126, 139], Operations: ['57+69=126', '72+67=139'] Exploring Operation: 126*139=17514, Resulting Numbers: [17514] 17514,73 unequal: No Solution Exploring Operation: 126+139=265, Resulting Numbers: [265] 265,73 unequal: No Solution Exploring Operation: 139-126=13, Resulting Numbers: [13] 13,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[129, 136], Operations: ['72+57=129', '67+69=136'] Exploring Operation: 129*136=17544, Resulting Numbers: [17544] 17544,73 unequal: No Solution Exploring Operation: 136-129=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 129+136=265, Resulting Numbers: [265] 265,73 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 53, 97, 5, 24 ]
99
[ "53-5=48", "48/24=2", "97+2=99" ]
Current State: 99:[53, 97, 5, 24], Operations: [] Exploring Operation: 53-5=48, Resulting Numbers: [97, 24, 48] Generated Node #2: [97, 24, 48] from Operation: 53-5=48 Current State: 99:[97, 24, 48], Operations: ['53-5=48'] Exploring Operation: 48/24=2, Resulting Numbers: [97, 2] Generated Node #3: [97, 2] from Operation: 48/24=2 Current State: 99:[97, 2], Operations: ['53-5=48', '48/24=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[53, 97, 5, 24], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [5, 24, 44] Generated Node #0,0: 99:[5, 24, 44] Operation: 97-53=44 Exploring Operation: 53-5=48, Resulting Numbers: [97, 24, 48] Generated Node #0,1: 99:[97, 24, 48] Operation: 53-5=48 Exploring Operation: 53-24=29, Resulting Numbers: [97, 5, 29] Generated Node #0,2: 99:[97, 5, 29] Operation: 53-24=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[97, 5, 29], Operations: ['53-24=29'] Exploring Operation: 97+5=102, Resulting Numbers: [29, 102] Generated Node #0,2,0: 99:[29, 102] Operation: 97+5=102 Exploring Operation: 5+29=34, Resulting Numbers: [97, 34] Generated Node #0,2,1: 99:[97, 34] Operation: 5+29=34 Exploring Operation: 97-5=92, Resulting Numbers: [29, 92] Generated Node #0,2,2: 99:[29, 92] Operation: 97-5=92 Moving to Node #0,2,1 Current State: 99:[97, 34], Operations: ['53-24=29', '5+29=34'] Exploring Operation: 97*34=3298, Resulting Numbers: [3298] 3298,99 unequal: No Solution Exploring Operation: 97+34=131, Resulting Numbers: [131] 131,99 unequal: No Solution Exploring Operation: 97-34=63, Resulting Numbers: [63] 63,99 unequal: No Solution Moving to Node #0,2,0 Current State: 99:[29, 102], Operations: ['53-24=29', '97+5=102'] Exploring Operation: 29*102=2958, Resulting Numbers: [2958] 2958,99 unequal: No Solution Exploring Operation: 102-29=73, Resulting Numbers: [73] 73,99 unequal: No Solution Exploring Operation: 29+102=131, Resulting Numbers: [131] 131,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[29, 92], Operations: ['53-24=29', '97-5=92'] Exploring Operation: 29+92=121, Resulting Numbers: [121] 121,99 unequal: No Solution Exploring Operation: 29*92=2668, Resulting Numbers: [2668] 2668,99 unequal: No Solution Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[5, 24, 44], Operations: ['97-53=44'] Exploring Operation: 44-24=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 99:[5, 20] Operation: 44-24=20 Exploring Operation: 5+24=29, Resulting Numbers: [44, 29] Generated Node #0,0,1: 99:[44, 29] Operation: 5+24=29 Exploring Operation: 44-5=39, Resulting Numbers: [24, 39] Generated Node #0,0,2: 99:[24, 39] Operation: 44-5=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[5, 20], Operations: ['97-53=44', '44-24=20'] Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,99 unequal: No Solution No 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: 99:[44, 29], Operations: ['97-53=44', '5+24=29'] Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,99 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,99 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,99 unequal: No Solution No 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: 99:[24, 39], Operations: ['97-53=44', '44-5=39'] Exploring Operation: 24+39=63, Resulting Numbers: [63] 63,99 unequal: No Solution Exploring Operation: 39-24=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 24*39=936, Resulting Numbers: [936] 936,99 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: 99:[97, 24, 48], Operations: ['53-5=48'] Exploring Operation: 97-48=49, Resulting Numbers: [24, 49] Generated Node #0,1,0: 99:[24, 49] Operation: 97-48=49 Exploring Operation: 48/24=2, Resulting Numbers: [97, 2] Generated Node #0,1,1: 99:[97, 2] Operation: 48/24=2 Exploring Operation: 48-24=24, Resulting Numbers: [97, 24] Generated Node #0,1,2: 99:[97, 24] Operation: 48-24=24 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[97, 2], Operations: ['53-5=48', '48/24=2'] Exploring Operation: 97*2=194, Resulting Numbers: [194] 194,99 unequal: No Solution Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[53, 97, 5, 24], Operations: [] Exploring Operation: 53-5=48, Resulting Numbers: [97, 24, 48] Generated Node #0,1: 99:[97, 24, 48] Operation: 53-5=48 Moving to Node #0,1 Current State: 99:[97, 24, 48], Operations: ['53-5=48'] Exploring Operation: 48/24=2, Resulting Numbers: [97, 2] Generated Node #0,1,1: 99:[97, 2] Operation: 48/24=2 Moving to Node #0,1,1 Current State: 99:[97, 2], Operations: ['53-5=48', '48/24=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 7, 44, 49, 8 ]
20
[ "44-7=37", "49+8=57", "57-37=20" ]
Current State: 20:[7, 44, 49, 8], Operations: [] Exploring Operation: 44-7=37, Resulting Numbers: [49, 8, 37] Generated Node #2: [49, 8, 37] from Operation: 44-7=37 Current State: 20:[49, 8, 37], Operations: ['44-7=37'] Exploring Operation: 49+8=57, Resulting Numbers: [37, 57] Generated Node #3: [37, 57] from Operation: 49+8=57 Current State: 20:[37, 57], Operations: ['44-7=37', '49+8=57'] Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 44, 49, 8], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [7, 8, 5] Generated Node #0,0: 20:[7, 8, 5] Operation: 49-44=5 Moving to Node #0,0 Current State: 20:[7, 8, 5], Operations: ['49-44=5'] Exploring Operation: 8-7=1, Resulting Numbers: [5, 1] Generated Node #0,0,0: 20:[5, 1] Operation: 8-7=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[5, 1], Operations: ['49-44=5', '8-7=1'] Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,20 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
[ 40, 84, 42, 32 ]
70
[ "40+32=72", "84/42=2", "72-2=70" ]
Current State: 70:[40, 84, 42, 32], Operations: [] Exploring Operation: 40+32=72, Resulting Numbers: [84, 42, 72] Generated Node #2: [84, 42, 72] from Operation: 40+32=72 Current State: 70:[84, 42, 72], Operations: ['40+32=72'] Exploring Operation: 84/42=2, Resulting Numbers: [72, 2] Generated Node #3: [72, 2] from Operation: 84/42=2 Current State: 70:[72, 2], Operations: ['40+32=72', '84/42=2'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[40, 84, 42, 32], Operations: [] Exploring Operation: 42-40=2, Resulting Numbers: [84, 32, 2] Generated Node #0,0: 70:[84, 32, 2] Operation: 42-40=2 Exploring Operation: 84-42=42, Resulting Numbers: [40, 32, 42] Generated Node #0,1: 70:[40, 32, 42] Operation: 84-42=42 Exploring Operation: 84/42=2, Resulting Numbers: [40, 32, 2] Generated Node #0,2: 70:[40, 32, 2] Operation: 84/42=2 Exploring Operation: 84-40=44, Resulting Numbers: [42, 32, 44] Generated Node #0,3: 70:[42, 32, 44] Operation: 84-40=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[40, 32, 2], Operations: ['84/42=2'] Exploring Operation: 32+2=34, Resulting Numbers: [40, 34] Generated Node #0,2,0: 70:[40, 34] Operation: 32+2=34 Exploring Operation: 40-2=38, Resulting Numbers: [32, 38] Generated Node #0,2,1: 70:[32, 38] Operation: 40-2=38 Exploring Operation: 40+32=72, Resulting Numbers: [2, 72] Generated Node #0,2,2: 70:[2, 72] Operation: 40+32=72 Exploring Operation: 40-32=8, Resulting Numbers: [2, 8] Generated Node #0,2,3: 70:[2, 8] Operation: 40-32=8 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 70:[2, 8], Operations: ['84/42=2', '40-32=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,70 unequal: No Solution No 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: 70:[2, 72], Operations: ['84/42=2', '40+32=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,70 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[40, 84, 42, 32], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [40, 32, 2] Generated Node #0,2: 70:[40, 32, 2] Operation: 84/42=2 Moving to Node #0,2 Current State: 70:[40, 32, 2], Operations: ['84/42=2'] Exploring Operation: 40+32=72, Resulting Numbers: [2, 72] Generated Node #0,2,2: 70:[2, 72] Operation: 40+32=72 Moving to Node #0,2,2 Current State: 70:[2, 72], Operations: ['84/42=2', '40+32=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 2, 89, 11, 1 ]
95
[ "11+1=12", "12/2=6", "89+6=95" ]
Current State: 95:[2, 89, 11, 1], Operations: [] Exploring Operation: 11+1=12, Resulting Numbers: [2, 89, 12] Generated Node #2: [2, 89, 12] from Operation: 11+1=12 Current State: 95:[2, 89, 12], Operations: ['11+1=12'] Exploring Operation: 12/2=6, Resulting Numbers: [89, 6] Generated Node #3: [89, 6] from Operation: 12/2=6 Current State: 95:[89, 6], Operations: ['11+1=12', '12/2=6'] Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[2, 89, 11, 1], Operations: [] Exploring Operation: 89+11=100, Resulting Numbers: [2, 1, 100] Generated Node #0,0: 95:[2, 1, 100] Operation: 89+11=100 Moving to Node #0,0 Current State: 95:[2, 1, 100], Operations: ['89+11=100'] Exploring Operation: 2+1=3, Resulting Numbers: [100, 3] Generated Node #0,0,0: 95:[100, 3] Operation: 2+1=3 Moving to Node #0,0,0 Current State: 95:[100, 3], Operations: ['89+11=100', '2+1=3'] Exploring Operation: 100-3=97, Resulting Numbers: [97] 97,95 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 28, 68, 4, 93 ]
48
[ "93-28=65", "68/4=17", "65-17=48" ]
Current State: 48:[28, 68, 4, 93], Operations: [] Exploring Operation: 93-28=65, Resulting Numbers: [68, 4, 65] Generated Node #2: [68, 4, 65] from Operation: 93-28=65 Current State: 48:[68, 4, 65], Operations: ['93-28=65'] Exploring Operation: 68/4=17, Resulting Numbers: [65, 17] Generated Node #3: [65, 17] from Operation: 68/4=17 Current State: 48:[65, 17], Operations: ['93-28=65', '68/4=17'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[28, 68, 4, 93], Operations: [] Exploring Operation: 93-68=25, Resulting Numbers: [28, 4, 25] Generated Node #0,0: 48:[28, 4, 25] Operation: 93-68=25 Exploring Operation: 93-28=65, Resulting Numbers: [68, 4, 65] Generated Node #0,1: 48:[68, 4, 65] Operation: 93-28=65 Exploring Operation: 68-28=40, Resulting Numbers: [4, 93, 40] Generated Node #0,2: 48:[4, 93, 40] Operation: 68-28=40 Exploring Operation: 68/4=17, Resulting Numbers: [28, 93, 17] Generated Node #0,3: 48:[28, 93, 17] Operation: 68/4=17 Moving to Node #0,0 Current State: 48:[28, 4, 25], Operations: ['93-68=25'] Exploring Operation: 28/4=7, Resulting Numbers: [25, 7] Generated Node #0,0,0: 48:[25, 7] Operation: 28/4=7 Exploring Operation: 28+25=53, Resulting Numbers: [4, 53] Generated Node #0,0,1: 48:[4, 53] Operation: 28+25=53 Exploring Operation: 28-25=3, Resulting Numbers: [4, 3] Generated Node #0,0,2: 48:[4, 3] Operation: 28-25=3 Exploring Operation: 28-4=24, Resulting Numbers: [25, 24] Generated Node #0,0,3: 48:[25, 24] Operation: 28-4=24 Moving to Node #0,1 Current State: 48:[68, 4, 65], Operations: ['93-28=65'] Exploring Operation: 68-65=3, Resulting Numbers: [4, 3] Generated Node #0,1,0: 48:[4, 3] Operation: 68-65=3 Exploring Operation: 68/4=17, Resulting Numbers: [65, 17] Generated Node #0,1,1: 48:[65, 17] Operation: 68/4=17 Exploring Operation: 68-4=64, Resulting Numbers: [65, 64] Generated Node #0,1,2: 48:[65, 64] Operation: 68-4=64 Exploring Operation: 65-4=61, Resulting Numbers: [68, 61] Generated Node #0,1,3: 48:[68, 61] Operation: 65-4=61 Moving to Node #0,3 Current State: 48:[28, 93, 17], Operations: ['68/4=17'] Exploring Operation: 93-28=65, Resulting Numbers: [17, 65] Generated Node #0,3,0: 48:[17, 65] Operation: 93-28=65 Exploring Operation: 28-17=11, Resulting Numbers: [93, 11] Generated Node #0,3,1: 48:[93, 11] Operation: 28-17=11 Exploring Operation: 93-17=76, Resulting Numbers: [28, 76] Generated Node #0,3,2: 48:[28, 76] Operation: 93-17=76 Exploring Operation: 28+17=45, Resulting Numbers: [93, 45] Generated Node #0,3,3: 48:[93, 45] Operation: 28+17=45 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[17, 65], Operations: ['68/4=17', '93-28=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[28, 68, 4, 93], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [28, 93, 17] Generated Node #0,3: 48:[28, 93, 17] Operation: 68/4=17 Moving to Node #0,3 Current State: 48:[28, 93, 17], Operations: ['68/4=17'] Exploring Operation: 93-28=65, Resulting Numbers: [17, 65] Generated Node #0,3,0: 48:[17, 65] Operation: 93-28=65 Moving to Node #0,3,0 Current State: 48:[17, 65], Operations: ['68/4=17', '93-28=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic