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
[ 90, 21, 4, 54 ]
48
[ "90-54=36", "21*4=84", "84-36=48" ]
Current State: 48:[90, 21, 4, 54], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [21, 4, 36] Generated Node #2: [21, 4, 36] from Operation: 90-54=36 Current State: 48:[21, 4, 36], Operations: ['90-54=36'] Exploring Operation: 21*4=84, Resulting Numbers: [36, 84] Generated Node #3: [36, 84] from Operation: 21*4=84 Current State: 48:[36, 84], Operations: ['90-54=36', '21*4=84'] Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[90, 21, 4, 54], Operations: [] Exploring Operation: 90-21=69, Resulting Numbers: [4, 54, 69] Generated Node #0,0: 48:[4, 54, 69] Operation: 90-21=69 Exploring Operation: 21+4=25, Resulting Numbers: [90, 54, 25] Generated Node #0,1: 48:[90, 54, 25] Operation: 21+4=25 Exploring Operation: 54-4=50, Resulting Numbers: [90, 21, 50] Generated Node #0,2: 48:[90, 21, 50] Operation: 54-4=50 Exploring Operation: 90-54=36, Resulting Numbers: [21, 4, 36] Generated Node #0,3: 48:[21, 4, 36] Operation: 90-54=36 Exploring Operation: 90-4=86, Resulting Numbers: [21, 54, 86] Generated Node #0,4: 48:[21, 54, 86] Operation: 90-4=86 Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[21, 4, 36], Operations: ['90-54=36'] Exploring Operation: 4+36=40, Resulting Numbers: [21, 40] Generated Node #0,3,0: 48:[21, 40] Operation: 4+36=40 Exploring Operation: 36/4=9, Resulting Numbers: [21, 9] Generated Node #0,3,1: 48:[21, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [21, 32] Generated Node #0,3,2: 48:[21, 32] Operation: 36-4=32 Exploring Operation: 21+36=57, Resulting Numbers: [4, 57] Generated Node #0,3,3: 48:[4, 57] Operation: 21+36=57 Exploring Operation: 36-21=15, Resulting Numbers: [4, 15] Generated Node #0,3,4: 48:[4, 15] Operation: 36-21=15 Moving to Node #0,3,4 Current State: 48:[4, 15], Operations: ['90-54=36', '36-21=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[21, 9], Operations: ['90-54=36', '36/4=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,48 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,48 unequal: No Solution Moving to Node #0,3,3 Current State: 48:[4, 57], Operations: ['90-54=36', '21+36=57'] Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,48 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,48 unequal: No Solution Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[21, 40], Operations: ['90-54=36', '4+36=40'] Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,48 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[21, 32], Operations: ['90-54=36', '36-4=32'] Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,48 unequal: No Solution Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,48 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[4, 54, 69], Operations: ['90-21=69'] Exploring Operation: 69-54=15, Resulting Numbers: [4, 15] Generated Node #0,0,0: 48:[4, 15] Operation: 69-54=15 Exploring Operation: 4+69=73, Resulting Numbers: [54, 73] Generated Node #0,0,1: 48:[54, 73] Operation: 4+69=73 Exploring Operation: 4+54=58, Resulting Numbers: [69, 58] Generated Node #0,0,2: 48:[69, 58] Operation: 4+54=58 Exploring Operation: 54-4=50, Resulting Numbers: [69, 50] Generated Node #0,0,3: 48:[69, 50] Operation: 54-4=50 Exploring Operation: 69-4=65, Resulting Numbers: [54, 65] Generated Node #0,0,4: 48:[54, 65] Operation: 69-4=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[4, 15], Operations: ['90-21=69', '69-54=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 48:[69, 50], Operations: ['90-21=69', '54-4=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,48 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 48:[54, 65], Operations: ['90-21=69', '69-4=65'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[54, 73], Operations: ['90-21=69', '4+69=73'] Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,48 unequal: No Solution Exploring Operation: 54*73=3942, Resulting Numbers: [3942] 3942,48 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 48:[69, 58], Operations: ['90-21=69', '4+54=58'] Exploring Operation: 69*58=4002, Resulting Numbers: [4002] 4002,48 unequal: No Solution Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 69+58=127, Resulting Numbers: [127] 127,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[90, 21, 50], Operations: ['54-4=50'] Exploring Operation: 21+50=71, Resulting Numbers: [90, 71] Generated Node #0,2,0: 48:[90, 71] Operation: 21+50=71 Exploring Operation: 90-21=69, Resulting Numbers: [50, 69] Generated Node #0,2,1: 48:[50, 69] Operation: 90-21=69 Exploring Operation: 50-21=29, Resulting Numbers: [90, 29] Generated Node #0,2,2: 48:[90, 29] Operation: 50-21=29 Exploring Operation: 90+21=111, Resulting Numbers: [50, 111] Generated Node #0,2,3: 48:[50, 111] Operation: 90+21=111 Exploring Operation: 90-50=40, Resulting Numbers: [21, 40] Generated Node #0,2,4: 48:[21, 40] Operation: 90-50=40 Moving to Node #0,2,4 Current State: 48:[21, 40], Operations: ['54-4=50', '90-50=40'] Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,48 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[50, 69], Operations: ['54-4=50', '90-21=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[90, 29], Operations: ['54-4=50', '50-21=29'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 90*29=2610, Resulting Numbers: [2610] 2610,48 unequal: No Solution Exploring Operation: 90+29=119, Resulting Numbers: [119] 119,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[90, 71], Operations: ['54-4=50', '21+50=71'] Exploring Operation: 90+71=161, Resulting Numbers: [161] 161,48 unequal: No Solution Exploring Operation: 90*71=6390, Resulting Numbers: [6390] 6390,48 unequal: No Solution Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,48 unequal: No Solution Moving to Node #0,2,3 Current State: 48:[50, 111], Operations: ['54-4=50', '90+21=111'] Exploring Operation: 111-50=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 50+111=161, Resulting Numbers: [161] 161,48 unequal: No Solution Exploring Operation: 50*111=5550, Resulting Numbers: [5550] 5550,48 unequal: No Solution No 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: 48:[21, 54, 86], Operations: ['90-4=86'] Exploring Operation: 21+86=107, Resulting Numbers: [54, 107] Generated Node #0,4,0: 48:[54, 107] Operation: 21+86=107 Exploring Operation: 54-21=33, Resulting Numbers: [86, 33] Generated Node #0,4,1: 48:[86, 33] Operation: 54-21=33 Exploring Operation: 86-21=65, Resulting Numbers: [54, 65] Generated Node #0,4,2: 48:[54, 65] Operation: 86-21=65 Exploring Operation: 86-54=32, Resulting Numbers: [21, 32] Generated Node #0,4,3: 48:[21, 32] Operation: 86-54=32 Exploring Operation: 21+54=75, Resulting Numbers: [86, 75] Generated Node #0,4,4: 48:[86, 75] Operation: 21+54=75 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 48:[21, 32], Operations: ['90-4=86', '86-54=32'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 21*32=672, Resulting Numbers: [672] 672,48 unequal: No Solution Exploring Operation: 21+32=53, Resulting Numbers: [53] 53,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 48:[54, 65], Operations: ['90-4=86', '86-21=65'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,48 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 48:[86, 33], Operations: ['90-4=86', '54-21=33'] Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,48 unequal: No Solution Exploring Operation: 86*33=2838, Resulting Numbers: [2838] 2838,48 unequal: No Solution Exploring Operation: 86+33=119, Resulting Numbers: [119] 119,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 48:[54, 107], Operations: ['90-4=86', '21+86=107'] Exploring Operation: 54*107=5778, Resulting Numbers: [5778] 5778,48 unequal: No Solution Exploring Operation: 54+107=161, Resulting Numbers: [161] 161,48 unequal: No Solution Exploring Operation: 107-54=53, Resulting Numbers: [53] 53,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 48:[86, 75], Operations: ['90-4=86', '21+54=75'] Exploring Operation: 86-75=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 86+75=161, Resulting Numbers: [161] 161,48 unequal: No Solution Exploring Operation: 86*75=6450, Resulting Numbers: [6450] 6450,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[90, 54, 25], Operations: ['21+4=25'] Exploring Operation: 90-54=36, Resulting Numbers: [25, 36] Generated Node #0,1,0: 48:[25, 36] Operation: 90-54=36 Exploring Operation: 90-25=65, Resulting Numbers: [54, 65] Generated Node #0,1,1: 48:[54, 65] Operation: 90-25=65 Exploring Operation: 54-25=29, Resulting Numbers: [90, 29] Generated Node #0,1,2: 48:[90, 29] Operation: 54-25=29 Exploring Operation: 90+25=115, Resulting Numbers: [54, 115] Generated Node #0,1,3: 48:[54, 115] Operation: 90+25=115 Exploring Operation: 54+25=79, Resulting Numbers: [90, 79] Generated Node #0,1,4: 48:[90, 79] Operation: 54+25=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[25, 36], Operations: ['21+4=25', '90-54=36'] Exploring Operation: 25*36=900, Resulting Numbers: [900] 900,48 unequal: No Solution Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[54, 65], Operations: ['21+4=25', '90-25=65'] Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,48 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[90, 29], Operations: ['21+4=25', '54-25=29'] Exploring Operation: 90+29=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 90*29=2610, Resulting Numbers: [2610] 2610,48 unequal: No Solution Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 48:[54, 115], Operations: ['21+4=25', '90+25=115'] Exploring Operation: 115-54=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 54*115=6210, Resulting Numbers: [6210] 6210,48 unequal: No Solution Exploring Operation: 54+115=169, Resulting Numbers: [169] 169,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 48:[90, 79], Operations: ['21+4=25', '54+25=79'] Exploring Operation: 90+79=169, Resulting Numbers: [169] 169,48 unequal: No Solution Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 90*79=7110, Resulting Numbers: [7110] 7110,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 34, 78, 38, 90 ]
42
[ "38-34=4", "78+90=168", "168/4=42" ]
Current State: 42:[34, 78, 38, 90], Operations: [] Exploring Operation: 38-34=4, Resulting Numbers: [78, 90, 4] Generated Node #2: [78, 90, 4] from Operation: 38-34=4 Current State: 42:[78, 90, 4], Operations: ['38-34=4'] Exploring Operation: 78+90=168, Resulting Numbers: [4, 168] Generated Node #3: [4, 168] from Operation: 78+90=168 Current State: 42:[4, 168], Operations: ['38-34=4', '78+90=168'] Exploring Operation: 168/4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[34, 78, 38, 90], Operations: [] Exploring Operation: 90-34=56, Resulting Numbers: [78, 38, 56] Generated Node #0,0: 42:[78, 38, 56] Operation: 90-34=56 Exploring Operation: 90-78=12, Resulting Numbers: [34, 38, 12] Generated Node #0,1: 42:[34, 38, 12] Operation: 90-78=12 Exploring Operation: 78-34=44, Resulting Numbers: [38, 90, 44] Generated Node #0,2: 42:[38, 90, 44] Operation: 78-34=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[34, 38, 12], Operations: ['90-78=12'] Exploring Operation: 34-12=22, Resulting Numbers: [38, 22] Generated Node #0,1,0: 42:[38, 22] Operation: 34-12=22 Exploring Operation: 38-34=4, Resulting Numbers: [12, 4] Generated Node #0,1,1: 42:[12, 4] Operation: 38-34=4 Exploring Operation: 34+12=46, Resulting Numbers: [38, 46] Generated Node #0,1,2: 42:[38, 46] Operation: 34+12=46 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[12, 4], Operations: ['90-78=12', '38-34=4'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,42 unequal: No Solution No 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: 42:[38, 22], Operations: ['90-78=12', '34-12=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,42 unequal: No Solution No 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: 42:[38, 46], Operations: ['90-78=12', '34+12=46'] Exploring Operation: 38*46=1748, Resulting Numbers: [1748] 1748,42 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,42 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: 42:[78, 38, 56], Operations: ['90-34=56'] Exploring Operation: 78-56=22, Resulting Numbers: [38, 22] Generated Node #0,0,0: 42:[38, 22] Operation: 78-56=22 Exploring Operation: 78-38=40, Resulting Numbers: [56, 40] Generated Node #0,0,1: 42:[56, 40] Operation: 78-38=40 Exploring Operation: 56-38=18, Resulting Numbers: [78, 18] Generated Node #0,0,2: 42:[78, 18] Operation: 56-38=18 Moving to Node #0,0,0 Current State: 42:[38, 22], Operations: ['90-34=56', '78-56=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[56, 40], Operations: ['90-34=56', '78-38=40'] Exploring Operation: 56+40=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 56*40=2240, Resulting Numbers: [2240] 2240,42 unequal: No Solution Exploring Operation: 56-40=16, Resulting Numbers: [16] 16,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[78, 18], Operations: ['90-34=56', '56-38=18'] Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,42 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[38, 90, 44], Operations: ['78-34=44'] Exploring Operation: 44-38=6, Resulting Numbers: [90, 6] Generated Node #0,2,0: 42:[90, 6] Operation: 44-38=6 Exploring Operation: 90-44=46, Resulting Numbers: [38, 46] Generated Node #0,2,1: 42:[38, 46] Operation: 90-44=46 Exploring Operation: 90-38=52, Resulting Numbers: [44, 52] Generated Node #0,2,2: 42:[44, 52] Operation: 90-38=52 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 42:[38, 46], Operations: ['78-34=44', '90-44=46'] Exploring Operation: 38*46=1748, Resulting Numbers: [1748] 1748,42 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 38+46=84, Resulting Numbers: [84] 84,42 unequal: No Solution No 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: 42:[44, 52], Operations: ['78-34=44', '90-38=52'] Exploring Operation: 44*52=2288, Resulting Numbers: [2288] 2288,42 unequal: No Solution Exploring Operation: 44+52=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,42 unequal: No Solution No 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: 42:[90, 6], Operations: ['78-34=44', '44-38=6'] Exploring Operation: 90+6=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 90/6=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,42 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
[ 80, 72, 86, 82 ]
94
[ "86-80=6", "72/6=12", "82+12=94" ]
Current State: 94:[80, 72, 86, 82], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [72, 82, 6] Generated Node #2: [72, 82, 6] from Operation: 86-80=6 Current State: 94:[72, 82, 6], Operations: ['86-80=6'] Exploring Operation: 72/6=12, Resulting Numbers: [82, 12] Generated Node #3: [82, 12] from Operation: 72/6=12 Current State: 94:[82, 12], Operations: ['86-80=6', '72/6=12'] Exploring Operation: 82+12=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[80, 72, 86, 82], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [86, 82, 8] Generated Node #0,0: 94:[86, 82, 8] Operation: 80-72=8 Moving to Node #0,0 Current State: 94:[86, 82, 8], Operations: ['80-72=8'] Exploring Operation: 86-82=4, Resulting Numbers: [8, 4] Generated Node #0,0,0: 94:[8, 4] Operation: 86-82=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[8, 4], Operations: ['80-72=8', '86-82=4'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 3, 51, 14, 38 ]
81
[ "51+14=65", "65-38=27", "3*27=81" ]
Current State: 81:[3, 51, 14, 38], Operations: [] Exploring Operation: 51+14=65, Resulting Numbers: [3, 38, 65] Generated Node #2: [3, 38, 65] from Operation: 51+14=65 Current State: 81:[3, 38, 65], Operations: ['51+14=65'] Exploring Operation: 65-38=27, Resulting Numbers: [3, 27] Generated Node #3: [3, 27] from Operation: 65-38=27 Current State: 81:[3, 27], Operations: ['51+14=65', '65-38=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[3, 51, 14, 38], Operations: [] Exploring Operation: 51+38=89, Resulting Numbers: [3, 14, 89] Generated Node #0,0: 81:[3, 14, 89] Operation: 51+38=89 Exploring Operation: 51-14=37, Resulting Numbers: [3, 38, 37] Generated Node #0,1: 81:[3, 38, 37] Operation: 51-14=37 Exploring Operation: 51-38=13, Resulting Numbers: [3, 14, 13] Generated Node #0,2: 81:[3, 14, 13] Operation: 51-38=13 Exploring Operation: 51/3=17, Resulting Numbers: [14, 38, 17] Generated Node #0,3: 81:[14, 38, 17] Operation: 51/3=17 Exploring Operation: 51+14=65, Resulting Numbers: [3, 38, 65] Generated Node #0,4: 81:[3, 38, 65] Operation: 51+14=65 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[3, 14, 13], Operations: ['51-38=13'] Exploring Operation: 14+13=27, Resulting Numbers: [3, 27] Generated Node #0,2,0: 81:[3, 27] Operation: 14+13=27 Exploring Operation: 14-13=1, Resulting Numbers: [3, 1] Generated Node #0,2,1: 81:[3, 1] Operation: 14-13=1 Exploring Operation: 14-3=11, Resulting Numbers: [13, 11] Generated Node #0,2,2: 81:[13, 11] Operation: 14-3=11 Exploring Operation: 13-3=10, Resulting Numbers: [14, 10] Generated Node #0,2,3: 81:[14, 10] Operation: 13-3=10 Exploring Operation: 3+14=17, Resulting Numbers: [13, 17] Generated Node #0,2,4: 81:[13, 17] Operation: 3+14=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[3, 27], Operations: ['51-38=13', '14+13=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[3, 51, 14, 38], Operations: [] Exploring Operation: 51-38=13, Resulting Numbers: [3, 14, 13] Generated Node #0,2: 81:[3, 14, 13] Operation: 51-38=13 Moving to Node #0,2 Current State: 81:[3, 14, 13], Operations: ['51-38=13'] Exploring Operation: 14+13=27, Resulting Numbers: [3, 27] Generated Node #0,2,0: 81:[3, 27] Operation: 14+13=27 Moving to Node #0,2,0 Current State: 81:[3, 27], Operations: ['51-38=13', '14+13=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 17, 86, 87, 65 ]
47
[ "86-17=69", "87-65=22", "69-22=47" ]
Current State: 47:[17, 86, 87, 65], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [87, 65, 69] Generated Node #2: [87, 65, 69] from Operation: 86-17=69 Current State: 47:[87, 65, 69], Operations: ['86-17=69'] Exploring Operation: 87-65=22, Resulting Numbers: [69, 22] Generated Node #3: [69, 22] from Operation: 87-65=22 Current State: 47:[69, 22], Operations: ['86-17=69', '87-65=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[17, 86, 87, 65], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [87, 65, 69] Generated Node #0,0: 47:[87, 65, 69] Operation: 86-17=69 Moving to Node #0,0 Current State: 47:[87, 65, 69], Operations: ['86-17=69'] Exploring Operation: 87-65=22, Resulting Numbers: [69, 22] Generated Node #0,0,0: 47:[69, 22] Operation: 87-65=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[69, 22], Operations: ['86-17=69', '87-65=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[17, 86, 87, 65], Operations: [] Exploring Operation: 86-17=69, Resulting Numbers: [87, 65, 69] Generated Node #0,0: 47:[87, 65, 69] Operation: 86-17=69 Moving to Node #0,0 Current State: 47:[87, 65, 69], Operations: ['86-17=69'] Exploring Operation: 87-65=22, Resulting Numbers: [69, 22] Generated Node #0,0,0: 47:[69, 22] Operation: 87-65=22 Moving to Node #0,0,0 Current State: 47:[69, 22], Operations: ['86-17=69', '87-65=22'] Exploring Operation: 69-22=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 50, 61, 87, 90 ]
53
[ "90-61=29", "87/29=3", "50+3=53" ]
Current State: 53:[50, 61, 87, 90], Operations: [] Exploring Operation: 90-61=29, Resulting Numbers: [50, 87, 29] Generated Node #2: [50, 87, 29] from Operation: 90-61=29 Current State: 53:[50, 87, 29], Operations: ['90-61=29'] Exploring Operation: 87/29=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 87/29=3 Current State: 53:[50, 3], Operations: ['90-61=29', '87/29=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[50, 61, 87, 90], Operations: [] Exploring Operation: 90-50=40, Resulting Numbers: [61, 87, 40] Generated Node #0,0: 53:[61, 87, 40] Operation: 90-50=40 Exploring Operation: 90-61=29, Resulting Numbers: [50, 87, 29] Generated Node #0,1: 53:[50, 87, 29] Operation: 90-61=29 Exploring Operation: 87-50=37, Resulting Numbers: [61, 90, 37] Generated Node #0,2: 53:[61, 90, 37] Operation: 87-50=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[61, 87, 40], Operations: ['90-50=40'] Exploring Operation: 87-40=47, Resulting Numbers: [61, 47] Generated Node #0,0,0: 53:[61, 47] Operation: 87-40=47 Exploring Operation: 61-40=21, Resulting Numbers: [87, 21] Generated Node #0,0,1: 53:[87, 21] Operation: 61-40=21 Exploring Operation: 87-61=26, Resulting Numbers: [40, 26] Generated Node #0,0,2: 53:[40, 26] Operation: 87-61=26 Moving to Node #0,0,0 Current State: 53:[61, 47], Operations: ['90-50=40', '87-40=47'] Exploring Operation: 61*47=2867, Resulting Numbers: [2867] 2867,53 unequal: No Solution Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,53 unequal: No Solution Exploring Operation: 61+47=108, Resulting Numbers: [108] 108,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[40, 26], Operations: ['90-50=40', '87-61=26'] Exploring Operation: 40*26=1040, Resulting Numbers: [1040] 1040,53 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,53 unequal: No Solution Exploring Operation: 40+26=66, Resulting Numbers: [66] 66,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[87, 21], Operations: ['90-50=40', '61-40=21'] Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,53 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,53 unequal: No Solution Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,53 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 #0,1 Current State: 53:[50, 87, 29], Operations: ['90-61=29'] Exploring Operation: 87/29=3, Resulting Numbers: [50, 3] Generated Node #0,1,0: 53:[50, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [50, 58] Generated Node #0,1,1: 53:[50, 58] Operation: 87-29=58 Exploring Operation: 87-50=37, Resulting Numbers: [29, 37] Generated Node #0,1,2: 53:[29, 37] Operation: 87-50=37 Moving to Node #0,1,1 Current State: 53:[50, 58], Operations: ['90-61=29', '87-29=58'] Exploring Operation: 58-50=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 50+58=108, Resulting Numbers: [108] 108,53 unequal: No Solution Exploring Operation: 50*58=2900, Resulting Numbers: [2900] 2900,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[29, 37], Operations: ['90-61=29', '87-50=37'] Exploring Operation: 29+37=66, Resulting Numbers: [66] 66,53 unequal: No Solution Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 29*37=1073, Resulting Numbers: [1073] 1073,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[50, 3], Operations: ['90-61=29', '87/29=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:[50, 61, 87, 90], Operations: [] Exploring Operation: 90-61=29, Resulting Numbers: [50, 87, 29] Generated Node #0,1: 53:[50, 87, 29] Operation: 90-61=29 Moving to Node #0,1 Current State: 53:[50, 87, 29], Operations: ['90-61=29'] Exploring Operation: 87/29=3, Resulting Numbers: [50, 3] Generated Node #0,1,0: 53:[50, 3] Operation: 87/29=3 Moving to Node #0,1,0 Current State: 53:[50, 3], Operations: ['90-61=29', '87/29=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
mult_heuristic
[ 84, 66, 97, 81 ]
93
[ "84-81=3", "97-66=31", "3*31=93" ]
Current State: 93:[84, 66, 97, 81], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [66, 97, 3] Generated Node #2: [66, 97, 3] from Operation: 84-81=3 Current State: 93:[66, 97, 3], Operations: ['84-81=3'] Exploring Operation: 97-66=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 97-66=31 Current State: 93:[3, 31], Operations: ['84-81=3', '97-66=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[84, 66, 97, 81], Operations: [] Exploring Operation: 97-66=31, Resulting Numbers: [84, 81, 31] Generated Node #0,0: 93:[84, 81, 31] Operation: 97-66=31 Exploring Operation: 84-66=18, Resulting Numbers: [97, 81, 18] Generated Node #0,1: 93:[97, 81, 18] Operation: 84-66=18 Exploring Operation: 81-66=15, Resulting Numbers: [84, 97, 15] Generated Node #0,2: 93:[84, 97, 15] Operation: 81-66=15 Exploring Operation: 84-81=3, Resulting Numbers: [66, 97, 3] Generated Node #0,3: 93:[66, 97, 3] Operation: 84-81=3 Moving to Node #0,0 Current State: 93:[84, 81, 31], Operations: ['97-66=31'] Exploring Operation: 84-81=3, Resulting Numbers: [31, 3] Generated Node #0,0,0: 93:[31, 3] Operation: 84-81=3 Exploring Operation: 81+31=112, Resulting Numbers: [84, 112] Generated Node #0,0,1: 93:[84, 112] Operation: 81+31=112 Exploring Operation: 81-31=50, Resulting Numbers: [84, 50] Generated Node #0,0,2: 93:[84, 50] Operation: 81-31=50 Exploring Operation: 84+31=115, Resulting Numbers: [81, 115] Generated Node #0,0,3: 93:[81, 115] Operation: 84+31=115 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[31, 3], Operations: ['97-66=31', '84-81=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,93 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[84, 66, 97, 81], Operations: [] Exploring Operation: 97-66=31, Resulting Numbers: [84, 81, 31] Generated Node #0,0: 93:[84, 81, 31] Operation: 97-66=31 Moving to Node #0,0 Current State: 93:[84, 81, 31], Operations: ['97-66=31'] Exploring Operation: 84-81=3, Resulting Numbers: [31, 3] Generated Node #0,0,0: 93:[31, 3] Operation: 84-81=3 Moving to Node #0,0,0 Current State: 93:[31, 3], Operations: ['97-66=31', '84-81=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 11, 20, 33, 5 ]
48
[ "11+33=44", "20/5=4", "44+4=48" ]
Current State: 48:[11, 20, 33, 5], Operations: [] Exploring Operation: 11+33=44, Resulting Numbers: [20, 5, 44] Generated Node #2: [20, 5, 44] from Operation: 11+33=44 Current State: 48:[20, 5, 44], Operations: ['11+33=44'] Exploring Operation: 20/5=4, Resulting Numbers: [44, 4] Generated Node #3: [44, 4] from Operation: 20/5=4 Current State: 48:[44, 4], Operations: ['11+33=44', '20/5=4'] Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[11, 20, 33, 5], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [20, 5, 3] Generated Node #0,0: 48:[20, 5, 3] Operation: 33/11=3 Exploring Operation: 33-20=13, Resulting Numbers: [11, 5, 13] Generated Node #0,1: 48:[11, 5, 13] Operation: 33-20=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[11, 5, 13], Operations: ['33-20=13'] Exploring Operation: 11+5=16, Resulting Numbers: [13, 16] Generated Node #0,1,0: 48:[13, 16] Operation: 11+5=16 Exploring Operation: 11-5=6, Resulting Numbers: [13, 6] Generated Node #0,1,1: 48:[13, 6] Operation: 11-5=6 Moving to Node #0,1,0 Current State: 48:[13, 16], Operations: ['33-20=13', '11+5=16'] Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,48 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[13, 6], Operations: ['33-20=13', '11-5=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[20, 5, 3], Operations: ['33/11=3'] Exploring Operation: 20+5=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 48:[3, 25] Operation: 20+5=25 Exploring Operation: 20/5=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 48:[3, 4] Operation: 20/5=4 Moving to Node #0,0,1 Current State: 48:[3, 4], Operations: ['33/11=3', '20/5=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[3, 25], Operations: ['33/11=3', '20+5=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 8, 38, 38, 20 ]
27
[ "8+20=28", "38/38=1", "28-1=27" ]
Current State: 27:[8, 38, 38, 20], Operations: [] Exploring Operation: 8+20=28, Resulting Numbers: [38, 38, 28] Generated Node #2: [38, 38, 28] from Operation: 8+20=28 Current State: 27:[38, 38, 28], Operations: ['8+20=28'] Exploring Operation: 38/38=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 38/38=1 Current State: 27:[28, 1], Operations: ['8+20=28', '38/38=1'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[8, 38, 38, 20], Operations: [] Exploring Operation: 38/38=1, Resulting Numbers: [8, 20, 1] Generated Node #0,0: 27:[8, 20, 1] Operation: 38/38=1 Moving to Node #0,0 Current State: 27:[8, 20, 1], Operations: ['38/38=1'] Exploring Operation: 8+20=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 8+20=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['38/38=1', '8+20=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[8, 38, 38, 20], Operations: [] Exploring Operation: 38/38=1, Resulting Numbers: [8, 20, 1] Generated Node #0,0: 27:[8, 20, 1] Operation: 38/38=1 Moving to Node #0,0 Current State: 27:[8, 20, 1], Operations: ['38/38=1'] Exploring Operation: 8+20=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 27:[1, 28] Operation: 8+20=28 Moving to Node #0,0,0 Current State: 27:[1, 28], Operations: ['38/38=1', '8+20=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 51, 2, 4, 85 ]
17
[ "51*4=204", "204/2=102", "102-85=17" ]
Current State: 17:[51, 2, 4, 85], Operations: [] Exploring Operation: 51*4=204, Resulting Numbers: [2, 85, 204] Generated Node #2: [2, 85, 204] from Operation: 51*4=204 Current State: 17:[2, 85, 204], Operations: ['51*4=204'] Exploring Operation: 204/2=102, Resulting Numbers: [85, 102] Generated Node #3: [85, 102] from Operation: 204/2=102 Current State: 17:[85, 102], Operations: ['51*4=204', '204/2=102'] Exploring Operation: 102-85=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[51, 2, 4, 85], Operations: [] Exploring Operation: 85-51=34, Resulting Numbers: [2, 4, 34] Generated Node #0,0: 17:[2, 4, 34] Operation: 85-51=34 Exploring Operation: 2*4=8, Resulting Numbers: [51, 85, 8] Generated Node #0,1: 17:[51, 85, 8] Operation: 2*4=8 Moving to Node #0,0 Current State: 17:[2, 4, 34], Operations: ['85-51=34'] Exploring Operation: 34/2=17, Resulting Numbers: [4, 17] Generated Node #0,0,0: 17:[4, 17] Operation: 34/2=17 Exploring Operation: 2*4=8, Resulting Numbers: [34, 8] Generated Node #0,0,1: 17:[34, 8] Operation: 2*4=8 Moving to Node #0,1 Current State: 17:[51, 85, 8], Operations: ['2*4=8'] Exploring Operation: 51-8=43, Resulting Numbers: [85, 43] Generated Node #0,1,0: 17:[85, 43] Operation: 51-8=43 Exploring Operation: 85-51=34, Resulting Numbers: [8, 34] Generated Node #0,1,1: 17:[8, 34] Operation: 85-51=34 Moving to Node #0,0,0 Current State: 17:[4, 17], Operations: ['85-51=34', '34/2=17'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[8, 34], Operations: ['2*4=8', '85-51=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,17 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[34, 8], Operations: ['85-51=34', '2*4=8'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[85, 43], Operations: ['2*4=8', '51-8=43'] Exploring Operation: 85-43=42, Resulting Numbers: [42] 42,17 unequal: No Solution Exploring Operation: 85+43=128, Resulting Numbers: [128] 128,17 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 94, 71, 5, 64 ]
36
[ "94-71=23", "64-5=59", "59-23=36" ]
Current State: 36:[94, 71, 5, 64], Operations: [] Exploring Operation: 94-71=23, Resulting Numbers: [5, 64, 23] Generated Node #2: [5, 64, 23] from Operation: 94-71=23 Current State: 36:[5, 64, 23], Operations: ['94-71=23'] Exploring Operation: 64-5=59, Resulting Numbers: [23, 59] Generated Node #3: [23, 59] from Operation: 64-5=59 Current State: 36:[23, 59], Operations: ['94-71=23', '64-5=59'] Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[94, 71, 5, 64], Operations: [] Exploring Operation: 94-71=23, Resulting Numbers: [5, 64, 23] Generated Node #0,0: 36:[5, 64, 23] Operation: 94-71=23 Exploring Operation: 94-64=30, Resulting Numbers: [71, 5, 30] Generated Node #0,1: 36:[71, 5, 30] Operation: 94-64=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[5, 64, 23], Operations: ['94-71=23'] Exploring Operation: 64-5=59, Resulting Numbers: [23, 59] Generated Node #0,0,0: 36:[23, 59] Operation: 64-5=59 Exploring Operation: 64-23=41, Resulting Numbers: [5, 41] Generated Node #0,0,1: 36:[5, 41] Operation: 64-23=41 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[5, 41], Operations: ['94-71=23', '64-23=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[94, 71, 5, 64], Operations: [] Exploring Operation: 94-71=23, Resulting Numbers: [5, 64, 23] Generated Node #0,0: 36:[5, 64, 23] Operation: 94-71=23 Moving to Node #0,0 Current State: 36:[5, 64, 23], Operations: ['94-71=23'] Exploring Operation: 64-23=41, Resulting Numbers: [5, 41] Generated Node #0,0,1: 36:[5, 41] Operation: 64-23=41 Moving to Node #0,0,1 Current State: 36:[5, 41], Operations: ['94-71=23', '64-23=41'] Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 3, 3, 75, 5 ]
31
[ "3+75=78", "78/3=26", "5+26=31" ]
Current State: 31:[3, 3, 75, 5], Operations: [] Exploring Operation: 3+75=78, Resulting Numbers: [5, 78] Generated Node #2: [5, 78] from Operation: 3+75=78 Current State: 31:[5, 78], Operations: ['3+75=78'] Exploring Operation: 78/3=26, Resulting Numbers: [5, 26] Generated Node #3: [5, 26] from Operation: 78/3=26 Current State: 31:[5, 26], Operations: ['3+75=78', '78/3=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[3, 3, 75, 5], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [3, 5, 25] Generated Node #0,0: 31:[3, 5, 25] Operation: 75/3=25 Exploring Operation: 75/3=25, Resulting Numbers: [3, 5, 25] Generated Node #0,1: 31:[3, 5, 25] Operation: 75/3=25 Moving to Node #0,0 Current State: 31:[3, 5, 25], Operations: ['75/3=25'] Exploring Operation: 3+5=8, Resulting Numbers: [25, 8] Generated Node #0,0,0: 31:[25, 8] Operation: 3+5=8 Exploring Operation: 3*5=15, Resulting Numbers: [25, 15] Generated Node #0,0,1: 31:[25, 15] Operation: 3*5=15 Moving to Node #0,1 Current State: 31:[3, 5, 25], Operations: ['75/3=25'] Exploring Operation: 3+5=8, Resulting Numbers: [25, 8] Generated Node #0,1,0: 31:[25, 8] Operation: 3+5=8 Exploring Operation: 3*5=15, Resulting Numbers: [25, 15] Generated Node #0,1,1: 31:[25, 15] Operation: 3*5=15 Moving to Node #0,0,1 Current State: 31:[25, 15], Operations: ['75/3=25', '3*5=15'] Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[25, 15], Operations: ['75/3=25', '3*5=15'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[25, 8], Operations: ['75/3=25', '3+5=8'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[25, 8], Operations: ['75/3=25', '3+5=8'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 3, 59, 34 ]
79
[ "11+3=14", "59+34=93", "93-14=79" ]
Current State: 79:[11, 3, 59, 34], Operations: [] Exploring Operation: 11+3=14, Resulting Numbers: [59, 34, 14] Generated Node #2: [59, 34, 14] from Operation: 11+3=14 Current State: 79:[59, 34, 14], Operations: ['11+3=14'] Exploring Operation: 59+34=93, Resulting Numbers: [14, 93] Generated Node #3: [14, 93] from Operation: 59+34=93 Current State: 79:[14, 93], Operations: ['11+3=14', '59+34=93'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[11, 3, 59, 34], Operations: [] Exploring Operation: 3*34=102, Resulting Numbers: [11, 59, 102] Generated Node #0,0: 79:[11, 59, 102] Operation: 3*34=102 Exploring Operation: 11+3=14, Resulting Numbers: [59, 34, 14] Generated Node #0,1: 79:[59, 34, 14] Operation: 11+3=14 Exploring Operation: 11+59=70, Resulting Numbers: [3, 34, 70] Generated Node #0,2: 79:[3, 34, 70] Operation: 11+59=70 Exploring Operation: 11*3=33, Resulting Numbers: [59, 34, 33] Generated Node #0,3: 79:[59, 34, 33] Operation: 11*3=33 Exploring Operation: 11+34=45, Resulting Numbers: [3, 59, 45] Generated Node #0,4: 79:[3, 59, 45] Operation: 11+34=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[11, 59, 102], Operations: ['3*34=102'] Exploring Operation: 11+59=70, Resulting Numbers: [102, 70] Generated Node #0,0,0: 79:[102, 70] Operation: 11+59=70 Exploring Operation: 102-59=43, Resulting Numbers: [11, 43] Generated Node #0,0,1: 79:[11, 43] Operation: 102-59=43 Exploring Operation: 11+102=113, Resulting Numbers: [59, 113] Generated Node #0,0,2: 79:[59, 113] Operation: 11+102=113 Exploring Operation: 102-11=91, Resulting Numbers: [59, 91] Generated Node #0,0,3: 79:[59, 91] Operation: 102-11=91 Exploring Operation: 59-11=48, Resulting Numbers: [102, 48] Generated Node #0,0,4: 79:[102, 48] Operation: 59-11=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[102, 70], Operations: ['3*34=102', '11+59=70'] Exploring Operation: 102+70=172, Resulting Numbers: [172] 172,79 unequal: No Solution Exploring Operation: 102*70=7140, Resulting Numbers: [7140] 7140,79 unequal: No Solution Exploring Operation: 102-70=32, Resulting Numbers: [32] 32,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 79:[59, 91], Operations: ['3*34=102', '102-11=91'] Exploring Operation: 59+91=150, Resulting Numbers: [150] 150,79 unequal: No Solution Exploring Operation: 59*91=5369, Resulting Numbers: [5369] 5369,79 unequal: No Solution Exploring Operation: 91-59=32, Resulting Numbers: [32] 32,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[59, 113], Operations: ['3*34=102', '11+102=113'] Exploring Operation: 59+113=172, Resulting Numbers: [172] 172,79 unequal: No Solution Exploring Operation: 59*113=6667, Resulting Numbers: [6667] 6667,79 unequal: No Solution Exploring Operation: 113-59=54, Resulting Numbers: [54] 54,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 79:[102, 48], Operations: ['3*34=102', '59-11=48'] Exploring Operation: 102-48=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 102*48=4896, Resulting Numbers: [4896] 4896,79 unequal: No Solution Exploring Operation: 102+48=150, Resulting Numbers: [150] 150,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[11, 43], Operations: ['3*34=102', '102-59=43'] Exploring Operation: 11+43=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 11*43=473, Resulting Numbers: [473] 473,79 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[59, 34, 33], Operations: ['11*3=33'] Exploring Operation: 59+33=92, Resulting Numbers: [34, 92] Generated Node #0,3,0: 79:[34, 92] Operation: 59+33=92 Exploring Operation: 59-33=26, Resulting Numbers: [34, 26] Generated Node #0,3,1: 79:[34, 26] Operation: 59-33=26 Exploring Operation: 34+33=67, Resulting Numbers: [59, 67] Generated Node #0,3,2: 79:[59, 67] Operation: 34+33=67 Exploring Operation: 59+34=93, Resulting Numbers: [33, 93] Generated Node #0,3,3: 79:[33, 93] Operation: 59+34=93 Exploring Operation: 34-33=1, Resulting Numbers: [59, 1] Generated Node #0,3,4: 79:[59, 1] Operation: 34-33=1 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 79:[59, 67], Operations: ['11*3=33', '34+33=67'] Exploring Operation: 59*67=3953, Resulting Numbers: [3953] 3953,79 unequal: No Solution Exploring Operation: 59+67=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 79:[34, 92], Operations: ['11*3=33', '59+33=92'] Exploring Operation: 34+92=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 34*92=3128, Resulting Numbers: [3128] 3128,79 unequal: No Solution Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 79:[33, 93], Operations: ['11*3=33', '59+34=93'] Exploring Operation: 33+93=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 33*93=3069, Resulting Numbers: [3069] 3069,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 79:[34, 26], Operations: ['11*3=33', '59-33=26'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 34+26=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 34*26=884, Resulting Numbers: [884] 884,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 79:[59, 1], Operations: ['11*3=33', '34-33=1'] Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,79 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[59, 34, 14], Operations: ['11+3=14'] Exploring Operation: 59+34=93, Resulting Numbers: [14, 93] Generated Node #0,1,0: 79:[14, 93] Operation: 59+34=93 Exploring Operation: 59-14=45, Resulting Numbers: [34, 45] Generated Node #0,1,1: 79:[34, 45] Operation: 59-14=45 Exploring Operation: 59+14=73, Resulting Numbers: [34, 73] Generated Node #0,1,2: 79:[34, 73] Operation: 59+14=73 Exploring Operation: 34-14=20, Resulting Numbers: [59, 20] Generated Node #0,1,3: 79:[59, 20] Operation: 34-14=20 Exploring Operation: 34+14=48, Resulting Numbers: [59, 48] Generated Node #0,1,4: 79:[59, 48] Operation: 34+14=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[34, 73], Operations: ['11+3=14', '59+14=73'] Exploring Operation: 34+73=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 34*73=2482, Resulting Numbers: [2482] 2482,79 unequal: No Solution Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 79:[59, 48], Operations: ['11+3=14', '34+14=48'] Exploring Operation: 59+48=107, Resulting Numbers: [107] 107,79 unequal: No Solution Exploring Operation: 59*48=2832, Resulting Numbers: [2832] 2832,79 unequal: No Solution Exploring Operation: 59-48=11, Resulting Numbers: [11] 11,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[14, 93], Operations: ['11+3=14', '59+34=93'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[11, 3, 59, 34], Operations: [] Exploring Operation: 11+3=14, Resulting Numbers: [59, 34, 14] Generated Node #0,1: 79:[59, 34, 14] Operation: 11+3=14 Moving to Node #0,1 Current State: 79:[59, 34, 14], Operations: ['11+3=14'] Exploring Operation: 59+34=93, Resulting Numbers: [14, 93] Generated Node #0,1,0: 79:[14, 93] Operation: 59+34=93 Moving to Node #0,1,0 Current State: 79:[14, 93], Operations: ['11+3=14', '59+34=93'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.946181
hs_5
mult_heuristic
[ 86, 49, 35, 14 ]
28
[ "86-49=37", "37-35=2", "14*2=28" ]
Current State: 28:[86, 49, 35, 14], Operations: [] Exploring Operation: 86-49=37, Resulting Numbers: [35, 14, 37] Generated Node #2: [35, 14, 37] from Operation: 86-49=37 Current State: 28:[35, 14, 37], Operations: ['86-49=37'] Exploring Operation: 37-35=2, Resulting Numbers: [14, 2] Generated Node #3: [14, 2] from Operation: 37-35=2 Current State: 28:[14, 2], Operations: ['86-49=37', '37-35=2'] Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[86, 49, 35, 14], Operations: [] Exploring Operation: 86-49=37, Resulting Numbers: [35, 14, 37] Generated Node #0,0: 28:[35, 14, 37] Operation: 86-49=37 Exploring Operation: 86-35=51, Resulting Numbers: [49, 14, 51] Generated Node #0,1: 28:[49, 14, 51] Operation: 86-35=51 Exploring Operation: 49-35=14, Resulting Numbers: [86, 14, 14] Generated Node #0,2: 28:[86, 14, 14] Operation: 49-35=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[35, 14, 37], Operations: ['86-49=37'] Exploring Operation: 37-35=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 28:[14, 2] Operation: 37-35=2 Exploring Operation: 35-14=21, Resulting Numbers: [37, 21] Generated Node #0,0,1: 28:[37, 21] Operation: 35-14=21 Exploring Operation: 37-14=23, Resulting Numbers: [35, 23] Generated Node #0,0,2: 28:[35, 23] Operation: 37-14=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[14, 2], Operations: ['86-49=37', '37-35=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[86, 49, 35, 14], Operations: [] Exploring Operation: 86-49=37, Resulting Numbers: [35, 14, 37] Generated Node #0,0: 28:[35, 14, 37] Operation: 86-49=37 Moving to Node #0,0 Current State: 28:[35, 14, 37], Operations: ['86-49=37'] Exploring Operation: 37-35=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 28:[14, 2] Operation: 37-35=2 Moving to Node #0,0,0 Current State: 28:[14, 2], Operations: ['86-49=37', '37-35=2'] Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 65, 38, 89, 53 ]
93
[ "65*53=3445", "89+3445=3534", "3534/38=93" ]
Current State: 93:[65, 38, 89, 53], Operations: [] Exploring Operation: 65*53=3445, Resulting Numbers: [38, 89, 3445] Generated Node #2: [38, 89, 3445] from Operation: 65*53=3445 Current State: 93:[38, 89, 3445], Operations: ['65*53=3445'] Exploring Operation: 89+3445=3534, Resulting Numbers: [38, 3534] Generated Node #3: [38, 3534] from Operation: 89+3445=3534 Current State: 93:[38, 3534], Operations: ['65*53=3445', '89+3445=3534'] Exploring Operation: 3534/38=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[65, 38, 89, 53], Operations: [] Exploring Operation: 65-53=12, Resulting Numbers: [38, 89, 12] Generated Node #0,0: 93:[38, 89, 12] Operation: 65-53=12 Moving to Node #0,0 Current State: 93:[38, 89, 12], Operations: ['65-53=12'] Exploring Operation: 38-12=26, Resulting Numbers: [89, 26] Generated Node #0,0,0: 93:[89, 26] Operation: 38-12=26 Moving to Node #0,0,0 Current State: 93:[89, 26], Operations: ['65-53=12', '38-12=26'] Exploring Operation: 89+26=115, Resulting Numbers: [115] 115,93 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 78, 28, 57, 30 ]
96
[ "30-28=2", "78/2=39", "57+39=96" ]
Current State: 96:[78, 28, 57, 30], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [78, 57, 2] Generated Node #2: [78, 57, 2] from Operation: 30-28=2 Current State: 96:[78, 57, 2], Operations: ['30-28=2'] Exploring Operation: 78/2=39, Resulting Numbers: [57, 39] Generated Node #3: [57, 39] from Operation: 78/2=39 Current State: 96:[57, 39], Operations: ['30-28=2', '78/2=39'] Exploring Operation: 57+39=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[78, 28, 57, 30], Operations: [] Exploring Operation: 78-57=21, Resulting Numbers: [28, 30, 21] Generated Node #0,0: 96:[28, 30, 21] Operation: 78-57=21 Exploring Operation: 78-30=48, Resulting Numbers: [28, 57, 48] Generated Node #0,1: 96:[28, 57, 48] Operation: 78-30=48 Exploring Operation: 78-28=50, Resulting Numbers: [57, 30, 50] Generated Node #0,2: 96:[57, 30, 50] Operation: 78-28=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[28, 30, 21], Operations: ['78-57=21'] Exploring Operation: 28+21=49, Resulting Numbers: [30, 49] Generated Node #0,0,0: 96:[30, 49] Operation: 28+21=49 Exploring Operation: 28-21=7, Resulting Numbers: [30, 7] Generated Node #0,0,1: 96:[30, 7] Operation: 28-21=7 Exploring Operation: 30-28=2, Resulting Numbers: [21, 2] Generated Node #0,0,2: 96:[21, 2] Operation: 30-28=2 Moving to Node #0,0,0 Current State: 96:[30, 49], Operations: ['78-57=21', '28+21=49'] Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,96 unequal: No Solution Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[30, 7], Operations: ['78-57=21', '28-21=7'] Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,96 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,96 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[21, 2], Operations: ['78-57=21', '30-28=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[28, 57, 48], Operations: ['78-30=48'] Exploring Operation: 57-48=9, Resulting Numbers: [28, 9] Generated Node #0,1,0: 96:[28, 9] Operation: 57-48=9 Exploring Operation: 28+57=85, Resulting Numbers: [48, 85] Generated Node #0,1,1: 96:[48, 85] Operation: 28+57=85 Exploring Operation: 57-28=29, Resulting Numbers: [48, 29] Generated Node #0,1,2: 96:[48, 29] Operation: 57-28=29 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[48, 29], Operations: ['78-30=48', '57-28=29'] Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 48*29=1392, Resulting Numbers: [1392] 1392,96 unequal: No Solution Exploring Operation: 48+29=77, Resulting Numbers: [77] 77,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[28, 9], Operations: ['78-30=48', '57-48=9'] Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,96 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,96 unequal: No Solution Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[48, 85], Operations: ['78-30=48', '28+57=85'] Exploring Operation: 85-48=37, Resulting Numbers: [37] 37,96 unequal: No Solution Exploring Operation: 48*85=4080, Resulting Numbers: [4080] 4080,96 unequal: No Solution Exploring Operation: 48+85=133, Resulting Numbers: [133] 133,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[57, 30, 50], Operations: ['78-28=50'] Exploring Operation: 57+30=87, Resulting Numbers: [50, 87] Generated Node #0,2,0: 96:[50, 87] Operation: 57+30=87 Exploring Operation: 57-30=27, Resulting Numbers: [50, 27] Generated Node #0,2,1: 96:[50, 27] Operation: 57-30=27 Exploring Operation: 57-50=7, Resulting Numbers: [30, 7] Generated Node #0,2,2: 96:[30, 7] Operation: 57-50=7 Moving to Node #0,2,2 Current State: 96:[30, 7], Operations: ['78-28=50', '57-50=7'] Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,96 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,96 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[50, 27], Operations: ['78-28=50', '57-30=27'] Exploring Operation: 50+27=77, Resulting Numbers: [77] 77,96 unequal: No Solution Exploring Operation: 50*27=1350, Resulting Numbers: [1350] 1350,96 unequal: No Solution Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[50, 87], Operations: ['78-28=50', '57+30=87'] Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,96 unequal: No Solution Exploring Operation: 50+87=137, Resulting Numbers: [137] 137,96 unequal: No Solution Exploring Operation: 50*87=4350, Resulting Numbers: [4350] 4350,96 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
[ 50, 10, 20, 28 ]
35
[ "50+20=70", "70/10=7", "28+7=35" ]
Current State: 35:[50, 10, 20, 28], Operations: [] Exploring Operation: 50+20=70, Resulting Numbers: [10, 28, 70] Generated Node #2: [10, 28, 70] from Operation: 50+20=70 Current State: 35:[10, 28, 70], Operations: ['50+20=70'] Exploring Operation: 70/10=7, Resulting Numbers: [28, 7] Generated Node #3: [28, 7] from Operation: 70/10=7 Current State: 35:[28, 7], Operations: ['50+20=70', '70/10=7'] Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[50, 10, 20, 28], Operations: [] Exploring Operation: 50-20=30, Resulting Numbers: [10, 28, 30] Generated Node #0,0: 35:[10, 28, 30] Operation: 50-20=30 Exploring Operation: 50/10=5, Resulting Numbers: [20, 28, 5] Generated Node #0,1: 35:[20, 28, 5] Operation: 50/10=5 Exploring Operation: 28-20=8, Resulting Numbers: [50, 10, 8] Generated Node #0,2: 35:[50, 10, 8] Operation: 28-20=8 Moving to Node #0,0 Current State: 35:[10, 28, 30], Operations: ['50-20=30'] Exploring Operation: 30-28=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 35:[10, 2] Operation: 30-28=2 Exploring Operation: 30/10=3, Resulting Numbers: [28, 3] Generated Node #0,0,1: 35:[28, 3] Operation: 30/10=3 Exploring Operation: 10+28=38, Resulting Numbers: [30, 38] Generated Node #0,0,2: 35:[30, 38] Operation: 10+28=38 Moving to Node #0,2 Current State: 35:[50, 10, 8], Operations: ['28-20=8'] Exploring Operation: 50/10=5, Resulting Numbers: [8, 5] Generated Node #0,2,0: 35:[8, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [8, 40] Generated Node #0,2,1: 35:[8, 40] Operation: 50-10=40 Exploring Operation: 50-8=42, Resulting Numbers: [10, 42] Generated Node #0,2,2: 35:[10, 42] Operation: 50-8=42 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 35:[8, 5], Operations: ['28-20=8', '50/10=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[8, 40], Operations: ['28-20=8', '50-10=40'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,35 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 35:[10, 42], Operations: ['28-20=8', '50-8=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,35 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,35 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,35 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: 35:[20, 28, 5], Operations: ['50/10=5'] Exploring Operation: 20/5=4, Resulting Numbers: [28, 4] Generated Node #0,1,0: 35:[28, 4] Operation: 20/5=4 Exploring Operation: 20+28=48, Resulting Numbers: [5, 48] Generated Node #0,1,1: 35:[5, 48] Operation: 20+28=48 Exploring Operation: 28-20=8, Resulting Numbers: [5, 8] Generated Node #0,1,2: 35:[5, 8] Operation: 28-20=8 Moving to Node #0,1,2 Current State: 35:[5, 8], Operations: ['50/10=5', '28-20=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[10, 2], Operations: ['50-20=30', '30-28=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[28, 4], Operations: ['50/10=5', '20/5=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,35 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,35 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[30, 38], Operations: ['50-20=30', '10+28=38'] Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,35 unequal: No Solution Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[28, 3], Operations: ['50-20=30', '30/10=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,35 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,35 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[5, 48], Operations: ['50/10=5', '20+28=48'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,35 unequal: No Solution Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,35 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 58, 24, 3, 11 ]
68
[ "58+24=82", "3+11=14", "82-14=68" ]
Current State: 68:[58, 24, 3, 11], Operations: [] Exploring Operation: 58+24=82, Resulting Numbers: [3, 11, 82] Generated Node #2: [3, 11, 82] from Operation: 58+24=82 Current State: 68:[3, 11, 82], Operations: ['58+24=82'] Exploring Operation: 3+11=14, Resulting Numbers: [82, 14] Generated Node #3: [82, 14] from Operation: 3+11=14 Current State: 68:[82, 14], Operations: ['58+24=82', '3+11=14'] Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[58, 24, 3, 11], Operations: [] Exploring Operation: 58+11=69, Resulting Numbers: [24, 3, 69] Generated Node #0,0: 68:[24, 3, 69] Operation: 58+11=69 Exploring Operation: 24-11=13, Resulting Numbers: [58, 3, 13] Generated Node #0,1: 68:[58, 3, 13] Operation: 24-11=13 Exploring Operation: 24+11=35, Resulting Numbers: [58, 3, 35] Generated Node #0,2: 68:[58, 3, 35] Operation: 24+11=35 Exploring Operation: 58-24=34, Resulting Numbers: [3, 11, 34] Generated Node #0,3: 68:[3, 11, 34] Operation: 58-24=34 Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[3, 11, 34], Operations: ['58-24=34'] Exploring Operation: 11-3=8, Resulting Numbers: [34, 8] Generated Node #0,3,0: 68:[34, 8] Operation: 11-3=8 Exploring Operation: 3*11=33, Resulting Numbers: [34, 33] Generated Node #0,3,1: 68:[34, 33] Operation: 3*11=33 Exploring Operation: 3+11=14, Resulting Numbers: [34, 14] Generated Node #0,3,2: 68:[34, 14] Operation: 3+11=14 Exploring Operation: 34-11=23, Resulting Numbers: [3, 23] Generated Node #0,3,3: 68:[3, 23] Operation: 34-11=23 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 68:[34, 33], Operations: ['58-24=34', '3*11=33'] Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,68 unequal: No Solution No 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: 68:[34, 14], Operations: ['58-24=34', '3+11=14'] Exploring Operation: 34*14=476, Resulting Numbers: [476] 476,68 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 34+14=48, Resulting Numbers: [48] 48,68 unequal: No Solution No 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: 68:[34, 8], Operations: ['58-24=34', '11-3=8'] Exploring Operation: 34*8=272, Resulting Numbers: [272] 272,68 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,68 unequal: No Solution No 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: 68:[3, 23], Operations: ['58-24=34', '34-11=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,68 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: 68:[24, 3, 69], Operations: ['58+11=69'] Exploring Operation: 24+3=27, Resulting Numbers: [69, 27] Generated Node #0,0,0: 68:[69, 27] Operation: 24+3=27 Exploring Operation: 24*3=72, Resulting Numbers: [69, 72] Generated Node #0,0,1: 68:[69, 72] Operation: 24*3=72 Exploring Operation: 24/3=8, Resulting Numbers: [69, 8] Generated Node #0,0,2: 68:[69, 8] Operation: 24/3=8 Exploring Operation: 24-3=21, Resulting Numbers: [69, 21] Generated Node #0,0,3: 68:[69, 21] Operation: 24-3=21 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[69, 72], Operations: ['58+11=69', '24*3=72'] Exploring Operation: 72-69=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 69+72=141, Resulting Numbers: [141] 141,68 unequal: No Solution Exploring Operation: 69*72=4968, Resulting Numbers: [4968] 4968,68 unequal: No Solution No 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: 68:[69, 8], Operations: ['58+11=69', '24/3=8'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,68 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,68 unequal: No Solution No 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: 68:[69, 21], Operations: ['58+11=69', '24-3=21'] Exploring Operation: 69+21=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 69-21=48, Resulting Numbers: [48] 48,68 unequal: No Solution Exploring Operation: 69*21=1449, Resulting Numbers: [1449] 1449,68 unequal: No Solution No 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: 68:[69, 27], Operations: ['58+11=69', '24+3=27'] Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,68 unequal: No Solution Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,68 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: 68:[58, 3, 35], Operations: ['24+11=35'] Exploring Operation: 58+3=61, Resulting Numbers: [35, 61] Generated Node #0,2,0: 68:[35, 61] Operation: 58+3=61 Exploring Operation: 58-35=23, Resulting Numbers: [3, 23] Generated Node #0,2,1: 68:[3, 23] Operation: 58-35=23 Exploring Operation: 35-3=32, Resulting Numbers: [58, 32] Generated Node #0,2,2: 68:[58, 32] Operation: 35-3=32 Exploring Operation: 58-3=55, Resulting Numbers: [35, 55] Generated Node #0,2,3: 68:[35, 55] Operation: 58-3=55 Moving to Node #0,2,1 Current State: 68:[3, 23], Operations: ['24+11=35', '58-35=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[35, 61], Operations: ['24+11=35', '58+3=61'] Exploring Operation: 35*61=2135, Resulting Numbers: [2135] 2135,68 unequal: No Solution Exploring Operation: 35+61=96, Resulting Numbers: [96] 96,68 unequal: No Solution Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[58, 32], Operations: ['24+11=35', '35-3=32'] Exploring Operation: 58*32=1856, Resulting Numbers: [1856] 1856,68 unequal: No Solution Exploring Operation: 58+32=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[35, 55], Operations: ['24+11=35', '58-3=55'] Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,68 unequal: No Solution Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,68 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,68 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 #0,1 Current State: 68:[58, 3, 13], Operations: ['24-11=13'] Exploring Operation: 58-13=45, Resulting Numbers: [3, 45] Generated Node #0,1,0: 68:[3, 45] Operation: 58-13=45 Exploring Operation: 3+13=16, Resulting Numbers: [58, 16] Generated Node #0,1,1: 68:[58, 16] Operation: 3+13=16 Exploring Operation: 58+13=71, Resulting Numbers: [3, 71] Generated Node #0,1,2: 68:[3, 71] Operation: 58+13=71 Exploring Operation: 58+3=61, Resulting Numbers: [13, 61] Generated Node #0,1,3: 68:[13, 61] Operation: 58+3=61 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[3, 71], Operations: ['24-11=13', '58+13=71'] Exploring Operation: 3*71=213, Resulting Numbers: [213] 213,68 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[58, 24, 3, 11], Operations: [] Exploring Operation: 24-11=13, Resulting Numbers: [58, 3, 13] Generated Node #0,1: 68:[58, 3, 13] Operation: 24-11=13 Moving to Node #0,1 Current State: 68:[58, 3, 13], Operations: ['24-11=13'] Exploring Operation: 58+13=71, Resulting Numbers: [3, 71] Generated Node #0,1,2: 68:[3, 71] Operation: 58+13=71 Moving to Node #0,1,2 Current State: 68:[3, 71], Operations: ['24-11=13', '58+13=71'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.946181
hs_4
sum_heuristic
[ 2, 50, 22, 3 ]
86
[ "50-22=28", "3*28=84", "2+84=86" ]
Current State: 86:[2, 50, 22, 3], Operations: [] Exploring Operation: 50-22=28, Resulting Numbers: [2, 3, 28] Generated Node #2: [2, 3, 28] from Operation: 50-22=28 Current State: 86:[2, 3, 28], Operations: ['50-22=28'] Exploring Operation: 3*28=84, Resulting Numbers: [2, 84] Generated Node #3: [2, 84] from Operation: 3*28=84 Current State: 86:[2, 84], Operations: ['50-22=28', '3*28=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[2, 50, 22, 3], Operations: [] Exploring Operation: 50+22=72, Resulting Numbers: [2, 3, 72] Generated Node #0,0: 86:[2, 3, 72] Operation: 50+22=72 Exploring Operation: 50-22=28, Resulting Numbers: [2, 3, 28] Generated Node #0,1: 86:[2, 3, 28] Operation: 50-22=28 Exploring Operation: 2*22=44, Resulting Numbers: [50, 3, 44] Generated Node #0,2: 86:[50, 3, 44] Operation: 2*22=44 Exploring Operation: 22/2=11, Resulting Numbers: [50, 3, 11] Generated Node #0,3: 86:[50, 3, 11] Operation: 22/2=11 Exploring Operation: 50-3=47, Resulting Numbers: [2, 22, 47] Generated Node #0,4: 86:[2, 22, 47] Operation: 50-3=47 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[50, 3, 44], Operations: ['2*22=44'] Exploring Operation: 50+44=94, Resulting Numbers: [3, 94] Generated Node #0,2,0: 86:[3, 94] Operation: 50+44=94 Exploring Operation: 44-3=41, Resulting Numbers: [50, 41] Generated Node #0,2,1: 86:[50, 41] Operation: 44-3=41 Exploring Operation: 50-44=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 86:[3, 6] Operation: 50-44=6 Exploring Operation: 50-3=47, Resulting Numbers: [44, 47] Generated Node #0,2,3: 86:[44, 47] Operation: 50-3=47 Exploring Operation: 50+3=53, Resulting Numbers: [44, 53] Generated Node #0,2,4: 86:[44, 53] Operation: 50+3=53 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[3, 6], Operations: ['2*22=44', '50-44=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 86:[44, 47], Operations: ['2*22=44', '50-3=47'] Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,86 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[3, 94], Operations: ['2*22=44', '50+44=94'] Exploring Operation: 3*94=282, Resulting Numbers: [282] 282,86 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[50, 41], Operations: ['2*22=44', '44-3=41'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,86 unequal: No Solution Exploring Operation: 50*41=2050, Resulting Numbers: [2050] 2050,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 86:[44, 53], Operations: ['2*22=44', '50+3=53'] Exploring Operation: 53-44=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 44+53=97, Resulting Numbers: [97] 97,86 unequal: No Solution Exploring Operation: 44*53=2332, Resulting Numbers: [2332] 2332,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[2, 3, 72], Operations: ['50+22=72'] Exploring Operation: 3-2=1, Resulting Numbers: [72, 1] Generated Node #0,0,0: 86:[72, 1] Operation: 3-2=1 Exploring Operation: 3+72=75, Resulting Numbers: [2, 75] Generated Node #0,0,1: 86:[2, 75] Operation: 3+72=75 Exploring Operation: 2+72=74, Resulting Numbers: [3, 74] Generated Node #0,0,2: 86:[3, 74] Operation: 2+72=74 Exploring Operation: 2+3=5, Resulting Numbers: [72, 5] Generated Node #0,0,3: 86:[72, 5] Operation: 2+3=5 Exploring Operation: 72/2=36, Resulting Numbers: [3, 36] Generated Node #0,0,4: 86:[3, 36] Operation: 72/2=36 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 86:[3, 36], Operations: ['50+22=72', '72/2=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,86 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[2, 75], Operations: ['50+22=72', '3+72=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,86 unequal: No Solution Exploring Operation: 2*75=150, Resulting Numbers: [150] 150,86 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[3, 74], Operations: ['50+22=72', '2+72=74'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,86 unequal: No Solution Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 3*74=222, Resulting Numbers: [222] 222,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[72, 1], Operations: ['50+22=72', '3-2=1'] Exploring Operation: 72+1=73, Resulting Numbers: [73] 73,86 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,86 unequal: No Solution Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[72, 5], Operations: ['50+22=72', '2+3=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,86 unequal: No Solution Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[2, 3, 28], Operations: ['50-22=28'] Exploring Operation: 2*28=56, Resulting Numbers: [3, 56] Generated Node #0,1,0: 86:[3, 56] Operation: 2*28=56 Exploring Operation: 3+28=31, Resulting Numbers: [2, 31] Generated Node #0,1,1: 86:[2, 31] Operation: 3+28=31 Exploring Operation: 3*28=84, Resulting Numbers: [2, 84] Generated Node #0,1,2: 86:[2, 84] Operation: 3*28=84 Exploring Operation: 2+28=30, Resulting Numbers: [3, 30] Generated Node #0,1,3: 86:[3, 30] Operation: 2+28=30 Exploring Operation: 28/2=14, Resulting Numbers: [3, 14] Generated Node #0,1,4: 86:[3, 14] Operation: 28/2=14 Moving to Node #0,1,2 Current State: 86:[2, 84], Operations: ['50-22=28', '3*28=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,86 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[2, 50, 22, 3], Operations: [] Exploring Operation: 50-22=28, Resulting Numbers: [2, 3, 28] Generated Node #0,1: 86:[2, 3, 28] Operation: 50-22=28 Moving to Node #0,1 Current State: 86:[2, 3, 28], Operations: ['50-22=28'] Exploring Operation: 3*28=84, Resulting Numbers: [2, 84] Generated Node #0,1,2: 86:[2, 84] Operation: 3*28=84 Moving to Node #0,1,2 Current State: 86:[2, 84], Operations: ['50-22=28', '3*28=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
sum_heuristic
[ 76, 55, 7, 38 ]
64
[ "76/38=2", "55+7=62", "2+62=64" ]
Current State: 64:[76, 55, 7, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [55, 7, 2] Generated Node #2: [55, 7, 2] from Operation: 76/38=2 Current State: 64:[55, 7, 2], Operations: ['76/38=2'] Exploring Operation: 55+7=62, Resulting Numbers: [2, 62] Generated Node #3: [2, 62] from Operation: 55+7=62 Current State: 64:[2, 62], Operations: ['76/38=2', '55+7=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[76, 55, 7, 38], Operations: [] Exploring Operation: 76-55=21, Resulting Numbers: [7, 38, 21] Generated Node #0,0: 64:[7, 38, 21] Operation: 76-55=21 Exploring Operation: 76-38=38, Resulting Numbers: [55, 7, 38] Generated Node #0,1: 64:[55, 7, 38] Operation: 76-38=38 Exploring Operation: 55-38=17, Resulting Numbers: [76, 7, 17] Generated Node #0,2: 64:[76, 7, 17] Operation: 55-38=17 Exploring Operation: 76/38=2, Resulting Numbers: [55, 7, 2] Generated Node #0,3: 64:[55, 7, 2] Operation: 76/38=2 Moving to Node #0,3 Current State: 64:[55, 7, 2], Operations: ['76/38=2'] Exploring Operation: 55+7=62, Resulting Numbers: [2, 62] Generated Node #0,3,0: 64:[2, 62] Operation: 55+7=62 Exploring Operation: 7-2=5, Resulting Numbers: [55, 5] Generated Node #0,3,1: 64:[55, 5] Operation: 7-2=5 Exploring Operation: 7+2=9, Resulting Numbers: [55, 9] Generated Node #0,3,2: 64:[55, 9] Operation: 7+2=9 Exploring Operation: 55+2=57, Resulting Numbers: [7, 57] Generated Node #0,3,3: 64:[7, 57] Operation: 55+2=57 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 64:[2, 62], Operations: ['76/38=2', '55+7=62'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,64 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[76, 55, 7, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [55, 7, 2] Generated Node #0,3: 64:[55, 7, 2] Operation: 76/38=2 Moving to Node #0,3 Current State: 64:[55, 7, 2], Operations: ['76/38=2'] Exploring Operation: 55+7=62, Resulting Numbers: [2, 62] Generated Node #0,3,0: 64:[2, 62] Operation: 55+7=62 Moving to Node #0,3,0 Current State: 64:[2, 62], Operations: ['76/38=2', '55+7=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 44, 68, 78, 6 ]
48
[ "68-44=24", "78-6=72", "72-24=48" ]
Current State: 48:[44, 68, 78, 6], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [78, 6, 24] Generated Node #2: [78, 6, 24] from Operation: 68-44=24 Current State: 48:[78, 6, 24], Operations: ['68-44=24'] Exploring Operation: 78-6=72, Resulting Numbers: [24, 72] Generated Node #3: [24, 72] from Operation: 78-6=72 Current State: 48:[24, 72], Operations: ['68-44=24', '78-6=72'] Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[44, 68, 78, 6], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [78, 6, 24] Generated Node #0,0: 48:[78, 6, 24] Operation: 68-44=24 Exploring Operation: 78-68=10, Resulting Numbers: [44, 6, 10] Generated Node #0,1: 48:[44, 6, 10] Operation: 78-68=10 Exploring Operation: 78/6=13, Resulting Numbers: [44, 68, 13] Generated Node #0,2: 48:[44, 68, 13] Operation: 78/6=13 Moving to Node #0,1 Current State: 48:[44, 6, 10], Operations: ['78-68=10'] Exploring Operation: 44+6=50, Resulting Numbers: [10, 50] Generated Node #0,1,0: 48:[10, 50] Operation: 44+6=50 Exploring Operation: 6+10=16, Resulting Numbers: [44, 16] Generated Node #0,1,1: 48:[44, 16] Operation: 6+10=16 Exploring Operation: 10-6=4, Resulting Numbers: [44, 4] Generated Node #0,1,2: 48:[44, 4] Operation: 10-6=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[10, 50], Operations: ['78-68=10', '44+6=50'] Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,48 unequal: No Solution Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,48 unequal: No Solution No 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: 48:[44, 16], Operations: ['78-68=10', '6+10=16'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 44+16=60, Resulting Numbers: [60] 60,48 unequal: No Solution Exploring Operation: 44*16=704, Resulting Numbers: [704] 704,48 unequal: No Solution No 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: 48:[44, 4], Operations: ['78-68=10', '10-6=4'] Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[44, 68, 78, 6], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [44, 6, 10] Generated Node #0,1: 48:[44, 6, 10] Operation: 78-68=10 Moving to Node #0,1 Current State: 48:[44, 6, 10], Operations: ['78-68=10'] Exploring Operation: 10-6=4, Resulting Numbers: [44, 4] Generated Node #0,1,2: 48:[44, 4] Operation: 10-6=4 Moving to Node #0,1,2 Current State: 48:[44, 4], Operations: ['78-68=10', '10-6=4'] Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 67, 2, 53, 87 ]
80
[ "67-53=14", "14/2=7", "87-7=80" ]
Current State: 80:[67, 2, 53, 87], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [2, 87, 14] Generated Node #2: [2, 87, 14] from Operation: 67-53=14 Current State: 80:[2, 87, 14], Operations: ['67-53=14'] Exploring Operation: 14/2=7, Resulting Numbers: [87, 7] Generated Node #3: [87, 7] from Operation: 14/2=7 Current State: 80:[87, 7], Operations: ['67-53=14', '14/2=7'] Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[67, 2, 53, 87], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [2, 87, 14] Generated Node #0,0: 80:[2, 87, 14] Operation: 67-53=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[2, 87, 14], Operations: ['67-53=14'] Exploring Operation: 87-2=85, Resulting Numbers: [14, 85] Generated Node #0,0,0: 80:[14, 85] Operation: 87-2=85 Moving to Node #0,0,0 Current State: 80:[14, 85], Operations: ['67-53=14', '87-2=85'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,80 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
[ 27, 61, 88, 86 ]
44
[ "27+61=88", "88-86=2", "88/2=44" ]
Current State: 44:[27, 61, 88, 86], Operations: [] Exploring Operation: 27+61=88, Resulting Numbers: [88, 86, 88] Generated Node #2: [88, 86, 88] from Operation: 27+61=88 Current State: 44:[88, 86, 88], Operations: ['27+61=88'] Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,44 equal: Goal Reached Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[27, 61, 88, 86], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [27, 86, 27] Generated Node #0,0: 44:[27, 86, 27] Operation: 88-61=27 Exploring Operation: 88-27=61, Resulting Numbers: [61, 86, 61] Generated Node #0,1: 44:[61, 86, 61] Operation: 88-27=61 Exploring Operation: 86-61=25, Resulting Numbers: [27, 88, 25] Generated Node #0,2: 44:[27, 88, 25] Operation: 86-61=25 Exploring Operation: 88-86=2, Resulting Numbers: [27, 61, 2] Generated Node #0,3: 44:[27, 61, 2] Operation: 88-86=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[27, 61, 2], Operations: ['88-86=2'] Exploring Operation: 27-2=25, Resulting Numbers: [61, 25] Generated Node #0,3,0: 44:[61, 25] Operation: 27-2=25 Exploring Operation: 61-27=34, Resulting Numbers: [2, 34] Generated Node #0,3,1: 44:[2, 34] Operation: 61-27=34 Exploring Operation: 61-2=59, Resulting Numbers: [27, 59] Generated Node #0,3,2: 44:[27, 59] Operation: 61-2=59 Exploring Operation: 27+2=29, Resulting Numbers: [61, 29] Generated Node #0,3,3: 44:[61, 29] Operation: 27+2=29 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 44:[2, 34], Operations: ['88-86=2', '61-27=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,44 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 44:[61, 25], Operations: ['88-86=2', '27-2=25'] Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 44:[27, 59], Operations: ['88-86=2', '61-2=59'] Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 44:[61, 29], Operations: ['88-86=2', '27+2=29'] Exploring Operation: 61*29=1769, Resulting Numbers: [1769] 1769,44 unequal: No Solution Exploring Operation: 61+29=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[27, 86, 27], Operations: ['88-61=27'] Exploring Operation: 86-27=59, Resulting Numbers: [27, 59] Generated Node #0,0,0: 44:[27, 59] Operation: 86-27=59 Exploring Operation: 27-27=0, Resulting Numbers: [86, 0] Generated Node #0,0,1: 44:[86, 0] Operation: 27-27=0 Exploring Operation: 27/27=1, Resulting Numbers: [86, 1] Generated Node #0,0,2: 44:[86, 1] Operation: 27/27=1 Exploring Operation: 86-27=59, Resulting Numbers: [27, 59] Generated Node #0,0,3: 44:[27, 59] Operation: 86-27=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[27, 59], Operations: ['88-61=27', '86-27=59'] Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 44:[27, 59], Operations: ['88-61=27', '86-27=59'] Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,44 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[86, 1], Operations: ['88-61=27', '27/27=1'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,44 unequal: No Solution Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[86, 0], Operations: ['88-61=27', '27-27=0'] Exploring Operation: 86-0=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 86*0=0, Resulting Numbers: [0] 0,44 unequal: No Solution Exploring Operation: 86+0=86, Resulting Numbers: [86] 86,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[27, 88, 25], Operations: ['86-61=25'] Exploring Operation: 88-27=61, Resulting Numbers: [25, 61] Generated Node #0,2,0: 44:[25, 61] Operation: 88-27=61 Exploring Operation: 27+25=52, Resulting Numbers: [88, 52] Generated Node #0,2,1: 44:[88, 52] Operation: 27+25=52 Exploring Operation: 27-25=2, Resulting Numbers: [88, 2] Generated Node #0,2,2: 44:[88, 2] Operation: 27-25=2 Exploring Operation: 88-25=63, Resulting Numbers: [27, 63] Generated Node #0,2,3: 44:[27, 63] Operation: 88-25=63 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[25, 61], Operations: ['86-61=25', '88-27=61'] Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 25+61=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 25*61=1525, Resulting Numbers: [1525] 1525,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[27, 63], Operations: ['86-61=25', '88-25=63'] Exploring Operation: 27+63=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 27*63=1701, Resulting Numbers: [1701] 1701,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[88, 2], Operations: ['86-61=25', '27-25=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[27, 61, 88, 86], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [27, 88, 25] Generated Node #0,2: 44:[27, 88, 25] Operation: 86-61=25 Moving to Node #0,2 Current State: 44:[27, 88, 25], Operations: ['86-61=25'] Exploring Operation: 27-25=2, Resulting Numbers: [88, 2] Generated Node #0,2,2: 44:[88, 2] Operation: 27-25=2 Moving to Node #0,2,2 Current State: 44:[88, 2], Operations: ['86-61=25', '27-25=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.953125
hs_4
sum_heuristic
[ 32, 5, 47, 88 ]
14
[ "32-5=27", "88-47=41", "41-27=14" ]
Current State: 14:[32, 5, 47, 88], Operations: [] Exploring Operation: 32-5=27, Resulting Numbers: [47, 88, 27] Generated Node #2: [47, 88, 27] from Operation: 32-5=27 Current State: 14:[47, 88, 27], Operations: ['32-5=27'] Exploring Operation: 88-47=41, Resulting Numbers: [27, 41] Generated Node #3: [27, 41] from Operation: 88-47=41 Current State: 14:[27, 41], Operations: ['32-5=27', '88-47=41'] Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[32, 5, 47, 88], Operations: [] Exploring Operation: 32-5=27, Resulting Numbers: [47, 88, 27] Generated Node #0,0: 14:[47, 88, 27] Operation: 32-5=27 Exploring Operation: 88-47=41, Resulting Numbers: [32, 5, 41] Generated Node #0,1: 14:[32, 5, 41] Operation: 88-47=41 Exploring Operation: 47-32=15, Resulting Numbers: [5, 88, 15] Generated Node #0,2: 14:[5, 88, 15] Operation: 47-32=15 Exploring Operation: 88-32=56, Resulting Numbers: [5, 47, 56] Generated Node #0,3: 14:[5, 47, 56] Operation: 88-32=56 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[32, 5, 41], Operations: ['88-47=41'] Exploring Operation: 32-5=27, Resulting Numbers: [41, 27] Generated Node #0,1,0: 14:[41, 27] Operation: 32-5=27 Exploring Operation: 32+5=37, Resulting Numbers: [41, 37] Generated Node #0,1,1: 14:[41, 37] Operation: 32+5=37 Exploring Operation: 41-5=36, Resulting Numbers: [32, 36] Generated Node #0,1,2: 14:[32, 36] Operation: 41-5=36 Exploring Operation: 41-32=9, Resulting Numbers: [5, 9] Generated Node #0,1,3: 14:[5, 9] Operation: 41-32=9 Moving to Node #0,1,3 Current State: 14:[5, 9], Operations: ['88-47=41', '41-32=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[32, 5, 47, 88], Operations: [] Exploring Operation: 88-47=41, Resulting Numbers: [32, 5, 41] Generated Node #0,1: 14:[32, 5, 41] Operation: 88-47=41 Moving to Node #0,1 Current State: 14:[32, 5, 41], Operations: ['88-47=41'] Exploring Operation: 41-32=9, Resulting Numbers: [5, 9] Generated Node #0,1,3: 14:[5, 9] Operation: 41-32=9 Moving to Node #0,1,3 Current State: 14:[5, 9], Operations: ['88-47=41', '41-32=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 8, 18, 87, 24 ]
81
[ "8*18=144", "87-24=63", "144-63=81" ]
Current State: 81:[8, 18, 87, 24], Operations: [] Exploring Operation: 8*18=144, Resulting Numbers: [87, 24, 144] Generated Node #2: [87, 24, 144] from Operation: 8*18=144 Current State: 81:[87, 24, 144], Operations: ['8*18=144'] Exploring Operation: 87-24=63, Resulting Numbers: [144, 63] Generated Node #3: [144, 63] from Operation: 87-24=63 Current State: 81:[144, 63], Operations: ['8*18=144', '87-24=63'] Exploring Operation: 144-63=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[8, 18, 87, 24], Operations: [] Exploring Operation: 87-8=79, Resulting Numbers: [18, 24, 79] Generated Node #0,0: 81:[18, 24, 79] Operation: 87-8=79 Exploring Operation: 24-18=6, Resulting Numbers: [8, 87, 6] Generated Node #0,1: 81:[8, 87, 6] Operation: 24-18=6 Exploring Operation: 18-8=10, Resulting Numbers: [87, 24, 10] Generated Node #0,2: 81:[87, 24, 10] Operation: 18-8=10 Exploring Operation: 8+18=26, Resulting Numbers: [87, 24, 26] Generated Node #0,3: 81:[87, 24, 26] Operation: 8+18=26 Moving to Node #0,1 Current State: 81:[8, 87, 6], Operations: ['24-18=6'] Exploring Operation: 8+6=14, Resulting Numbers: [87, 14] Generated Node #0,1,0: 81:[87, 14] Operation: 8+6=14 Exploring Operation: 8-6=2, Resulting Numbers: [87, 2] Generated Node #0,1,1: 81:[87, 2] Operation: 8-6=2 Exploring Operation: 87-6=81, Resulting Numbers: [8, 81] Generated Node #0,1,2: 81:[8, 81] Operation: 87-6=81 Exploring Operation: 87-8=79, Resulting Numbers: [6, 79] Generated Node #0,1,3: 81:[6, 79] Operation: 87-8=79 Moving to Node #0,3 Current State: 81:[87, 24, 26], Operations: ['8+18=26'] Exploring Operation: 87-24=63, Resulting Numbers: [26, 63] Generated Node #0,3,0: 81:[26, 63] Operation: 87-24=63 Exploring Operation: 24+26=50, Resulting Numbers: [87, 50] Generated Node #0,3,1: 81:[87, 50] Operation: 24+26=50 Exploring Operation: 26-24=2, Resulting Numbers: [87, 2] Generated Node #0,3,2: 81:[87, 2] Operation: 26-24=2 Exploring Operation: 87-26=61, Resulting Numbers: [24, 61] Generated Node #0,3,3: 81:[24, 61] Operation: 87-26=61 Moving to Node #0,2 Current State: 81:[87, 24, 10], Operations: ['18-8=10'] Exploring Operation: 24-10=14, Resulting Numbers: [87, 14] Generated Node #0,2,0: 81:[87, 14] Operation: 24-10=14 Exploring Operation: 87-24=63, Resulting Numbers: [10, 63] Generated Node #0,2,1: 81:[10, 63] Operation: 87-24=63 Exploring Operation: 24+10=34, Resulting Numbers: [87, 34] Generated Node #0,2,2: 81:[87, 34] Operation: 24+10=34 Exploring Operation: 87-10=77, Resulting Numbers: [24, 77] Generated Node #0,2,3: 81:[24, 77] Operation: 87-10=77 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 81:[24, 77], Operations: ['18-8=10', '87-10=77'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,81 unequal: No Solution Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[87, 14], Operations: ['18-8=10', '24-10=14'] Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,81 unequal: No Solution Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,81 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[87, 34], Operations: ['18-8=10', '24+10=34'] Exploring Operation: 87+34=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 87-34=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 87*34=2958, Resulting Numbers: [2958] 2958,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[10, 63], Operations: ['18-8=10', '87-24=63'] Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 10+63=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 10*63=630, Resulting Numbers: [630] 630,81 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: 81:[18, 24, 79], Operations: ['87-8=79'] Exploring Operation: 79-18=61, Resulting Numbers: [24, 61] Generated Node #0,0,0: 81:[24, 61] Operation: 79-18=61 Exploring Operation: 24-18=6, Resulting Numbers: [79, 6] Generated Node #0,0,1: 81:[79, 6] Operation: 24-18=6 Exploring Operation: 18+79=97, Resulting Numbers: [24, 97] Generated Node #0,0,2: 81:[24, 97] Operation: 18+79=97 Exploring Operation: 18+24=42, Resulting Numbers: [79, 42] Generated Node #0,0,3: 81:[79, 42] Operation: 18+24=42 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[79, 6], Operations: ['87-8=79', '24-18=6'] Exploring Operation: 79*6=474, Resulting Numbers: [474] 474,81 unequal: No Solution Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 81:[79, 42], Operations: ['87-8=79', '18+24=42'] Exploring Operation: 79*42=3318, Resulting Numbers: [3318] 3318,81 unequal: No Solution Exploring Operation: 79+42=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 81:[24, 97], Operations: ['87-8=79', '18+79=97'] Exploring Operation: 24*97=2328, Resulting Numbers: [2328] 2328,81 unequal: No Solution Exploring Operation: 24+97=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[24, 61], Operations: ['87-8=79', '79-18=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,81 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,81 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: 81:[8, 81], Operations: ['24-18=6', '87-6=81'] Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,81 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[6, 79], Operations: ['24-18=6', '87-8=79'] Exploring Operation: 6*79=474, Resulting Numbers: [474] 474,81 unequal: No Solution Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[87, 2], Operations: ['24-18=6', '8-6=2'] Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,81 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,81 unequal: No Solution Moving to Node #0,3,2 Current State: 81:[87, 2], Operations: ['8+18=26', '26-24=2'] Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,81 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[87, 14], Operations: ['24-18=6', '8+6=14'] Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,81 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,81 unequal: No Solution Moving to Node #0,3,0 Current State: 81:[26, 63], Operations: ['8+18=26', '87-24=63'] Exploring Operation: 26*63=1638, Resulting Numbers: [1638] 1638,81 unequal: No Solution Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[24, 61], Operations: ['8+18=26', '87-26=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,81 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,81 unequal: No Solution Moving to Node #0,3,1 Current State: 81:[87, 50], Operations: ['8+18=26', '24+26=50'] Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 87+50=137, Resulting Numbers: [137] 137,81 unequal: No Solution Exploring Operation: 87*50=4350, Resulting Numbers: [4350] 4350,81 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 67, 51, 68, 44 ]
96
[ "67-51=16", "68+44=112", "112-16=96" ]
Current State: 96:[67, 51, 68, 44], Operations: [] Exploring Operation: 67-51=16, Resulting Numbers: [68, 44, 16] Generated Node #2: [68, 44, 16] from Operation: 67-51=16 Current State: 96:[68, 44, 16], Operations: ['67-51=16'] Exploring Operation: 68+44=112, Resulting Numbers: [16, 112] Generated Node #3: [16, 112] from Operation: 68+44=112 Current State: 96:[16, 112], Operations: ['67-51=16', '68+44=112'] Exploring Operation: 112-16=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[67, 51, 68, 44], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [51, 44, 1] Generated Node #0,0: 96:[51, 44, 1] Operation: 68-67=1 Exploring Operation: 68-44=24, Resulting Numbers: [67, 51, 24] Generated Node #0,1: 96:[67, 51, 24] Operation: 68-44=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[51, 44, 1], Operations: ['68-67=1'] Exploring Operation: 51-44=7, Resulting Numbers: [1, 7] Generated Node #0,0,0: 96:[1, 7] Operation: 51-44=7 Exploring Operation: 51+44=95, Resulting Numbers: [1, 95] Generated Node #0,0,1: 96:[1, 95] Operation: 51+44=95 Moving to Node #0,0,0 Current State: 96:[1, 7], Operations: ['68-67=1', '51-44=7'] Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,96 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[1, 95], Operations: ['68-67=1', '51+44=95'] Exploring Operation: 1*95=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[67, 51, 68, 44], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [51, 44, 1] Generated Node #0,0: 96:[51, 44, 1] Operation: 68-67=1 Moving to Node #0,0 Current State: 96:[51, 44, 1], Operations: ['68-67=1'] Exploring Operation: 51+44=95, Resulting Numbers: [1, 95] Generated Node #0,0,1: 96:[1, 95] Operation: 51+44=95 Moving to Node #0,0,1 Current State: 96:[1, 95], Operations: ['68-67=1', '51+44=95'] Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 75, 79, 8, 14 ]
48
[ "79-75=4", "14*4=56", "56-8=48" ]
Current State: 48:[75, 79, 8, 14], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [8, 14, 4] Generated Node #2: [8, 14, 4] from Operation: 79-75=4 Current State: 48:[8, 14, 4], Operations: ['79-75=4'] Exploring Operation: 14*4=56, Resulting Numbers: [8, 56] Generated Node #3: [8, 56] from Operation: 14*4=56 Current State: 48:[8, 56], Operations: ['79-75=4', '14*4=56'] Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[75, 79, 8, 14], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [8, 14, 4] Generated Node #0,0: 48:[8, 14, 4] Operation: 79-75=4 Exploring Operation: 79-8=71, Resulting Numbers: [75, 14, 71] Generated Node #0,1: 48:[75, 14, 71] Operation: 79-8=71 Exploring Operation: 79-14=65, Resulting Numbers: [75, 8, 65] Generated Node #0,2: 48:[75, 8, 65] Operation: 79-14=65 Exploring Operation: 75-14=61, Resulting Numbers: [79, 8, 61] Generated Node #0,3: 48:[79, 8, 61] Operation: 75-14=61 Exploring Operation: 75-8=67, Resulting Numbers: [79, 14, 67] Generated Node #0,4: 48:[79, 14, 67] Operation: 75-8=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[8, 14, 4], Operations: ['79-75=4'] Exploring Operation: 8/4=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 48:[14, 2] Operation: 8/4=2 Exploring Operation: 8+14=22, Resulting Numbers: [4, 22] Generated Node #0,0,1: 48:[4, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [4, 6] Generated Node #0,0,2: 48:[4, 6] Operation: 14-8=6 Exploring Operation: 8-4=4, Resulting Numbers: [14, 4] Generated Node #0,0,3: 48:[14, 4] Operation: 8-4=4 Exploring Operation: 8+4=12, Resulting Numbers: [14, 12] Generated Node #0,0,4: 48:[14, 12] Operation: 8+4=12 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 48:[4, 6], Operations: ['79-75=4', '14-8=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[14, 2], Operations: ['79-75=4', '8/4=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,48 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[4, 22], Operations: ['79-75=4', '8+14=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,48 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 48:[14, 4], Operations: ['79-75=4', '8-4=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,48 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 48:[14, 12], Operations: ['79-75=4', '8+4=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,48 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[75, 8, 65], Operations: ['79-14=65'] Exploring Operation: 75-8=67, Resulting Numbers: [65, 67] Generated Node #0,2,0: 48:[65, 67] Operation: 75-8=67 Exploring Operation: 8+65=73, Resulting Numbers: [75, 73] Generated Node #0,2,1: 48:[75, 73] Operation: 8+65=73 Exploring Operation: 65-8=57, Resulting Numbers: [75, 57] Generated Node #0,2,2: 48:[75, 57] Operation: 65-8=57 Exploring Operation: 75-65=10, Resulting Numbers: [8, 10] Generated Node #0,2,3: 48:[8, 10] Operation: 75-65=10 Exploring Operation: 75+8=83, Resulting Numbers: [65, 83] Generated Node #0,2,4: 48:[65, 83] Operation: 75+8=83 Moving to Node #0,2,3 Current State: 48:[8, 10], Operations: ['79-14=65', '75-65=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,48 unequal: No Solution Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[75, 57], Operations: ['79-14=65', '65-8=57'] Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,48 unequal: No Solution Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[65, 67], Operations: ['79-14=65', '75-8=67'] Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 65+67=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 65*67=4355, Resulting Numbers: [4355] 4355,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[75, 73], Operations: ['79-14=65', '8+65=73'] Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,48 unequal: No Solution Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,48 unequal: No Solution Moving to Node #0,2,4 Current State: 48:[65, 83], Operations: ['79-14=65', '75+8=83'] Exploring Operation: 65+83=148, Resulting Numbers: [148] 148,48 unequal: No Solution Exploring Operation: 65*83=5395, Resulting Numbers: [5395] 5395,48 unequal: No Solution Exploring Operation: 83-65=18, Resulting Numbers: [18] 18,48 unequal: No Solution No 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: 48:[79, 8, 61], Operations: ['75-14=61'] Exploring Operation: 79-8=71, Resulting Numbers: [61, 71] Generated Node #0,3,0: 48:[61, 71] Operation: 79-8=71 Exploring Operation: 79+8=87, Resulting Numbers: [61, 87] Generated Node #0,3,1: 48:[61, 87] Operation: 79+8=87 Exploring Operation: 8+61=69, Resulting Numbers: [79, 69] Generated Node #0,3,2: 48:[79, 69] Operation: 8+61=69 Exploring Operation: 79-61=18, Resulting Numbers: [8, 18] Generated Node #0,3,3: 48:[8, 18] Operation: 79-61=18 Exploring Operation: 61-8=53, Resulting Numbers: [79, 53] Generated Node #0,3,4: 48:[79, 53] Operation: 61-8=53 Moving to Node #0,3,3 Current State: 48:[8, 18], Operations: ['75-14=61', '79-61=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,48 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[79, 53], Operations: ['75-14=61', '61-8=53'] Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,48 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[61, 71], Operations: ['75-14=61', '79-8=71'] Exploring Operation: 61*71=4331, Resulting Numbers: [4331] 4331,48 unequal: No Solution Exploring Operation: 61+71=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[61, 87], Operations: ['75-14=61', '79+8=87'] Exploring Operation: 87-61=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 61+87=148, Resulting Numbers: [148] 148,48 unequal: No Solution Exploring Operation: 61*87=5307, Resulting Numbers: [5307] 5307,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[79, 69], Operations: ['75-14=61', '8+61=69'] Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,48 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,48 unequal: No Solution No 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: 48:[75, 14, 71], Operations: ['79-8=71'] Exploring Operation: 75+14=89, Resulting Numbers: [71, 89] Generated Node #0,1,0: 48:[71, 89] Operation: 75+14=89 Exploring Operation: 75-71=4, Resulting Numbers: [14, 4] Generated Node #0,1,1: 48:[14, 4] Operation: 75-71=4 Exploring Operation: 75-14=61, Resulting Numbers: [71, 61] Generated Node #0,1,2: 48:[71, 61] Operation: 75-14=61 Exploring Operation: 71-14=57, Resulting Numbers: [75, 57] Generated Node #0,1,3: 48:[75, 57] Operation: 71-14=57 Exploring Operation: 14+71=85, Resulting Numbers: [75, 85] Generated Node #0,1,4: 48:[75, 85] Operation: 14+71=85 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[14, 4], Operations: ['79-8=71', '75-71=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,48 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[71, 61], Operations: ['79-8=71', '75-14=61'] Exploring Operation: 71*61=4331, Resulting Numbers: [4331] 4331,48 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 71+61=132, Resulting Numbers: [132] 132,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 48:[75, 57], Operations: ['79-8=71', '71-14=57'] Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[71, 89], Operations: ['79-8=71', '75+14=89'] Exploring Operation: 71*89=6319, Resulting Numbers: [6319] 6319,48 unequal: No Solution Exploring Operation: 89-71=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 71+89=160, Resulting Numbers: [160] 160,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 48:[75, 85], Operations: ['79-8=71', '14+71=85'] Exploring Operation: 75*85=6375, Resulting Numbers: [6375] 6375,48 unequal: No Solution Exploring Operation: 75+85=160, Resulting Numbers: [160] 160,48 unequal: No Solution Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 48:[79, 14, 67], Operations: ['75-8=67'] Exploring Operation: 79+14=93, Resulting Numbers: [67, 93] Generated Node #0,4,0: 48:[67, 93] Operation: 79+14=93 Exploring Operation: 79-67=12, Resulting Numbers: [14, 12] Generated Node #0,4,1: 48:[14, 12] Operation: 79-67=12 Exploring Operation: 67-14=53, Resulting Numbers: [79, 53] Generated Node #0,4,2: 48:[79, 53] Operation: 67-14=53 Exploring Operation: 79-14=65, Resulting Numbers: [67, 65] Generated Node #0,4,3: 48:[67, 65] Operation: 79-14=65 Exploring Operation: 14+67=81, Resulting Numbers: [79, 81] Generated Node #0,4,4: 48:[79, 81] Operation: 14+67=81 Moving to Node #0,4,1 Current State: 48:[14, 12], Operations: ['75-8=67', '79-67=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,48 unequal: No Solution Moving to Node #0,4,3 Current State: 48:[67, 65], Operations: ['75-8=67', '79-14=65'] Exploring Operation: 67+65=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 67*65=4355, Resulting Numbers: [4355] 4355,48 unequal: No Solution Moving to Node #0,4,2 Current State: 48:[79, 53], Operations: ['75-8=67', '67-14=53'] Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,48 unequal: No Solution Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,48 unequal: No Solution Moving to Node #0,4,0 Current State: 48:[67, 93], Operations: ['75-8=67', '79+14=93'] Exploring Operation: 93-67=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 67*93=6231, Resulting Numbers: [6231] 6231,48 unequal: No Solution Exploring Operation: 67+93=160, Resulting Numbers: [160] 160,48 unequal: No Solution Moving to Node #0,4,4 Current State: 48:[79, 81], Operations: ['75-8=67', '14+67=81'] Exploring Operation: 79*81=6399, Resulting Numbers: [6399] 6399,48 unequal: No Solution Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 79+81=160, Resulting Numbers: [160] 160,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 37, 10, 7, 6 ]
15
[ "37-10=27", "7*6=42", "42-27=15" ]
Current State: 15:[37, 10, 7, 6], Operations: [] Exploring Operation: 37-10=27, Resulting Numbers: [7, 6, 27] Generated Node #2: [7, 6, 27] from Operation: 37-10=27 Current State: 15:[7, 6, 27], Operations: ['37-10=27'] Exploring Operation: 7*6=42, Resulting Numbers: [27, 42] Generated Node #3: [27, 42] from Operation: 7*6=42 Current State: 15:[27, 42], Operations: ['37-10=27', '7*6=42'] Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[37, 10, 7, 6], Operations: [] Exploring Operation: 37-10=27, Resulting Numbers: [7, 6, 27] Generated Node #0,0: 15:[7, 6, 27] Operation: 37-10=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[7, 6, 27], Operations: ['37-10=27'] Exploring Operation: 27-7=20, Resulting Numbers: [6, 20] Generated Node #0,0,0: 15:[6, 20] Operation: 27-7=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[6, 20], Operations: ['37-10=27', '27-7=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 77, 4, 99, 11 ]
90
[ "77+4=81", "99/11=9", "81+9=90" ]
Current State: 90:[77, 4, 99, 11], Operations: [] Exploring Operation: 77+4=81, Resulting Numbers: [99, 11, 81] Generated Node #2: [99, 11, 81] from Operation: 77+4=81 Current State: 90:[99, 11, 81], Operations: ['77+4=81'] Exploring Operation: 99/11=9, Resulting Numbers: [81, 9] Generated Node #3: [81, 9] from Operation: 99/11=9 Current State: 90:[81, 9], Operations: ['77+4=81', '99/11=9'] Exploring Operation: 81+9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[77, 4, 99, 11], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [4, 99, 7] Generated Node #0,0: 90:[4, 99, 7] Operation: 77/11=7 Exploring Operation: 99/11=9, Resulting Numbers: [77, 4, 9] Generated Node #0,1: 90:[77, 4, 9] Operation: 99/11=9 Exploring Operation: 99-77=22, Resulting Numbers: [4, 11, 22] Generated Node #0,2: 90:[4, 11, 22] Operation: 99-77=22 Exploring Operation: 77+11=88, Resulting Numbers: [4, 99, 88] Generated Node #0,3: 90:[4, 99, 88] Operation: 77+11=88 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[4, 11, 22], Operations: ['99-77=22'] Exploring Operation: 22-4=18, Resulting Numbers: [11, 18] Generated Node #0,2,0: 90:[11, 18] Operation: 22-4=18 Exploring Operation: 22/11=2, Resulting Numbers: [4, 2] Generated Node #0,2,1: 90:[4, 2] Operation: 22/11=2 Exploring Operation: 22-11=11, Resulting Numbers: [4, 11] Generated Node #0,2,2: 90:[4, 11] Operation: 22-11=11 Exploring Operation: 4*22=88, Resulting Numbers: [11, 88] Generated Node #0,2,3: 90:[11, 88] Operation: 4*22=88 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[11, 18], Operations: ['99-77=22', '22-4=18'] Exploring Operation: 11*18=198, Resulting Numbers: [198] 198,90 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 11+18=29, Resulting Numbers: [29] 29,90 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:[4, 2], Operations: ['99-77=22', '22/11=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,90 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:[4, 11], Operations: ['99-77=22', '22-11=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,90 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 #0,2,3 Current State: 90:[11, 88], Operations: ['99-77=22', '4*22=88'] Exploring Operation: 88/11=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 11+88=99, Resulting Numbers: [99] 99,90 unequal: No Solution Exploring Operation: 11*88=968, Resulting Numbers: [968] 968,90 unequal: No Solution Exploring Operation: 88-11=77, Resulting Numbers: [77] 77,90 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:[4, 99, 7], Operations: ['77/11=7'] Exploring Operation: 99-4=95, Resulting Numbers: [7, 95] Generated Node #0,0,0: 90:[7, 95] Operation: 99-4=95 Exploring Operation: 7-4=3, Resulting Numbers: [99, 3] Generated Node #0,0,1: 90:[99, 3] Operation: 7-4=3 Exploring Operation: 4+7=11, Resulting Numbers: [99, 11] Generated Node #0,0,2: 90:[99, 11] Operation: 4+7=11 Exploring Operation: 99-7=92, Resulting Numbers: [4, 92] Generated Node #0,0,3: 90:[4, 92] Operation: 99-7=92 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 90:[4, 92], Operations: ['77/11=7', '99-7=92'] Exploring Operation: 4*92=368, Resulting Numbers: [368] 368,90 unequal: No Solution Exploring Operation: 4+92=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,90 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[7, 95], Operations: ['77/11=7', '99-4=95'] Exploring Operation: 7+95=102, Resulting Numbers: [102] 102,90 unequal: No Solution Exploring Operation: 7*95=665, Resulting Numbers: [665] 665,90 unequal: No Solution Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,90 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:[99, 3], Operations: ['77/11=7', '7-4=3'] Exploring Operation: 99+3=102, Resulting Numbers: [102] 102,90 unequal: No Solution Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 99*3=297, Resulting Numbers: [297] 297,90 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:[99, 11], Operations: ['77/11=7', '4+7=11'] Exploring Operation: 99*11=1089, Resulting Numbers: [1089] 1089,90 unequal: No Solution Exploring Operation: 99+11=110, Resulting Numbers: [110] 110,90 unequal: No Solution Exploring Operation: 99/11=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 99-11=88, Resulting Numbers: [88] 88,90 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 #0,3 Current State: 90:[4, 99, 88], Operations: ['77+11=88'] Exploring Operation: 99-88=11, Resulting Numbers: [4, 11] Generated Node #0,3,0: 90:[4, 11] Operation: 99-88=11 Exploring Operation: 99-4=95, Resulting Numbers: [88, 95] Generated Node #0,3,1: 90:[88, 95] Operation: 99-4=95 Exploring Operation: 4+88=92, Resulting Numbers: [99, 92] Generated Node #0,3,2: 90:[99, 92] Operation: 4+88=92 Exploring Operation: 88/4=22, Resulting Numbers: [99, 22] Generated Node #0,3,3: 90:[99, 22] Operation: 88/4=22 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[4, 11], Operations: ['77+11=88', '99-88=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,90 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[88, 95], Operations: ['77+11=88', '99-4=95'] Exploring Operation: 88*95=8360, Resulting Numbers: [8360] 8360,90 unequal: No Solution Exploring Operation: 95-88=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 88+95=183, Resulting Numbers: [183] 183,90 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 #0,3,2 Current State: 90:[99, 92], Operations: ['77+11=88', '4+88=92'] Exploring Operation: 99+92=191, Resulting Numbers: [191] 191,90 unequal: No Solution Exploring Operation: 99*92=9108, Resulting Numbers: [9108] 9108,90 unequal: No Solution Exploring Operation: 99-92=7, Resulting Numbers: [7] 7,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[99, 22], Operations: ['77+11=88', '88/4=22'] Exploring Operation: 99*22=2178, Resulting Numbers: [2178] 2178,90 unequal: No Solution Exploring Operation: 99+22=121, Resulting Numbers: [121] 121,90 unequal: No Solution Exploring Operation: 99-22=77, Resulting Numbers: [77] 77,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[77, 4, 9], Operations: ['99/11=9'] Exploring Operation: 9-4=5, Resulting Numbers: [77, 5] Generated Node #0,1,0: 90:[77, 5] Operation: 9-4=5 Exploring Operation: 4+9=13, Resulting Numbers: [77, 13] Generated Node #0,1,1: 90:[77, 13] Operation: 4+9=13 Exploring Operation: 77+9=86, Resulting Numbers: [4, 86] Generated Node #0,1,2: 90:[4, 86] Operation: 77+9=86 Exploring Operation: 77+4=81, Resulting Numbers: [9, 81] Generated Node #0,1,3: 90:[9, 81] Operation: 77+4=81 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[4, 86], Operations: ['99/11=9', '77+9=86'] Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,90 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[77, 4, 99, 11], Operations: [] Exploring Operation: 99/11=9, Resulting Numbers: [77, 4, 9] Generated Node #0,1: 90:[77, 4, 9] Operation: 99/11=9 Moving to Node #0,1 Current State: 90:[77, 4, 9], Operations: ['99/11=9'] Exploring Operation: 77+9=86, Resulting Numbers: [4, 86] Generated Node #0,1,2: 90:[4, 86] Operation: 77+9=86 Moving to Node #0,1,2 Current State: 90:[4, 86], Operations: ['99/11=9', '77+9=86'] Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.94184
hs_4
sum_heuristic
[ 13, 26, 2, 50 ]
49
[ "26/13=2", "2/2=1", "50-1=49" ]
Current State: 49:[13, 26, 2, 50], Operations: [] Exploring Operation: 26/13=2, Resulting Numbers: [2, 50, 2] Generated Node #2: [2, 50, 2] from Operation: 26/13=2 Current State: 49:[2, 50, 2], Operations: ['26/13=2'] Exploring Operation: 2/2=1, Resulting Numbers: [50, 1] Generated Node #3: [50, 1] from Operation: 2/2=1 Current State: 49:[50, 1], Operations: ['26/13=2', '2/2=1'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[13, 26, 2, 50], Operations: [] Exploring Operation: 26-13=13, Resulting Numbers: [2, 50, 13] Generated Node #0,0: 49:[2, 50, 13] Operation: 26-13=13 Exploring Operation: 26*2=52, Resulting Numbers: [13, 50, 52] Generated Node #0,1: 49:[13, 50, 52] Operation: 26*2=52 Exploring Operation: 26/13=2, Resulting Numbers: [2, 50, 2] Generated Node #0,2: 49:[2, 50, 2] Operation: 26/13=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[13, 50, 52], Operations: ['26*2=52'] Exploring Operation: 52-50=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 49:[13, 2] Operation: 52-50=2 Exploring Operation: 52/13=4, Resulting Numbers: [50, 4] Generated Node #0,1,1: 49:[50, 4] Operation: 52/13=4 Exploring Operation: 52-13=39, Resulting Numbers: [50, 39] Generated Node #0,1,2: 49:[50, 39] Operation: 52-13=39 Moving to Node #0,1,1 Current State: 49:[50, 4], Operations: ['26*2=52', '52/13=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,49 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,49 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[13, 2], Operations: ['26*2=52', '52-50=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,49 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[50, 39], Operations: ['26*2=52', '52-13=39'] Exploring Operation: 50*39=1950, Resulting Numbers: [1950] 1950,49 unequal: No Solution Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 50+39=89, Resulting Numbers: [89] 89,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[2, 50, 2], Operations: ['26/13=2'] Exploring Operation: 2+2=4, Resulting Numbers: [50, 4] Generated Node #0,2,0: 49:[50, 4] Operation: 2+2=4 Exploring Operation: 2*2=4, Resulting Numbers: [50, 4] Generated Node #0,2,1: 49:[50, 4] Operation: 2*2=4 Exploring Operation: 50-2=48, Resulting Numbers: [2, 48] Generated Node #0,2,2: 49:[2, 48] Operation: 50-2=48 Moving to Node #0,2,0 Current State: 49:[50, 4], Operations: ['26/13=2', '2+2=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,49 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[50, 4], Operations: ['26/13=2', '2*2=4'] Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,49 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[2, 48], Operations: ['26/13=2', '50-2=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[2, 50, 13], Operations: ['26-13=13'] Exploring Operation: 13-2=11, Resulting Numbers: [50, 11] Generated Node #0,0,0: 49:[50, 11] Operation: 13-2=11 Exploring Operation: 50-2=48, Resulting Numbers: [13, 48] Generated Node #0,0,1: 49:[13, 48] Operation: 50-2=48 Exploring Operation: 2+50=52, Resulting Numbers: [13, 52] Generated Node #0,0,2: 49:[13, 52] Operation: 2+50=52 Moving to Node #0,0,0 Current State: 49:[50, 11], Operations: ['26-13=13', '13-2=11'] Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,49 unequal: No Solution Exploring Operation: 50*11=550, Resulting Numbers: [550] 550,49 unequal: No Solution Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[13, 48], Operations: ['26-13=13', '50-2=48'] Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,49 unequal: No Solution Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,49 unequal: No Solution Exploring Operation: 13*48=624, Resulting Numbers: [624] 624,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[13, 52], Operations: ['26-13=13', '2+50=52'] Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,49 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,49 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 13, 21, 17, 23 ]
21
[ "13+21=34", "34/17=2", "23-2=21" ]
Current State: 21:[13, 21, 17, 23], Operations: [] Exploring Operation: 13+21=34, Resulting Numbers: [17, 23, 34] Generated Node #2: [17, 23, 34] from Operation: 13+21=34 Current State: 21:[17, 23, 34], Operations: ['13+21=34'] Exploring Operation: 34/17=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 34/17=2 Current State: 21:[23, 2], Operations: ['13+21=34', '34/17=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[13, 21, 17, 23], Operations: [] Exploring Operation: 23-13=10, Resulting Numbers: [21, 17, 10] Generated Node #0,0: 21:[21, 17, 10] Operation: 23-13=10 Exploring Operation: 21-13=8, Resulting Numbers: [17, 23, 8] Generated Node #0,1: 21:[17, 23, 8] Operation: 21-13=8 Exploring Operation: 17-13=4, Resulting Numbers: [21, 23, 4] Generated Node #0,2: 21:[21, 23, 4] Operation: 17-13=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[21, 23, 4], Operations: ['17-13=4'] Exploring Operation: 23-4=19, Resulting Numbers: [21, 19] Generated Node #0,2,0: 21:[21, 19] Operation: 23-4=19 Exploring Operation: 23-21=2, Resulting Numbers: [4, 2] Generated Node #0,2,1: 21:[4, 2] Operation: 23-21=2 Exploring Operation: 21+4=25, Resulting Numbers: [23, 25] Generated Node #0,2,2: 21:[23, 25] Operation: 21+4=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[21, 19], Operations: ['17-13=4', '23-4=19'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 21+19=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 21*19=399, Resulting Numbers: [399] 399,21 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:[4, 2], Operations: ['17-13=4', '23-21=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 4*2=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:[23, 25], Operations: ['17-13=4', '21+4=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,21 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 #0,0 Current State: 21:[21, 17, 10], Operations: ['23-13=10'] Exploring Operation: 21-17=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 21:[10, 4] Operation: 21-17=4 Exploring Operation: 17+10=27, Resulting Numbers: [21, 27] Generated Node #0,0,1: 21:[21, 27] Operation: 17+10=27 Exploring Operation: 17-10=7, Resulting Numbers: [21, 7] Generated Node #0,0,2: 21:[21, 7] Operation: 17-10=7 Moving to Node #0,0,2 Current State: 21:[21, 7], Operations: ['23-13=10', '17-10=7'] Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[10, 4], Operations: ['23-13=10', '21-17=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[21, 27], Operations: ['23-13=10', '17+10=27'] Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,21 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 Current State: 21:[17, 23, 8], Operations: ['21-13=8'] Exploring Operation: 17-8=9, Resulting Numbers: [23, 9] Generated Node #0,1,0: 21:[23, 9] Operation: 17-8=9 Exploring Operation: 23-17=6, Resulting Numbers: [8, 6] Generated Node #0,1,1: 21:[8, 6] Operation: 23-17=6 Exploring Operation: 17+8=25, Resulting Numbers: [23, 25] Generated Node #0,1,2: 21:[23, 25] Operation: 17+8=25 Moving to Node #0,1,1 Current State: 21:[8, 6], Operations: ['21-13=8', '23-17=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[23, 9], Operations: ['21-13=8', '17-8=9'] Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,21 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[23, 25], Operations: ['21-13=8', '17+8=25'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 80, 78, 26, 9 ]
15
[ "80-78=2", "26-9=17", "17-2=15" ]
Current State: 15:[80, 78, 26, 9], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [26, 9, 2] Generated Node #2: [26, 9, 2] from Operation: 80-78=2 Current State: 15:[26, 9, 2], Operations: ['80-78=2'] Exploring Operation: 26-9=17, Resulting Numbers: [2, 17] Generated Node #3: [2, 17] from Operation: 26-9=17 Current State: 15:[2, 17], Operations: ['80-78=2', '26-9=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[80, 78, 26, 9], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [26, 9, 2] Generated Node #0,0: 15:[26, 9, 2] Operation: 80-78=2 Exploring Operation: 78-26=52, Resulting Numbers: [80, 9, 52] Generated Node #0,1: 15:[80, 9, 52] Operation: 78-26=52 Exploring Operation: 80-9=71, Resulting Numbers: [78, 26, 71] Generated Node #0,2: 15:[78, 26, 71] Operation: 80-9=71 Exploring Operation: 80-26=54, Resulting Numbers: [78, 9, 54] Generated Node #0,3: 15:[78, 9, 54] Operation: 80-26=54 Exploring Operation: 78/26=3, Resulting Numbers: [80, 9, 3] Generated Node #0,4: 15:[80, 9, 3] Operation: 78/26=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[26, 9, 2], Operations: ['80-78=2'] Exploring Operation: 9-2=7, Resulting Numbers: [26, 7] Generated Node #0,0,0: 15:[26, 7] Operation: 9-2=7 Exploring Operation: 26-9=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 15:[2, 17] Operation: 26-9=17 Exploring Operation: 26/2=13, Resulting Numbers: [9, 13] Generated Node #0,0,2: 15:[9, 13] Operation: 26/2=13 Exploring Operation: 26-2=24, Resulting Numbers: [9, 24] Generated Node #0,0,3: 15:[9, 24] Operation: 26-2=24 Exploring Operation: 9*2=18, Resulting Numbers: [26, 18] Generated Node #0,0,4: 15:[26, 18] Operation: 9*2=18 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[2, 17], Operations: ['80-78=2', '26-9=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[80, 78, 26, 9], Operations: [] Exploring Operation: 80-78=2, Resulting Numbers: [26, 9, 2] Generated Node #0,0: 15:[26, 9, 2] Operation: 80-78=2 Moving to Node #0,0 Current State: 15:[26, 9, 2], Operations: ['80-78=2'] Exploring Operation: 26-9=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 15:[2, 17] Operation: 26-9=17 Moving to Node #0,0,1 Current State: 15:[2, 17], Operations: ['80-78=2', '26-9=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 36, 76, 88, 87 ]
39
[ "76-36=40", "88-87=1", "40-1=39" ]
Current State: 39:[36, 76, 88, 87], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [88, 87, 40] Generated Node #2: [88, 87, 40] from Operation: 76-36=40 Current State: 39:[88, 87, 40], Operations: ['76-36=40'] Exploring Operation: 88-87=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 88-87=1 Current State: 39:[40, 1], Operations: ['76-36=40', '88-87=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[36, 76, 88, 87], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [36, 87, 12] Generated Node #0,0: 39:[36, 87, 12] Operation: 88-76=12 Exploring Operation: 88-87=1, Resulting Numbers: [36, 76, 1] Generated Node #0,1: 39:[36, 76, 1] Operation: 88-87=1 Exploring Operation: 76-36=40, Resulting Numbers: [88, 87, 40] Generated Node #0,2: 39:[88, 87, 40] Operation: 76-36=40 Exploring Operation: 88-36=52, Resulting Numbers: [76, 87, 52] Generated Node #0,3: 39:[76, 87, 52] Operation: 88-36=52 Exploring Operation: 87-76=11, Resulting Numbers: [36, 88, 11] Generated Node #0,4: 39:[36, 88, 11] Operation: 87-76=11 Moving to Node #0,1 Current State: 39:[36, 76, 1], Operations: ['88-87=1'] Exploring Operation: 36+1=37, Resulting Numbers: [76, 37] Generated Node #0,1,0: 39:[76, 37] Operation: 36+1=37 Exploring Operation: 36*1=36, Resulting Numbers: [76, 36] Generated Node #0,1,1: 39:[76, 36] Operation: 36*1=36 Exploring Operation: 36/1=36, Resulting Numbers: [76, 36] Generated Node #0,1,2: 39:[76, 36] Operation: 36/1=36 Exploring Operation: 76-36=40, Resulting Numbers: [1, 40] Generated Node #0,1,3: 39:[1, 40] Operation: 76-36=40 Exploring Operation: 76-1=75, Resulting Numbers: [36, 75] Generated Node #0,1,4: 39:[36, 75] Operation: 76-1=75 Moving to Node #0,0 Current State: 39:[36, 87, 12], Operations: ['88-76=12'] Exploring Operation: 36-12=24, Resulting Numbers: [87, 24] Generated Node #0,0,0: 39:[87, 24] Operation: 36-12=24 Exploring Operation: 87-12=75, Resulting Numbers: [36, 75] Generated Node #0,0,1: 39:[36, 75] Operation: 87-12=75 Exploring Operation: 36/12=3, Resulting Numbers: [87, 3] Generated Node #0,0,2: 39:[87, 3] Operation: 36/12=3 Exploring Operation: 36+12=48, Resulting Numbers: [87, 48] Generated Node #0,0,3: 39:[87, 48] Operation: 36+12=48 Exploring Operation: 87-36=51, Resulting Numbers: [12, 51] Generated Node #0,0,4: 39:[12, 51] Operation: 87-36=51 Moving to Node #0,4 Current State: 39:[36, 88, 11], Operations: ['87-76=11'] Exploring Operation: 88/11=8, Resulting Numbers: [36, 8] Generated Node #0,4,0: 39:[36, 8] Operation: 88/11=8 Exploring Operation: 88-11=77, Resulting Numbers: [36, 77] Generated Node #0,4,1: 39:[36, 77] Operation: 88-11=77 Exploring Operation: 88-36=52, Resulting Numbers: [11, 52] Generated Node #0,4,2: 39:[11, 52] Operation: 88-36=52 Exploring Operation: 36+11=47, Resulting Numbers: [88, 47] Generated Node #0,4,3: 39:[88, 47] Operation: 36+11=47 Exploring Operation: 36-11=25, Resulting Numbers: [88, 25] Generated Node #0,4,4: 39:[88, 25] Operation: 36-11=25 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 39:[36, 8], Operations: ['87-76=11', '88/11=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,39 unequal: No Solution Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,39 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 39:[11, 52], Operations: ['87-76=11', '88-36=52'] Exploring Operation: 11+52=63, Resulting Numbers: [63] 63,39 unequal: No Solution Exploring Operation: 11*52=572, Resulting Numbers: [572] 572,39 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 39:[36, 77], Operations: ['87-76=11', '88-11=77'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 36+77=113, Resulting Numbers: [113] 113,39 unequal: No Solution Exploring Operation: 36*77=2772, Resulting Numbers: [2772] 2772,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 39:[88, 47], Operations: ['87-76=11', '36+11=47'] Exploring Operation: 88+47=135, Resulting Numbers: [135] 135,39 unequal: No Solution Exploring Operation: 88-47=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 88*47=4136, Resulting Numbers: [4136] 4136,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 39:[88, 25], Operations: ['87-76=11', '36-11=25'] Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,39 unequal: No Solution Exploring Operation: 88*25=2200, Resulting Numbers: [2200] 2200,39 unequal: No Solution Exploring Operation: 88+25=113, Resulting Numbers: [113] 113,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 39:[88, 87, 40], Operations: ['76-36=40'] Exploring Operation: 87-40=47, Resulting Numbers: [88, 47] Generated Node #0,2,0: 39:[88, 47] Operation: 87-40=47 Exploring Operation: 88+40=128, Resulting Numbers: [87, 128] Generated Node #0,2,1: 39:[87, 128] Operation: 88+40=128 Exploring Operation: 88-40=48, Resulting Numbers: [87, 48] Generated Node #0,2,2: 39:[87, 48] Operation: 88-40=48 Exploring Operation: 88-87=1, Resulting Numbers: [40, 1] Generated Node #0,2,3: 39:[40, 1] Operation: 88-87=1 Exploring Operation: 88+87=175, Resulting Numbers: [40, 175] Generated Node #0,2,4: 39:[40, 175] Operation: 88+87=175 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 39:[40, 1], Operations: ['76-36=40', '88-87=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[36, 76, 88, 87], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [88, 87, 40] Generated Node #0,2: 39:[88, 87, 40] Operation: 76-36=40 Moving to Node #0,2 Current State: 39:[88, 87, 40], Operations: ['76-36=40'] Exploring Operation: 88-87=1, Resulting Numbers: [40, 1] Generated Node #0,2,3: 39:[40, 1] Operation: 88-87=1 Moving to Node #0,2,3 Current State: 39:[40, 1], Operations: ['76-36=40', '88-87=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_5
mult_heuristic
[ 76, 72, 3, 64 ]
28
[ "76+72=148", "148-64=84", "84/3=28" ]
Current State: 28:[76, 72, 3, 64], Operations: [] Exploring Operation: 76+72=148, Resulting Numbers: [3, 64, 148] Generated Node #2: [3, 64, 148] from Operation: 76+72=148 Current State: 28:[3, 64, 148], Operations: ['76+72=148'] Exploring Operation: 148-64=84, Resulting Numbers: [3, 84] Generated Node #3: [3, 84] from Operation: 148-64=84 Current State: 28:[3, 84], Operations: ['76+72=148', '148-64=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[76, 72, 3, 64], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [3, 64, 4] Generated Node #0,0: 28:[3, 64, 4] Operation: 76-72=4 Exploring Operation: 76-64=12, Resulting Numbers: [72, 3, 12] Generated Node #0,1: 28:[72, 3, 12] Operation: 76-64=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[3, 64, 4], Operations: ['76-72=4'] Exploring Operation: 64-3=61, Resulting Numbers: [4, 61] Generated Node #0,0,0: 28:[4, 61] Operation: 64-3=61 Exploring Operation: 64/4=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 28:[3, 16] Operation: 64/4=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[3, 16], Operations: ['76-72=4', '64/4=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[4, 61], Operations: ['76-72=4', '64-3=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,28 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[72, 3, 12], Operations: ['76-64=12'] Exploring Operation: 72/3=24, Resulting Numbers: [12, 24] Generated Node #0,1,0: 28:[12, 24] Operation: 72/3=24 Exploring Operation: 72/12=6, Resulting Numbers: [3, 6] Generated Node #0,1,1: 28:[3, 6] Operation: 72/12=6 Moving to Node #0,1,1 Current State: 28:[3, 6], Operations: ['76-64=12', '72/12=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,28 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[12, 24], Operations: ['76-64=12', '72/3=24'] Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,28 unequal: No Solution Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 42, 45, 58, 67 ]
96
[ "42+45=87", "67-58=9", "87+9=96" ]
Current State: 96:[42, 45, 58, 67], Operations: [] Exploring Operation: 42+45=87, Resulting Numbers: [58, 67, 87] Generated Node #2: [58, 67, 87] from Operation: 42+45=87 Current State: 96:[58, 67, 87], Operations: ['42+45=87'] Exploring Operation: 67-58=9, Resulting Numbers: [87, 9] Generated Node #3: [87, 9] from Operation: 67-58=9 Current State: 96:[87, 9], Operations: ['42+45=87', '67-58=9'] Exploring Operation: 87+9=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[42, 45, 58, 67], Operations: [] Exploring Operation: 67-42=25, Resulting Numbers: [45, 58, 25] Generated Node #0,0: 96:[45, 58, 25] Operation: 67-42=25 Exploring Operation: 67-45=22, Resulting Numbers: [42, 58, 22] Generated Node #0,1: 96:[42, 58, 22] Operation: 67-45=22 Exploring Operation: 67-58=9, Resulting Numbers: [42, 45, 9] Generated Node #0,2: 96:[42, 45, 9] Operation: 67-58=9 Exploring Operation: 58-42=16, Resulting Numbers: [45, 67, 16] Generated Node #0,3: 96:[45, 67, 16] Operation: 58-42=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[42, 45, 9], Operations: ['67-58=9'] Exploring Operation: 45/9=5, Resulting Numbers: [42, 5] Generated Node #0,2,0: 96:[42, 5] Operation: 45/9=5 Exploring Operation: 42+9=51, Resulting Numbers: [45, 51] Generated Node #0,2,1: 96:[45, 51] Operation: 42+9=51 Exploring Operation: 42-9=33, Resulting Numbers: [45, 33] Generated Node #0,2,2: 96:[45, 33] Operation: 42-9=33 Exploring Operation: 45-42=3, Resulting Numbers: [9, 3] Generated Node #0,2,3: 96:[9, 3] Operation: 45-42=3 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 96:[9, 3], Operations: ['67-58=9', '45-42=3'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 96:[45, 33], Operations: ['67-58=9', '42-9=33'] Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 45*33=1485, Resulting Numbers: [1485] 1485,96 unequal: No Solution Exploring Operation: 45+33=78, Resulting Numbers: [78] 78,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[45, 51], Operations: ['67-58=9', '42+9=51'] Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[42, 45, 58, 67], Operations: [] Exploring Operation: 67-58=9, Resulting Numbers: [42, 45, 9] Generated Node #0,2: 96:[42, 45, 9] Operation: 67-58=9 Moving to Node #0,2 Current State: 96:[42, 45, 9], Operations: ['67-58=9'] Exploring Operation: 42+9=51, Resulting Numbers: [45, 51] Generated Node #0,2,1: 96:[45, 51] Operation: 42+9=51 Moving to Node #0,2,1 Current State: 96:[45, 51], Operations: ['67-58=9', '42+9=51'] Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 11, 46, 7, 72 ]
77
[ "46-11=35", "35/7=5", "72+5=77" ]
Current State: 77:[11, 46, 7, 72], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [7, 72, 35] Generated Node #2: [7, 72, 35] from Operation: 46-11=35 Current State: 77:[7, 72, 35], Operations: ['46-11=35'] Exploring Operation: 35/7=5, Resulting Numbers: [72, 5] Generated Node #3: [72, 5] from Operation: 35/7=5 Current State: 77:[72, 5], Operations: ['46-11=35', '35/7=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[11, 46, 7, 72], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [7, 72, 35] Generated Node #0,0: 77:[7, 72, 35] Operation: 46-11=35 Exploring Operation: 46+7=53, Resulting Numbers: [11, 72, 53] Generated Node #0,1: 77:[11, 72, 53] Operation: 46+7=53 Exploring Operation: 11+46=57, Resulting Numbers: [7, 72, 57] Generated Node #0,2: 77:[7, 72, 57] Operation: 11+46=57 Exploring Operation: 72-46=26, Resulting Numbers: [11, 7, 26] Generated Node #0,3: 77:[11, 7, 26] Operation: 72-46=26 Moving to Node #0,3 Current State: 77:[11, 7, 26], Operations: ['72-46=26'] Exploring Operation: 11-7=4, Resulting Numbers: [26, 4] Generated Node #0,3,0: 77:[26, 4] Operation: 11-7=4 Exploring Operation: 26-7=19, Resulting Numbers: [11, 19] Generated Node #0,3,1: 77:[11, 19] Operation: 26-7=19 Exploring Operation: 26-11=15, Resulting Numbers: [7, 15] Generated Node #0,3,2: 77:[7, 15] Operation: 26-11=15 Exploring Operation: 11*7=77, Resulting Numbers: [26, 77] Generated Node #0,3,3: 77:[26, 77] Operation: 11*7=77 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 77:[7, 15], Operations: ['72-46=26', '26-11=15'] Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,77 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,77 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:[11, 19], Operations: ['72-46=26', '26-7=19'] Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,77 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,77 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:[26, 77], Operations: ['72-46=26', '11*7=77'] Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,77 unequal: No Solution Exploring Operation: 26*77=2002, Resulting Numbers: [2002] 2002,77 unequal: No Solution Exploring Operation: 26+77=103, Resulting Numbers: [103] 103,77 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:[26, 4], Operations: ['72-46=26', '11-7=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,77 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,77 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: 77:[7, 72, 57], Operations: ['11+46=57'] Exploring Operation: 7+72=79, Resulting Numbers: [57, 79] Generated Node #0,2,0: 77:[57, 79] Operation: 7+72=79 Exploring Operation: 72-57=15, Resulting Numbers: [7, 15] Generated Node #0,2,1: 77:[7, 15] Operation: 72-57=15 Exploring Operation: 7+57=64, Resulting Numbers: [72, 64] Generated Node #0,2,2: 77:[72, 64] Operation: 7+57=64 Exploring Operation: 72-7=65, Resulting Numbers: [57, 65] Generated Node #0,2,3: 77:[57, 65] Operation: 72-7=65 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 77:[7, 15], Operations: ['11+46=57', '72-57=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,77 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:[72, 64], Operations: ['11+46=57', '7+57=64'] Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,77 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,77 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 #0,2,0 Current State: 77:[57, 79], Operations: ['11+46=57', '7+72=79'] Exploring Operation: 79-57=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 57*79=4503, Resulting Numbers: [4503] 4503,77 unequal: No Solution Exploring Operation: 57+79=136, Resulting Numbers: [136] 136,77 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:[57, 65], Operations: ['11+46=57', '72-7=65'] Exploring Operation: 57*65=3705, Resulting Numbers: [3705] 3705,77 unequal: No Solution Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 57+65=122, Resulting Numbers: [122] 122,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 77:[11, 72, 53], Operations: ['46+7=53'] Exploring Operation: 53-11=42, Resulting Numbers: [72, 42] Generated Node #0,1,0: 77:[72, 42] Operation: 53-11=42 Exploring Operation: 11+53=64, Resulting Numbers: [72, 64] Generated Node #0,1,1: 77:[72, 64] Operation: 11+53=64 Exploring Operation: 11+72=83, Resulting Numbers: [53, 83] Generated Node #0,1,2: 77:[53, 83] Operation: 11+72=83 Exploring Operation: 72-53=19, Resulting Numbers: [11, 19] Generated Node #0,1,3: 77:[11, 19] Operation: 72-53=19 Moving to Node #0,0 Current State: 77:[7, 72, 35], Operations: ['46-11=35'] Exploring Operation: 35-7=28, Resulting Numbers: [72, 28] Generated Node #0,0,0: 77:[72, 28] Operation: 35-7=28 Exploring Operation: 72-35=37, Resulting Numbers: [7, 37] Generated Node #0,0,1: 77:[7, 37] Operation: 72-35=37 Exploring Operation: 7+72=79, Resulting Numbers: [35, 79] Generated Node #0,0,2: 77:[35, 79] Operation: 7+72=79 Exploring Operation: 35/7=5, Resulting Numbers: [72, 5] Generated Node #0,0,3: 77:[72, 5] Operation: 35/7=5 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[72, 5], Operations: ['46-11=35', '35/7=5'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,77 unequal: No Solution Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[11, 46, 7, 72], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [7, 72, 35] Generated Node #0,0: 77:[7, 72, 35] Operation: 46-11=35 Moving to Node #0,0 Current State: 77:[7, 72, 35], Operations: ['46-11=35'] Exploring Operation: 35/7=5, Resulting Numbers: [72, 5] Generated Node #0,0,3: 77:[72, 5] Operation: 35/7=5 Moving to Node #0,0,3 Current State: 77:[72, 5], Operations: ['46-11=35', '35/7=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
mult_heuristic
[ 92, 36, 35, 3 ]
90
[ "92+36=128", "35+3=38", "128-38=90" ]
Current State: 90:[92, 36, 35, 3], Operations: [] Exploring Operation: 92+36=128, Resulting Numbers: [35, 3, 128] Generated Node #2: [35, 3, 128] from Operation: 92+36=128 Current State: 90:[35, 3, 128], Operations: ['92+36=128'] Exploring Operation: 35+3=38, Resulting Numbers: [128, 38] Generated Node #3: [128, 38] from Operation: 35+3=38 Current State: 90:[128, 38], Operations: ['92+36=128', '35+3=38'] Exploring Operation: 128-38=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[92, 36, 35, 3], Operations: [] Exploring Operation: 36/3=12, Resulting Numbers: [92, 35, 12] Generated Node #0,0: 90:[92, 35, 12] Operation: 36/3=12 Exploring Operation: 36-35=1, Resulting Numbers: [92, 3, 1] Generated Node #0,1: 90:[92, 3, 1] Operation: 36-35=1 Exploring Operation: 36-3=33, Resulting Numbers: [92, 35, 33] Generated Node #0,2: 90:[92, 35, 33] Operation: 36-3=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[92, 3, 1], Operations: ['36-35=1'] Exploring Operation: 92-3=89, Resulting Numbers: [1, 89] Generated Node #0,1,0: 90:[1, 89] Operation: 92-3=89 Exploring Operation: 92-1=91, Resulting Numbers: [3, 91] Generated Node #0,1,1: 90:[3, 91] Operation: 92-1=91 Exploring Operation: 92*1=92, Resulting Numbers: [3, 92] Generated Node #0,1,2: 90:[3, 92] Operation: 92*1=92 Moving to Node #0,1,1 Current State: 90:[3, 91], Operations: ['36-35=1', '92-1=91'] Exploring Operation: 3*91=273, Resulting Numbers: [273] 273,90 unequal: No Solution Exploring Operation: 3+91=94, Resulting Numbers: [94] 94,90 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[1, 89], Operations: ['36-35=1', '92-3=89'] Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[92, 36, 35, 3], Operations: [] Exploring Operation: 36-35=1, Resulting Numbers: [92, 3, 1] Generated Node #0,1: 90:[92, 3, 1] Operation: 36-35=1 Moving to Node #0,1 Current State: 90:[92, 3, 1], Operations: ['36-35=1'] Exploring Operation: 92-3=89, Resulting Numbers: [1, 89] Generated Node #0,1,0: 90:[1, 89] Operation: 92-3=89 Moving to Node #0,1,0 Current State: 90:[1, 89], Operations: ['36-35=1', '92-3=89'] Exploring Operation: 1+89=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 64, 15, 80, 38 ]
50
[ "64*15=960", "960/80=12", "38+12=50" ]
Current State: 50:[64, 15, 80, 38], Operations: [] Exploring Operation: 64*15=960, Resulting Numbers: [80, 38, 960] Generated Node #2: [80, 38, 960] from Operation: 64*15=960 Current State: 50:[80, 38, 960], Operations: ['64*15=960'] Exploring Operation: 960/80=12, Resulting Numbers: [38, 12] Generated Node #3: [38, 12] from Operation: 960/80=12 Current State: 50:[38, 12], Operations: ['64*15=960', '960/80=12'] Exploring Operation: 38+12=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[64, 15, 80, 38], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [64, 15, 42] Generated Node #0,0: 50:[64, 15, 42] Operation: 80-38=42 Exploring Operation: 80-64=16, Resulting Numbers: [15, 38, 16] Generated Node #0,1: 50:[15, 38, 16] Operation: 80-64=16 Moving to Node #0,1 Current State: 50:[15, 38, 16], Operations: ['80-64=16'] Exploring Operation: 38-15=23, Resulting Numbers: [16, 23] Generated Node #0,1,0: 50:[16, 23] Operation: 38-15=23 Exploring Operation: 38-16=22, Resulting Numbers: [15, 22] Generated Node #0,1,1: 50:[15, 22] Operation: 38-16=22 Moving to Node #0,0 Current State: 50:[64, 15, 42], Operations: ['80-38=42'] Exploring Operation: 64-42=22, Resulting Numbers: [15, 22] Generated Node #0,0,0: 50:[15, 22] Operation: 64-42=22 Exploring Operation: 64-15=49, Resulting Numbers: [42, 49] Generated Node #0,0,1: 50:[42, 49] Operation: 64-15=49 Moving to Node #0,1,0 Current State: 50:[16, 23], Operations: ['80-64=16', '38-15=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,50 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[15, 22], Operations: ['80-38=42', '64-42=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[15, 22], Operations: ['80-64=16', '38-16=22'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,50 unequal: No Solution Exploring Operation: 15+22=37, Resulting Numbers: [37] 37,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[42, 49], Operations: ['80-38=42', '64-15=49'] Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,50 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 83, 3, 70, 89 ]
88
[ "89-83=6", "3*6=18", "70+18=88" ]
Current State: 88:[83, 3, 70, 89], Operations: [] Exploring Operation: 89-83=6, Resulting Numbers: [3, 70, 6] Generated Node #2: [3, 70, 6] from Operation: 89-83=6 Current State: 88:[3, 70, 6], Operations: ['89-83=6'] Exploring Operation: 3*6=18, Resulting Numbers: [70, 18] Generated Node #3: [70, 18] from Operation: 3*6=18 Current State: 88:[70, 18], Operations: ['89-83=6', '3*6=18'] Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[83, 3, 70, 89], Operations: [] Exploring Operation: 83+3=86, Resulting Numbers: [70, 89, 86] Generated Node #0,0: 88:[70, 89, 86] Operation: 83+3=86 Exploring Operation: 89-70=19, Resulting Numbers: [83, 3, 19] Generated Node #0,1: 88:[83, 3, 19] Operation: 89-70=19 Exploring Operation: 83-70=13, Resulting Numbers: [3, 89, 13] Generated Node #0,2: 88:[3, 89, 13] Operation: 83-70=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[3, 89, 13], Operations: ['83-70=13'] Exploring Operation: 89-3=86, Resulting Numbers: [13, 86] Generated Node #0,2,0: 88:[13, 86] Operation: 89-3=86 Exploring Operation: 3+89=92, Resulting Numbers: [13, 92] Generated Node #0,2,1: 88:[13, 92] Operation: 3+89=92 Exploring Operation: 13-3=10, Resulting Numbers: [89, 10] Generated Node #0,2,2: 88:[89, 10] Operation: 13-3=10 Moving to Node #0,2,2 Current State: 88:[89, 10], Operations: ['83-70=13', '13-3=10'] Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 89*10=890, Resulting Numbers: [890] 890,88 unequal: No Solution Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[13, 86], Operations: ['83-70=13', '89-3=86'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 13*86=1118, Resulting Numbers: [1118] 1118,88 unequal: No Solution Exploring Operation: 13+86=99, Resulting Numbers: [99] 99,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[13, 92], Operations: ['83-70=13', '3+89=92'] Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 13*92=1196, Resulting Numbers: [1196] 1196,88 unequal: No Solution Exploring Operation: 13+92=105, Resulting Numbers: [105] 105,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[83, 3, 19], Operations: ['89-70=19'] Exploring Operation: 3+19=22, Resulting Numbers: [83, 22] Generated Node #0,1,0: 88:[83, 22] Operation: 3+19=22 Exploring Operation: 19-3=16, Resulting Numbers: [83, 16] Generated Node #0,1,1: 88:[83, 16] Operation: 19-3=16 Exploring Operation: 83+3=86, Resulting Numbers: [19, 86] Generated Node #0,1,2: 88:[19, 86] Operation: 83+3=86 Moving to Node #0,1,0 Current State: 88:[83, 22], Operations: ['89-70=19', '3+19=22'] Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,88 unequal: No Solution Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[19, 86], Operations: ['89-70=19', '83+3=86'] Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[83, 16], Operations: ['89-70=19', '19-3=16'] Exploring Operation: 83*16=1328, Resulting Numbers: [1328] 1328,88 unequal: No Solution Exploring Operation: 83+16=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,88 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:[70, 89, 86], Operations: ['83+3=86'] Exploring Operation: 89-86=3, Resulting Numbers: [70, 3] Generated Node #0,0,0: 88:[70, 3] Operation: 89-86=3 Exploring Operation: 89-70=19, Resulting Numbers: [86, 19] Generated Node #0,0,1: 88:[86, 19] Operation: 89-70=19 Exploring Operation: 86-70=16, Resulting Numbers: [89, 16] Generated Node #0,0,2: 88:[89, 16] Operation: 86-70=16 Moving to Node #0,0,1 Current State: 88:[86, 19], Operations: ['83+3=86', '89-70=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,88 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[89, 16], Operations: ['83+3=86', '86-70=16'] Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,88 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[70, 3], Operations: ['83+3=86', '89-86=3'] Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,88 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 78, 1, 46, 65 ]
32
[ "78+1=79", "46+65=111", "111-79=32" ]
Current State: 32:[78, 1, 46, 65], Operations: [] Exploring Operation: 78+1=79, Resulting Numbers: [46, 65, 79] Generated Node #2: [46, 65, 79] from Operation: 78+1=79 Current State: 32:[46, 65, 79], Operations: ['78+1=79'] Exploring Operation: 46+65=111, Resulting Numbers: [79, 111] Generated Node #3: [79, 111] from Operation: 46+65=111 Current State: 32:[79, 111], Operations: ['78+1=79', '46+65=111'] Exploring Operation: 111-79=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[78, 1, 46, 65], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [1, 46, 13] Generated Node #0,0: 32:[1, 46, 13] Operation: 78-65=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[1, 46, 13], Operations: ['78-65=13'] Exploring Operation: 46-13=33, Resulting Numbers: [1, 33] Generated Node #0,0,0: 32:[1, 33] Operation: 46-13=33 Moving to Node #0,0,0 Current State: 32:[1, 33], Operations: ['78-65=13', '46-13=33'] Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[78, 1, 46, 65], Operations: [] Exploring Operation: 78-65=13, Resulting Numbers: [1, 46, 13] Generated Node #0,0: 32:[1, 46, 13] Operation: 78-65=13 Moving to Node #0,0 Current State: 32:[1, 46, 13], Operations: ['78-65=13'] Exploring Operation: 46-13=33, Resulting Numbers: [1, 33] Generated Node #0,0,0: 32:[1, 33] Operation: 46-13=33 Moving to Node #0,0,0 Current State: 32:[1, 33], Operations: ['78-65=13', '46-13=33'] Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 7, 28, 38, 55 ]
58
[ "7+28=35", "38+55=93", "93-35=58" ]
Current State: 58:[7, 28, 38, 55], Operations: [] Exploring Operation: 7+28=35, Resulting Numbers: [38, 55, 35] Generated Node #2: [38, 55, 35] from Operation: 7+28=35 Current State: 58:[38, 55, 35], Operations: ['7+28=35'] Exploring Operation: 38+55=93, Resulting Numbers: [35, 93] Generated Node #3: [35, 93] from Operation: 38+55=93 Current State: 58:[35, 93], Operations: ['7+28=35', '38+55=93'] Exploring Operation: 93-35=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[7, 28, 38, 55], Operations: [] Exploring Operation: 38-7=31, Resulting Numbers: [28, 55, 31] Generated Node #0,0: 58:[28, 55, 31] Operation: 38-7=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[28, 55, 31], Operations: ['38-7=31'] Exploring Operation: 55-28=27, Resulting Numbers: [31, 27] Generated Node #0,0,0: 58:[31, 27] Operation: 55-28=27 Moving to Node #0,0,0 Current State: 58:[31, 27], Operations: ['38-7=31', '55-28=27'] Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[7, 28, 38, 55], Operations: [] Exploring Operation: 38-7=31, Resulting Numbers: [28, 55, 31] Generated Node #0,0: 58:[28, 55, 31] Operation: 38-7=31 Moving to Node #0,0 Current State: 58:[28, 55, 31], Operations: ['38-7=31'] Exploring Operation: 55-28=27, Resulting Numbers: [31, 27] Generated Node #0,0,0: 58:[31, 27] Operation: 55-28=27 Moving to Node #0,0,0 Current State: 58:[31, 27], Operations: ['38-7=31', '55-28=27'] Exploring Operation: 31+27=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 31, 15, 76, 25 ]
55
[ "31+15=46", "76+25=101", "101-46=55" ]
Current State: 55:[31, 15, 76, 25], Operations: [] Exploring Operation: 31+15=46, Resulting Numbers: [76, 25, 46] Generated Node #2: [76, 25, 46] from Operation: 31+15=46 Current State: 55:[76, 25, 46], Operations: ['31+15=46'] Exploring Operation: 76+25=101, Resulting Numbers: [46, 101] Generated Node #3: [46, 101] from Operation: 76+25=101 Current State: 55:[46, 101], Operations: ['31+15=46', '76+25=101'] Exploring Operation: 101-46=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[31, 15, 76, 25], Operations: [] Exploring Operation: 31+25=56, Resulting Numbers: [15, 76, 56] Generated Node #0,0: 55:[15, 76, 56] Operation: 31+25=56 Exploring Operation: 31-25=6, Resulting Numbers: [15, 76, 6] Generated Node #0,1: 55:[15, 76, 6] Operation: 31-25=6 Moving to Node #0,0 Current State: 55:[15, 76, 56], Operations: ['31+25=56'] Exploring Operation: 76-15=61, Resulting Numbers: [56, 61] Generated Node #0,0,0: 55:[56, 61] Operation: 76-15=61 Exploring Operation: 76-56=20, Resulting Numbers: [15, 20] Generated Node #0,0,1: 55:[15, 20] Operation: 76-56=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[56, 61], Operations: ['31+25=56', '76-15=61'] Exploring Operation: 56+61=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 61-56=5, Resulting Numbers: [5] 5,55 unequal: No Solution No 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: 55:[15, 20], Operations: ['31+25=56', '76-56=20'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,55 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: 55:[15, 76, 6], Operations: ['31-25=6'] Exploring Operation: 76-15=61, Resulting Numbers: [6, 61] Generated Node #0,1,0: 55:[6, 61] Operation: 76-15=61 Exploring Operation: 76-6=70, Resulting Numbers: [15, 70] Generated Node #0,1,1: 55:[15, 70] Operation: 76-6=70 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[6, 61], Operations: ['31-25=6', '76-15=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[31, 15, 76, 25], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [15, 76, 6] Generated Node #0,1: 55:[15, 76, 6] Operation: 31-25=6 Moving to Node #0,1 Current State: 55:[15, 76, 6], Operations: ['31-25=6'] Exploring Operation: 76-15=61, Resulting Numbers: [6, 61] Generated Node #0,1,0: 55:[6, 61] Operation: 76-15=61 Moving to Node #0,1,0 Current State: 55:[6, 61], Operations: ['31-25=6', '76-15=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 69, 56, 82, 2 ]
99
[ "82-69=13", "56*2=112", "112-13=99" ]
Current State: 99:[69, 56, 82, 2], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [56, 2, 13] Generated Node #2: [56, 2, 13] from Operation: 82-69=13 Current State: 99:[56, 2, 13], Operations: ['82-69=13'] Exploring Operation: 56*2=112, Resulting Numbers: [13, 112] Generated Node #3: [13, 112] from Operation: 56*2=112 Current State: 99:[13, 112], Operations: ['82-69=13', '56*2=112'] Exploring Operation: 112-13=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[69, 56, 82, 2], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [56, 2, 13] Generated Node #0,0: 99:[56, 2, 13] Operation: 82-69=13 Exploring Operation: 69-56=13, Resulting Numbers: [82, 2, 13] Generated Node #0,1: 99:[82, 2, 13] Operation: 69-56=13 Exploring Operation: 82-56=26, Resulting Numbers: [69, 2, 26] Generated Node #0,2: 99:[69, 2, 26] Operation: 82-56=26 Moving to Node #0,1 Current State: 99:[82, 2, 13], Operations: ['69-56=13'] Exploring Operation: 82+13=95, Resulting Numbers: [2, 95] Generated Node #0,1,0: 99:[2, 95] Operation: 82+13=95 Exploring Operation: 82/2=41, Resulting Numbers: [13, 41] Generated Node #0,1,1: 99:[13, 41] Operation: 82/2=41 Exploring Operation: 82+2=84, Resulting Numbers: [13, 84] Generated Node #0,1,2: 99:[13, 84] Operation: 82+2=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[2, 95], Operations: ['69-56=13', '82+13=95'] Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,99 unequal: No Solution Exploring Operation: 2*95=190, Resulting Numbers: [190] 190,99 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,99 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 #0,1,1 Current State: 99:[13, 41], Operations: ['69-56=13', '82/2=41'] Exploring Operation: 13+41=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 13*41=533, Resulting Numbers: [533] 533,99 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,99 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 #0,1,2 Current State: 99:[13, 84], Operations: ['69-56=13', '82+2=84'] Exploring Operation: 13*84=1092, Resulting Numbers: [1092] 1092,99 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,99 unequal: No Solution Exploring Operation: 13+84=97, Resulting Numbers: [97] 97,99 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: 99:[56, 2, 13], Operations: ['82-69=13'] Exploring Operation: 56*2=112, Resulting Numbers: [13, 112] Generated Node #0,0,0: 99:[13, 112] Operation: 56*2=112 Exploring Operation: 56-13=43, Resulting Numbers: [2, 43] Generated Node #0,0,1: 99:[2, 43] Operation: 56-13=43 Exploring Operation: 56/2=28, Resulting Numbers: [13, 28] Generated Node #0,0,2: 99:[13, 28] Operation: 56/2=28 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[13, 28], Operations: ['82-69=13', '56/2=28'] Exploring Operation: 13*28=364, Resulting Numbers: [364] 364,99 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[2, 43], Operations: ['82-69=13', '56-13=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,99 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,99 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[13, 112], Operations: ['82-69=13', '56*2=112'] Exploring Operation: 13+112=125, Resulting Numbers: [125] 125,99 unequal: No Solution Exploring Operation: 13*112=1456, Resulting Numbers: [1456] 1456,99 unequal: No Solution Exploring Operation: 112-13=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[69, 56, 82, 2], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [56, 2, 13] Generated Node #0,0: 99:[56, 2, 13] Operation: 82-69=13 Moving to Node #0,0 Current State: 99:[56, 2, 13], Operations: ['82-69=13'] Exploring Operation: 56*2=112, Resulting Numbers: [13, 112] Generated Node #0,0,0: 99:[13, 112] Operation: 56*2=112 Moving to Node #0,0,0 Current State: 99:[13, 112], Operations: ['82-69=13', '56*2=112'] Exploring Operation: 112-13=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 23, 44, 26, 4 ]
49
[ "44-26=18", "4*18=72", "72-23=49" ]
Current State: 49:[23, 44, 26, 4], Operations: [] Exploring Operation: 44-26=18, Resulting Numbers: [23, 4, 18] Generated Node #2: [23, 4, 18] from Operation: 44-26=18 Current State: 49:[23, 4, 18], Operations: ['44-26=18'] Exploring Operation: 4*18=72, Resulting Numbers: [23, 72] Generated Node #3: [23, 72] from Operation: 4*18=72 Current State: 49:[23, 72], Operations: ['44-26=18', '4*18=72'] Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[23, 44, 26, 4], Operations: [] Exploring Operation: 44-26=18, Resulting Numbers: [23, 4, 18] Generated Node #0,0: 49:[23, 4, 18] Operation: 44-26=18 Exploring Operation: 26-23=3, Resulting Numbers: [44, 4, 3] Generated Node #0,1: 49:[44, 4, 3] Operation: 26-23=3 Exploring Operation: 23+26=49, Resulting Numbers: [44, 4, 49] Generated Node #0,2: 49:[44, 4, 49] Operation: 23+26=49 Exploring Operation: 23-4=19, Resulting Numbers: [44, 26, 19] Generated Node #0,3: 49:[44, 26, 19] Operation: 23-4=19 Exploring Operation: 44-23=21, Resulting Numbers: [26, 4, 21] Generated Node #0,4: 49:[26, 4, 21] Operation: 44-23=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[44, 4, 49], Operations: ['23+26=49'] Exploring Operation: 44/4=11, Resulting Numbers: [49, 11] Generated Node #0,2,0: 49:[49, 11] Operation: 44/4=11 Exploring Operation: 44+4=48, Resulting Numbers: [49, 48] Generated Node #0,2,1: 49:[49, 48] Operation: 44+4=48 Exploring Operation: 44-4=40, Resulting Numbers: [49, 40] Generated Node #0,2,2: 49:[49, 40] Operation: 44-4=40 Exploring Operation: 49-44=5, Resulting Numbers: [4, 5] Generated Node #0,2,3: 49:[4, 5] Operation: 49-44=5 Exploring Operation: 4+49=53, Resulting Numbers: [44, 53] Generated Node #0,2,4: 49:[44, 53] Operation: 4+49=53 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[49, 48], Operations: ['23+26=49', '44+4=48'] Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[49, 11], Operations: ['23+26=49', '44/4=11'] Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,49 unequal: No Solution Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,49 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 49:[4, 5], Operations: ['23+26=49', '49-44=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 49:[49, 40], Operations: ['23+26=49', '44-4=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,49 unequal: No Solution Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 49:[44, 53], Operations: ['23+26=49', '4+49=53'] Exploring Operation: 53-44=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 44+53=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 44*53=2332, Resulting Numbers: [2332] 2332,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[44, 4, 3], Operations: ['26-23=3'] Exploring Operation: 4+3=7, Resulting Numbers: [44, 7] Generated Node #0,1,0: 49:[44, 7] Operation: 4+3=7 Exploring Operation: 44+3=47, Resulting Numbers: [4, 47] Generated Node #0,1,1: 49:[4, 47] Operation: 44+3=47 Exploring Operation: 44+4=48, Resulting Numbers: [3, 48] Generated Node #0,1,2: 49:[3, 48] Operation: 44+4=48 Exploring Operation: 4*3=12, Resulting Numbers: [44, 12] Generated Node #0,1,3: 49:[44, 12] Operation: 4*3=12 Exploring Operation: 44/4=11, Resulting Numbers: [3, 11] Generated Node #0,1,4: 49:[3, 11] Operation: 44/4=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 49:[44, 7], Operations: ['26-23=3', '4+3=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,49 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[4, 47], Operations: ['26-23=3', '44+3=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[3, 48], Operations: ['26-23=3', '44+4=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,49 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 49:[3, 11], Operations: ['26-23=3', '44/4=11'] Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,49 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,49 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[44, 12], Operations: ['26-23=3', '4*3=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,49 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[23, 4, 18], Operations: ['44-26=18'] Exploring Operation: 23-4=19, Resulting Numbers: [18, 19] Generated Node #0,0,0: 49:[18, 19] Operation: 23-4=19 Exploring Operation: 23+4=27, Resulting Numbers: [18, 27] Generated Node #0,0,1: 49:[18, 27] Operation: 23+4=27 Exploring Operation: 18-4=14, Resulting Numbers: [23, 14] Generated Node #0,0,2: 49:[23, 14] Operation: 18-4=14 Exploring Operation: 23+18=41, Resulting Numbers: [4, 41] Generated Node #0,0,3: 49:[4, 41] Operation: 23+18=41 Exploring Operation: 23-18=5, Resulting Numbers: [4, 5] Generated Node #0,0,4: 49:[4, 5] Operation: 23-18=5 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 49:[4, 5], Operations: ['44-26=18', '23-18=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[4, 41], Operations: ['44-26=18', '23+18=41'] Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,49 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[18, 19], Operations: ['44-26=18', '23-4=19'] Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,49 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[23, 14], Operations: ['44-26=18', '18-4=14'] Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[18, 27], Operations: ['44-26=18', '23+4=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,49 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,49 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[44, 26, 19], Operations: ['23-4=19'] Exploring Operation: 44+26=70, Resulting Numbers: [19, 70] Generated Node #0,3,0: 49:[19, 70] Operation: 44+26=70 Exploring Operation: 44+19=63, Resulting Numbers: [26, 63] Generated Node #0,3,1: 49:[26, 63] Operation: 44+19=63 Exploring Operation: 26-19=7, Resulting Numbers: [44, 7] Generated Node #0,3,2: 49:[44, 7] Operation: 26-19=7 Exploring Operation: 44-26=18, Resulting Numbers: [19, 18] Generated Node #0,3,3: 49:[19, 18] Operation: 44-26=18 Exploring Operation: 26+19=45, Resulting Numbers: [44, 45] Generated Node #0,3,4: 49:[44, 45] Operation: 26+19=45 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 49:[44, 7], Operations: ['23-4=19', '26-19=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 49:[44, 45], Operations: ['23-4=19', '26+19=45'] Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 44+45=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 44*45=1980, Resulting Numbers: [1980] 1980,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 49:[19, 18], Operations: ['23-4=19', '44-26=18'] Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 49:[19, 70], Operations: ['23-4=19', '44+26=70'] Exploring Operation: 19*70=1330, Resulting Numbers: [1330] 1330,49 unequal: No Solution Exploring Operation: 19+70=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 70-19=51, Resulting Numbers: [51] 51,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 49:[26, 63], Operations: ['23-4=19', '44+19=63'] Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 26*63=1638, Resulting Numbers: [1638] 1638,49 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[26, 4, 21], Operations: ['44-23=21'] Exploring Operation: 26+4=30, Resulting Numbers: [21, 30] Generated Node #0,4,0: 49:[21, 30] Operation: 26+4=30 Exploring Operation: 21-4=17, Resulting Numbers: [26, 17] Generated Node #0,4,1: 49:[26, 17] Operation: 21-4=17 Exploring Operation: 26+21=47, Resulting Numbers: [4, 47] Generated Node #0,4,2: 49:[4, 47] Operation: 26+21=47 Exploring Operation: 26-21=5, Resulting Numbers: [4, 5] Generated Node #0,4,3: 49:[4, 5] Operation: 26-21=5 Exploring Operation: 26-4=22, Resulting Numbers: [21, 22] Generated Node #0,4,4: 49:[21, 22] Operation: 26-4=22 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 49:[4, 47], Operations: ['44-23=21', '26+21=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,49 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 49:[4, 5], Operations: ['44-23=21', '26-21=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 49:[26, 17], Operations: ['44-23=21', '21-4=17'] Exploring Operation: 26*17=442, Resulting Numbers: [442] 442,49 unequal: No Solution Exploring Operation: 26+17=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 49:[21, 22], Operations: ['44-23=21', '26-4=22'] Exploring Operation: 21+22=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 21*22=462, Resulting Numbers: [462] 462,49 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 49:[21, 30], Operations: ['44-23=21', '26+4=30'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,49 unequal: No Solution Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,49 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_5
sum_heuristic
[ 32, 45, 84, 37 ]
16
[ "84-45=39", "39-37=2", "32/2=16" ]
Current State: 16:[32, 45, 84, 37], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [32, 37, 39] Generated Node #2: [32, 37, 39] from Operation: 84-45=39 Current State: 16:[32, 37, 39], Operations: ['84-45=39'] Exploring Operation: 39-37=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 39-37=2 Current State: 16:[32, 2], Operations: ['84-45=39', '39-37=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[32, 45, 84, 37], Operations: [] Exploring Operation: 45-37=8, Resulting Numbers: [32, 84, 8] Generated Node #0,0: 16:[32, 84, 8] Operation: 45-37=8 Exploring Operation: 45-32=13, Resulting Numbers: [84, 37, 13] Generated Node #0,1: 16:[84, 37, 13] Operation: 45-32=13 Exploring Operation: 84-45=39, Resulting Numbers: [32, 37, 39] Generated Node #0,2: 16:[32, 37, 39] Operation: 84-45=39 Exploring Operation: 84-37=47, Resulting Numbers: [32, 45, 47] Generated Node #0,3: 16:[32, 45, 47] Operation: 84-37=47 Exploring Operation: 84-32=52, Resulting Numbers: [45, 37, 52] Generated Node #0,4: 16:[45, 37, 52] Operation: 84-32=52 Moving to Node #0,2 Current State: 16:[32, 37, 39], Operations: ['84-45=39'] Exploring Operation: 39-32=7, Resulting Numbers: [37, 7] Generated Node #0,2,0: 16:[37, 7] Operation: 39-32=7 Exploring Operation: 32+39=71, Resulting Numbers: [37, 71] Generated Node #0,2,1: 16:[37, 71] Operation: 32+39=71 Exploring Operation: 32+37=69, Resulting Numbers: [39, 69] Generated Node #0,2,2: 16:[39, 69] Operation: 32+37=69 Exploring Operation: 37-32=5, Resulting Numbers: [39, 5] Generated Node #0,2,3: 16:[39, 5] Operation: 37-32=5 Exploring Operation: 39-37=2, Resulting Numbers: [32, 2] Generated Node #0,2,4: 16:[32, 2] Operation: 39-37=2 Moving to Node #0,3 Current State: 16:[32, 45, 47], Operations: ['84-37=47'] Exploring Operation: 47-45=2, Resulting Numbers: [32, 2] Generated Node #0,3,0: 16:[32, 2] Operation: 47-45=2 Exploring Operation: 32+47=79, Resulting Numbers: [45, 79] Generated Node #0,3,1: 16:[45, 79] Operation: 32+47=79 Exploring Operation: 47-32=15, Resulting Numbers: [45, 15] Generated Node #0,3,2: 16:[45, 15] Operation: 47-32=15 Exploring Operation: 45-32=13, Resulting Numbers: [47, 13] Generated Node #0,3,3: 16:[47, 13] Operation: 45-32=13 Exploring Operation: 32+45=77, Resulting Numbers: [47, 77] Generated Node #0,3,4: 16:[47, 77] Operation: 32+45=77 Moving to Node #0,0 Current State: 16:[32, 84, 8], Operations: ['45-37=8'] Exploring Operation: 84-8=76, Resulting Numbers: [32, 76] Generated Node #0,0,0: 16:[32, 76] Operation: 84-8=76 Exploring Operation: 84-32=52, Resulting Numbers: [8, 52] Generated Node #0,0,1: 16:[8, 52] Operation: 84-32=52 Exploring Operation: 32+8=40, Resulting Numbers: [84, 40] Generated Node #0,0,2: 16:[84, 40] Operation: 32+8=40 Exploring Operation: 32/8=4, Resulting Numbers: [84, 4] Generated Node #0,0,3: 16:[84, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [84, 24] Generated Node #0,0,4: 16:[84, 24] Operation: 32-8=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[8, 52], Operations: ['45-37=8', '84-32=52'] Exploring Operation: 8*52=416, Resulting Numbers: [416] 416,16 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,16 unequal: No Solution Exploring Operation: 8+52=60, Resulting Numbers: [60] 60,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[84, 4], Operations: ['45-37=8', '32/8=4'] Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 84*4=336, Resulting Numbers: [336] 336,16 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,16 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[32, 76], Operations: ['45-37=8', '84-8=76'] Exploring Operation: 32+76=108, Resulting Numbers: [108] 108,16 unequal: No Solution Exploring Operation: 76-32=44, Resulting Numbers: [44] 44,16 unequal: No Solution Exploring Operation: 32*76=2432, Resulting Numbers: [2432] 2432,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 16:[84, 24], Operations: ['45-37=8', '32-8=24'] Exploring Operation: 84*24=2016, Resulting Numbers: [2016] 2016,16 unequal: No Solution Exploring Operation: 84-24=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 84+24=108, Resulting Numbers: [108] 108,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[84, 40], Operations: ['45-37=8', '32+8=40'] Exploring Operation: 84*40=3360, Resulting Numbers: [3360] 3360,16 unequal: No Solution Exploring Operation: 84+40=124, Resulting Numbers: [124] 124,16 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,16 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: 16:[45, 37, 52], Operations: ['84-32=52'] Exploring Operation: 45+52=97, Resulting Numbers: [37, 97] Generated Node #0,4,0: 16:[37, 97] Operation: 45+52=97 Exploring Operation: 45+37=82, Resulting Numbers: [52, 82] Generated Node #0,4,1: 16:[52, 82] Operation: 45+37=82 Exploring Operation: 52-37=15, Resulting Numbers: [45, 15] Generated Node #0,4,2: 16:[45, 15] Operation: 52-37=15 Exploring Operation: 52-45=7, Resulting Numbers: [37, 7] Generated Node #0,4,3: 16:[37, 7] Operation: 52-45=7 Exploring Operation: 45-37=8, Resulting Numbers: [52, 8] Generated Node #0,4,4: 16:[52, 8] Operation: 45-37=8 Moving to Node #0,1 Current State: 16:[84, 37, 13], Operations: ['45-32=13'] Exploring Operation: 37+13=50, Resulting Numbers: [84, 50] Generated Node #0,1,0: 16:[84, 50] Operation: 37+13=50 Exploring Operation: 84+13=97, Resulting Numbers: [37, 97] Generated Node #0,1,1: 16:[37, 97] Operation: 84+13=97 Exploring Operation: 84-13=71, Resulting Numbers: [37, 71] Generated Node #0,1,2: 16:[37, 71] Operation: 84-13=71 Exploring Operation: 37-13=24, Resulting Numbers: [84, 24] Generated Node #0,1,3: 16:[84, 24] Operation: 37-13=24 Exploring Operation: 84-37=47, Resulting Numbers: [13, 47] Generated Node #0,1,4: 16:[13, 47] Operation: 84-37=47 Moving to Node #0,2,4 Current State: 16:[32, 2], Operations: ['84-45=39', '39-37=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,16 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[32, 45, 84, 37], Operations: [] Exploring Operation: 84-45=39, Resulting Numbers: [32, 37, 39] Generated Node #0,2: 16:[32, 37, 39] Operation: 84-45=39 Moving to Node #0,2 Current State: 16:[32, 37, 39], Operations: ['84-45=39'] Exploring Operation: 39-37=2, Resulting Numbers: [32, 2] Generated Node #0,2,4: 16:[32, 2] Operation: 39-37=2 Moving to Node #0,2,4 Current State: 16:[32, 2], Operations: ['84-45=39', '39-37=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.953993
hs_5
sum_heuristic
[ 16, 34, 12, 8 ]
78
[ "34-16=18", "12*8=96", "96-18=78" ]
Current State: 78:[16, 34, 12, 8], Operations: [] Exploring Operation: 34-16=18, Resulting Numbers: [12, 8, 18] Generated Node #2: [12, 8, 18] from Operation: 34-16=18 Current State: 78:[12, 8, 18], Operations: ['34-16=18'] Exploring Operation: 12*8=96, Resulting Numbers: [18, 96] Generated Node #3: [18, 96] from Operation: 12*8=96 Current State: 78:[18, 96], Operations: ['34-16=18', '12*8=96'] Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[16, 34, 12, 8], Operations: [] Exploring Operation: 34-8=26, Resulting Numbers: [16, 12, 26] Generated Node #0,0: 78:[16, 12, 26] Operation: 34-8=26 Exploring Operation: 34+8=42, Resulting Numbers: [16, 12, 42] Generated Node #0,1: 78:[16, 12, 42] Operation: 34+8=42 Exploring Operation: 34-16=18, Resulting Numbers: [12, 8, 18] Generated Node #0,2: 78:[12, 8, 18] Operation: 34-16=18 Exploring Operation: 16/8=2, Resulting Numbers: [34, 12, 2] Generated Node #0,3: 78:[34, 12, 2] Operation: 16/8=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[16, 12, 26], Operations: ['34-8=26'] Exploring Operation: 16+26=42, Resulting Numbers: [12, 42] Generated Node #0,0,0: 78:[12, 42] Operation: 16+26=42 Exploring Operation: 16-12=4, Resulting Numbers: [26, 4] Generated Node #0,0,1: 78:[26, 4] Operation: 16-12=4 Exploring Operation: 26-16=10, Resulting Numbers: [12, 10] Generated Node #0,0,2: 78:[12, 10] Operation: 26-16=10 Exploring Operation: 16+12=28, Resulting Numbers: [26, 28] Generated Node #0,0,3: 78:[26, 28] Operation: 16+12=28 Moving to Node #0,0,1 Current State: 78:[26, 4], Operations: ['34-8=26', '16-12=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[26, 28], Operations: ['34-8=26', '16+12=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,78 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,78 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[12, 10], Operations: ['34-8=26', '26-16=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[12, 42], Operations: ['34-8=26', '16+26=42'] Exploring Operation: 12+42=54, Resulting Numbers: [54] 54,78 unequal: No Solution Exploring Operation: 12*42=504, Resulting Numbers: [504] 504,78 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[34, 12, 2], Operations: ['16/8=2'] Exploring Operation: 12/2=6, Resulting Numbers: [34, 6] Generated Node #0,3,0: 78:[34, 6] Operation: 12/2=6 Exploring Operation: 34+2=36, Resulting Numbers: [12, 36] Generated Node #0,3,1: 78:[12, 36] Operation: 34+2=36 Exploring Operation: 34-12=22, Resulting Numbers: [2, 22] Generated Node #0,3,2: 78:[2, 22] Operation: 34-12=22 Exploring Operation: 34/2=17, Resulting Numbers: [12, 17] Generated Node #0,3,3: 78:[12, 17] Operation: 34/2=17 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 78:[12, 36], Operations: ['16/8=2', '34+2=36'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,78 unequal: No Solution Exploring Operation: 12*36=432, Resulting Numbers: [432] 432,78 unequal: No Solution No 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: 78:[2, 22], Operations: ['16/8=2', '34-12=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,78 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,78 unequal: No Solution No 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: 78:[34, 6], Operations: ['16/8=2', '12/2=6'] Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,78 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,78 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,78 unequal: No Solution No 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: 78:[12, 17], Operations: ['16/8=2', '34/2=17'] Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,78 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,78 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: 78:[16, 12, 42], Operations: ['34+8=42'] Exploring Operation: 16+12=28, Resulting Numbers: [42, 28] Generated Node #0,1,0: 78:[42, 28] Operation: 16+12=28 Exploring Operation: 16-12=4, Resulting Numbers: [42, 4] Generated Node #0,1,1: 78:[42, 4] Operation: 16-12=4 Exploring Operation: 42-12=30, Resulting Numbers: [16, 30] Generated Node #0,1,2: 78:[16, 30] Operation: 42-12=30 Exploring Operation: 42-16=26, Resulting Numbers: [12, 26] Generated Node #0,1,3: 78:[12, 26] Operation: 42-16=26 Moving to Node #0,1,3 Current State: 78:[12, 26], Operations: ['34+8=42', '42-16=26'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 12*26=312, Resulting Numbers: [312] 312,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[42, 4], Operations: ['34+8=42', '16-12=4'] Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,78 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[42, 28], Operations: ['34+8=42', '16+12=28'] Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,78 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[16, 30], Operations: ['34+8=42', '42-12=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[12, 8, 18], Operations: ['34-16=18'] Exploring Operation: 18-8=10, Resulting Numbers: [12, 10] Generated Node #0,2,0: 78:[12, 10] Operation: 18-8=10 Exploring Operation: 18-12=6, Resulting Numbers: [8, 6] Generated Node #0,2,1: 78:[8, 6] Operation: 18-12=6 Exploring Operation: 8+18=26, Resulting Numbers: [12, 26] Generated Node #0,2,2: 78:[12, 26] Operation: 8+18=26 Exploring Operation: 12-8=4, Resulting Numbers: [18, 4] Generated Node #0,2,3: 78:[18, 4] Operation: 12-8=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 78:[12, 26], Operations: ['34-16=18', '8+18=26'] Exploring Operation: 12*26=312, Resulting Numbers: [312] 312,78 unequal: No Solution Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 12+26=38, Resulting Numbers: [38] 38,78 unequal: No Solution No 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: 78:[8, 6], Operations: ['34-16=18', '18-12=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,78 unequal: No Solution No 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: 78:[12, 10], Operations: ['34-16=18', '18-8=10'] Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,78 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,78 unequal: No Solution No 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: 78:[18, 4], Operations: ['34-16=18', '12-8=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,78 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
[ 75, 17, 76, 75 ]
94
[ "75/75=1", "17+76=93", "1+93=94" ]
Current State: 94:[75, 17, 76, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [17, 76, 1] Generated Node #2: [17, 76, 1] from Operation: 75/75=1 Current State: 94:[17, 76, 1], Operations: ['75/75=1'] Exploring Operation: 17+76=93, Resulting Numbers: [1, 93] Generated Node #3: [1, 93] from Operation: 17+76=93 Current State: 94:[1, 93], Operations: ['75/75=1', '17+76=93'] Exploring Operation: 1+93=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[75, 17, 76, 75], Operations: [] Exploring Operation: 76-75=1, Resulting Numbers: [17, 75, 1] Generated Node #0,0: 94:[17, 75, 1] Operation: 76-75=1 Exploring Operation: 75/75=1, Resulting Numbers: [17, 76, 1] Generated Node #0,1: 94:[17, 76, 1] Operation: 75/75=1 Exploring Operation: 75-75=0, Resulting Numbers: [17, 76, 0] Generated Node #0,2: 94:[17, 76, 0] Operation: 75-75=0 Moving to Node #0,1 Current State: 94:[17, 76, 1], Operations: ['75/75=1'] Exploring Operation: 17-1=16, Resulting Numbers: [76, 16] Generated Node #0,1,0: 94:[76, 16] Operation: 17-1=16 Exploring Operation: 17+76=93, Resulting Numbers: [1, 93] Generated Node #0,1,1: 94:[1, 93] Operation: 17+76=93 Exploring Operation: 76-17=59, Resulting Numbers: [1, 59] Generated Node #0,1,2: 94:[1, 59] Operation: 76-17=59 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[1, 93], Operations: ['75/75=1', '17+76=93'] Exploring Operation: 1*93=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 1+93=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[75, 17, 76, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [17, 76, 1] Generated Node #0,1: 94:[17, 76, 1] Operation: 75/75=1 Moving to Node #0,1 Current State: 94:[17, 76, 1], Operations: ['75/75=1'] Exploring Operation: 17+76=93, Resulting Numbers: [1, 93] Generated Node #0,1,1: 94:[1, 93] Operation: 17+76=93 Moving to Node #0,1,1 Current State: 94:[1, 93], Operations: ['75/75=1', '17+76=93'] Exploring Operation: 1+93=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 7, 51, 10, 50 ]
39
[ "51-7=44", "50/10=5", "44-5=39" ]
Current State: 39:[7, 51, 10, 50], Operations: [] Exploring Operation: 51-7=44, Resulting Numbers: [10, 50, 44] Generated Node #2: [10, 50, 44] from Operation: 51-7=44 Current State: 39:[10, 50, 44], Operations: ['51-7=44'] Exploring Operation: 50/10=5, Resulting Numbers: [44, 5] Generated Node #3: [44, 5] from Operation: 50/10=5 Current State: 39:[44, 5], Operations: ['51-7=44', '50/10=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[7, 51, 10, 50], Operations: [] Exploring Operation: 50-10=40, Resulting Numbers: [7, 51, 40] Generated Node #0,0: 39:[7, 51, 40] Operation: 50-10=40 Exploring Operation: 51-10=41, Resulting Numbers: [7, 50, 41] Generated Node #0,1: 39:[7, 50, 41] Operation: 51-10=41 Exploring Operation: 51-50=1, Resulting Numbers: [7, 10, 1] Generated Node #0,2: 39:[7, 10, 1] Operation: 51-50=1 Moving to Node #0,2 Current State: 39:[7, 10, 1], Operations: ['51-50=1'] Exploring Operation: 10-7=3, Resulting Numbers: [1, 3] Generated Node #0,2,0: 39:[1, 3] Operation: 10-7=3 Exploring Operation: 7-1=6, Resulting Numbers: [10, 6] Generated Node #0,2,1: 39:[10, 6] Operation: 7-1=6 Exploring Operation: 7+10=17, Resulting Numbers: [1, 17] Generated Node #0,2,2: 39:[1, 17] Operation: 7+10=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[1, 3], Operations: ['51-50=1', '10-7=3'] Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[10, 6], Operations: ['51-50=1', '7-1=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[1, 17], Operations: ['51-50=1', '7+10=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,39 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 39:[7, 51, 40], Operations: ['50-10=40'] Exploring Operation: 51-40=11, Resulting Numbers: [7, 11] Generated Node #0,0,0: 39:[7, 11] Operation: 51-40=11 Exploring Operation: 51-7=44, Resulting Numbers: [40, 44] Generated Node #0,0,1: 39:[40, 44] Operation: 51-7=44 Exploring Operation: 40-7=33, Resulting Numbers: [51, 33] Generated Node #0,0,2: 39:[51, 33] Operation: 40-7=33 Moving to Node #0,1 Current State: 39:[7, 50, 41], Operations: ['51-10=41'] Exploring Operation: 41-7=34, Resulting Numbers: [50, 34] Generated Node #0,1,0: 39:[50, 34] Operation: 41-7=34 Exploring Operation: 50-41=9, Resulting Numbers: [7, 9] Generated Node #0,1,1: 39:[7, 9] Operation: 50-41=9 Exploring Operation: 50-7=43, Resulting Numbers: [41, 43] Generated Node #0,1,2: 39:[41, 43] Operation: 50-7=43 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[41, 43], Operations: ['51-10=41', '50-7=43'] Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 41+43=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 41*43=1763, Resulting Numbers: [1763] 1763,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[7, 9], Operations: ['51-10=41', '50-41=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,39 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[50, 34], Operations: ['51-10=41', '41-7=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,39 unequal: No Solution Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 50*34=1700, Resulting Numbers: [1700] 1700,39 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: 39:[7, 11], Operations: ['50-10=40', '51-40=11'] Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,39 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[40, 44], Operations: ['50-10=40', '51-7=44'] Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 40*44=1760, Resulting Numbers: [1760] 1760,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[51, 33], Operations: ['50-10=40', '40-7=33'] Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 51+33=84, Resulting Numbers: [84] 84,39 unequal: No Solution Exploring Operation: 51*33=1683, Resulting Numbers: [1683] 1683,39 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 20, 54, 26, 41 ]
72
[ "20*54=1080", "41-26=15", "1080/15=72" ]
Current State: 72:[20, 54, 26, 41], Operations: [] Exploring Operation: 20*54=1080, Resulting Numbers: [26, 41, 1080] Generated Node #2: [26, 41, 1080] from Operation: 20*54=1080 Current State: 72:[26, 41, 1080], Operations: ['20*54=1080'] Exploring Operation: 41-26=15, Resulting Numbers: [1080, 15] Generated Node #3: [1080, 15] from Operation: 41-26=15 Current State: 72:[1080, 15], Operations: ['20*54=1080', '41-26=15'] Exploring Operation: 1080/15=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[20, 54, 26, 41], Operations: [] Exploring Operation: 54-20=34, Resulting Numbers: [26, 41, 34] Generated Node #0,0: 72:[26, 41, 34] Operation: 54-20=34 Exploring Operation: 54-26=28, Resulting Numbers: [20, 41, 28] Generated Node #0,1: 72:[20, 41, 28] Operation: 54-26=28 Exploring Operation: 54+26=80, Resulting Numbers: [20, 41, 80] Generated Node #0,2: 72:[20, 41, 80] Operation: 54+26=80 Exploring Operation: 54-41=13, Resulting Numbers: [20, 26, 13] Generated Node #0,3: 72:[20, 26, 13] Operation: 54-41=13 Exploring Operation: 20+54=74, Resulting Numbers: [26, 41, 74] Generated Node #0,4: 72:[26, 41, 74] Operation: 20+54=74 Moving to Node #0,3 Current State: 72:[20, 26, 13], Operations: ['54-41=13'] Exploring Operation: 26-20=6, Resulting Numbers: [13, 6] Generated Node #0,3,0: 72:[13, 6] Operation: 26-20=6 Exploring Operation: 26/13=2, Resulting Numbers: [20, 2] Generated Node #0,3,1: 72:[20, 2] Operation: 26/13=2 Exploring Operation: 20+13=33, Resulting Numbers: [26, 33] Generated Node #0,3,2: 72:[26, 33] Operation: 20+13=33 Exploring Operation: 26-13=13, Resulting Numbers: [20, 13] Generated Node #0,3,3: 72:[20, 13] Operation: 26-13=13 Exploring Operation: 20-13=7, Resulting Numbers: [26, 7] Generated Node #0,3,4: 72:[26, 7] Operation: 20-13=7 Moving to Node #0,4 Current State: 72:[26, 41, 74], Operations: ['20+54=74'] Exploring Operation: 74-41=33, Resulting Numbers: [26, 33] Generated Node #0,4,0: 72:[26, 33] Operation: 74-41=33 Exploring Operation: 26+41=67, Resulting Numbers: [74, 67] Generated Node #0,4,1: 72:[74, 67] Operation: 26+41=67 Exploring Operation: 41-26=15, Resulting Numbers: [74, 15] Generated Node #0,4,2: 72:[74, 15] Operation: 41-26=15 Exploring Operation: 74-26=48, Resulting Numbers: [41, 48] Generated Node #0,4,3: 72:[41, 48] Operation: 74-26=48 Exploring Operation: 26+74=100, Resulting Numbers: [41, 100] Generated Node #0,4,4: 72:[41, 100] Operation: 26+74=100 Moving to Node #0,0 Current State: 72:[26, 41, 34], Operations: ['54-20=34'] Exploring Operation: 26+41=67, Resulting Numbers: [34, 67] Generated Node #0,0,0: 72:[34, 67] Operation: 26+41=67 Exploring Operation: 41+34=75, Resulting Numbers: [26, 75] Generated Node #0,0,1: 72:[26, 75] Operation: 41+34=75 Exploring Operation: 41-34=7, Resulting Numbers: [26, 7] Generated Node #0,0,2: 72:[26, 7] Operation: 41-34=7 Exploring Operation: 41-26=15, Resulting Numbers: [34, 15] Generated Node #0,0,3: 72:[34, 15] Operation: 41-26=15 Exploring Operation: 34-26=8, Resulting Numbers: [41, 8] Generated Node #0,0,4: 72:[41, 8] Operation: 34-26=8 Moving to Node #0,1 Current State: 72:[20, 41, 28], Operations: ['54-26=28'] Exploring Operation: 41-28=13, Resulting Numbers: [20, 13] Generated Node #0,1,0: 72:[20, 13] Operation: 41-28=13 Exploring Operation: 28-20=8, Resulting Numbers: [41, 8] Generated Node #0,1,1: 72:[41, 8] Operation: 28-20=8 Exploring Operation: 20+41=61, Resulting Numbers: [28, 61] Generated Node #0,1,2: 72:[28, 61] Operation: 20+41=61 Exploring Operation: 41-20=21, Resulting Numbers: [28, 21] Generated Node #0,1,3: 72:[28, 21] Operation: 41-20=21 Exploring Operation: 41+28=69, Resulting Numbers: [20, 69] Generated Node #0,1,4: 72:[20, 69] Operation: 41+28=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[20, 13], Operations: ['54-26=28', '41-28=13'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[41, 8], Operations: ['54-26=28', '28-20=8'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,72 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 72:[20, 69], Operations: ['54-26=28', '41+28=69'] Exploring Operation: 20*69=1380, Resulting Numbers: [1380] 1380,72 unequal: No Solution Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 20+69=89, Resulting Numbers: [89] 89,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 72:[28, 21], Operations: ['54-26=28', '41-20=21'] Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,72 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 72:[28, 61], Operations: ['54-26=28', '20+41=61'] Exploring Operation: 28+61=89, Resulting Numbers: [89] 89,72 unequal: No Solution Exploring Operation: 28*61=1708, Resulting Numbers: [1708] 1708,72 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,72 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: 72:[20, 41, 80], Operations: ['54+26=80'] Exploring Operation: 80-41=39, Resulting Numbers: [20, 39] Generated Node #0,2,0: 72:[20, 39] Operation: 80-41=39 Exploring Operation: 20+41=61, Resulting Numbers: [80, 61] Generated Node #0,2,1: 72:[80, 61] Operation: 20+41=61 Exploring Operation: 80-20=60, Resulting Numbers: [41, 60] Generated Node #0,2,2: 72:[41, 60] Operation: 80-20=60 Exploring Operation: 41-20=21, Resulting Numbers: [80, 21] Generated Node #0,2,3: 72:[80, 21] Operation: 41-20=21 Exploring Operation: 80/20=4, Resulting Numbers: [41, 4] Generated Node #0,2,4: 72:[41, 4] Operation: 80/20=4 Moving to Node #0,3,0 Current State: 72:[13, 6], Operations: ['54-41=13', '26-20=6'] Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,72 unequal: No Solution Moving to Node #0,3,1 Current State: 72:[20, 2], Operations: ['54-41=13', '26/13=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,72 unequal: No Solution Moving to Node #0,3,3 Current State: 72:[20, 13], Operations: ['54-41=13', '26-13=13'] Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,72 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[26, 7], Operations: ['54-20=34', '41-34=7'] Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,72 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,72 unequal: No Solution Moving to Node #0,3,4 Current State: 72:[26, 7], Operations: ['54-41=13', '20-13=7'] Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,72 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[74, 15], Operations: ['20+54=74', '41-26=15'] Exploring Operation: 74+15=89, Resulting Numbers: [89] 89,72 unequal: No Solution Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 74*15=1110, Resulting Numbers: [1110] 1110,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[41, 8], Operations: ['54-20=34', '34-26=8'] Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,72 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[26, 33], Operations: ['20+54=74', '74-41=33'] Exploring Operation: 26*33=858, Resulting Numbers: [858] 858,72 unequal: No Solution Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[34, 15], Operations: ['54-20=34', '41-26=15'] Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,72 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[26, 75], Operations: ['54-20=34', '41+34=75'] Exploring Operation: 26+75=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 26*75=1950, Resulting Numbers: [1950] 1950,72 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,72 unequal: No Solution Moving to Node #0,3,2 Current State: 72:[26, 33], Operations: ['54-41=13', '20+13=33'] Exploring Operation: 33-26=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 26+33=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 26*33=858, Resulting Numbers: [858] 858,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[20, 39], Operations: ['54+26=80', '80-41=39'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 20*39=780, Resulting Numbers: [780] 780,72 unequal: No Solution Moving to Node #0,2,4 Current State: 72:[41, 4], Operations: ['54+26=80', '80/20=4'] Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 41*4=164, Resulting Numbers: [164] 164,72 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[34, 67], Operations: ['54-20=34', '26+41=67'] Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 34+67=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 34*67=2278, Resulting Numbers: [2278] 2278,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[74, 67], Operations: ['20+54=74', '26+41=67'] Exploring Operation: 74*67=4958, Resulting Numbers: [4958] 4958,72 unequal: No Solution Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 74+67=141, Resulting Numbers: [141] 141,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[80, 21], Operations: ['54+26=80', '41-20=21'] Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,72 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[41, 60], Operations: ['54+26=80', '80-20=60'] Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 41*60=2460, Resulting Numbers: [2460] 2460,72 unequal: No Solution Exploring Operation: 41+60=101, Resulting Numbers: [101] 101,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[41, 48], Operations: ['20+54=74', '74-26=48'] Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 41*48=1968, Resulting Numbers: [1968] 1968,72 unequal: No Solution Exploring Operation: 41+48=89, Resulting Numbers: [89] 89,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[80, 61], Operations: ['54+26=80', '20+41=61'] Exploring Operation: 80-61=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 80+61=141, Resulting Numbers: [141] 141,72 unequal: No Solution Exploring Operation: 80*61=4880, Resulting Numbers: [4880] 4880,72 unequal: No Solution Moving to Node #0,4,4 Current State: 72:[41, 100], Operations: ['20+54=74', '26+74=100'] Exploring Operation: 41+100=141, Resulting Numbers: [141] 141,72 unequal: No Solution Exploring Operation: 100-41=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 41*100=4100, Resulting Numbers: [4100] 4100,72 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 32, 96, 78, 68 ]
74
[ "96-32=64", "78-68=10", "64+10=74" ]
Current State: 74:[32, 96, 78, 68], Operations: [] Exploring Operation: 96-32=64, Resulting Numbers: [78, 68, 64] Generated Node #2: [78, 68, 64] from Operation: 96-32=64 Current State: 74:[78, 68, 64], Operations: ['96-32=64'] Exploring Operation: 78-68=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 78-68=10 Current State: 74:[64, 10], Operations: ['96-32=64', '78-68=10'] Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[32, 96, 78, 68], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [78, 68, 3] Generated Node #0,0: 74:[78, 68, 3] Operation: 96/32=3 Exploring Operation: 96-32=64, Resulting Numbers: [78, 68, 64] Generated Node #0,1: 74:[78, 68, 64] Operation: 96-32=64 Exploring Operation: 96-68=28, Resulting Numbers: [32, 78, 28] Generated Node #0,2: 74:[32, 78, 28] Operation: 96-68=28 Exploring Operation: 68-32=36, Resulting Numbers: [96, 78, 36] Generated Node #0,3: 74:[96, 78, 36] Operation: 68-32=36 Moving to Node #0,0 Current State: 74:[78, 68, 3], Operations: ['96/32=3'] Exploring Operation: 78-68=10, Resulting Numbers: [3, 10] Generated Node #0,0,0: 74:[3, 10] Operation: 78-68=10 Exploring Operation: 78+3=81, Resulting Numbers: [68, 81] Generated Node #0,0,1: 74:[68, 81] Operation: 78+3=81 Exploring Operation: 78-3=75, Resulting Numbers: [68, 75] Generated Node #0,0,2: 74:[68, 75] Operation: 78-3=75 Exploring Operation: 68+3=71, Resulting Numbers: [78, 71] Generated Node #0,0,3: 74:[78, 71] Operation: 68+3=71 Moving to Node #0,2 Current State: 74:[32, 78, 28], Operations: ['96-68=28'] Exploring Operation: 32+28=60, Resulting Numbers: [78, 60] Generated Node #0,2,0: 74:[78, 60] Operation: 32+28=60 Exploring Operation: 78-32=46, Resulting Numbers: [28, 46] Generated Node #0,2,1: 74:[28, 46] Operation: 78-32=46 Exploring Operation: 78-28=50, Resulting Numbers: [32, 50] Generated Node #0,2,2: 74:[32, 50] Operation: 78-28=50 Exploring Operation: 32-28=4, Resulting Numbers: [78, 4] Generated Node #0,2,3: 74:[78, 4] Operation: 32-28=4 Moving to Node #0,1 Current State: 74:[78, 68, 64], Operations: ['96-32=64'] Exploring Operation: 68-64=4, Resulting Numbers: [78, 4] Generated Node #0,1,0: 74:[78, 4] Operation: 68-64=4 Exploring Operation: 78-64=14, Resulting Numbers: [68, 14] Generated Node #0,1,1: 74:[68, 14] Operation: 78-64=14 Exploring Operation: 68+64=132, Resulting Numbers: [78, 132] Generated Node #0,1,2: 74:[78, 132] Operation: 68+64=132 Exploring Operation: 78-68=10, Resulting Numbers: [64, 10] Generated Node #0,1,3: 74:[64, 10] Operation: 78-68=10 Moving to Node #0,3 Current State: 74:[96, 78, 36], Operations: ['68-32=36'] Exploring Operation: 96+36=132, Resulting Numbers: [78, 132] Generated Node #0,3,0: 74:[78, 132] Operation: 96+36=132 Exploring Operation: 96-36=60, Resulting Numbers: [78, 60] Generated Node #0,3,1: 74:[78, 60] Operation: 96-36=60 Exploring Operation: 96-78=18, Resulting Numbers: [36, 18] Generated Node #0,3,2: 74:[36, 18] Operation: 96-78=18 Exploring Operation: 78-36=42, Resulting Numbers: [96, 42] Generated Node #0,3,3: 74:[96, 42] Operation: 78-36=42 Moving to Node #0,2,3 Current State: 74:[78, 4], Operations: ['96-68=28', '32-28=4'] Exploring Operation: 78+4=82, Resulting Numbers: [82] 82,74 unequal: No Solution Exploring Operation: 78*4=312, Resulting Numbers: [312] 312,74 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[32, 96, 78, 68], Operations: [] Exploring Operation: 96-68=28, Resulting Numbers: [32, 78, 28] Generated Node #0,2: 74:[32, 78, 28] Operation: 96-68=28 Moving to Node #0,2 Current State: 74:[32, 78, 28], Operations: ['96-68=28'] Exploring Operation: 32-28=4, Resulting Numbers: [78, 4] Generated Node #0,2,3: 74:[78, 4] Operation: 32-28=4 Moving to Node #0,2,3 Current State: 74:[78, 4], Operations: ['96-68=28', '32-28=4'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
0.976563
hs_4
mult_heuristic
[ 95, 94, 41, 6 ]
47
[ "95-94=1", "41+6=47", "1*47=47" ]
Current State: 47:[95, 94, 41, 6], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [41, 6, 1] Generated Node #2: [41, 6, 1] from Operation: 95-94=1 Current State: 47:[41, 6, 1], Operations: ['95-94=1'] Exploring Operation: 41+6=47, Resulting Numbers: [1, 47] Generated Node #3: [1, 47] from Operation: 41+6=47 Current State: 47:[1, 47], Operations: ['95-94=1', '41+6=47'] Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[95, 94, 41, 6], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [41, 6, 1] Generated Node #0,0: 47:[41, 6, 1] Operation: 95-94=1 Exploring Operation: 95-6=89, Resulting Numbers: [94, 41, 89] Generated Node #0,1: 47:[94, 41, 89] Operation: 95-6=89 Exploring Operation: 95-41=54, Resulting Numbers: [94, 6, 54] Generated Node #0,2: 47:[94, 6, 54] Operation: 95-41=54 Moving to Node #0,0 Current State: 47:[41, 6, 1], Operations: ['95-94=1'] Exploring Operation: 41+1=42, Resulting Numbers: [6, 42] Generated Node #0,0,0: 47:[6, 42] Operation: 41+1=42 Exploring Operation: 6+1=7, Resulting Numbers: [41, 7] Generated Node #0,0,1: 47:[41, 7] Operation: 6+1=7 Exploring Operation: 41+6=47, Resulting Numbers: [1, 47] Generated Node #0,0,2: 47:[1, 47] Operation: 41+6=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[6, 42], Operations: ['95-94=1', '41+1=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,47 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:[41, 7], Operations: ['95-94=1', '6+1=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,47 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,47 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,47 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:[1, 47], Operations: ['95-94=1', '41+6=47'] Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[95, 94, 41, 6], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [41, 6, 1] Generated Node #0,0: 47:[41, 6, 1] Operation: 95-94=1 Moving to Node #0,0 Current State: 47:[41, 6, 1], Operations: ['95-94=1'] Exploring Operation: 41+6=47, Resulting Numbers: [1, 47] Generated Node #0,0,2: 47:[1, 47] Operation: 41+6=47 Moving to Node #0,0,2 Current State: 47:[1, 47], Operations: ['95-94=1', '41+6=47'] Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 56, 19, 71, 59 ]
14
[ "59-56=3", "19*3=57", "71-57=14" ]
Current State: 14:[56, 19, 71, 59], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [19, 71, 3] Generated Node #2: [19, 71, 3] from Operation: 59-56=3 Current State: 14:[19, 71, 3], Operations: ['59-56=3'] Exploring Operation: 19*3=57, Resulting Numbers: [71, 57] Generated Node #3: [71, 57] from Operation: 19*3=57 Current State: 14:[71, 57], Operations: ['59-56=3', '19*3=57'] Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[56, 19, 71, 59], Operations: [] Exploring Operation: 71-59=12, Resulting Numbers: [56, 19, 12] Generated Node #0,0: 14:[56, 19, 12] Operation: 71-59=12 Exploring Operation: 71-56=15, Resulting Numbers: [19, 59, 15] Generated Node #0,1: 14:[19, 59, 15] Operation: 71-56=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[56, 19, 12], Operations: ['71-59=12'] Exploring Operation: 56-12=44, Resulting Numbers: [19, 44] Generated Node #0,0,0: 14:[19, 44] Operation: 56-12=44 Exploring Operation: 56-19=37, Resulting Numbers: [12, 37] Generated Node #0,0,1: 14:[12, 37] Operation: 56-19=37 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[12, 37], Operations: ['71-59=12', '56-19=37'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[19, 44], Operations: ['71-59=12', '56-12=44'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[19, 59, 15], Operations: ['71-56=15'] Exploring Operation: 59-15=44, Resulting Numbers: [19, 44] Generated Node #0,1,0: 14:[19, 44] Operation: 59-15=44 Exploring Operation: 59-19=40, Resulting Numbers: [15, 40] Generated Node #0,1,1: 14:[15, 40] Operation: 59-19=40 Moving to Node #0,1,1 Current State: 14:[15, 40], Operations: ['71-56=15', '59-19=40'] Exploring Operation: 15+40=55, Resulting Numbers: [55] 55,14 unequal: No Solution Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[19, 44], Operations: ['71-56=15', '59-15=44'] Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,14 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,14 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
[ 1, 91, 73, 28 ]
45
[ "91-1=90", "73-28=45", "90-45=45" ]
Current State: 45:[1, 91, 73, 28], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [73, 28, 90] Generated Node #2: [73, 28, 90] from Operation: 91-1=90 Current State: 45:[73, 28, 90], Operations: ['91-1=90'] Exploring Operation: 73-28=45, Resulting Numbers: [90, 45] Generated Node #3: [90, 45] from Operation: 73-28=45 Current State: 45:[90, 45], Operations: ['91-1=90', '73-28=45'] Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[1, 91, 73, 28], Operations: [] Exploring Operation: 91-73=18, Resulting Numbers: [1, 28, 18] Generated Node #0,0: 45:[1, 28, 18] Operation: 91-73=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[1, 28, 18], Operations: ['91-73=18'] Exploring Operation: 28+18=46, Resulting Numbers: [1, 46] Generated Node #0,0,0: 45:[1, 46] Operation: 28+18=46 Moving to Node #0,0,0 Current State: 45:[1, 46], Operations: ['91-73=18', '28+18=46'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[1, 91, 73, 28], Operations: [] Exploring Operation: 91-73=18, Resulting Numbers: [1, 28, 18] Generated Node #0,0: 45:[1, 28, 18] Operation: 91-73=18 Moving to Node #0,0 Current State: 45:[1, 28, 18], Operations: ['91-73=18'] Exploring Operation: 28+18=46, Resulting Numbers: [1, 46] Generated Node #0,0,0: 45:[1, 46] Operation: 28+18=46 Moving to Node #0,0,0 Current State: 45:[1, 46], Operations: ['91-73=18', '28+18=46'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 72, 76, 47, 13 ]
99
[ "76-72=4", "13*4=52", "47+52=99" ]
Current State: 99:[72, 76, 47, 13], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [47, 13, 4] Generated Node #2: [47, 13, 4] from Operation: 76-72=4 Current State: 99:[47, 13, 4], Operations: ['76-72=4'] Exploring Operation: 13*4=52, Resulting Numbers: [47, 52] Generated Node #3: [47, 52] from Operation: 13*4=52 Current State: 99:[47, 52], Operations: ['76-72=4', '13*4=52'] Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[72, 76, 47, 13], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [47, 13, 4] Generated Node #0,0: 99:[47, 13, 4] Operation: 76-72=4 Moving to Node #0,0 Current State: 99:[47, 13, 4], Operations: ['76-72=4'] Exploring Operation: 47-13=34, Resulting Numbers: [4, 34] Generated Node #0,0,0: 99:[4, 34] Operation: 47-13=34 Moving to Node #0,0,0 Current State: 99:[4, 34], Operations: ['76-72=4', '47-13=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,99 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 29, 83, 17, 32 ]
69
[ "83-29=54", "32-17=15", "54+15=69" ]
Current State: 69:[29, 83, 17, 32], Operations: [] Exploring Operation: 83-29=54, Resulting Numbers: [17, 32, 54] Generated Node #2: [17, 32, 54] from Operation: 83-29=54 Current State: 69:[17, 32, 54], Operations: ['83-29=54'] Exploring Operation: 32-17=15, Resulting Numbers: [54, 15] Generated Node #3: [54, 15] from Operation: 32-17=15 Current State: 69:[54, 15], Operations: ['83-29=54', '32-17=15'] Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[29, 83, 17, 32], Operations: [] Exploring Operation: 83-17=66, Resulting Numbers: [29, 32, 66] Generated Node #0,0: 69:[29, 32, 66] Operation: 83-17=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[29, 32, 66], Operations: ['83-17=66'] Exploring Operation: 32-29=3, Resulting Numbers: [66, 3] Generated Node #0,0,0: 69:[66, 3] Operation: 32-29=3 Moving to Node #0,0,0 Current State: 69:[66, 3], Operations: ['83-17=66', '32-29=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[29, 83, 17, 32], Operations: [] Exploring Operation: 83-17=66, Resulting Numbers: [29, 32, 66] Generated Node #0,0: 69:[29, 32, 66] Operation: 83-17=66 Moving to Node #0,0 Current State: 69:[29, 32, 66], Operations: ['83-17=66'] Exploring Operation: 32-29=3, Resulting Numbers: [66, 3] Generated Node #0,0,0: 69:[66, 3] Operation: 32-29=3 Moving to Node #0,0,0 Current State: 69:[66, 3], Operations: ['83-17=66', '32-29=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 2, 6, 26, 27 ]
20
[ "26/2=13", "6+27=33", "33-13=20" ]
Current State: 20:[2, 6, 26, 27], Operations: [] Exploring Operation: 26/2=13, Resulting Numbers: [6, 27, 13] Generated Node #2: [6, 27, 13] from Operation: 26/2=13 Current State: 20:[6, 27, 13], Operations: ['26/2=13'] Exploring Operation: 6+27=33, Resulting Numbers: [13, 33] Generated Node #3: [13, 33] from Operation: 6+27=33 Current State: 20:[13, 33], Operations: ['26/2=13', '6+27=33'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[2, 6, 26, 27], Operations: [] Exploring Operation: 27-26=1, Resulting Numbers: [2, 6, 1] Generated Node #0,0: 20:[2, 6, 1] Operation: 27-26=1 Moving to Node #0,0 Current State: 20:[2, 6, 1], Operations: ['27-26=1'] Exploring Operation: 6-1=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 20:[2, 5] Operation: 6-1=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[2, 5], Operations: ['27-26=1', '6-1=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 32, 87, 85, 12 ]
22
[ "32+87=119", "85+12=97", "119-97=22" ]
Current State: 22:[32, 87, 85, 12], Operations: [] Exploring Operation: 32+87=119, Resulting Numbers: [85, 12, 119] Generated Node #2: [85, 12, 119] from Operation: 32+87=119 Current State: 22:[85, 12, 119], Operations: ['32+87=119'] Exploring Operation: 85+12=97, Resulting Numbers: [119, 97] Generated Node #3: [119, 97] from Operation: 85+12=97 Current State: 22:[119, 97], Operations: ['32+87=119', '85+12=97'] Exploring Operation: 119-97=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[32, 87, 85, 12], Operations: [] Exploring Operation: 87-32=55, Resulting Numbers: [85, 12, 55] Generated Node #0,0: 22:[85, 12, 55] Operation: 87-32=55 Exploring Operation: 87-85=2, Resulting Numbers: [32, 12, 2] Generated Node #0,1: 22:[32, 12, 2] Operation: 87-85=2 Exploring Operation: 85-32=53, Resulting Numbers: [87, 12, 53] Generated Node #0,2: 22:[87, 12, 53] Operation: 85-32=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[32, 12, 2], Operations: ['87-85=2'] Exploring Operation: 32-12=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 22:[2, 20] Operation: 32-12=20 Exploring Operation: 32/2=16, Resulting Numbers: [12, 16] Generated Node #0,1,1: 22:[12, 16] Operation: 32/2=16 Exploring Operation: 32-2=30, Resulting Numbers: [12, 30] Generated Node #0,1,2: 22:[12, 30] Operation: 32-2=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[2, 20], Operations: ['87-85=2', '32-12=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[32, 87, 85, 12], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [32, 12, 2] Generated Node #0,1: 22:[32, 12, 2] Operation: 87-85=2 Moving to Node #0,1 Current State: 22:[32, 12, 2], Operations: ['87-85=2'] Exploring Operation: 32-12=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 22:[2, 20] Operation: 32-12=20 Moving to Node #0,1,0 Current State: 22:[2, 20], Operations: ['87-85=2', '32-12=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 20, 12, 67, 69 ]
13
[ "20+67=87", "69+87=156", "156/12=13" ]
Current State: 13:[20, 12, 67, 69], Operations: [] Exploring Operation: 20+67=87, Resulting Numbers: [12, 69, 87] Generated Node #2: [12, 69, 87] from Operation: 20+67=87 Current State: 13:[12, 69, 87], Operations: ['20+67=87'] Exploring Operation: 69+87=156, Resulting Numbers: [12, 156] Generated Node #3: [12, 156] from Operation: 69+87=156 Current State: 13:[12, 156], Operations: ['20+67=87', '69+87=156'] Exploring Operation: 156/12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[20, 12, 67, 69], Operations: [] Exploring Operation: 67-12=55, Resulting Numbers: [20, 69, 55] Generated Node #0,0: 13:[20, 69, 55] Operation: 67-12=55 Exploring Operation: 67-20=47, Resulting Numbers: [12, 69, 47] Generated Node #0,1: 13:[12, 69, 47] Operation: 67-20=47 Exploring Operation: 69-20=49, Resulting Numbers: [12, 67, 49] Generated Node #0,2: 13:[12, 67, 49] Operation: 69-20=49 Exploring Operation: 69-67=2, Resulting Numbers: [20, 12, 2] Generated Node #0,3: 13:[20, 12, 2] Operation: 69-67=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[20, 12, 2], Operations: ['69-67=2'] Exploring Operation: 20/2=10, Resulting Numbers: [12, 10] Generated Node #0,3,0: 13:[12, 10] Operation: 20/2=10 Exploring Operation: 20-2=18, Resulting Numbers: [12, 18] Generated Node #0,3,1: 13:[12, 18] Operation: 20-2=18 Exploring Operation: 20+2=22, Resulting Numbers: [12, 22] Generated Node #0,3,2: 13:[12, 22] Operation: 20+2=22 Exploring Operation: 12+2=14, Resulting Numbers: [20, 14] Generated Node #0,3,3: 13:[20, 14] Operation: 12+2=14 Moving to Node #0,3,0 Current State: 13:[12, 10], Operations: ['69-67=2', '20/2=10'] Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,13 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[12, 18], Operations: ['69-67=2', '20-2=18'] Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,13 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,13 unequal: No Solution Moving to Node #0,3,3 Current State: 13:[20, 14], Operations: ['69-67=2', '12+2=14'] Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,13 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[12, 22], Operations: ['69-67=2', '20+2=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[12, 69, 47], Operations: ['67-20=47'] Exploring Operation: 69-47=22, Resulting Numbers: [12, 22] Generated Node #0,1,0: 13:[12, 22] Operation: 69-47=22 Exploring Operation: 12+69=81, Resulting Numbers: [47, 81] Generated Node #0,1,1: 13:[47, 81] Operation: 12+69=81 Exploring Operation: 47-12=35, Resulting Numbers: [69, 35] Generated Node #0,1,2: 13:[69, 35] Operation: 47-12=35 Exploring Operation: 69-12=57, Resulting Numbers: [47, 57] Generated Node #0,1,3: 13:[47, 57] Operation: 69-12=57 Moving to Node #0,1,0 Current State: 13:[12, 22], Operations: ['67-20=47', '69-47=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[47, 57], Operations: ['67-20=47', '69-12=57'] Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,13 unequal: No Solution Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[69, 35], Operations: ['67-20=47', '47-12=35'] Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,13 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[47, 81], Operations: ['67-20=47', '12+69=81'] Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 47+81=128, Resulting Numbers: [128] 128,13 unequal: No Solution Exploring Operation: 47*81=3807, Resulting Numbers: [3807] 3807,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[12, 67, 49], Operations: ['69-20=49'] Exploring Operation: 67-49=18, Resulting Numbers: [12, 18] Generated Node #0,2,0: 13:[12, 18] Operation: 67-49=18 Exploring Operation: 12+67=79, Resulting Numbers: [49, 79] Generated Node #0,2,1: 13:[49, 79] Operation: 12+67=79 Exploring Operation: 49-12=37, Resulting Numbers: [67, 37] Generated Node #0,2,2: 13:[67, 37] Operation: 49-12=37 Exploring Operation: 67-12=55, Resulting Numbers: [49, 55] Generated Node #0,2,3: 13:[49, 55] Operation: 67-12=55 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[12, 18], Operations: ['69-20=49', '67-49=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,13 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,13 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:[67, 37], Operations: ['69-20=49', '49-12=37'] Exploring Operation: 67-37=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 67*37=2479, Resulting Numbers: [2479] 2479,13 unequal: No Solution Exploring Operation: 67+37=104, Resulting Numbers: [104] 104,13 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 #0,2,3 Current State: 13:[49, 55], Operations: ['69-20=49', '67-12=55'] Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 49*55=2695, Resulting Numbers: [2695] 2695,13 unequal: No Solution Exploring Operation: 49+55=104, Resulting Numbers: [104] 104,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[49, 79], Operations: ['69-20=49', '12+67=79'] Exploring Operation: 79-49=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 49+79=128, Resulting Numbers: [128] 128,13 unequal: No Solution Exploring Operation: 49*79=3871, Resulting Numbers: [3871] 3871,13 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:[20, 69, 55], Operations: ['67-12=55'] Exploring Operation: 69-55=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 13:[20, 14] Operation: 69-55=14 Exploring Operation: 69-20=49, Resulting Numbers: [55, 49] Generated Node #0,0,1: 13:[55, 49] Operation: 69-20=49 Exploring Operation: 55-20=35, Resulting Numbers: [69, 35] Generated Node #0,0,2: 13:[69, 35] Operation: 55-20=35 Exploring Operation: 20+69=89, Resulting Numbers: [55, 89] Generated Node #0,0,3: 13:[55, 89] Operation: 20+69=89 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[20, 14], Operations: ['67-12=55', '69-55=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,13 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,13 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:[55, 49], Operations: ['67-12=55', '69-20=49'] Exploring Operation: 55+49=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 55-49=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 55*49=2695, Resulting Numbers: [2695] 2695,13 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:[69, 35], Operations: ['67-12=55', '55-20=35'] Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,13 unequal: No Solution Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,13 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 #0,0,3 Current State: 13:[55, 89], Operations: ['67-12=55', '20+69=89'] Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,13 unequal: No Solution Exploring Operation: 55+89=144, Resulting Numbers: [144] 144,13 unequal: No Solution Exploring Operation: 55*89=4895, Resulting Numbers: [4895] 4895,13 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_4
sum_heuristic
[ 21, 63, 24, 71 ]
53
[ "63-21=42", "24+71=95", "95-42=53" ]
Current State: 53:[21, 63, 24, 71], Operations: [] Exploring Operation: 63-21=42, Resulting Numbers: [24, 71, 42] Generated Node #2: [24, 71, 42] from Operation: 63-21=42 Current State: 53:[24, 71, 42], Operations: ['63-21=42'] Exploring Operation: 24+71=95, Resulting Numbers: [42, 95] Generated Node #3: [42, 95] from Operation: 24+71=95 Current State: 53:[42, 95], Operations: ['63-21=42', '24+71=95'] Exploring Operation: 95-42=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[21, 63, 24, 71], Operations: [] Exploring Operation: 71-21=50, Resulting Numbers: [63, 24, 50] Generated Node #0,0: 53:[63, 24, 50] Operation: 71-21=50 Exploring Operation: 63-21=42, Resulting Numbers: [24, 71, 42] Generated Node #0,1: 53:[24, 71, 42] Operation: 63-21=42 Exploring Operation: 21+24=45, Resulting Numbers: [63, 71, 45] Generated Node #0,2: 53:[63, 71, 45] Operation: 21+24=45 Exploring Operation: 71-24=47, Resulting Numbers: [21, 63, 47] Generated Node #0,3: 53:[21, 63, 47] Operation: 71-24=47 Moving to Node #0,2 Current State: 53:[63, 71, 45], Operations: ['21+24=45'] Exploring Operation: 63-45=18, Resulting Numbers: [71, 18] Generated Node #0,2,0: 53:[71, 18] Operation: 63-45=18 Exploring Operation: 63+45=108, Resulting Numbers: [71, 108] Generated Node #0,2,1: 53:[71, 108] Operation: 63+45=108 Exploring Operation: 71-63=8, Resulting Numbers: [45, 8] Generated Node #0,2,2: 53:[45, 8] Operation: 71-63=8 Exploring Operation: 71-45=26, Resulting Numbers: [63, 26] Generated Node #0,2,3: 53:[63, 26] Operation: 71-45=26 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 53:[63, 26], Operations: ['21+24=45', '71-45=26'] Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,53 unequal: No Solution Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[71, 18], Operations: ['21+24=45', '63-45=18'] Exploring Operation: 71*18=1278, Resulting Numbers: [1278] 1278,53 unequal: No Solution Exploring Operation: 71+18=89, Resulting Numbers: [89] 89,53 unequal: No Solution Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[21, 63, 24, 71], Operations: [] Exploring Operation: 21+24=45, Resulting Numbers: [63, 71, 45] Generated Node #0,2: 53:[63, 71, 45] Operation: 21+24=45 Moving to Node #0,2 Current State: 53:[63, 71, 45], Operations: ['21+24=45'] Exploring Operation: 63-45=18, Resulting Numbers: [71, 18] Generated Node #0,2,0: 53:[71, 18] Operation: 63-45=18 Moving to Node #0,2,0 Current State: 53:[71, 18], Operations: ['21+24=45', '63-45=18'] Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 4, 2, 51, 11 ]
16
[ "2+51=53", "11+53=64", "64/4=16" ]
Current State: 16:[4, 2, 51, 11], Operations: [] Exploring Operation: 2+51=53, Resulting Numbers: [4, 11, 53] Generated Node #2: [4, 11, 53] from Operation: 2+51=53 Current State: 16:[4, 11, 53], Operations: ['2+51=53'] Exploring Operation: 11+53=64, Resulting Numbers: [4, 64] Generated Node #3: [4, 64] from Operation: 11+53=64 Current State: 16:[4, 64], Operations: ['2+51=53', '11+53=64'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[4, 2, 51, 11], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [4, 2, 40] Generated Node #0,0: 16:[4, 2, 40] Operation: 51-11=40 Exploring Operation: 51-4=47, Resulting Numbers: [2, 11, 47] Generated Node #0,1: 16:[2, 11, 47] Operation: 51-4=47 Exploring Operation: 11-4=7, Resulting Numbers: [2, 51, 7] Generated Node #0,2: 16:[2, 51, 7] Operation: 11-4=7 Exploring Operation: 4+11=15, Resulting Numbers: [2, 51, 15] Generated Node #0,3: 16:[2, 51, 15] Operation: 4+11=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[4, 2, 40], Operations: ['51-11=40'] Exploring Operation: 40/2=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 16:[4, 20] Operation: 40/2=20 Exploring Operation: 40/4=10, Resulting Numbers: [2, 10] Generated Node #0,0,1: 16:[2, 10] Operation: 40/4=10 Exploring Operation: 40-2=38, Resulting Numbers: [4, 38] Generated Node #0,0,2: 16:[4, 38] Operation: 40-2=38 Exploring Operation: 40-4=36, Resulting Numbers: [2, 36] Generated Node #0,0,3: 16:[2, 36] Operation: 40-4=36 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[2, 10], Operations: ['51-11=40', '40/4=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,16 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,16 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 #0,0,0 Current State: 16:[4, 20], Operations: ['51-11=40', '40/2=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[4, 2, 51, 11], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [4, 2, 40] Generated Node #0,0: 16:[4, 2, 40] Operation: 51-11=40 Moving to Node #0,0 Current State: 16:[4, 2, 40], Operations: ['51-11=40'] Exploring Operation: 40/2=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 16:[4, 20] Operation: 40/2=20 Moving to Node #0,0,0 Current State: 16:[4, 20], Operations: ['51-11=40', '40/2=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 55, 21, 9, 62 ]
42
[ "55+9=64", "64-62=2", "21*2=42" ]
Current State: 42:[55, 21, 9, 62], Operations: [] Exploring Operation: 55+9=64, Resulting Numbers: [21, 62, 64] Generated Node #2: [21, 62, 64] from Operation: 55+9=64 Current State: 42:[21, 62, 64], Operations: ['55+9=64'] Exploring Operation: 64-62=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 64-62=2 Current State: 42:[21, 2], Operations: ['55+9=64', '64-62=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[55, 21, 9, 62], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [55, 9, 41] Generated Node #0,0: 42:[55, 9, 41] Operation: 62-21=41 Exploring Operation: 62-55=7, Resulting Numbers: [21, 9, 7] Generated Node #0,1: 42:[21, 9, 7] Operation: 62-55=7 Moving to Node #0,1 Current State: 42:[21, 9, 7], Operations: ['62-55=7'] Exploring Operation: 9-7=2, Resulting Numbers: [21, 2] Generated Node #0,1,0: 42:[21, 2] Operation: 9-7=2 Exploring Operation: 21-9=12, Resulting Numbers: [7, 12] Generated Node #0,1,1: 42:[7, 12] Operation: 21-9=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[21, 2], Operations: ['62-55=7', '9-7=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[55, 21, 9, 62], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [21, 9, 7] Generated Node #0,1: 42:[21, 9, 7] Operation: 62-55=7 Moving to Node #0,1 Current State: 42:[21, 9, 7], Operations: ['62-55=7'] Exploring Operation: 9-7=2, Resulting Numbers: [21, 2] Generated Node #0,1,0: 42:[21, 2] Operation: 9-7=2 Moving to Node #0,1,0 Current State: 42:[21, 2], Operations: ['62-55=7', '9-7=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 73, 80, 6, 67 ]
92
[ "73+80=153", "67-6=61", "153-61=92" ]
Current State: 92:[73, 80, 6, 67], Operations: [] Exploring Operation: 73+80=153, Resulting Numbers: [6, 67, 153] Generated Node #2: [6, 67, 153] from Operation: 73+80=153 Current State: 92:[6, 67, 153], Operations: ['73+80=153'] Exploring Operation: 67-6=61, Resulting Numbers: [153, 61] Generated Node #3: [153, 61] from Operation: 67-6=61 Current State: 92:[153, 61], Operations: ['73+80=153', '67-6=61'] Exploring Operation: 153-61=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[73, 80, 6, 67], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [80, 6, 6] Generated Node #0,0: 92:[80, 6, 6] Operation: 73-67=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[80, 6, 6], Operations: ['73-67=6'] Exploring Operation: 80+6=86, Resulting Numbers: [6, 86] Generated Node #0,0,0: 92:[6, 86] Operation: 80+6=86 Moving to Node #0,0,0 Current State: 92:[6, 86], Operations: ['73-67=6', '80+6=86'] Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[73, 80, 6, 67], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [80, 6, 6] Generated Node #0,0: 92:[80, 6, 6] Operation: 73-67=6 Moving to Node #0,0 Current State: 92:[80, 6, 6], Operations: ['73-67=6'] Exploring Operation: 80+6=86, Resulting Numbers: [6, 86] Generated Node #0,0,0: 92:[6, 86] Operation: 80+6=86 Moving to Node #0,0,0 Current State: 92:[6, 86], Operations: ['73-67=6', '80+6=86'] Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 41, 40, 9, 21 ]
69
[ "41+40=81", "21-9=12", "81-12=69" ]
Current State: 69:[41, 40, 9, 21], Operations: [] Exploring Operation: 41+40=81, Resulting Numbers: [9, 21, 81] Generated Node #2: [9, 21, 81] from Operation: 41+40=81 Current State: 69:[9, 21, 81], Operations: ['41+40=81'] Exploring Operation: 21-9=12, Resulting Numbers: [81, 12] Generated Node #3: [81, 12] from Operation: 21-9=12 Current State: 69:[81, 12], Operations: ['41+40=81', '21-9=12'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[41, 40, 9, 21], Operations: [] Exploring Operation: 41-40=1, Resulting Numbers: [9, 21, 1] Generated Node #0,0: 69:[9, 21, 1] Operation: 41-40=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[9, 21, 1], Operations: ['41-40=1'] Exploring Operation: 9-1=8, Resulting Numbers: [21, 8] Generated Node #0,0,0: 69:[21, 8] Operation: 9-1=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[21, 8], Operations: ['41-40=1', '9-1=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 33, 75, 11, 23 ]
95
[ "33/11=3", "75+23=98", "98-3=95" ]
Current State: 95:[33, 75, 11, 23], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [75, 23, 3] Generated Node #2: [75, 23, 3] from Operation: 33/11=3 Current State: 95:[75, 23, 3], Operations: ['33/11=3'] Exploring Operation: 75+23=98, Resulting Numbers: [3, 98] Generated Node #3: [3, 98] from Operation: 75+23=98 Current State: 95:[3, 98], Operations: ['33/11=3', '75+23=98'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[33, 75, 11, 23], Operations: [] Exploring Operation: 75+11=86, Resulting Numbers: [33, 23, 86] Generated Node #0,0: 95:[33, 23, 86] Operation: 75+11=86 Exploring Operation: 33-11=22, Resulting Numbers: [75, 23, 22] Generated Node #0,1: 95:[75, 23, 22] Operation: 33-11=22 Exploring Operation: 75+23=98, Resulting Numbers: [33, 11, 98] Generated Node #0,2: 95:[33, 11, 98] Operation: 75+23=98 Exploring Operation: 33+75=108, Resulting Numbers: [11, 23, 108] Generated Node #0,3: 95:[11, 23, 108] Operation: 33+75=108 Exploring Operation: 33/11=3, Resulting Numbers: [75, 23, 3] Generated Node #0,4: 95:[75, 23, 3] Operation: 33/11=3 Moving to Node #0,2 Current State: 95:[33, 11, 98], Operations: ['75+23=98'] Exploring Operation: 33/11=3, Resulting Numbers: [98, 3] Generated Node #0,2,0: 95:[98, 3] Operation: 33/11=3 Exploring Operation: 33-11=22, Resulting Numbers: [98, 22] Generated Node #0,2,1: 95:[98, 22] Operation: 33-11=22 Exploring Operation: 98-11=87, Resulting Numbers: [33, 87] Generated Node #0,2,2: 95:[33, 87] Operation: 98-11=87 Exploring Operation: 11+98=109, Resulting Numbers: [33, 109] Generated Node #0,2,3: 95:[33, 109] Operation: 11+98=109 Exploring Operation: 33+11=44, Resulting Numbers: [98, 44] Generated Node #0,2,4: 95:[98, 44] Operation: 33+11=44 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[98, 3], Operations: ['75+23=98', '33/11=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[33, 75, 11, 23], Operations: [] Exploring Operation: 75+23=98, Resulting Numbers: [33, 11, 98] Generated Node #0,2: 95:[33, 11, 98] Operation: 75+23=98 Moving to Node #0,2 Current State: 95:[33, 11, 98], Operations: ['75+23=98'] Exploring Operation: 33/11=3, Resulting Numbers: [98, 3] Generated Node #0,2,0: 95:[98, 3] Operation: 33/11=3 Moving to Node #0,2,0 Current State: 95:[98, 3], Operations: ['75+23=98', '33/11=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 78, 64, 78, 46 ]
80
[ "78-46=32", "64/32=2", "78+2=80" ]
Current State: 80:[78, 64, 78, 46], Operations: [] Exploring Operation: 78-46=32, Resulting Numbers: [64, 32] Generated Node #2: [64, 32] from Operation: 78-46=32 Current State: 80:[64, 32], Operations: ['78-46=32'] Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,80 equal: Goal Reached Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[78, 64, 78, 46], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [78, 78, 18] Generated Node #0,0: 80:[78, 78, 18] Operation: 64-46=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[78, 78, 18], Operations: ['64-46=18'] Exploring Operation: 78/78=1, Resulting Numbers: [18, 1] Generated Node #0,0,0: 80:[18, 1] Operation: 78/78=1 Moving to Node #0,0,0 Current State: 80:[18, 1], Operations: ['64-46=18', '78/78=1'] Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 94, 24, 91, 2 ]
68
[ "94/2=47", "24+91=115", "115-47=68" ]
Current State: 68:[94, 24, 91, 2], Operations: [] Exploring Operation: 94/2=47, Resulting Numbers: [24, 91, 47] Generated Node #2: [24, 91, 47] from Operation: 94/2=47 Current State: 68:[24, 91, 47], Operations: ['94/2=47'] Exploring Operation: 24+91=115, Resulting Numbers: [47, 115] Generated Node #3: [47, 115] from Operation: 24+91=115 Current State: 68:[47, 115], Operations: ['94/2=47', '24+91=115'] Exploring Operation: 115-47=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[94, 24, 91, 2], Operations: [] Exploring Operation: 94-24=70, Resulting Numbers: [91, 2, 70] Generated Node #0,0: 68:[91, 2, 70] Operation: 94-24=70 Exploring Operation: 91-24=67, Resulting Numbers: [94, 2, 67] Generated Node #0,1: 68:[94, 2, 67] Operation: 91-24=67 Exploring Operation: 94-91=3, Resulting Numbers: [24, 2, 3] Generated Node #0,2: 68:[24, 2, 3] Operation: 94-91=3 Moving to Node #0,2 Current State: 68:[24, 2, 3], Operations: ['94-91=3'] Exploring Operation: 24*3=72, Resulting Numbers: [2, 72] Generated Node #0,2,0: 68:[2, 72] Operation: 24*3=72 Exploring Operation: 24/3=8, Resulting Numbers: [2, 8] Generated Node #0,2,1: 68:[2, 8] Operation: 24/3=8 Exploring Operation: 24-3=21, Resulting Numbers: [2, 21] Generated Node #0,2,2: 68:[2, 21] Operation: 24-3=21 Moving to Node #0,0 Current State: 68:[91, 2, 70], Operations: ['94-24=70'] Exploring Operation: 91-70=21, Resulting Numbers: [2, 21] Generated Node #0,0,0: 68:[2, 21] Operation: 91-70=21 Exploring Operation: 70-2=68, Resulting Numbers: [91, 68] Generated Node #0,0,1: 68:[91, 68] Operation: 70-2=68 Exploring Operation: 91-2=89, Resulting Numbers: [70, 89] Generated Node #0,0,2: 68:[70, 89] Operation: 91-2=89 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[2, 21], Operations: ['94-24=70', '91-70=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,68 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 #0,0,1 Current State: 68:[91, 68], Operations: ['94-24=70', '70-2=68'] Exploring Operation: 91*68=6188, Resulting Numbers: [6188] 6188,68 unequal: No Solution Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 91+68=159, Resulting Numbers: [159] 159,68 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:[70, 89], Operations: ['94-24=70', '91-2=89'] Exploring Operation: 70*89=6230, Resulting Numbers: [6230] 6230,68 unequal: No Solution Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 70+89=159, Resulting Numbers: [159] 159,68 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:[94, 2, 67], Operations: ['91-24=67'] Exploring Operation: 94-2=92, Resulting Numbers: [67, 92] Generated Node #0,1,0: 68:[67, 92] Operation: 94-2=92 Exploring Operation: 94-67=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 68:[2, 27] Operation: 94-67=27 Exploring Operation: 94/2=47, Resulting Numbers: [67, 47] Generated Node #0,1,2: 68:[67, 47] Operation: 94/2=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 68:[2, 27], Operations: ['91-24=67', '94-67=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,68 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,68 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 #0,1,2 Current State: 68:[67, 47], Operations: ['91-24=67', '94/2=47'] Exploring Operation: 67-47=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 67+47=114, Resulting Numbers: [114] 114,68 unequal: No Solution Exploring Operation: 67*47=3149, Resulting Numbers: [3149] 3149,68 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 #0,1,0 Current State: 68:[67, 92], Operations: ['91-24=67', '94-2=92'] Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 67*92=6164, Resulting Numbers: [6164] 6164,68 unequal: No Solution Exploring Operation: 67+92=159, Resulting Numbers: [159] 159,68 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: 68:[2, 72], Operations: ['94-91=3', '24*3=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,68 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[2, 8], Operations: ['94-91=3', '24/3=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[2, 21], Operations: ['94-91=3', '24-3=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,68 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,68 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 85, 58, 2, 92 ]
44
[ "92-85=7", "2*7=14", "58-14=44" ]
Current State: 44:[85, 58, 2, 92], Operations: [] Exploring Operation: 92-85=7, Resulting Numbers: [58, 2, 7] Generated Node #2: [58, 2, 7] from Operation: 92-85=7 Current State: 44:[58, 2, 7], Operations: ['92-85=7'] Exploring Operation: 2*7=14, Resulting Numbers: [58, 14] Generated Node #3: [58, 14] from Operation: 2*7=14 Current State: 44:[58, 14], Operations: ['92-85=7', '2*7=14'] Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[85, 58, 2, 92], Operations: [] Exploring Operation: 92-85=7, Resulting Numbers: [58, 2, 7] Generated Node #0,0: 44:[58, 2, 7] Operation: 92-85=7 Exploring Operation: 92-58=34, Resulting Numbers: [85, 2, 34] Generated Node #0,1: 44:[85, 2, 34] Operation: 92-58=34 Exploring Operation: 92/2=46, Resulting Numbers: [85, 58, 46] Generated Node #0,2: 44:[85, 58, 46] Operation: 92/2=46 Exploring Operation: 85-58=27, Resulting Numbers: [2, 92, 27] Generated Node #0,3: 44:[2, 92, 27] Operation: 85-58=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[58, 2, 7], Operations: ['92-85=7'] Exploring Operation: 7-2=5, Resulting Numbers: [58, 5] Generated Node #0,0,0: 44:[58, 5] Operation: 7-2=5 Exploring Operation: 58-7=51, Resulting Numbers: [2, 51] Generated Node #0,0,1: 44:[2, 51] Operation: 58-7=51 Exploring Operation: 58-2=56, Resulting Numbers: [7, 56] Generated Node #0,0,2: 44:[7, 56] Operation: 58-2=56 Exploring Operation: 58/2=29, Resulting Numbers: [7, 29] Generated Node #0,0,3: 44:[7, 29] Operation: 58/2=29 Moving to Node #0,0,1 Current State: 44:[2, 51], Operations: ['92-85=7', '58-7=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,44 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,44 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,44 unequal: No Solution Moving to Node #0,0,3 Current State: 44:[7, 29], Operations: ['92-85=7', '58/2=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,44 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,44 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[7, 56], Operations: ['92-85=7', '58-2=56'] Exploring Operation: 7*56=392, Resulting Numbers: [392] 392,44 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[58, 5], Operations: ['92-85=7', '7-2=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,44 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,44 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[85, 2, 34], Operations: ['92-58=34'] Exploring Operation: 34/2=17, Resulting Numbers: [85, 17] Generated Node #0,1,0: 44:[85, 17] Operation: 34/2=17 Exploring Operation: 2+34=36, Resulting Numbers: [85, 36] Generated Node #0,1,1: 44:[85, 36] Operation: 2+34=36 Exploring Operation: 85-2=83, Resulting Numbers: [34, 83] Generated Node #0,1,2: 44:[34, 83] Operation: 85-2=83 Exploring Operation: 85-34=51, Resulting Numbers: [2, 51] Generated Node #0,1,3: 44:[2, 51] Operation: 85-34=51 Moving to Node #0,1,3 Current State: 44:[2, 51], Operations: ['92-58=34', '85-34=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,44 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,44 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[85, 17], Operations: ['92-58=34', '34/2=17'] Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 85+17=102, Resulting Numbers: [102] 102,44 unequal: No Solution Exploring Operation: 85-17=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 85*17=1445, Resulting Numbers: [1445] 1445,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[34, 83], Operations: ['92-58=34', '85-2=83'] Exploring Operation: 34+83=117, Resulting Numbers: [117] 117,44 unequal: No Solution Exploring Operation: 34*83=2822, Resulting Numbers: [2822] 2822,44 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[85, 36], Operations: ['92-58=34', '2+34=36'] Exploring Operation: 85-36=49, Resulting Numbers: [49] 49,44 unequal: No Solution Exploring Operation: 85*36=3060, Resulting Numbers: [3060] 3060,44 unequal: No Solution Exploring Operation: 85+36=121, Resulting Numbers: [121] 121,44 unequal: No Solution No 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: 44:[2, 92, 27], Operations: ['85-58=27'] Exploring Operation: 92/2=46, Resulting Numbers: [27, 46] Generated Node #0,3,0: 44:[27, 46] Operation: 92/2=46 Exploring Operation: 92-27=65, Resulting Numbers: [2, 65] Generated Node #0,3,1: 44:[2, 65] Operation: 92-27=65 Exploring Operation: 92-2=90, Resulting Numbers: [27, 90] Generated Node #0,3,2: 44:[27, 90] Operation: 92-2=90 Exploring Operation: 27-2=25, Resulting Numbers: [92, 25] Generated Node #0,3,3: 44:[92, 25] Operation: 27-2=25 Moving to Node #0,3,0 Current State: 44:[27, 46], Operations: ['85-58=27', '92/2=46'] Exploring Operation: 27*46=1242, Resulting Numbers: [1242] 1242,44 unequal: No Solution Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[2, 65], Operations: ['85-58=27', '92-27=65'] Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,44 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[92, 25], Operations: ['85-58=27', '27-2=25'] Exploring Operation: 92+25=117, Resulting Numbers: [117] 117,44 unequal: No Solution Exploring Operation: 92*25=2300, Resulting Numbers: [2300] 2300,44 unequal: No Solution Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[27, 90], Operations: ['85-58=27', '92-2=90'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 27+90=117, Resulting Numbers: [117] 117,44 unequal: No Solution Exploring Operation: 27*90=2430, Resulting Numbers: [2430] 2430,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[85, 58, 46], Operations: ['92/2=46'] Exploring Operation: 85-46=39, Resulting Numbers: [58, 39] Generated Node #0,2,0: 44:[58, 39] Operation: 85-46=39 Exploring Operation: 58-46=12, Resulting Numbers: [85, 12] Generated Node #0,2,1: 44:[85, 12] Operation: 58-46=12 Exploring Operation: 85-58=27, Resulting Numbers: [46, 27] Generated Node #0,2,2: 44:[46, 27] Operation: 85-58=27 Exploring Operation: 85+58=143, Resulting Numbers: [46, 143] Generated Node #0,2,3: 44:[46, 143] Operation: 85+58=143 Moving to Node #0,2,2 Current State: 44:[46, 27], Operations: ['92/2=46', '85-58=27'] Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,44 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[58, 39], Operations: ['92/2=46', '85-46=39'] Exploring Operation: 58+39=97, Resulting Numbers: [97] 97,44 unequal: No Solution Exploring Operation: 58*39=2262, Resulting Numbers: [2262] 2262,44 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[85, 12], Operations: ['92/2=46', '58-46=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 85*12=1020, Resulting Numbers: [1020] 1020,44 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[46, 143], Operations: ['92/2=46', '85+58=143'] Exploring Operation: 46*143=6578, Resulting Numbers: [6578] 6578,44 unequal: No Solution Exploring Operation: 143-46=97, Resulting Numbers: [97] 97,44 unequal: No Solution Exploring Operation: 46+143=189, Resulting Numbers: [189] 189,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 89, 45, 24, 22 ]
48
[ "89-45=44", "24*44=1056", "1056/22=48" ]
Current State: 48:[89, 45, 24, 22], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [24, 22, 44] Generated Node #2: [24, 22, 44] from Operation: 89-45=44 Current State: 48:[24, 22, 44], Operations: ['89-45=44'] Exploring Operation: 24*44=1056, Resulting Numbers: [22, 1056] Generated Node #3: [22, 1056] from Operation: 24*44=1056 Current State: 48:[22, 1056], Operations: ['89-45=44', '24*44=1056'] Exploring Operation: 1056/22=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[89, 45, 24, 22], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [24, 22, 44] Generated Node #0,0: 48:[24, 22, 44] Operation: 89-45=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[24, 22, 44], Operations: ['89-45=44'] Exploring Operation: 44/22=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 48:[24, 2] Operation: 44/22=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[24, 2], Operations: ['89-45=44', '44/22=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[89, 45, 24, 22], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [24, 22, 44] Generated Node #0,0: 48:[24, 22, 44] Operation: 89-45=44 Moving to Node #0,0 Current State: 48:[24, 22, 44], Operations: ['89-45=44'] Exploring Operation: 44/22=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 48:[24, 2] Operation: 44/22=2 Moving to Node #0,0,0 Current State: 48:[24, 2], Operations: ['89-45=44', '44/22=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 9, 20, 18, 72 ]
94
[ "18/9=2", "20+72=92", "2+92=94" ]
Current State: 94:[9, 20, 18, 72], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [20, 72, 2] Generated Node #2: [20, 72, 2] from Operation: 18/9=2 Current State: 94:[20, 72, 2], Operations: ['18/9=2'] Exploring Operation: 20+72=92, Resulting Numbers: [2, 92] Generated Node #3: [2, 92] from Operation: 20+72=92 Current State: 94:[2, 92], Operations: ['18/9=2', '20+72=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[9, 20, 18, 72], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [9, 20, 4] Generated Node #0,0: 94:[9, 20, 4] Operation: 72/18=4 Exploring Operation: 72-20=52, Resulting Numbers: [9, 18, 52] Generated Node #0,1: 94:[9, 18, 52] Operation: 72-20=52 Exploring Operation: 20+72=92, Resulting Numbers: [9, 18, 92] Generated Node #0,2: 94:[9, 18, 92] Operation: 20+72=92 Moving to Node #0,2 Current State: 94:[9, 18, 92], Operations: ['20+72=92'] Exploring Operation: 9+18=27, Resulting Numbers: [92, 27] Generated Node #0,2,0: 94:[92, 27] Operation: 9+18=27 Exploring Operation: 18-9=9, Resulting Numbers: [92, 9] Generated Node #0,2,1: 94:[92, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [92, 2] Generated Node #0,2,2: 94:[92, 2] Operation: 18/9=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[92, 2], Operations: ['20+72=92', '18/9=2'] Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,94 unequal: No Solution Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[9, 20, 18, 72], Operations: [] Exploring Operation: 20+72=92, Resulting Numbers: [9, 18, 92] Generated Node #0,2: 94:[9, 18, 92] Operation: 20+72=92 Moving to Node #0,2 Current State: 94:[9, 18, 92], Operations: ['20+72=92'] Exploring Operation: 18/9=2, Resulting Numbers: [92, 2] Generated Node #0,2,2: 94:[92, 2] Operation: 18/9=2 Moving to Node #0,2,2 Current State: 94:[92, 2], Operations: ['20+72=92', '18/9=2'] Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 30, 56, 30, 94 ]
90
[ "56-30=26", "94-30=64", "26+64=90" ]
Current State: 90:[30, 56, 30, 94], Operations: [] Exploring Operation: 56-30=26, Resulting Numbers: [94, 26] Generated Node #2: [94, 26] from Operation: 56-30=26 Current State: 90:[94, 26], Operations: ['56-30=26'] Exploring Operation: 94-30=64, Resulting Numbers: [26, 64] Generated Node #3: [26, 64] from Operation: 94-30=64 Current State: 90:[26, 64], Operations: ['56-30=26', '94-30=64'] Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[30, 56, 30, 94], Operations: [] Exploring Operation: 94-56=38, Resulting Numbers: [30, 30, 38] Generated Node #0,0: 90:[30, 30, 38] Operation: 94-56=38 Exploring Operation: 30+56=86, Resulting Numbers: [30, 94, 86] Generated Node #0,1: 90:[30, 94, 86] Operation: 30+56=86 Moving to Node #0,0 Current State: 90:[30, 30, 38], Operations: ['94-56=38'] Exploring Operation: 38-30=8, Resulting Numbers: [30, 8] Generated Node #0,0,0: 90:[30, 8] Operation: 38-30=8 Exploring Operation: 38-30=8, Resulting Numbers: [30, 8] Generated Node #0,0,1: 90:[30, 8] Operation: 38-30=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[30, 8], Operations: ['94-56=38', '38-30=8'] Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[30, 8], Operations: ['94-56=38', '38-30=8'] Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,90 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: 90:[30, 94, 86], Operations: ['30+56=86'] Exploring Operation: 86-30=56, Resulting Numbers: [94, 56] Generated Node #0,1,0: 90:[94, 56] Operation: 86-30=56 Exploring Operation: 94-86=8, Resulting Numbers: [30, 8] Generated Node #0,1,1: 90:[30, 8] Operation: 94-86=8 Moving to Node #0,1,1 Current State: 90:[30, 8], Operations: ['30+56=86', '94-86=8'] Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,90 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[94, 56], Operations: ['30+56=86', '86-30=56'] Exploring Operation: 94+56=150, Resulting Numbers: [150] 150,90 unequal: No Solution Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,90 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 38, 23, 97, 63 ]
92
[ "97-38=59", "63-59=4", "23*4=92" ]
Current State: 92:[38, 23, 97, 63], Operations: [] Exploring Operation: 97-38=59, Resulting Numbers: [23, 63, 59] Generated Node #2: [23, 63, 59] from Operation: 97-38=59 Current State: 92:[23, 63, 59], Operations: ['97-38=59'] Exploring Operation: 63-59=4, Resulting Numbers: [23, 4] Generated Node #3: [23, 4] from Operation: 63-59=4 Current State: 92:[23, 4], Operations: ['97-38=59', '63-59=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[38, 23, 97, 63], Operations: [] Exploring Operation: 38+63=101, Resulting Numbers: [23, 97, 101] Generated Node #0,0: 92:[23, 97, 101] Operation: 38+63=101 Exploring Operation: 63-38=25, Resulting Numbers: [23, 97, 25] Generated Node #0,1: 92:[23, 97, 25] Operation: 63-38=25 Exploring Operation: 23+63=86, Resulting Numbers: [38, 97, 86] Generated Node #0,2: 92:[38, 97, 86] Operation: 23+63=86 Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[23, 97, 25], Operations: ['63-38=25'] Exploring Operation: 25-23=2, Resulting Numbers: [97, 2] Generated Node #0,1,0: 92:[97, 2] Operation: 25-23=2 Exploring Operation: 23+25=48, Resulting Numbers: [97, 48] Generated Node #0,1,1: 92:[97, 48] Operation: 23+25=48 Exploring Operation: 97-23=74, Resulting Numbers: [25, 74] Generated Node #0,1,2: 92:[25, 74] Operation: 97-23=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 92:[97, 2], Operations: ['63-38=25', '25-23=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,92 unequal: No Solution Exploring Operation: 97*2=194, Resulting Numbers: [194] 194,92 unequal: No Solution Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,92 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:[97, 48], Operations: ['63-38=25', '23+25=48'] Exploring Operation: 97-48=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 97*48=4656, Resulting Numbers: [4656] 4656,92 unequal: No Solution Exploring Operation: 97+48=145, Resulting Numbers: [145] 145,92 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:[25, 74], Operations: ['63-38=25', '97-23=74'] Exploring Operation: 25*74=1850, Resulting Numbers: [1850] 1850,92 unequal: No Solution Exploring Operation: 25+74=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 74-25=49, Resulting Numbers: [49] 49,92 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:[23, 97, 101], Operations: ['38+63=101'] Exploring Operation: 101-23=78, Resulting Numbers: [97, 78] Generated Node #0,0,0: 92:[97, 78] Operation: 101-23=78 Exploring Operation: 97-23=74, Resulting Numbers: [101, 74] Generated Node #0,0,1: 92:[101, 74] Operation: 97-23=74 Exploring Operation: 101-97=4, Resulting Numbers: [23, 4] Generated Node #0,0,2: 92:[23, 4] Operation: 101-97=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 92:[23, 4], Operations: ['38+63=101', '101-97=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[38, 23, 97, 63], Operations: [] Exploring Operation: 38+63=101, Resulting Numbers: [23, 97, 101] Generated Node #0,0: 92:[23, 97, 101] Operation: 38+63=101 Moving to Node #0,0 Current State: 92:[23, 97, 101], Operations: ['38+63=101'] Exploring Operation: 101-97=4, Resulting Numbers: [23, 4] Generated Node #0,0,2: 92:[23, 4] Operation: 101-97=4 Moving to Node #0,0,2 Current State: 92:[23, 4], Operations: ['38+63=101', '101-97=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 49, 18, 64, 72 ]
95
[ "72-64=8", "18*8=144", "144-49=95" ]
Current State: 95:[49, 18, 64, 72], Operations: [] Exploring Operation: 72-64=8, Resulting Numbers: [49, 18, 8] Generated Node #2: [49, 18, 8] from Operation: 72-64=8 Current State: 95:[49, 18, 8], Operations: ['72-64=8'] Exploring Operation: 18*8=144, Resulting Numbers: [49, 144] Generated Node #3: [49, 144] from Operation: 18*8=144 Current State: 95:[49, 144], Operations: ['72-64=8', '18*8=144'] Exploring Operation: 144-49=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[49, 18, 64, 72], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [18, 72, 15] Generated Node #0,0: 95:[18, 72, 15] Operation: 64-49=15 Exploring Operation: 72-64=8, Resulting Numbers: [49, 18, 8] Generated Node #0,1: 95:[49, 18, 8] Operation: 72-64=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[18, 72, 15], Operations: ['64-49=15'] Exploring Operation: 72/18=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 95:[15, 4] Operation: 72/18=4 Exploring Operation: 18+72=90, Resulting Numbers: [15, 90] Generated Node #0,0,1: 95:[15, 90] Operation: 18+72=90 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[15, 4], Operations: ['64-49=15', '72/18=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[15, 90], Operations: ['64-49=15', '18+72=90'] Exploring Operation: 90/15=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 15+90=105, Resulting Numbers: [105] 105,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[49, 18, 8], Operations: ['72-64=8'] Exploring Operation: 49-8=41, Resulting Numbers: [18, 41] Generated Node #0,1,0: 95:[18, 41] Operation: 49-8=41 Exploring Operation: 49-18=31, Resulting Numbers: [8, 31] Generated Node #0,1,1: 95:[8, 31] Operation: 49-18=31 Moving to Node #0,1,1 Current State: 95:[8, 31], Operations: ['72-64=8', '49-18=31'] Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[18, 41], Operations: ['72-64=8', '49-8=41'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,95 unequal: No Solution Exploring Operation: 18+41=59, Resulting Numbers: [59] 59,95 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
[ 60, 43, 48, 44 ]
98
[ "60*44=2640", "2640/48=55", "43+55=98" ]
Current State: 98:[60, 43, 48, 44], Operations: [] Exploring Operation: 60*44=2640, Resulting Numbers: [43, 48, 2640] Generated Node #2: [43, 48, 2640] from Operation: 60*44=2640 Current State: 98:[43, 48, 2640], Operations: ['60*44=2640'] Exploring Operation: 2640/48=55, Resulting Numbers: [43, 55] Generated Node #3: [43, 55] from Operation: 2640/48=55 Current State: 98:[43, 55], Operations: ['60*44=2640', '2640/48=55'] Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[60, 43, 48, 44], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [43, 48, 16] Generated Node #0,0: 98:[43, 48, 16] Operation: 60-44=16 Exploring Operation: 60-43=17, Resulting Numbers: [48, 44, 17] Generated Node #0,1: 98:[48, 44, 17] Operation: 60-43=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[43, 48, 16], Operations: ['60-44=16'] Exploring Operation: 48/16=3, Resulting Numbers: [43, 3] Generated Node #0,0,0: 98:[43, 3] Operation: 48/16=3 Exploring Operation: 48-43=5, Resulting Numbers: [16, 5] Generated Node #0,0,1: 98:[16, 5] Operation: 48-43=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[16, 5], Operations: ['60-44=16', '48-43=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,98 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[43, 3], Operations: ['60-44=16', '48/16=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,98 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[48, 44, 17], Operations: ['60-43=17'] Exploring Operation: 48+44=92, Resulting Numbers: [17, 92] Generated Node #0,1,0: 98:[17, 92] Operation: 48+44=92 Exploring Operation: 48-44=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 98:[17, 4] Operation: 48-44=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[17, 4], Operations: ['60-43=17', '48-44=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[17, 92], Operations: ['60-43=17', '48+44=92'] Exploring Operation: 92-17=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 17+92=109, Resulting Numbers: [109] 109,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 18, 37, 61, 40 ]
30
[ "18*40=720", "61-37=24", "720/24=30" ]
Current State: 30:[18, 37, 61, 40], Operations: [] Exploring Operation: 18*40=720, Resulting Numbers: [37, 61, 720] Generated Node #2: [37, 61, 720] from Operation: 18*40=720 Current State: 30:[37, 61, 720], Operations: ['18*40=720'] Exploring Operation: 61-37=24, Resulting Numbers: [720, 24] Generated Node #3: [720, 24] from Operation: 61-37=24 Current State: 30:[720, 24], Operations: ['18*40=720', '61-37=24'] Exploring Operation: 720/24=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[18, 37, 61, 40], Operations: [] Exploring Operation: 61-37=24, Resulting Numbers: [18, 40, 24] Generated Node #0,0: 30:[18, 40, 24] Operation: 61-37=24 Exploring Operation: 61-40=21, Resulting Numbers: [18, 37, 21] Generated Node #0,1: 30:[18, 37, 21] Operation: 61-40=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[18, 37, 21], Operations: ['61-40=21'] Exploring Operation: 37-21=16, Resulting Numbers: [18, 16] Generated Node #0,1,0: 30:[18, 16] Operation: 37-21=16 Exploring Operation: 21-18=3, Resulting Numbers: [37, 3] Generated Node #0,1,1: 30:[37, 3] Operation: 21-18=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[18, 16], Operations: ['61-40=21', '37-21=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,30 unequal: No Solution No 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: 30:[37, 3], Operations: ['61-40=21', '21-18=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,30 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: 30:[18, 40, 24], Operations: ['61-37=24'] Exploring Operation: 24-18=6, Resulting Numbers: [40, 6] Generated Node #0,0,0: 30:[40, 6] Operation: 24-18=6 Exploring Operation: 40-24=16, Resulting Numbers: [18, 16] Generated Node #0,0,1: 30:[18, 16] Operation: 40-24=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[18, 16], Operations: ['61-37=24', '40-24=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,30 unequal: No Solution No 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: 30:[40, 6], Operations: ['61-37=24', '24-18=6'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 65, 42, 51, 94 ]
66
[ "65-42=23", "94-51=43", "23+43=66" ]
Current State: 66:[65, 42, 51, 94], Operations: [] Exploring Operation: 65-42=23, Resulting Numbers: [51, 94, 23] Generated Node #2: [51, 94, 23] from Operation: 65-42=23 Current State: 66:[51, 94, 23], Operations: ['65-42=23'] Exploring Operation: 94-51=43, Resulting Numbers: [23, 43] Generated Node #3: [23, 43] from Operation: 94-51=43 Current State: 66:[23, 43], Operations: ['65-42=23', '94-51=43'] Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[65, 42, 51, 94], Operations: [] Exploring Operation: 51-42=9, Resulting Numbers: [65, 94, 9] Generated Node #0,0: 66:[65, 94, 9] Operation: 51-42=9 Exploring Operation: 94-42=52, Resulting Numbers: [65, 51, 52] Generated Node #0,1: 66:[65, 51, 52] Operation: 94-42=52 Exploring Operation: 94-65=29, Resulting Numbers: [42, 51, 29] Generated Node #0,2: 66:[42, 51, 29] Operation: 94-65=29 Exploring Operation: 94-51=43, Resulting Numbers: [65, 42, 43] Generated Node #0,3: 66:[65, 42, 43] Operation: 94-51=43 Moving to Node #0,3 Current State: 66:[65, 42, 43], Operations: ['94-51=43'] Exploring Operation: 65-43=22, Resulting Numbers: [42, 22] Generated Node #0,3,0: 66:[42, 22] Operation: 65-43=22 Exploring Operation: 43-42=1, Resulting Numbers: [65, 1] Generated Node #0,3,1: 66:[65, 1] Operation: 43-42=1 Exploring Operation: 65-42=23, Resulting Numbers: [43, 23] Generated Node #0,3,2: 66:[43, 23] Operation: 65-42=23 Exploring Operation: 42+43=85, Resulting Numbers: [65, 85] Generated Node #0,3,3: 66:[65, 85] Operation: 42+43=85 Moving to Node #0,2 Current State: 66:[42, 51, 29], Operations: ['94-65=29'] Exploring Operation: 51-42=9, Resulting Numbers: [29, 9] Generated Node #0,2,0: 66:[29, 9] Operation: 51-42=9 Exploring Operation: 42+29=71, Resulting Numbers: [51, 71] Generated Node #0,2,1: 66:[51, 71] Operation: 42+29=71 Exploring Operation: 51-29=22, Resulting Numbers: [42, 22] Generated Node #0,2,2: 66:[42, 22] Operation: 51-29=22 Exploring Operation: 42-29=13, Resulting Numbers: [51, 13] Generated Node #0,2,3: 66:[51, 13] Operation: 42-29=13 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[29, 9], Operations: ['94-65=29', '51-42=9'] Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,66 unequal: No Solution Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,66 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,66 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 #0,2,2 Current State: 66:[42, 22], Operations: ['94-65=29', '51-29=22'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,66 unequal: No Solution Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,66 unequal: No Solution Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 66:[51, 13], Operations: ['94-65=29', '42-29=13'] Exploring Operation: 51*13=663, Resulting Numbers: [663] 663,66 unequal: No Solution Exploring Operation: 51+13=64, Resulting Numbers: [64] 64,66 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,66 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 #0,2,1 Current State: 66:[51, 71], Operations: ['94-65=29', '42+29=71'] Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,66 unequal: No Solution Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,66 unequal: No Solution Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,66 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: 66:[65, 51, 52], Operations: ['94-42=52'] Exploring Operation: 65-51=14, Resulting Numbers: [52, 14] Generated Node #0,1,0: 66:[52, 14] Operation: 65-51=14 Exploring Operation: 51+52=103, Resulting Numbers: [65, 103] Generated Node #0,1,1: 66:[65, 103] Operation: 51+52=103 Exploring Operation: 65-52=13, Resulting Numbers: [51, 13] Generated Node #0,1,2: 66:[51, 13] Operation: 65-52=13 Exploring Operation: 52-51=1, Resulting Numbers: [65, 1] Generated Node #0,1,3: 66:[65, 1] Operation: 52-51=1 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 66:[65, 1], Operations: ['94-42=52', '52-51=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[65, 42, 51, 94], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [65, 51, 52] Generated Node #0,1: 66:[65, 51, 52] Operation: 94-42=52 Moving to Node #0,1 Current State: 66:[65, 51, 52], Operations: ['94-42=52'] Exploring Operation: 52-51=1, Resulting Numbers: [65, 1] Generated Node #0,1,3: 66:[65, 1] Operation: 52-51=1 Moving to Node #0,1,3 Current State: 66:[65, 1], Operations: ['94-42=52', '52-51=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 97, 98, 49, 50 ]
98
[ "98-97=1", "49+50=99", "99-1=98" ]
Current State: 98:[97, 98, 49, 50], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [49, 50, 1] Generated Node #2: [49, 50, 1] from Operation: 98-97=1 Current State: 98:[49, 50, 1], Operations: ['98-97=1'] Exploring Operation: 49+50=99, Resulting Numbers: [1, 99] Generated Node #3: [1, 99] from Operation: 49+50=99 Current State: 98:[1, 99], Operations: ['98-97=1', '49+50=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[97, 98, 49, 50], Operations: [] Exploring Operation: 97-49=48, Resulting Numbers: [98, 50, 48] Generated Node #0,0: 98:[98, 50, 48] Operation: 97-49=48 Exploring Operation: 98-97=1, Resulting Numbers: [49, 50, 1] Generated Node #0,1: 98:[49, 50, 1] Operation: 98-97=1 Exploring Operation: 97-50=47, Resulting Numbers: [98, 49, 47] Generated Node #0,2: 98:[98, 49, 47] Operation: 97-50=47 Exploring Operation: 98-49=49, Resulting Numbers: [97, 50, 49] Generated Node #0,3: 98:[97, 50, 49] Operation: 98-49=49 Exploring Operation: 98/49=2, Resulting Numbers: [97, 50, 2] Generated Node #0,4: 98:[97, 50, 2] Operation: 98/49=2 Moving to Node #0,0 Current State: 98:[98, 50, 48], Operations: ['97-49=48'] Exploring Operation: 50-48=2, Resulting Numbers: [98, 2] Generated Node #0,0,0: 98:[98, 2] Operation: 50-48=2 Exploring Operation: 98-48=50, Resulting Numbers: [50, 50] Generated Node #0,0,1: 98:[50, 50] Operation: 98-48=50 Exploring Operation: 50+48=98, Resulting Numbers: [98, 98] Generated Node #0,0,2: 98:[98, 98] Operation: 50+48=98 Exploring Operation: 98+48=146, Resulting Numbers: [50, 146] Generated Node #0,0,3: 98:[50, 146] Operation: 98+48=146 Exploring Operation: 98-50=48, Resulting Numbers: [48, 48] Generated Node #0,0,4: 98:[48, 48] Operation: 98-50=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[98, 2], Operations: ['97-49=48', '50-48=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,98 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[98, 98], Operations: ['97-49=48', '50+48=98'] Exploring Operation: 98-98=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 98*98=9604, Resulting Numbers: [9604] 9604,98 unequal: No Solution Exploring Operation: 98+98=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 98/98=1, Resulting Numbers: [1] 1,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[50, 50], Operations: ['97-49=48', '98-48=50'] Exploring Operation: 50*50=2500, Resulting Numbers: [2500] 2500,98 unequal: No Solution Exploring Operation: 50-50=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 50+50=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 50/50=1, Resulting Numbers: [1] 1,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 98:[48, 48], Operations: ['97-49=48', '98-50=48'] Exploring Operation: 48*48=2304, Resulting Numbers: [2304] 2304,98 unequal: No Solution Exploring Operation: 48+48=96, Resulting Numbers: [96] 96,98 unequal: No Solution Exploring Operation: 48-48=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 48/48=1, Resulting Numbers: [1] 1,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 98:[50, 146], Operations: ['97-49=48', '98+48=146'] Exploring Operation: 146-50=96, Resulting Numbers: [96] 96,98 unequal: No Solution Exploring Operation: 50+146=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 50*146=7300, Resulting Numbers: [7300] 7300,98 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: 98:[98, 49, 47], Operations: ['97-50=47'] Exploring Operation: 98-49=49, Resulting Numbers: [47, 49] Generated Node #0,2,0: 98:[47, 49] Operation: 98-49=49 Exploring Operation: 49-47=2, Resulting Numbers: [98, 2] Generated Node #0,2,1: 98:[98, 2] Operation: 49-47=2 Exploring Operation: 98-47=51, Resulting Numbers: [49, 51] Generated Node #0,2,2: 98:[49, 51] Operation: 98-47=51 Exploring Operation: 98/49=2, Resulting Numbers: [47, 2] Generated Node #0,2,3: 98:[47, 2] Operation: 98/49=2 Exploring Operation: 49+47=96, Resulting Numbers: [98, 96] Generated Node #0,2,4: 98:[98, 96] Operation: 49+47=96 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[98, 2], Operations: ['97-50=47', '49-47=2'] Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,98 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,98 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[47, 49], Operations: ['97-50=47', '98-49=49'] Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 47*49=2303, Resulting Numbers: [2303] 2303,98 unequal: No Solution Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[49, 51], Operations: ['97-50=47', '98-47=51'] Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,98 unequal: No Solution Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 98:[47, 2], Operations: ['97-50=47', '98/49=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 98:[98, 96], Operations: ['97-50=47', '49+47=96'] Exploring Operation: 98+96=194, Resulting Numbers: [194] 194,98 unequal: No Solution Exploring Operation: 98*96=9408, Resulting Numbers: [9408] 9408,98 unequal: No Solution Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,98 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: 98:[97, 50, 2], Operations: ['98/49=2'] Exploring Operation: 97+2=99, Resulting Numbers: [50, 99] Generated Node #0,4,0: 98:[50, 99] Operation: 97+2=99 Exploring Operation: 50*2=100, Resulting Numbers: [97, 100] Generated Node #0,4,1: 98:[97, 100] Operation: 50*2=100 Exploring Operation: 97-2=95, Resulting Numbers: [50, 95] Generated Node #0,4,2: 98:[50, 95] Operation: 97-2=95 Exploring Operation: 97-50=47, Resulting Numbers: [2, 47] Generated Node #0,4,3: 98:[2, 47] Operation: 97-50=47 Exploring Operation: 50-2=48, Resulting Numbers: [97, 48] Generated Node #0,4,4: 98:[97, 48] Operation: 50-2=48 Moving to Node #0,1 Current State: 98:[49, 50, 1], Operations: ['98-97=1'] Exploring Operation: 50/1=50, Resulting Numbers: [49, 50] Generated Node #0,1,0: 98:[49, 50] Operation: 50/1=50 Exploring Operation: 50-1=49, Resulting Numbers: [49, 49] Generated Node #0,1,1: 98:[49, 49] Operation: 50-1=49 Exploring Operation: 49*1=49, Resulting Numbers: [50, 49] Generated Node #0,1,2: 98:[50, 49] Operation: 49*1=49 Exploring Operation: 49/1=49, Resulting Numbers: [50, 49] Generated Node #0,1,3: 98:[50, 49] Operation: 49/1=49 Exploring Operation: 50*1=50, Resulting Numbers: [49, 50] Generated Node #0,1,4: 98:[49, 50] Operation: 50*1=50 Moving to Node #0,3 Current State: 98:[97, 50, 49], Operations: ['98-49=49'] Exploring Operation: 50+49=99, Resulting Numbers: [97, 99] Generated Node #0,3,0: 98:[97, 99] Operation: 50+49=99 Exploring Operation: 97+50=147, Resulting Numbers: [49, 147] Generated Node #0,3,1: 98:[49, 147] Operation: 97+50=147 Exploring Operation: 50-49=1, Resulting Numbers: [97, 1] Generated Node #0,3,2: 98:[97, 1] Operation: 50-49=1 Exploring Operation: 97-50=47, Resulting Numbers: [49, 47] Generated Node #0,3,3: 98:[49, 47] Operation: 97-50=47 Exploring Operation: 97-49=48, Resulting Numbers: [50, 48] Generated Node #0,3,4: 98:[50, 48] Operation: 97-49=48 Moving to Node #0,1,1 Current State: 98:[49, 49], Operations: ['98-97=1', '50-1=49'] Exploring Operation: 49/49=1, Resulting Numbers: [1] 1,98 unequal: No Solution Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[97, 98, 49, 50], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [49, 50, 1] Generated Node #0,1: 98:[49, 50, 1] Operation: 98-97=1 Moving to Node #0,1 Current State: 98:[49, 50, 1], Operations: ['98-97=1'] Exploring Operation: 50-1=49, Resulting Numbers: [49, 49] Generated Node #0,1,1: 98:[49, 49] Operation: 50-1=49 Moving to Node #0,1,1 Current State: 98:[49, 49], Operations: ['98-97=1', '50-1=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.938368
hs_5
mult_heuristic
[ 83, 7, 90, 14 ]
75
[ "83+90=173", "7*14=98", "173-98=75" ]
Current State: 75:[83, 7, 90, 14], Operations: [] Exploring Operation: 83+90=173, Resulting Numbers: [7, 14, 173] Generated Node #2: [7, 14, 173] from Operation: 83+90=173 Current State: 75:[7, 14, 173], Operations: ['83+90=173'] Exploring Operation: 7*14=98, Resulting Numbers: [173, 98] Generated Node #3: [173, 98] from Operation: 7*14=98 Current State: 75:[173, 98], Operations: ['83+90=173', '7*14=98'] Exploring Operation: 173-98=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[83, 7, 90, 14], Operations: [] Exploring Operation: 90-14=76, Resulting Numbers: [83, 7, 76] Generated Node #0,0: 75:[83, 7, 76] Operation: 90-14=76 Exploring Operation: 83-7=76, Resulting Numbers: [90, 14, 76] Generated Node #0,1: 75:[90, 14, 76] Operation: 83-7=76 Exploring Operation: 90-83=7, Resulting Numbers: [7, 14, 7] Generated Node #0,2: 75:[7, 14, 7] Operation: 90-83=7 Exploring Operation: 90-7=83, Resulting Numbers: [83, 14, 83] Generated Node #0,3: 75:[83, 14, 83] Operation: 90-7=83 Moving to Node #0,2 Current State: 75:[7, 14, 7], Operations: ['90-83=7'] Exploring Operation: 7/7=1, Resulting Numbers: [14, 1] Generated Node #0,2,0: 75:[14, 1] Operation: 7/7=1 Exploring Operation: 7+7=14, Resulting Numbers: [14, 14] Generated Node #0,2,1: 75:[14, 14] Operation: 7+7=14 Exploring Operation: 14/7=2, Resulting Numbers: [7, 2] Generated Node #0,2,2: 75:[7, 2] Operation: 14/7=2 Exploring Operation: 14/7=2, Resulting Numbers: [7, 2] Generated Node #0,2,3: 75:[7, 2] Operation: 14/7=2 Moving to Node #0,0 Current State: 75:[83, 7, 76], Operations: ['90-14=76'] Exploring Operation: 83-7=76, Resulting Numbers: [76, 76] Generated Node #0,0,0: 75:[76, 76] Operation: 83-7=76 Exploring Operation: 76-7=69, Resulting Numbers: [83, 69] Generated Node #0,0,1: 75:[83, 69] Operation: 76-7=69 Exploring Operation: 83-76=7, Resulting Numbers: [7, 7] Generated Node #0,0,2: 75:[7, 7] Operation: 83-76=7 Exploring Operation: 83+7=90, Resulting Numbers: [76, 90] Generated Node #0,0,3: 75:[76, 90] Operation: 83+7=90 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[76, 76], Operations: ['90-14=76', '83-7=76'] Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,75 unequal: No Solution Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,75 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,75 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 #0,0,2 Current State: 75:[7, 7], Operations: ['90-14=76', '83-76=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,75 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:[83, 69], Operations: ['90-14=76', '76-7=69'] Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 83+69=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 83*69=5727, Resulting Numbers: [5727] 5727,75 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 #0,0,3 Current State: 75:[76, 90], Operations: ['90-14=76', '83+7=90'] Exploring Operation: 90-76=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 76+90=166, Resulting Numbers: [166] 166,75 unequal: No Solution Exploring Operation: 76*90=6840, Resulting Numbers: [6840] 6840,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 75:[83, 14, 83], Operations: ['90-7=83'] Exploring Operation: 83/83=1, Resulting Numbers: [14, 1] Generated Node #0,3,0: 75:[14, 1] Operation: 83/83=1 Exploring Operation: 83-14=69, Resulting Numbers: [83, 69] Generated Node #0,3,1: 75:[83, 69] Operation: 83-14=69 Exploring Operation: 83-14=69, Resulting Numbers: [83, 69] Generated Node #0,3,2: 75:[83, 69] Operation: 83-14=69 Exploring Operation: 83-83=0, Resulting Numbers: [14, 0] Generated Node #0,3,3: 75:[14, 0] Operation: 83-83=0 Moving to Node #0,1 Current State: 75:[90, 14, 76], Operations: ['83-7=76'] Exploring Operation: 90+14=104, Resulting Numbers: [76, 104] Generated Node #0,1,0: 75:[76, 104] Operation: 90+14=104 Exploring Operation: 90-76=14, Resulting Numbers: [14, 14] Generated Node #0,1,1: 75:[14, 14] Operation: 90-76=14 Exploring Operation: 90-14=76, Resulting Numbers: [76, 76] Generated Node #0,1,2: 75:[76, 76] Operation: 90-14=76 Exploring Operation: 76-14=62, Resulting Numbers: [90, 62] Generated Node #0,1,3: 75:[90, 62] Operation: 76-14=62 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[14, 14], Operations: ['83-7=76', '90-76=14'] Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,75 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,75 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 #0,1,2 Current State: 75:[76, 76], Operations: ['83-7=76', '90-14=76'] Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,75 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,75 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 #0,1,3 Current State: 75:[90, 62], Operations: ['83-7=76', '76-14=62'] Exploring Operation: 90+62=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 90*62=5580, Resulting Numbers: [5580] 5580,75 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 #0,1,0 Current State: 75:[76, 104], Operations: ['83-7=76', '90+14=104'] Exploring Operation: 104-76=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 76+104=180, Resulting Numbers: [180] 180,75 unequal: No Solution Exploring Operation: 76*104=7904, Resulting Numbers: [7904] 7904,75 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: 75:[14, 14], Operations: ['90-83=7', '7+7=14'] Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,75 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[7, 2], Operations: ['90-83=7', '14/7=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[14, 1], Operations: ['90-83=7', '7/7=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Moving to Node #0,3,0 Current State: 75:[14, 1], Operations: ['90-7=83', '83/83=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,75 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[7, 2], Operations: ['90-83=7', '14/7=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,75 unequal: No Solution Moving to Node #0,3,3 Current State: 75:[14, 0], Operations: ['90-7=83', '83-83=0'] Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,75 unequal: No Solution Moving to Node #0,3,2 Current State: 75:[83, 69], Operations: ['90-7=83', '83-14=69'] Exploring Operation: 83+69=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 83*69=5727, Resulting Numbers: [5727] 5727,75 unequal: No Solution Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,75 unequal: No Solution Moving to Node #0,3,1 Current State: 75:[83, 69], Operations: ['90-7=83', '83-14=69'] Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 83*69=5727, Resulting Numbers: [5727] 5727,75 unequal: No Solution Exploring Operation: 83+69=152, Resulting Numbers: [152] 152,75 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 26, 30, 8, 45 ]
38
[ "26+30=56", "56/8=7", "45-7=38" ]
Current State: 38:[26, 30, 8, 45], Operations: [] Exploring Operation: 26+30=56, Resulting Numbers: [8, 45, 56] Generated Node #2: [8, 45, 56] from Operation: 26+30=56 Current State: 38:[8, 45, 56], Operations: ['26+30=56'] Exploring Operation: 56/8=7, Resulting Numbers: [45, 7] Generated Node #3: [45, 7] from Operation: 56/8=7 Current State: 38:[45, 7], Operations: ['26+30=56', '56/8=7'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[26, 30, 8, 45], Operations: [] Exploring Operation: 26-8=18, Resulting Numbers: [30, 45, 18] Generated Node #0,0: 38:[30, 45, 18] Operation: 26-8=18 Exploring Operation: 30+8=38, Resulting Numbers: [26, 45, 38] Generated Node #0,1: 38:[26, 45, 38] Operation: 30+8=38 Exploring Operation: 30-26=4, Resulting Numbers: [8, 45, 4] Generated Node #0,2: 38:[8, 45, 4] Operation: 30-26=4 Exploring Operation: 45-26=19, Resulting Numbers: [30, 8, 19] Generated Node #0,3: 38:[30, 8, 19] Operation: 45-26=19 Moving to Node #0,1 Current State: 38:[26, 45, 38], Operations: ['30+8=38'] Exploring Operation: 45-26=19, Resulting Numbers: [38, 19] Generated Node #0,1,0: 38:[38, 19] Operation: 45-26=19 Exploring Operation: 45-38=7, Resulting Numbers: [26, 7] Generated Node #0,1,1: 38:[26, 7] Operation: 45-38=7 Exploring Operation: 38-26=12, Resulting Numbers: [45, 12] Generated Node #0,1,2: 38:[45, 12] Operation: 38-26=12 Exploring Operation: 26+45=71, Resulting Numbers: [38, 71] Generated Node #0,1,3: 38:[38, 71] Operation: 26+45=71 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[38, 19], Operations: ['30+8=38', '45-26=19'] Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 38+19=57, Resulting Numbers: [57] 57,38 unequal: No Solution Exploring Operation: 38*19=722, Resulting Numbers: [722] 722,38 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 38:[26, 7], Operations: ['30+8=38', '45-38=7'] Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 38:[45, 12], Operations: ['30+8=38', '38-26=12'] Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,38 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 38:[38, 71], Operations: ['30+8=38', '26+45=71'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 38*71=2698, Resulting Numbers: [2698] 2698,38 unequal: No Solution Exploring Operation: 38+71=109, Resulting Numbers: [109] 109,38 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: 38:[30, 8, 19], Operations: ['45-26=19'] Exploring Operation: 30-8=22, Resulting Numbers: [19, 22] Generated Node #0,3,0: 38:[19, 22] Operation: 30-8=22 Exploring Operation: 8+19=27, Resulting Numbers: [30, 27] Generated Node #0,3,1: 38:[30, 27] Operation: 8+19=27 Exploring Operation: 30+8=38, Resulting Numbers: [19, 38] Generated Node #0,3,2: 38:[19, 38] Operation: 30+8=38 Exploring Operation: 30-19=11, Resulting Numbers: [8, 11] Generated Node #0,3,3: 38:[8, 11] Operation: 30-19=11 Moving to Node #0,2 Current State: 38:[8, 45, 4], Operations: ['30-26=4'] Exploring Operation: 8-4=4, Resulting Numbers: [45, 4] Generated Node #0,2,0: 38:[45, 4] Operation: 8-4=4 Exploring Operation: 8/4=2, Resulting Numbers: [45, 2] Generated Node #0,2,1: 38:[45, 2] Operation: 8/4=2 Exploring Operation: 45-4=41, Resulting Numbers: [8, 41] Generated Node #0,2,2: 38:[8, 41] Operation: 45-4=41 Exploring Operation: 45-8=37, Resulting Numbers: [4, 37] Generated Node #0,2,3: 38:[4, 37] Operation: 45-8=37 Moving to Node #0,0 Current State: 38:[30, 45, 18], Operations: ['26-8=18'] Exploring Operation: 30-18=12, Resulting Numbers: [45, 12] Generated Node #0,0,0: 38:[45, 12] Operation: 30-18=12 Exploring Operation: 45-18=27, Resulting Numbers: [30, 27] Generated Node #0,0,1: 38:[30, 27] Operation: 45-18=27 Exploring Operation: 30+18=48, Resulting Numbers: [45, 48] Generated Node #0,0,2: 38:[45, 48] Operation: 30+18=48 Exploring Operation: 45-30=15, Resulting Numbers: [18, 15] Generated Node #0,0,3: 38:[18, 15] Operation: 45-30=15 Moving to Node #0,3,2 Current State: 38:[19, 38], Operations: ['45-26=19', '30+8=38'] Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,38 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,38 unequal: No Solution Moving to Node #0,3,0 Current State: 38:[19, 22], Operations: ['45-26=19', '30-8=22'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,38 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[4, 37], Operations: ['30-26=4', '45-8=37'] Exploring Operation: 4*37=148, Resulting Numbers: [148] 148,38 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,38 unequal: No Solution Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[18, 15], Operations: ['26-8=18', '45-30=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,38 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[45, 2], Operations: ['30-26=4', '8/4=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,38 unequal: No Solution Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[45, 4], Operations: ['30-26=4', '8-4=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,38 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,38 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[8, 41], Operations: ['30-26=4', '45-4=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,38 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,38 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,38 unequal: No Solution Moving to Node #0,3,3 Current State: 38:[8, 11], Operations: ['45-26=19', '30-19=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,38 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[45, 12], Operations: ['26-8=18', '30-18=12'] Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,38 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,38 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,38 unequal: No Solution Moving to Node #0,3,1 Current State: 38:[30, 27], Operations: ['45-26=19', '8+19=27'] Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,38 unequal: No Solution Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,38 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[30, 27], Operations: ['26-8=18', '45-18=27'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 30*27=810, Resulting Numbers: [810] 810,38 unequal: No Solution Exploring Operation: 30+27=57, Resulting Numbers: [57] 57,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[45, 48], Operations: ['26-8=18', '30+18=48'] Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,38 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 34, 1, 43, 15 ]
25
[ "34-1=33", "43+15=58", "58-33=25" ]
Current State: 25:[34, 1, 43, 15], Operations: [] Exploring Operation: 34-1=33, Resulting Numbers: [43, 15, 33] Generated Node #2: [43, 15, 33] from Operation: 34-1=33 Current State: 25:[43, 15, 33], Operations: ['34-1=33'] Exploring Operation: 43+15=58, Resulting Numbers: [33, 58] Generated Node #3: [33, 58] from Operation: 43+15=58 Current State: 25:[33, 58], Operations: ['34-1=33', '43+15=58'] Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[34, 1, 43, 15], Operations: [] Exploring Operation: 43-34=9, Resulting Numbers: [1, 15, 9] Generated Node #0,0: 25:[1, 15, 9] Operation: 43-34=9 Exploring Operation: 43-15=28, Resulting Numbers: [34, 1, 28] Generated Node #0,1: 25:[34, 1, 28] Operation: 43-15=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[34, 1, 28], Operations: ['43-15=28'] Exploring Operation: 34-28=6, Resulting Numbers: [1, 6] Generated Node #0,1,0: 25:[1, 6] Operation: 34-28=6 Exploring Operation: 34-1=33, Resulting Numbers: [28, 33] Generated Node #0,1,1: 25:[28, 33] Operation: 34-1=33 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[1, 6], Operations: ['43-15=28', '34-28=6'] Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[28, 33], Operations: ['43-15=28', '34-1=33'] Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 28+33=61, Resulting Numbers: [61] 61,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[1, 15, 9], Operations: ['43-34=9'] Exploring Operation: 15-9=6, Resulting Numbers: [1, 6] Generated Node #0,0,0: 25:[1, 6] Operation: 15-9=6 Exploring Operation: 15+9=24, Resulting Numbers: [1, 24] Generated Node #0,0,1: 25:[1, 24] Operation: 15+9=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[1, 6], Operations: ['43-34=9', '15-9=6'] Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,25 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[1, 24], Operations: ['43-34=9', '15+9=24'] Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[34, 1, 43, 15], Operations: [] Exploring Operation: 43-34=9, Resulting Numbers: [1, 15, 9] Generated Node #0,0: 25:[1, 15, 9] Operation: 43-34=9 Moving to Node #0,0 Current State: 25:[1, 15, 9], Operations: ['43-34=9'] Exploring Operation: 15+9=24, Resulting Numbers: [1, 24] Generated Node #0,0,1: 25:[1, 24] Operation: 15+9=24 Moving to Node #0,0,1 Current State: 25:[1, 24], Operations: ['43-34=9', '15+9=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 25, 69, 29, 21 ]
15
[ "29-25=4", "21*4=84", "84-69=15" ]
Current State: 15:[25, 69, 29, 21], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [69, 21, 4] Generated Node #2: [69, 21, 4] from Operation: 29-25=4 Current State: 15:[69, 21, 4], Operations: ['29-25=4'] Exploring Operation: 21*4=84, Resulting Numbers: [69, 84] Generated Node #3: [69, 84] from Operation: 21*4=84 Current State: 15:[69, 84], Operations: ['29-25=4', '21*4=84'] Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[25, 69, 29, 21], Operations: [] Exploring Operation: 69-29=40, Resulting Numbers: [25, 21, 40] Generated Node #0,0: 15:[25, 21, 40] Operation: 69-29=40 Moving to Node #0,0 Current State: 15:[25, 21, 40], Operations: ['69-29=40'] Exploring Operation: 40-25=15, Resulting Numbers: [21, 15] Generated Node #0,0,0: 15:[21, 15] Operation: 40-25=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[21, 15], Operations: ['69-29=40', '40-25=15'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,15 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
[ 71, 83, 34, 3 ]
81
[ "71-3=68", "68/34=2", "83-2=81" ]
Current State: 81:[71, 83, 34, 3], Operations: [] Exploring Operation: 71-3=68, Resulting Numbers: [83, 34, 68] Generated Node #2: [83, 34, 68] from Operation: 71-3=68 Current State: 81:[83, 34, 68], Operations: ['71-3=68'] Exploring Operation: 68/34=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 68/34=2 Current State: 81:[83, 2], Operations: ['71-3=68', '68/34=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[71, 83, 34, 3], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [34, 3, 12] Generated Node #0,0: 81:[34, 3, 12] Operation: 83-71=12 Moving to Node #0,0 Current State: 81:[34, 3, 12], Operations: ['83-71=12'] Exploring Operation: 34-12=22, Resulting Numbers: [3, 22] Generated Node #0,0,0: 81:[3, 22] Operation: 34-12=22 Moving to Node #0,0,0 Current State: 81:[3, 22], Operations: ['83-71=12', '34-12=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,81 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 61, 90, 6, 57 ]
60
[ "61-57=4", "90/6=15", "4*15=60" ]
Current State: 60:[61, 90, 6, 57], Operations: [] Exploring Operation: 61-57=4, Resulting Numbers: [90, 6, 4] Generated Node #2: [90, 6, 4] from Operation: 61-57=4 Current State: 60:[90, 6, 4], Operations: ['61-57=4'] Exploring Operation: 90/6=15, Resulting Numbers: [4, 15] Generated Node #3: [4, 15] from Operation: 90/6=15 Current State: 60:[4, 15], Operations: ['61-57=4', '90/6=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[61, 90, 6, 57], Operations: [] Exploring Operation: 90-6=84, Resulting Numbers: [61, 57, 84] Generated Node #0,0: 60:[61, 57, 84] Operation: 90-6=84 Exploring Operation: 90-61=29, Resulting Numbers: [6, 57, 29] Generated Node #0,1: 60:[6, 57, 29] Operation: 90-61=29 Exploring Operation: 90-57=33, Resulting Numbers: [61, 6, 33] Generated Node #0,2: 60:[61, 6, 33] Operation: 90-57=33 Exploring Operation: 90/6=15, Resulting Numbers: [61, 57, 15] Generated Node #0,3: 60:[61, 57, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[6, 57, 29], Operations: ['90-61=29'] Exploring Operation: 57-29=28, Resulting Numbers: [6, 28] Generated Node #0,1,0: 60:[6, 28] Operation: 57-29=28 Exploring Operation: 29-6=23, Resulting Numbers: [57, 23] Generated Node #0,1,1: 60:[57, 23] Operation: 29-6=23 Exploring Operation: 6+57=63, Resulting Numbers: [29, 63] Generated Node #0,1,2: 60:[29, 63] Operation: 6+57=63 Exploring Operation: 6+29=35, Resulting Numbers: [57, 35] Generated Node #0,1,3: 60:[57, 35] Operation: 6+29=35 Moving to Node #0,1,0 Current State: 60:[6, 28], Operations: ['90-61=29', '57-29=28'] Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,60 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,60 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[29, 63], Operations: ['90-61=29', '6+57=63'] Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,60 unequal: No Solution Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,60 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[57, 23], Operations: ['90-61=29', '29-6=23'] Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,60 unequal: No Solution Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[57, 35], Operations: ['90-61=29', '6+29=35'] Exploring Operation: 57*35=1995, Resulting Numbers: [1995] 1995,60 unequal: No Solution Exploring Operation: 57-35=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 57+35=92, Resulting Numbers: [92] 92,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[61, 6, 33], Operations: ['90-57=33'] Exploring Operation: 61-33=28, Resulting Numbers: [6, 28] Generated Node #0,2,0: 60:[6, 28] Operation: 61-33=28 Exploring Operation: 61+6=67, Resulting Numbers: [33, 67] Generated Node #0,2,1: 60:[33, 67] Operation: 61+6=67 Exploring Operation: 33-6=27, Resulting Numbers: [61, 27] Generated Node #0,2,2: 60:[61, 27] Operation: 33-6=27 Exploring Operation: 61-6=55, Resulting Numbers: [33, 55] Generated Node #0,2,3: 60:[33, 55] Operation: 61-6=55 Moving to Node #0,2,0 Current State: 60:[6, 28], Operations: ['90-57=33', '61-33=28'] Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,60 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,60 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[61, 27], Operations: ['90-57=33', '33-6=27'] Exploring Operation: 61*27=1647, Resulting Numbers: [1647] 1647,60 unequal: No Solution Exploring Operation: 61+27=88, Resulting Numbers: [88] 88,60 unequal: No Solution Exploring Operation: 61-27=34, Resulting Numbers: [34] 34,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[33, 55], Operations: ['90-57=33', '61-6=55'] Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,60 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[33, 67], Operations: ['90-57=33', '61+6=67'] Exploring Operation: 33*67=2211, Resulting Numbers: [2211] 2211,60 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,60 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 60:[61, 57, 15], Operations: ['90/6=15'] Exploring Operation: 57-15=42, Resulting Numbers: [61, 42] Generated Node #0,3,0: 60:[61, 42] Operation: 57-15=42 Exploring Operation: 57+15=72, Resulting Numbers: [61, 72] Generated Node #0,3,1: 60:[61, 72] Operation: 57+15=72 Exploring Operation: 61-15=46, Resulting Numbers: [57, 46] Generated Node #0,3,2: 60:[57, 46] Operation: 61-15=46 Exploring Operation: 61-57=4, Resulting Numbers: [15, 4] Generated Node #0,3,3: 60:[15, 4] Operation: 61-57=4 Moving to Node #0,3,3 Current State: 60:[15, 4], Operations: ['90/6=15', '61-57=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[61, 90, 6, 57], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [61, 57, 15] Generated Node #0,3: 60:[61, 57, 15] Operation: 90/6=15 Moving to Node #0,3 Current State: 60:[61, 57, 15], Operations: ['90/6=15'] Exploring Operation: 61-57=4, Resulting Numbers: [15, 4] Generated Node #0,3,3: 60:[15, 4] Operation: 61-57=4 Moving to Node #0,3,3 Current State: 60:[15, 4], Operations: ['90/6=15', '61-57=4'] Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_4
mult_heuristic
[ 70, 61, 24, 84 ]
12
[ "70-61=9", "24+84=108", "108/9=12" ]
Current State: 12:[70, 61, 24, 84], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [24, 84, 9] Generated Node #2: [24, 84, 9] from Operation: 70-61=9 Current State: 12:[24, 84, 9], Operations: ['70-61=9'] Exploring Operation: 24+84=108, Resulting Numbers: [9, 108] Generated Node #3: [9, 108] from Operation: 24+84=108 Current State: 12:[9, 108], Operations: ['70-61=9', '24+84=108'] Exploring Operation: 108/9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[70, 61, 24, 84], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [61, 24, 14] Generated Node #0,0: 12:[61, 24, 14] Operation: 84-70=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[61, 24, 14], Operations: ['84-70=14'] Exploring Operation: 61-24=37, Resulting Numbers: [14, 37] Generated Node #0,0,0: 12:[14, 37] Operation: 61-24=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[14, 37], Operations: ['84-70=14', '61-24=37'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 22, 11, 19, 69 ]
86
[ "22/11=2", "19+69=88", "88-2=86" ]
Current State: 86:[22, 11, 19, 69], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [19, 69, 2] Generated Node #2: [19, 69, 2] from Operation: 22/11=2 Current State: 86:[19, 69, 2], Operations: ['22/11=2'] Exploring Operation: 19+69=88, Resulting Numbers: [2, 88] Generated Node #3: [2, 88] from Operation: 19+69=88 Current State: 86:[2, 88], Operations: ['22/11=2', '19+69=88'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[22, 11, 19, 69], Operations: [] Exploring Operation: 22+69=91, Resulting Numbers: [11, 19, 91] Generated Node #0,0: 86:[11, 19, 91] Operation: 22+69=91 Exploring Operation: 22-19=3, Resulting Numbers: [11, 69, 3] Generated Node #0,1: 86:[11, 69, 3] Operation: 22-19=3 Exploring Operation: 19+69=88, Resulting Numbers: [22, 11, 88] Generated Node #0,2: 86:[22, 11, 88] Operation: 19+69=88 Exploring Operation: 69-22=47, Resulting Numbers: [11, 19, 47] Generated Node #0,3: 86:[11, 19, 47] Operation: 69-22=47 Exploring Operation: 22+19=41, Resulting Numbers: [11, 69, 41] Generated Node #0,4: 86:[11, 69, 41] Operation: 22+19=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[11, 69, 3], Operations: ['22-19=3'] Exploring Operation: 11-3=8, Resulting Numbers: [69, 8] Generated Node #0,1,0: 86:[69, 8] Operation: 11-3=8 Exploring Operation: 11+69=80, Resulting Numbers: [3, 80] Generated Node #0,1,1: 86:[3, 80] Operation: 11+69=80 Exploring Operation: 69+3=72, Resulting Numbers: [11, 72] Generated Node #0,1,2: 86:[11, 72] Operation: 69+3=72 Exploring Operation: 11*3=33, Resulting Numbers: [69, 33] Generated Node #0,1,3: 86:[69, 33] Operation: 11*3=33 Exploring Operation: 69-11=58, Resulting Numbers: [3, 58] Generated Node #0,1,4: 86:[3, 58] Operation: 69-11=58 Moving to Node #0,1,1 Current State: 86:[3, 80], Operations: ['22-19=3', '11+69=80'] Exploring Operation: 3+80=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 3*80=240, Resulting Numbers: [240] 240,86 unequal: No Solution Moving to Node #0,1,4 Current State: 86:[3, 58], Operations: ['22-19=3', '69-11=58'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,86 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,86 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[69, 8], Operations: ['22-19=3', '11-3=8'] Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,86 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,86 unequal: No Solution Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[11, 72], Operations: ['22-19=3', '69+3=72'] Exploring Operation: 11*72=792, Resulting Numbers: [792] 792,86 unequal: No Solution Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,86 unequal: No Solution Exploring Operation: 11+72=83, Resulting Numbers: [83] 83,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[69, 33], Operations: ['22-19=3', '11*3=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,86 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[11, 69, 41], Operations: ['22+19=41'] Exploring Operation: 69-11=58, Resulting Numbers: [41, 58] Generated Node #0,4,0: 86:[41, 58] Operation: 69-11=58 Exploring Operation: 69-41=28, Resulting Numbers: [11, 28] Generated Node #0,4,1: 86:[11, 28] Operation: 69-41=28 Exploring Operation: 41-11=30, Resulting Numbers: [69, 30] Generated Node #0,4,2: 86:[69, 30] Operation: 41-11=30 Exploring Operation: 11+69=80, Resulting Numbers: [41, 80] Generated Node #0,4,3: 86:[41, 80] Operation: 11+69=80 Exploring Operation: 11+41=52, Resulting Numbers: [69, 52] Generated Node #0,4,4: 86:[69, 52] Operation: 11+41=52 Moving to Node #0,4,3 Current State: 86:[41, 80], Operations: ['22+19=41', '11+69=80'] Exploring Operation: 41+80=121, Resulting Numbers: [121] 121,86 unequal: No Solution Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 41*80=3280, Resulting Numbers: [3280] 3280,86 unequal: No Solution Moving to Node #0,4,0 Current State: 86:[41, 58], Operations: ['22+19=41', '69-11=58'] Exploring Operation: 41+58=99, Resulting Numbers: [99] 99,86 unequal: No Solution Exploring Operation: 58-41=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 41*58=2378, Resulting Numbers: [2378] 2378,86 unequal: No Solution Moving to Node #0,4,1 Current State: 86:[11, 28], Operations: ['22+19=41', '69-41=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,86 unequal: No Solution Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,86 unequal: No Solution Moving to Node #0,4,4 Current State: 86:[69, 52], Operations: ['22+19=41', '11+41=52'] Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,86 unequal: No Solution Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,86 unequal: No Solution Moving to Node #0,4,2 Current State: 86:[69, 30], Operations: ['22+19=41', '41-11=30'] Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,86 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,86 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[11, 19, 47], Operations: ['69-22=47'] Exploring Operation: 19-11=8, Resulting Numbers: [47, 8] Generated Node #0,3,0: 86:[47, 8] Operation: 19-11=8 Exploring Operation: 47-11=36, Resulting Numbers: [19, 36] Generated Node #0,3,1: 86:[19, 36] Operation: 47-11=36 Exploring Operation: 19+47=66, Resulting Numbers: [11, 66] Generated Node #0,3,2: 86:[11, 66] Operation: 19+47=66 Exploring Operation: 47-19=28, Resulting Numbers: [11, 28] Generated Node #0,3,3: 86:[11, 28] Operation: 47-19=28 Exploring Operation: 11+19=30, Resulting Numbers: [47, 30] Generated Node #0,3,4: 86:[47, 30] Operation: 11+19=30 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 86:[47, 8], Operations: ['69-22=47', '19-11=8'] Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,86 unequal: No Solution Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,86 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 86:[47, 30], Operations: ['69-22=47', '11+19=30'] Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,86 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 86:[19, 36], Operations: ['69-22=47', '47-11=36'] Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,86 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,86 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 86:[11, 28], Operations: ['69-22=47', '47-19=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,86 unequal: No Solution Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,86 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 86:[11, 66], Operations: ['69-22=47', '19+47=66'] Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,86 unequal: No Solution Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,86 unequal: No Solution Exploring Operation: 11*66=726, Resulting Numbers: [726] 726,86 unequal: No Solution Exploring Operation: 11+66=77, Resulting Numbers: [77] 77,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[11, 19, 91], Operations: ['22+69=91'] Exploring Operation: 91-11=80, Resulting Numbers: [19, 80] Generated Node #0,0,0: 86:[19, 80] Operation: 91-11=80 Exploring Operation: 91-19=72, Resulting Numbers: [11, 72] Generated Node #0,0,1: 86:[11, 72] Operation: 91-19=72 Exploring Operation: 11+19=30, Resulting Numbers: [91, 30] Generated Node #0,0,2: 86:[91, 30] Operation: 11+19=30 Exploring Operation: 19-11=8, Resulting Numbers: [91, 8] Generated Node #0,0,3: 86:[91, 8] Operation: 19-11=8 Exploring Operation: 11+91=102, Resulting Numbers: [19, 102] Generated Node #0,0,4: 86:[19, 102] Operation: 11+91=102 Moving to Node #0,0,3 Current State: 86:[91, 8], Operations: ['22+69=91', '19-11=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 91*8=728, Resulting Numbers: [728] 728,86 unequal: No Solution Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[91, 30], Operations: ['22+69=91', '11+19=30'] Exploring Operation: 91*30=2730, Resulting Numbers: [2730] 2730,86 unequal: No Solution Exploring Operation: 91+30=121, Resulting Numbers: [121] 121,86 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[19, 80], Operations: ['22+69=91', '91-11=80'] Exploring Operation: 19+80=99, Resulting Numbers: [99] 99,86 unequal: No Solution Exploring Operation: 19*80=1520, Resulting Numbers: [1520] 1520,86 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[11, 72], Operations: ['22+69=91', '91-19=72'] Exploring Operation: 11*72=792, Resulting Numbers: [792] 792,86 unequal: No Solution Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,86 unequal: No Solution Exploring Operation: 11+72=83, Resulting Numbers: [83] 83,86 unequal: No Solution Moving to Node #0,0,4 Current State: 86:[19, 102], Operations: ['22+69=91', '11+91=102'] Exploring Operation: 102-19=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 19*102=1938, Resulting Numbers: [1938] 1938,86 unequal: No Solution Exploring Operation: 19+102=121, Resulting Numbers: [121] 121,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[22, 11, 88], Operations: ['19+69=88'] Exploring Operation: 22+11=33, Resulting Numbers: [88, 33] Generated Node #0,2,0: 86:[88, 33] Operation: 22+11=33 Exploring Operation: 88/11=8, Resulting Numbers: [22, 8] Generated Node #0,2,1: 86:[22, 8] Operation: 88/11=8 Exploring Operation: 22-11=11, Resulting Numbers: [88, 11] Generated Node #0,2,2: 86:[88, 11] Operation: 22-11=11 Exploring Operation: 88/22=4, Resulting Numbers: [11, 4] Generated Node #0,2,3: 86:[11, 4] Operation: 88/22=4 Exploring Operation: 22/11=2, Resulting Numbers: [88, 2] Generated Node #0,2,4: 86:[88, 2] Operation: 22/11=2 Moving to Node #0,2,4 Current State: 86:[88, 2], Operations: ['19+69=88', '22/11=2'] Exploring Operation: 88*2=176, Resulting Numbers: [176] 176,86 unequal: No Solution Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[22, 11, 19, 69], Operations: [] Exploring Operation: 19+69=88, Resulting Numbers: [22, 11, 88] Generated Node #0,2: 86:[22, 11, 88] Operation: 19+69=88 Moving to Node #0,2 Current State: 86:[22, 11, 88], Operations: ['19+69=88'] Exploring Operation: 22/11=2, Resulting Numbers: [88, 2] Generated Node #0,2,4: 86:[88, 2] Operation: 22/11=2 Moving to Node #0,2,4 Current State: 86:[88, 2], Operations: ['19+69=88', '22/11=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.914931
hs_5
mult_heuristic
[ 11, 2, 64, 62 ]
52
[ "64+62=126", "126/2=63", "63-11=52" ]
Current State: 52:[11, 2, 64, 62], Operations: [] Exploring Operation: 64+62=126, Resulting Numbers: [11, 2, 126] Generated Node #2: [11, 2, 126] from Operation: 64+62=126 Current State: 52:[11, 2, 126], Operations: ['64+62=126'] Exploring Operation: 126/2=63, Resulting Numbers: [11, 63] Generated Node #3: [11, 63] from Operation: 126/2=63 Current State: 52:[11, 63], Operations: ['64+62=126', '126/2=63'] Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[11, 2, 64, 62], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [11, 2, 2] Generated Node #0,0: 52:[11, 2, 2] Operation: 64-62=2 Moving to Node #0,0 Current State: 52:[11, 2, 2], Operations: ['64-62=2'] Exploring Operation: 11+2=13, Resulting Numbers: [2, 13] Generated Node #0,0,0: 52:[2, 13] Operation: 11+2=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[2, 13], Operations: ['64-62=2', '11+2=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,52 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
[ 66, 22, 70, 91 ]
65
[ "66-22=44", "91-70=21", "44+21=65" ]
Current State: 65:[66, 22, 70, 91], Operations: [] Exploring Operation: 66-22=44, Resulting Numbers: [70, 91, 44] Generated Node #2: [70, 91, 44] from Operation: 66-22=44 Current State: 65:[70, 91, 44], Operations: ['66-22=44'] Exploring Operation: 91-70=21, Resulting Numbers: [44, 21] Generated Node #3: [44, 21] from Operation: 91-70=21 Current State: 65:[44, 21], Operations: ['66-22=44', '91-70=21'] Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[66, 22, 70, 91], Operations: [] Exploring Operation: 91-22=69, Resulting Numbers: [66, 70, 69] Generated Node #0,0: 65:[66, 70, 69] Operation: 91-22=69 Moving to Node #0,0 Current State: 65:[66, 70, 69], Operations: ['91-22=69'] Exploring Operation: 70-66=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 65:[69, 4] Operation: 70-66=4 Moving to Node #0,0,0 Current State: 65:[69, 4], Operations: ['91-22=69', '70-66=4'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[66, 22, 70, 91], Operations: [] Exploring Operation: 91-22=69, Resulting Numbers: [66, 70, 69] Generated Node #0,0: 65:[66, 70, 69] Operation: 91-22=69 Moving to Node #0,0 Current State: 65:[66, 70, 69], Operations: ['91-22=69'] Exploring Operation: 70-66=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 65:[69, 4] Operation: 70-66=4 Moving to Node #0,0,0 Current State: 65:[69, 4], Operations: ['91-22=69', '70-66=4'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 50, 21, 2, 48 ]
79
[ "50-21=29", "2+48=50", "29+50=79" ]
Current State: 79:[50, 21, 2, 48], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [2, 48, 29] Generated Node #2: [2, 48, 29] from Operation: 50-21=29 Current State: 79:[2, 48, 29], Operations: ['50-21=29'] Exploring Operation: 2+48=50, Resulting Numbers: [29, 50] Generated Node #3: [29, 50] from Operation: 2+48=50 Current State: 79:[29, 50], Operations: ['50-21=29', '2+48=50'] Exploring Operation: 29+50=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[50, 21, 2, 48], Operations: [] Exploring Operation: 2*48=96, Resulting Numbers: [50, 21, 96] Generated Node #0,0: 79:[50, 21, 96] Operation: 2*48=96 Exploring Operation: 50*2=100, Resulting Numbers: [21, 48, 100] Generated Node #0,1: 79:[21, 48, 100] Operation: 50*2=100 Exploring Operation: 21*2=42, Resulting Numbers: [50, 48, 42] Generated Node #0,2: 79:[50, 48, 42] Operation: 21*2=42 Moving to Node #0,2 Current State: 79:[50, 48, 42], Operations: ['21*2=42'] Exploring Operation: 50+42=92, Resulting Numbers: [48, 92] Generated Node #0,2,0: 79:[48, 92] Operation: 50+42=92 Exploring Operation: 48+42=90, Resulting Numbers: [50, 90] Generated Node #0,2,1: 79:[50, 90] Operation: 48+42=90 Exploring Operation: 50+48=98, Resulting Numbers: [42, 98] Generated Node #0,2,2: 79:[42, 98] Operation: 50+48=98 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[50, 90], Operations: ['21*2=42', '48+42=90'] Exploring Operation: 50*90=4500, Resulting Numbers: [4500] 4500,79 unequal: No Solution Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,79 unequal: No Solution Exploring Operation: 50+90=140, Resulting Numbers: [140] 140,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[48, 92], Operations: ['21*2=42', '50+42=92'] Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 48+92=140, Resulting Numbers: [140] 140,79 unequal: No Solution Exploring Operation: 48*92=4416, Resulting Numbers: [4416] 4416,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[42, 98], Operations: ['21*2=42', '50+48=98'] Exploring Operation: 42+98=140, Resulting Numbers: [140] 140,79 unequal: No Solution Exploring Operation: 42*98=4116, Resulting Numbers: [4116] 4116,79 unequal: No Solution Exploring Operation: 98-42=56, Resulting Numbers: [56] 56,79 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: 79:[50, 21, 96], Operations: ['2*48=96'] Exploring Operation: 96-21=75, Resulting Numbers: [50, 75] Generated Node #0,0,0: 79:[50, 75] Operation: 96-21=75 Exploring Operation: 50-21=29, Resulting Numbers: [96, 29] Generated Node #0,0,1: 79:[96, 29] Operation: 50-21=29 Exploring Operation: 50+21=71, Resulting Numbers: [96, 71] Generated Node #0,0,2: 79:[96, 71] Operation: 50+21=71 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[96, 71], Operations: ['2*48=96', '50+21=71'] Exploring Operation: 96-71=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 96+71=167, Resulting Numbers: [167] 167,79 unequal: No Solution Exploring Operation: 96*71=6816, Resulting Numbers: [6816] 6816,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[50, 75], Operations: ['2*48=96', '96-21=75'] Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 50*75=3750, Resulting Numbers: [3750] 3750,79 unequal: No Solution Exploring Operation: 50+75=125, Resulting Numbers: [125] 125,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[96, 29], Operations: ['2*48=96', '50-21=29'] Exploring Operation: 96*29=2784, Resulting Numbers: [2784] 2784,79 unequal: No Solution Exploring Operation: 96+29=125, Resulting Numbers: [125] 125,79 unequal: No Solution Exploring Operation: 96-29=67, Resulting Numbers: [67] 67,79 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: 79:[21, 48, 100], Operations: ['50*2=100'] Exploring Operation: 48-21=27, Resulting Numbers: [100, 27] Generated Node #0,1,0: 79:[100, 27] Operation: 48-21=27 Exploring Operation: 21+48=69, Resulting Numbers: [100, 69] Generated Node #0,1,1: 79:[100, 69] Operation: 21+48=69 Exploring Operation: 100-21=79, Resulting Numbers: [48, 79] Generated Node #0,1,2: 79:[48, 79] Operation: 100-21=79 Moving to Node #0,1,1 Current State: 79:[100, 69], Operations: ['50*2=100', '21+48=69'] Exploring Operation: 100*69=6900, Resulting Numbers: [6900] 6900,79 unequal: No Solution Exploring Operation: 100-69=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 100+69=169, Resulting Numbers: [169] 169,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[48, 79], Operations: ['50*2=100', '100-21=79'] Exploring Operation: 48*79=3792, Resulting Numbers: [3792] 3792,79 unequal: No Solution Exploring Operation: 48+79=127, Resulting Numbers: [127] 127,79 unequal: No Solution Exploring Operation: 79-48=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[100, 27], Operations: ['50*2=100', '48-21=27'] Exploring Operation: 100+27=127, Resulting Numbers: [127] 127,79 unequal: No Solution Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,79 unequal: No Solution Exploring Operation: 100*27=2700, Resulting Numbers: [2700] 2700,79 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 43, 73, 65, 64 ]
13
[ "43+73=116", "65+64=129", "129-116=13" ]
Current State: 13:[43, 73, 65, 64], Operations: [] Exploring Operation: 43+73=116, Resulting Numbers: [65, 64, 116] Generated Node #2: [65, 64, 116] from Operation: 43+73=116 Current State: 13:[65, 64, 116], Operations: ['43+73=116'] Exploring Operation: 65+64=129, Resulting Numbers: [116, 129] Generated Node #3: [116, 129] from Operation: 65+64=129 Current State: 13:[116, 129], Operations: ['43+73=116', '65+64=129'] Exploring Operation: 129-116=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[43, 73, 65, 64], Operations: [] Exploring Operation: 73-65=8, Resulting Numbers: [43, 64, 8] Generated Node #0,0: 13:[43, 64, 8] Operation: 73-65=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[43, 64, 8], Operations: ['73-65=8'] Exploring Operation: 64-43=21, Resulting Numbers: [8, 21] Generated Node #0,0,0: 13:[8, 21] Operation: 64-43=21 Moving to Node #0,0,0 Current State: 13:[8, 21], Operations: ['73-65=8', '64-43=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[43, 73, 65, 64], Operations: [] Exploring Operation: 73-65=8, Resulting Numbers: [43, 64, 8] Generated Node #0,0: 13:[43, 64, 8] Operation: 73-65=8 Moving to Node #0,0 Current State: 13:[43, 64, 8], Operations: ['73-65=8'] Exploring Operation: 64-43=21, Resulting Numbers: [8, 21] Generated Node #0,0,0: 13:[8, 21] Operation: 64-43=21 Moving to Node #0,0,0 Current State: 13:[8, 21], Operations: ['73-65=8', '64-43=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 15, 30, 46 ]
44
[ "15*46=690", "690-30=660", "660/15=44" ]
Current State: 44:[15, 15, 30, 46], Operations: [] Exploring Operation: 15*46=690, Resulting Numbers: [30, 690] Generated Node #2: [30, 690] from Operation: 15*46=690 Current State: 44:[30, 690], Operations: ['15*46=690'] Exploring Operation: 690-30=660, Resulting Numbers: [660] 660,44 equal: Goal Reached Exploring Operation: 660/15=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[15, 15, 30, 46], Operations: [] Exploring Operation: 30/15=2, Resulting Numbers: [15, 46, 2] Generated Node #0,0: 44:[15, 46, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[15, 46, 2], Operations: ['30/15=2'] Exploring Operation: 15-2=13, Resulting Numbers: [46, 13] Generated Node #0,0,0: 44:[46, 13] Operation: 15-2=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[46, 13], Operations: ['30/15=2', '15-2=13'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 63, 76, 42, 21 ]
89
[ "76*42=3192", "3192/21=152", "152-63=89" ]
Current State: 89:[63, 76, 42, 21], Operations: [] Exploring Operation: 76*42=3192, Resulting Numbers: [63, 21, 3192] Generated Node #2: [63, 21, 3192] from Operation: 76*42=3192 Current State: 89:[63, 21, 3192], Operations: ['76*42=3192'] Exploring Operation: 3192/21=152, Resulting Numbers: [63, 152] Generated Node #3: [63, 152] from Operation: 3192/21=152 Current State: 89:[63, 152], Operations: ['76*42=3192', '3192/21=152'] Exploring Operation: 152-63=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[63, 76, 42, 21], Operations: [] Exploring Operation: 42+21=63, Resulting Numbers: [63, 76, 63] Generated Node #0,0: 89:[63, 76, 63] Operation: 42+21=63 Exploring Operation: 63+21=84, Resulting Numbers: [76, 42, 84] Generated Node #0,1: 89:[76, 42, 84] Operation: 63+21=84 Exploring Operation: 63+42=105, Resulting Numbers: [76, 21, 105] Generated Node #0,2: 89:[76, 21, 105] Operation: 63+42=105 Exploring Operation: 76+21=97, Resulting Numbers: [63, 42, 97] Generated Node #0,3: 89:[63, 42, 97] Operation: 76+21=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[63, 76, 63], Operations: ['42+21=63'] Exploring Operation: 76+63=139, Resulting Numbers: [63, 139] Generated Node #0,0,0: 89:[63, 139] Operation: 76+63=139 Exploring Operation: 63/63=1, Resulting Numbers: [76, 1] Generated Node #0,0,1: 89:[76, 1] Operation: 63/63=1 Exploring Operation: 63+76=139, Resulting Numbers: [63, 139] Generated Node #0,0,2: 89:[63, 139] Operation: 63+76=139 Exploring Operation: 63+63=126, Resulting Numbers: [76, 126] Generated Node #0,0,3: 89:[76, 126] Operation: 63+63=126 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[76, 126], Operations: ['42+21=63', '63+63=126'] Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,89 unequal: No Solution Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[63, 139], Operations: ['42+21=63', '76+63=139'] Exploring Operation: 139-63=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 63+139=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 63*139=8757, Resulting Numbers: [8757] 8757,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[63, 139], Operations: ['42+21=63', '63+76=139'] Exploring Operation: 139-63=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 63+139=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 63*139=8757, Resulting Numbers: [8757] 8757,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[76, 1], Operations: ['42+21=63', '63/63=1'] Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,89 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[76, 42, 84], Operations: ['63+21=84'] Exploring Operation: 42+84=126, Resulting Numbers: [76, 126] Generated Node #0,1,0: 89:[76, 126] Operation: 42+84=126 Exploring Operation: 84-42=42, Resulting Numbers: [76, 42] Generated Node #0,1,1: 89:[76, 42] Operation: 84-42=42 Exploring Operation: 76-42=34, Resulting Numbers: [84, 34] Generated Node #0,1,2: 89:[84, 34] Operation: 76-42=34 Exploring Operation: 76+42=118, Resulting Numbers: [84, 118] Generated Node #0,1,3: 89:[84, 118] Operation: 76+42=118 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 89:[84, 118], Operations: ['63+21=84', '76+42=118'] Exploring Operation: 118-84=34, Resulting Numbers: [34] 34,89 unequal: No Solution Exploring Operation: 84+118=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 84*118=9912, Resulting Numbers: [9912] 9912,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[76, 126], Operations: ['63+21=84', '42+84=126'] Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[76, 42], Operations: ['63+21=84', '84-42=42'] Exploring Operation: 76*42=3192, Resulting Numbers: [3192] 3192,89 unequal: No Solution Exploring Operation: 76+42=118, Resulting Numbers: [118] 118,89 unequal: No Solution Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[84, 34], Operations: ['63+21=84', '76-42=34'] Exploring Operation: 84*34=2856, Resulting Numbers: [2856] 2856,89 unequal: No Solution Exploring Operation: 84+34=118, Resulting Numbers: [118] 118,89 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[63, 42, 97], Operations: ['76+21=97'] Exploring Operation: 63+42=105, Resulting Numbers: [97, 105] Generated Node #0,3,0: 89:[97, 105] Operation: 63+42=105 Exploring Operation: 42+97=139, Resulting Numbers: [63, 139] Generated Node #0,3,1: 89:[63, 139] Operation: 42+97=139 Exploring Operation: 97-42=55, Resulting Numbers: [63, 55] Generated Node #0,3,2: 89:[63, 55] Operation: 97-42=55 Exploring Operation: 63-42=21, Resulting Numbers: [97, 21] Generated Node #0,3,3: 89:[97, 21] Operation: 63-42=21 Moving to Node #0,3,0 Current State: 89:[97, 105], Operations: ['76+21=97', '63+42=105'] Exploring Operation: 97+105=202, Resulting Numbers: [202] 202,89 unequal: No Solution Exploring Operation: 97*105=10185, Resulting Numbers: [10185] 10185,89 unequal: No Solution Exploring Operation: 105-97=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[63, 55], Operations: ['76+21=97', '97-42=55'] Exploring Operation: 63-55=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 63*55=3465, Resulting Numbers: [3465] 3465,89 unequal: No Solution Exploring Operation: 63+55=118, Resulting Numbers: [118] 118,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[97, 21], Operations: ['76+21=97', '63-42=21'] Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,89 unequal: No Solution Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[63, 139], Operations: ['76+21=97', '42+97=139'] Exploring Operation: 139-63=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 63*139=8757, Resulting Numbers: [8757] 8757,89 unequal: No Solution Exploring Operation: 63+139=202, Resulting Numbers: [202] 202,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[76, 21, 105], Operations: ['63+42=105'] Exploring Operation: 105-21=84, Resulting Numbers: [76, 84] Generated Node #0,2,0: 89:[76, 84] Operation: 105-21=84 Exploring Operation: 21+105=126, Resulting Numbers: [76, 126] Generated Node #0,2,1: 89:[76, 126] Operation: 21+105=126 Exploring Operation: 76+21=97, Resulting Numbers: [105, 97] Generated Node #0,2,2: 89:[105, 97] Operation: 76+21=97 Exploring Operation: 76-21=55, Resulting Numbers: [105, 55] Generated Node #0,2,3: 89:[105, 55] Operation: 76-21=55 Moving to Node #0,2,0 Current State: 89:[76, 84], Operations: ['63+42=105', '105-21=84'] Exploring Operation: 76*84=6384, Resulting Numbers: [6384] 6384,89 unequal: No Solution Exploring Operation: 76+84=160, Resulting Numbers: [160] 160,89 unequal: No Solution Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[105, 97], Operations: ['63+42=105', '76+21=97'] Exploring Operation: 105*97=10185, Resulting Numbers: [10185] 10185,89 unequal: No Solution Exploring Operation: 105-97=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 105+97=202, Resulting Numbers: [202] 202,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[105, 55], Operations: ['63+42=105', '76-21=55'] Exploring Operation: 105*55=5775, Resulting Numbers: [5775] 5775,89 unequal: No Solution Exploring Operation: 105+55=160, Resulting Numbers: [160] 160,89 unequal: No Solution Exploring Operation: 105-55=50, Resulting Numbers: [50] 50,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[76, 126], Operations: ['63+42=105', '21+105=126'] Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,89 unequal: No Solution Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,89 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
[ 58, 66, 74, 2 ]
45
[ "66-58=8", "74/2=37", "8+37=45" ]
Current State: 45:[58, 66, 74, 2], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [74, 2, 8] Generated Node #2: [74, 2, 8] from Operation: 66-58=8 Current State: 45:[74, 2, 8], Operations: ['66-58=8'] Exploring Operation: 74/2=37, Resulting Numbers: [8, 37] Generated Node #3: [8, 37] from Operation: 74/2=37 Current State: 45:[8, 37], Operations: ['66-58=8', '74/2=37'] Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[58, 66, 74, 2], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [58, 2, 8] Generated Node #0,0: 45:[58, 2, 8] Operation: 74-66=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[58, 2, 8], Operations: ['74-66=8'] Exploring Operation: 58-8=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 45:[2, 50] Operation: 58-8=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[2, 50], Operations: ['74-66=8', '58-8=50'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,45 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
[ 48, 20, 44, 45 ]
100
[ "48-44=4", "45-20=25", "4*25=100" ]
Current State: 100:[48, 20, 44, 45], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [20, 45, 4] Generated Node #2: [20, 45, 4] from Operation: 48-44=4 Current State: 100:[20, 45, 4], Operations: ['48-44=4'] Exploring Operation: 45-20=25, Resulting Numbers: [4, 25] Generated Node #3: [4, 25] from Operation: 45-20=25 Current State: 100:[4, 25], Operations: ['48-44=4', '45-20=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[48, 20, 44, 45], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [20, 45, 4] Generated Node #0,0: 100:[20, 45, 4] Operation: 48-44=4 Exploring Operation: 45-44=1, Resulting Numbers: [48, 20, 1] Generated Node #0,1: 100:[48, 20, 1] Operation: 45-44=1 Moving to Node #0,1 Current State: 100:[48, 20, 1], Operations: ['45-44=1'] Exploring Operation: 48+1=49, Resulting Numbers: [20, 49] Generated Node #0,1,0: 100:[20, 49] Operation: 48+1=49 Exploring Operation: 48*1=48, Resulting Numbers: [20, 48] Generated Node #0,1,1: 100:[20, 48] Operation: 48*1=48 Moving to Node #0,0 Current State: 100:[20, 45, 4], Operations: ['48-44=4'] Exploring Operation: 45-20=25, Resulting Numbers: [4, 25] Generated Node #0,0,0: 100:[4, 25] Operation: 45-20=25 Exploring Operation: 45+4=49, Resulting Numbers: [20, 49] Generated Node #0,0,1: 100:[20, 49] Operation: 45+4=49 Moving to Node #0,0,0 Current State: 100:[4, 25], Operations: ['48-44=4', '45-20=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,100 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[48, 20, 44, 45], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [20, 45, 4] Generated Node #0,0: 100:[20, 45, 4] Operation: 48-44=4 Moving to Node #0,0 Current State: 100:[20, 45, 4], Operations: ['48-44=4'] Exploring Operation: 45-20=25, Resulting Numbers: [4, 25] Generated Node #0,0,0: 100:[4, 25] Operation: 45-20=25 Moving to Node #0,0,0 Current State: 100:[4, 25], Operations: ['48-44=4', '45-20=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 94, 25, 99, 7 ]
37
[ "94-25=69", "99+7=106", "106-69=37" ]
Current State: 37:[94, 25, 99, 7], Operations: [] Exploring Operation: 94-25=69, Resulting Numbers: [99, 7, 69] Generated Node #2: [99, 7, 69] from Operation: 94-25=69 Current State: 37:[99, 7, 69], Operations: ['94-25=69'] Exploring Operation: 99+7=106, Resulting Numbers: [69, 106] Generated Node #3: [69, 106] from Operation: 99+7=106 Current State: 37:[69, 106], Operations: ['94-25=69', '99+7=106'] Exploring Operation: 106-69=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[94, 25, 99, 7], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [25, 7, 5] Generated Node #0,0: 37:[25, 7, 5] Operation: 99-94=5 Moving to Node #0,0 Current State: 37:[25, 7, 5], Operations: ['99-94=5'] Exploring Operation: 7*5=35, Resulting Numbers: [25, 35] Generated Node #0,0,0: 37:[25, 35] Operation: 7*5=35 Moving to Node #0,0,0 Current State: 37:[25, 35], Operations: ['99-94=5', '7*5=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,37 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 58, 30, 10, 92 ]
74
[ "58-30=28", "10+92=102", "102-28=74" ]
Current State: 74:[58, 30, 10, 92], Operations: [] Exploring Operation: 58-30=28, Resulting Numbers: [10, 92, 28] Generated Node #2: [10, 92, 28] from Operation: 58-30=28 Current State: 74:[10, 92, 28], Operations: ['58-30=28'] Exploring Operation: 10+92=102, Resulting Numbers: [28, 102] Generated Node #3: [28, 102] from Operation: 10+92=102 Current State: 74:[28, 102], Operations: ['58-30=28', '10+92=102'] Exploring Operation: 102-28=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[58, 30, 10, 92], Operations: [] Exploring Operation: 92-58=34, Resulting Numbers: [30, 10, 34] Generated Node #0,0: 74:[30, 10, 34] Operation: 92-58=34 Exploring Operation: 92-10=82, Resulting Numbers: [58, 30, 82] Generated Node #0,1: 74:[58, 30, 82] Operation: 92-10=82 Exploring Operation: 58+10=68, Resulting Numbers: [30, 92, 68] Generated Node #0,2: 74:[30, 92, 68] Operation: 58+10=68 Exploring Operation: 58-30=28, Resulting Numbers: [10, 92, 28] Generated Node #0,3: 74:[10, 92, 28] Operation: 58-30=28 Moving to Node #0,0 Current State: 74:[30, 10, 34], Operations: ['92-58=34'] Exploring Operation: 34-30=4, Resulting Numbers: [10, 4] Generated Node #0,0,0: 74:[10, 4] Operation: 34-30=4 Exploring Operation: 30/10=3, Resulting Numbers: [34, 3] Generated Node #0,0,1: 74:[34, 3] Operation: 30/10=3 Exploring Operation: 10+34=44, Resulting Numbers: [30, 44] Generated Node #0,0,2: 74:[30, 44] Operation: 10+34=44 Exploring Operation: 30+10=40, Resulting Numbers: [34, 40] Generated Node #0,0,3: 74:[34, 40] Operation: 30+10=40 Moving to Node #0,2 Current State: 74:[30, 92, 68], Operations: ['58+10=68'] Exploring Operation: 92-68=24, Resulting Numbers: [30, 24] Generated Node #0,2,0: 74:[30, 24] Operation: 92-68=24 Exploring Operation: 92-30=62, Resulting Numbers: [68, 62] Generated Node #0,2,1: 74:[68, 62] Operation: 92-30=62 Exploring Operation: 30+68=98, Resulting Numbers: [92, 98] Generated Node #0,2,2: 74:[92, 98] Operation: 30+68=98 Exploring Operation: 68-30=38, Resulting Numbers: [92, 38] Generated Node #0,2,3: 74:[92, 38] Operation: 68-30=38 Moving to Node #0,1 Current State: 74:[58, 30, 82], Operations: ['92-10=82'] Exploring Operation: 58-30=28, Resulting Numbers: [82, 28] Generated Node #0,1,0: 74:[82, 28] Operation: 58-30=28 Exploring Operation: 58+30=88, Resulting Numbers: [82, 88] Generated Node #0,1,1: 74:[82, 88] Operation: 58+30=88 Exploring Operation: 82-58=24, Resulting Numbers: [30, 24] Generated Node #0,1,2: 74:[30, 24] Operation: 82-58=24 Exploring Operation: 82-30=52, Resulting Numbers: [58, 52] Generated Node #0,1,3: 74:[58, 52] Operation: 82-30=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[82, 28], Operations: ['92-10=82', '58-30=28'] Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,74 unequal: No Solution No 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: 74:[30, 24], Operations: ['92-10=82', '82-58=24'] Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 30*24=720, Resulting Numbers: [720] 720,74 unequal: No Solution No 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: 74:[82, 88], Operations: ['92-10=82', '58+30=88'] Exploring Operation: 82+88=170, Resulting Numbers: [170] 170,74 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 82*88=7216, Resulting Numbers: [7216] 7216,74 unequal: No Solution No 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: 74:[58, 52], Operations: ['92-10=82', '82-30=52'] Exploring Operation: 58*52=3016, Resulting Numbers: [3016] 3016,74 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 58+52=110, Resulting Numbers: [110] 110,74 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: 74:[10, 92, 28], Operations: ['58-30=28'] Exploring Operation: 92-28=64, Resulting Numbers: [10, 64] Generated Node #0,3,0: 74:[10, 64] Operation: 92-28=64 Exploring Operation: 10+28=38, Resulting Numbers: [92, 38] Generated Node #0,3,1: 74:[92, 38] Operation: 10+28=38 Exploring Operation: 28-10=18, Resulting Numbers: [92, 18] Generated Node #0,3,2: 74:[92, 18] Operation: 28-10=18 Exploring Operation: 92-10=82, Resulting Numbers: [28, 82] Generated Node #0,3,3: 74:[28, 82] Operation: 92-10=82 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[28, 82], Operations: ['58-30=28', '92-10=82'] Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,74 unequal: No Solution Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,74 unequal: No Solution No 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: 74:[10, 64], Operations: ['58-30=28', '92-28=64'] Exploring Operation: 10*64=640, Resulting Numbers: [640] 640,74 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[58, 30, 10, 92], Operations: [] Exploring Operation: 58-30=28, Resulting Numbers: [10, 92, 28] Generated Node #0,3: 74:[10, 92, 28] Operation: 58-30=28 Moving to Node #0,3 Current State: 74:[10, 92, 28], Operations: ['58-30=28'] Exploring Operation: 92-28=64, Resulting Numbers: [10, 64] Generated Node #0,3,0: 74:[10, 64] Operation: 92-28=64 Moving to Node #0,3,0 Current State: 74:[10, 64], Operations: ['58-30=28', '92-28=64'] Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_4
mult_heuristic
[ 75, 19, 3, 8 ]
84
[ "19+8=27", "27/3=9", "75+9=84" ]
Current State: 84:[75, 19, 3, 8], Operations: [] Exploring Operation: 19+8=27, Resulting Numbers: [75, 3, 27] Generated Node #2: [75, 3, 27] from Operation: 19+8=27 Current State: 84:[75, 3, 27], Operations: ['19+8=27'] Exploring Operation: 27/3=9, Resulting Numbers: [75, 9] Generated Node #3: [75, 9] from Operation: 27/3=9 Current State: 84:[75, 9], Operations: ['19+8=27', '27/3=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[75, 19, 3, 8], Operations: [] Exploring Operation: 19-8=11, Resulting Numbers: [75, 3, 11] Generated Node #0,0: 84:[75, 3, 11] Operation: 19-8=11 Exploring Operation: 75+8=83, Resulting Numbers: [19, 3, 83] Generated Node #0,1: 84:[19, 3, 83] Operation: 75+8=83 Exploring Operation: 75+3=78, Resulting Numbers: [19, 8, 78] Generated Node #0,2: 84:[19, 8, 78] Operation: 75+3=78 Exploring Operation: 75/3=25, Resulting Numbers: [19, 8, 25] Generated Node #0,3: 84:[19, 8, 25] Operation: 75/3=25 Exploring Operation: 19+8=27, Resulting Numbers: [75, 3, 27] Generated Node #0,4: 84:[75, 3, 27] Operation: 19+8=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[19, 3, 83], Operations: ['75+8=83'] Exploring Operation: 83-3=80, Resulting Numbers: [19, 80] Generated Node #0,1,0: 84:[19, 80] Operation: 83-3=80 Exploring Operation: 3+83=86, Resulting Numbers: [19, 86] Generated Node #0,1,1: 84:[19, 86] Operation: 3+83=86 Exploring Operation: 19+3=22, Resulting Numbers: [83, 22] Generated Node #0,1,2: 84:[83, 22] Operation: 19+3=22 Exploring Operation: 19-3=16, Resulting Numbers: [83, 16] Generated Node #0,1,3: 84:[83, 16] Operation: 19-3=16 Exploring Operation: 19*3=57, Resulting Numbers: [83, 57] Generated Node #0,1,4: 84:[83, 57] Operation: 19*3=57 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 84:[83, 22], Operations: ['75+8=83', '19+3=22'] Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,84 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 84:[83, 16], Operations: ['75+8=83', '19-3=16'] Exploring Operation: 83+16=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 83*16=1328, Resulting Numbers: [1328] 1328,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 84:[19, 86], Operations: ['75+8=83', '3+83=86'] Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,84 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 84:[19, 80], Operations: ['75+8=83', '83-3=80'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,84 unequal: No Solution Exploring Operation: 19+80=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 19*80=1520, Resulting Numbers: [1520] 1520,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 84:[83, 57], Operations: ['75+8=83', '19*3=57'] Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,84 unequal: No Solution Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,84 unequal: No Solution Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[19, 8, 25], Operations: ['75/3=25'] Exploring Operation: 25-19=6, Resulting Numbers: [8, 6] Generated Node #0,3,0: 84:[8, 6] Operation: 25-19=6 Exploring Operation: 19-8=11, Resulting Numbers: [25, 11] Generated Node #0,3,1: 84:[25, 11] Operation: 19-8=11 Exploring Operation: 25-8=17, Resulting Numbers: [19, 17] Generated Node #0,3,2: 84:[19, 17] Operation: 25-8=17 Exploring Operation: 19+8=27, Resulting Numbers: [25, 27] Generated Node #0,3,3: 84:[25, 27] Operation: 19+8=27 Exploring Operation: 19+25=44, Resulting Numbers: [8, 44] Generated Node #0,3,4: 84:[8, 44] Operation: 19+25=44 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 84:[8, 6], Operations: ['75/3=25', '25-19=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 84:[8, 44], Operations: ['75/3=25', '19+25=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,84 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 84:[25, 11], Operations: ['75/3=25', '19-8=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,84 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 84:[25, 27], Operations: ['75/3=25', '19+8=27'] Exploring Operation: 25*27=675, Resulting Numbers: [675] 675,84 unequal: No Solution Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 25+27=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 84:[19, 17], Operations: ['75/3=25', '25-8=17'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 19*17=323, Resulting Numbers: [323] 323,84 unequal: No Solution Exploring Operation: 19+17=36, Resulting Numbers: [36] 36,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[19, 8, 78], Operations: ['75+3=78'] Exploring Operation: 19+78=97, Resulting Numbers: [8, 97] Generated Node #0,2,0: 84:[8, 97] Operation: 19+78=97 Exploring Operation: 19+8=27, Resulting Numbers: [78, 27] Generated Node #0,2,1: 84:[78, 27] Operation: 19+8=27 Exploring Operation: 78-8=70, Resulting Numbers: [19, 70] Generated Node #0,2,2: 84:[19, 70] Operation: 78-8=70 Exploring Operation: 8+78=86, Resulting Numbers: [19, 86] Generated Node #0,2,3: 84:[19, 86] Operation: 8+78=86 Exploring Operation: 19-8=11, Resulting Numbers: [78, 11] Generated Node #0,2,4: 84:[78, 11] Operation: 19-8=11 Moving to Node #0,2,3 Current State: 84:[19, 86], Operations: ['75+3=78', '8+78=86'] Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,84 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,2,4 Current State: 84:[78, 11], Operations: ['75+3=78', '19-8=11'] Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 78*11=858, Resulting Numbers: [858] 858,84 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[78, 27], Operations: ['75+3=78', '19+8=27'] Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 78*27=2106, Resulting Numbers: [2106] 2106,84 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[8, 97], Operations: ['75+3=78', '19+78=97'] Exploring Operation: 8*97=776, Resulting Numbers: [776] 776,84 unequal: No Solution Exploring Operation: 8+97=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[19, 70], Operations: ['75+3=78', '78-8=70'] Exploring Operation: 70-19=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 19+70=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 19*70=1330, Resulting Numbers: [1330] 1330,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[75, 3, 11], Operations: ['19-8=11'] Exploring Operation: 75+3=78, Resulting Numbers: [11, 78] Generated Node #0,0,0: 84:[11, 78] Operation: 75+3=78 Exploring Operation: 75+11=86, Resulting Numbers: [3, 86] Generated Node #0,0,1: 84:[3, 86] Operation: 75+11=86 Exploring Operation: 3+11=14, Resulting Numbers: [75, 14] Generated Node #0,0,2: 84:[75, 14] Operation: 3+11=14 Exploring Operation: 75/3=25, Resulting Numbers: [11, 25] Generated Node #0,0,3: 84:[11, 25] Operation: 75/3=25 Exploring Operation: 11-3=8, Resulting Numbers: [75, 8] Generated Node #0,0,4: 84:[75, 8] Operation: 11-3=8 Moving to Node #0,0,1 Current State: 84:[3, 86], Operations: ['19-8=11', '75+11=86'] Exploring Operation: 3+86=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,84 unequal: No Solution Exploring Operation: 3*86=258, Resulting Numbers: [258] 258,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[11, 25], Operations: ['19-8=11', '75/3=25'] Exploring Operation: 11*25=275, Resulting Numbers: [275] 275,84 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 11+25=36, Resulting Numbers: [36] 36,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[11, 78], Operations: ['19-8=11', '75+3=78'] Exploring Operation: 11*78=858, Resulting Numbers: [858] 858,84 unequal: No Solution Exploring Operation: 11+78=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[75, 14], Operations: ['19-8=11', '3+11=14'] Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,84 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,84 unequal: No Solution Moving to Node #0,0,4 Current State: 84:[75, 8], Operations: ['19-8=11', '11-3=8'] Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,84 unequal: No Solution Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 84:[75, 3, 27], Operations: ['19+8=27'] Exploring Operation: 75/3=25, Resulting Numbers: [27, 25] Generated Node #0,4,0: 84:[27, 25] Operation: 75/3=25 Exploring Operation: 75-27=48, Resulting Numbers: [3, 48] Generated Node #0,4,1: 84:[3, 48] Operation: 75-27=48 Exploring Operation: 27/3=9, Resulting Numbers: [75, 9] Generated Node #0,4,2: 84:[75, 9] Operation: 27/3=9 Exploring Operation: 3+27=30, Resulting Numbers: [75, 30] Generated Node #0,4,3: 84:[75, 30] Operation: 3+27=30 Exploring Operation: 75+3=78, Resulting Numbers: [27, 78] Generated Node #0,4,4: 84:[27, 78] Operation: 75+3=78 Moving to Node #0,4,0 Current State: 84:[27, 25], Operations: ['19+8=27', '75/3=25'] Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 27+25=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 27*25=675, Resulting Numbers: [675] 675,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[3, 48], Operations: ['19+8=27', '75-27=48'] Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,84 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,84 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[27, 78], Operations: ['19+8=27', '75+3=78'] Exploring Operation: 27+78=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 27*78=2106, Resulting Numbers: [2106] 2106,84 unequal: No Solution Moving to Node #0,4,2 Current State: 84:[75, 9], Operations: ['19+8=27', '27/3=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[75, 19, 3, 8], Operations: [] Exploring Operation: 19+8=27, Resulting Numbers: [75, 3, 27] Generated Node #0,4: 84:[75, 3, 27] Operation: 19+8=27 Moving to Node #0,4 Current State: 84:[75, 3, 27], Operations: ['19+8=27'] Exploring Operation: 27/3=9, Resulting Numbers: [75, 9] Generated Node #0,4,2: 84:[75, 9] Operation: 27/3=9 Moving to Node #0,4,2 Current State: 84:[75, 9], Operations: ['19+8=27', '27/3=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.908854
hs_5
mult_heuristic
[ 2, 3, 38, 14 ]
54
[ "3+38=41", "41-14=27", "2*27=54" ]
Current State: 54:[2, 3, 38, 14], Operations: [] Exploring Operation: 3+38=41, Resulting Numbers: [2, 14, 41] Generated Node #2: [2, 14, 41] from Operation: 3+38=41 Current State: 54:[2, 14, 41], Operations: ['3+38=41'] Exploring Operation: 41-14=27, Resulting Numbers: [2, 27] Generated Node #3: [2, 27] from Operation: 41-14=27 Current State: 54:[2, 27], Operations: ['3+38=41', '41-14=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[2, 3, 38, 14], Operations: [] Exploring Operation: 2*14=28, Resulting Numbers: [3, 38, 28] Generated Node #0,0: 54:[3, 38, 28] Operation: 2*14=28 Exploring Operation: 38/2=19, Resulting Numbers: [3, 14, 19] Generated Node #0,1: 54:[3, 14, 19] Operation: 38/2=19 Exploring Operation: 38+14=52, Resulting Numbers: [2, 3, 52] Generated Node #0,2: 54:[2, 3, 52] Operation: 38+14=52 Exploring Operation: 38-14=24, Resulting Numbers: [2, 3, 24] Generated Node #0,3: 54:[2, 3, 24] Operation: 38-14=24 Exploring Operation: 14/2=7, Resulting Numbers: [3, 38, 7] Generated Node #0,4: 54:[3, 38, 7] Operation: 14/2=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[2, 3, 52], Operations: ['38+14=52'] Exploring Operation: 2+3=5, Resulting Numbers: [52, 5] Generated Node #0,2,0: 54:[52, 5] Operation: 2+3=5 Exploring Operation: 52/2=26, Resulting Numbers: [3, 26] Generated Node #0,2,1: 54:[3, 26] Operation: 52/2=26 Exploring Operation: 2+52=54, Resulting Numbers: [3, 54] Generated Node #0,2,2: 54:[3, 54] Operation: 2+52=54 Exploring Operation: 2*3=6, Resulting Numbers: [52, 6] Generated Node #0,2,3: 54:[52, 6] Operation: 2*3=6 Exploring Operation: 3+52=55, Resulting Numbers: [2, 55] Generated Node #0,2,4: 54:[2, 55] Operation: 3+52=55 Moving to Node #0,2,2 Current State: 54:[3, 54], Operations: ['38+14=52', '2+52=54'] Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,54 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,54 unequal: No Solution Moving to Node #0,2,4 Current State: 54:[2, 55], Operations: ['38+14=52', '3+52=55'] Exploring Operation: 2*55=110, Resulting Numbers: [110] 110,54 unequal: No Solution Exploring Operation: 2+55=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[3, 26], Operations: ['38+14=52', '52/2=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[52, 6], Operations: ['38+14=52', '2*3=6'] Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,54 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[52, 5], Operations: ['38+14=52', '2+3=5'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 52+5=57, Resulting Numbers: [57] 57,54 unequal: No Solution Exploring Operation: 52*5=260, Resulting Numbers: [260] 260,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[2, 3, 24], Operations: ['38-14=24'] Exploring Operation: 2+24=26, Resulting Numbers: [3, 26] Generated Node #0,3,0: 54:[3, 26] Operation: 2+24=26 Exploring Operation: 3+24=27, Resulting Numbers: [2, 27] Generated Node #0,3,1: 54:[2, 27] Operation: 3+24=27 Exploring Operation: 24/3=8, Resulting Numbers: [2, 8] Generated Node #0,3,2: 54:[2, 8] Operation: 24/3=8 Exploring Operation: 24/2=12, Resulting Numbers: [3, 12] Generated Node #0,3,3: 54:[3, 12] Operation: 24/2=12 Exploring Operation: 2*3=6, Resulting Numbers: [24, 6] Generated Node #0,3,4: 54:[24, 6] Operation: 2*3=6 Moving to Node #0,3,1 Current State: 54:[2, 27], Operations: ['38-14=24', '3+24=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[2, 3, 38, 14], Operations: [] Exploring Operation: 38-14=24, Resulting Numbers: [2, 3, 24] Generated Node #0,3: 54:[2, 3, 24] Operation: 38-14=24 Moving to Node #0,3 Current State: 54:[2, 3, 24], Operations: ['38-14=24'] Exploring Operation: 3+24=27, Resulting Numbers: [2, 27] Generated Node #0,3,1: 54:[2, 27] Operation: 3+24=27 Moving to Node #0,3,1 Current State: 54:[2, 27], Operations: ['38-14=24', '3+24=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 51, 89, 4, 23 ]
23
[ "51-23=28", "4*28=112", "112-89=23" ]
Current State: 23:[51, 89, 4, 23], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [89, 4, 28] Generated Node #2: [89, 4, 28] from Operation: 51-23=28 Current State: 23:[89, 4, 28], Operations: ['51-23=28'] Exploring Operation: 4*28=112, Resulting Numbers: [89, 112] Generated Node #3: [89, 112] from Operation: 4*28=112 Current State: 23:[89, 112], Operations: ['51-23=28', '4*28=112'] Exploring Operation: 112-89=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[51, 89, 4, 23], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [51, 23, 85] Generated Node #0,0: 23:[51, 23, 85] Operation: 89-4=85 Exploring Operation: 89-51=38, Resulting Numbers: [4, 23, 38] Generated Node #0,1: 23:[4, 23, 38] Operation: 89-51=38 Exploring Operation: 51-4=47, Resulting Numbers: [89, 23, 47] Generated Node #0,2: 23:[89, 23, 47] Operation: 51-4=47 Exploring Operation: 51-23=28, Resulting Numbers: [89, 4, 28] Generated Node #0,3: 23:[89, 4, 28] Operation: 51-23=28 Moving to Node #0,1 Current State: 23:[4, 23, 38], Operations: ['89-51=38'] Exploring Operation: 23-4=19, Resulting Numbers: [38, 19] Generated Node #0,1,0: 23:[38, 19] Operation: 23-4=19 Exploring Operation: 38-4=34, Resulting Numbers: [23, 34] Generated Node #0,1,1: 23:[23, 34] Operation: 38-4=34 Exploring Operation: 4+23=27, Resulting Numbers: [38, 27] Generated Node #0,1,2: 23:[38, 27] Operation: 4+23=27 Exploring Operation: 4+38=42, Resulting Numbers: [23, 42] Generated Node #0,1,3: 23:[23, 42] Operation: 4+38=42 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[23, 34], Operations: ['89-51=38', '38-4=34'] Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[38, 19], Operations: ['89-51=38', '23-4=19'] Exploring Operation: 38*19=722, Resulting Numbers: [722] 722,23 unequal: No Solution Exploring Operation: 38+19=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[38, 27], Operations: ['89-51=38', '4+23=27'] Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,23 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[23, 42], Operations: ['89-51=38', '4+38=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,23 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: 23:[89, 23, 47], Operations: ['51-4=47'] Exploring Operation: 89-47=42, Resulting Numbers: [23, 42] Generated Node #0,2,0: 23:[23, 42] Operation: 89-47=42 Exploring Operation: 89-23=66, Resulting Numbers: [47, 66] Generated Node #0,2,1: 23:[47, 66] Operation: 89-23=66 Exploring Operation: 47-23=24, Resulting Numbers: [89, 24] Generated Node #0,2,2: 23:[89, 24] Operation: 47-23=24 Exploring Operation: 89+23=112, Resulting Numbers: [47, 112] Generated Node #0,2,3: 23:[47, 112] Operation: 89+23=112 Moving to Node #0,0 Current State: 23:[51, 23, 85], Operations: ['89-4=85'] Exploring Operation: 51-23=28, Resulting Numbers: [85, 28] Generated Node #0,0,0: 23:[85, 28] Operation: 51-23=28 Exploring Operation: 51+23=74, Resulting Numbers: [85, 74] Generated Node #0,0,1: 23:[85, 74] Operation: 51+23=74 Exploring Operation: 85-51=34, Resulting Numbers: [23, 34] Generated Node #0,0,2: 23:[23, 34] Operation: 85-51=34 Exploring Operation: 85-23=62, Resulting Numbers: [51, 62] Generated Node #0,0,3: 23:[51, 62] Operation: 85-23=62 Moving to Node #0,3 Current State: 23:[89, 4, 28], Operations: ['51-23=28'] Exploring Operation: 89-28=61, Resulting Numbers: [4, 61] Generated Node #0,3,0: 23:[4, 61] Operation: 89-28=61 Exploring Operation: 28-4=24, Resulting Numbers: [89, 24] Generated Node #0,3,1: 23:[89, 24] Operation: 28-4=24 Exploring Operation: 89+4=93, Resulting Numbers: [28, 93] Generated Node #0,3,2: 23:[28, 93] Operation: 89+4=93 Exploring Operation: 89-4=85, Resulting Numbers: [28, 85] Generated Node #0,3,3: 23:[28, 85] Operation: 89-4=85 Moving to Node #0,0,2 Current State: 23:[23, 34], Operations: ['89-4=85', '85-51=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 23*34=782, Resulting Numbers: [782] 782,23 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[23, 42], Operations: ['51-4=47', '89-47=42'] Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,23 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[4, 61], Operations: ['51-23=28', '89-28=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[89, 24], Operations: ['51-4=47', '47-23=24'] Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 89*24=2136, Resulting Numbers: [2136] 2136,23 unequal: No Solution Exploring Operation: 89+24=113, Resulting Numbers: [113] 113,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[51, 62], Operations: ['89-4=85', '85-23=62'] Exploring Operation: 62-51=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 51*62=3162, Resulting Numbers: [3162] 3162,23 unequal: No Solution Exploring Operation: 51+62=113, Resulting Numbers: [113] 113,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[28, 85], Operations: ['51-23=28', '89-4=85'] Exploring Operation: 28+85=113, Resulting Numbers: [113] 113,23 unequal: No Solution Exploring Operation: 28*85=2380, Resulting Numbers: [2380] 2380,23 unequal: No Solution Exploring Operation: 85-28=57, Resulting Numbers: [57] 57,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[85, 28], Operations: ['89-4=85', '51-23=28'] Exploring Operation: 85*28=2380, Resulting Numbers: [2380] 2380,23 unequal: No Solution Exploring Operation: 85-28=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 85+28=113, Resulting Numbers: [113] 113,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[47, 66], Operations: ['51-4=47', '89-23=66'] Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 47*66=3102, Resulting Numbers: [3102] 3102,23 unequal: No Solution Exploring Operation: 47+66=113, Resulting Numbers: [113] 113,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[89, 24], Operations: ['51-23=28', '28-4=24'] Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 89+24=113, Resulting Numbers: [113] 113,23 unequal: No Solution Exploring Operation: 89*24=2136, Resulting Numbers: [2136] 2136,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[28, 93], Operations: ['51-23=28', '89+4=93'] Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,23 unequal: No Solution Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[47, 112], Operations: ['51-4=47', '89+23=112'] Exploring Operation: 47*112=5264, Resulting Numbers: [5264] 5264,23 unequal: No Solution Exploring Operation: 47+112=159, Resulting Numbers: [159] 159,23 unequal: No Solution Exploring Operation: 112-47=65, Resulting Numbers: [65] 65,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[85, 74], Operations: ['89-4=85', '51+23=74'] Exploring Operation: 85*74=6290, Resulting Numbers: [6290] 6290,23 unequal: No Solution Exploring Operation: 85+74=159, Resulting Numbers: [159] 159,23 unequal: No Solution Exploring Operation: 85-74=11, Resulting Numbers: [11] 11,23 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 52, 54, 12, 51 ]
43
[ "52+54=106", "12+51=63", "106-63=43" ]
Current State: 43:[52, 54, 12, 51], Operations: [] Exploring Operation: 52+54=106, Resulting Numbers: [12, 51, 106] Generated Node #2: [12, 51, 106] from Operation: 52+54=106 Current State: 43:[12, 51, 106], Operations: ['52+54=106'] Exploring Operation: 12+51=63, Resulting Numbers: [106, 63] Generated Node #3: [106, 63] from Operation: 12+51=63 Current State: 43:[106, 63], Operations: ['52+54=106', '12+51=63'] Exploring Operation: 106-63=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[52, 54, 12, 51], Operations: [] Exploring Operation: 54-12=42, Resulting Numbers: [52, 51, 42] Generated Node #0,0: 43:[52, 51, 42] Operation: 54-12=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[52, 51, 42], Operations: ['54-12=42'] Exploring Operation: 52-42=10, Resulting Numbers: [51, 10] Generated Node #0,0,0: 43:[51, 10] Operation: 52-42=10 Moving to Node #0,0,0 Current State: 43:[51, 10], Operations: ['54-12=42', '52-42=10'] Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,43 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
[ 61, 32, 2, 4 ]
55
[ "61+2=63", "32/4=8", "63-8=55" ]
Current State: 55:[61, 32, 2, 4], Operations: [] Exploring Operation: 61+2=63, Resulting Numbers: [32, 4, 63] Generated Node #2: [32, 4, 63] from Operation: 61+2=63 Current State: 55:[32, 4, 63], Operations: ['61+2=63'] Exploring Operation: 32/4=8, Resulting Numbers: [63, 8] Generated Node #3: [63, 8] from Operation: 32/4=8 Current State: 55:[63, 8], Operations: ['61+2=63', '32/4=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[61, 32, 2, 4], Operations: [] Exploring Operation: 61-2=59, Resulting Numbers: [32, 4, 59] Generated Node #0,0: 55:[32, 4, 59] Operation: 61-2=59 Exploring Operation: 32/2=16, Resulting Numbers: [61, 4, 16] Generated Node #0,1: 55:[61, 4, 16] Operation: 32/2=16 Exploring Operation: 61-32=29, Resulting Numbers: [2, 4, 29] Generated Node #0,2: 55:[2, 4, 29] Operation: 61-32=29 Exploring Operation: 32/4=8, Resulting Numbers: [61, 2, 8] Generated Node #0,3: 55:[61, 2, 8] Operation: 32/4=8 Exploring Operation: 32*2=64, Resulting Numbers: [61, 4, 64] Generated Node #0,4: 55:[61, 4, 64] Operation: 32*2=64 Moving to Node #0,1 Current State: 55:[61, 4, 16], Operations: ['32/2=16'] Exploring Operation: 16/4=4, Resulting Numbers: [61, 4] Generated Node #0,1,0: 55:[61, 4] Operation: 16/4=4 Exploring Operation: 61+4=65, Resulting Numbers: [16, 65] Generated Node #0,1,1: 55:[16, 65] Operation: 61+4=65 Exploring Operation: 61-4=57, Resulting Numbers: [16, 57] Generated Node #0,1,2: 55:[16, 57] Operation: 61-4=57 Exploring Operation: 61-16=45, Resulting Numbers: [4, 45] Generated Node #0,1,3: 55:[4, 45] Operation: 61-16=45 Exploring Operation: 16-4=12, Resulting Numbers: [61, 12] Generated Node #0,1,4: 55:[61, 12] Operation: 16-4=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[61, 4], Operations: ['32/2=16', '16/4=4'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 61+4=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 61*4=244, Resulting Numbers: [244] 244,55 unequal: No Solution No 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: 55:[16, 57], Operations: ['32/2=16', '61-4=57'] Exploring Operation: 16*57=912, Resulting Numbers: [912] 912,55 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,55 unequal: No Solution No 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: 55:[61, 12], Operations: ['32/2=16', '16-4=12'] Exploring Operation: 61-12=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 61*12=732, Resulting Numbers: [732] 732,55 unequal: No Solution Exploring Operation: 61+12=73, Resulting Numbers: [73] 73,55 unequal: No Solution No 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: 55:[4, 45], Operations: ['32/2=16', '61-16=45'] Exploring Operation: 4*45=180, Resulting Numbers: [180] 180,55 unequal: No Solution Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,55 unequal: No Solution No 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: 55:[16, 65], Operations: ['32/2=16', '61+4=65'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,55 unequal: No Solution Exploring Operation: 16*65=1040, Resulting Numbers: [1040] 1040,55 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: 55:[61, 2, 8], Operations: ['32/4=8'] Exploring Operation: 61-8=53, Resulting Numbers: [2, 53] Generated Node #0,3,0: 55:[2, 53] Operation: 61-8=53 Exploring Operation: 61-2=59, Resulting Numbers: [8, 59] Generated Node #0,3,1: 55:[8, 59] Operation: 61-2=59 Exploring Operation: 8/2=4, Resulting Numbers: [61, 4] Generated Node #0,3,2: 55:[61, 4] Operation: 8/2=4 Exploring Operation: 2+8=10, Resulting Numbers: [61, 10] Generated Node #0,3,3: 55:[61, 10] Operation: 2+8=10 Exploring Operation: 8-2=6, Resulting Numbers: [61, 6] Generated Node #0,3,4: 55:[61, 6] Operation: 8-2=6 Moving to Node #0,4 Current State: 55:[61, 4, 64], Operations: ['32*2=64'] Exploring Operation: 64/4=16, Resulting Numbers: [61, 16] Generated Node #0,4,0: 55:[61, 16] Operation: 64/4=16 Exploring Operation: 61+4=65, Resulting Numbers: [64, 65] Generated Node #0,4,1: 55:[64, 65] Operation: 61+4=65 Exploring Operation: 64-4=60, Resulting Numbers: [61, 60] Generated Node #0,4,2: 55:[61, 60] Operation: 64-4=60 Exploring Operation: 64-61=3, Resulting Numbers: [4, 3] Generated Node #0,4,3: 55:[4, 3] Operation: 64-61=3 Exploring Operation: 61-4=57, Resulting Numbers: [64, 57] Generated Node #0,4,4: 55:[64, 57] Operation: 61-4=57 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 55:[4, 3], Operations: ['32*2=64', '64-61=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,55 unequal: No Solution No 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: 55:[61, 16], Operations: ['32*2=64', '64/4=16'] Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,55 unequal: No Solution Exploring Operation: 61+16=77, Resulting Numbers: [77] 77,55 unequal: No Solution Exploring Operation: 61*16=976, Resulting Numbers: [976] 976,55 unequal: No Solution No 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: 55:[61, 60], Operations: ['32*2=64', '64-4=60'] Exploring Operation: 61*60=3660, Resulting Numbers: [3660] 3660,55 unequal: No Solution Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 61+60=121, Resulting Numbers: [121] 121,55 unequal: No Solution No 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: 55:[64, 57], Operations: ['32*2=64', '61-4=57'] Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 64*57=3648, Resulting Numbers: [3648] 3648,55 unequal: No Solution Exploring Operation: 64+57=121, Resulting Numbers: [121] 121,55 unequal: No Solution No 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: 55:[64, 65], Operations: ['32*2=64', '61+4=65'] Exploring Operation: 65-64=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 64+65=129, Resulting Numbers: [129] 129,55 unequal: No Solution Exploring Operation: 64*65=4160, Resulting Numbers: [4160] 4160,55 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: 55:[2, 4, 29], Operations: ['61-32=29'] Exploring Operation: 2*29=58, Resulting Numbers: [4, 58] Generated Node #0,2,0: 55:[4, 58] Operation: 2*29=58 Exploring Operation: 2+4=6, Resulting Numbers: [29, 6] Generated Node #0,2,1: 55:[29, 6] Operation: 2+4=6 Exploring Operation: 2*4=8, Resulting Numbers: [29, 8] Generated Node #0,2,2: 55:[29, 8] Operation: 2*4=8 Exploring Operation: 29-4=25, Resulting Numbers: [2, 25] Generated Node #0,2,3: 55:[2, 25] Operation: 29-4=25 Exploring Operation: 29-2=27, Resulting Numbers: [4, 27] Generated Node #0,2,4: 55:[4, 27] Operation: 29-2=27 Moving to Node #0,0 Current State: 55:[32, 4, 59], Operations: ['61-2=59'] Exploring Operation: 32/4=8, Resulting Numbers: [59, 8] Generated Node #0,0,0: 55:[59, 8] Operation: 32/4=8 Exploring Operation: 59-32=27, Resulting Numbers: [4, 27] Generated Node #0,0,1: 55:[4, 27] Operation: 59-32=27 Exploring Operation: 32+4=36, Resulting Numbers: [59, 36] Generated Node #0,0,2: 55:[59, 36] Operation: 32+4=36 Exploring Operation: 59-4=55, Resulting Numbers: [32, 55] Generated Node #0,0,3: 55:[32, 55] Operation: 59-4=55 Exploring Operation: 32-4=28, Resulting Numbers: [59, 28] Generated Node #0,0,4: 55:[59, 28] Operation: 32-4=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[59, 8], Operations: ['61-2=59', '32/4=8'] Exploring Operation: 59+8=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 59*8=472, Resulting Numbers: [472] 472,55 unequal: No Solution Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,55 unequal: No Solution No 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: 55:[4, 27], Operations: ['61-2=59', '59-32=27'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,55 unequal: No Solution No 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: 55:[32, 55], Operations: ['61-2=59', '59-4=55'] Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,55 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,55 unequal: No Solution No 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: 55:[59, 28], Operations: ['61-2=59', '32-4=28'] Exploring Operation: 59*28=1652, Resulting Numbers: [1652] 1652,55 unequal: No Solution Exploring Operation: 59+28=87, Resulting Numbers: [87] 87,55 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,55 unequal: No Solution No 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: 55:[59, 36], Operations: ['61-2=59', '32+4=36'] Exploring Operation: 59+36=95, Resulting Numbers: [95] 95,55 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,55 unequal: No Solution Exploring Operation: 59*36=2124, Resulting Numbers: [2124] 2124,55 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: 55:[4, 58], Operations: ['61-32=29', '2*29=58'] Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,55 unequal: No Solution Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,55 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[2, 53], Operations: ['32/4=8', '61-8=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,55 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[61, 32, 2, 4], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [61, 2, 8] Generated Node #0,3: 55:[61, 2, 8] Operation: 32/4=8 Moving to Node #0,3 Current State: 55:[61, 2, 8], Operations: ['32/4=8'] Exploring Operation: 61-8=53, Resulting Numbers: [2, 53] Generated Node #0,3,0: 55:[2, 53] Operation: 61-8=53 Moving to Node #0,3,0 Current State: 55:[2, 53], Operations: ['32/4=8', '61-8=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.927083
hs_5
sum_heuristic
[ 79, 81, 14, 84 ]
62
[ "79+81=160", "14+84=98", "160-98=62" ]
Current State: 62:[79, 81, 14, 84], Operations: [] Exploring Operation: 79+81=160, Resulting Numbers: [14, 84, 160] Generated Node #2: [14, 84, 160] from Operation: 79+81=160 Current State: 62:[14, 84, 160], Operations: ['79+81=160'] Exploring Operation: 14+84=98, Resulting Numbers: [160, 98] Generated Node #3: [160, 98] from Operation: 14+84=98 Current State: 62:[160, 98], Operations: ['79+81=160', '14+84=98'] Exploring Operation: 160-98=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[79, 81, 14, 84], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [79, 14, 3] Generated Node #0,0: 62:[79, 14, 3] Operation: 84-81=3 Moving to Node #0,0 Current State: 62:[79, 14, 3], Operations: ['84-81=3'] Exploring Operation: 79-14=65, Resulting Numbers: [3, 65] Generated Node #0,0,0: 62:[3, 65] Operation: 79-14=65 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[3, 65], Operations: ['84-81=3', '79-14=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[79, 81, 14, 84], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [79, 14, 3] Generated Node #0,0: 62:[79, 14, 3] Operation: 84-81=3 Moving to Node #0,0 Current State: 62:[79, 14, 3], Operations: ['84-81=3'] Exploring Operation: 79-14=65, Resulting Numbers: [3, 65] Generated Node #0,0,0: 62:[3, 65] Operation: 79-14=65 Moving to Node #0,0,0 Current State: 62:[3, 65], Operations: ['84-81=3', '79-14=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic