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
[ 91, 49, 3, 11 ]
45
[ "91+11=102", "49*3=147", "147-102=45" ]
Current State: 45:[91, 49, 3, 11], Operations: [] Exploring Operation: 91+11=102, Resulting Numbers: [49, 3, 102] Generated Node #2: [49, 3, 102] from Operation: 91+11=102 Current State: 45:[49, 3, 102], Operations: ['91+11=102'] Exploring Operation: 49*3=147, Resulting Numbers: [102, 147] Generated Node #3: [102, 147] from Operation: 49*3=147 Current State: 45:[102, 147], Operations: ['91+11=102', '49*3=147'] Exploring Operation: 147-102=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[91, 49, 3, 11], Operations: [] Exploring Operation: 91-11=80, Resulting Numbers: [49, 3, 80] Generated Node #0,0: 45:[49, 3, 80] Operation: 91-11=80 Exploring Operation: 91-49=42, Resulting Numbers: [3, 11, 42] Generated Node #0,1: 45:[3, 11, 42] Operation: 91-49=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[3, 11, 42], Operations: ['91-49=42'] Exploring Operation: 42/3=14, Resulting Numbers: [11, 14] Generated Node #0,1,0: 45:[11, 14] Operation: 42/3=14 Exploring Operation: 3+42=45, Resulting Numbers: [11, 45] Generated Node #0,1,1: 45:[11, 45] Operation: 3+42=45 Moving to Node #0,1,1 Current State: 45:[11, 45], Operations: ['91-49=42', '3+42=45'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 11+45=56, Resulting Numbers: [56] 56,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[11, 14], Operations: ['91-49=42', '42/3=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[49, 3, 80], Operations: ['91-11=80'] Exploring Operation: 80-49=31, Resulting Numbers: [3, 31] Generated Node #0,0,0: 45:[3, 31] Operation: 80-49=31 Exploring Operation: 49-3=46, Resulting Numbers: [80, 46] Generated Node #0,0,1: 45:[80, 46] Operation: 49-3=46 Moving to Node #0,0,0 Current State: 45:[3, 31], Operations: ['91-11=80', '80-49=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[80, 46], Operations: ['91-11=80', '49-3=46'] Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,45 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
[ 35, 12, 7, 22 ]
29
[ "35/7=5", "12+22=34", "34-5=29" ]
Current State: 29:[35, 12, 7, 22], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [12, 22, 5] Generated Node #2: [12, 22, 5] from Operation: 35/7=5 Current State: 29:[12, 22, 5], Operations: ['35/7=5'] Exploring Operation: 12+22=34, Resulting Numbers: [5, 34] Generated Node #3: [5, 34] from Operation: 12+22=34 Current State: 29:[5, 34], Operations: ['35/7=5', '12+22=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[35, 12, 7, 22], Operations: [] Exploring Operation: 12+7=19, Resulting Numbers: [35, 22, 19] Generated Node #0,0: 29:[35, 22, 19] Operation: 12+7=19 Exploring Operation: 35-7=28, Resulting Numbers: [12, 22, 28] Generated Node #0,1: 29:[12, 22, 28] Operation: 35-7=28 Exploring Operation: 7+22=29, Resulting Numbers: [35, 12, 29] Generated Node #0,2: 29:[35, 12, 29] Operation: 7+22=29 Exploring Operation: 35-12=23, Resulting Numbers: [7, 22, 23] Generated Node #0,3: 29:[7, 22, 23] Operation: 35-12=23 Exploring Operation: 12+22=34, Resulting Numbers: [35, 7, 34] Generated Node #0,4: 29:[35, 7, 34] Operation: 12+22=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[35, 22, 19], Operations: ['12+7=19'] Exploring Operation: 22+19=41, Resulting Numbers: [35, 41] Generated Node #0,0,0: 29:[35, 41] Operation: 22+19=41 Exploring Operation: 35-19=16, Resulting Numbers: [22, 16] Generated Node #0,0,1: 29:[22, 16] Operation: 35-19=16 Exploring Operation: 35+19=54, Resulting Numbers: [22, 54] Generated Node #0,0,2: 29:[22, 54] Operation: 35+19=54 Exploring Operation: 22-19=3, Resulting Numbers: [35, 3] Generated Node #0,0,3: 29:[35, 3] Operation: 22-19=3 Exploring Operation: 35-22=13, Resulting Numbers: [19, 13] Generated Node #0,0,4: 29:[19, 13] Operation: 35-22=13 Moving to Node #0,0,0 Current State: 29:[35, 41], Operations: ['12+7=19', '22+19=41'] Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[22, 16], Operations: ['12+7=19', '35-19=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,29 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[19, 13], Operations: ['12+7=19', '35-22=13'] Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 19*13=247, Resulting Numbers: [247] 247,29 unequal: No Solution Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[22, 54], Operations: ['12+7=19', '35+19=54'] Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,29 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[35, 3], Operations: ['12+7=19', '22-19=3'] Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,29 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[35, 12, 29], Operations: ['7+22=29'] Exploring Operation: 29-12=17, Resulting Numbers: [35, 17] Generated Node #0,2,0: 29:[35, 17] Operation: 29-12=17 Exploring Operation: 35-12=23, Resulting Numbers: [29, 23] Generated Node #0,2,1: 29:[29, 23] Operation: 35-12=23 Exploring Operation: 35+12=47, Resulting Numbers: [29, 47] Generated Node #0,2,2: 29:[29, 47] Operation: 35+12=47 Exploring Operation: 12+29=41, Resulting Numbers: [35, 41] Generated Node #0,2,3: 29:[35, 41] Operation: 12+29=41 Exploring Operation: 35-29=6, Resulting Numbers: [12, 6] Generated Node #0,2,4: 29:[12, 6] Operation: 35-29=6 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 29:[29, 23], Operations: ['7+22=29', '35-12=23'] Exploring Operation: 29*23=667, Resulting Numbers: [667] 667,29 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 29+23=52, Resulting Numbers: [52] 52,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 29:[35, 17], Operations: ['7+22=29', '29-12=17'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,29 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 29:[29, 47], Operations: ['7+22=29', '35+12=47'] Exploring Operation: 47-29=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 29*47=1363, Resulting Numbers: [1363] 1363,29 unequal: No Solution Exploring Operation: 29+47=76, Resulting Numbers: [76] 76,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 29:[35, 41], Operations: ['7+22=29', '12+29=41'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 29:[12, 6], Operations: ['7+22=29', '35-29=6'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[12, 22, 28], Operations: ['35-7=28'] Exploring Operation: 22+28=50, Resulting Numbers: [12, 50] Generated Node #0,1,0: 29:[12, 50] Operation: 22+28=50 Exploring Operation: 12+28=40, Resulting Numbers: [22, 40] Generated Node #0,1,1: 29:[22, 40] Operation: 12+28=40 Exploring Operation: 12+22=34, Resulting Numbers: [28, 34] Generated Node #0,1,2: 29:[28, 34] Operation: 12+22=34 Exploring Operation: 28-12=16, Resulting Numbers: [22, 16] Generated Node #0,1,3: 29:[22, 16] Operation: 28-12=16 Exploring Operation: 22-12=10, Resulting Numbers: [28, 10] Generated Node #0,1,4: 29:[28, 10] Operation: 22-12=10 Moving to Node #0,1,2 Current State: 29:[28, 34], Operations: ['35-7=28', '12+22=34'] Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[22, 40], Operations: ['35-7=28', '12+28=40'] Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,29 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[22, 16], Operations: ['35-7=28', '28-12=16'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,29 unequal: No Solution Moving to Node #0,1,4 Current State: 29:[28, 10], Operations: ['35-7=28', '22-12=10'] Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,29 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[12, 50], Operations: ['35-7=28', '22+28=50'] Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 29:[35, 7, 34], Operations: ['12+22=34'] Exploring Operation: 35/7=5, Resulting Numbers: [34, 5] Generated Node #0,4,0: 29:[34, 5] Operation: 35/7=5 Exploring Operation: 35+7=42, Resulting Numbers: [34, 42] Generated Node #0,4,1: 29:[34, 42] Operation: 35+7=42 Exploring Operation: 34-7=27, Resulting Numbers: [35, 27] Generated Node #0,4,2: 29:[35, 27] Operation: 34-7=27 Exploring Operation: 35-7=28, Resulting Numbers: [34, 28] Generated Node #0,4,3: 29:[34, 28] Operation: 35-7=28 Exploring Operation: 7+34=41, Resulting Numbers: [35, 41] Generated Node #0,4,4: 29:[35, 41] Operation: 7+34=41 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 29:[34, 28], Operations: ['12+22=34', '35-7=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,29 unequal: No Solution Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 34*28=952, Resulting Numbers: [952] 952,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 29:[35, 27], Operations: ['12+22=34', '34-7=27'] Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,29 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 29:[34, 42], Operations: ['12+22=34', '35+7=42'] Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,29 unequal: No Solution Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 29:[35, 41], Operations: ['12+22=34', '7+34=41'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 29:[34, 5], Operations: ['12+22=34', '35/7=5'] Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,29 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[35, 12, 7, 22], Operations: [] Exploring Operation: 12+22=34, Resulting Numbers: [35, 7, 34] Generated Node #0,4: 29:[35, 7, 34] Operation: 12+22=34 Moving to Node #0,4 Current State: 29:[35, 7, 34], Operations: ['12+22=34'] Exploring Operation: 35/7=5, Resulting Numbers: [34, 5] Generated Node #0,4,0: 29:[34, 5] Operation: 35/7=5 Moving to Node #0,4,0 Current State: 29:[34, 5], Operations: ['12+22=34', '35/7=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.922743
hs_5
sum_heuristic
[ 48, 81, 14, 40 ]
59
[ "81-48=33", "40-14=26", "33+26=59" ]
Current State: 59:[48, 81, 14, 40], Operations: [] Exploring Operation: 81-48=33, Resulting Numbers: [14, 40, 33] Generated Node #2: [14, 40, 33] from Operation: 81-48=33 Current State: 59:[14, 40, 33], Operations: ['81-48=33'] Exploring Operation: 40-14=26, Resulting Numbers: [33, 26] Generated Node #3: [33, 26] from Operation: 40-14=26 Current State: 59:[33, 26], Operations: ['81-48=33', '40-14=26'] Exploring Operation: 33+26=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[48, 81, 14, 40], Operations: [] Exploring Operation: 81-14=67, Resulting Numbers: [48, 40, 67] Generated Node #0,0: 59:[48, 40, 67] Operation: 81-14=67 Exploring Operation: 14+40=54, Resulting Numbers: [48, 81, 54] Generated Node #0,1: 59:[48, 81, 54] Operation: 14+40=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[48, 40, 67], Operations: ['81-14=67'] Exploring Operation: 48+40=88, Resulting Numbers: [67, 88] Generated Node #0,0,0: 59:[67, 88] Operation: 48+40=88 Exploring Operation: 67-40=27, Resulting Numbers: [48, 27] Generated Node #0,0,1: 59:[48, 27] Operation: 67-40=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[67, 88], Operations: ['81-14=67', '48+40=88'] Exploring Operation: 67+88=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 88-67=21, Resulting Numbers: [21] 21,59 unequal: No Solution No 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: 59:[48, 27], Operations: ['81-14=67', '67-40=27'] Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,59 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: 59:[48, 81, 54], Operations: ['14+40=54'] Exploring Operation: 81-54=27, Resulting Numbers: [48, 27] Generated Node #0,1,0: 59:[48, 27] Operation: 81-54=27 Exploring Operation: 81-48=33, Resulting Numbers: [54, 33] Generated Node #0,1,1: 59:[54, 33] Operation: 81-48=33 Moving to Node #0,1,1 Current State: 59:[54, 33], Operations: ['14+40=54', '81-48=33'] Exploring Operation: 54-33=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 54+33=87, Resulting Numbers: [87] 87,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[48, 27], Operations: ['14+40=54', '81-54=27'] Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,59 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
[ 15, 38, 22, 2 ]
47
[ "38-15=23", "22+2=24", "23+24=47" ]
Current State: 47:[15, 38, 22, 2], Operations: [] Exploring Operation: 38-15=23, Resulting Numbers: [22, 2, 23] Generated Node #2: [22, 2, 23] from Operation: 38-15=23 Current State: 47:[22, 2, 23], Operations: ['38-15=23'] Exploring Operation: 22+2=24, Resulting Numbers: [23, 24] Generated Node #3: [23, 24] from Operation: 22+2=24 Current State: 47:[23, 24], Operations: ['38-15=23', '22+2=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[15, 38, 22, 2], Operations: [] Exploring Operation: 15*2=30, Resulting Numbers: [38, 22, 30] Generated Node #0,0: 47:[38, 22, 30] Operation: 15*2=30 Exploring Operation: 15+2=17, Resulting Numbers: [38, 22, 17] Generated Node #0,1: 47:[38, 22, 17] Operation: 15+2=17 Exploring Operation: 38+2=40, Resulting Numbers: [15, 22, 40] Generated Node #0,2: 47:[15, 22, 40] Operation: 38+2=40 Exploring Operation: 22*2=44, Resulting Numbers: [15, 38, 44] Generated Node #0,3: 47:[15, 38, 44] Operation: 22*2=44 Exploring Operation: 15+22=37, Resulting Numbers: [38, 2, 37] Generated Node #0,4: 47:[38, 2, 37] Operation: 15+22=37 Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[15, 38, 44], Operations: ['22*2=44'] Exploring Operation: 15+38=53, Resulting Numbers: [44, 53] Generated Node #0,3,0: 47:[44, 53] Operation: 15+38=53 Exploring Operation: 44-15=29, Resulting Numbers: [38, 29] Generated Node #0,3,1: 47:[38, 29] Operation: 44-15=29 Exploring Operation: 38+44=82, Resulting Numbers: [15, 82] Generated Node #0,3,2: 47:[15, 82] Operation: 38+44=82 Exploring Operation: 38-15=23, Resulting Numbers: [44, 23] Generated Node #0,3,3: 47:[44, 23] Operation: 38-15=23 Exploring Operation: 15+44=59, Resulting Numbers: [38, 59] Generated Node #0,3,4: 47:[38, 59] Operation: 15+44=59 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 47:[44, 53], Operations: ['22*2=44', '15+38=53'] Exploring Operation: 44*53=2332, Resulting Numbers: [2332] 2332,47 unequal: No Solution Exploring Operation: 44+53=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 53-44=9, Resulting Numbers: [9] 9,47 unequal: No Solution No 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: 47:[38, 59], Operations: ['22*2=44', '15+44=59'] Exploring Operation: 38*59=2242, Resulting Numbers: [2242] 2242,47 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 38+59=97, Resulting Numbers: [97] 97,47 unequal: No Solution No 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: 47:[38, 29], Operations: ['22*2=44', '44-15=29'] Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 38*29=1102, Resulting Numbers: [1102] 1102,47 unequal: No Solution Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,47 unequal: No Solution No 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: 47:[44, 23], Operations: ['22*2=44', '38-15=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,47 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,47 unequal: No Solution No 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: 47:[15, 82], Operations: ['22*2=44', '38+44=82'] Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,47 unequal: No Solution Exploring Operation: 15+82=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 15*82=1230, Resulting Numbers: [1230] 1230,47 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: 47:[38, 22, 30], Operations: ['15*2=30'] Exploring Operation: 30-22=8, Resulting Numbers: [38, 8] Generated Node #0,0,0: 47:[38, 8] Operation: 30-22=8 Exploring Operation: 22+30=52, Resulting Numbers: [38, 52] Generated Node #0,0,1: 47:[38, 52] Operation: 22+30=52 Exploring Operation: 38+22=60, Resulting Numbers: [30, 60] Generated Node #0,0,2: 47:[30, 60] Operation: 38+22=60 Exploring Operation: 38+30=68, Resulting Numbers: [22, 68] Generated Node #0,0,3: 47:[22, 68] Operation: 38+30=68 Exploring Operation: 38-22=16, Resulting Numbers: [30, 16] Generated Node #0,0,4: 47:[30, 16] Operation: 38-22=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[38, 52], Operations: ['15*2=30', '22+30=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,47 unequal: No Solution No 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: 47:[30, 60], Operations: ['15*2=30', '38+22=60'] Exploring Operation: 30*60=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 60-30=30, Resulting Numbers: [30] 30,47 unequal: No Solution Exploring Operation: 30+60=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 60/30=2, Resulting Numbers: [2] 2,47 unequal: No Solution No 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: 47:[22, 68], Operations: ['15*2=30', '38+30=68'] Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 22+68=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 22*68=1496, Resulting Numbers: [1496] 1496,47 unequal: No Solution No 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: 47:[38, 8], Operations: ['15*2=30', '30-22=8'] Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,47 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,47 unequal: No Solution No 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: 47:[30, 16], Operations: ['15*2=30', '38-22=16'] Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,47 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,47 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: 47:[38, 22, 17], Operations: ['15+2=17'] Exploring Operation: 22-17=5, Resulting Numbers: [38, 5] Generated Node #0,1,0: 47:[38, 5] Operation: 22-17=5 Exploring Operation: 38+22=60, Resulting Numbers: [17, 60] Generated Node #0,1,1: 47:[17, 60] Operation: 38+22=60 Exploring Operation: 38-17=21, Resulting Numbers: [22, 21] Generated Node #0,1,2: 47:[22, 21] Operation: 38-17=21 Exploring Operation: 22+17=39, Resulting Numbers: [38, 39] Generated Node #0,1,3: 47:[38, 39] Operation: 22+17=39 Exploring Operation: 38+17=55, Resulting Numbers: [22, 55] Generated Node #0,1,4: 47:[22, 55] Operation: 38+17=55 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 47:[38, 39], Operations: ['15+2=17', '22+17=39'] Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 38*39=1482, Resulting Numbers: [1482] 1482,47 unequal: No Solution No 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: 47:[22, 55], Operations: ['15+2=17', '38+17=55'] Exploring Operation: 22+55=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 22*55=1210, Resulting Numbers: [1210] 1210,47 unequal: No Solution No 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: 47:[17, 60], Operations: ['15+2=17', '38+22=60'] Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 17*60=1020, Resulting Numbers: [1020] 1020,47 unequal: No Solution Exploring Operation: 17+60=77, Resulting Numbers: [77] 77,47 unequal: No Solution No 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: 47:[38, 5], Operations: ['15+2=17', '22-17=5'] Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,47 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,47 unequal: No Solution No 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: 47:[22, 21], Operations: ['15+2=17', '38-17=21'] Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,47 unequal: No Solution Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,47 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: 47:[15, 22, 40], Operations: ['38+2=40'] Exploring Operation: 15+40=55, Resulting Numbers: [22, 55] Generated Node #0,2,0: 47:[22, 55] Operation: 15+40=55 Exploring Operation: 22-15=7, Resulting Numbers: [40, 7] Generated Node #0,2,1: 47:[40, 7] Operation: 22-15=7 Exploring Operation: 22+40=62, Resulting Numbers: [15, 62] Generated Node #0,2,2: 47:[15, 62] Operation: 22+40=62 Exploring Operation: 15+22=37, Resulting Numbers: [40, 37] Generated Node #0,2,3: 47:[40, 37] Operation: 15+22=37 Exploring Operation: 40-15=25, Resulting Numbers: [22, 25] Generated Node #0,2,4: 47:[22, 25] Operation: 40-15=25 Moving to Node #0,2,3 Current State: 47:[40, 37], Operations: ['38+2=40', '15+22=37'] Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,47 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[22, 55], Operations: ['38+2=40', '15+40=55'] Exploring Operation: 22*55=1210, Resulting Numbers: [1210] 1210,47 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 22+55=77, Resulting Numbers: [77] 77,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[40, 7], Operations: ['38+2=40', '22-15=7'] Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,47 unequal: No Solution Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[15, 38, 22, 2], Operations: [] Exploring Operation: 38+2=40, Resulting Numbers: [15, 22, 40] Generated Node #0,2: 47:[15, 22, 40] Operation: 38+2=40 Moving to Node #0,2 Current State: 47:[15, 22, 40], Operations: ['38+2=40'] Exploring Operation: 22-15=7, Resulting Numbers: [40, 7] Generated Node #0,2,1: 47:[40, 7] Operation: 22-15=7 Moving to Node #0,2,1 Current State: 47:[40, 7], Operations: ['38+2=40', '22-15=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.927951
hs_5
sum_heuristic
[ 91, 49, 21, 67 ]
56
[ "91-67=24", "49*24=1176", "1176/21=56" ]
Current State: 56:[91, 49, 21, 67], Operations: [] Exploring Operation: 91-67=24, Resulting Numbers: [49, 21, 24] Generated Node #2: [49, 21, 24] from Operation: 91-67=24 Current State: 56:[49, 21, 24], Operations: ['91-67=24'] Exploring Operation: 49*24=1176, Resulting Numbers: [21, 1176] Generated Node #3: [21, 1176] from Operation: 49*24=1176 Current State: 56:[21, 1176], Operations: ['91-67=24', '49*24=1176'] Exploring Operation: 1176/21=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[91, 49, 21, 67], Operations: [] Exploring Operation: 91-67=24, Resulting Numbers: [49, 21, 24] Generated Node #0,0: 56:[49, 21, 24] Operation: 91-67=24 Exploring Operation: 91-49=42, Resulting Numbers: [21, 67, 42] Generated Node #0,1: 56:[21, 67, 42] Operation: 91-49=42 Exploring Operation: 49-21=28, Resulting Numbers: [91, 67, 28] Generated Node #0,2: 56:[91, 67, 28] Operation: 49-21=28 Exploring Operation: 91-21=70, Resulting Numbers: [49, 67, 70] Generated Node #0,3: 56:[49, 67, 70] Operation: 91-21=70 Moving to Node #0,0 Current State: 56:[49, 21, 24], Operations: ['91-67=24'] Exploring Operation: 49-24=25, Resulting Numbers: [21, 25] Generated Node #0,0,0: 56:[21, 25] Operation: 49-24=25 Exploring Operation: 49-21=28, Resulting Numbers: [24, 28] Generated Node #0,0,1: 56:[24, 28] Operation: 49-21=28 Exploring Operation: 49+21=70, Resulting Numbers: [24, 70] Generated Node #0,0,2: 56:[24, 70] Operation: 49+21=70 Exploring Operation: 24-21=3, Resulting Numbers: [49, 3] Generated Node #0,0,3: 56:[49, 3] Operation: 24-21=3 Moving to Node #0,3 Current State: 56:[49, 67, 70], Operations: ['91-21=70'] Exploring Operation: 67-49=18, Resulting Numbers: [70, 18] Generated Node #0,3,0: 56:[70, 18] Operation: 67-49=18 Exploring Operation: 49+67=116, Resulting Numbers: [70, 116] Generated Node #0,3,1: 56:[70, 116] Operation: 49+67=116 Exploring Operation: 70-49=21, Resulting Numbers: [67, 21] Generated Node #0,3,2: 56:[67, 21] Operation: 70-49=21 Exploring Operation: 70-67=3, Resulting Numbers: [49, 3] Generated Node #0,3,3: 56:[49, 3] Operation: 70-67=3 Moving to Node #0,1 Current State: 56:[21, 67, 42], Operations: ['91-49=42'] Exploring Operation: 42/21=2, Resulting Numbers: [67, 2] Generated Node #0,1,0: 56:[67, 2] Operation: 42/21=2 Exploring Operation: 67-42=25, Resulting Numbers: [21, 25] Generated Node #0,1,1: 56:[21, 25] Operation: 67-42=25 Exploring Operation: 42-21=21, Resulting Numbers: [67, 21] Generated Node #0,1,2: 56:[67, 21] Operation: 42-21=21 Exploring Operation: 21+42=63, Resulting Numbers: [67, 63] Generated Node #0,1,3: 56:[67, 63] Operation: 21+42=63 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[21, 25], Operations: ['91-49=42', '67-42=25'] Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,56 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 56:[67, 2], Operations: ['91-49=42', '42/21=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,56 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 56:[67, 21], Operations: ['91-49=42', '42-21=21'] Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,56 unequal: No Solution Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 56:[67, 63], Operations: ['91-49=42', '21+42=63'] Exploring Operation: 67*63=4221, Resulting Numbers: [4221] 4221,56 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 67+63=130, Resulting Numbers: [130] 130,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 56:[91, 67, 28], Operations: ['49-21=28'] Exploring Operation: 67-28=39, Resulting Numbers: [91, 39] Generated Node #0,2,0: 56:[91, 39] Operation: 67-28=39 Exploring Operation: 91+28=119, Resulting Numbers: [67, 119] Generated Node #0,2,1: 56:[67, 119] Operation: 91+28=119 Exploring Operation: 91-67=24, Resulting Numbers: [28, 24] Generated Node #0,2,2: 56:[28, 24] Operation: 91-67=24 Exploring Operation: 91-28=63, Resulting Numbers: [67, 63] Generated Node #0,2,3: 56:[67, 63] Operation: 91-28=63 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[28, 24], Operations: ['49-21=28', '91-67=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 56:[67, 63], Operations: ['49-21=28', '91-28=63'] Exploring Operation: 67+63=130, Resulting Numbers: [130] 130,56 unequal: No Solution Exploring Operation: 67*63=4221, Resulting Numbers: [4221] 4221,56 unequal: No Solution Exploring Operation: 67-63=4, Resulting Numbers: [4] 4,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[91, 39], Operations: ['49-21=28', '67-28=39'] Exploring Operation: 91-39=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 91*39=3549, Resulting Numbers: [3549] 3549,56 unequal: No Solution Exploring Operation: 91+39=130, Resulting Numbers: [130] 130,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[67, 119], Operations: ['49-21=28', '91+28=119'] Exploring Operation: 67+119=186, Resulting Numbers: [186] 186,56 unequal: No Solution Exploring Operation: 67*119=7973, Resulting Numbers: [7973] 7973,56 unequal: No Solution Exploring Operation: 119-67=52, Resulting Numbers: [52] 52,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 56:[24, 28], Operations: ['91-67=24', '49-21=28'] Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,56 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[49, 3], Operations: ['91-67=24', '24-21=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,56 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[49, 3], Operations: ['91-21=70', '70-67=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[21, 25], Operations: ['91-67=24', '49-24=25'] Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,56 unequal: No Solution Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,56 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[70, 18], Operations: ['91-21=70', '67-49=18'] Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,56 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[24, 70], Operations: ['91-67=24', '49+21=70'] Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,56 unequal: No Solution Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,56 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[67, 21], Operations: ['91-21=70', '70-49=21'] Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,56 unequal: No Solution Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,56 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[70, 116], Operations: ['91-21=70', '49+67=116'] Exploring Operation: 70+116=186, Resulting Numbers: [186] 186,56 unequal: No Solution Exploring Operation: 70*116=8120, Resulting Numbers: [8120] 8120,56 unequal: No Solution Exploring Operation: 116-70=46, Resulting Numbers: [46] 46,56 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 99, 39, 51, 68 ]
47
[ "39*68=2652", "2652/51=52", "99-52=47" ]
Current State: 47:[99, 39, 51, 68], Operations: [] Exploring Operation: 39*68=2652, Resulting Numbers: [99, 51, 2652] Generated Node #2: [99, 51, 2652] from Operation: 39*68=2652 Current State: 47:[99, 51, 2652], Operations: ['39*68=2652'] Exploring Operation: 2652/51=52, Resulting Numbers: [99, 52] Generated Node #3: [99, 52] from Operation: 2652/51=52 Current State: 47:[99, 52], Operations: ['39*68=2652', '2652/51=52'] Exploring Operation: 99-52=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[99, 39, 51, 68], Operations: [] Exploring Operation: 99-68=31, Resulting Numbers: [39, 51, 31] Generated Node #0,0: 47:[39, 51, 31] Operation: 99-68=31 Exploring Operation: 99-51=48, Resulting Numbers: [39, 68, 48] Generated Node #0,1: 47:[39, 68, 48] Operation: 99-51=48 Exploring Operation: 99-39=60, Resulting Numbers: [51, 68, 60] Generated Node #0,2: 47:[51, 68, 60] Operation: 99-39=60 Exploring Operation: 68-51=17, Resulting Numbers: [99, 39, 17] Generated Node #0,3: 47:[99, 39, 17] Operation: 68-51=17 Exploring Operation: 68-39=29, Resulting Numbers: [99, 51, 29] Generated Node #0,4: 47:[99, 51, 29] Operation: 68-39=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[39, 51, 31], Operations: ['99-68=31'] Exploring Operation: 39+31=70, Resulting Numbers: [51, 70] Generated Node #0,0,0: 47:[51, 70] Operation: 39+31=70 Exploring Operation: 39-31=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 47:[51, 8] Operation: 39-31=8 Exploring Operation: 51-31=20, Resulting Numbers: [39, 20] Generated Node #0,0,2: 47:[39, 20] Operation: 51-31=20 Exploring Operation: 51-39=12, Resulting Numbers: [31, 12] Generated Node #0,0,3: 47:[31, 12] Operation: 51-39=12 Exploring Operation: 51+31=82, Resulting Numbers: [39, 82] Generated Node #0,0,4: 47:[39, 82] Operation: 51+31=82 Moving to Node #0,0,0 Current State: 47:[51, 70], Operations: ['99-68=31', '39+31=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[39, 20], Operations: ['99-68=31', '51-31=20'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,47 unequal: No Solution Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[51, 8], Operations: ['99-68=31', '39-31=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution Moving to Node #0,0,4 Current State: 47:[39, 82], Operations: ['99-68=31', '51+31=82'] Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,47 unequal: No Solution Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[31, 12], Operations: ['99-68=31', '51-39=12'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 31*12=372, Resulting Numbers: [372] 372,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[39, 68, 48], Operations: ['99-51=48'] Exploring Operation: 48-39=9, Resulting Numbers: [68, 9] Generated Node #0,1,0: 47:[68, 9] Operation: 48-39=9 Exploring Operation: 39+48=87, Resulting Numbers: [68, 87] Generated Node #0,1,1: 47:[68, 87] Operation: 39+48=87 Exploring Operation: 68-48=20, Resulting Numbers: [39, 20] Generated Node #0,1,2: 47:[39, 20] Operation: 68-48=20 Exploring Operation: 68-39=29, Resulting Numbers: [48, 29] Generated Node #0,1,3: 47:[48, 29] Operation: 68-39=29 Exploring Operation: 39+68=107, Resulting Numbers: [48, 107] Generated Node #0,1,4: 47:[48, 107] Operation: 39+68=107 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 47:[48, 29], Operations: ['99-51=48', '68-39=29'] Exploring Operation: 48*29=1392, Resulting Numbers: [1392] 1392,47 unequal: No Solution Exploring Operation: 48+29=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,47 unequal: No Solution No 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: 47:[39, 20], Operations: ['99-51=48', '68-48=20'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,47 unequal: No Solution Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,47 unequal: No Solution No 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: 47:[68, 9], Operations: ['99-51=48', '48-39=9'] Exploring Operation: 68+9=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 68*9=612, Resulting Numbers: [612] 612,47 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,47 unequal: No Solution No 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: 47:[68, 87], Operations: ['99-51=48', '39+48=87'] Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 68+87=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 68*87=5916, Resulting Numbers: [5916] 5916,47 unequal: No Solution No 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: 47:[48, 107], Operations: ['99-51=48', '39+68=107'] Exploring Operation: 48*107=5136, Resulting Numbers: [5136] 5136,47 unequal: No Solution Exploring Operation: 48+107=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 107-48=59, Resulting Numbers: [59] 59,47 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: 47:[51, 68, 60], Operations: ['99-39=60'] Exploring Operation: 68-60=8, Resulting Numbers: [51, 8] Generated Node #0,2,0: 47:[51, 8] Operation: 68-60=8 Exploring Operation: 51+68=119, Resulting Numbers: [60, 119] Generated Node #0,2,1: 47:[60, 119] Operation: 51+68=119 Exploring Operation: 60-51=9, Resulting Numbers: [68, 9] Generated Node #0,2,2: 47:[68, 9] Operation: 60-51=9 Exploring Operation: 51+60=111, Resulting Numbers: [68, 111] Generated Node #0,2,3: 47:[68, 111] Operation: 51+60=111 Exploring Operation: 68-51=17, Resulting Numbers: [60, 17] Generated Node #0,2,4: 47:[60, 17] Operation: 68-51=17 Moving to Node #0,2,0 Current State: 47:[51, 8], Operations: ['99-39=60', '68-60=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution Moving to Node #0,2,4 Current State: 47:[60, 17], Operations: ['99-39=60', '68-51=17'] Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 60+17=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 60*17=1020, Resulting Numbers: [1020] 1020,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[68, 9], Operations: ['99-39=60', '60-51=9'] Exploring Operation: 68*9=612, Resulting Numbers: [612] 612,47 unequal: No Solution Exploring Operation: 68+9=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[60, 119], Operations: ['99-39=60', '51+68=119'] Exploring Operation: 60+119=179, Resulting Numbers: [179] 179,47 unequal: No Solution Exploring Operation: 60*119=7140, Resulting Numbers: [7140] 7140,47 unequal: No Solution Exploring Operation: 119-60=59, Resulting Numbers: [59] 59,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[68, 111], Operations: ['99-39=60', '51+60=111'] Exploring Operation: 111-68=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 68*111=7548, Resulting Numbers: [7548] 7548,47 unequal: No Solution Exploring Operation: 68+111=179, Resulting Numbers: [179] 179,47 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 #0,4 Current State: 47:[99, 51, 29], Operations: ['68-39=29'] Exploring Operation: 99-29=70, Resulting Numbers: [51, 70] Generated Node #0,4,0: 47:[51, 70] Operation: 99-29=70 Exploring Operation: 99-51=48, Resulting Numbers: [29, 48] Generated Node #0,4,1: 47:[29, 48] Operation: 99-51=48 Exploring Operation: 51-29=22, Resulting Numbers: [99, 22] Generated Node #0,4,2: 47:[99, 22] Operation: 51-29=22 Exploring Operation: 51+29=80, Resulting Numbers: [99, 80] Generated Node #0,4,3: 47:[99, 80] Operation: 51+29=80 Exploring Operation: 99+29=128, Resulting Numbers: [51, 128] Generated Node #0,4,4: 47:[51, 128] Operation: 99+29=128 Moving to Node #0,4,1 Current State: 47:[29, 48], Operations: ['68-39=29', '99-51=48'] Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 29+48=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 29*48=1392, Resulting Numbers: [1392] 1392,47 unequal: No Solution Moving to Node #0,4,0 Current State: 47:[51, 70], Operations: ['68-39=29', '99-29=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,47 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,47 unequal: No Solution Moving to Node #0,4,2 Current State: 47:[99, 22], Operations: ['68-39=29', '51-29=22'] Exploring Operation: 99-22=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 99+22=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 99*22=2178, Resulting Numbers: [2178] 2178,47 unequal: No Solution Moving to Node #0,4,3 Current State: 47:[99, 80], Operations: ['68-39=29', '51+29=80'] Exploring Operation: 99+80=179, Resulting Numbers: [179] 179,47 unequal: No Solution Exploring Operation: 99*80=7920, Resulting Numbers: [7920] 7920,47 unequal: No Solution Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,47 unequal: No Solution Moving to Node #0,4,4 Current State: 47:[51, 128], Operations: ['68-39=29', '99+29=128'] Exploring Operation: 51+128=179, Resulting Numbers: [179] 179,47 unequal: No Solution Exploring Operation: 128-51=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 51*128=6528, Resulting Numbers: [6528] 6528,47 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 #0,3 Current State: 47:[99, 39, 17], Operations: ['68-51=17'] Exploring Operation: 39+17=56, Resulting Numbers: [99, 56] Generated Node #0,3,0: 47:[99, 56] Operation: 39+17=56 Exploring Operation: 99-39=60, Resulting Numbers: [17, 60] Generated Node #0,3,1: 47:[17, 60] Operation: 99-39=60 Exploring Operation: 39-17=22, Resulting Numbers: [99, 22] Generated Node #0,3,2: 47:[99, 22] Operation: 39-17=22 Exploring Operation: 99+17=116, Resulting Numbers: [39, 116] Generated Node #0,3,3: 47:[39, 116] Operation: 99+17=116 Exploring Operation: 99-17=82, Resulting Numbers: [39, 82] Generated Node #0,3,4: 47:[39, 82] Operation: 99-17=82 Moving to Node #0,3,1 Current State: 47:[17, 60], Operations: ['68-51=17', '99-39=60'] Exploring Operation: 17+60=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 60-17=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 17*60=1020, Resulting Numbers: [1020] 1020,47 unequal: No Solution Moving to Node #0,3,4 Current State: 47:[39, 82], Operations: ['68-51=17', '99-17=82'] Exploring Operation: 82-39=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 39+82=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 39*82=3198, Resulting Numbers: [3198] 3198,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[99, 56], Operations: ['68-51=17', '39+17=56'] Exploring Operation: 99*56=5544, Resulting Numbers: [5544] 5544,47 unequal: No Solution Exploring Operation: 99+56=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 99-56=43, Resulting Numbers: [43] 43,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[99, 22], Operations: ['68-51=17', '39-17=22'] Exploring Operation: 99-22=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 99+22=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 99*22=2178, Resulting Numbers: [2178] 2178,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[39, 116], Operations: ['68-51=17', '99+17=116'] Exploring Operation: 116-39=77, Resulting Numbers: [77] 77,47 unequal: No Solution Exploring Operation: 39+116=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 39*116=4524, Resulting Numbers: [4524] 4524,47 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
[ 49, 66, 46, 40 ]
78
[ "49-46=3", "66-40=26", "3*26=78" ]
Current State: 78:[49, 66, 46, 40], Operations: [] Exploring Operation: 49-46=3, Resulting Numbers: [66, 40, 3] Generated Node #2: [66, 40, 3] from Operation: 49-46=3 Current State: 78:[66, 40, 3], Operations: ['49-46=3'] Exploring Operation: 66-40=26, Resulting Numbers: [3, 26] Generated Node #3: [3, 26] from Operation: 66-40=26 Current State: 78:[3, 26], Operations: ['49-46=3', '66-40=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[49, 66, 46, 40], Operations: [] Exploring Operation: 66-49=17, Resulting Numbers: [46, 40, 17] Generated Node #0,0: 78:[46, 40, 17] Operation: 66-49=17 Exploring Operation: 49-46=3, Resulting Numbers: [66, 40, 3] Generated Node #0,1: 78:[66, 40, 3] Operation: 49-46=3 Moving to Node #0,0 Current State: 78:[46, 40, 17], Operations: ['66-49=17'] Exploring Operation: 46-17=29, Resulting Numbers: [40, 29] Generated Node #0,0,0: 78:[40, 29] Operation: 46-17=29 Exploring Operation: 46-40=6, Resulting Numbers: [17, 6] Generated Node #0,0,1: 78:[17, 6] Operation: 46-40=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[40, 29], Operations: ['66-49=17', '46-17=29'] Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,78 unequal: No Solution Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[17, 6], Operations: ['66-49=17', '46-40=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 78:[66, 40, 3], Operations: ['49-46=3'] Exploring Operation: 66/3=22, Resulting Numbers: [40, 22] Generated Node #0,1,0: 78:[40, 22] Operation: 66/3=22 Exploring Operation: 66-40=26, Resulting Numbers: [3, 26] Generated Node #0,1,1: 78:[3, 26] Operation: 66-40=26 Moving to Node #0,1,1 Current State: 78:[3, 26], Operations: ['49-46=3', '66-40=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[49, 66, 46, 40], Operations: [] Exploring Operation: 49-46=3, Resulting Numbers: [66, 40, 3] Generated Node #0,1: 78:[66, 40, 3] Operation: 49-46=3 Moving to Node #0,1 Current State: 78:[66, 40, 3], Operations: ['49-46=3'] Exploring Operation: 66-40=26, Resulting Numbers: [3, 26] Generated Node #0,1,1: 78:[3, 26] Operation: 66-40=26 Moving to Node #0,1,1 Current State: 78:[3, 26], Operations: ['49-46=3', '66-40=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 56, 95, 10, 20 ]
69
[ "95-56=39", "10+20=30", "39+30=69" ]
Current State: 69:[56, 95, 10, 20], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [10, 20, 39] Generated Node #2: [10, 20, 39] from Operation: 95-56=39 Current State: 69:[10, 20, 39], Operations: ['95-56=39'] Exploring Operation: 10+20=30, Resulting Numbers: [39, 30] Generated Node #3: [39, 30] from Operation: 10+20=30 Current State: 69:[39, 30], Operations: ['95-56=39', '10+20=30'] Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[56, 95, 10, 20], Operations: [] Exploring Operation: 95-20=75, Resulting Numbers: [56, 10, 75] Generated Node #0,0: 69:[56, 10, 75] Operation: 95-20=75 Exploring Operation: 95-10=85, Resulting Numbers: [56, 20, 85] Generated Node #0,1: 69:[56, 20, 85] Operation: 95-10=85 Exploring Operation: 95-56=39, Resulting Numbers: [10, 20, 39] Generated Node #0,2: 69:[10, 20, 39] Operation: 95-56=39 Exploring Operation: 56+10=66, Resulting Numbers: [95, 20, 66] Generated Node #0,3: 69:[95, 20, 66] Operation: 56+10=66 Moving to Node #0,0 Current State: 69:[56, 10, 75], Operations: ['95-20=75'] Exploring Operation: 56-10=46, Resulting Numbers: [75, 46] Generated Node #0,0,0: 69:[75, 46] Operation: 56-10=46 Exploring Operation: 75-10=65, Resulting Numbers: [56, 65] Generated Node #0,0,1: 69:[56, 65] Operation: 75-10=65 Exploring Operation: 56+10=66, Resulting Numbers: [75, 66] Generated Node #0,0,2: 69:[75, 66] Operation: 56+10=66 Exploring Operation: 75-56=19, Resulting Numbers: [10, 19] Generated Node #0,0,3: 69:[10, 19] Operation: 75-56=19 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[75, 66], Operations: ['95-20=75', '56+10=66'] Exploring Operation: 75+66=141, Resulting Numbers: [141] 141,69 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 75*66=4950, Resulting Numbers: [4950] 4950,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[10, 19], Operations: ['95-20=75', '75-56=19'] Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,69 unequal: No Solution Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[56, 65], Operations: ['95-20=75', '75-10=65'] Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,69 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[75, 46], Operations: ['95-20=75', '56-10=46'] Exploring Operation: 75+46=121, Resulting Numbers: [121] 121,69 unequal: No Solution Exploring Operation: 75*46=3450, Resulting Numbers: [3450] 3450,69 unequal: No Solution Exploring Operation: 75-46=29, Resulting Numbers: [29] 29,69 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: 69:[10, 20, 39], Operations: ['95-56=39'] Exploring Operation: 20/10=2, Resulting Numbers: [39, 2] Generated Node #0,2,0: 69:[39, 2] Operation: 20/10=2 Exploring Operation: 39-10=29, Resulting Numbers: [20, 29] Generated Node #0,2,1: 69:[20, 29] Operation: 39-10=29 Exploring Operation: 39-20=19, Resulting Numbers: [10, 19] Generated Node #0,2,2: 69:[10, 19] Operation: 39-20=19 Exploring Operation: 20+39=59, Resulting Numbers: [10, 59] Generated Node #0,2,3: 69:[10, 59] Operation: 20+39=59 Moving to Node #0,3 Current State: 69:[95, 20, 66], Operations: ['56+10=66'] Exploring Operation: 95-20=75, Resulting Numbers: [66, 75] Generated Node #0,3,0: 69:[66, 75] Operation: 95-20=75 Exploring Operation: 95+20=115, Resulting Numbers: [66, 115] Generated Node #0,3,1: 69:[66, 115] Operation: 95+20=115 Exploring Operation: 95-66=29, Resulting Numbers: [20, 29] Generated Node #0,3,2: 69:[20, 29] Operation: 95-66=29 Exploring Operation: 20+66=86, Resulting Numbers: [95, 86] Generated Node #0,3,3: 69:[95, 86] Operation: 20+66=86 Moving to Node #0,1 Current State: 69:[56, 20, 85], Operations: ['95-10=85'] Exploring Operation: 56-20=36, Resulting Numbers: [85, 36] Generated Node #0,1,0: 69:[85, 36] Operation: 56-20=36 Exploring Operation: 85-20=65, Resulting Numbers: [56, 65] Generated Node #0,1,1: 69:[56, 65] Operation: 85-20=65 Exploring Operation: 85-56=29, Resulting Numbers: [20, 29] Generated Node #0,1,2: 69:[20, 29] Operation: 85-56=29 Exploring Operation: 56+20=76, Resulting Numbers: [85, 76] Generated Node #0,1,3: 69:[85, 76] Operation: 56+20=76 Moving to Node #0,2,1 Current State: 69:[20, 29], Operations: ['95-56=39', '39-10=29'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[20, 29], Operations: ['56+10=66', '95-66=29'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,69 unequal: No Solution Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[66, 75], Operations: ['56+10=66', '95-20=75'] Exploring Operation: 66+75=141, Resulting Numbers: [141] 141,69 unequal: No Solution Exploring Operation: 66*75=4950, Resulting Numbers: [4950] 4950,69 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[20, 29], Operations: ['95-10=85', '85-56=29'] Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,69 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[10, 19], Operations: ['95-56=39', '39-20=19'] Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,69 unequal: No Solution Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[39, 2], Operations: ['95-56=39', '20/10=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,69 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[56, 65], Operations: ['95-10=85', '85-20=65'] Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,69 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,69 unequal: No Solution Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[10, 59], Operations: ['95-56=39', '20+39=59'] Exploring Operation: 59-10=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 10+59=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[56, 95, 10, 20], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [10, 20, 39] Generated Node #0,2: 69:[10, 20, 39] Operation: 95-56=39 Moving to Node #0,2 Current State: 69:[10, 20, 39], Operations: ['95-56=39'] Exploring Operation: 20+39=59, Resulting Numbers: [10, 59] Generated Node #0,2,3: 69:[10, 59] Operation: 20+39=59 Moving to Node #0,2,3 Current State: 69:[10, 59], Operations: ['95-56=39', '20+39=59'] Exploring Operation: 10+59=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.948785
hs_4
sum_heuristic
[ 94, 98, 20, 84 ]
68
[ "98-94=4", "84-20=64", "4+64=68" ]
Current State: 68:[94, 98, 20, 84], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [20, 84, 4] Generated Node #2: [20, 84, 4] from Operation: 98-94=4 Current State: 68:[20, 84, 4], Operations: ['98-94=4'] Exploring Operation: 84-20=64, Resulting Numbers: [4, 64] Generated Node #3: [4, 64] from Operation: 84-20=64 Current State: 68:[4, 64], Operations: ['98-94=4', '84-20=64'] Exploring Operation: 4+64=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[94, 98, 20, 84], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [20, 84, 4] Generated Node #0,0: 68:[20, 84, 4] Operation: 98-94=4 Exploring Operation: 98-84=14, Resulting Numbers: [94, 20, 14] Generated Node #0,1: 68:[94, 20, 14] Operation: 98-84=14 Exploring Operation: 94-84=10, Resulting Numbers: [98, 20, 10] Generated Node #0,2: 68:[98, 20, 10] Operation: 94-84=10 Moving to Node #0,0 Current State: 68:[20, 84, 4], Operations: ['98-94=4'] Exploring Operation: 84/4=21, Resulting Numbers: [20, 21] Generated Node #0,0,0: 68:[20, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [20, 80] Generated Node #0,0,1: 68:[20, 80] Operation: 84-4=80 Exploring Operation: 84-20=64, Resulting Numbers: [4, 64] Generated Node #0,0,2: 68:[4, 64] Operation: 84-20=64 Moving to Node #0,1 Current State: 68:[94, 20, 14], Operations: ['98-84=14'] Exploring Operation: 94-14=80, Resulting Numbers: [20, 80] Generated Node #0,1,0: 68:[20, 80] Operation: 94-14=80 Exploring Operation: 20+14=34, Resulting Numbers: [94, 34] Generated Node #0,1,1: 68:[94, 34] Operation: 20+14=34 Exploring Operation: 94-20=74, Resulting Numbers: [14, 74] Generated Node #0,1,2: 68:[14, 74] Operation: 94-20=74 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 68:[14, 74], Operations: ['98-84=14', '94-20=74'] Exploring Operation: 14+74=88, Resulting Numbers: [88] 88,68 unequal: No Solution Exploring Operation: 14*74=1036, Resulting Numbers: [1036] 1036,68 unequal: No Solution Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,68 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:[20, 80], Operations: ['98-84=14', '94-14=80'] Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 20+80=100, Resulting Numbers: [100] 100,68 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,68 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 #0,1,1 Current State: 68:[94, 34], Operations: ['98-84=14', '20+14=34'] Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,68 unequal: No Solution Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,68 unequal: No Solution Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,68 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: 68:[98, 20, 10], Operations: ['94-84=10'] Exploring Operation: 20/10=2, Resulting Numbers: [98, 2] Generated Node #0,2,0: 68:[98, 2] Operation: 20/10=2 Exploring Operation: 98-20=78, Resulting Numbers: [10, 78] Generated Node #0,2,1: 68:[10, 78] Operation: 98-20=78 Exploring Operation: 98-10=88, Resulting Numbers: [20, 88] Generated Node #0,2,2: 68:[20, 88] Operation: 98-10=88 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[10, 78], Operations: ['94-84=10', '98-20=78'] Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,68 unequal: No Solution Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,68 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[94, 98, 20, 84], Operations: [] Exploring Operation: 94-84=10, Resulting Numbers: [98, 20, 10] Generated Node #0,2: 68:[98, 20, 10] Operation: 94-84=10 Moving to Node #0,2 Current State: 68:[98, 20, 10], Operations: ['94-84=10'] Exploring Operation: 98-20=78, Resulting Numbers: [10, 78] Generated Node #0,2,1: 68:[10, 78] Operation: 98-20=78 Moving to Node #0,2,1 Current State: 68:[10, 78], Operations: ['94-84=10', '98-20=78'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 25, 41, 86, 34 ]
68
[ "41-25=16", "86-34=52", "16+52=68" ]
Current State: 68:[25, 41, 86, 34], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [86, 34, 16] Generated Node #2: [86, 34, 16] from Operation: 41-25=16 Current State: 68:[86, 34, 16], Operations: ['41-25=16'] Exploring Operation: 86-34=52, Resulting Numbers: [16, 52] Generated Node #3: [16, 52] from Operation: 86-34=52 Current State: 68:[16, 52], Operations: ['41-25=16', '86-34=52'] Exploring Operation: 16+52=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[25, 41, 86, 34], Operations: [] Exploring Operation: 86-25=61, Resulting Numbers: [41, 34, 61] Generated Node #0,0: 68:[41, 34, 61] Operation: 86-25=61 Moving to Node #0,0 Current State: 68:[41, 34, 61], Operations: ['86-25=61'] Exploring Operation: 61-41=20, Resulting Numbers: [34, 20] Generated Node #0,0,0: 68:[34, 20] Operation: 61-41=20 Moving to Node #0,0,0 Current State: 68:[34, 20], Operations: ['86-25=61', '61-41=20'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,68 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 5, 2, 74, 71 ]
78
[ "5+71=76", "2*76=152", "152-74=78" ]
Current State: 78:[5, 2, 74, 71], Operations: [] Exploring Operation: 5+71=76, Resulting Numbers: [2, 74, 76] Generated Node #2: [2, 74, 76] from Operation: 5+71=76 Current State: 78:[2, 74, 76], Operations: ['5+71=76'] Exploring Operation: 2*76=152, Resulting Numbers: [74, 152] Generated Node #3: [74, 152] from Operation: 2*76=152 Current State: 78:[74, 152], Operations: ['5+71=76', '2*76=152'] Exploring Operation: 152-74=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[5, 2, 74, 71], Operations: [] Exploring Operation: 5+71=76, Resulting Numbers: [2, 74, 76] Generated Node #0,0: 78:[2, 74, 76] Operation: 5+71=76 Exploring Operation: 5+74=79, Resulting Numbers: [2, 71, 79] Generated Node #0,1: 78:[2, 71, 79] Operation: 5+74=79 Exploring Operation: 2+74=76, Resulting Numbers: [5, 71, 76] Generated Node #0,2: 78:[5, 71, 76] Operation: 2+74=76 Exploring Operation: 74-71=3, Resulting Numbers: [5, 2, 3] Generated Node #0,3: 78:[5, 2, 3] Operation: 74-71=3 Moving to Node #0,3 Current State: 78:[5, 2, 3], Operations: ['74-71=3'] Exploring Operation: 5-2=3, Resulting Numbers: [3, 3] Generated Node #0,3,0: 78:[3, 3] Operation: 5-2=3 Exploring Operation: 2*3=6, Resulting Numbers: [5, 6] Generated Node #0,3,1: 78:[5, 6] Operation: 2*3=6 Exploring Operation: 5+2=7, Resulting Numbers: [3, 7] Generated Node #0,3,2: 78:[3, 7] Operation: 5+2=7 Exploring Operation: 5-3=2, Resulting Numbers: [2, 2] Generated Node #0,3,3: 78:[2, 2] Operation: 5-3=2 Moving to Node #0,0 Current State: 78:[2, 74, 76], Operations: ['5+71=76'] Exploring Operation: 76-74=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 78:[2, 2] Operation: 76-74=2 Exploring Operation: 74/2=37, Resulting Numbers: [76, 37] Generated Node #0,0,1: 78:[76, 37] Operation: 74/2=37 Exploring Operation: 2+76=78, Resulting Numbers: [74, 78] Generated Node #0,0,2: 78:[74, 78] Operation: 2+76=78 Exploring Operation: 2+74=76, Resulting Numbers: [76, 76] Generated Node #0,0,3: 78:[76, 76] Operation: 2+74=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[2, 2], Operations: ['5+71=76', '76-74=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[76, 37], Operations: ['5+71=76', '74/2=37'] Exploring Operation: 76*37=2812, Resulting Numbers: [2812] 2812,78 unequal: No Solution Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 76+37=113, Resulting Numbers: [113] 113,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[74, 78], Operations: ['5+71=76', '2+76=78'] Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,78 unequal: No Solution Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[76, 76], Operations: ['5+71=76', '2+74=76'] Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,78 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 78:[2, 71, 79], Operations: ['5+74=79'] Exploring Operation: 71-2=69, Resulting Numbers: [79, 69] Generated Node #0,1,0: 78:[79, 69] Operation: 71-2=69 Exploring Operation: 79-2=77, Resulting Numbers: [71, 77] Generated Node #0,1,1: 78:[71, 77] Operation: 79-2=77 Exploring Operation: 2+71=73, Resulting Numbers: [79, 73] Generated Node #0,1,2: 78:[79, 73] Operation: 2+71=73 Exploring Operation: 79-71=8, Resulting Numbers: [2, 8] Generated Node #0,1,3: 78:[2, 8] Operation: 79-71=8 Moving to Node #0,2 Current State: 78:[5, 71, 76], Operations: ['2+74=76'] Exploring Operation: 5+71=76, Resulting Numbers: [76, 76] Generated Node #0,2,0: 78:[76, 76] Operation: 5+71=76 Exploring Operation: 5+76=81, Resulting Numbers: [71, 81] Generated Node #0,2,1: 78:[71, 81] Operation: 5+76=81 Exploring Operation: 71-5=66, Resulting Numbers: [76, 66] Generated Node #0,2,2: 78:[76, 66] Operation: 71-5=66 Exploring Operation: 76-71=5, Resulting Numbers: [5, 5] Generated Node #0,2,3: 78:[5, 5] Operation: 76-71=5 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[5, 5], Operations: ['2+74=76', '76-71=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,78 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 #0,2,0 Current State: 78:[76, 76], Operations: ['2+74=76', '5+71=76'] Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,78 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,78 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 #0,2,1 Current State: 78:[71, 81], Operations: ['2+74=76', '5+76=81'] Exploring Operation: 81-71=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 71*81=5751, Resulting Numbers: [5751] 5751,78 unequal: No Solution Exploring Operation: 71+81=152, Resulting Numbers: [152] 152,78 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 #0,2,2 Current State: 78:[76, 66], Operations: ['2+74=76', '71-5=66'] Exploring Operation: 76*66=5016, Resulting Numbers: [5016] 5016,78 unequal: No Solution Exploring Operation: 76-66=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 76+66=142, Resulting Numbers: [142] 142,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 78:[3, 3], Operations: ['74-71=3', '5-2=3'] Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[2, 2], Operations: ['74-71=3', '5-3=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[5, 6], Operations: ['74-71=3', '2*3=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,78 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[3, 7], Operations: ['74-71=3', '5+2=7'] Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[2, 8], Operations: ['5+74=79', '79-71=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,78 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[79, 73], Operations: ['5+74=79', '2+71=73'] Exploring Operation: 79*73=5767, Resulting Numbers: [5767] 5767,78 unequal: No Solution Exploring Operation: 79+73=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 79-73=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[71, 77], Operations: ['5+74=79', '79-2=77'] Exploring Operation: 71+77=148, Resulting Numbers: [148] 148,78 unequal: No Solution Exploring Operation: 71*77=5467, Resulting Numbers: [5467] 5467,78 unequal: No Solution Exploring Operation: 77-71=6, Resulting Numbers: [6] 6,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[79, 69], Operations: ['5+74=79', '71-2=69'] Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,78 unequal: No Solution Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,78 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,78 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 42, 27, 71, 83 ]
57
[ "42+27=69", "83-71=12", "69-12=57" ]
Current State: 57:[42, 27, 71, 83], Operations: [] Exploring Operation: 42+27=69, Resulting Numbers: [71, 83, 69] Generated Node #2: [71, 83, 69] from Operation: 42+27=69 Current State: 57:[71, 83, 69], Operations: ['42+27=69'] Exploring Operation: 83-71=12, Resulting Numbers: [69, 12] Generated Node #3: [69, 12] from Operation: 83-71=12 Current State: 57:[69, 12], Operations: ['42+27=69', '83-71=12'] Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[42, 27, 71, 83], Operations: [] Exploring Operation: 83-27=56, Resulting Numbers: [42, 71, 56] Generated Node #0,0: 57:[42, 71, 56] Operation: 83-27=56 Exploring Operation: 83-71=12, Resulting Numbers: [42, 27, 12] Generated Node #0,1: 57:[42, 27, 12] Operation: 83-71=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[42, 71, 56], Operations: ['83-27=56'] Exploring Operation: 71-42=29, Resulting Numbers: [56, 29] Generated Node #0,0,0: 57:[56, 29] Operation: 71-42=29 Exploring Operation: 56-42=14, Resulting Numbers: [71, 14] Generated Node #0,0,1: 57:[71, 14] Operation: 56-42=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[56, 29], Operations: ['83-27=56', '71-42=29'] Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[71, 14], Operations: ['83-27=56', '56-42=14'] Exploring Operation: 71+14=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[42, 27, 71, 83], Operations: [] Exploring Operation: 83-27=56, Resulting Numbers: [42, 71, 56] Generated Node #0,0: 57:[42, 71, 56] Operation: 83-27=56 Moving to Node #0,0 Current State: 57:[42, 71, 56], Operations: ['83-27=56'] Exploring Operation: 56-42=14, Resulting Numbers: [71, 14] Generated Node #0,0,1: 57:[71, 14] Operation: 56-42=14 Moving to Node #0,0,1 Current State: 57:[71, 14], Operations: ['83-27=56', '56-42=14'] Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 12, 37, 17, 53 ]
61
[ "37-12=25", "53-17=36", "25+36=61" ]
Current State: 61:[12, 37, 17, 53], Operations: [] Exploring Operation: 37-12=25, Resulting Numbers: [17, 53, 25] Generated Node #2: [17, 53, 25] from Operation: 37-12=25 Current State: 61:[17, 53, 25], Operations: ['37-12=25'] Exploring Operation: 53-17=36, Resulting Numbers: [25, 36] Generated Node #3: [25, 36] from Operation: 53-17=36 Current State: 61:[25, 36], Operations: ['37-12=25', '53-17=36'] Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[12, 37, 17, 53], Operations: [] Exploring Operation: 12+53=65, Resulting Numbers: [37, 17, 65] Generated Node #0,0: 61:[37, 17, 65] Operation: 12+53=65 Exploring Operation: 37+17=54, Resulting Numbers: [12, 53, 54] Generated Node #0,1: 61:[12, 53, 54] Operation: 37+17=54 Exploring Operation: 12+17=29, Resulting Numbers: [37, 53, 29] Generated Node #0,2: 61:[37, 53, 29] Operation: 12+17=29 Exploring Operation: 17+53=70, Resulting Numbers: [12, 37, 70] Generated Node #0,3: 61:[12, 37, 70] Operation: 17+53=70 Exploring Operation: 12+37=49, Resulting Numbers: [17, 53, 49] Generated Node #0,4: 61:[17, 53, 49] Operation: 12+37=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[12, 53, 54], Operations: ['37+17=54'] Exploring Operation: 53+54=107, Resulting Numbers: [12, 107] Generated Node #0,1,0: 61:[12, 107] Operation: 53+54=107 Exploring Operation: 12+53=65, Resulting Numbers: [54, 65] Generated Node #0,1,1: 61:[54, 65] Operation: 12+53=65 Exploring Operation: 12+54=66, Resulting Numbers: [53, 66] Generated Node #0,1,2: 61:[53, 66] Operation: 12+54=66 Exploring Operation: 54-12=42, Resulting Numbers: [53, 42] Generated Node #0,1,3: 61:[53, 42] Operation: 54-12=42 Exploring Operation: 53-12=41, Resulting Numbers: [54, 41] Generated Node #0,1,4: 61:[54, 41] Operation: 53-12=41 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[54, 65], Operations: ['37+17=54', '12+53=65'] Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,61 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[53, 66], Operations: ['37+17=54', '12+54=66'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 61:[53, 42], Operations: ['37+17=54', '54-12=42'] Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,61 unequal: No Solution Exploring Operation: 53*42=2226, Resulting Numbers: [2226] 2226,61 unequal: No Solution Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 61:[54, 41], Operations: ['37+17=54', '53-12=41'] Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 54*41=2214, Resulting Numbers: [2214] 2214,61 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[12, 107], Operations: ['37+17=54', '53+54=107'] Exploring Operation: 107-12=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 12+107=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 12*107=1284, Resulting Numbers: [1284] 1284,61 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: 61:[37, 53, 29], Operations: ['12+17=29'] Exploring Operation: 37+29=66, Resulting Numbers: [53, 66] Generated Node #0,2,0: 61:[53, 66] Operation: 37+29=66 Exploring Operation: 37-29=8, Resulting Numbers: [53, 8] Generated Node #0,2,1: 61:[53, 8] Operation: 37-29=8 Exploring Operation: 53+29=82, Resulting Numbers: [37, 82] Generated Node #0,2,2: 61:[37, 82] Operation: 53+29=82 Exploring Operation: 37+53=90, Resulting Numbers: [29, 90] Generated Node #0,2,3: 61:[29, 90] Operation: 37+53=90 Exploring Operation: 53-29=24, Resulting Numbers: [37, 24] Generated Node #0,2,4: 61:[37, 24] Operation: 53-29=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[53, 66], Operations: ['12+17=29', '37+29=66'] Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,61 unequal: No Solution Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[37, 82], Operations: ['12+17=29', '53+29=82'] Exploring Operation: 37+82=119, Resulting Numbers: [119] 119,61 unequal: No Solution Exploring Operation: 82-37=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 37*82=3034, Resulting Numbers: [3034] 3034,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[53, 8], Operations: ['12+17=29', '37-29=8'] Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,61 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[12, 37, 17, 53], Operations: [] Exploring Operation: 12+17=29, Resulting Numbers: [37, 53, 29] Generated Node #0,2: 61:[37, 53, 29] Operation: 12+17=29 Moving to Node #0,2 Current State: 61:[37, 53, 29], Operations: ['12+17=29'] Exploring Operation: 37-29=8, Resulting Numbers: [53, 8] Generated Node #0,2,1: 61:[53, 8] Operation: 37-29=8 Moving to Node #0,2,1 Current State: 61:[53, 8], Operations: ['12+17=29', '37-29=8'] Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 20, 77, 4, 78 ]
16
[ "20-4=16", "78-77=1", "16*1=16" ]
Current State: 16:[20, 77, 4, 78], Operations: [] Exploring Operation: 20-4=16, Resulting Numbers: [77, 78, 16] Generated Node #2: [77, 78, 16] from Operation: 20-4=16 Current State: 16:[77, 78, 16], Operations: ['20-4=16'] Exploring Operation: 78-77=1, Resulting Numbers: [16, 1] Generated Node #3: [16, 1] from Operation: 78-77=1 Current State: 16:[16, 1], Operations: ['20-4=16', '78-77=1'] Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[20, 77, 4, 78], Operations: [] Exploring Operation: 77-20=57, Resulting Numbers: [4, 78, 57] Generated Node #0,0: 16:[4, 78, 57] Operation: 77-20=57 Exploring Operation: 78-77=1, Resulting Numbers: [20, 4, 1] Generated Node #0,1: 16:[20, 4, 1] Operation: 78-77=1 Exploring Operation: 78-20=58, Resulting Numbers: [77, 4, 58] Generated Node #0,2: 16:[77, 4, 58] Operation: 78-20=58 Moving to Node #0,1 Current State: 16:[20, 4, 1], Operations: ['78-77=1'] Exploring Operation: 20-1=19, Resulting Numbers: [4, 19] Generated Node #0,1,0: 16:[4, 19] Operation: 20-1=19 Exploring Operation: 20-4=16, Resulting Numbers: [1, 16] Generated Node #0,1,1: 16:[1, 16] Operation: 20-4=16 Exploring Operation: 20/4=5, Resulting Numbers: [1, 5] Generated Node #0,1,2: 16:[1, 5] Operation: 20/4=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[1, 16], Operations: ['78-77=1', '20-4=16'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[20, 77, 4, 78], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [20, 4, 1] Generated Node #0,1: 16:[20, 4, 1] Operation: 78-77=1 Moving to Node #0,1 Current State: 16:[20, 4, 1], Operations: ['78-77=1'] Exploring Operation: 20-4=16, Resulting Numbers: [1, 16] Generated Node #0,1,1: 16:[1, 16] Operation: 20-4=16 Moving to Node #0,1,1 Current State: 16:[1, 16], Operations: ['78-77=1', '20-4=16'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 27, 31, 6, 39 ]
54
[ "31+6=37", "39-37=2", "27*2=54" ]
Current State: 54:[27, 31, 6, 39], Operations: [] Exploring Operation: 31+6=37, Resulting Numbers: [27, 39, 37] Generated Node #2: [27, 39, 37] from Operation: 31+6=37 Current State: 54:[27, 39, 37], Operations: ['31+6=37'] Exploring Operation: 39-37=2, Resulting Numbers: [27, 2] Generated Node #3: [27, 2] from Operation: 39-37=2 Current State: 54:[27, 2], Operations: ['31+6=37', '39-37=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[27, 31, 6, 39], Operations: [] Exploring Operation: 39-31=8, Resulting Numbers: [27, 6, 8] Generated Node #0,0: 54:[27, 6, 8] Operation: 39-31=8 Exploring Operation: 39-27=12, Resulting Numbers: [31, 6, 12] Generated Node #0,1: 54:[31, 6, 12] Operation: 39-27=12 Moving to Node #0,0 Current State: 54:[27, 6, 8], Operations: ['39-31=8'] Exploring Operation: 27-8=19, Resulting Numbers: [6, 19] Generated Node #0,0,0: 54:[6, 19] Operation: 27-8=19 Exploring Operation: 8-6=2, Resulting Numbers: [27, 2] Generated Node #0,0,1: 54:[27, 2] Operation: 8-6=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[27, 2], Operations: ['39-31=8', '8-6=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[27, 31, 6, 39], Operations: [] Exploring Operation: 39-31=8, Resulting Numbers: [27, 6, 8] Generated Node #0,0: 54:[27, 6, 8] Operation: 39-31=8 Moving to Node #0,0 Current State: 54:[27, 6, 8], Operations: ['39-31=8'] Exploring Operation: 8-6=2, Resulting Numbers: [27, 2] Generated Node #0,0,1: 54:[27, 2] Operation: 8-6=2 Moving to Node #0,0,1 Current State: 54:[27, 2], Operations: ['39-31=8', '8-6=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 76, 28, 1, 10 ]
94
[ "76+28=104", "1*10=10", "104-10=94" ]
Current State: 94:[76, 28, 1, 10], Operations: [] Exploring Operation: 76+28=104, Resulting Numbers: [1, 10, 104] Generated Node #2: [1, 10, 104] from Operation: 76+28=104 Current State: 94:[1, 10, 104], Operations: ['76+28=104'] Exploring Operation: 1*10=10, Resulting Numbers: [104, 10] Generated Node #3: [104, 10] from Operation: 1*10=10 Current State: 94:[104, 10], Operations: ['76+28=104', '1*10=10'] Exploring Operation: 104-10=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[76, 28, 1, 10], Operations: [] Exploring Operation: 76-28=48, Resulting Numbers: [1, 10, 48] Generated Node #0,0: 94:[1, 10, 48] Operation: 76-28=48 Moving to Node #0,0 Current State: 94:[1, 10, 48], Operations: ['76-28=48'] Exploring Operation: 10-1=9, Resulting Numbers: [48, 9] Generated Node #0,0,0: 94:[48, 9] Operation: 10-1=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[48, 9], Operations: ['76-28=48', '10-1=9'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,94 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
[ 1, 91, 88, 42 ]
15
[ "91-88=3", "42/3=14", "1+14=15" ]
Current State: 15:[1, 91, 88, 42], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [1, 42, 3] Generated Node #2: [1, 42, 3] from Operation: 91-88=3 Current State: 15:[1, 42, 3], Operations: ['91-88=3'] Exploring Operation: 42/3=14, Resulting Numbers: [1, 14] Generated Node #3: [1, 14] from Operation: 42/3=14 Current State: 15:[1, 14], Operations: ['91-88=3', '42/3=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[1, 91, 88, 42], Operations: [] Exploring Operation: 91-42=49, Resulting Numbers: [1, 88, 49] Generated Node #0,0: 15:[1, 88, 49] Operation: 91-42=49 Exploring Operation: 91-88=3, Resulting Numbers: [1, 42, 3] Generated Node #0,1: 15:[1, 42, 3] Operation: 91-88=3 Exploring Operation: 88-42=46, Resulting Numbers: [1, 91, 46] Generated Node #0,2: 15:[1, 91, 46] Operation: 88-42=46 Exploring Operation: 91-1=90, Resulting Numbers: [88, 42, 90] Generated Node #0,3: 15:[88, 42, 90] Operation: 91-1=90 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[1, 42, 3], Operations: ['91-88=3'] Exploring Operation: 42-3=39, Resulting Numbers: [1, 39] Generated Node #0,1,0: 15:[1, 39] Operation: 42-3=39 Exploring Operation: 42-1=41, Resulting Numbers: [3, 41] Generated Node #0,1,1: 15:[3, 41] Operation: 42-1=41 Exploring Operation: 42/3=14, Resulting Numbers: [1, 14] Generated Node #0,1,2: 15:[1, 14] Operation: 42/3=14 Exploring Operation: 1*42=42, Resulting Numbers: [3, 42] Generated Node #0,1,3: 15:[3, 42] Operation: 1*42=42 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 15:[1, 14], Operations: ['91-88=3', '42/3=14'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,15 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[1, 91, 88, 42], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [1, 42, 3] Generated Node #0,1: 15:[1, 42, 3] Operation: 91-88=3 Moving to Node #0,1 Current State: 15:[1, 42, 3], Operations: ['91-88=3'] Exploring Operation: 42/3=14, Resulting Numbers: [1, 14] Generated Node #0,1,2: 15:[1, 14] Operation: 42/3=14 Moving to Node #0,1,2 Current State: 15:[1, 14], Operations: ['91-88=3', '42/3=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 12, 17, 45, 74 ]
90
[ "12+17=29", "45+74=119", "119-29=90" ]
Current State: 90:[12, 17, 45, 74], Operations: [] Exploring Operation: 12+17=29, Resulting Numbers: [45, 74, 29] Generated Node #2: [45, 74, 29] from Operation: 12+17=29 Current State: 90:[45, 74, 29], Operations: ['12+17=29'] Exploring Operation: 45+74=119, Resulting Numbers: [29, 119] Generated Node #3: [29, 119] from Operation: 45+74=119 Current State: 90:[29, 119], Operations: ['12+17=29', '45+74=119'] Exploring Operation: 119-29=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[12, 17, 45, 74], Operations: [] Exploring Operation: 17+74=91, Resulting Numbers: [12, 45, 91] Generated Node #0,0: 90:[12, 45, 91] Operation: 17+74=91 Moving to Node #0,0 Current State: 90:[12, 45, 91], Operations: ['17+74=91'] Exploring Operation: 91-45=46, Resulting Numbers: [12, 46] Generated Node #0,0,0: 90:[12, 46] Operation: 91-45=46 Moving to Node #0,0,0 Current State: 90:[12, 46], Operations: ['17+74=91', '91-45=46'] Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,90 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 80, 9, 95, 68 ]
98
[ "80-9=71", "95-68=27", "71+27=98" ]
Current State: 98:[80, 9, 95, 68], Operations: [] Exploring Operation: 80-9=71, Resulting Numbers: [95, 68, 71] Generated Node #2: [95, 68, 71] from Operation: 80-9=71 Current State: 98:[95, 68, 71], Operations: ['80-9=71'] Exploring Operation: 95-68=27, Resulting Numbers: [71, 27] Generated Node #3: [71, 27] from Operation: 95-68=27 Current State: 98:[71, 27], Operations: ['80-9=71', '95-68=27'] Exploring Operation: 71+27=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[80, 9, 95, 68], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [9, 95, 12] Generated Node #0,0: 98:[9, 95, 12] Operation: 80-68=12 Exploring Operation: 80+9=89, Resulting Numbers: [95, 68, 89] Generated Node #0,1: 98:[95, 68, 89] Operation: 80+9=89 Exploring Operation: 95-80=15, Resulting Numbers: [9, 68, 15] Generated Node #0,2: 98:[9, 68, 15] Operation: 95-80=15 Moving to Node #0,0 Current State: 98:[9, 95, 12], Operations: ['80-68=12'] Exploring Operation: 12-9=3, Resulting Numbers: [95, 3] Generated Node #0,0,0: 98:[95, 3] Operation: 12-9=3 Exploring Operation: 9+12=21, Resulting Numbers: [95, 21] Generated Node #0,0,1: 98:[95, 21] Operation: 9+12=21 Exploring Operation: 9+95=104, Resulting Numbers: [12, 104] Generated Node #0,0,2: 98:[12, 104] Operation: 9+95=104 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[95, 3], Operations: ['80-68=12', '12-9=3'] Exploring Operation: 95*3=285, Resulting Numbers: [285] 285,98 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,98 unequal: No Solution Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[80, 9, 95, 68], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [9, 95, 12] Generated Node #0,0: 98:[9, 95, 12] Operation: 80-68=12 Moving to Node #0,0 Current State: 98:[9, 95, 12], Operations: ['80-68=12'] Exploring Operation: 12-9=3, Resulting Numbers: [95, 3] Generated Node #0,0,0: 98:[95, 3] Operation: 12-9=3 Moving to Node #0,0,0 Current State: 98:[95, 3], Operations: ['80-68=12', '12-9=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 94, 44, 38, 88 ]
76
[ "94-44=50", "38+88=126", "126-50=76" ]
Current State: 76:[94, 44, 38, 88], Operations: [] Exploring Operation: 94-44=50, Resulting Numbers: [38, 88, 50] Generated Node #2: [38, 88, 50] from Operation: 94-44=50 Current State: 76:[38, 88, 50], Operations: ['94-44=50'] Exploring Operation: 38+88=126, Resulting Numbers: [50, 126] Generated Node #3: [50, 126] from Operation: 38+88=126 Current State: 76:[50, 126], Operations: ['94-44=50', '38+88=126'] Exploring Operation: 126-50=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[94, 44, 38, 88], Operations: [] Exploring Operation: 88-44=44, Resulting Numbers: [94, 38, 44] Generated Node #0,0: 76:[94, 38, 44] Operation: 88-44=44 Exploring Operation: 44-38=6, Resulting Numbers: [94, 88, 6] Generated Node #0,1: 76:[94, 88, 6] Operation: 44-38=6 Exploring Operation: 94-88=6, Resulting Numbers: [44, 38, 6] Generated Node #0,2: 76:[44, 38, 6] Operation: 94-88=6 Exploring Operation: 88/44=2, Resulting Numbers: [94, 38, 2] Generated Node #0,3: 76:[94, 38, 2] Operation: 88/44=2 Exploring Operation: 94-44=50, Resulting Numbers: [38, 88, 50] Generated Node #0,4: 76:[38, 88, 50] Operation: 94-44=50 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[44, 38, 6], Operations: ['94-88=6'] Exploring Operation: 44+38=82, Resulting Numbers: [6, 82] Generated Node #0,2,0: 76:[6, 82] Operation: 44+38=82 Exploring Operation: 44-6=38, Resulting Numbers: [38, 38] Generated Node #0,2,1: 76:[38, 38] Operation: 44-6=38 Exploring Operation: 44+6=50, Resulting Numbers: [38, 50] Generated Node #0,2,2: 76:[38, 50] Operation: 44+6=50 Exploring Operation: 44-38=6, Resulting Numbers: [6, 6] Generated Node #0,2,3: 76:[6, 6] Operation: 44-38=6 Exploring Operation: 38+6=44, Resulting Numbers: [44, 44] Generated Node #0,2,4: 76:[44, 44] Operation: 38+6=44 Moving to Node #0,2,1 Current State: 76:[38, 38], Operations: ['94-88=6', '44-6=38'] Exploring Operation: 38*38=1444, Resulting Numbers: [1444] 1444,76 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[94, 44, 38, 88], Operations: [] Exploring Operation: 94-88=6, Resulting Numbers: [44, 38, 6] Generated Node #0,2: 76:[44, 38, 6] Operation: 94-88=6 Moving to Node #0,2 Current State: 76:[44, 38, 6], Operations: ['94-88=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38, 38] Generated Node #0,2,1: 76:[38, 38] Operation: 44-6=38 Moving to Node #0,2,1 Current State: 76:[38, 38], Operations: ['94-88=6', '44-6=38'] Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 50, 5, 2, 51 ]
12
[ "50-5=45", "51-45=6", "2*6=12" ]
Current State: 12:[50, 5, 2, 51], Operations: [] Exploring Operation: 50-5=45, Resulting Numbers: [2, 51, 45] Generated Node #2: [2, 51, 45] from Operation: 50-5=45 Current State: 12:[2, 51, 45], Operations: ['50-5=45'] Exploring Operation: 51-45=6, Resulting Numbers: [2, 6] Generated Node #3: [2, 6] from Operation: 51-45=6 Current State: 12:[2, 6], Operations: ['50-5=45', '51-45=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[50, 5, 2, 51], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [5, 2, 1] Generated Node #0,0: 12:[5, 2, 1] Operation: 51-50=1 Exploring Operation: 50/5=10, Resulting Numbers: [2, 51, 10] Generated Node #0,1: 12:[2, 51, 10] Operation: 50/5=10 Exploring Operation: 50-5=45, Resulting Numbers: [2, 51, 45] Generated Node #0,2: 12:[2, 51, 45] Operation: 50-5=45 Exploring Operation: 50/2=25, Resulting Numbers: [5, 51, 25] Generated Node #0,3: 12:[5, 51, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[5, 2, 1], Operations: ['51-50=1'] Exploring Operation: 5-1=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 12:[2, 4] Operation: 5-1=4 Exploring Operation: 5+1=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 12:[2, 6] Operation: 5+1=6 Exploring Operation: 5*1=5, Resulting Numbers: [2, 5] Generated Node #0,0,2: 12:[2, 5] Operation: 5*1=5 Exploring Operation: 5-2=3, Resulting Numbers: [1, 3] Generated Node #0,0,3: 12:[1, 3] Operation: 5-2=3 Moving to Node #0,0,0 Current State: 12:[2, 4], Operations: ['51-50=1', '5-1=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[2, 6], Operations: ['51-50=1', '5+1=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[50, 5, 2, 51], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [5, 2, 1] Generated Node #0,0: 12:[5, 2, 1] Operation: 51-50=1 Moving to Node #0,0 Current State: 12:[5, 2, 1], Operations: ['51-50=1'] Exploring Operation: 5+1=6, Resulting Numbers: [2, 6] Generated Node #0,0,1: 12:[2, 6] Operation: 5+1=6 Moving to Node #0,0,1 Current State: 12:[2, 6], Operations: ['51-50=1', '5+1=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 27, 45, 48, 72 ]
40
[ "72-48=24", "45*24=1080", "1080/27=40" ]
Current State: 40:[27, 45, 48, 72], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [27, 45, 24] Generated Node #2: [27, 45, 24] from Operation: 72-48=24 Current State: 40:[27, 45, 24], Operations: ['72-48=24'] Exploring Operation: 45*24=1080, Resulting Numbers: [27, 1080] Generated Node #3: [27, 1080] from Operation: 45*24=1080 Current State: 40:[27, 1080], Operations: ['72-48=24', '45*24=1080'] Exploring Operation: 1080/27=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[27, 45, 48, 72], Operations: [] Exploring Operation: 72-45=27, Resulting Numbers: [27, 48, 27] Generated Node #0,0: 40:[27, 48, 27] Operation: 72-45=27 Exploring Operation: 72-27=45, Resulting Numbers: [45, 48, 45] Generated Node #0,1: 40:[45, 48, 45] Operation: 72-27=45 Exploring Operation: 72-48=24, Resulting Numbers: [27, 45, 24] Generated Node #0,2: 40:[27, 45, 24] Operation: 72-48=24 Moving to Node #0,2 Current State: 40:[27, 45, 24], Operations: ['72-48=24'] Exploring Operation: 45-27=18, Resulting Numbers: [24, 18] Generated Node #0,2,0: 40:[24, 18] Operation: 45-27=18 Exploring Operation: 45-24=21, Resulting Numbers: [27, 21] Generated Node #0,2,1: 40:[27, 21] Operation: 45-24=21 Exploring Operation: 27-24=3, Resulting Numbers: [45, 3] Generated Node #0,2,2: 40:[45, 3] Operation: 27-24=3 Moving to Node #0,1 Current State: 40:[45, 48, 45], Operations: ['72-27=45'] Exploring Operation: 45/45=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 40:[48, 1] Operation: 45/45=1 Exploring Operation: 48-45=3, Resulting Numbers: [45, 3] Generated Node #0,1,1: 40:[45, 3] Operation: 48-45=3 Exploring Operation: 48-45=3, Resulting Numbers: [45, 3] Generated Node #0,1,2: 40:[45, 3] Operation: 48-45=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[45, 3], Operations: ['72-27=45', '48-45=3'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[45, 3], Operations: ['72-27=45', '48-45=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[48, 1], Operations: ['72-27=45', '45/45=1'] Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,40 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,40 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: 40:[27, 48, 27], Operations: ['72-45=27'] Exploring Operation: 48-27=21, Resulting Numbers: [27, 21] Generated Node #0,0,0: 40:[27, 21] Operation: 48-27=21 Exploring Operation: 27/27=1, Resulting Numbers: [48, 1] Generated Node #0,0,1: 40:[48, 1] Operation: 27/27=1 Exploring Operation: 48-27=21, Resulting Numbers: [27, 21] Generated Node #0,0,2: 40:[27, 21] Operation: 48-27=21 Moving to Node #0,2,0 Current State: 40:[24, 18], Operations: ['72-48=24', '45-27=18'] Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,40 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[45, 3], Operations: ['72-48=24', '27-24=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,40 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[27, 21], Operations: ['72-48=24', '45-24=21'] Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,40 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[27, 21], Operations: ['72-45=27', '48-27=21'] Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,40 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,40 unequal: No Solution Moving to Node #0,0,0 Current State: 40:[27, 21], Operations: ['72-45=27', '48-27=21'] Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[48, 1], Operations: ['72-45=27', '27/27=1'] Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,40 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 68, 48, 60, 4 ]
40
[ "68+4=72", "48*60=2880", "2880/72=40" ]
Current State: 40:[68, 48, 60, 4], Operations: [] Exploring Operation: 68+4=72, Resulting Numbers: [48, 60, 72] Generated Node #2: [48, 60, 72] from Operation: 68+4=72 Current State: 40:[48, 60, 72], Operations: ['68+4=72'] Exploring Operation: 48*60=2880, Resulting Numbers: [72, 2880] Generated Node #3: [72, 2880] from Operation: 48*60=2880 Current State: 40:[72, 2880], Operations: ['68+4=72', '48*60=2880'] Exploring Operation: 2880/72=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[68, 48, 60, 4], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [48, 4, 8] Generated Node #0,0: 40:[48, 4, 8] Operation: 68-60=8 Exploring Operation: 68-48=20, Resulting Numbers: [60, 4, 20] Generated Node #0,1: 40:[60, 4, 20] Operation: 68-48=20 Exploring Operation: 60-48=12, Resulting Numbers: [68, 4, 12] Generated Node #0,2: 40:[68, 4, 12] Operation: 60-48=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[48, 4, 8], Operations: ['68-60=8'] Exploring Operation: 48-8=40, Resulting Numbers: [4, 40] Generated Node #0,0,0: 40:[4, 40] Operation: 48-8=40 Exploring Operation: 48/8=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 40:[4, 6] Operation: 48/8=6 Exploring Operation: 48/4=12, Resulting Numbers: [8, 12] Generated Node #0,0,2: 40:[8, 12] Operation: 48/4=12 Moving to Node #0,0,0 Current State: 40:[4, 40], Operations: ['68-60=8', '48-8=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[4, 6], Operations: ['68-60=8', '48/8=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,40 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[8, 12], Operations: ['68-60=8', '48/4=12'] Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[60, 4, 20], Operations: ['68-48=20'] Exploring Operation: 60/4=15, Resulting Numbers: [20, 15] Generated Node #0,1,0: 40:[20, 15] Operation: 60/4=15 Exploring Operation: 60/20=3, Resulting Numbers: [4, 3] Generated Node #0,1,1: 40:[4, 3] Operation: 60/20=3 Exploring Operation: 60-20=40, Resulting Numbers: [4, 40] Generated Node #0,1,2: 40:[4, 40] Operation: 60-20=40 Moving to Node #0,1,2 Current State: 40:[4, 40], Operations: ['68-48=20', '60-20=40'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,40 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[4, 3], Operations: ['68-48=20', '60/20=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,40 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[20, 15], Operations: ['68-48=20', '60/4=15'] Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,40 unequal: No Solution Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,40 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[68, 4, 12], Operations: ['60-48=12'] Exploring Operation: 68/4=17, Resulting Numbers: [12, 17] Generated Node #0,2,0: 40:[12, 17] Operation: 68/4=17 Exploring Operation: 68-4=64, Resulting Numbers: [12, 64] Generated Node #0,2,1: 40:[12, 64] Operation: 68-4=64 Exploring Operation: 68-12=56, Resulting Numbers: [4, 56] Generated Node #0,2,2: 40:[4, 56] Operation: 68-12=56 Moving to Node #0,2,0 Current State: 40:[12, 17], Operations: ['60-48=12', '68/4=17'] Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,40 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,40 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[4, 56], Operations: ['60-48=12', '68-12=56'] Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,40 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[12, 64], Operations: ['60-48=12', '68-4=64'] Exploring Operation: 12+64=76, Resulting Numbers: [76] 76,40 unequal: No Solution Exploring Operation: 12*64=768, Resulting Numbers: [768] 768,40 unequal: No Solution Exploring Operation: 64-12=52, Resulting Numbers: [52] 52,40 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
[ 36, 88, 48, 5 ]
81
[ "36+88=124", "48-5=43", "124-43=81" ]
Current State: 81:[36, 88, 48, 5], Operations: [] Exploring Operation: 36+88=124, Resulting Numbers: [48, 5, 124] Generated Node #2: [48, 5, 124] from Operation: 36+88=124 Current State: 81:[48, 5, 124], Operations: ['36+88=124'] Exploring Operation: 48-5=43, Resulting Numbers: [124, 43] Generated Node #3: [124, 43] from Operation: 48-5=43 Current State: 81:[124, 43], Operations: ['36+88=124', '48-5=43'] Exploring Operation: 124-43=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[36, 88, 48, 5], Operations: [] Exploring Operation: 48-36=12, Resulting Numbers: [88, 5, 12] Generated Node #0,0: 81:[88, 5, 12] Operation: 48-36=12 Exploring Operation: 88-48=40, Resulting Numbers: [36, 5, 40] Generated Node #0,1: 81:[36, 5, 40] Operation: 88-48=40 Exploring Operation: 36-5=31, Resulting Numbers: [88, 48, 31] Generated Node #0,2: 81:[88, 48, 31] Operation: 36-5=31 Exploring Operation: 36+48=84, Resulting Numbers: [88, 5, 84] Generated Node #0,3: 81:[88, 5, 84] Operation: 36+48=84 Moving to Node #0,0 Current State: 81:[88, 5, 12], Operations: ['48-36=12'] Exploring Operation: 88-5=83, Resulting Numbers: [12, 83] Generated Node #0,0,0: 81:[12, 83] Operation: 88-5=83 Exploring Operation: 88-12=76, Resulting Numbers: [5, 76] Generated Node #0,0,1: 81:[5, 76] Operation: 88-12=76 Exploring Operation: 12-5=7, Resulting Numbers: [88, 7] Generated Node #0,0,2: 81:[88, 7] Operation: 12-5=7 Exploring Operation: 88+5=93, Resulting Numbers: [12, 93] Generated Node #0,0,3: 81:[12, 93] Operation: 88+5=93 Moving to Node #0,3 Current State: 81:[88, 5, 84], Operations: ['36+48=84'] Exploring Operation: 84-5=79, Resulting Numbers: [88, 79] Generated Node #0,3,0: 81:[88, 79] Operation: 84-5=79 Exploring Operation: 88-5=83, Resulting Numbers: [84, 83] Generated Node #0,3,1: 81:[84, 83] Operation: 88-5=83 Exploring Operation: 88-84=4, Resulting Numbers: [5, 4] Generated Node #0,3,2: 81:[5, 4] Operation: 88-84=4 Exploring Operation: 88+5=93, Resulting Numbers: [84, 93] Generated Node #0,3,3: 81:[84, 93] Operation: 88+5=93 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 81:[5, 4], Operations: ['36+48=84', '88-84=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[84, 83], Operations: ['36+48=84', '88-5=83'] Exploring Operation: 84+83=167, Resulting Numbers: [167] 167,81 unequal: No Solution Exploring Operation: 84*83=6972, Resulting Numbers: [6972] 6972,81 unequal: No Solution Exploring Operation: 84-83=1, Resulting Numbers: [1] 1,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 81:[88, 79], Operations: ['36+48=84', '84-5=79'] Exploring Operation: 88+79=167, Resulting Numbers: [167] 167,81 unequal: No Solution Exploring Operation: 88*79=6952, Resulting Numbers: [6952] 6952,81 unequal: No Solution Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 81:[84, 93], Operations: ['36+48=84', '88+5=93'] Exploring Operation: 84*93=7812, Resulting Numbers: [7812] 7812,81 unequal: No Solution Exploring Operation: 93-84=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 84+93=177, Resulting Numbers: [177] 177,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 81:[36, 5, 40], Operations: ['88-48=40'] Exploring Operation: 40-36=4, Resulting Numbers: [5, 4] Generated Node #0,1,0: 81:[5, 4] Operation: 40-36=4 Exploring Operation: 40/5=8, Resulting Numbers: [36, 8] Generated Node #0,1,1: 81:[36, 8] Operation: 40/5=8 Exploring Operation: 36-5=31, Resulting Numbers: [40, 31] Generated Node #0,1,2: 81:[40, 31] Operation: 36-5=31 Exploring Operation: 36+40=76, Resulting Numbers: [5, 76] Generated Node #0,1,3: 81:[5, 76] Operation: 36+40=76 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[5, 4], Operations: ['88-48=40', '40-36=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 81:[5, 76], Operations: ['88-48=40', '36+40=76'] Exploring Operation: 5+76=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[36, 88, 48, 5], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [36, 5, 40] Generated Node #0,1: 81:[36, 5, 40] Operation: 88-48=40 Moving to Node #0,1 Current State: 81:[36, 5, 40], Operations: ['88-48=40'] Exploring Operation: 36+40=76, Resulting Numbers: [5, 76] Generated Node #0,1,3: 81:[5, 76] Operation: 36+40=76 Moving to Node #0,1,3 Current State: 81:[5, 76], Operations: ['88-48=40', '36+40=76'] Exploring Operation: 5+76=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 79, 80, 79, 98 ]
19
[ "80-79=1", "98-79=19", "1*19=19" ]
Current State: 19:[79, 80, 79, 98], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [98, 1] Generated Node #2: [98, 1] from Operation: 80-79=1 Current State: 19:[98, 1], Operations: ['80-79=1'] Exploring Operation: 98-79=19, Resulting Numbers: [1, 19] Generated Node #3: [1, 19] from Operation: 98-79=19 Current State: 19:[1, 19], Operations: ['80-79=1', '98-79=19'] Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[79, 80, 79, 98], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [80, 79, 19] Generated Node #0,0: 19:[80, 79, 19] Operation: 98-79=19 Moving to Node #0,0 Current State: 19:[80, 79, 19], Operations: ['98-79=19'] Exploring Operation: 80-79=1, Resulting Numbers: [19, 1] Generated Node #0,0,0: 19:[19, 1] Operation: 80-79=1 Moving to Node #0,0,0 Current State: 19:[19, 1], Operations: ['98-79=19', '80-79=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[79, 80, 79, 98], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [80, 79, 19] Generated Node #0,0: 19:[80, 79, 19] Operation: 98-79=19 Moving to Node #0,0 Current State: 19:[80, 79, 19], Operations: ['98-79=19'] Exploring Operation: 80-79=1, Resulting Numbers: [19, 1] Generated Node #0,0,0: 19:[19, 1] Operation: 80-79=1 Moving to Node #0,0,0 Current State: 19:[19, 1], Operations: ['98-79=19', '80-79=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 86, 21, 77, 99 ]
86
[ "21+77=98", "99-98=1", "86*1=86" ]
Current State: 86:[86, 21, 77, 99], Operations: [] Exploring Operation: 21+77=98, Resulting Numbers: [86, 99, 98] Generated Node #2: [86, 99, 98] from Operation: 21+77=98 Current State: 86:[86, 99, 98], Operations: ['21+77=98'] Exploring Operation: 99-98=1, Resulting Numbers: [86, 1] Generated Node #3: [86, 1] from Operation: 99-98=1 Current State: 86:[86, 1], Operations: ['21+77=98', '99-98=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[86, 21, 77, 99], Operations: [] Exploring Operation: 77-21=56, Resulting Numbers: [86, 99, 56] Generated Node #0,0: 86:[86, 99, 56] Operation: 77-21=56 Exploring Operation: 99-21=78, Resulting Numbers: [86, 77, 78] Generated Node #0,1: 86:[86, 77, 78] Operation: 99-21=78 Exploring Operation: 21+77=98, Resulting Numbers: [86, 99, 98] Generated Node #0,2: 86:[86, 99, 98] Operation: 21+77=98 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[86, 77, 78], Operations: ['99-21=78'] Exploring Operation: 86-78=8, Resulting Numbers: [77, 8] Generated Node #0,1,0: 86:[77, 8] Operation: 86-78=8 Exploring Operation: 78-77=1, Resulting Numbers: [86, 1] Generated Node #0,1,1: 86:[86, 1] Operation: 78-77=1 Exploring Operation: 86-77=9, Resulting Numbers: [78, 9] Generated Node #0,1,2: 86:[78, 9] Operation: 86-77=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[86, 1], Operations: ['99-21=78', '78-77=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[86, 21, 77, 99], Operations: [] Exploring Operation: 99-21=78, Resulting Numbers: [86, 77, 78] Generated Node #0,1: 86:[86, 77, 78] Operation: 99-21=78 Moving to Node #0,1 Current State: 86:[86, 77, 78], Operations: ['99-21=78'] Exploring Operation: 78-77=1, Resulting Numbers: [86, 1] Generated Node #0,1,1: 86:[86, 1] Operation: 78-77=1 Moving to Node #0,1,1 Current State: 86:[86, 1], Operations: ['99-21=78', '78-77=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 42, 94, 77, 12 ]
37
[ "94-42=52", "77+12=89", "89-52=37" ]
Current State: 37:[42, 94, 77, 12], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [77, 12, 52] Generated Node #2: [77, 12, 52] from Operation: 94-42=52 Current State: 37:[77, 12, 52], Operations: ['94-42=52'] Exploring Operation: 77+12=89, Resulting Numbers: [52, 89] Generated Node #3: [52, 89] from Operation: 77+12=89 Current State: 37:[52, 89], Operations: ['94-42=52', '77+12=89'] Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[42, 94, 77, 12], Operations: [] Exploring Operation: 94-77=17, Resulting Numbers: [42, 12, 17] Generated Node #0,0: 37:[42, 12, 17] Operation: 94-77=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[42, 12, 17], Operations: ['94-77=17'] Exploring Operation: 12+17=29, Resulting Numbers: [42, 29] Generated Node #0,0,0: 37:[42, 29] Operation: 12+17=29 Moving to Node #0,0,0 Current State: 37:[42, 29], Operations: ['94-77=17', '12+17=29'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,37 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
[ 86, 39, 70, 54 ]
41
[ "86+54=140", "140/70=2", "39+2=41" ]
Current State: 41:[86, 39, 70, 54], Operations: [] Exploring Operation: 86+54=140, Resulting Numbers: [39, 70, 140] Generated Node #2: [39, 70, 140] from Operation: 86+54=140 Current State: 41:[39, 70, 140], Operations: ['86+54=140'] Exploring Operation: 140/70=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 140/70=2 Current State: 41:[39, 2], Operations: ['86+54=140', '140/70=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[86, 39, 70, 54], Operations: [] Exploring Operation: 86-54=32, Resulting Numbers: [39, 70, 32] Generated Node #0,0: 41:[39, 70, 32] Operation: 86-54=32 Exploring Operation: 86-39=47, Resulting Numbers: [70, 54, 47] Generated Node #0,1: 41:[70, 54, 47] Operation: 86-39=47 Exploring Operation: 86-70=16, Resulting Numbers: [39, 54, 16] Generated Node #0,2: 41:[39, 54, 16] Operation: 86-70=16 Moving to Node #0,0 Current State: 41:[39, 70, 32], Operations: ['86-54=32'] Exploring Operation: 39+32=71, Resulting Numbers: [70, 71] Generated Node #0,0,0: 41:[70, 71] Operation: 39+32=71 Exploring Operation: 70-39=31, Resulting Numbers: [32, 31] Generated Node #0,0,1: 41:[32, 31] Operation: 70-39=31 Exploring Operation: 70-32=38, Resulting Numbers: [39, 38] Generated Node #0,0,2: 41:[39, 38] Operation: 70-32=38 Moving to Node #0,2 Current State: 41:[39, 54, 16], Operations: ['86-70=16'] Exploring Operation: 39-16=23, Resulting Numbers: [54, 23] Generated Node #0,2,0: 41:[54, 23] Operation: 39-16=23 Exploring Operation: 39+16=55, Resulting Numbers: [54, 55] Generated Node #0,2,1: 41:[54, 55] Operation: 39+16=55 Exploring Operation: 54-16=38, Resulting Numbers: [39, 38] Generated Node #0,2,2: 41:[39, 38] Operation: 54-16=38 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[39, 38], Operations: ['86-70=16', '54-16=38'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 39*38=1482, Resulting Numbers: [1482] 1482,41 unequal: No Solution Exploring Operation: 39+38=77, Resulting Numbers: [77] 77,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 41:[54, 55], Operations: ['86-70=16', '39+16=55'] Exploring Operation: 54+55=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 54*55=2970, Resulting Numbers: [2970] 2970,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[54, 23], Operations: ['86-70=16', '39-16=23'] Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 54*23=1242, Resulting Numbers: [1242] 1242,41 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,41 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: 41:[70, 54, 47], Operations: ['86-39=47'] Exploring Operation: 70-54=16, Resulting Numbers: [47, 16] Generated Node #0,1,0: 41:[47, 16] Operation: 70-54=16 Exploring Operation: 54-47=7, Resulting Numbers: [70, 7] Generated Node #0,1,1: 41:[70, 7] Operation: 54-47=7 Exploring Operation: 70-47=23, Resulting Numbers: [54, 23] Generated Node #0,1,2: 41:[54, 23] Operation: 70-47=23 Moving to Node #0,0,2 Current State: 41:[39, 38], Operations: ['86-54=32', '70-32=38'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 39+38=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 39*38=1482, Resulting Numbers: [1482] 1482,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[32, 31], Operations: ['86-54=32', '70-39=31'] Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[54, 23], Operations: ['86-39=47', '70-47=23'] Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 54*23=1242, Resulting Numbers: [1242] 1242,41 unequal: No Solution Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[47, 16], Operations: ['86-39=47', '70-54=16'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 47*16=752, Resulting Numbers: [752] 752,41 unequal: No Solution Exploring Operation: 47+16=63, Resulting Numbers: [63] 63,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[70, 71], Operations: ['86-54=32', '39+32=71'] Exploring Operation: 71-70=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 70*71=4970, Resulting Numbers: [4970] 4970,41 unequal: No Solution Exploring Operation: 70+71=141, Resulting Numbers: [141] 141,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[70, 7], Operations: ['86-39=47', '54-47=7'] Exploring Operation: 70+7=77, Resulting Numbers: [77] 77,41 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 74, 50, 79, 99 ]
44
[ "74-50=24", "99-79=20", "24+20=44" ]
Current State: 44:[74, 50, 79, 99], Operations: [] Exploring Operation: 74-50=24, Resulting Numbers: [79, 99, 24] Generated Node #2: [79, 99, 24] from Operation: 74-50=24 Current State: 44:[79, 99, 24], Operations: ['74-50=24'] Exploring Operation: 99-79=20, Resulting Numbers: [24, 20] Generated Node #3: [24, 20] from Operation: 99-79=20 Current State: 44:[24, 20], Operations: ['74-50=24', '99-79=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[74, 50, 79, 99], Operations: [] Exploring Operation: 99-50=49, Resulting Numbers: [74, 79, 49] Generated Node #0,0: 44:[74, 79, 49] Operation: 99-50=49 Exploring Operation: 79-74=5, Resulting Numbers: [50, 99, 5] Generated Node #0,1: 44:[50, 99, 5] Operation: 79-74=5 Exploring Operation: 99-74=25, Resulting Numbers: [50, 79, 25] Generated Node #0,2: 44:[50, 79, 25] Operation: 99-74=25 Exploring Operation: 99-79=20, Resulting Numbers: [74, 50, 20] Generated Node #0,3: 44:[74, 50, 20] Operation: 99-79=20 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[74, 50, 20], Operations: ['99-79=20'] Exploring Operation: 74+20=94, Resulting Numbers: [50, 94] Generated Node #0,3,0: 44:[50, 94] Operation: 74+20=94 Exploring Operation: 50-20=30, Resulting Numbers: [74, 30] Generated Node #0,3,1: 44:[74, 30] Operation: 50-20=30 Exploring Operation: 74-50=24, Resulting Numbers: [20, 24] Generated Node #0,3,2: 44:[20, 24] Operation: 74-50=24 Exploring Operation: 74-20=54, Resulting Numbers: [50, 54] Generated Node #0,3,3: 44:[50, 54] Operation: 74-20=54 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 44:[20, 24], Operations: ['99-79=20', '74-50=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[74, 50, 79, 99], Operations: [] Exploring Operation: 99-79=20, Resulting Numbers: [74, 50, 20] Generated Node #0,3: 44:[74, 50, 20] Operation: 99-79=20 Moving to Node #0,3 Current State: 44:[74, 50, 20], Operations: ['99-79=20'] Exploring Operation: 74-50=24, Resulting Numbers: [20, 24] Generated Node #0,3,2: 44:[20, 24] Operation: 74-50=24 Moving to Node #0,3,2 Current State: 44:[20, 24], Operations: ['99-79=20', '74-50=24'] Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 73, 70, 67, 33 ]
78
[ "73-70=3", "33/3=11", "67+11=78" ]
Current State: 78:[73, 70, 67, 33], Operations: [] Exploring Operation: 73-70=3, Resulting Numbers: [67, 33, 3] Generated Node #2: [67, 33, 3] from Operation: 73-70=3 Current State: 78:[67, 33, 3], Operations: ['73-70=3'] Exploring Operation: 33/3=11, Resulting Numbers: [67, 11] Generated Node #3: [67, 11] from Operation: 33/3=11 Current State: 78:[67, 11], Operations: ['73-70=3', '33/3=11'] Exploring Operation: 67+11=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[73, 70, 67, 33], Operations: [] Exploring Operation: 73-67=6, Resulting Numbers: [70, 33, 6] Generated Node #0,0: 78:[70, 33, 6] Operation: 73-67=6 Exploring Operation: 73-70=3, Resulting Numbers: [67, 33, 3] Generated Node #0,1: 78:[67, 33, 3] Operation: 73-70=3 Exploring Operation: 70-33=37, Resulting Numbers: [73, 67, 37] Generated Node #0,2: 78:[73, 67, 37] Operation: 70-33=37 Exploring Operation: 70-67=3, Resulting Numbers: [73, 33, 3] Generated Node #0,3: 78:[73, 33, 3] Operation: 70-67=3 Moving to Node #0,3 Current State: 78:[73, 33, 3], Operations: ['70-67=3'] Exploring Operation: 33/3=11, Resulting Numbers: [73, 11] Generated Node #0,3,0: 78:[73, 11] Operation: 33/3=11 Exploring Operation: 73-33=40, Resulting Numbers: [3, 40] Generated Node #0,3,1: 78:[3, 40] Operation: 73-33=40 Exploring Operation: 33+3=36, Resulting Numbers: [73, 36] Generated Node #0,3,2: 78:[73, 36] Operation: 33+3=36 Exploring Operation: 73+3=76, Resulting Numbers: [33, 76] Generated Node #0,3,3: 78:[33, 76] Operation: 73+3=76 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[3, 40], Operations: ['70-67=3', '73-33=40'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,78 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,78 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 #0,3,0 Current State: 78:[73, 11], Operations: ['70-67=3', '33/3=11'] Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,78 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,78 unequal: No Solution Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,78 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 #0,3,2 Current State: 78:[73, 36], Operations: ['70-67=3', '33+3=36'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 73*36=2628, Resulting Numbers: [2628] 2628,78 unequal: No Solution Exploring Operation: 73+36=109, Resulting Numbers: [109] 109,78 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 #0,3,3 Current State: 78:[33, 76], Operations: ['70-67=3', '73+3=76'] Exploring Operation: 33+76=109, Resulting Numbers: [109] 109,78 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 33*76=2508, Resulting Numbers: [2508] 2508,78 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: 78:[70, 33, 6], Operations: ['73-67=6'] Exploring Operation: 33+6=39, Resulting Numbers: [70, 39] Generated Node #0,0,0: 78:[70, 39] Operation: 33+6=39 Exploring Operation: 70+6=76, Resulting Numbers: [33, 76] Generated Node #0,0,1: 78:[33, 76] Operation: 70+6=76 Exploring Operation: 33-6=27, Resulting Numbers: [70, 27] Generated Node #0,0,2: 78:[70, 27] Operation: 33-6=27 Exploring Operation: 70-33=37, Resulting Numbers: [6, 37] Generated Node #0,0,3: 78:[6, 37] Operation: 70-33=37 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[6, 37], Operations: ['73-67=6', '70-33=37'] Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,78 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[70, 39], Operations: ['73-67=6', '33+6=39'] Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 70*39=2730, Resulting Numbers: [2730] 2730,78 unequal: No Solution Exploring Operation: 70+39=109, Resulting Numbers: [109] 109,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[33, 76], Operations: ['73-67=6', '70+6=76'] Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 33+76=109, Resulting Numbers: [109] 109,78 unequal: No Solution Exploring Operation: 33*76=2508, Resulting Numbers: [2508] 2508,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[70, 27], Operations: ['73-67=6', '33-6=27'] Exploring Operation: 70+27=97, Resulting Numbers: [97] 97,78 unequal: No Solution Exploring Operation: 70*27=1890, Resulting Numbers: [1890] 1890,78 unequal: No Solution Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 78:[67, 33, 3], Operations: ['73-70=3'] Exploring Operation: 67-33=34, Resulting Numbers: [3, 34] Generated Node #0,1,0: 78:[3, 34] Operation: 67-33=34 Exploring Operation: 33+3=36, Resulting Numbers: [67, 36] Generated Node #0,1,1: 78:[67, 36] Operation: 33+3=36 Exploring Operation: 33/3=11, Resulting Numbers: [67, 11] Generated Node #0,1,2: 78:[67, 11] Operation: 33/3=11 Exploring Operation: 67+3=70, Resulting Numbers: [33, 70] Generated Node #0,1,3: 78:[33, 70] Operation: 67+3=70 Moving to Node #0,2 Current State: 78:[73, 67, 37], Operations: ['70-33=37'] Exploring Operation: 67-37=30, Resulting Numbers: [73, 30] Generated Node #0,2,0: 78:[73, 30] Operation: 67-37=30 Exploring Operation: 67+37=104, Resulting Numbers: [73, 104] Generated Node #0,2,1: 78:[73, 104] Operation: 67+37=104 Exploring Operation: 73-37=36, Resulting Numbers: [67, 36] Generated Node #0,2,2: 78:[67, 36] Operation: 73-37=36 Exploring Operation: 73-67=6, Resulting Numbers: [37, 6] Generated Node #0,2,3: 78:[37, 6] Operation: 73-67=6 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[37, 6], Operations: ['70-33=37', '73-67=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,78 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,78 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 #0,2,0 Current State: 78:[73, 30], Operations: ['70-33=37', '67-37=30'] Exploring Operation: 73-30=43, Resulting Numbers: [43] 43,78 unequal: No Solution Exploring Operation: 73*30=2190, Resulting Numbers: [2190] 2190,78 unequal: No Solution Exploring Operation: 73+30=103, Resulting Numbers: [103] 103,78 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 #0,2,2 Current State: 78:[67, 36], Operations: ['70-33=37', '73-37=36'] Exploring Operation: 67+36=103, Resulting Numbers: [103] 103,78 unequal: No Solution Exploring Operation: 67-36=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 67*36=2412, Resulting Numbers: [2412] 2412,78 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 #0,2,1 Current State: 78:[73, 104], Operations: ['70-33=37', '67+37=104'] Exploring Operation: 73*104=7592, Resulting Numbers: [7592] 7592,78 unequal: No Solution Exploring Operation: 73+104=177, Resulting Numbers: [177] 177,78 unequal: No Solution Exploring Operation: 104-73=31, Resulting Numbers: [31] 31,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 78:[3, 34], Operations: ['73-70=3', '67-33=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,78 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[67, 11], Operations: ['73-70=3', '33/3=11'] Exploring Operation: 67-11=56, Resulting Numbers: [56] 56,78 unequal: No Solution Exploring Operation: 67*11=737, Resulting Numbers: [737] 737,78 unequal: No Solution Exploring Operation: 67+11=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[73, 70, 67, 33], Operations: [] Exploring Operation: 73-70=3, Resulting Numbers: [67, 33, 3] Generated Node #0,1: 78:[67, 33, 3] Operation: 73-70=3 Moving to Node #0,1 Current State: 78:[67, 33, 3], Operations: ['73-70=3'] Exploring Operation: 33/3=11, Resulting Numbers: [67, 11] Generated Node #0,1,2: 78:[67, 11] Operation: 33/3=11 Moving to Node #0,1,2 Current State: 78:[67, 11], Operations: ['73-70=3', '33/3=11'] Exploring Operation: 67+11=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.942708
hs_4
sum_heuristic
[ 20, 85, 74, 92 ]
87
[ "20+85=105", "92-74=18", "105-18=87" ]
Current State: 87:[20, 85, 74, 92], Operations: [] Exploring Operation: 20+85=105, Resulting Numbers: [74, 92, 105] Generated Node #2: [74, 92, 105] from Operation: 20+85=105 Current State: 87:[74, 92, 105], Operations: ['20+85=105'] Exploring Operation: 92-74=18, Resulting Numbers: [105, 18] Generated Node #3: [105, 18] from Operation: 92-74=18 Current State: 87:[105, 18], Operations: ['20+85=105', '92-74=18'] Exploring Operation: 105-18=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[20, 85, 74, 92], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [20, 85, 18] Generated Node #0,0: 87:[20, 85, 18] Operation: 92-74=18 Exploring Operation: 20+74=94, Resulting Numbers: [85, 92, 94] Generated Node #0,1: 87:[85, 92, 94] Operation: 20+74=94 Exploring Operation: 85-74=11, Resulting Numbers: [20, 92, 11] Generated Node #0,2: 87:[20, 92, 11] Operation: 85-74=11 Exploring Operation: 92-20=72, Resulting Numbers: [85, 74, 72] Generated Node #0,3: 87:[85, 74, 72] Operation: 92-20=72 Exploring Operation: 92-85=7, Resulting Numbers: [20, 74, 7] Generated Node #0,4: 87:[20, 74, 7] Operation: 92-85=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[85, 92, 94], Operations: ['20+74=94'] Exploring Operation: 85+92=177, Resulting Numbers: [94, 177] Generated Node #0,1,0: 87:[94, 177] Operation: 85+92=177 Exploring Operation: 92-85=7, Resulting Numbers: [94, 7] Generated Node #0,1,1: 87:[94, 7] Operation: 92-85=7 Exploring Operation: 94-92=2, Resulting Numbers: [85, 2] Generated Node #0,1,2: 87:[85, 2] Operation: 94-92=2 Exploring Operation: 94-85=9, Resulting Numbers: [92, 9] Generated Node #0,1,3: 87:[92, 9] Operation: 94-85=9 Exploring Operation: 85+94=179, Resulting Numbers: [92, 179] Generated Node #0,1,4: 87:[92, 179] Operation: 85+94=179 Moving to Node #0,1,2 Current State: 87:[85, 2], Operations: ['20+74=94', '94-92=2'] Exploring Operation: 85*2=170, Resulting Numbers: [170] 170,87 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,87 unequal: No Solution Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[20, 85, 74, 92], Operations: [] Exploring Operation: 20+74=94, Resulting Numbers: [85, 92, 94] Generated Node #0,1: 87:[85, 92, 94] Operation: 20+74=94 Moving to Node #0,1 Current State: 87:[85, 92, 94], Operations: ['20+74=94'] Exploring Operation: 94-92=2, Resulting Numbers: [85, 2] Generated Node #0,1,2: 87:[85, 2] Operation: 94-92=2 Moving to Node #0,1,2 Current State: 87:[85, 2], Operations: ['20+74=94', '94-92=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 27, 16, 42, 5 ]
80
[ "27+16=43", "42-5=37", "43+37=80" ]
Current State: 80:[27, 16, 42, 5], Operations: [] Exploring Operation: 27+16=43, Resulting Numbers: [42, 5, 43] Generated Node #2: [42, 5, 43] from Operation: 27+16=43 Current State: 80:[42, 5, 43], Operations: ['27+16=43'] Exploring Operation: 42-5=37, Resulting Numbers: [43, 37] Generated Node #3: [43, 37] from Operation: 42-5=37 Current State: 80:[43, 37], Operations: ['27+16=43', '42-5=37'] Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[27, 16, 42, 5], Operations: [] Exploring Operation: 27-5=22, Resulting Numbers: [16, 42, 22] Generated Node #0,0: 80:[16, 42, 22] Operation: 27-5=22 Exploring Operation: 16*5=80, Resulting Numbers: [27, 42, 80] Generated Node #0,1: 80:[27, 42, 80] Operation: 16*5=80 Exploring Operation: 27-16=11, Resulting Numbers: [42, 5, 11] Generated Node #0,2: 80:[42, 5, 11] Operation: 27-16=11 Exploring Operation: 27+16=43, Resulting Numbers: [42, 5, 43] Generated Node #0,3: 80:[42, 5, 43] Operation: 27+16=43 Exploring Operation: 42-27=15, Resulting Numbers: [16, 5, 15] Generated Node #0,4: 80:[16, 5, 15] Operation: 42-27=15 Moving to Node #0,4 Current State: 80:[16, 5, 15], Operations: ['42-27=15'] Exploring Operation: 15/5=3, Resulting Numbers: [16, 3] Generated Node #0,4,0: 80:[16, 3] Operation: 15/5=3 Exploring Operation: 16*5=80, Resulting Numbers: [15, 80] Generated Node #0,4,1: 80:[15, 80] Operation: 16*5=80 Exploring Operation: 16-15=1, Resulting Numbers: [5, 1] Generated Node #0,4,2: 80:[5, 1] Operation: 16-15=1 Exploring Operation: 15-5=10, Resulting Numbers: [16, 10] Generated Node #0,4,3: 80:[16, 10] Operation: 15-5=10 Exploring Operation: 5+15=20, Resulting Numbers: [16, 20] Generated Node #0,4,4: 80:[16, 20] Operation: 5+15=20 Moving to Node #0,2 Current State: 80:[42, 5, 11], Operations: ['27-16=11'] Exploring Operation: 42-5=37, Resulting Numbers: [11, 37] Generated Node #0,2,0: 80:[11, 37] Operation: 42-5=37 Exploring Operation: 42-11=31, Resulting Numbers: [5, 31] Generated Node #0,2,1: 80:[5, 31] Operation: 42-11=31 Exploring Operation: 11-5=6, Resulting Numbers: [42, 6] Generated Node #0,2,2: 80:[42, 6] Operation: 11-5=6 Exploring Operation: 5+11=16, Resulting Numbers: [42, 16] Generated Node #0,2,3: 80:[42, 16] Operation: 5+11=16 Exploring Operation: 42+5=47, Resulting Numbers: [11, 47] Generated Node #0,2,4: 80:[11, 47] Operation: 42+5=47 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[42, 16], Operations: ['27-16=11', '5+11=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,80 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,80 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,80 unequal: No Solution No 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: 80:[42, 6], Operations: ['27-16=11', '11-5=6'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 42*6=252, Resulting Numbers: [252] 252,80 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,80 unequal: No Solution No 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: 80:[11, 37], Operations: ['27-16=11', '42-5=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 11*37=407, Resulting Numbers: [407] 407,80 unequal: No Solution No 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: 80:[11, 47], Operations: ['27-16=11', '42+5=47'] Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 11*47=517, Resulting Numbers: [517] 517,80 unequal: No Solution Exploring Operation: 11+47=58, Resulting Numbers: [58] 58,80 unequal: No Solution No 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: 80:[5, 31], Operations: ['27-16=11', '42-11=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,80 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,80 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,80 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: 80:[16, 42, 22], Operations: ['27-5=22'] Exploring Operation: 16+22=38, Resulting Numbers: [42, 38] Generated Node #0,0,0: 80:[42, 38] Operation: 16+22=38 Exploring Operation: 42+22=64, Resulting Numbers: [16, 64] Generated Node #0,0,1: 80:[16, 64] Operation: 42+22=64 Exploring Operation: 42-16=26, Resulting Numbers: [22, 26] Generated Node #0,0,2: 80:[22, 26] Operation: 42-16=26 Exploring Operation: 42-22=20, Resulting Numbers: [16, 20] Generated Node #0,0,3: 80:[16, 20] Operation: 42-22=20 Exploring Operation: 22-16=6, Resulting Numbers: [42, 6] Generated Node #0,0,4: 80:[42, 6] Operation: 22-16=6 Moving to Node #0,3 Current State: 80:[42, 5, 43], Operations: ['27+16=43'] Exploring Operation: 43-5=38, Resulting Numbers: [42, 38] Generated Node #0,3,0: 80:[42, 38] Operation: 43-5=38 Exploring Operation: 42+5=47, Resulting Numbers: [43, 47] Generated Node #0,3,1: 80:[43, 47] Operation: 42+5=47 Exploring Operation: 42+43=85, Resulting Numbers: [5, 85] Generated Node #0,3,2: 80:[5, 85] Operation: 42+43=85 Exploring Operation: 43-42=1, Resulting Numbers: [5, 1] Generated Node #0,3,3: 80:[5, 1] Operation: 43-42=1 Exploring Operation: 42-5=37, Resulting Numbers: [43, 37] Generated Node #0,3,4: 80:[43, 37] Operation: 42-5=37 Moving to Node #0,1 Current State: 80:[27, 42, 80], Operations: ['16*5=80'] Exploring Operation: 42-27=15, Resulting Numbers: [80, 15] Generated Node #0,1,0: 80:[80, 15] Operation: 42-27=15 Exploring Operation: 27+42=69, Resulting Numbers: [80, 69] Generated Node #0,1,1: 80:[80, 69] Operation: 27+42=69 Exploring Operation: 80-42=38, Resulting Numbers: [27, 38] Generated Node #0,1,2: 80:[27, 38] Operation: 80-42=38 Exploring Operation: 27+80=107, Resulting Numbers: [42, 107] Generated Node #0,1,3: 80:[42, 107] Operation: 27+80=107 Exploring Operation: 80-27=53, Resulting Numbers: [42, 53] Generated Node #0,1,4: 80:[42, 53] Operation: 80-27=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[80, 15], Operations: ['16*5=80', '42-27=15'] Exploring Operation: 80+15=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 80*15=1200, Resulting Numbers: [1200] 1200,80 unequal: No Solution No 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: 80:[27, 38], Operations: ['16*5=80', '80-42=38'] Exploring Operation: 27*38=1026, Resulting Numbers: [1026] 1026,80 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 27+38=65, Resulting Numbers: [65] 65,80 unequal: No Solution No 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: 80:[80, 69], Operations: ['16*5=80', '27+42=69'] Exploring Operation: 80*69=5520, Resulting Numbers: [5520] 5520,80 unequal: No Solution Exploring Operation: 80-69=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 80+69=149, Resulting Numbers: [149] 149,80 unequal: No Solution No 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: 80:[42, 53], Operations: ['16*5=80', '80-27=53'] Exploring Operation: 42*53=2226, Resulting Numbers: [2226] 2226,80 unequal: No Solution Exploring Operation: 42+53=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,80 unequal: No Solution No 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: 80:[42, 107], Operations: ['16*5=80', '27+80=107'] Exploring Operation: 42*107=4494, Resulting Numbers: [4494] 4494,80 unequal: No Solution Exploring Operation: 42+107=149, Resulting Numbers: [149] 149,80 unequal: No Solution Exploring Operation: 107-42=65, Resulting Numbers: [65] 65,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 80:[16, 10], Operations: ['42-27=15', '15-5=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,80 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[16, 20], Operations: ['27-5=22', '42-22=20'] Exploring Operation: 16*20=320, Resulting Numbers: [320] 320,80 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[16, 20], Operations: ['42-27=15', '5+15=20'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 16*20=320, Resulting Numbers: [320] 320,80 unequal: No Solution Moving to Node #0,4,0 Current State: 80:[16, 3], Operations: ['42-27=15', '15/5=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[5, 1], Operations: ['42-27=15', '16-15=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[5, 1], Operations: ['27+16=43', '43-42=1'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[15, 80], Operations: ['42-27=15', '16*5=80'] Exploring Operation: 15+80=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 15*80=1200, Resulting Numbers: [1200] 1200,80 unequal: No Solution Moving to Node #0,0,4 Current State: 80:[42, 6], Operations: ['27-5=22', '22-16=6'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 42*6=252, Resulting Numbers: [252] 252,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[42, 38], Operations: ['27+16=43', '43-5=38'] Exploring Operation: 42*38=1596, Resulting Numbers: [1596] 1596,80 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[27, 16, 42, 5], Operations: [] Exploring Operation: 27+16=43, Resulting Numbers: [42, 5, 43] Generated Node #0,3: 80:[42, 5, 43] Operation: 27+16=43 Moving to Node #0,3 Current State: 80:[42, 5, 43], Operations: ['27+16=43'] Exploring Operation: 43-5=38, Resulting Numbers: [42, 38] Generated Node #0,3,0: 80:[42, 38] Operation: 43-5=38 Moving to Node #0,3,0 Current State: 80:[42, 38], Operations: ['27+16=43', '43-5=38'] Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.917535
hs_5
mult_heuristic
[ 74, 2, 3, 62 ]
46
[ "74+2=76", "62+76=138", "138/3=46" ]
Current State: 46:[74, 2, 3, 62], Operations: [] Exploring Operation: 74+2=76, Resulting Numbers: [3, 62, 76] Generated Node #2: [3, 62, 76] from Operation: 74+2=76 Current State: 46:[3, 62, 76], Operations: ['74+2=76'] Exploring Operation: 62+76=138, Resulting Numbers: [3, 138] Generated Node #3: [3, 138] from Operation: 62+76=138 Current State: 46:[3, 138], Operations: ['74+2=76', '62+76=138'] Exploring Operation: 138/3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[74, 2, 3, 62], Operations: [] Exploring Operation: 74/2=37, Resulting Numbers: [3, 62, 37] Generated Node #0,0: 46:[3, 62, 37] Operation: 74/2=37 Exploring Operation: 74-62=12, Resulting Numbers: [2, 3, 12] Generated Node #0,1: 46:[2, 3, 12] Operation: 74-62=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[2, 3, 12], Operations: ['74-62=12'] Exploring Operation: 2*12=24, Resulting Numbers: [3, 24] Generated Node #0,1,0: 46:[3, 24] Operation: 2*12=24 Exploring Operation: 12/3=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 46:[2, 4] Operation: 12/3=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[3, 24], Operations: ['74-62=12', '2*12=24'] Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[2, 4], Operations: ['74-62=12', '12/3=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[3, 62, 37], Operations: ['74/2=37'] Exploring Operation: 62-37=25, Resulting Numbers: [3, 25] Generated Node #0,0,0: 46:[3, 25] Operation: 62-37=25 Exploring Operation: 62-3=59, Resulting Numbers: [37, 59] Generated Node #0,0,1: 46:[37, 59] Operation: 62-3=59 Moving to Node #0,0,0 Current State: 46:[3, 25], Operations: ['74/2=37', '62-37=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,46 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[37, 59], Operations: ['74/2=37', '62-3=59'] Exploring Operation: 37+59=96, Resulting Numbers: [96] 96,46 unequal: No Solution Exploring Operation: 59-37=22, Resulting Numbers: [22] 22,46 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
[ 52, 45, 55, 81 ]
39
[ "52+45=97", "55+81=136", "136-97=39" ]
Current State: 39:[52, 45, 55, 81], Operations: [] Exploring Operation: 52+45=97, Resulting Numbers: [55, 81, 97] Generated Node #2: [55, 81, 97] from Operation: 52+45=97 Current State: 39:[55, 81, 97], Operations: ['52+45=97'] Exploring Operation: 55+81=136, Resulting Numbers: [97, 136] Generated Node #3: [97, 136] from Operation: 55+81=136 Current State: 39:[97, 136], Operations: ['52+45=97', '55+81=136'] Exploring Operation: 136-97=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[52, 45, 55, 81], Operations: [] Exploring Operation: 81-45=36, Resulting Numbers: [52, 55, 36] Generated Node #0,0: 39:[52, 55, 36] Operation: 81-45=36 Exploring Operation: 81-52=29, Resulting Numbers: [45, 55, 29] Generated Node #0,1: 39:[45, 55, 29] Operation: 81-52=29 Exploring Operation: 81-55=26, Resulting Numbers: [52, 45, 26] Generated Node #0,2: 39:[52, 45, 26] Operation: 81-55=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[52, 55, 36], Operations: ['81-45=36'] Exploring Operation: 52-36=16, Resulting Numbers: [55, 16] Generated Node #0,0,0: 39:[55, 16] Operation: 52-36=16 Exploring Operation: 55-36=19, Resulting Numbers: [52, 19] Generated Node #0,0,1: 39:[52, 19] Operation: 55-36=19 Exploring Operation: 55-52=3, Resulting Numbers: [36, 3] Generated Node #0,0,2: 39:[36, 3] Operation: 55-52=3 Moving to Node #0,0,2 Current State: 39:[36, 3], Operations: ['81-45=36', '55-52=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[52, 45, 55, 81], Operations: [] Exploring Operation: 81-45=36, Resulting Numbers: [52, 55, 36] Generated Node #0,0: 39:[52, 55, 36] Operation: 81-45=36 Moving to Node #0,0 Current State: 39:[52, 55, 36], Operations: ['81-45=36'] Exploring Operation: 55-52=3, Resulting Numbers: [36, 3] Generated Node #0,0,2: 39:[36, 3] Operation: 55-52=3 Moving to Node #0,0,2 Current State: 39:[36, 3], Operations: ['81-45=36', '55-52=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 54, 57, 29, 59 ]
50
[ "54-29=25", "59-57=2", "25*2=50" ]
Current State: 50:[54, 57, 29, 59], Operations: [] Exploring Operation: 54-29=25, Resulting Numbers: [57, 59, 25] Generated Node #2: [57, 59, 25] from Operation: 54-29=25 Current State: 50:[57, 59, 25], Operations: ['54-29=25'] Exploring Operation: 59-57=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 59-57=2 Current State: 50:[25, 2], Operations: ['54-29=25', '59-57=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[54, 57, 29, 59], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [57, 29, 5] Generated Node #0,0: 50:[57, 29, 5] Operation: 59-54=5 Exploring Operation: 57-54=3, Resulting Numbers: [29, 59, 3] Generated Node #0,1: 50:[29, 59, 3] Operation: 57-54=3 Exploring Operation: 54-29=25, Resulting Numbers: [57, 59, 25] Generated Node #0,2: 50:[57, 59, 25] Operation: 54-29=25 Exploring Operation: 59-57=2, Resulting Numbers: [54, 29, 2] Generated Node #0,3: 50:[54, 29, 2] Operation: 59-57=2 Moving to Node #0,3 Current State: 50:[54, 29, 2], Operations: ['59-57=2'] Exploring Operation: 29-2=27, Resulting Numbers: [54, 27] Generated Node #0,3,0: 50:[54, 27] Operation: 29-2=27 Exploring Operation: 54-2=52, Resulting Numbers: [29, 52] Generated Node #0,3,1: 50:[29, 52] Operation: 54-2=52 Exploring Operation: 54-29=25, Resulting Numbers: [2, 25] Generated Node #0,3,2: 50:[2, 25] Operation: 54-29=25 Exploring Operation: 54/2=27, Resulting Numbers: [29, 27] Generated Node #0,3,3: 50:[29, 27] Operation: 54/2=27 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 50:[2, 25], Operations: ['59-57=2', '54-29=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,50 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[54, 57, 29, 59], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [54, 29, 2] Generated Node #0,3: 50:[54, 29, 2] Operation: 59-57=2 Moving to Node #0,3 Current State: 50:[54, 29, 2], Operations: ['59-57=2'] Exploring Operation: 54-29=25, Resulting Numbers: [2, 25] Generated Node #0,3,2: 50:[2, 25] Operation: 54-29=25 Moving to Node #0,3,2 Current State: 50:[2, 25], Operations: ['59-57=2', '54-29=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 11, 42, 95, 60 ]
77
[ "95-42=53", "60-53=7", "11*7=77" ]
Current State: 77:[11, 42, 95, 60], Operations: [] Exploring Operation: 95-42=53, Resulting Numbers: [11, 60, 53] Generated Node #2: [11, 60, 53] from Operation: 95-42=53 Current State: 77:[11, 60, 53], Operations: ['95-42=53'] Exploring Operation: 60-53=7, Resulting Numbers: [11, 7] Generated Node #3: [11, 7] from Operation: 60-53=7 Current State: 77:[11, 7], Operations: ['95-42=53', '60-53=7'] Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[11, 42, 95, 60], Operations: [] Exploring Operation: 42+60=102, Resulting Numbers: [11, 95, 102] Generated Node #0,0: 77:[11, 95, 102] Operation: 42+60=102 Exploring Operation: 42-11=31, Resulting Numbers: [95, 60, 31] Generated Node #0,1: 77:[95, 60, 31] Operation: 42-11=31 Exploring Operation: 60-42=18, Resulting Numbers: [11, 95, 18] Generated Node #0,2: 77:[11, 95, 18] Operation: 60-42=18 Exploring Operation: 95-42=53, Resulting Numbers: [11, 60, 53] Generated Node #0,3: 77:[11, 60, 53] Operation: 95-42=53 Exploring Operation: 95-11=84, Resulting Numbers: [42, 60, 84] Generated Node #0,4: 77:[42, 60, 84] Operation: 95-11=84 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[11, 95, 18], Operations: ['60-42=18'] Exploring Operation: 95-18=77, Resulting Numbers: [11, 77] Generated Node #0,2,0: 77:[11, 77] Operation: 95-18=77 Exploring Operation: 18-11=7, Resulting Numbers: [95, 7] Generated Node #0,2,1: 77:[95, 7] Operation: 18-11=7 Exploring Operation: 11+18=29, Resulting Numbers: [95, 29] Generated Node #0,2,2: 77:[95, 29] Operation: 11+18=29 Exploring Operation: 95-11=84, Resulting Numbers: [18, 84] Generated Node #0,2,3: 77:[18, 84] Operation: 95-11=84 Exploring Operation: 11+95=106, Resulting Numbers: [18, 106] Generated Node #0,2,4: 77:[18, 106] Operation: 11+95=106 Moving to Node #0,2,0 Current State: 77:[11, 77], Operations: ['60-42=18', '95-18=77'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 11*77=847, Resulting Numbers: [847] 847,77 unequal: No Solution Exploring Operation: 11+77=88, Resulting Numbers: [88] 88,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[18, 84], Operations: ['60-42=18', '95-11=84'] Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 18*84=1512, Resulting Numbers: [1512] 1512,77 unequal: No Solution Exploring Operation: 18+84=102, Resulting Numbers: [102] 102,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[95, 7], Operations: ['60-42=18', '18-11=7'] Exploring Operation: 95+7=102, Resulting Numbers: [102] 102,77 unequal: No Solution Exploring Operation: 95*7=665, Resulting Numbers: [665] 665,77 unequal: No Solution Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[95, 29], Operations: ['60-42=18', '11+18=29'] Exploring Operation: 95*29=2755, Resulting Numbers: [2755] 2755,77 unequal: No Solution Exploring Operation: 95+29=124, Resulting Numbers: [124] 124,77 unequal: No Solution Exploring Operation: 95-29=66, Resulting Numbers: [66] 66,77 unequal: No Solution Moving to Node #0,2,4 Current State: 77:[18, 106], Operations: ['60-42=18', '11+95=106'] Exploring Operation: 18+106=124, Resulting Numbers: [124] 124,77 unequal: No Solution Exploring Operation: 18*106=1908, Resulting Numbers: [1908] 1908,77 unequal: No Solution Exploring Operation: 106-18=88, Resulting Numbers: [88] 88,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[11, 60, 53], Operations: ['95-42=53'] Exploring Operation: 11+60=71, Resulting Numbers: [53, 71] Generated Node #0,3,0: 77:[53, 71] Operation: 11+60=71 Exploring Operation: 60+53=113, Resulting Numbers: [11, 113] Generated Node #0,3,1: 77:[11, 113] Operation: 60+53=113 Exploring Operation: 53-11=42, Resulting Numbers: [60, 42] Generated Node #0,3,2: 77:[60, 42] Operation: 53-11=42 Exploring Operation: 60-53=7, Resulting Numbers: [11, 7] Generated Node #0,3,3: 77:[11, 7] Operation: 60-53=7 Exploring Operation: 11+53=64, Resulting Numbers: [60, 64] Generated Node #0,3,4: 77:[60, 64] Operation: 11+53=64 Moving to Node #0,3,3 Current State: 77:[11, 7], Operations: ['95-42=53', '60-53=7'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[11, 42, 95, 60], Operations: [] Exploring Operation: 95-42=53, Resulting Numbers: [11, 60, 53] Generated Node #0,3: 77:[11, 60, 53] Operation: 95-42=53 Moving to Node #0,3 Current State: 77:[11, 60, 53], Operations: ['95-42=53'] Exploring Operation: 60-53=7, Resulting Numbers: [11, 7] Generated Node #0,3,3: 77:[11, 7] Operation: 60-53=7 Moving to Node #0,3,3 Current State: 77:[11, 7], Operations: ['95-42=53', '60-53=7'] Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 12, 82, 66, 3 ]
56
[ "12+66=78", "78/3=26", "82-26=56" ]
Current State: 56:[12, 82, 66, 3], Operations: [] Exploring Operation: 12+66=78, Resulting Numbers: [82, 3, 78] Generated Node #2: [82, 3, 78] from Operation: 12+66=78 Current State: 56:[82, 3, 78], Operations: ['12+66=78'] Exploring Operation: 78/3=26, Resulting Numbers: [82, 26] Generated Node #3: [82, 26] from Operation: 78/3=26 Current State: 56:[82, 26], Operations: ['12+66=78', '78/3=26'] Exploring Operation: 82-26=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[12, 82, 66, 3], Operations: [] Exploring Operation: 82-66=16, Resulting Numbers: [12, 3, 16] Generated Node #0,0: 56:[12, 3, 16] Operation: 82-66=16 Exploring Operation: 66-12=54, Resulting Numbers: [82, 3, 54] Generated Node #0,1: 56:[82, 3, 54] Operation: 66-12=54 Exploring Operation: 82-12=70, Resulting Numbers: [66, 3, 70] Generated Node #0,2: 56:[66, 3, 70] Operation: 82-12=70 Moving to Node #0,0 Current State: 56:[12, 3, 16], Operations: ['82-66=16'] Exploring Operation: 12+16=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 56:[3, 28] Operation: 12+16=28 Exploring Operation: 16-12=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 56:[3, 4] Operation: 16-12=4 Exploring Operation: 12/3=4, Resulting Numbers: [16, 4] Generated Node #0,0,2: 56:[16, 4] Operation: 12/3=4 Moving to Node #0,2 Current State: 56:[66, 3, 70], Operations: ['82-12=70'] Exploring Operation: 70-66=4, Resulting Numbers: [3, 4] Generated Node #0,2,0: 56:[3, 4] Operation: 70-66=4 Exploring Operation: 66/3=22, Resulting Numbers: [70, 22] Generated Node #0,2,1: 56:[70, 22] Operation: 66/3=22 Exploring Operation: 66-3=63, Resulting Numbers: [70, 63] Generated Node #0,2,2: 56:[70, 63] Operation: 66-3=63 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[3, 4], Operations: ['82-12=70', '70-66=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[70, 22], Operations: ['82-12=70', '66/3=22'] Exploring Operation: 70*22=1540, Resulting Numbers: [1540] 1540,56 unequal: No Solution Exploring Operation: 70+22=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[70, 63], Operations: ['82-12=70', '66-3=63'] Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,56 unequal: No Solution Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 56:[82, 3, 54], Operations: ['66-12=54'] Exploring Operation: 3+54=57, Resulting Numbers: [82, 57] Generated Node #0,1,0: 56:[82, 57] Operation: 3+54=57 Exploring Operation: 82-3=79, Resulting Numbers: [54, 79] Generated Node #0,1,1: 56:[54, 79] Operation: 82-3=79 Exploring Operation: 82-54=28, Resulting Numbers: [3, 28] Generated Node #0,1,2: 56:[3, 28] Operation: 82-54=28 Moving to Node #0,0,0 Current State: 56:[3, 28], Operations: ['82-66=16', '12+16=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,56 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[3, 4], Operations: ['82-66=16', '16-12=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[3, 28], Operations: ['66-12=54', '82-54=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,56 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Moving to Node #0,0,2 Current State: 56:[16, 4], Operations: ['82-66=16', '12/3=4'] Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,56 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[54, 79], Operations: ['66-12=54', '82-3=79'] Exploring Operation: 54*79=4266, Resulting Numbers: [4266] 4266,56 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 54+79=133, Resulting Numbers: [133] 133,56 unequal: No Solution Moving to Node #0,1,0 Current State: 56:[82, 57], Operations: ['66-12=54', '3+54=57'] Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 82*57=4674, Resulting Numbers: [4674] 4674,56 unequal: No Solution Exploring Operation: 82+57=139, Resulting Numbers: [139] 139,56 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 74, 99, 87, 42 ]
44
[ "74+99=173", "87+42=129", "173-129=44" ]
Current State: 44:[74, 99, 87, 42], Operations: [] Exploring Operation: 74+99=173, Resulting Numbers: [87, 42, 173] Generated Node #2: [87, 42, 173] from Operation: 74+99=173 Current State: 44:[87, 42, 173], Operations: ['74+99=173'] Exploring Operation: 87+42=129, Resulting Numbers: [173, 129] Generated Node #3: [173, 129] from Operation: 87+42=129 Current State: 44:[173, 129], Operations: ['74+99=173', '87+42=129'] Exploring Operation: 173-129=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[74, 99, 87, 42], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [74, 42, 12] Generated Node #0,0: 44:[74, 42, 12] Operation: 99-87=12 Exploring Operation: 99-42=57, Resulting Numbers: [74, 87, 57] Generated Node #0,1: 44:[74, 87, 57] Operation: 99-42=57 Exploring Operation: 87-42=45, Resulting Numbers: [74, 99, 45] Generated Node #0,2: 44:[74, 99, 45] Operation: 87-42=45 Exploring Operation: 99-74=25, Resulting Numbers: [87, 42, 25] Generated Node #0,3: 44:[87, 42, 25] Operation: 99-74=25 Exploring Operation: 87-74=13, Resulting Numbers: [99, 42, 13] Generated Node #0,4: 44:[99, 42, 13] Operation: 87-74=13 Moving to Node #0,0 Current State: 44:[74, 42, 12], Operations: ['99-87=12'] Exploring Operation: 42-12=30, Resulting Numbers: [74, 30] Generated Node #0,0,0: 44:[74, 30] Operation: 42-12=30 Exploring Operation: 74-12=62, Resulting Numbers: [42, 62] Generated Node #0,0,1: 44:[42, 62] Operation: 74-12=62 Exploring Operation: 74-42=32, Resulting Numbers: [12, 32] Generated Node #0,0,2: 44:[12, 32] Operation: 74-42=32 Exploring Operation: 74+12=86, Resulting Numbers: [42, 86] Generated Node #0,0,3: 44:[42, 86] Operation: 74+12=86 Exploring Operation: 42+12=54, Resulting Numbers: [74, 54] Generated Node #0,0,4: 44:[74, 54] Operation: 42+12=54 Moving to Node #0,3 Current State: 44:[87, 42, 25], Operations: ['99-74=25'] Exploring Operation: 87-25=62, Resulting Numbers: [42, 62] Generated Node #0,3,0: 44:[42, 62] Operation: 87-25=62 Exploring Operation: 42+25=67, Resulting Numbers: [87, 67] Generated Node #0,3,1: 44:[87, 67] Operation: 42+25=67 Exploring Operation: 87+25=112, Resulting Numbers: [42, 112] Generated Node #0,3,2: 44:[42, 112] Operation: 87+25=112 Exploring Operation: 87-42=45, Resulting Numbers: [25, 45] Generated Node #0,3,3: 44:[25, 45] Operation: 87-42=45 Exploring Operation: 42-25=17, Resulting Numbers: [87, 17] Generated Node #0,3,4: 44:[87, 17] Operation: 42-25=17 Moving to Node #0,4 Current State: 44:[99, 42, 13], Operations: ['87-74=13'] Exploring Operation: 42-13=29, Resulting Numbers: [99, 29] Generated Node #0,4,0: 44:[99, 29] Operation: 42-13=29 Exploring Operation: 99+13=112, Resulting Numbers: [42, 112] Generated Node #0,4,1: 44:[42, 112] Operation: 99+13=112 Exploring Operation: 99-13=86, Resulting Numbers: [42, 86] Generated Node #0,4,2: 44:[42, 86] Operation: 99-13=86 Exploring Operation: 99-42=57, Resulting Numbers: [13, 57] Generated Node #0,4,3: 44:[13, 57] Operation: 99-42=57 Exploring Operation: 42+13=55, Resulting Numbers: [99, 55] Generated Node #0,4,4: 44:[99, 55] Operation: 42+13=55 Moving to Node #0,1 Current State: 44:[74, 87, 57], Operations: ['99-42=57'] Exploring Operation: 87-74=13, Resulting Numbers: [57, 13] Generated Node #0,1,0: 44:[57, 13] Operation: 87-74=13 Exploring Operation: 74+87=161, Resulting Numbers: [57, 161] Generated Node #0,1,1: 44:[57, 161] Operation: 74+87=161 Exploring Operation: 74-57=17, Resulting Numbers: [87, 17] Generated Node #0,1,2: 44:[87, 17] Operation: 74-57=17 Exploring Operation: 74+57=131, Resulting Numbers: [87, 131] Generated Node #0,1,3: 44:[87, 131] Operation: 74+57=131 Exploring Operation: 87-57=30, Resulting Numbers: [74, 30] Generated Node #0,1,4: 44:[74, 30] Operation: 87-57=30 Moving to Node #0,2 Current State: 44:[74, 99, 45], Operations: ['87-42=45'] Exploring Operation: 99-45=54, Resulting Numbers: [74, 54] Generated Node #0,2,0: 44:[74, 54] Operation: 99-45=54 Exploring Operation: 74+45=119, Resulting Numbers: [99, 119] Generated Node #0,2,1: 44:[99, 119] Operation: 74+45=119 Exploring Operation: 99-74=25, Resulting Numbers: [45, 25] Generated Node #0,2,2: 44:[45, 25] Operation: 99-74=25 Exploring Operation: 74+99=173, Resulting Numbers: [45, 173] Generated Node #0,2,3: 44:[45, 173] Operation: 74+99=173 Exploring Operation: 74-45=29, Resulting Numbers: [99, 29] Generated Node #0,2,4: 44:[99, 29] Operation: 74-45=29 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[45, 25], Operations: ['87-42=45', '99-74=25'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,44 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,44 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 #0,2,0 Current State: 44:[74, 54], Operations: ['87-42=45', '99-45=54'] Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 74+54=128, Resulting Numbers: [128] 128,44 unequal: No Solution Exploring Operation: 74*54=3996, Resulting Numbers: [3996] 3996,44 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 #0,2,4 Current State: 44:[99, 29], Operations: ['87-42=45', '74-45=29'] Exploring Operation: 99-29=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 99*29=2871, Resulting Numbers: [2871] 2871,44 unequal: No Solution Exploring Operation: 99+29=128, Resulting Numbers: [128] 128,44 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 #0,2,1 Current State: 44:[99, 119], Operations: ['87-42=45', '74+45=119'] Exploring Operation: 119-99=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 99+119=218, Resulting Numbers: [218] 218,44 unequal: No Solution Exploring Operation: 99*119=11781, Resulting Numbers: [11781] 11781,44 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 #0,2,3 Current State: 44:[45, 173], Operations: ['87-42=45', '74+99=173'] Exploring Operation: 45*173=7785, Resulting Numbers: [7785] 7785,44 unequal: No Solution Exploring Operation: 45+173=218, Resulting Numbers: [218] 218,44 unequal: No Solution Exploring Operation: 173-45=128, Resulting Numbers: [128] 128,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 44:[25, 45], Operations: ['99-74=25', '87-42=45'] Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,44 unequal: No Solution Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,44 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[12, 32], Operations: ['99-87=12', '74-42=32'] Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,44 unequal: No Solution Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[74, 99, 87, 42], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [74, 42, 12] Generated Node #0,0: 44:[74, 42, 12] Operation: 99-87=12 Moving to Node #0,0 Current State: 44:[74, 42, 12], Operations: ['99-87=12'] Exploring Operation: 74-42=32, Resulting Numbers: [12, 32] Generated Node #0,0,2: 44:[12, 32] Operation: 74-42=32 Moving to Node #0,0,2 Current State: 44:[12, 32], Operations: ['99-87=12', '74-42=32'] Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.953125
hs_5
mult_heuristic
[ 57, 2, 5, 85 ]
86
[ "5-2=3", "57*3=171", "171-85=86" ]
Current State: 86:[57, 2, 5, 85], Operations: [] Exploring Operation: 5-2=3, Resulting Numbers: [57, 85, 3] Generated Node #2: [57, 85, 3] from Operation: 5-2=3 Current State: 86:[57, 85, 3], Operations: ['5-2=3'] Exploring Operation: 57*3=171, Resulting Numbers: [85, 171] Generated Node #3: [85, 171] from Operation: 57*3=171 Current State: 86:[85, 171], Operations: ['5-2=3', '57*3=171'] Exploring Operation: 171-85=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[57, 2, 5, 85], Operations: [] Exploring Operation: 57-5=52, Resulting Numbers: [2, 85, 52] Generated Node #0,0: 86:[2, 85, 52] Operation: 57-5=52 Exploring Operation: 57-2=55, Resulting Numbers: [5, 85, 55] Generated Node #0,1: 86:[5, 85, 55] Operation: 57-2=55 Exploring Operation: 5-2=3, Resulting Numbers: [57, 85, 3] Generated Node #0,2: 86:[57, 85, 3] Operation: 5-2=3 Moving to Node #0,0 Current State: 86:[2, 85, 52], Operations: ['57-5=52'] Exploring Operation: 2+85=87, Resulting Numbers: [52, 87] Generated Node #0,0,0: 86:[52, 87] Operation: 2+85=87 Exploring Operation: 52-2=50, Resulting Numbers: [85, 50] Generated Node #0,0,1: 86:[85, 50] Operation: 52-2=50 Exploring Operation: 85-52=33, Resulting Numbers: [2, 33] Generated Node #0,0,2: 86:[2, 33] Operation: 85-52=33 Moving to Node #0,1 Current State: 86:[5, 85, 55], Operations: ['57-2=55'] Exploring Operation: 5+85=90, Resulting Numbers: [55, 90] Generated Node #0,1,0: 86:[55, 90] Operation: 5+85=90 Exploring Operation: 55-5=50, Resulting Numbers: [85, 50] Generated Node #0,1,1: 86:[85, 50] Operation: 55-5=50 Exploring Operation: 55/5=11, Resulting Numbers: [85, 11] Generated Node #0,1,2: 86:[85, 11] Operation: 55/5=11 Moving to Node #0,2 Current State: 86:[57, 85, 3], Operations: ['5-2=3'] Exploring Operation: 85+3=88, Resulting Numbers: [57, 88] Generated Node #0,2,0: 86:[57, 88] Operation: 85+3=88 Exploring Operation: 85-57=28, Resulting Numbers: [3, 28] Generated Node #0,2,1: 86:[3, 28] Operation: 85-57=28 Exploring Operation: 57-3=54, Resulting Numbers: [85, 54] Generated Node #0,2,2: 86:[85, 54] Operation: 57-3=54 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[85, 54], Operations: ['5-2=3', '57-3=54'] Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 85+54=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 85*54=4590, Resulting Numbers: [4590] 4590,86 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 #0,2,0 Current State: 86:[57, 88], Operations: ['5-2=3', '85+3=88'] Exploring Operation: 88-57=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 57+88=145, Resulting Numbers: [145] 145,86 unequal: No Solution Exploring Operation: 57*88=5016, Resulting Numbers: [5016] 5016,86 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 #0,2,1 Current State: 86:[3, 28], Operations: ['5-2=3', '85-57=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,86 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 86:[85, 50], Operations: ['57-5=52', '52-2=50'] Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,86 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[85, 50], Operations: ['57-2=55', '55-5=50'] Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,86 unequal: No Solution Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[2, 33], Operations: ['57-5=52', '85-52=33'] Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[85, 11], Operations: ['57-2=55', '55/5=11'] Exploring Operation: 85+11=96, Resulting Numbers: [96] 96,86 unequal: No Solution Exploring Operation: 85*11=935, Resulting Numbers: [935] 935,86 unequal: No Solution Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[52, 87], Operations: ['57-5=52', '2+85=87'] Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 52+87=139, Resulting Numbers: [139] 139,86 unequal: No Solution Exploring Operation: 52*87=4524, Resulting Numbers: [4524] 4524,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[55, 90], Operations: ['57-2=55', '5+85=90'] Exploring Operation: 90-55=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 55*90=4950, Resulting Numbers: [4950] 4950,86 unequal: No Solution Exploring Operation: 55+90=145, Resulting Numbers: [145] 145,86 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 72, 37, 78, 11 ]
20
[ "72+37=109", "78+11=89", "109-89=20" ]
Current State: 20:[72, 37, 78, 11], Operations: [] Exploring Operation: 72+37=109, Resulting Numbers: [78, 11, 109] Generated Node #2: [78, 11, 109] from Operation: 72+37=109 Current State: 20:[78, 11, 109], Operations: ['72+37=109'] Exploring Operation: 78+11=89, Resulting Numbers: [109, 89] Generated Node #3: [109, 89] from Operation: 78+11=89 Current State: 20:[109, 89], Operations: ['72+37=109', '78+11=89'] Exploring Operation: 109-89=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[72, 37, 78, 11], Operations: [] Exploring Operation: 78-37=41, Resulting Numbers: [72, 11, 41] Generated Node #0,0: 20:[72, 11, 41] Operation: 78-37=41 Exploring Operation: 78-72=6, Resulting Numbers: [37, 11, 6] Generated Node #0,1: 20:[37, 11, 6] Operation: 78-72=6 Exploring Operation: 72-37=35, Resulting Numbers: [78, 11, 35] Generated Node #0,2: 20:[78, 11, 35] Operation: 72-37=35 Exploring Operation: 72-11=61, Resulting Numbers: [37, 78, 61] Generated Node #0,3: 20:[37, 78, 61] Operation: 72-11=61 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[37, 11, 6], Operations: ['78-72=6'] Exploring Operation: 37-6=31, Resulting Numbers: [11, 31] Generated Node #0,1,0: 20:[11, 31] Operation: 37-6=31 Exploring Operation: 11-6=5, Resulting Numbers: [37, 5] Generated Node #0,1,1: 20:[37, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [37, 17] Generated Node #0,1,2: 20:[37, 17] Operation: 11+6=17 Exploring Operation: 37-11=26, Resulting Numbers: [6, 26] Generated Node #0,1,3: 20:[6, 26] Operation: 37-11=26 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 20:[6, 26], Operations: ['78-72=6', '37-11=26'] Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[72, 37, 78, 11], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [37, 11, 6] Generated Node #0,1: 20:[37, 11, 6] Operation: 78-72=6 Moving to Node #0,1 Current State: 20:[37, 11, 6], Operations: ['78-72=6'] Exploring Operation: 37-11=26, Resulting Numbers: [6, 26] Generated Node #0,1,3: 20:[6, 26] Operation: 37-11=26 Moving to Node #0,1,3 Current State: 20:[6, 26], Operations: ['78-72=6', '37-11=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 60, 3, 65, 45 ]
37
[ "60-3=57", "65-45=20", "57-20=37" ]
Current State: 37:[60, 3, 65, 45], Operations: [] Exploring Operation: 60-3=57, Resulting Numbers: [65, 45, 57] Generated Node #2: [65, 45, 57] from Operation: 60-3=57 Current State: 37:[65, 45, 57], Operations: ['60-3=57'] Exploring Operation: 65-45=20, Resulting Numbers: [57, 20] Generated Node #3: [57, 20] from Operation: 65-45=20 Current State: 37:[57, 20], Operations: ['60-3=57', '65-45=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[60, 3, 65, 45], Operations: [] Exploring Operation: 60/3=20, Resulting Numbers: [65, 45, 20] Generated Node #0,0: 37:[65, 45, 20] Operation: 60/3=20 Exploring Operation: 60-3=57, Resulting Numbers: [65, 45, 57] Generated Node #0,1: 37:[65, 45, 57] Operation: 60-3=57 Exploring Operation: 60+3=63, Resulting Numbers: [65, 45, 63] Generated Node #0,2: 37:[65, 45, 63] Operation: 60+3=63 Exploring Operation: 45-3=42, Resulting Numbers: [60, 65, 42] Generated Node #0,3: 37:[60, 65, 42] Operation: 45-3=42 Exploring Operation: 65-3=62, Resulting Numbers: [60, 45, 62] Generated Node #0,4: 37:[60, 45, 62] Operation: 65-3=62 Moving to Node #0,0 Current State: 37:[65, 45, 20], Operations: ['60/3=20'] Exploring Operation: 65-20=45, Resulting Numbers: [45, 45] Generated Node #0,0,0: 37:[45, 45] Operation: 65-20=45 Exploring Operation: 45-20=25, Resulting Numbers: [65, 25] Generated Node #0,0,1: 37:[65, 25] Operation: 45-20=25 Exploring Operation: 65-45=20, Resulting Numbers: [20, 20] Generated Node #0,0,2: 37:[20, 20] Operation: 65-45=20 Exploring Operation: 45+20=65, Resulting Numbers: [65, 65] Generated Node #0,0,3: 37:[65, 65] Operation: 45+20=65 Exploring Operation: 65+20=85, Resulting Numbers: [45, 85] Generated Node #0,0,4: 37:[45, 85] Operation: 65+20=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[45, 45], Operations: ['60/3=20', '65-20=45'] Exploring Operation: 45/45=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 45*45=2025, Resulting Numbers: [2025] 2025,37 unequal: No Solution Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 45-45=0, Resulting Numbers: [0] 0,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[20, 20], Operations: ['60/3=20', '65-45=20'] Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,37 unequal: No Solution Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[65, 25], Operations: ['60/3=20', '45-20=25'] Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,37 unequal: No Solution Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,37 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[65, 65], Operations: ['60/3=20', '45+20=65'] Exploring Operation: 65+65=130, Resulting Numbers: [130] 130,37 unequal: No Solution Exploring Operation: 65/65=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 65-65=0, Resulting Numbers: [0] 0,37 unequal: No Solution Exploring Operation: 65*65=4225, Resulting Numbers: [4225] 4225,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 37:[45, 85], Operations: ['60/3=20', '65+20=85'] Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,37 unequal: No Solution Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,37 unequal: No Solution Exploring Operation: 45*85=3825, Resulting Numbers: [3825] 3825,37 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: 37:[60, 65, 42], Operations: ['45-3=42'] Exploring Operation: 65-60=5, Resulting Numbers: [42, 5] Generated Node #0,3,0: 37:[42, 5] Operation: 65-60=5 Exploring Operation: 65-42=23, Resulting Numbers: [60, 23] Generated Node #0,3,1: 37:[60, 23] Operation: 65-42=23 Exploring Operation: 60+65=125, Resulting Numbers: [42, 125] Generated Node #0,3,2: 37:[42, 125] Operation: 60+65=125 Exploring Operation: 60-42=18, Resulting Numbers: [65, 18] Generated Node #0,3,3: 37:[65, 18] Operation: 60-42=18 Exploring Operation: 60+42=102, Resulting Numbers: [65, 102] Generated Node #0,3,4: 37:[65, 102] Operation: 60+42=102 Moving to Node #0,1 Current State: 37:[65, 45, 57], Operations: ['60-3=57'] Exploring Operation: 65+45=110, Resulting Numbers: [57, 110] Generated Node #0,1,0: 37:[57, 110] Operation: 65+45=110 Exploring Operation: 65-45=20, Resulting Numbers: [57, 20] Generated Node #0,1,1: 37:[57, 20] Operation: 65-45=20 Exploring Operation: 65-57=8, Resulting Numbers: [45, 8] Generated Node #0,1,2: 37:[45, 8] Operation: 65-57=8 Exploring Operation: 57-45=12, Resulting Numbers: [65, 12] Generated Node #0,1,3: 37:[65, 12] Operation: 57-45=12 Exploring Operation: 65+57=122, Resulting Numbers: [45, 122] Generated Node #0,1,4: 37:[45, 122] Operation: 65+57=122 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[57, 20], Operations: ['60-3=57', '65-45=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[60, 3, 65, 45], Operations: [] Exploring Operation: 60-3=57, Resulting Numbers: [65, 45, 57] Generated Node #0,1: 37:[65, 45, 57] Operation: 60-3=57 Moving to Node #0,1 Current State: 37:[65, 45, 57], Operations: ['60-3=57'] Exploring Operation: 65-45=20, Resulting Numbers: [57, 20] Generated Node #0,1,1: 37:[57, 20] Operation: 65-45=20 Moving to Node #0,1,1 Current State: 37:[57, 20], Operations: ['60-3=57', '65-45=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 92, 40, 5, 21 ]
76
[ "40/5=8", "21*8=168", "168-92=76" ]
Current State: 76:[92, 40, 5, 21], Operations: [] Exploring Operation: 40/5=8, Resulting Numbers: [92, 21, 8] Generated Node #2: [92, 21, 8] from Operation: 40/5=8 Current State: 76:[92, 21, 8], Operations: ['40/5=8'] Exploring Operation: 21*8=168, Resulting Numbers: [92, 168] Generated Node #3: [92, 168] from Operation: 21*8=168 Current State: 76:[92, 168], Operations: ['40/5=8', '21*8=168'] Exploring Operation: 168-92=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[92, 40, 5, 21], Operations: [] Exploring Operation: 92-21=71, Resulting Numbers: [40, 5, 71] Generated Node #0,0: 76:[40, 5, 71] Operation: 92-21=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[40, 5, 71], Operations: ['92-21=71'] Exploring Operation: 5+71=76, Resulting Numbers: [40, 76] Generated Node #0,0,0: 76:[40, 76] Operation: 5+71=76 Moving to Node #0,0,0 Current State: 76:[40, 76], Operations: ['92-21=71', '5+71=76'] Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,76 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
[ 51, 46, 86, 94 ]
83
[ "51+46=97", "86+94=180", "180-97=83" ]
Current State: 83:[51, 46, 86, 94], Operations: [] Exploring Operation: 51+46=97, Resulting Numbers: [86, 94, 97] Generated Node #2: [86, 94, 97] from Operation: 51+46=97 Current State: 83:[86, 94, 97], Operations: ['51+46=97'] Exploring Operation: 86+94=180, Resulting Numbers: [97, 180] Generated Node #3: [97, 180] from Operation: 86+94=180 Current State: 83:[97, 180], Operations: ['51+46=97', '86+94=180'] Exploring Operation: 180-97=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[51, 46, 86, 94], Operations: [] Exploring Operation: 51+46=97, Resulting Numbers: [86, 94, 97] Generated Node #0,0: 83:[86, 94, 97] Operation: 51+46=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[86, 94, 97], Operations: ['51+46=97'] Exploring Operation: 97-86=11, Resulting Numbers: [94, 11] Generated Node #0,0,0: 83:[94, 11] Operation: 97-86=11 Moving to Node #0,0,0 Current State: 83:[94, 11], Operations: ['51+46=97', '97-86=11'] Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[51, 46, 86, 94], Operations: [] Exploring Operation: 51+46=97, Resulting Numbers: [86, 94, 97] Generated Node #0,0: 83:[86, 94, 97] Operation: 51+46=97 Moving to Node #0,0 Current State: 83:[86, 94, 97], Operations: ['51+46=97'] Exploring Operation: 97-86=11, Resulting Numbers: [94, 11] Generated Node #0,0,0: 83:[94, 11] Operation: 97-86=11 Moving to Node #0,0,0 Current State: 83:[94, 11], Operations: ['51+46=97', '97-86=11'] Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 14, 37, 31, 44 ]
62
[ "14*31=434", "44-37=7", "434/7=62" ]
Current State: 62:[14, 37, 31, 44], Operations: [] Exploring Operation: 14*31=434, Resulting Numbers: [37, 44, 434] Generated Node #2: [37, 44, 434] from Operation: 14*31=434 Current State: 62:[37, 44, 434], Operations: ['14*31=434'] Exploring Operation: 44-37=7, Resulting Numbers: [434, 7] Generated Node #3: [434, 7] from Operation: 44-37=7 Current State: 62:[434, 7], Operations: ['14*31=434', '44-37=7'] Exploring Operation: 434/7=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[14, 37, 31, 44], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [14, 31, 7] Generated Node #0,0: 62:[14, 31, 7] Operation: 44-37=7 Exploring Operation: 44-14=30, Resulting Numbers: [37, 31, 30] Generated Node #0,1: 62:[37, 31, 30] Operation: 44-14=30 Exploring Operation: 14+44=58, Resulting Numbers: [37, 31, 58] Generated Node #0,2: 62:[37, 31, 58] Operation: 14+44=58 Moving to Node #0,1 Current State: 62:[37, 31, 30], Operations: ['44-14=30'] Exploring Operation: 37+30=67, Resulting Numbers: [31, 67] Generated Node #0,1,0: 62:[31, 67] Operation: 37+30=67 Exploring Operation: 37-30=7, Resulting Numbers: [31, 7] Generated Node #0,1,1: 62:[31, 7] Operation: 37-30=7 Exploring Operation: 37-31=6, Resulting Numbers: [30, 6] Generated Node #0,1,2: 62:[30, 6] Operation: 37-31=6 Moving to Node #0,2 Current State: 62:[37, 31, 58], Operations: ['14+44=58'] Exploring Operation: 58-37=21, Resulting Numbers: [31, 21] Generated Node #0,2,0: 62:[31, 21] Operation: 58-37=21 Exploring Operation: 37+31=68, Resulting Numbers: [58, 68] Generated Node #0,2,1: 62:[58, 68] Operation: 37+31=68 Exploring Operation: 37-31=6, Resulting Numbers: [58, 6] Generated Node #0,2,2: 62:[58, 6] Operation: 37-31=6 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[58, 6], Operations: ['14+44=58', '37-31=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,62 unequal: No Solution Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,62 unequal: No Solution Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 62:[31, 21], Operations: ['14+44=58', '58-37=21'] Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,62 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,62 unequal: No Solution Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[58, 68], Operations: ['14+44=58', '37+31=68'] Exploring Operation: 68-58=10, Resulting Numbers: [10] 10,62 unequal: No Solution Exploring Operation: 58+68=126, Resulting Numbers: [126] 126,62 unequal: No Solution Exploring Operation: 58*68=3944, Resulting Numbers: [3944] 3944,62 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: 62:[14, 31, 7], Operations: ['44-37=7'] Exploring Operation: 14/7=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 14/7=2 Exploring Operation: 14+7=21, Resulting Numbers: [31, 21] Generated Node #0,0,1: 62:[31, 21] Operation: 14+7=21 Exploring Operation: 14-7=7, Resulting Numbers: [31, 7] Generated Node #0,0,2: 62:[31, 7] Operation: 14-7=7 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['44-37=7', '14/7=2'] Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[14, 37, 31, 44], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [14, 31, 7] Generated Node #0,0: 62:[14, 31, 7] Operation: 44-37=7 Moving to Node #0,0 Current State: 62:[14, 31, 7], Operations: ['44-37=7'] Exploring Operation: 14/7=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 14/7=2 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['44-37=7', '14/7=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 65, 51, 72, 38 ]
96
[ "65-51=14", "72+38=110", "110-14=96" ]
Current State: 96:[65, 51, 72, 38], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [72, 38, 14] Generated Node #2: [72, 38, 14] from Operation: 65-51=14 Current State: 96:[72, 38, 14], Operations: ['65-51=14'] Exploring Operation: 72+38=110, Resulting Numbers: [14, 110] Generated Node #3: [14, 110] from Operation: 72+38=110 Current State: 96:[14, 110], Operations: ['65-51=14', '72+38=110'] Exploring Operation: 110-14=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[65, 51, 72, 38], Operations: [] Exploring Operation: 72-38=34, Resulting Numbers: [65, 51, 34] Generated Node #0,0: 96:[65, 51, 34] Operation: 72-38=34 Exploring Operation: 72-65=7, Resulting Numbers: [51, 38, 7] Generated Node #0,1: 96:[51, 38, 7] Operation: 72-65=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[51, 38, 7], Operations: ['72-65=7'] Exploring Operation: 38-7=31, Resulting Numbers: [51, 31] Generated Node #0,1,0: 96:[51, 31] Operation: 38-7=31 Exploring Operation: 51-38=13, Resulting Numbers: [7, 13] Generated Node #0,1,1: 96:[7, 13] Operation: 51-38=13 Moving to Node #0,1,1 Current State: 96:[7, 13], Operations: ['72-65=7', '51-38=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[51, 31], Operations: ['72-65=7', '38-7=31'] Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 51+31=82, Resulting Numbers: [82] 82,96 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 #0,0 Current State: 96:[65, 51, 34], Operations: ['72-38=34'] Exploring Operation: 65-51=14, Resulting Numbers: [34, 14] Generated Node #0,0,0: 96:[34, 14] Operation: 65-51=14 Exploring Operation: 65-34=31, Resulting Numbers: [51, 31] Generated Node #0,0,1: 96:[51, 31] Operation: 65-34=31 Moving to Node #0,0,0 Current State: 96:[34, 14], Operations: ['72-38=34', '65-51=14'] Exploring Operation: 34+14=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[51, 31], Operations: ['72-38=34', '65-34=31'] Exploring Operation: 51+31=82, Resulting Numbers: [82] 82,96 unequal: No Solution Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,96 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
[ 94, 13, 1, 50 ]
58
[ "94+13=107", "50-1=49", "107-49=58" ]
Current State: 58:[94, 13, 1, 50], Operations: [] Exploring Operation: 94+13=107, Resulting Numbers: [1, 50, 107] Generated Node #2: [1, 50, 107] from Operation: 94+13=107 Current State: 58:[1, 50, 107], Operations: ['94+13=107'] Exploring Operation: 50-1=49, Resulting Numbers: [107, 49] Generated Node #3: [107, 49] from Operation: 50-1=49 Current State: 58:[107, 49], Operations: ['94+13=107', '50-1=49'] Exploring Operation: 107-49=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[94, 13, 1, 50], Operations: [] Exploring Operation: 13+50=63, Resulting Numbers: [94, 1, 63] Generated Node #0,0: 58:[94, 1, 63] Operation: 13+50=63 Exploring Operation: 94-13=81, Resulting Numbers: [1, 50, 81] Generated Node #0,1: 58:[1, 50, 81] Operation: 94-13=81 Exploring Operation: 94-50=44, Resulting Numbers: [13, 1, 44] Generated Node #0,2: 58:[13, 1, 44] Operation: 94-50=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[13, 1, 44], Operations: ['94-50=44'] Exploring Operation: 13+44=57, Resulting Numbers: [1, 57] Generated Node #0,2,0: 58:[1, 57] Operation: 13+44=57 Exploring Operation: 13-1=12, Resulting Numbers: [44, 12] Generated Node #0,2,1: 58:[44, 12] Operation: 13-1=12 Exploring Operation: 44-13=31, Resulting Numbers: [1, 31] Generated Node #0,2,2: 58:[1, 31] Operation: 44-13=31 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[1, 57], Operations: ['94-50=44', '13+44=57'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[94, 13, 1, 50], Operations: [] Exploring Operation: 94-50=44, Resulting Numbers: [13, 1, 44] Generated Node #0,2: 58:[13, 1, 44] Operation: 94-50=44 Moving to Node #0,2 Current State: 58:[13, 1, 44], Operations: ['94-50=44'] Exploring Operation: 13+44=57, Resulting Numbers: [1, 57] Generated Node #0,2,0: 58:[1, 57] Operation: 13+44=57 Moving to Node #0,2,0 Current State: 58:[1, 57], Operations: ['94-50=44', '13+44=57'] Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 41, 15, 81, 30 ]
15
[ "41*30=1230", "15*81=1215", "1230-1215=15" ]
Current State: 15:[41, 15, 81, 30], Operations: [] Exploring Operation: 41*30=1230, Resulting Numbers: [15, 81, 1230] Generated Node #2: [15, 81, 1230] from Operation: 41*30=1230 Current State: 15:[15, 81, 1230], Operations: ['41*30=1230'] Exploring Operation: 15*81=1215, Resulting Numbers: [1230, 1215] Generated Node #3: [1230, 1215] from Operation: 15*81=1215 Current State: 15:[1230, 1215], Operations: ['41*30=1230', '15*81=1215'] Exploring Operation: 1230-1215=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[41, 15, 81, 30], Operations: [] Exploring Operation: 41-15=26, Resulting Numbers: [81, 30, 26] Generated Node #0,0: 15:[81, 30, 26] Operation: 41-15=26 Exploring Operation: 81-30=51, Resulting Numbers: [41, 15, 51] Generated Node #0,1: 15:[41, 15, 51] Operation: 81-30=51 Exploring Operation: 81-41=40, Resulting Numbers: [15, 30, 40] Generated Node #0,2: 15:[15, 30, 40] Operation: 81-41=40 Exploring Operation: 81-15=66, Resulting Numbers: [41, 30, 66] Generated Node #0,3: 15:[41, 30, 66] Operation: 81-15=66 Exploring Operation: 41-30=11, Resulting Numbers: [15, 81, 11] Generated Node #0,4: 15:[15, 81, 11] Operation: 41-30=11 Moving to Node #0,2 Current State: 15:[15, 30, 40], Operations: ['81-41=40'] Exploring Operation: 15+30=45, Resulting Numbers: [40, 45] Generated Node #0,2,0: 15:[40, 45] Operation: 15+30=45 Exploring Operation: 40-15=25, Resulting Numbers: [30, 25] Generated Node #0,2,1: 15:[30, 25] Operation: 40-15=25 Exploring Operation: 40-30=10, Resulting Numbers: [15, 10] Generated Node #0,2,2: 15:[15, 10] Operation: 40-30=10 Exploring Operation: 30-15=15, Resulting Numbers: [40, 15] Generated Node #0,2,3: 15:[40, 15] Operation: 30-15=15 Exploring Operation: 30/15=2, Resulting Numbers: [40, 2] Generated Node #0,2,4: 15:[40, 2] Operation: 30/15=2 Moving to Node #0,1 Current State: 15:[41, 15, 51], Operations: ['81-30=51'] Exploring Operation: 51-41=10, Resulting Numbers: [15, 10] Generated Node #0,1,0: 15:[15, 10] Operation: 51-41=10 Exploring Operation: 41+51=92, Resulting Numbers: [15, 92] Generated Node #0,1,1: 15:[15, 92] Operation: 41+51=92 Exploring Operation: 41+15=56, Resulting Numbers: [51, 56] Generated Node #0,1,2: 15:[51, 56] Operation: 41+15=56 Exploring Operation: 41-15=26, Resulting Numbers: [51, 26] Generated Node #0,1,3: 15:[51, 26] Operation: 41-15=26 Exploring Operation: 51-15=36, Resulting Numbers: [41, 36] Generated Node #0,1,4: 15:[41, 36] Operation: 51-15=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[15, 10], Operations: ['81-30=51', '51-41=10'] Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 15:[51, 26], Operations: ['81-30=51', '41-15=26'] Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,15 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 15:[41, 36], Operations: ['81-30=51', '51-15=36'] Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,15 unequal: No Solution Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[15, 92], Operations: ['81-30=51', '41+51=92'] Exploring Operation: 15+92=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 15*92=1380, Resulting Numbers: [1380] 1380,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[51, 56], Operations: ['81-30=51', '41+15=56'] Exploring Operation: 51+56=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 51*56=2856, Resulting Numbers: [2856] 2856,15 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: 15:[15, 81, 11], Operations: ['41-30=11'] Exploring Operation: 15+11=26, Resulting Numbers: [81, 26] Generated Node #0,4,0: 15:[81, 26] Operation: 15+11=26 Exploring Operation: 15-11=4, Resulting Numbers: [81, 4] Generated Node #0,4,1: 15:[81, 4] Operation: 15-11=4 Exploring Operation: 81-15=66, Resulting Numbers: [11, 66] Generated Node #0,4,2: 15:[11, 66] Operation: 81-15=66 Exploring Operation: 81+11=92, Resulting Numbers: [15, 92] Generated Node #0,4,3: 15:[15, 92] Operation: 81+11=92 Exploring Operation: 81-11=70, Resulting Numbers: [15, 70] Generated Node #0,4,4: 15:[15, 70] Operation: 81-11=70 Moving to Node #0,0 Current State: 15:[81, 30, 26], Operations: ['41-15=26'] Exploring Operation: 81-26=55, Resulting Numbers: [30, 55] Generated Node #0,0,0: 15:[30, 55] Operation: 81-26=55 Exploring Operation: 81+26=107, Resulting Numbers: [30, 107] Generated Node #0,0,1: 15:[30, 107] Operation: 81+26=107 Exploring Operation: 81-30=51, Resulting Numbers: [26, 51] Generated Node #0,0,2: 15:[26, 51] Operation: 81-30=51 Exploring Operation: 81+30=111, Resulting Numbers: [26, 111] Generated Node #0,0,3: 15:[26, 111] Operation: 81+30=111 Exploring Operation: 30-26=4, Resulting Numbers: [81, 4] Generated Node #0,0,4: 15:[81, 4] Operation: 30-26=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[26, 51], Operations: ['41-15=26', '81-30=51'] Exploring Operation: 26*51=1326, Resulting Numbers: [1326] 1326,15 unequal: No Solution Exploring Operation: 26+51=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[30, 55], Operations: ['41-15=26', '81-26=55'] Exploring Operation: 30+55=85, Resulting Numbers: [85] 85,15 unequal: No Solution Exploring Operation: 30*55=1650, Resulting Numbers: [1650] 1650,15 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 15:[81, 4], Operations: ['41-15=26', '30-26=4'] Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,15 unequal: No Solution Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,15 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[30, 107], Operations: ['41-15=26', '81+26=107'] Exploring Operation: 30*107=3210, Resulting Numbers: [3210] 3210,15 unequal: No Solution Exploring Operation: 107-30=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 30+107=137, Resulting Numbers: [137] 137,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 15:[26, 111], Operations: ['41-15=26', '81+30=111'] Exploring Operation: 111-26=85, Resulting Numbers: [85] 85,15 unequal: No Solution Exploring Operation: 26+111=137, Resulting Numbers: [137] 137,15 unequal: No Solution Exploring Operation: 26*111=2886, Resulting Numbers: [2886] 2886,15 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: 15:[41, 30, 66], Operations: ['81-15=66'] Exploring Operation: 66-41=25, Resulting Numbers: [30, 25] Generated Node #0,3,0: 15:[30, 25] Operation: 66-41=25 Exploring Operation: 41+30=71, Resulting Numbers: [66, 71] Generated Node #0,3,1: 15:[66, 71] Operation: 41+30=71 Exploring Operation: 66-30=36, Resulting Numbers: [41, 36] Generated Node #0,3,2: 15:[41, 36] Operation: 66-30=36 Exploring Operation: 41-30=11, Resulting Numbers: [66, 11] Generated Node #0,3,3: 15:[66, 11] Operation: 41-30=11 Exploring Operation: 41+66=107, Resulting Numbers: [30, 107] Generated Node #0,3,4: 15:[30, 107] Operation: 41+66=107 Moving to Node #0,2,2 Current State: 15:[15, 10], Operations: ['81-41=40', '40-30=10'] Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,15 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[40, 15], Operations: ['81-41=40', '30-15=15'] Exploring Operation: 40+15=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 40*15=600, Resulting Numbers: [600] 600,15 unequal: No Solution Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[30, 25], Operations: ['81-41=40', '40-15=25'] Exploring Operation: 30*25=750, Resulting Numbers: [750] 750,15 unequal: No Solution Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[30, 25], Operations: ['81-15=66', '66-41=25'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 30*25=750, Resulting Numbers: [750] 750,15 unequal: No Solution Moving to Node #0,2,4 Current State: 15:[40, 2], Operations: ['81-41=40', '30/15=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[41, 36], Operations: ['81-15=66', '66-30=36'] Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,15 unequal: No Solution Moving to Node #0,4,4 Current State: 15:[15, 70], Operations: ['41-30=11', '81-11=70'] Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,15 unequal: No Solution Exploring Operation: 15*70=1050, Resulting Numbers: [1050] 1050,15 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[66, 11], Operations: ['81-15=66', '41-30=11'] Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 66+11=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 66*11=726, Resulting Numbers: [726] 726,15 unequal: No Solution Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[40, 45], Operations: ['81-41=40', '15+30=45'] Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 40*45=1800, Resulting Numbers: [1800] 1800,15 unequal: No Solution Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,15 unequal: No Solution Moving to Node #0,4,2 Current State: 15:[11, 66], Operations: ['41-30=11', '81-15=66'] Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 66-11=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 11+66=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 11*66=726, Resulting Numbers: [726] 726,15 unequal: No Solution Moving to Node #0,4,1 Current State: 15:[81, 4], Operations: ['41-30=11', '15-11=4'] Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,15 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,15 unequal: No Solution Moving to Node #0,4,3 Current State: 15:[15, 92], Operations: ['41-30=11', '81+11=92'] Exploring Operation: 15+92=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 15*92=1380, Resulting Numbers: [1380] 1380,15 unequal: No Solution Moving to Node #0,4,0 Current State: 15:[81, 26], Operations: ['41-30=11', '15+11=26'] Exploring Operation: 81*26=2106, Resulting Numbers: [2106] 2106,15 unequal: No Solution Exploring Operation: 81+26=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[66, 71], Operations: ['81-15=66', '41+30=71'] Exploring Operation: 66+71=137, Resulting Numbers: [137] 137,15 unequal: No Solution Exploring Operation: 71-66=5, Resulting Numbers: [5] 5,15 unequal: No Solution Exploring Operation: 66*71=4686, Resulting Numbers: [4686] 4686,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[30, 107], Operations: ['81-15=66', '41+66=107'] Exploring Operation: 30+107=137, Resulting Numbers: [137] 137,15 unequal: No Solution Exploring Operation: 30*107=3210, Resulting Numbers: [3210] 3210,15 unequal: No Solution Exploring Operation: 107-30=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 19, 54, 43, 7 ]
48
[ "54-19=35", "35/7=5", "43+5=48" ]
Current State: 48:[19, 54, 43, 7], Operations: [] Exploring Operation: 54-19=35, Resulting Numbers: [43, 7, 35] Generated Node #2: [43, 7, 35] from Operation: 54-19=35 Current State: 48:[43, 7, 35], Operations: ['54-19=35'] Exploring Operation: 35/7=5, Resulting Numbers: [43, 5] Generated Node #3: [43, 5] from Operation: 35/7=5 Current State: 48:[43, 5], Operations: ['54-19=35', '35/7=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[19, 54, 43, 7], Operations: [] Exploring Operation: 19-7=12, Resulting Numbers: [54, 43, 12] Generated Node #0,0: 48:[54, 43, 12] Operation: 19-7=12 Exploring Operation: 54-7=47, Resulting Numbers: [19, 43, 47] Generated Node #0,1: 48:[19, 43, 47] Operation: 54-7=47 Exploring Operation: 54-43=11, Resulting Numbers: [19, 7, 11] Generated Node #0,2: 48:[19, 7, 11] Operation: 54-43=11 Exploring Operation: 43+7=50, Resulting Numbers: [19, 54, 50] Generated Node #0,3: 48:[19, 54, 50] Operation: 43+7=50 Exploring Operation: 43-19=24, Resulting Numbers: [54, 7, 24] Generated Node #0,4: 48:[54, 7, 24] Operation: 43-19=24 Moving to Node #0,2 Current State: 48:[19, 7, 11], Operations: ['54-43=11'] Exploring Operation: 19+7=26, Resulting Numbers: [11, 26] Generated Node #0,2,0: 48:[11, 26] Operation: 19+7=26 Exploring Operation: 19-11=8, Resulting Numbers: [7, 8] Generated Node #0,2,1: 48:[7, 8] Operation: 19-11=8 Exploring Operation: 11-7=4, Resulting Numbers: [19, 4] Generated Node #0,2,2: 48:[19, 4] Operation: 11-7=4 Exploring Operation: 19-7=12, Resulting Numbers: [11, 12] Generated Node #0,2,3: 48:[11, 12] Operation: 19-7=12 Exploring Operation: 7+11=18, Resulting Numbers: [19, 18] Generated Node #0,2,4: 48:[19, 18] Operation: 7+11=18 Moving to Node #0,4 Current State: 48:[54, 7, 24], Operations: ['43-19=24'] Exploring Operation: 54-24=30, Resulting Numbers: [7, 30] Generated Node #0,4,0: 48:[7, 30] Operation: 54-24=30 Exploring Operation: 54+7=61, Resulting Numbers: [24, 61] Generated Node #0,4,1: 48:[24, 61] Operation: 54+7=61 Exploring Operation: 54-7=47, Resulting Numbers: [24, 47] Generated Node #0,4,2: 48:[24, 47] Operation: 54-7=47 Exploring Operation: 24-7=17, Resulting Numbers: [54, 17] Generated Node #0,4,3: 48:[54, 17] Operation: 24-7=17 Exploring Operation: 7+24=31, Resulting Numbers: [54, 31] Generated Node #0,4,4: 48:[54, 31] Operation: 7+24=31 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 48:[24, 47], Operations: ['43-19=24', '54-7=47'] Exploring Operation: 24*47=1128, Resulting Numbers: [1128] 1128,48 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 24+47=71, Resulting Numbers: [71] 71,48 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 #0,4,0 Current State: 48:[7, 30], Operations: ['43-19=24', '54-24=30'] Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,48 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,48 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 #0,4,3 Current State: 48:[54, 17], Operations: ['43-19=24', '24-7=17'] Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,48 unequal: No Solution Exploring Operation: 54*17=918, Resulting Numbers: [918] 918,48 unequal: No Solution Exploring Operation: 54+17=71, Resulting Numbers: [71] 71,48 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 #0,4,1 Current State: 48:[24, 61], Operations: ['43-19=24', '54+7=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,48 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,48 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 #0,4,4 Current State: 48:[54, 31], Operations: ['43-19=24', '7+24=31'] Exploring Operation: 54*31=1674, Resulting Numbers: [1674] 1674,48 unequal: No Solution Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,48 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: 48:[19, 43, 47], Operations: ['54-7=47'] Exploring Operation: 47-43=4, Resulting Numbers: [19, 4] Generated Node #0,1,0: 48:[19, 4] Operation: 47-43=4 Exploring Operation: 19+47=66, Resulting Numbers: [43, 66] Generated Node #0,1,1: 48:[43, 66] Operation: 19+47=66 Exploring Operation: 47-19=28, Resulting Numbers: [43, 28] Generated Node #0,1,2: 48:[43, 28] Operation: 47-19=28 Exploring Operation: 43-19=24, Resulting Numbers: [47, 24] Generated Node #0,1,3: 48:[47, 24] Operation: 43-19=24 Exploring Operation: 19+43=62, Resulting Numbers: [47, 62] Generated Node #0,1,4: 48:[47, 62] Operation: 19+43=62 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 48:[47, 24], Operations: ['54-7=47', '43-19=24'] Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,48 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,48 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,48 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 #0,1,0 Current State: 48:[19, 4], Operations: ['54-7=47', '47-43=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,48 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:[43, 28], Operations: ['54-7=47', '47-19=28'] Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 43*28=1204, Resulting Numbers: [1204] 1204,48 unequal: No Solution Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,48 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 #0,1,4 Current State: 48:[47, 62], Operations: ['54-7=47', '19+43=62'] Exploring Operation: 47*62=2914, Resulting Numbers: [2914] 2914,48 unequal: No Solution Exploring Operation: 47+62=109, Resulting Numbers: [109] 109,48 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,48 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:[43, 66], Operations: ['54-7=47', '19+47=66'] Exploring Operation: 43+66=109, Resulting Numbers: [109] 109,48 unequal: No Solution Exploring Operation: 43*66=2838, Resulting Numbers: [2838] 2838,48 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,48 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: 48:[54, 43, 12], Operations: ['19-7=12'] Exploring Operation: 54-43=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 48:[12, 11] Operation: 54-43=11 Exploring Operation: 43-12=31, Resulting Numbers: [54, 31] Generated Node #0,0,1: 48:[54, 31] Operation: 43-12=31 Exploring Operation: 54+12=66, Resulting Numbers: [43, 66] Generated Node #0,0,2: 48:[43, 66] Operation: 54+12=66 Exploring Operation: 54-12=42, Resulting Numbers: [43, 42] Generated Node #0,0,3: 48:[43, 42] Operation: 54-12=42 Exploring Operation: 43+12=55, Resulting Numbers: [54, 55] Generated Node #0,0,4: 48:[54, 55] Operation: 43+12=55 Moving to Node #0,3 Current State: 48:[19, 54, 50], Operations: ['43+7=50'] Exploring Operation: 19+54=73, Resulting Numbers: [50, 73] Generated Node #0,3,0: 48:[50, 73] Operation: 19+54=73 Exploring Operation: 50-19=31, Resulting Numbers: [54, 31] Generated Node #0,3,1: 48:[54, 31] Operation: 50-19=31 Exploring Operation: 19+50=69, Resulting Numbers: [54, 69] Generated Node #0,3,2: 48:[54, 69] Operation: 19+50=69 Exploring Operation: 54-50=4, Resulting Numbers: [19, 4] Generated Node #0,3,3: 48:[19, 4] Operation: 54-50=4 Exploring Operation: 54-19=35, Resulting Numbers: [50, 35] Generated Node #0,3,4: 48:[50, 35] Operation: 54-19=35 Moving to Node #0,2,1 Current State: 48:[7, 8], Operations: ['54-43=11', '19-11=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,48 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[12, 11], Operations: ['19-7=12', '54-43=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,48 unequal: No Solution Moving to Node #0,2,3 Current State: 48:[11, 12], Operations: ['54-43=11', '19-7=12'] Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,48 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[11, 26], Operations: ['54-43=11', '19+7=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,48 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,48 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,48 unequal: No Solution Moving to Node #0,3,3 Current State: 48:[19, 4], Operations: ['43+7=50', '54-50=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[19, 4], Operations: ['54-43=11', '11-7=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,48 unequal: No Solution Moving to Node #0,2,4 Current State: 48:[19, 18], Operations: ['54-43=11', '7+11=18'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,48 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,48 unequal: No Solution Moving to Node #0,0,3 Current State: 48:[43, 42], Operations: ['19-7=12', '54-12=42'] Exploring Operation: 43-42=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 43+42=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 43*42=1806, Resulting Numbers: [1806] 1806,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[50, 35], Operations: ['43+7=50', '54-19=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,48 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,48 unequal: No Solution Moving to Node #0,0,1 Current State: 48:[54, 31], Operations: ['19-7=12', '43-12=31'] Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 54*31=1674, Resulting Numbers: [1674] 1674,48 unequal: No Solution Moving to Node #0,0,4 Current State: 48:[54, 55], Operations: ['19-7=12', '43+12=55'] Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 54+55=109, Resulting Numbers: [109] 109,48 unequal: No Solution Exploring Operation: 54*55=2970, Resulting Numbers: [2970] 2970,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[54, 31], Operations: ['43+7=50', '50-19=31'] Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,48 unequal: No Solution Exploring Operation: 54*31=1674, Resulting Numbers: [1674] 1674,48 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[43, 66], Operations: ['19-7=12', '54+12=66'] Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 43+66=109, Resulting Numbers: [109] 109,48 unequal: No Solution Exploring Operation: 43*66=2838, Resulting Numbers: [2838] 2838,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[54, 69], Operations: ['43+7=50', '19+50=69'] Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,48 unequal: No Solution Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,48 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[50, 73], Operations: ['43+7=50', '19+54=73'] Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,48 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,48 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 82, 95, 73, 39 ]
65
[ "82+95=177", "73+39=112", "177-112=65" ]
Current State: 65:[82, 95, 73, 39], Operations: [] Exploring Operation: 82+95=177, Resulting Numbers: [73, 39, 177] Generated Node #2: [73, 39, 177] from Operation: 82+95=177 Current State: 65:[73, 39, 177], Operations: ['82+95=177'] Exploring Operation: 73+39=112, Resulting Numbers: [177, 112] Generated Node #3: [177, 112] from Operation: 73+39=112 Current State: 65:[177, 112], Operations: ['82+95=177', '73+39=112'] Exploring Operation: 177-112=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[82, 95, 73, 39], Operations: [] Exploring Operation: 95-82=13, Resulting Numbers: [73, 39, 13] Generated Node #0,0: 65:[73, 39, 13] Operation: 95-82=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[73, 39, 13], Operations: ['95-82=13'] Exploring Operation: 39/13=3, Resulting Numbers: [73, 3] Generated Node #0,0,0: 65:[73, 3] Operation: 39/13=3 Moving to Node #0,0,0 Current State: 65:[73, 3], Operations: ['95-82=13', '39/13=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 82, 47, 42, 81 ]
88
[ "82-47=35", "42+81=123", "123-35=88" ]
Current State: 88:[82, 47, 42, 81], Operations: [] Exploring Operation: 82-47=35, Resulting Numbers: [42, 81, 35] Generated Node #2: [42, 81, 35] from Operation: 82-47=35 Current State: 88:[42, 81, 35], Operations: ['82-47=35'] Exploring Operation: 42+81=123, Resulting Numbers: [35, 123] Generated Node #3: [35, 123] from Operation: 42+81=123 Current State: 88:[35, 123], Operations: ['82-47=35', '42+81=123'] Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[82, 47, 42, 81], Operations: [] Exploring Operation: 47-42=5, Resulting Numbers: [82, 81, 5] Generated Node #0,0: 88:[82, 81, 5] Operation: 47-42=5 Exploring Operation: 82-81=1, Resulting Numbers: [47, 42, 1] Generated Node #0,1: 88:[47, 42, 1] Operation: 82-81=1 Exploring Operation: 47+42=89, Resulting Numbers: [82, 81, 89] Generated Node #0,2: 88:[82, 81, 89] Operation: 47+42=89 Exploring Operation: 82-42=40, Resulting Numbers: [47, 81, 40] Generated Node #0,3: 88:[47, 81, 40] Operation: 82-42=40 Moving to Node #0,1 Current State: 88:[47, 42, 1], Operations: ['82-81=1'] Exploring Operation: 47+42=89, Resulting Numbers: [1, 89] Generated Node #0,1,0: 88:[1, 89] Operation: 47+42=89 Exploring Operation: 42+1=43, Resulting Numbers: [47, 43] Generated Node #0,1,1: 88:[47, 43] Operation: 42+1=43 Exploring Operation: 47-42=5, Resulting Numbers: [1, 5] Generated Node #0,1,2: 88:[1, 5] Operation: 47-42=5 Exploring Operation: 47-1=46, Resulting Numbers: [42, 46] Generated Node #0,1,3: 88:[42, 46] Operation: 47-1=46 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[1, 89], Operations: ['82-81=1', '47+42=89'] Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[82, 47, 42, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [47, 42, 1] Generated Node #0,1: 88:[47, 42, 1] Operation: 82-81=1 Moving to Node #0,1 Current State: 88:[47, 42, 1], Operations: ['82-81=1'] Exploring Operation: 47+42=89, Resulting Numbers: [1, 89] Generated Node #0,1,0: 88:[1, 89] Operation: 47+42=89 Moving to Node #0,1,0 Current State: 88:[1, 89], Operations: ['82-81=1', '47+42=89'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 20, 40, 64, 41 ]
85
[ "40-20=20", "64+41=105", "105-20=85" ]
Current State: 85:[20, 40, 64, 41], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [64, 41, 20] Generated Node #2: [64, 41, 20] from Operation: 40-20=20 Current State: 85:[64, 41, 20], Operations: ['40-20=20'] Exploring Operation: 64+41=105, Resulting Numbers: [20, 105] Generated Node #3: [20, 105] from Operation: 64+41=105 Current State: 85:[20, 105], Operations: ['40-20=20', '64+41=105'] Exploring Operation: 105-20=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[20, 40, 64, 41], Operations: [] Exploring Operation: 40+41=81, Resulting Numbers: [20, 64, 81] Generated Node #0,0: 85:[20, 64, 81] Operation: 40+41=81 Exploring Operation: 41-40=1, Resulting Numbers: [20, 64, 1] Generated Node #0,1: 85:[20, 64, 1] Operation: 41-40=1 Exploring Operation: 40+64=104, Resulting Numbers: [20, 41, 104] Generated Node #0,2: 85:[20, 41, 104] Operation: 40+64=104 Exploring Operation: 64-41=23, Resulting Numbers: [20, 40, 23] Generated Node #0,3: 85:[20, 40, 23] Operation: 64-41=23 Exploring Operation: 64-40=24, Resulting Numbers: [20, 41, 24] Generated Node #0,4: 85:[20, 41, 24] Operation: 64-40=24 Moving to Node #0,0 Current State: 85:[20, 64, 81], Operations: ['40+41=81'] Exploring Operation: 20+64=84, Resulting Numbers: [81, 84] Generated Node #0,0,0: 85:[81, 84] Operation: 20+64=84 Exploring Operation: 20+81=101, Resulting Numbers: [64, 101] Generated Node #0,0,1: 85:[64, 101] Operation: 20+81=101 Exploring Operation: 64-20=44, Resulting Numbers: [81, 44] Generated Node #0,0,2: 85:[81, 44] Operation: 64-20=44 Exploring Operation: 81-20=61, Resulting Numbers: [64, 61] Generated Node #0,0,3: 85:[64, 61] Operation: 81-20=61 Exploring Operation: 81-64=17, Resulting Numbers: [20, 17] Generated Node #0,0,4: 85:[20, 17] Operation: 81-64=17 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 85:[20, 17], Operations: ['40+41=81', '81-64=17'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,85 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[81, 84], Operations: ['40+41=81', '20+64=84'] Exploring Operation: 81+84=165, Resulting Numbers: [165] 165,85 unequal: No Solution Exploring Operation: 81*84=6804, Resulting Numbers: [6804] 6804,85 unequal: No Solution Exploring Operation: 84-81=3, Resulting Numbers: [3] 3,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 85:[81, 44], Operations: ['40+41=81', '64-20=44'] Exploring Operation: 81-44=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 81*44=3564, Resulting Numbers: [3564] 3564,85 unequal: No Solution Exploring Operation: 81+44=125, Resulting Numbers: [125] 125,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[64, 101], Operations: ['40+41=81', '20+81=101'] Exploring Operation: 101-64=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 64*101=6464, Resulting Numbers: [6464] 6464,85 unequal: No Solution Exploring Operation: 64+101=165, Resulting Numbers: [165] 165,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 85:[64, 61], Operations: ['40+41=81', '81-20=61'] Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,85 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,85 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: 85:[20, 64, 1], Operations: ['41-40=1'] Exploring Operation: 20*1=20, Resulting Numbers: [64, 20] Generated Node #0,1,0: 85:[64, 20] Operation: 20*1=20 Exploring Operation: 20+64=84, Resulting Numbers: [1, 84] Generated Node #0,1,1: 85:[1, 84] Operation: 20+64=84 Exploring Operation: 64+1=65, Resulting Numbers: [20, 65] Generated Node #0,1,2: 85:[20, 65] Operation: 64+1=65 Exploring Operation: 20-1=19, Resulting Numbers: [64, 19] Generated Node #0,1,3: 85:[64, 19] Operation: 20-1=19 Exploring Operation: 20/1=20, Resulting Numbers: [64, 20] Generated Node #0,1,4: 85:[64, 20] Operation: 20/1=20 Moving to Node #0,3 Current State: 85:[20, 40, 23], Operations: ['64-41=23'] Exploring Operation: 40-20=20, Resulting Numbers: [23, 20] Generated Node #0,3,0: 85:[23, 20] Operation: 40-20=20 Exploring Operation: 23-20=3, Resulting Numbers: [40, 3] Generated Node #0,3,1: 85:[40, 3] Operation: 23-20=3 Exploring Operation: 40+23=63, Resulting Numbers: [20, 63] Generated Node #0,3,2: 85:[20, 63] Operation: 40+23=63 Exploring Operation: 40/20=2, Resulting Numbers: [23, 2] Generated Node #0,3,3: 85:[23, 2] Operation: 40/20=2 Exploring Operation: 40-23=17, Resulting Numbers: [20, 17] Generated Node #0,3,4: 85:[20, 17] Operation: 40-23=17 Moving to Node #0,4 Current State: 85:[20, 41, 24], Operations: ['64-40=24'] Exploring Operation: 20+41=61, Resulting Numbers: [24, 61] Generated Node #0,4,0: 85:[24, 61] Operation: 20+41=61 Exploring Operation: 41+24=65, Resulting Numbers: [20, 65] Generated Node #0,4,1: 85:[20, 65] Operation: 41+24=65 Exploring Operation: 41-24=17, Resulting Numbers: [20, 17] Generated Node #0,4,2: 85:[20, 17] Operation: 41-24=17 Exploring Operation: 24-20=4, Resulting Numbers: [41, 4] Generated Node #0,4,3: 85:[41, 4] Operation: 24-20=4 Exploring Operation: 41-20=21, Resulting Numbers: [24, 21] Generated Node #0,4,4: 85:[24, 21] Operation: 41-20=21 Moving to Node #0,2 Current State: 85:[20, 41, 104], Operations: ['40+64=104'] Exploring Operation: 20+41=61, Resulting Numbers: [104, 61] Generated Node #0,2,0: 85:[104, 61] Operation: 20+41=61 Exploring Operation: 104-41=63, Resulting Numbers: [20, 63] Generated Node #0,2,1: 85:[20, 63] Operation: 104-41=63 Exploring Operation: 104-20=84, Resulting Numbers: [41, 84] Generated Node #0,2,2: 85:[41, 84] Operation: 104-20=84 Exploring Operation: 20+104=124, Resulting Numbers: [41, 124] Generated Node #0,2,3: 85:[41, 124] Operation: 20+104=124 Exploring Operation: 41-20=21, Resulting Numbers: [104, 21] Generated Node #0,2,4: 85:[104, 21] Operation: 41-20=21 Moving to Node #0,3,4 Current State: 85:[20, 17], Operations: ['64-41=23', '40-23=17'] Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,85 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[20, 17], Operations: ['64-40=24', '41-24=17'] Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,85 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[1, 84], Operations: ['41-40=1', '20+64=84'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,85 unequal: No Solution Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[20, 40, 64, 41], Operations: [] Exploring Operation: 41-40=1, Resulting Numbers: [20, 64, 1] Generated Node #0,1: 85:[20, 64, 1] Operation: 41-40=1 Moving to Node #0,1 Current State: 85:[20, 64, 1], Operations: ['41-40=1'] Exploring Operation: 20+64=84, Resulting Numbers: [1, 84] Generated Node #0,1,1: 85:[1, 84] Operation: 20+64=84 Moving to Node #0,1,1 Current State: 85:[1, 84], Operations: ['41-40=1', '20+64=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.948785
hs_5
sum_heuristic
[ 2, 90, 19, 5 ]
43
[ "2+5=7", "19*7=133", "133-90=43" ]
Current State: 43:[2, 90, 19, 5], Operations: [] Exploring Operation: 2+5=7, Resulting Numbers: [90, 19, 7] Generated Node #2: [90, 19, 7] from Operation: 2+5=7 Current State: 43:[90, 19, 7], Operations: ['2+5=7'] Exploring Operation: 19*7=133, Resulting Numbers: [90, 133] Generated Node #3: [90, 133] from Operation: 19*7=133 Current State: 43:[90, 133], Operations: ['2+5=7', '19*7=133'] Exploring Operation: 133-90=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[2, 90, 19, 5], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [19, 5, 45] Generated Node #0,0: 43:[19, 5, 45] Operation: 90/2=45 Exploring Operation: 2*19=38, Resulting Numbers: [90, 5, 38] Generated Node #0,1: 43:[90, 5, 38] Operation: 2*19=38 Exploring Operation: 2*5=10, Resulting Numbers: [90, 19, 10] Generated Node #0,2: 43:[90, 19, 10] Operation: 2*5=10 Exploring Operation: 90/5=18, Resulting Numbers: [2, 19, 18] Generated Node #0,3: 43:[2, 19, 18] Operation: 90/5=18 Moving to Node #0,0 Current State: 43:[19, 5, 45], Operations: ['90/2=45'] Exploring Operation: 19+5=24, Resulting Numbers: [45, 24] Generated Node #0,0,0: 43:[45, 24] Operation: 19+5=24 Exploring Operation: 19-5=14, Resulting Numbers: [45, 14] Generated Node #0,0,1: 43:[45, 14] Operation: 19-5=14 Exploring Operation: 5+45=50, Resulting Numbers: [19, 50] Generated Node #0,0,2: 43:[19, 50] Operation: 5+45=50 Exploring Operation: 45-5=40, Resulting Numbers: [19, 40] Generated Node #0,0,3: 43:[19, 40] Operation: 45-5=40 Moving to Node #0,3 Current State: 43:[2, 19, 18], Operations: ['90/5=18'] Exploring Operation: 2*18=36, Resulting Numbers: [19, 36] Generated Node #0,3,0: 43:[19, 36] Operation: 2*18=36 Exploring Operation: 2+18=20, Resulting Numbers: [19, 20] Generated Node #0,3,1: 43:[19, 20] Operation: 2+18=20 Exploring Operation: 2+19=21, Resulting Numbers: [18, 21] Generated Node #0,3,2: 43:[18, 21] Operation: 2+19=21 Exploring Operation: 2*19=38, Resulting Numbers: [18, 38] Generated Node #0,3,3: 43:[18, 38] Operation: 2*19=38 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 43:[18, 38], Operations: ['90/5=18', '2*19=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,43 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,43 unequal: No Solution No 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: 43:[19, 36], Operations: ['90/5=18', '2*18=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,43 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,43 unequal: No Solution No 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: 43:[19, 20], Operations: ['90/5=18', '2+18=20'] Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,43 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 43:[18, 21], Operations: ['90/5=18', '2+19=21'] Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,43 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,43 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: 43:[90, 5, 38], Operations: ['2*19=38'] Exploring Operation: 5+38=43, Resulting Numbers: [90, 43] Generated Node #0,1,0: 43:[90, 43] Operation: 5+38=43 Exploring Operation: 90/5=18, Resulting Numbers: [38, 18] Generated Node #0,1,1: 43:[38, 18] Operation: 90/5=18 Exploring Operation: 90-5=85, Resulting Numbers: [38, 85] Generated Node #0,1,2: 43:[38, 85] Operation: 90-5=85 Exploring Operation: 90-38=52, Resulting Numbers: [5, 52] Generated Node #0,1,3: 43:[5, 52] Operation: 90-38=52 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[38, 18], Operations: ['2*19=38', '90/5=18'] Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 38+18=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 38*18=684, Resulting Numbers: [684] 684,43 unequal: No Solution No 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: 43:[90, 43], Operations: ['2*19=38', '5+38=43'] Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,43 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,43 unequal: No Solution Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,43 unequal: No Solution No 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: 43:[38, 85], Operations: ['2*19=38', '90-5=85'] Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 38*85=3230, Resulting Numbers: [3230] 3230,43 unequal: No Solution Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,43 unequal: No Solution No 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: 43:[5, 52], Operations: ['2*19=38', '90-38=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,43 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,43 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: 43:[90, 19, 10], Operations: ['2*5=10'] Exploring Operation: 90-19=71, Resulting Numbers: [10, 71] Generated Node #0,2,0: 43:[10, 71] Operation: 90-19=71 Exploring Operation: 90-10=80, Resulting Numbers: [19, 80] Generated Node #0,2,1: 43:[19, 80] Operation: 90-10=80 Exploring Operation: 90/10=9, Resulting Numbers: [19, 9] Generated Node #0,2,2: 43:[19, 9] Operation: 90/10=9 Exploring Operation: 19+10=29, Resulting Numbers: [90, 29] Generated Node #0,2,3: 43:[90, 29] Operation: 19+10=29 Moving to Node #0,0,0 Current State: 43:[45, 24], Operations: ['90/2=45', '19+5=24'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[19, 40], Operations: ['90/2=45', '45-5=40'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,43 unequal: No Solution Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,43 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[45, 14], Operations: ['90/2=45', '19-5=14'] Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,43 unequal: No Solution Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,43 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[19, 50], Operations: ['90/2=45', '5+45=50'] Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,43 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,43 unequal: No Solution Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[19, 9], Operations: ['2*5=10', '90/10=9'] Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,43 unequal: No Solution Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,43 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[10, 71], Operations: ['2*5=10', '90-19=71'] Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,43 unequal: No Solution Exploring Operation: 10*71=710, Resulting Numbers: [710] 710,43 unequal: No Solution Exploring Operation: 10+71=81, Resulting Numbers: [81] 81,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[90, 29], Operations: ['2*5=10', '19+10=29'] Exploring Operation: 90*29=2610, Resulting Numbers: [2610] 2610,43 unequal: No Solution Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,43 unequal: No Solution Exploring Operation: 90+29=119, Resulting Numbers: [119] 119,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[19, 80], Operations: ['2*5=10', '90-10=80'] Exploring Operation: 19*80=1520, Resulting Numbers: [1520] 1520,43 unequal: No Solution Exploring Operation: 19+80=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,43 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 6, 18, 79, 88 ]
59
[ "6*18=108", "79+88=167", "167-108=59" ]
Current State: 59:[6, 18, 79, 88], Operations: [] Exploring Operation: 6*18=108, Resulting Numbers: [79, 88, 108] Generated Node #2: [79, 88, 108] from Operation: 6*18=108 Current State: 59:[79, 88, 108], Operations: ['6*18=108'] Exploring Operation: 79+88=167, Resulting Numbers: [108, 167] Generated Node #3: [108, 167] from Operation: 79+88=167 Current State: 59:[108, 167], Operations: ['6*18=108', '79+88=167'] Exploring Operation: 167-108=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[6, 18, 79, 88], Operations: [] Exploring Operation: 88-6=82, Resulting Numbers: [18, 79, 82] Generated Node #0,0: 59:[18, 79, 82] Operation: 88-6=82 Exploring Operation: 6+18=24, Resulting Numbers: [79, 88, 24] Generated Node #0,1: 59:[79, 88, 24] Operation: 6+18=24 Exploring Operation: 88-18=70, Resulting Numbers: [6, 79, 70] Generated Node #0,2: 59:[6, 79, 70] Operation: 88-18=70 Exploring Operation: 79-18=61, Resulting Numbers: [6, 88, 61] Generated Node #0,3: 59:[6, 88, 61] Operation: 79-18=61 Exploring Operation: 79-6=73, Resulting Numbers: [18, 88, 73] Generated Node #0,4: 59:[18, 88, 73] Operation: 79-6=73 Moving to Node #0,0 Current State: 59:[18, 79, 82], Operations: ['88-6=82'] Exploring Operation: 18+82=100, Resulting Numbers: [79, 100] Generated Node #0,0,0: 59:[79, 100] Operation: 18+82=100 Exploring Operation: 82-79=3, Resulting Numbers: [18, 3] Generated Node #0,0,1: 59:[18, 3] Operation: 82-79=3 Exploring Operation: 79-18=61, Resulting Numbers: [82, 61] Generated Node #0,0,2: 59:[82, 61] Operation: 79-18=61 Exploring Operation: 82-18=64, Resulting Numbers: [79, 64] Generated Node #0,0,3: 59:[79, 64] Operation: 82-18=64 Exploring Operation: 18+79=97, Resulting Numbers: [82, 97] Generated Node #0,0,4: 59:[82, 97] Operation: 18+79=97 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[82, 61], Operations: ['88-6=82', '79-18=61'] Exploring Operation: 82+61=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 82*61=5002, Resulting Numbers: [5002] 5002,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 59:[79, 64], Operations: ['88-6=82', '82-18=64'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[79, 100], Operations: ['88-6=82', '18+82=100'] Exploring Operation: 79*100=7900, Resulting Numbers: [7900] 7900,59 unequal: No Solution Exploring Operation: 79+100=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 100-79=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 59:[82, 97], Operations: ['88-6=82', '18+79=97'] Exploring Operation: 82*97=7954, Resulting Numbers: [7954] 7954,59 unequal: No Solution Exploring Operation: 82+97=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[18, 3], Operations: ['88-6=82', '82-79=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,59 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[6, 79, 70], Operations: ['88-18=70'] Exploring Operation: 6+70=76, Resulting Numbers: [79, 76] Generated Node #0,2,0: 59:[79, 76] Operation: 6+70=76 Exploring Operation: 6+79=85, Resulting Numbers: [70, 85] Generated Node #0,2,1: 59:[70, 85] Operation: 6+79=85 Exploring Operation: 79-70=9, Resulting Numbers: [6, 9] Generated Node #0,2,2: 59:[6, 9] Operation: 79-70=9 Exploring Operation: 79-6=73, Resulting Numbers: [70, 73] Generated Node #0,2,3: 59:[70, 73] Operation: 79-6=73 Exploring Operation: 70-6=64, Resulting Numbers: [79, 64] Generated Node #0,2,4: 59:[79, 64] Operation: 70-6=64 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 59:[70, 73], Operations: ['88-18=70', '79-6=73'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 70+73=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 70*73=5110, Resulting Numbers: [5110] 5110,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 59:[79, 64], Operations: ['88-18=70', '70-6=64'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[79, 76], Operations: ['88-18=70', '6+70=76'] Exploring Operation: 79+76=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 79*76=6004, Resulting Numbers: [6004] 6004,59 unequal: No Solution Exploring Operation: 79-76=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[70, 85], Operations: ['88-18=70', '6+79=85'] Exploring Operation: 70+85=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 70*85=5950, Resulting Numbers: [5950] 5950,59 unequal: No Solution Exploring Operation: 85-70=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[6, 9], Operations: ['88-18=70', '79-70=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,59 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,59 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: 59:[18, 88, 73], Operations: ['79-6=73'] Exploring Operation: 88-18=70, Resulting Numbers: [73, 70] Generated Node #0,4,0: 59:[73, 70] Operation: 88-18=70 Exploring Operation: 18+88=106, Resulting Numbers: [73, 106] Generated Node #0,4,1: 59:[73, 106] Operation: 18+88=106 Exploring Operation: 88-73=15, Resulting Numbers: [18, 15] Generated Node #0,4,2: 59:[18, 15] Operation: 88-73=15 Exploring Operation: 73-18=55, Resulting Numbers: [88, 55] Generated Node #0,4,3: 59:[88, 55] Operation: 73-18=55 Exploring Operation: 18+73=91, Resulting Numbers: [88, 91] Generated Node #0,4,4: 59:[88, 91] Operation: 18+73=91 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 59:[73, 70], Operations: ['79-6=73', '88-18=70'] Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 59:[88, 55], Operations: ['79-6=73', '73-18=55'] Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,59 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 59:[73, 106], Operations: ['79-6=73', '18+88=106'] Exploring Operation: 73+106=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 73*106=7738, Resulting Numbers: [7738] 7738,59 unequal: No Solution Exploring Operation: 106-73=33, Resulting Numbers: [33] 33,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 59:[88, 91], Operations: ['79-6=73', '18+73=91'] Exploring Operation: 91-88=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 88+91=179, Resulting Numbers: [179] 179,59 unequal: No Solution Exploring Operation: 88*91=8008, Resulting Numbers: [8008] 8008,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 59:[18, 15], Operations: ['79-6=73', '88-73=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,59 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 59:[79, 88, 24], Operations: ['6+18=24'] Exploring Operation: 79-24=55, Resulting Numbers: [88, 55] Generated Node #0,1,0: 59:[88, 55] Operation: 79-24=55 Exploring Operation: 79+24=103, Resulting Numbers: [88, 103] Generated Node #0,1,1: 59:[88, 103] Operation: 79+24=103 Exploring Operation: 88+24=112, Resulting Numbers: [79, 112] Generated Node #0,1,2: 59:[79, 112] Operation: 88+24=112 Exploring Operation: 88-24=64, Resulting Numbers: [79, 64] Generated Node #0,1,3: 59:[79, 64] Operation: 88-24=64 Exploring Operation: 88-79=9, Resulting Numbers: [24, 9] Generated Node #0,1,4: 59:[24, 9] Operation: 88-79=9 Moving to Node #0,3 Current State: 59:[6, 88, 61], Operations: ['79-18=61'] Exploring Operation: 88-6=82, Resulting Numbers: [61, 82] Generated Node #0,3,0: 59:[61, 82] Operation: 88-6=82 Exploring Operation: 88-61=27, Resulting Numbers: [6, 27] Generated Node #0,3,1: 59:[6, 27] Operation: 88-61=27 Exploring Operation: 61-6=55, Resulting Numbers: [88, 55] Generated Node #0,3,2: 59:[88, 55] Operation: 61-6=55 Exploring Operation: 6+61=67, Resulting Numbers: [88, 67] Generated Node #0,3,3: 59:[88, 67] Operation: 6+61=67 Exploring Operation: 6+88=94, Resulting Numbers: [61, 94] Generated Node #0,3,4: 59:[61, 94] Operation: 6+88=94 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[61, 82], Operations: ['79-18=61', '88-6=82'] Exploring Operation: 61*82=5002, Resulting Numbers: [5002] 5002,59 unequal: No Solution Exploring Operation: 61+82=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[88, 55], Operations: ['79-18=61', '61-6=55'] Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,59 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[88, 67], Operations: ['79-18=61', '6+61=67'] Exploring Operation: 88-67=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 88*67=5896, Resulting Numbers: [5896] 5896,59 unequal: No Solution Exploring Operation: 88+67=155, Resulting Numbers: [155] 155,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 59:[61, 94], Operations: ['79-18=61', '6+88=94'] Exploring Operation: 94-61=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 61+94=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 61*94=5734, Resulting Numbers: [5734] 5734,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[6, 27], Operations: ['79-18=61', '88-61=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,59 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 59:[79, 64], Operations: ['6+18=24', '88-24=64'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[88, 55], Operations: ['6+18=24', '79-24=55'] Exploring Operation: 88-55=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 88+55=143, Resulting Numbers: [143] 143,59 unequal: No Solution Exploring Operation: 88*55=4840, Resulting Numbers: [4840] 4840,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[88, 103], Operations: ['6+18=24', '79+24=103'] Exploring Operation: 88+103=191, Resulting Numbers: [191] 191,59 unequal: No Solution Exploring Operation: 88*103=9064, Resulting Numbers: [9064] 9064,59 unequal: No Solution Exploring Operation: 103-88=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[79, 112], Operations: ['6+18=24', '88+24=112'] Exploring Operation: 79*112=8848, Resulting Numbers: [8848] 8848,59 unequal: No Solution Exploring Operation: 112-79=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 79+112=191, Resulting Numbers: [191] 191,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[24, 9], Operations: ['6+18=24', '88-79=9'] Exploring Operation: 24*9=216, Resulting Numbers: [216] 216,59 unequal: No Solution Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,59 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 2, 25, 49, 14 ]
12
[ "25-2=23", "49-14=35", "35-23=12" ]
Current State: 12:[2, 25, 49, 14], Operations: [] Exploring Operation: 25-2=23, Resulting Numbers: [49, 14, 23] Generated Node #2: [49, 14, 23] from Operation: 25-2=23 Current State: 12:[49, 14, 23], Operations: ['25-2=23'] Exploring Operation: 49-14=35, Resulting Numbers: [23, 35] Generated Node #3: [23, 35] from Operation: 49-14=35 Current State: 12:[23, 35], Operations: ['25-2=23', '49-14=35'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[2, 25, 49, 14], Operations: [] Exploring Operation: 49-14=35, Resulting Numbers: [2, 25, 35] Generated Node #0,0: 12:[2, 25, 35] Operation: 49-14=35 Exploring Operation: 49-25=24, Resulting Numbers: [2, 14, 24] Generated Node #0,1: 12:[2, 14, 24] Operation: 49-25=24 Moving to Node #0,1 Current State: 12:[2, 14, 24], Operations: ['49-25=24'] Exploring Operation: 24-14=10, Resulting Numbers: [2, 10] Generated Node #0,1,0: 12:[2, 10] Operation: 24-14=10 Exploring Operation: 24/2=12, Resulting Numbers: [14, 12] Generated Node #0,1,1: 12:[14, 12] Operation: 24/2=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[2, 10], Operations: ['49-25=24', '24-14=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[2, 25, 49, 14], Operations: [] Exploring Operation: 49-25=24, Resulting Numbers: [2, 14, 24] Generated Node #0,1: 12:[2, 14, 24] Operation: 49-25=24 Moving to Node #0,1 Current State: 12:[2, 14, 24], Operations: ['49-25=24'] Exploring Operation: 24-14=10, Resulting Numbers: [2, 10] Generated Node #0,1,0: 12:[2, 10] Operation: 24-14=10 Moving to Node #0,1,0 Current State: 12:[2, 10], Operations: ['49-25=24', '24-14=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 86, 34, 8, 99 ]
29
[ "86+34=120", "99-8=91", "120-91=29" ]
Current State: 29:[86, 34, 8, 99], Operations: [] Exploring Operation: 86+34=120, Resulting Numbers: [8, 99, 120] Generated Node #2: [8, 99, 120] from Operation: 86+34=120 Current State: 29:[8, 99, 120], Operations: ['86+34=120'] Exploring Operation: 99-8=91, Resulting Numbers: [120, 91] Generated Node #3: [120, 91] from Operation: 99-8=91 Current State: 29:[120, 91], Operations: ['86+34=120', '99-8=91'] Exploring Operation: 120-91=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[86, 34, 8, 99], Operations: [] Exploring Operation: 99-86=13, Resulting Numbers: [34, 8, 13] Generated Node #0,0: 29:[34, 8, 13] Operation: 99-86=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[34, 8, 13], Operations: ['99-86=13'] Exploring Operation: 8+13=21, Resulting Numbers: [34, 21] Generated Node #0,0,0: 29:[34, 21] Operation: 8+13=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[34, 21], Operations: ['99-86=13', '8+13=21'] Exploring Operation: 34-21=13, Resulting Numbers: [13] 13,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 54, 2, 91, 55 ]
72
[ "54*2=108", "91-55=36", "108-36=72" ]
Current State: 72:[54, 2, 91, 55], Operations: [] Exploring Operation: 54*2=108, Resulting Numbers: [91, 55, 108] Generated Node #2: [91, 55, 108] from Operation: 54*2=108 Current State: 72:[91, 55, 108], Operations: ['54*2=108'] Exploring Operation: 91-55=36, Resulting Numbers: [108, 36] Generated Node #3: [108, 36] from Operation: 91-55=36 Current State: 72:[108, 36], Operations: ['54*2=108', '91-55=36'] Exploring Operation: 108-36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[54, 2, 91, 55], Operations: [] Exploring Operation: 91-54=37, Resulting Numbers: [2, 55, 37] Generated Node #0,0: 72:[2, 55, 37] Operation: 91-54=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[2, 55, 37], Operations: ['91-54=37'] Exploring Operation: 55-37=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 72:[2, 18] Operation: 55-37=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[2, 18], Operations: ['91-54=37', '55-37=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 52, 31, 9, 4 ]
96
[ "52+31=83", "9+4=13", "83+13=96" ]
Current State: 96:[52, 31, 9, 4], Operations: [] Exploring Operation: 52+31=83, Resulting Numbers: [9, 4, 83] Generated Node #2: [9, 4, 83] from Operation: 52+31=83 Current State: 96:[9, 4, 83], Operations: ['52+31=83'] Exploring Operation: 9+4=13, Resulting Numbers: [83, 13] Generated Node #3: [83, 13] from Operation: 9+4=13 Current State: 96:[83, 13], Operations: ['52+31=83', '9+4=13'] Exploring Operation: 83+13=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[52, 31, 9, 4], Operations: [] Exploring Operation: 52/4=13, Resulting Numbers: [31, 9, 13] Generated Node #0,0: 96:[31, 9, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [31, 9, 48] Generated Node #0,1: 96:[31, 9, 48] Operation: 52-4=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[31, 9, 48], Operations: ['52-4=48'] Exploring Operation: 48-31=17, Resulting Numbers: [9, 17] Generated Node #0,1,0: 96:[9, 17] Operation: 48-31=17 Exploring Operation: 31-9=22, Resulting Numbers: [48, 22] Generated Node #0,1,1: 96:[48, 22] Operation: 31-9=22 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[9, 17], Operations: ['52-4=48', '48-31=17'] Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,96 unequal: No Solution Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,96 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, 22], Operations: ['52-4=48', '31-9=22'] Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,96 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 #0,0 Current State: 96:[31, 9, 13], Operations: ['52/4=13'] Exploring Operation: 13-9=4, Resulting Numbers: [31, 4] Generated Node #0,0,0: 96:[31, 4] Operation: 13-9=4 Exploring Operation: 31-9=22, Resulting Numbers: [13, 22] Generated Node #0,0,1: 96:[13, 22] Operation: 31-9=22 Moving to Node #0,0,0 Current State: 96:[31, 4], Operations: ['52/4=13', '13-9=4'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,96 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[13, 22], Operations: ['52/4=13', '31-9=22'] Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,96 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
[ 41, 47, 61, 42 ]
13
[ "47-41=6", "61-42=19", "19-6=13" ]
Current State: 13:[41, 47, 61, 42], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [61, 42, 6] Generated Node #2: [61, 42, 6] from Operation: 47-41=6 Current State: 13:[61, 42, 6], Operations: ['47-41=6'] Exploring Operation: 61-42=19, Resulting Numbers: [6, 19] Generated Node #3: [6, 19] from Operation: 61-42=19 Current State: 13:[6, 19], Operations: ['47-41=6', '61-42=19'] Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[41, 47, 61, 42], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [41, 42, 14] Generated Node #0,0: 13:[41, 42, 14] Operation: 61-47=14 Exploring Operation: 61-42=19, Resulting Numbers: [41, 47, 19] Generated Node #0,1: 13:[41, 47, 19] Operation: 61-42=19 Moving to Node #0,0 Current State: 13:[41, 42, 14], Operations: ['61-47=14'] Exploring Operation: 42-41=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 13:[14, 1] Operation: 42-41=1 Exploring Operation: 42/14=3, Resulting Numbers: [41, 3] Generated Node #0,0,1: 13:[41, 3] Operation: 42/14=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[14, 1], Operations: ['61-47=14', '42-41=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[41, 47, 61, 42], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [41, 42, 14] Generated Node #0,0: 13:[41, 42, 14] Operation: 61-47=14 Moving to Node #0,0 Current State: 13:[41, 42, 14], Operations: ['61-47=14'] Exploring Operation: 42-41=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 13:[14, 1] Operation: 42-41=1 Moving to Node #0,0,0 Current State: 13:[14, 1], Operations: ['61-47=14', '42-41=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 94, 62, 94, 98 ]
36
[ "94+62=156", "94+98=192", "192-156=36" ]
Current State: 36:[94, 62, 94, 98], Operations: [] Exploring Operation: 94+62=156, Resulting Numbers: [98, 156] Generated Node #2: [98, 156] from Operation: 94+62=156 Current State: 36:[98, 156], Operations: ['94+62=156'] Exploring Operation: 94+98=192, Resulting Numbers: [156, 192] Generated Node #3: [156, 192] from Operation: 94+98=192 Current State: 36:[156, 192], Operations: ['94+62=156', '94+98=192'] Exploring Operation: 192-156=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[94, 62, 94, 98], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [94, 62, 4] Generated Node #0,0: 36:[94, 62, 4] Operation: 98-94=4 Exploring Operation: 98-94=4, Resulting Numbers: [62, 94, 4] Generated Node #0,1: 36:[62, 94, 4] Operation: 98-94=4 Exploring Operation: 94-94=0, Resulting Numbers: [62, 98, 0] Generated Node #0,2: 36:[62, 98, 0] Operation: 94-94=0 Exploring Operation: 98-62=36, Resulting Numbers: [94, 94, 36] Generated Node #0,3: 36:[94, 94, 36] Operation: 98-62=36 Exploring Operation: 94/94=1, Resulting Numbers: [62, 98, 1] Generated Node #0,4: 36:[62, 98, 1] Operation: 94/94=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[94, 62, 4], Operations: ['98-94=4'] Exploring Operation: 94+4=98, Resulting Numbers: [62, 98] Generated Node #0,0,0: 36:[62, 98] Operation: 94+4=98 Exploring Operation: 62-4=58, Resulting Numbers: [94, 58] Generated Node #0,0,1: 36:[94, 58] Operation: 62-4=58 Exploring Operation: 94-62=32, Resulting Numbers: [4, 32] Generated Node #0,0,2: 36:[4, 32] Operation: 94-62=32 Exploring Operation: 94-4=90, Resulting Numbers: [62, 90] Generated Node #0,0,3: 36:[62, 90] Operation: 94-4=90 Exploring Operation: 62+4=66, Resulting Numbers: [94, 66] Generated Node #0,0,4: 36:[94, 66] Operation: 62+4=66 Moving to Node #0,0,2 Current State: 36:[4, 32], Operations: ['98-94=4', '94-62=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,36 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[94, 62, 94, 98], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [94, 62, 4] Generated Node #0,0: 36:[94, 62, 4] Operation: 98-94=4 Moving to Node #0,0 Current State: 36:[94, 62, 4], Operations: ['98-94=4'] Exploring Operation: 94-62=32, Resulting Numbers: [4, 32] Generated Node #0,0,2: 36:[4, 32] Operation: 94-62=32 Moving to Node #0,0,2 Current State: 36:[4, 32], Operations: ['98-94=4', '94-62=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 83, 30, 73, 2 ]
40
[ "83-30=53", "73-53=20", "2*20=40" ]
Current State: 40:[83, 30, 73, 2], Operations: [] Exploring Operation: 83-30=53, Resulting Numbers: [73, 2, 53] Generated Node #2: [73, 2, 53] from Operation: 83-30=53 Current State: 40:[73, 2, 53], Operations: ['83-30=53'] Exploring Operation: 73-53=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 73-53=20 Current State: 40:[2, 20], Operations: ['83-30=53', '73-53=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[83, 30, 73, 2], Operations: [] Exploring Operation: 83-30=53, Resulting Numbers: [73, 2, 53] Generated Node #0,0: 40:[73, 2, 53] Operation: 83-30=53 Exploring Operation: 73-30=43, Resulting Numbers: [83, 2, 43] Generated Node #0,1: 40:[83, 2, 43] Operation: 73-30=43 Exploring Operation: 83-73=10, Resulting Numbers: [30, 2, 10] Generated Node #0,2: 40:[30, 2, 10] Operation: 83-73=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[30, 2, 10], Operations: ['83-73=10'] Exploring Operation: 30/10=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 40:[2, 3] Operation: 30/10=3 Exploring Operation: 30-10=20, Resulting Numbers: [2, 20] Generated Node #0,2,1: 40:[2, 20] Operation: 30-10=20 Exploring Operation: 30+10=40, Resulting Numbers: [2, 40] Generated Node #0,2,2: 40:[2, 40] Operation: 30+10=40 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[2, 20], Operations: ['83-73=10', '30-10=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[83, 30, 73, 2], Operations: [] Exploring Operation: 83-73=10, Resulting Numbers: [30, 2, 10] Generated Node #0,2: 40:[30, 2, 10] Operation: 83-73=10 Moving to Node #0,2 Current State: 40:[30, 2, 10], Operations: ['83-73=10'] Exploring Operation: 30-10=20, Resulting Numbers: [2, 20] Generated Node #0,2,1: 40:[2, 20] Operation: 30-10=20 Moving to Node #0,2,1 Current State: 40:[2, 20], Operations: ['83-73=10', '30-10=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 55, 33, 70, 54 ]
72
[ "55+33=88", "70-54=16", "88-16=72" ]
Current State: 72:[55, 33, 70, 54], Operations: [] Exploring Operation: 55+33=88, Resulting Numbers: [70, 54, 88] Generated Node #2: [70, 54, 88] from Operation: 55+33=88 Current State: 72:[70, 54, 88], Operations: ['55+33=88'] Exploring Operation: 70-54=16, Resulting Numbers: [88, 16] Generated Node #3: [88, 16] from Operation: 70-54=16 Current State: 72:[88, 16], Operations: ['55+33=88', '70-54=16'] Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[55, 33, 70, 54], Operations: [] Exploring Operation: 55-54=1, Resulting Numbers: [33, 70, 1] Generated Node #0,0: 72:[33, 70, 1] Operation: 55-54=1 Exploring Operation: 54-33=21, Resulting Numbers: [55, 70, 21] Generated Node #0,1: 72:[55, 70, 21] Operation: 54-33=21 Exploring Operation: 55-33=22, Resulting Numbers: [70, 54, 22] Generated Node #0,2: 72:[70, 54, 22] Operation: 55-33=22 Exploring Operation: 70-54=16, Resulting Numbers: [55, 33, 16] Generated Node #0,3: 72:[55, 33, 16] Operation: 70-54=16 Moving to Node #0,0 Current State: 72:[33, 70, 1], Operations: ['55-54=1'] Exploring Operation: 33+1=34, Resulting Numbers: [70, 34] Generated Node #0,0,0: 72:[70, 34] Operation: 33+1=34 Exploring Operation: 70-33=37, Resulting Numbers: [1, 37] Generated Node #0,0,1: 72:[1, 37] Operation: 70-33=37 Exploring Operation: 33*1=33, Resulting Numbers: [70, 33] Generated Node #0,0,2: 72:[70, 33] Operation: 33*1=33 Exploring Operation: 70+1=71, Resulting Numbers: [33, 71] Generated Node #0,0,3: 72:[33, 71] Operation: 70+1=71 Moving to Node #0,2 Current State: 72:[70, 54, 22], Operations: ['55-33=22'] Exploring Operation: 54+22=76, Resulting Numbers: [70, 76] Generated Node #0,2,0: 72:[70, 76] Operation: 54+22=76 Exploring Operation: 54-22=32, Resulting Numbers: [70, 32] Generated Node #0,2,1: 72:[70, 32] Operation: 54-22=32 Exploring Operation: 70-54=16, Resulting Numbers: [22, 16] Generated Node #0,2,2: 72:[22, 16] Operation: 70-54=16 Exploring Operation: 70-22=48, Resulting Numbers: [54, 48] Generated Node #0,2,3: 72:[54, 48] Operation: 70-22=48 Moving to Node #0,1 Current State: 72:[55, 70, 21], Operations: ['54-33=21'] Exploring Operation: 55-21=34, Resulting Numbers: [70, 34] Generated Node #0,1,0: 72:[70, 34] Operation: 55-21=34 Exploring Operation: 55+21=76, Resulting Numbers: [70, 76] Generated Node #0,1,1: 72:[70, 76] Operation: 55+21=76 Exploring Operation: 70-21=49, Resulting Numbers: [55, 49] Generated Node #0,1,2: 72:[55, 49] Operation: 70-21=49 Exploring Operation: 70-55=15, Resulting Numbers: [21, 15] Generated Node #0,1,3: 72:[21, 15] Operation: 70-55=15 Moving to Node #0,3 Current State: 72:[55, 33, 16], Operations: ['70-54=16'] Exploring Operation: 55-33=22, Resulting Numbers: [16, 22] Generated Node #0,3,0: 72:[16, 22] Operation: 55-33=22 Exploring Operation: 55+16=71, Resulting Numbers: [33, 71] Generated Node #0,3,1: 72:[33, 71] Operation: 55+16=71 Exploring Operation: 55+33=88, Resulting Numbers: [16, 88] Generated Node #0,3,2: 72:[16, 88] Operation: 55+33=88 Exploring Operation: 55-16=39, Resulting Numbers: [33, 39] Generated Node #0,3,3: 72:[33, 39] Operation: 55-16=39 Moving to Node #0,0,1 Current State: 72:[1, 37], Operations: ['55-54=1', '70-33=37'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[33, 71], Operations: ['55-54=1', '70+1=71'] Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,72 unequal: No Solution Moving to Node #0,3,1 Current State: 72:[33, 71], Operations: ['70-54=16', '55+16=71'] Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[16, 22], Operations: ['70-54=16', '55-33=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[70, 34], Operations: ['55-54=1', '33+1=34'] Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,72 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[22, 16], Operations: ['55-33=22', '70-54=16'] Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,72 unequal: No Solution Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[70, 34], Operations: ['54-33=21', '55-21=34'] Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,72 unequal: No Solution Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,72 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[70, 33], Operations: ['55-54=1', '33*1=33'] Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 70+33=103, Resulting Numbers: [103] 103,72 unequal: No Solution Exploring Operation: 70*33=2310, Resulting Numbers: [2310] 2310,72 unequal: No Solution Moving to Node #0,3,3 Current State: 72:[33, 39], Operations: ['70-54=16', '55-16=39'] Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,72 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[55, 33, 70, 54], Operations: [] Exploring Operation: 70-54=16, Resulting Numbers: [55, 33, 16] Generated Node #0,3: 72:[55, 33, 16] Operation: 70-54=16 Moving to Node #0,3 Current State: 72:[55, 33, 16], Operations: ['70-54=16'] Exploring Operation: 55-16=39, Resulting Numbers: [33, 39] Generated Node #0,3,3: 72:[33, 39] Operation: 55-16=39 Moving to Node #0,3,3 Current State: 72:[33, 39], Operations: ['70-54=16', '55-16=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 18, 26, 2, 22 ]
36
[ "26-18=8", "2*22=44", "44-8=36" ]
Current State: 36:[18, 26, 2, 22], Operations: [] Exploring Operation: 26-18=8, Resulting Numbers: [2, 22, 8] Generated Node #2: [2, 22, 8] from Operation: 26-18=8 Current State: 36:[2, 22, 8], Operations: ['26-18=8'] Exploring Operation: 2*22=44, Resulting Numbers: [8, 44] Generated Node #3: [8, 44] from Operation: 2*22=44 Current State: 36:[8, 44], Operations: ['26-18=8', '2*22=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[18, 26, 2, 22], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [18, 2, 4] Generated Node #0,0: 36:[18, 2, 4] Operation: 26-22=4 Exploring Operation: 26/2=13, Resulting Numbers: [18, 22, 13] Generated Node #0,1: 36:[18, 22, 13] Operation: 26/2=13 Exploring Operation: 22-18=4, Resulting Numbers: [26, 2, 4] Generated Node #0,2: 36:[26, 2, 4] Operation: 22-18=4 Exploring Operation: 26-18=8, Resulting Numbers: [2, 22, 8] Generated Node #0,3: 36:[2, 22, 8] Operation: 26-18=8 Moving to Node #0,0 Current State: 36:[18, 2, 4], Operations: ['26-22=4'] Exploring Operation: 18*2=36, Resulting Numbers: [4, 36] Generated Node #0,0,0: 36:[4, 36] Operation: 18*2=36 Exploring Operation: 18/2=9, Resulting Numbers: [4, 9] Generated Node #0,0,1: 36:[4, 9] Operation: 18/2=9 Exploring Operation: 2+4=6, Resulting Numbers: [18, 6] Generated Node #0,0,2: 36:[18, 6] Operation: 2+4=6 Exploring Operation: 4-2=2, Resulting Numbers: [18, 2] Generated Node #0,0,3: 36:[18, 2] Operation: 4-2=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[4, 36], Operations: ['26-22=4', '18*2=36'] Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,36 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,36 unequal: No Solution Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,36 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[4, 9], Operations: ['26-22=4', '18/2=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[18, 26, 2, 22], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [18, 2, 4] Generated Node #0,0: 36:[18, 2, 4] Operation: 26-22=4 Moving to Node #0,0 Current State: 36:[18, 2, 4], Operations: ['26-22=4'] Exploring Operation: 18/2=9, Resulting Numbers: [4, 9] Generated Node #0,0,1: 36:[4, 9] Operation: 18/2=9 Moving to Node #0,0,1 Current State: 36:[4, 9], Operations: ['26-22=4', '18/2=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 4, 36, 86, 84 ]
20
[ "4+36=40", "86-84=2", "40/2=20" ]
Current State: 20:[4, 36, 86, 84], Operations: [] Exploring Operation: 4+36=40, Resulting Numbers: [86, 84, 40] Generated Node #2: [86, 84, 40] from Operation: 4+36=40 Current State: 20:[86, 84, 40], Operations: ['4+36=40'] Exploring Operation: 86-84=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 86-84=2 Current State: 20:[40, 2], Operations: ['4+36=40', '86-84=2'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[4, 36, 86, 84], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [36, 86, 21] Generated Node #0,0: 20:[36, 86, 21] Operation: 84/4=21 Exploring Operation: 86-84=2, Resulting Numbers: [4, 36, 2] Generated Node #0,1: 20:[4, 36, 2] Operation: 86-84=2 Exploring Operation: 84-36=48, Resulting Numbers: [4, 86, 48] Generated Node #0,2: 20:[4, 86, 48] Operation: 84-36=48 Exploring Operation: 86-36=50, Resulting Numbers: [4, 84, 50] Generated Node #0,3: 20:[4, 84, 50] Operation: 86-36=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[4, 36, 2], Operations: ['86-84=2'] Exploring Operation: 36-4=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 20:[2, 32] Operation: 36-4=32 Exploring Operation: 36-2=34, Resulting Numbers: [4, 34] Generated Node #0,1,1: 20:[4, 34] Operation: 36-2=34 Exploring Operation: 36/4=9, Resulting Numbers: [2, 9] Generated Node #0,1,2: 20:[2, 9] Operation: 36/4=9 Exploring Operation: 36/2=18, Resulting Numbers: [4, 18] Generated Node #0,1,3: 20:[4, 18] Operation: 36/2=18 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 20:[2, 9], Operations: ['86-84=2', '36/4=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,20 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 20:[4, 18], Operations: ['86-84=2', '36/2=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,20 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[2, 32], Operations: ['86-84=2', '36-4=32'] Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,20 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[4, 34], Operations: ['86-84=2', '36-2=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,20 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[36, 86, 21], Operations: ['84/4=21'] Exploring Operation: 86-36=50, Resulting Numbers: [21, 50] Generated Node #0,0,0: 20:[21, 50] Operation: 86-36=50 Exploring Operation: 86-21=65, Resulting Numbers: [36, 65] Generated Node #0,0,1: 20:[36, 65] Operation: 86-21=65 Exploring Operation: 36+86=122, Resulting Numbers: [21, 122] Generated Node #0,0,2: 20:[21, 122] Operation: 36+86=122 Exploring Operation: 36-21=15, Resulting Numbers: [86, 15] Generated Node #0,0,3: 20:[86, 15] Operation: 36-21=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[21, 50], Operations: ['84/4=21', '86-36=50'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 21+50=71, Resulting Numbers: [71] 71,20 unequal: No Solution Exploring Operation: 21*50=1050, Resulting Numbers: [1050] 1050,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[36, 65], Operations: ['84/4=21', '86-21=65'] Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,20 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 20:[86, 15], Operations: ['84/4=21', '36-21=15'] Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,20 unequal: No Solution Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,20 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 20:[21, 122], Operations: ['84/4=21', '36+86=122'] Exploring Operation: 21*122=2562, Resulting Numbers: [2562] 2562,20 unequal: No Solution Exploring Operation: 122-21=101, Resulting Numbers: [101] 101,20 unequal: No Solution Exploring Operation: 21+122=143, Resulting Numbers: [143] 143,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 20:[4, 86, 48], Operations: ['84-36=48'] Exploring Operation: 86-48=38, Resulting Numbers: [4, 38] Generated Node #0,2,0: 20:[4, 38] Operation: 86-48=38 Exploring Operation: 86-4=82, Resulting Numbers: [48, 82] Generated Node #0,2,1: 20:[48, 82] Operation: 86-4=82 Exploring Operation: 48-4=44, Resulting Numbers: [86, 44] Generated Node #0,2,2: 20:[86, 44] Operation: 48-4=44 Exploring Operation: 48/4=12, Resulting Numbers: [86, 12] Generated Node #0,2,3: 20:[86, 12] Operation: 48/4=12 Moving to Node #0,2,0 Current State: 20:[4, 38], Operations: ['84-36=48', '86-48=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,20 unequal: No Solution Moving to Node #0,2,3 Current State: 20:[86, 12], Operations: ['84-36=48', '48/4=12'] Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,20 unequal: No Solution Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,20 unequal: No Solution Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[86, 44], Operations: ['84-36=48', '48-4=44'] Exploring Operation: 86+44=130, Resulting Numbers: [130] 130,20 unequal: No Solution Exploring Operation: 86-44=42, Resulting Numbers: [42] 42,20 unequal: No Solution Exploring Operation: 86*44=3784, Resulting Numbers: [3784] 3784,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[48, 82], Operations: ['84-36=48', '86-4=82'] Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 48*82=3936, Resulting Numbers: [3936] 3936,20 unequal: No Solution Exploring Operation: 48+82=130, Resulting Numbers: [130] 130,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[4, 84, 50], Operations: ['86-36=50'] Exploring Operation: 84-50=34, Resulting Numbers: [4, 34] Generated Node #0,3,0: 20:[4, 34] Operation: 84-50=34 Exploring Operation: 84/4=21, Resulting Numbers: [50, 21] Generated Node #0,3,1: 20:[50, 21] Operation: 84/4=21 Exploring Operation: 50-4=46, Resulting Numbers: [84, 46] Generated Node #0,3,2: 20:[84, 46] Operation: 50-4=46 Exploring Operation: 84-4=80, Resulting Numbers: [50, 80] Generated Node #0,3,3: 20:[50, 80] Operation: 84-4=80 Moving to Node #0,3,0 Current State: 20:[4, 34], Operations: ['86-36=50', '84-50=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,20 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,20 unequal: No Solution Moving to Node #0,3,1 Current State: 20:[50, 21], Operations: ['86-36=50', '84/4=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,20 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,20 unequal: No Solution Exploring Operation: 50*21=1050, Resulting Numbers: [1050] 1050,20 unequal: No Solution Moving to Node #0,3,3 Current State: 20:[50, 80], Operations: ['86-36=50', '84-4=80'] Exploring Operation: 50+80=130, Resulting Numbers: [130] 130,20 unequal: No Solution Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 50*80=4000, Resulting Numbers: [4000] 4000,20 unequal: No Solution Moving to Node #0,3,2 Current State: 20:[84, 46], Operations: ['86-36=50', '50-4=46'] Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,20 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,20 unequal: No Solution Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 6, 50, 15, 50 ]
22
[ "6+15=21", "50/50=1", "21+1=22" ]
Current State: 22:[6, 50, 15, 50], Operations: [] Exploring Operation: 6+15=21, Resulting Numbers: [50, 50, 21] Generated Node #2: [50, 50, 21] from Operation: 6+15=21 Current State: 22:[50, 50, 21], Operations: ['6+15=21'] Exploring Operation: 50/50=1, Resulting Numbers: [21, 1] Generated Node #3: [21, 1] from Operation: 50/50=1 Current State: 22:[21, 1], Operations: ['6+15=21', '50/50=1'] Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[6, 50, 15, 50], Operations: [] Exploring Operation: 50-50=0, Resulting Numbers: [6, 15, 0] Generated Node #0,0: 22:[6, 15, 0] Operation: 50-50=0 Exploring Operation: 50/50=1, Resulting Numbers: [6, 15, 1] Generated Node #0,1: 22:[6, 15, 1] Operation: 50/50=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[6, 15, 1], Operations: ['50/50=1'] Exploring Operation: 6+15=21, Resulting Numbers: [1, 21] Generated Node #0,1,0: 22:[1, 21] Operation: 6+15=21 Exploring Operation: 15-6=9, Resulting Numbers: [1, 9] Generated Node #0,1,1: 22:[1, 9] Operation: 15-6=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[1, 21], Operations: ['50/50=1', '6+15=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[6, 50, 15, 50], Operations: [] Exploring Operation: 50/50=1, Resulting Numbers: [6, 15, 1] Generated Node #0,1: 22:[6, 15, 1] Operation: 50/50=1 Moving to Node #0,1 Current State: 22:[6, 15, 1], Operations: ['50/50=1'] Exploring Operation: 6+15=21, Resulting Numbers: [1, 21] Generated Node #0,1,0: 22:[1, 21] Operation: 6+15=21 Moving to Node #0,1,0 Current State: 22:[1, 21], Operations: ['50/50=1', '6+15=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 98, 74, 93, 90 ]
92
[ "98-93=5", "90/5=18", "74+18=92" ]
Current State: 92:[98, 74, 93, 90], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [74, 90, 5] Generated Node #2: [74, 90, 5] from Operation: 98-93=5 Current State: 92:[74, 90, 5], Operations: ['98-93=5'] Exploring Operation: 90/5=18, Resulting Numbers: [74, 18] Generated Node #3: [74, 18] from Operation: 90/5=18 Current State: 92:[74, 18], Operations: ['98-93=5', '90/5=18'] Exploring Operation: 74+18=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[98, 74, 93, 90], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [98, 90, 19] Generated Node #0,0: 92:[98, 90, 19] Operation: 93-74=19 Exploring Operation: 98-74=24, Resulting Numbers: [93, 90, 24] Generated Node #0,1: 92:[93, 90, 24] Operation: 98-74=24 Moving to Node #0,1 Current State: 92:[93, 90, 24], Operations: ['98-74=24'] Exploring Operation: 93-90=3, Resulting Numbers: [24, 3] Generated Node #0,1,0: 92:[24, 3] Operation: 93-90=3 Exploring Operation: 90-24=66, Resulting Numbers: [93, 66] Generated Node #0,1,1: 92:[93, 66] Operation: 90-24=66 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[24, 3], Operations: ['98-74=24', '93-90=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[93, 66], Operations: ['98-74=24', '90-24=66'] Exploring Operation: 93-66=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 93+66=159, Resulting Numbers: [159] 159,92 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: 92:[98, 90, 19], Operations: ['93-74=19'] Exploring Operation: 98-19=79, Resulting Numbers: [90, 79] Generated Node #0,0,0: 92:[90, 79] Operation: 98-19=79 Exploring Operation: 98-90=8, Resulting Numbers: [19, 8] Generated Node #0,0,1: 92:[19, 8] Operation: 98-90=8 Moving to Node #0,0,1 Current State: 92:[19, 8], Operations: ['93-74=19', '98-90=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[90, 79], Operations: ['93-74=19', '98-19=79'] Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 90+79=169, Resulting Numbers: [169] 169,92 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 87, 76, 87, 54 ]
76
[ "87-87=0", "54*0=0", "76+0=76" ]
Current State: 76:[87, 76, 87, 54], Operations: [] Exploring Operation: 87-87=0, Resulting Numbers: [76, 54, 0] Generated Node #2: [76, 54, 0] from Operation: 87-87=0 Current State: 76:[76, 54, 0], Operations: ['87-87=0'] Exploring Operation: 54*0=0, Resulting Numbers: [76, 0] Generated Node #3: [76, 0] from Operation: 54*0=0 Current State: 76:[76, 0], Operations: ['87-87=0', '54*0=0'] Exploring Operation: 76+0=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[87, 76, 87, 54], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [76, 87, 33] Generated Node #0,0: 76:[76, 87, 33] Operation: 87-54=33 Moving to Node #0,0 Current State: 76:[76, 87, 33], Operations: ['87-54=33'] Exploring Operation: 87-76=11, Resulting Numbers: [33, 11] Generated Node #0,0,0: 76:[33, 11] Operation: 87-76=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[33, 11], Operations: ['87-54=33', '87-76=11'] Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,76 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
[ 8, 83, 52, 43 ]
82
[ "8+83=91", "52-43=9", "91-9=82" ]
Current State: 82:[8, 83, 52, 43], Operations: [] Exploring Operation: 8+83=91, Resulting Numbers: [52, 43, 91] Generated Node #2: [52, 43, 91] from Operation: 8+83=91 Current State: 82:[52, 43, 91], Operations: ['8+83=91'] Exploring Operation: 52-43=9, Resulting Numbers: [91, 9] Generated Node #3: [91, 9] from Operation: 52-43=9 Current State: 82:[91, 9], Operations: ['8+83=91', '52-43=9'] Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[8, 83, 52, 43], Operations: [] Exploring Operation: 52-8=44, Resulting Numbers: [83, 43, 44] Generated Node #0,0: 82:[83, 43, 44] Operation: 52-8=44 Moving to Node #0,0 Current State: 82:[83, 43, 44], Operations: ['52-8=44'] Exploring Operation: 44-43=1, Resulting Numbers: [83, 1] Generated Node #0,0,0: 82:[83, 1] Operation: 44-43=1 Moving to Node #0,0,0 Current State: 82:[83, 1], Operations: ['52-8=44', '44-43=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[8, 83, 52, 43], Operations: [] Exploring Operation: 52-8=44, Resulting Numbers: [83, 43, 44] Generated Node #0,0: 82:[83, 43, 44] Operation: 52-8=44 Moving to Node #0,0 Current State: 82:[83, 43, 44], Operations: ['52-8=44'] Exploring Operation: 44-43=1, Resulting Numbers: [83, 1] Generated Node #0,0,0: 82:[83, 1] Operation: 44-43=1 Moving to Node #0,0,0 Current State: 82:[83, 1], Operations: ['52-8=44', '44-43=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 48, 2, 34, 60 ]
85
[ "48/2=24", "34*60=2040", "2040/24=85" ]
Current State: 85:[48, 2, 34, 60], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [34, 60, 24] Generated Node #2: [34, 60, 24] from Operation: 48/2=24 Current State: 85:[34, 60, 24], Operations: ['48/2=24'] Exploring Operation: 34*60=2040, Resulting Numbers: [24, 2040] Generated Node #3: [24, 2040] from Operation: 34*60=2040 Current State: 85:[24, 2040], Operations: ['48/2=24', '34*60=2040'] Exploring Operation: 2040/24=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[48, 2, 34, 60], Operations: [] Exploring Operation: 48-34=14, Resulting Numbers: [2, 60, 14] Generated Node #0,0: 85:[2, 60, 14] Operation: 48-34=14 Exploring Operation: 60-48=12, Resulting Numbers: [2, 34, 12] Generated Node #0,1: 85:[2, 34, 12] Operation: 60-48=12 Exploring Operation: 48+34=82, Resulting Numbers: [2, 60, 82] Generated Node #0,2: 85:[2, 60, 82] Operation: 48+34=82 Moving to Node #0,1 Current State: 85:[2, 34, 12], Operations: ['60-48=12'] Exploring Operation: 12/2=6, Resulting Numbers: [34, 6] Generated Node #0,1,0: 85:[34, 6] Operation: 12/2=6 Exploring Operation: 34-12=22, Resulting Numbers: [2, 22] Generated Node #0,1,1: 85:[2, 22] Operation: 34-12=22 Exploring Operation: 34/2=17, Resulting Numbers: [12, 17] Generated Node #0,1,2: 85:[12, 17] Operation: 34/2=17 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 85:[12, 17], Operations: ['60-48=12', '34/2=17'] Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,85 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[2, 22], Operations: ['60-48=12', '34-12=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[34, 6], Operations: ['60-48=12', '12/2=6'] Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,85 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,85 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: 85:[2, 60, 14], Operations: ['48-34=14'] Exploring Operation: 60/2=30, Resulting Numbers: [14, 30] Generated Node #0,0,0: 85:[14, 30] Operation: 60/2=30 Exploring Operation: 2+60=62, Resulting Numbers: [14, 62] Generated Node #0,0,1: 85:[14, 62] Operation: 2+60=62 Exploring Operation: 60+14=74, Resulting Numbers: [2, 74] Generated Node #0,0,2: 85:[2, 74] Operation: 60+14=74 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 85:[2, 74], Operations: ['48-34=14', '60+14=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[14, 30], Operations: ['48-34=14', '60/2=30'] Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,85 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,85 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[14, 62], Operations: ['48-34=14', '2+60=62'] Exploring Operation: 14+62=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,85 unequal: No Solution Exploring Operation: 14*62=868, Resulting Numbers: [868] 868,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 85:[2, 60, 82], Operations: ['48+34=82'] Exploring Operation: 82-60=22, Resulting Numbers: [2, 22] Generated Node #0,2,0: 85:[2, 22] Operation: 82-60=22 Exploring Operation: 2+60=62, Resulting Numbers: [82, 62] Generated Node #0,2,1: 85:[82, 62] Operation: 2+60=62 Exploring Operation: 60/2=30, Resulting Numbers: [82, 30] Generated Node #0,2,2: 85:[82, 30] Operation: 60/2=30 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 85:[2, 22], Operations: ['48+34=82', '82-60=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 85:[82, 30], Operations: ['48+34=82', '60/2=30'] Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,85 unequal: No Solution Exploring Operation: 82*30=2460, Resulting Numbers: [2460] 2460,85 unequal: No Solution Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[82, 62], Operations: ['48+34=82', '2+60=62'] Exploring Operation: 82*62=5084, Resulting Numbers: [5084] 5084,85 unequal: No Solution Exploring Operation: 82-62=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 82+62=144, Resulting Numbers: [144] 144,85 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
[ 37, 79, 69, 84 ]
27
[ "79-37=42", "84-69=15", "42-15=27" ]
Current State: 27:[37, 79, 69, 84], Operations: [] Exploring Operation: 79-37=42, Resulting Numbers: [69, 84, 42] Generated Node #2: [69, 84, 42] from Operation: 79-37=42 Current State: 27:[69, 84, 42], Operations: ['79-37=42'] Exploring Operation: 84-69=15, Resulting Numbers: [42, 15] Generated Node #3: [42, 15] from Operation: 84-69=15 Current State: 27:[42, 15], Operations: ['79-37=42', '84-69=15'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[37, 79, 69, 84], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [37, 69, 5] Generated Node #0,0: 27:[37, 69, 5] Operation: 84-79=5 Moving to Node #0,0 Current State: 27:[37, 69, 5], Operations: ['84-79=5'] Exploring Operation: 69-37=32, Resulting Numbers: [5, 32] Generated Node #0,0,0: 27:[5, 32] Operation: 69-37=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[5, 32], Operations: ['84-79=5', '69-37=32'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[37, 79, 69, 84], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [37, 69, 5] Generated Node #0,0: 27:[37, 69, 5] Operation: 84-79=5 Moving to Node #0,0 Current State: 27:[37, 69, 5], Operations: ['84-79=5'] Exploring Operation: 69-37=32, Resulting Numbers: [5, 32] Generated Node #0,0,0: 27:[5, 32] Operation: 69-37=32 Moving to Node #0,0,0 Current State: 27:[5, 32], Operations: ['84-79=5', '69-37=32'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 3, 5, 65, 37 ]
72
[ "65/5=13", "37-13=24", "3*24=72" ]
Current State: 72:[3, 5, 65, 37], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [3, 37, 13] Generated Node #2: [3, 37, 13] from Operation: 65/5=13 Current State: 72:[3, 37, 13], Operations: ['65/5=13'] Exploring Operation: 37-13=24, Resulting Numbers: [3, 24] Generated Node #3: [3, 24] from Operation: 37-13=24 Current State: 72:[3, 24], Operations: ['65/5=13', '37-13=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[3, 5, 65, 37], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [3, 37, 13] Generated Node #0,0: 72:[3, 37, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[3, 37, 13], Operations: ['65/5=13'] Exploring Operation: 37-13=24, Resulting Numbers: [3, 24] Generated Node #0,0,0: 72:[3, 24] Operation: 37-13=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[3, 24], Operations: ['65/5=13', '37-13=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[3, 5, 65, 37], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [3, 37, 13] Generated Node #0,0: 72:[3, 37, 13] Operation: 65/5=13 Moving to Node #0,0 Current State: 72:[3, 37, 13], Operations: ['65/5=13'] Exploring Operation: 37-13=24, Resulting Numbers: [3, 24] Generated Node #0,0,0: 72:[3, 24] Operation: 37-13=24 Moving to Node #0,0,0 Current State: 72:[3, 24], Operations: ['65/5=13', '37-13=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 22, 68, 25, 94 ]
73
[ "68-22=46", "25+94=119", "119-46=73" ]
Current State: 73:[22, 68, 25, 94], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [25, 94, 46] Generated Node #2: [25, 94, 46] from Operation: 68-22=46 Current State: 73:[25, 94, 46], Operations: ['68-22=46'] Exploring Operation: 25+94=119, Resulting Numbers: [46, 119] Generated Node #3: [46, 119] from Operation: 25+94=119 Current State: 73:[46, 119], Operations: ['68-22=46', '25+94=119'] Exploring Operation: 119-46=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[22, 68, 25, 94], Operations: [] Exploring Operation: 94-25=69, Resulting Numbers: [22, 68, 69] Generated Node #0,0: 73:[22, 68, 69] Operation: 94-25=69 Exploring Operation: 94-22=72, Resulting Numbers: [68, 25, 72] Generated Node #0,1: 73:[68, 25, 72] Operation: 94-22=72 Exploring Operation: 22+25=47, Resulting Numbers: [68, 94, 47] Generated Node #0,2: 73:[68, 94, 47] Operation: 22+25=47 Moving to Node #0,2 Current State: 73:[68, 94, 47], Operations: ['22+25=47'] Exploring Operation: 68+47=115, Resulting Numbers: [94, 115] Generated Node #0,2,0: 73:[94, 115] Operation: 68+47=115 Exploring Operation: 94-68=26, Resulting Numbers: [47, 26] Generated Node #0,2,1: 73:[47, 26] Operation: 94-68=26 Exploring Operation: 94-47=47, Resulting Numbers: [68, 47] Generated Node #0,2,2: 73:[68, 47] Operation: 94-47=47 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 73:[68, 47], Operations: ['22+25=47', '94-47=47'] Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 68+47=115, Resulting Numbers: [115] 115,73 unequal: No Solution Exploring Operation: 68*47=3196, Resulting Numbers: [3196] 3196,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 73:[94, 115], Operations: ['22+25=47', '68+47=115'] Exploring Operation: 94*115=10810, Resulting Numbers: [10810] 10810,73 unequal: No Solution Exploring Operation: 115-94=21, Resulting Numbers: [21] 21,73 unequal: No Solution Exploring Operation: 94+115=209, Resulting Numbers: [209] 209,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 73:[47, 26], Operations: ['22+25=47', '94-68=26'] Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,73 unequal: No Solution Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[22, 68, 25, 94], Operations: [] Exploring Operation: 22+25=47, Resulting Numbers: [68, 94, 47] Generated Node #0,2: 73:[68, 94, 47] Operation: 22+25=47 Moving to Node #0,2 Current State: 73:[68, 94, 47], Operations: ['22+25=47'] Exploring Operation: 94-68=26, Resulting Numbers: [47, 26] Generated Node #0,2,1: 73:[47, 26] Operation: 94-68=26 Moving to Node #0,2,1 Current State: 73:[47, 26], Operations: ['22+25=47', '94-68=26'] Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 11, 4, 32, 78 ]
81
[ "11+78=89", "32/4=8", "89-8=81" ]
Current State: 81:[11, 4, 32, 78], Operations: [] Exploring Operation: 11+78=89, Resulting Numbers: [4, 32, 89] Generated Node #2: [4, 32, 89] from Operation: 11+78=89 Current State: 81:[4, 32, 89], Operations: ['11+78=89'] Exploring Operation: 32/4=8, Resulting Numbers: [89, 8] Generated Node #3: [89, 8] from Operation: 32/4=8 Current State: 81:[89, 8], Operations: ['11+78=89', '32/4=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[11, 4, 32, 78], Operations: [] Exploring Operation: 32-4=28, Resulting Numbers: [11, 78, 28] Generated Node #0,0: 81:[11, 78, 28] Operation: 32-4=28 Exploring Operation: 11-4=7, Resulting Numbers: [32, 78, 7] Generated Node #0,1: 81:[32, 78, 7] Operation: 11-4=7 Exploring Operation: 32/4=8, Resulting Numbers: [11, 78, 8] Generated Node #0,2: 81:[11, 78, 8] Operation: 32/4=8 Exploring Operation: 4+78=82, Resulting Numbers: [11, 32, 82] Generated Node #0,3: 81:[11, 32, 82] Operation: 4+78=82 Moving to Node #0,0 Current State: 81:[11, 78, 28], Operations: ['32-4=28'] Exploring Operation: 11+78=89, Resulting Numbers: [28, 89] Generated Node #0,0,0: 81:[28, 89] Operation: 11+78=89 Exploring Operation: 28-11=17, Resulting Numbers: [78, 17] Generated Node #0,0,1: 81:[78, 17] Operation: 28-11=17 Exploring Operation: 78-11=67, Resulting Numbers: [28, 67] Generated Node #0,0,2: 81:[28, 67] Operation: 78-11=67 Exploring Operation: 11+28=39, Resulting Numbers: [78, 39] Generated Node #0,0,3: 81:[78, 39] Operation: 11+28=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[28, 89], Operations: ['32-4=28', '11+78=89'] Exploring Operation: 28*89=2492, Resulting Numbers: [2492] 2492,81 unequal: No Solution Exploring Operation: 28+89=117, Resulting Numbers: [117] 117,81 unequal: No Solution Exploring Operation: 89-28=61, Resulting Numbers: [61] 61,81 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 #0,0,1 Current State: 81:[78, 17], Operations: ['32-4=28', '28-11=17'] Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,81 unequal: No Solution Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 78*17=1326, Resulting Numbers: [1326] 1326,81 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:[28, 67], Operations: ['32-4=28', '78-11=67'] Exploring Operation: 28+67=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 28*67=1876, Resulting Numbers: [1876] 1876,81 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,81 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:[78, 39], Operations: ['32-4=28', '11+28=39'] Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 78+39=117, Resulting Numbers: [117] 117,81 unequal: No Solution Exploring Operation: 78*39=3042, Resulting Numbers: [3042] 3042,81 unequal: No Solution Exploring Operation: 78/39=2, Resulting Numbers: [2] 2,81 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: 81:[11, 78, 8], Operations: ['32/4=8'] Exploring Operation: 78+8=86, Resulting Numbers: [11, 86] Generated Node #0,2,0: 81:[11, 86] Operation: 78+8=86 Exploring Operation: 11*8=88, Resulting Numbers: [78, 88] Generated Node #0,2,1: 81:[78, 88] Operation: 11*8=88 Exploring Operation: 11-8=3, Resulting Numbers: [78, 3] Generated Node #0,2,2: 81:[78, 3] Operation: 11-8=3 Exploring Operation: 11+78=89, Resulting Numbers: [8, 89] Generated Node #0,2,3: 81:[8, 89] Operation: 11+78=89 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[78, 3], Operations: ['32/4=8', '11-8=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[11, 4, 32, 78], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [11, 78, 8] Generated Node #0,2: 81:[11, 78, 8] Operation: 32/4=8 Moving to Node #0,2 Current State: 81:[11, 78, 8], Operations: ['32/4=8'] Exploring Operation: 11-8=3, Resulting Numbers: [78, 3] Generated Node #0,2,2: 81:[78, 3] Operation: 11-8=3 Moving to Node #0,2,2 Current State: 81:[78, 3], Operations: ['32/4=8', '11-8=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 65, 39, 30, 15 ]
25
[ "30-15=15", "65*15=975", "975/39=25" ]
Current State: 25:[65, 39, 30, 15], Operations: [] Exploring Operation: 30-15=15, Resulting Numbers: [65, 39, 15] Generated Node #2: [65, 39, 15] from Operation: 30-15=15 Current State: 25:[65, 39, 15], Operations: ['30-15=15'] Exploring Operation: 65*15=975, Resulting Numbers: [39, 975] Generated Node #3: [39, 975] from Operation: 65*15=975 Current State: 25:[39, 975], Operations: ['30-15=15', '65*15=975'] Exploring Operation: 975/39=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[65, 39, 30, 15], Operations: [] Exploring Operation: 65-30=35, Resulting Numbers: [39, 15, 35] Generated Node #0,0: 25:[39, 15, 35] Operation: 65-30=35 Exploring Operation: 65-39=26, Resulting Numbers: [30, 15, 26] Generated Node #0,1: 25:[30, 15, 26] Operation: 65-39=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[30, 15, 26], Operations: ['65-39=26'] Exploring Operation: 30-15=15, Resulting Numbers: [26, 15] Generated Node #0,1,0: 25:[26, 15] Operation: 30-15=15 Exploring Operation: 30/15=2, Resulting Numbers: [26, 2] Generated Node #0,1,1: 25:[26, 2] Operation: 30/15=2 Moving to Node #0,1,1 Current State: 25:[26, 2], Operations: ['65-39=26', '30/15=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[26, 15], Operations: ['65-39=26', '30-15=15'] Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[39, 15, 35], Operations: ['65-30=35'] Exploring Operation: 39-35=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 25:[15, 4] Operation: 39-35=4 Exploring Operation: 39-15=24, Resulting Numbers: [35, 24] Generated Node #0,0,1: 25:[35, 24] Operation: 39-15=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[15, 4], Operations: ['65-30=35', '39-35=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,25 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:[35, 24], Operations: ['65-30=35', '39-15=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,25 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 No solution found.
0
hs_2
sum_heuristic
[ 92, 40, 86, 33 ]
66
[ "92*33=3036", "86-40=46", "3036/46=66" ]
Current State: 66:[92, 40, 86, 33], Operations: [] Exploring Operation: 92*33=3036, Resulting Numbers: [40, 86, 3036] Generated Node #2: [40, 86, 3036] from Operation: 92*33=3036 Current State: 66:[40, 86, 3036], Operations: ['92*33=3036'] Exploring Operation: 86-40=46, Resulting Numbers: [3036, 46] Generated Node #3: [3036, 46] from Operation: 86-40=46 Current State: 66:[3036, 46], Operations: ['92*33=3036', '86-40=46'] Exploring Operation: 3036/46=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[92, 40, 86, 33], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [40, 33, 6] Generated Node #0,0: 66:[40, 33, 6] Operation: 92-86=6 Moving to Node #0,0 Current State: 66:[40, 33, 6], Operations: ['92-86=6'] Exploring Operation: 40-33=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 66:[6, 7] Operation: 40-33=7 Moving to Node #0,0,0 Current State: 66:[6, 7], Operations: ['92-86=6', '40-33=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,66 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 62, 79, 97, 28 ]
86
[ "79-62=17", "97-28=69", "17+69=86" ]
Current State: 86:[62, 79, 97, 28], Operations: [] Exploring Operation: 79-62=17, Resulting Numbers: [97, 28, 17] Generated Node #2: [97, 28, 17] from Operation: 79-62=17 Current State: 86:[97, 28, 17], Operations: ['79-62=17'] Exploring Operation: 97-28=69, Resulting Numbers: [17, 69] Generated Node #3: [17, 69] from Operation: 97-28=69 Current State: 86:[17, 69], Operations: ['79-62=17', '97-28=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[62, 79, 97, 28], Operations: [] Exploring Operation: 62-28=34, Resulting Numbers: [79, 97, 34] Generated Node #0,0: 86:[79, 97, 34] Operation: 62-28=34 Exploring Operation: 62+28=90, Resulting Numbers: [79, 97, 90] Generated Node #0,1: 86:[79, 97, 90] Operation: 62+28=90 Exploring Operation: 97-62=35, Resulting Numbers: [79, 28, 35] Generated Node #0,2: 86:[79, 28, 35] Operation: 97-62=35 Exploring Operation: 79-28=51, Resulting Numbers: [62, 97, 51] Generated Node #0,3: 86:[62, 97, 51] Operation: 79-28=51 Moving to Node #0,1 Current State: 86:[79, 97, 90], Operations: ['62+28=90'] Exploring Operation: 97-90=7, Resulting Numbers: [79, 7] Generated Node #0,1,0: 86:[79, 7] Operation: 97-90=7 Exploring Operation: 90-79=11, Resulting Numbers: [97, 11] Generated Node #0,1,1: 86:[97, 11] Operation: 90-79=11 Exploring Operation: 97-79=18, Resulting Numbers: [90, 18] Generated Node #0,1,2: 86:[90, 18] Operation: 97-79=18 Exploring Operation: 79+97=176, Resulting Numbers: [90, 176] Generated Node #0,1,3: 86:[90, 176] Operation: 79+97=176 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[79, 7], Operations: ['62+28=90', '97-90=7'] Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,86 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[62, 79, 97, 28], Operations: [] Exploring Operation: 62+28=90, Resulting Numbers: [79, 97, 90] Generated Node #0,1: 86:[79, 97, 90] Operation: 62+28=90 Moving to Node #0,1 Current State: 86:[79, 97, 90], Operations: ['62+28=90'] Exploring Operation: 97-90=7, Resulting Numbers: [79, 7] Generated Node #0,1,0: 86:[79, 7] Operation: 97-90=7 Moving to Node #0,1,0 Current State: 86:[79, 7], Operations: ['62+28=90', '97-90=7'] Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 8, 2, 25, 4 ]
73
[ "2+4=6", "8*6=48", "25+48=73" ]
Current State: 73:[8, 2, 25, 4], Operations: [] Exploring Operation: 2+4=6, Resulting Numbers: [8, 25, 6] Generated Node #2: [8, 25, 6] from Operation: 2+4=6 Current State: 73:[8, 25, 6], Operations: ['2+4=6'] Exploring Operation: 8*6=48, Resulting Numbers: [25, 48] Generated Node #3: [25, 48] from Operation: 8*6=48 Current State: 73:[25, 48], Operations: ['2+4=6', '8*6=48'] Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[8, 2, 25, 4], Operations: [] Exploring Operation: 8*2=16, Resulting Numbers: [25, 4, 16] Generated Node #0,0: 73:[25, 4, 16] Operation: 8*2=16 Exploring Operation: 2*4=8, Resulting Numbers: [8, 25, 8] Generated Node #0,1: 73:[8, 25, 8] Operation: 2*4=8 Exploring Operation: 2*25=50, Resulting Numbers: [8, 4, 50] Generated Node #0,2: 73:[8, 4, 50] Operation: 2*25=50 Exploring Operation: 8*4=32, Resulting Numbers: [2, 25, 32] Generated Node #0,3: 73:[2, 25, 32] Operation: 8*4=32 Exploring Operation: 25*4=100, Resulting Numbers: [8, 2, 100] Generated Node #0,4: 73:[8, 2, 100] Operation: 25*4=100 Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[8, 4, 50], Operations: ['2*25=50'] Exploring Operation: 8-4=4, Resulting Numbers: [50, 4] Generated Node #0,2,0: 73:[50, 4] Operation: 8-4=4 Exploring Operation: 8+50=58, Resulting Numbers: [4, 58] Generated Node #0,2,1: 73:[4, 58] Operation: 8+50=58 Exploring Operation: 4+50=54, Resulting Numbers: [8, 54] Generated Node #0,2,2: 73:[8, 54] Operation: 4+50=54 Exploring Operation: 8+4=12, Resulting Numbers: [50, 12] Generated Node #0,2,3: 73:[50, 12] Operation: 8+4=12 Exploring Operation: 8*4=32, Resulting Numbers: [50, 32] Generated Node #0,2,4: 73:[50, 32] Operation: 8*4=32 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 73:[50, 32], Operations: ['2*25=50', '8*4=32'] Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,73 unequal: No Solution Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,73 unequal: No Solution No 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: 73:[4, 58], Operations: ['2*25=50', '8+50=58'] Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,73 unequal: No Solution No 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: 73:[8, 54], Operations: ['2*25=50', '4+50=54'] Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,73 unequal: No Solution No 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: 73:[50, 12], Operations: ['2*25=50', '8+4=12'] Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,73 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,73 unequal: No Solution No 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: 73:[50, 4], Operations: ['2*25=50', '8-4=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,73 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[2, 25, 32], Operations: ['8*4=32'] Exploring Operation: 2*25=50, Resulting Numbers: [32, 50] Generated Node #0,3,0: 73:[32, 50] Operation: 2*25=50 Exploring Operation: 2*32=64, Resulting Numbers: [25, 64] Generated Node #0,3,1: 73:[25, 64] Operation: 2*32=64 Exploring Operation: 25+32=57, Resulting Numbers: [2, 57] Generated Node #0,3,2: 73:[2, 57] Operation: 25+32=57 Exploring Operation: 2+25=27, Resulting Numbers: [32, 27] Generated Node #0,3,3: 73:[32, 27] Operation: 2+25=27 Exploring Operation: 2+32=34, Resulting Numbers: [25, 34] Generated Node #0,3,4: 73:[25, 34] Operation: 2+32=34 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[25, 64], Operations: ['8*4=32', '2*32=64'] Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,73 unequal: No Solution Exploring Operation: 25*64=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Exploring Operation: 25+64=89, Resulting Numbers: [89] 89,73 unequal: No Solution No 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: 73:[32, 50], Operations: ['8*4=32', '2*25=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,73 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,73 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution No 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: 73:[2, 57], Operations: ['8*4=32', '25+32=57'] Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,73 unequal: No Solution No 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: 73:[32, 27], Operations: ['8*4=32', '2+25=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,73 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,73 unequal: No Solution No 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: 73:[25, 34], Operations: ['8*4=32', '2+32=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 73:[8, 2, 100], Operations: ['25*4=100'] Exploring Operation: 100/2=50, Resulting Numbers: [8, 50] Generated Node #0,4,0: 73:[8, 50] Operation: 100/2=50 Exploring Operation: 100-2=98, Resulting Numbers: [8, 98] Generated Node #0,4,1: 73:[8, 98] Operation: 100-2=98 Exploring Operation: 8+2=10, Resulting Numbers: [100, 10] Generated Node #0,4,2: 73:[100, 10] Operation: 8+2=10 Exploring Operation: 100-8=92, Resulting Numbers: [2, 92] Generated Node #0,4,3: 73:[2, 92] Operation: 100-8=92 Exploring Operation: 8*2=16, Resulting Numbers: [100, 16] Generated Node #0,4,4: 73:[100, 16] Operation: 8*2=16 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 73:[100, 16], Operations: ['25*4=100', '8*2=16'] Exploring Operation: 100-16=84, Resulting Numbers: [84] 84,73 unequal: No Solution Exploring Operation: 100*16=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Exploring Operation: 100+16=116, Resulting Numbers: [116] 116,73 unequal: No Solution No 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: 73:[8, 50], Operations: ['25*4=100', '100/2=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,73 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,73 unequal: No Solution Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,73 unequal: No Solution No 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: 73:[8, 98], Operations: ['25*4=100', '100-2=98'] Exploring Operation: 8+98=106, Resulting Numbers: [106] 106,73 unequal: No Solution Exploring Operation: 8*98=784, Resulting Numbers: [784] 784,73 unequal: No Solution Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,73 unequal: No Solution No 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: 73:[100, 10], Operations: ['25*4=100', '8+2=10'] Exploring Operation: 100-10=90, Resulting Numbers: [90] 90,73 unequal: No Solution Exploring Operation: 100*10=1000, Resulting Numbers: [1000] 1000,73 unequal: No Solution Exploring Operation: 100/10=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 100+10=110, Resulting Numbers: [110] 110,73 unequal: No Solution No 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: 73:[2, 92], Operations: ['25*4=100', '100-8=92'] Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,73 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,73 unequal: No Solution Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,73 unequal: No Solution Exploring Operation: 2*92=184, Resulting Numbers: [184] 184,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[25, 4, 16], Operations: ['8*2=16'] Exploring Operation: 25*4=100, Resulting Numbers: [16, 100] Generated Node #0,0,0: 73:[16, 100] Operation: 25*4=100 Exploring Operation: 25+16=41, Resulting Numbers: [4, 41] Generated Node #0,0,1: 73:[4, 41] Operation: 25+16=41 Exploring Operation: 4*16=64, Resulting Numbers: [25, 64] Generated Node #0,0,2: 73:[25, 64] Operation: 4*16=64 Exploring Operation: 4+16=20, Resulting Numbers: [25, 20] Generated Node #0,0,3: 73:[25, 20] Operation: 4+16=20 Exploring Operation: 25+4=29, Resulting Numbers: [16, 29] Generated Node #0,0,4: 73:[16, 29] Operation: 25+4=29 Moving to Node #0,0,2 Current State: 73:[25, 64], Operations: ['8*2=16', '4*16=64'] Exploring Operation: 25+64=89, Resulting Numbers: [89] 89,73 unequal: No Solution Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,73 unequal: No Solution Exploring Operation: 25*64=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[16, 100], Operations: ['8*2=16', '25*4=100'] Exploring Operation: 16+100=116, Resulting Numbers: [116] 116,73 unequal: No Solution Exploring Operation: 100-16=84, Resulting Numbers: [84] 84,73 unequal: No Solution Exploring Operation: 16*100=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[4, 41], Operations: ['8*2=16', '25+16=41'] Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,73 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[25, 20], Operations: ['8*2=16', '4+16=20'] Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,73 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[16, 29], Operations: ['8*2=16', '25+4=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,73 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[8, 25, 8], Operations: ['2*4=8'] Exploring Operation: 8+8=16, Resulting Numbers: [25, 16] Generated Node #0,1,0: 73:[25, 16] Operation: 8+8=16 Exploring Operation: 8+25=33, Resulting Numbers: [8, 33] Generated Node #0,1,1: 73:[8, 33] Operation: 8+25=33 Exploring Operation: 25+8=33, Resulting Numbers: [8, 33] Generated Node #0,1,2: 73:[8, 33] Operation: 25+8=33 Exploring Operation: 8/8=1, Resulting Numbers: [25, 1] Generated Node #0,1,3: 73:[25, 1] Operation: 8/8=1 Exploring Operation: 8*8=64, Resulting Numbers: [25, 64] Generated Node #0,1,4: 73:[25, 64] Operation: 8*8=64 Moving to Node #0,1,4 Current State: 73:[25, 64], Operations: ['2*4=8', '8*8=64'] Exploring Operation: 25+64=89, Resulting Numbers: [89] 89,73 unequal: No Solution Exploring Operation: 25*64=1600, Resulting Numbers: [1600] 1600,73 unequal: No Solution Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[8, 33], Operations: ['2*4=8', '8+25=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,73 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[25, 16], Operations: ['2*4=8', '8+8=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,73 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[8, 33], Operations: ['2*4=8', '25+8=33'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,73 unequal: No Solution Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[25, 1], Operations: ['2*4=8', '8/8=1'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,73 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,73 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,73 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
[ 11, 80, 89, 58 ]
100
[ "80-11=69", "89-58=31", "69+31=100" ]
Current State: 100:[11, 80, 89, 58], Operations: [] Exploring Operation: 80-11=69, Resulting Numbers: [89, 58, 69] Generated Node #2: [89, 58, 69] from Operation: 80-11=69 Current State: 100:[89, 58, 69], Operations: ['80-11=69'] Exploring Operation: 89-58=31, Resulting Numbers: [69, 31] Generated Node #3: [69, 31] from Operation: 89-58=31 Current State: 100:[69, 31], Operations: ['80-11=69', '89-58=31'] Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[11, 80, 89, 58], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [11, 58, 9] Generated Node #0,0: 100:[11, 58, 9] Operation: 89-80=9 Moving to Node #0,0 Current State: 100:[11, 58, 9], Operations: ['89-80=9'] Exploring Operation: 58-9=49, Resulting Numbers: [11, 49] Generated Node #0,0,0: 100:[11, 49] Operation: 58-9=49 Moving to Node #0,0,0 Current State: 100:[11, 49], Operations: ['89-80=9', '58-9=49'] Exploring Operation: 11+49=60, Resulting Numbers: [60] 60,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 33, 2, 1, 16 ]
36
[ "33+1=34", "34-16=18", "2*18=36" ]
Current State: 36:[33, 2, 1, 16], Operations: [] Exploring Operation: 33+1=34, Resulting Numbers: [2, 16, 34] Generated Node #2: [2, 16, 34] from Operation: 33+1=34 Current State: 36:[2, 16, 34], Operations: ['33+1=34'] Exploring Operation: 34-16=18, Resulting Numbers: [2, 18] Generated Node #3: [2, 18] from Operation: 34-16=18 Current State: 36:[2, 18], Operations: ['33+1=34', '34-16=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[33, 2, 1, 16], Operations: [] Exploring Operation: 33-16=17, Resulting Numbers: [2, 1, 17] Generated Node #0,0: 36:[2, 1, 17] Operation: 33-16=17 Exploring Operation: 33+2=35, Resulting Numbers: [1, 16, 35] Generated Node #0,1: 36:[1, 16, 35] Operation: 33+2=35 Exploring Operation: 33+1=34, Resulting Numbers: [2, 16, 34] Generated Node #0,2: 36:[2, 16, 34] Operation: 33+1=34 Moving to Node #0,0 Current State: 36:[2, 1, 17], Operations: ['33-16=17'] Exploring Operation: 2+1=3, Resulting Numbers: [17, 3] Generated Node #0,0,0: 36:[17, 3] Operation: 2+1=3 Exploring Operation: 2*1=2, Resulting Numbers: [17, 2] Generated Node #0,0,1: 36:[17, 2] Operation: 2*1=2 Exploring Operation: 1+17=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 36:[2, 18] Operation: 1+17=18 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[2, 18], Operations: ['33-16=17', '1+17=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[33, 2, 1, 16], Operations: [] Exploring Operation: 33-16=17, Resulting Numbers: [2, 1, 17] Generated Node #0,0: 36:[2, 1, 17] Operation: 33-16=17 Moving to Node #0,0 Current State: 36:[2, 1, 17], Operations: ['33-16=17'] Exploring Operation: 1+17=18, Resulting Numbers: [2, 18] Generated Node #0,0,2: 36:[2, 18] Operation: 1+17=18 Moving to Node #0,0,2 Current State: 36:[2, 18], Operations: ['33-16=17', '1+17=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 61, 74, 64, 25 ]
76
[ "74-61=13", "64+25=89", "89-13=76" ]
Current State: 76:[61, 74, 64, 25], Operations: [] Exploring Operation: 74-61=13, Resulting Numbers: [64, 25, 13] Generated Node #2: [64, 25, 13] from Operation: 74-61=13 Current State: 76:[64, 25, 13], Operations: ['74-61=13'] Exploring Operation: 64+25=89, Resulting Numbers: [13, 89] Generated Node #3: [13, 89] from Operation: 64+25=89 Current State: 76:[13, 89], Operations: ['74-61=13', '64+25=89'] Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[61, 74, 64, 25], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [74, 25, 3] Generated Node #0,0: 76:[74, 25, 3] Operation: 64-61=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[74, 25, 3], Operations: ['64-61=3'] Exploring Operation: 25*3=75, Resulting Numbers: [74, 75] Generated Node #0,0,0: 76:[74, 75] Operation: 25*3=75 Moving to Node #0,0,0 Current State: 76:[74, 75], Operations: ['64-61=3', '25*3=75'] Exploring Operation: 75-74=1, Resulting Numbers: [1] 1,76 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
[ 89, 6, 1, 99 ]
84
[ "89+1=90", "90/6=15", "99-15=84" ]
Current State: 84:[89, 6, 1, 99], Operations: [] Exploring Operation: 89+1=90, Resulting Numbers: [6, 99, 90] Generated Node #2: [6, 99, 90] from Operation: 89+1=90 Current State: 84:[6, 99, 90], Operations: ['89+1=90'] Exploring Operation: 90/6=15, Resulting Numbers: [99, 15] Generated Node #3: [99, 15] from Operation: 90/6=15 Current State: 84:[99, 15], Operations: ['89+1=90', '90/6=15'] Exploring Operation: 99-15=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[89, 6, 1, 99], Operations: [] Exploring Operation: 99-89=10, Resulting Numbers: [6, 1, 10] Generated Node #0,0: 84:[6, 1, 10] Operation: 99-89=10 Exploring Operation: 89-1=88, Resulting Numbers: [6, 99, 88] Generated Node #0,1: 84:[6, 99, 88] Operation: 89-1=88 Exploring Operation: 89-6=83, Resulting Numbers: [1, 99, 83] Generated Node #0,2: 84:[1, 99, 83] Operation: 89-6=83 Exploring Operation: 99-6=93, Resulting Numbers: [89, 1, 93] Generated Node #0,3: 84:[89, 1, 93] Operation: 99-6=93 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[6, 1, 10], Operations: ['99-89=10'] Exploring Operation: 6+1=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 84:[10, 7] Operation: 6+1=7 Exploring Operation: 1+10=11, Resulting Numbers: [6, 11] Generated Node #0,0,1: 84:[6, 11] Operation: 1+10=11 Exploring Operation: 10-6=4, Resulting Numbers: [1, 4] Generated Node #0,0,2: 84:[1, 4] Operation: 10-6=4 Exploring Operation: 6*1=6, Resulting Numbers: [10, 6] Generated Node #0,0,3: 84:[10, 6] Operation: 6*1=6 Moving to Node #0,0,1 Current State: 84:[6, 11], Operations: ['99-89=10', '1+10=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[1, 4], Operations: ['99-89=10', '10-6=4'] Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[10, 6], Operations: ['99-89=10', '6*1=6'] Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[10, 7], Operations: ['99-89=10', '6+1=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[89, 1, 93], Operations: ['99-6=93'] Exploring Operation: 89*1=89, Resulting Numbers: [93, 89] Generated Node #0,3,0: 84:[93, 89] Operation: 89*1=89 Exploring Operation: 93-89=4, Resulting Numbers: [1, 4] Generated Node #0,3,1: 84:[1, 4] Operation: 93-89=4 Exploring Operation: 93-1=92, Resulting Numbers: [89, 92] Generated Node #0,3,2: 84:[89, 92] Operation: 93-1=92 Exploring Operation: 89-1=88, Resulting Numbers: [93, 88] Generated Node #0,3,3: 84:[93, 88] Operation: 89-1=88 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 84:[1, 4], Operations: ['99-6=93', '93-89=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,84 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:[89, 92], Operations: ['99-6=93', '93-1=92'] Exploring Operation: 89+92=181, Resulting Numbers: [181] 181,84 unequal: No Solution Exploring Operation: 92-89=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 89*92=8188, Resulting Numbers: [8188] 8188,84 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:[93, 88], Operations: ['99-6=93', '89-1=88'] Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 93*88=8184, Resulting Numbers: [8184] 8184,84 unequal: No Solution Exploring Operation: 93+88=181, Resulting Numbers: [181] 181,84 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 #0,3,0 Current State: 84:[93, 89], Operations: ['99-6=93', '89*1=89'] Exploring Operation: 93+89=182, Resulting Numbers: [182] 182,84 unequal: No Solution Exploring Operation: 93-89=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 93*89=8277, Resulting Numbers: [8277] 8277,84 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:[1, 99, 83], Operations: ['89-6=83'] Exploring Operation: 99-83=16, Resulting Numbers: [1, 16] Generated Node #0,2,0: 84:[1, 16] Operation: 99-83=16 Exploring Operation: 99-1=98, Resulting Numbers: [83, 98] Generated Node #0,2,1: 84:[83, 98] Operation: 99-1=98 Exploring Operation: 1*99=99, Resulting Numbers: [83, 99] Generated Node #0,2,2: 84:[83, 99] Operation: 1*99=99 Exploring Operation: 1+83=84, Resulting Numbers: [99, 84] Generated Node #0,2,3: 84:[99, 84] Operation: 1+83=84 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 84:[1, 16], Operations: ['89-6=83', '99-83=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,84 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 #0,2,1 Current State: 84:[83, 98], Operations: ['89-6=83', '99-1=98'] Exploring Operation: 98-83=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 83+98=181, Resulting Numbers: [181] 181,84 unequal: No Solution Exploring Operation: 83*98=8134, Resulting Numbers: [8134] 8134,84 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 #0,2,3 Current State: 84:[99, 84], Operations: ['89-6=83', '1+83=84'] Exploring Operation: 99+84=183, Resulting Numbers: [183] 183,84 unequal: No Solution Exploring Operation: 99*84=8316, Resulting Numbers: [8316] 8316,84 unequal: No Solution Exploring Operation: 99-84=15, Resulting Numbers: [15] 15,84 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 #0,2,2 Current State: 84:[83, 99], Operations: ['89-6=83', '1*99=99'] Exploring Operation: 83*99=8217, Resulting Numbers: [8217] 8217,84 unequal: No Solution Exploring Operation: 83+99=182, Resulting Numbers: [182] 182,84 unequal: No Solution Exploring Operation: 99-83=16, Resulting Numbers: [16] 16,84 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 #0,1 Current State: 84:[6, 99, 88], Operations: ['89-1=88'] Exploring Operation: 99-88=11, Resulting Numbers: [6, 11] Generated Node #0,1,0: 84:[6, 11] Operation: 99-88=11 Exploring Operation: 99-6=93, Resulting Numbers: [88, 93] Generated Node #0,1,1: 84:[88, 93] Operation: 99-6=93 Exploring Operation: 88-6=82, Resulting Numbers: [99, 82] Generated Node #0,1,2: 84:[99, 82] Operation: 88-6=82 Exploring Operation: 6+99=105, Resulting Numbers: [88, 105] Generated Node #0,1,3: 84:[88, 105] Operation: 6+99=105 Moving to Node #0,1,0 Current State: 84:[6, 11], Operations: ['89-1=88', '99-88=11'] Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,84 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[88, 93], Operations: ['89-1=88', '99-6=93'] Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 88+93=181, Resulting Numbers: [181] 181,84 unequal: No Solution Exploring Operation: 88*93=8184, Resulting Numbers: [8184] 8184,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[99, 82], Operations: ['89-1=88', '88-6=82'] Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 99*82=8118, Resulting Numbers: [8118] 8118,84 unequal: No Solution Exploring Operation: 99+82=181, Resulting Numbers: [181] 181,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[88, 105], Operations: ['89-1=88', '6+99=105'] Exploring Operation: 88*105=9240, Resulting Numbers: [9240] 9240,84 unequal: No Solution Exploring Operation: 105-88=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 88+105=193, Resulting Numbers: [193] 193,84 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
[ 97, 8, 61, 90 ]
20
[ "97-61=36", "8*90=720", "720/36=20" ]
Current State: 20:[97, 8, 61, 90], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [8, 90, 36] Generated Node #2: [8, 90, 36] from Operation: 97-61=36 Current State: 20:[8, 90, 36], Operations: ['97-61=36'] Exploring Operation: 8*90=720, Resulting Numbers: [36, 720] Generated Node #3: [36, 720] from Operation: 8*90=720 Current State: 20:[36, 720], Operations: ['97-61=36', '8*90=720'] Exploring Operation: 720/36=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[97, 8, 61, 90], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [8, 61, 7] Generated Node #0,0: 20:[8, 61, 7] Operation: 97-90=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[8, 61, 7], Operations: ['97-90=7'] Exploring Operation: 61-8=53, Resulting Numbers: [7, 53] Generated Node #0,0,0: 20:[7, 53] Operation: 61-8=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[7, 53], Operations: ['97-90=7', '61-8=53'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 86, 92, 64, 40 ]
62
[ "86-40=46", "92/46=2", "64-2=62" ]
Current State: 62:[86, 92, 64, 40], Operations: [] Exploring Operation: 86-40=46, Resulting Numbers: [92, 64, 46] Generated Node #2: [92, 64, 46] from Operation: 86-40=46 Current State: 62:[92, 64, 46], Operations: ['86-40=46'] Exploring Operation: 92/46=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 92/46=2 Current State: 62:[64, 2], Operations: ['86-40=46', '92/46=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[86, 92, 64, 40], Operations: [] Exploring Operation: 92-86=6, Resulting Numbers: [64, 40, 6] Generated Node #0,0: 62:[64, 40, 6] Operation: 92-86=6 Exploring Operation: 92-64=28, Resulting Numbers: [86, 40, 28] Generated Node #0,1: 62:[86, 40, 28] Operation: 92-64=28 Moving to Node #0,0 Current State: 62:[64, 40, 6], Operations: ['92-86=6'] Exploring Operation: 64-40=24, Resulting Numbers: [6, 24] Generated Node #0,0,0: 62:[6, 24] Operation: 64-40=24 Exploring Operation: 40-6=34, Resulting Numbers: [64, 34] Generated Node #0,0,1: 62:[64, 34] Operation: 40-6=34 Moving to Node #0,1 Current State: 62:[86, 40, 28], Operations: ['92-64=28'] Exploring Operation: 86-28=58, Resulting Numbers: [40, 58] Generated Node #0,1,0: 62:[40, 58] Operation: 86-28=58 Exploring Operation: 86-40=46, Resulting Numbers: [28, 46] Generated Node #0,1,1: 62:[28, 46] Operation: 86-40=46 Moving to Node #0,0,1 Current State: 62:[64, 34], Operations: ['92-86=6', '40-6=34'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 64+34=98, Resulting Numbers: [98] 98,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[6, 24], Operations: ['92-86=6', '64-40=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[40, 58], Operations: ['92-64=28', '86-28=58'] Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,62 unequal: No Solution Exploring Operation: 40+58=98, Resulting Numbers: [98] 98,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[28, 46], Operations: ['92-64=28', '86-40=46'] Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,62 unequal: No Solution Exploring Operation: 28+46=74, Resulting Numbers: [74] 74,62 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 17, 25, 35, 63 ]
20
[ "25-17=8", "63-35=28", "28-8=20" ]
Current State: 20:[17, 25, 35, 63], Operations: [] Exploring Operation: 25-17=8, Resulting Numbers: [35, 63, 8] Generated Node #2: [35, 63, 8] from Operation: 25-17=8 Current State: 20:[35, 63, 8], Operations: ['25-17=8'] Exploring Operation: 63-35=28, Resulting Numbers: [8, 28] Generated Node #3: [8, 28] from Operation: 63-35=28 Current State: 20:[8, 28], Operations: ['25-17=8', '63-35=28'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[17, 25, 35, 63], Operations: [] Exploring Operation: 63-25=38, Resulting Numbers: [17, 35, 38] Generated Node #0,0: 20:[17, 35, 38] Operation: 63-25=38 Exploring Operation: 63-35=28, Resulting Numbers: [17, 25, 28] Generated Node #0,1: 20:[17, 25, 28] Operation: 63-35=28 Exploring Operation: 63-17=46, Resulting Numbers: [25, 35, 46] Generated Node #0,2: 20:[25, 35, 46] Operation: 63-17=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[17, 25, 28], Operations: ['63-35=28'] Exploring Operation: 28-17=11, Resulting Numbers: [25, 11] Generated Node #0,1,0: 20:[25, 11] Operation: 28-17=11 Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 20:[17, 3] Operation: 28-25=3 Exploring Operation: 25-17=8, Resulting Numbers: [28, 8] Generated Node #0,1,2: 20:[28, 8] Operation: 25-17=8 Moving to Node #0,1,1 Current State: 20:[17, 3], Operations: ['63-35=28', '28-25=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[17, 25, 35, 63], Operations: [] Exploring Operation: 63-35=28, Resulting Numbers: [17, 25, 28] Generated Node #0,1: 20:[17, 25, 28] Operation: 63-35=28 Moving to Node #0,1 Current State: 20:[17, 25, 28], Operations: ['63-35=28'] Exploring Operation: 28-25=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 20:[17, 3] Operation: 28-25=3 Moving to Node #0,1,1 Current State: 20:[17, 3], Operations: ['63-35=28', '28-25=3'] Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 33, 8, 50, 67 ]
10
[ "33+67=100", "100/50=2", "8+2=10" ]
Current State: 10:[33, 8, 50, 67], Operations: [] Exploring Operation: 33+67=100, Resulting Numbers: [8, 50, 100] Generated Node #2: [8, 50, 100] from Operation: 33+67=100 Current State: 10:[8, 50, 100], Operations: ['33+67=100'] Exploring Operation: 100/50=2, Resulting Numbers: [8, 2] Generated Node #3: [8, 2] from Operation: 100/50=2 Current State: 10:[8, 2], Operations: ['33+67=100', '100/50=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[33, 8, 50, 67], Operations: [] Exploring Operation: 67-50=17, Resulting Numbers: [33, 8, 17] Generated Node #0,0: 10:[33, 8, 17] Operation: 67-50=17 Exploring Operation: 33-8=25, Resulting Numbers: [50, 67, 25] Generated Node #0,1: 10:[50, 67, 25] Operation: 33-8=25 Exploring Operation: 67-33=34, Resulting Numbers: [8, 50, 34] Generated Node #0,2: 10:[8, 50, 34] Operation: 67-33=34 Exploring Operation: 50-33=17, Resulting Numbers: [8, 67, 17] Generated Node #0,3: 10:[8, 67, 17] Operation: 50-33=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[33, 8, 17], Operations: ['67-50=17'] Exploring Operation: 33-17=16, Resulting Numbers: [8, 16] Generated Node #0,0,0: 10:[8, 16] Operation: 33-17=16 Exploring Operation: 17-8=9, Resulting Numbers: [33, 9] Generated Node #0,0,1: 10:[33, 9] Operation: 17-8=9 Exploring Operation: 33+8=41, Resulting Numbers: [17, 41] Generated Node #0,0,2: 10:[17, 41] Operation: 33+8=41 Exploring Operation: 33-8=25, Resulting Numbers: [17, 25] Generated Node #0,0,3: 10:[17, 25] Operation: 33-8=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[8, 16], Operations: ['67-50=17', '33-17=16'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,10 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,10 unequal: No Solution No 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: 10:[17, 25], Operations: ['67-50=17', '33-8=25'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,10 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,10 unequal: No Solution No 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: 10:[33, 9], Operations: ['67-50=17', '17-8=9'] Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,10 unequal: No Solution Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,10 unequal: No Solution No 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: 10:[17, 41], Operations: ['67-50=17', '33+8=41'] Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,10 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,10 unequal: No Solution Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,10 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: 10:[8, 50, 34], Operations: ['67-33=34'] Exploring Operation: 50-8=42, Resulting Numbers: [34, 42] Generated Node #0,2,0: 10:[34, 42] Operation: 50-8=42 Exploring Operation: 34-8=26, Resulting Numbers: [50, 26] Generated Node #0,2,1: 10:[50, 26] Operation: 34-8=26 Exploring Operation: 50-34=16, Resulting Numbers: [8, 16] Generated Node #0,2,2: 10:[8, 16] Operation: 50-34=16 Exploring Operation: 8+50=58, Resulting Numbers: [34, 58] Generated Node #0,2,3: 10:[34, 58] Operation: 8+50=58 Moving to Node #0,2,2 Current State: 10:[8, 16], Operations: ['67-33=34', '50-34=16'] Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,10 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,10 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[50, 26], Operations: ['67-33=34', '34-8=26'] Exploring Operation: 50*26=1300, Resulting Numbers: [1300] 1300,10 unequal: No Solution Exploring Operation: 50+26=76, Resulting Numbers: [76] 76,10 unequal: No Solution Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,10 unequal: No Solution Moving to Node #0,2,0 Current State: 10:[34, 42], Operations: ['67-33=34', '50-8=42'] Exploring Operation: 34+42=76, Resulting Numbers: [76] 76,10 unequal: No Solution Exploring Operation: 34*42=1428, Resulting Numbers: [1428] 1428,10 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,10 unequal: No Solution Moving to Node #0,2,3 Current State: 10:[34, 58], Operations: ['67-33=34', '8+50=58'] Exploring Operation: 34+58=92, Resulting Numbers: [92] 92,10 unequal: No Solution Exploring Operation: 34*58=1972, Resulting Numbers: [1972] 1972,10 unequal: No Solution Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,10 unequal: No Solution No 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: 10:[8, 67, 17], Operations: ['50-33=17'] Exploring Operation: 17-8=9, Resulting Numbers: [67, 9] Generated Node #0,3,0: 10:[67, 9] Operation: 17-8=9 Exploring Operation: 8+67=75, Resulting Numbers: [17, 75] Generated Node #0,3,1: 10:[17, 75] Operation: 8+67=75 Exploring Operation: 67-17=50, Resulting Numbers: [8, 50] Generated Node #0,3,2: 10:[8, 50] Operation: 67-17=50 Exploring Operation: 67-8=59, Resulting Numbers: [17, 59] Generated Node #0,3,3: 10:[17, 59] Operation: 67-8=59 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 10:[8, 50], Operations: ['50-33=17', '67-17=50'] Exploring Operation: 8+50=58, Resulting Numbers: [58] 58,10 unequal: No Solution Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,10 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,10 unequal: No Solution No 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: 10:[17, 59], Operations: ['50-33=17', '67-8=59'] Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,10 unequal: No Solution Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,10 unequal: No Solution No 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: 10:[67, 9], Operations: ['50-33=17', '17-8=9'] Exploring Operation: 67*9=603, Resulting Numbers: [603] 603,10 unequal: No Solution Exploring Operation: 67+9=76, Resulting Numbers: [76] 76,10 unequal: No Solution Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,10 unequal: No Solution No 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: 10:[17, 75], Operations: ['50-33=17', '8+67=75'] Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,10 unequal: No Solution Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,10 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,10 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: 10:[50, 67, 25], Operations: ['33-8=25'] Exploring Operation: 50/25=2, Resulting Numbers: [67, 2] Generated Node #0,1,0: 10:[67, 2] Operation: 50/25=2 Exploring Operation: 67-50=17, Resulting Numbers: [25, 17] Generated Node #0,1,1: 10:[25, 17] Operation: 67-50=17 Exploring Operation: 67-25=42, Resulting Numbers: [50, 42] Generated Node #0,1,2: 10:[50, 42] Operation: 67-25=42 Exploring Operation: 50-25=25, Resulting Numbers: [67, 25] Generated Node #0,1,3: 10:[67, 25] Operation: 50-25=25 Moving to Node #0,1,1 Current State: 10:[25, 17], Operations: ['33-8=25', '67-50=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,10 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[67, 2], Operations: ['33-8=25', '50/25=2'] Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,10 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,10 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,10 unequal: No Solution Moving to Node #0,1,3 Current State: 10:[67, 25], Operations: ['33-8=25', '50-25=25'] Exploring Operation: 67+25=92, Resulting Numbers: [92] 92,10 unequal: No Solution Exploring Operation: 67*25=1675, Resulting Numbers: [1675] 1675,10 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[50, 42], Operations: ['33-8=25', '67-25=42'] Exploring Operation: 50+42=92, Resulting Numbers: [92] 92,10 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 50*42=2100, Resulting Numbers: [2100] 2100,10 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
[ 29, 60, 24, 84 ]
72
[ "29-24=5", "60/5=12", "84-12=72" ]
Current State: 72:[29, 60, 24, 84], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [60, 84, 5] Generated Node #2: [60, 84, 5] from Operation: 29-24=5 Current State: 72:[60, 84, 5], Operations: ['29-24=5'] Exploring Operation: 60/5=12, Resulting Numbers: [84, 12] Generated Node #3: [84, 12] from Operation: 60/5=12 Current State: 72:[84, 12], Operations: ['29-24=5', '60/5=12'] Exploring Operation: 84-12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[29, 60, 24, 84], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [60, 84, 5] Generated Node #0,0: 72:[60, 84, 5] Operation: 29-24=5 Exploring Operation: 60-29=31, Resulting Numbers: [24, 84, 31] Generated Node #0,1: 72:[24, 84, 31] Operation: 60-29=31 Exploring Operation: 84-60=24, Resulting Numbers: [29, 24, 24] Generated Node #0,2: 72:[29, 24, 24] Operation: 84-60=24 Exploring Operation: 60-24=36, Resulting Numbers: [29, 84, 36] Generated Node #0,3: 72:[29, 84, 36] Operation: 60-24=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[29, 24, 24], Operations: ['84-60=24'] Exploring Operation: 24/24=1, Resulting Numbers: [29, 1] Generated Node #0,2,0: 72:[29, 1] Operation: 24/24=1 Exploring Operation: 29-24=5, Resulting Numbers: [24, 5] Generated Node #0,2,1: 72:[24, 5] Operation: 29-24=5 Exploring Operation: 24-24=0, Resulting Numbers: [29, 0] Generated Node #0,2,2: 72:[29, 0] Operation: 24-24=0 Exploring Operation: 29-24=5, Resulting Numbers: [24, 5] Generated Node #0,2,3: 72:[24, 5] Operation: 29-24=5 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[24, 5], Operations: ['84-60=24', '29-24=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 72:[24, 5], Operations: ['84-60=24', '29-24=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,72 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[29, 1], Operations: ['84-60=24', '24/24=1'] Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[29, 0], Operations: ['84-60=24', '24-24=0'] Exploring Operation: 29*0=0, Resulting Numbers: [0] 0,72 unequal: No Solution Exploring Operation: 29-0=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 29+0=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[24, 84, 31], Operations: ['60-29=31'] Exploring Operation: 84-24=60, Resulting Numbers: [31, 60] Generated Node #0,1,0: 72:[31, 60] Operation: 84-24=60 Exploring Operation: 31-24=7, Resulting Numbers: [84, 7] Generated Node #0,1,1: 72:[84, 7] Operation: 31-24=7 Exploring Operation: 84-31=53, Resulting Numbers: [24, 53] Generated Node #0,1,2: 72:[24, 53] Operation: 84-31=53 Exploring Operation: 24+31=55, Resulting Numbers: [84, 55] Generated Node #0,1,3: 72:[84, 55] Operation: 24+31=55 Moving to Node #0,1,1 Current State: 72:[84, 7], Operations: ['60-29=31', '31-24=7'] Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,72 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 84*7=588, Resulting Numbers: [588] 588,72 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[24, 53], Operations: ['60-29=31', '84-31=53'] Exploring Operation: 24+53=77, Resulting Numbers: [77] 77,72 unequal: No Solution Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 24*53=1272, Resulting Numbers: [1272] 1272,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[31, 60], Operations: ['60-29=31', '84-24=60'] Exploring Operation: 31+60=91, Resulting Numbers: [91] 91,72 unequal: No Solution Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 31*60=1860, Resulting Numbers: [1860] 1860,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[84, 55], Operations: ['60-29=31', '24+31=55'] Exploring Operation: 84*55=4620, Resulting Numbers: [4620] 4620,72 unequal: No Solution Exploring Operation: 84+55=139, Resulting Numbers: [139] 139,72 unequal: No Solution Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[29, 84, 36], Operations: ['60-24=36'] Exploring Operation: 84-36=48, Resulting Numbers: [29, 48] Generated Node #0,3,0: 72:[29, 48] Operation: 84-36=48 Exploring Operation: 36-29=7, Resulting Numbers: [84, 7] Generated Node #0,3,1: 72:[84, 7] Operation: 36-29=7 Exploring Operation: 84-29=55, Resulting Numbers: [36, 55] Generated Node #0,3,2: 72:[36, 55] Operation: 84-29=55 Exploring Operation: 29+36=65, Resulting Numbers: [84, 65] Generated Node #0,3,3: 72:[84, 65] Operation: 29+36=65 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[84, 7], Operations: ['60-24=36', '36-29=7'] Exploring Operation: 84+7=91, Resulting Numbers: [91] 91,72 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 84*7=588, Resulting Numbers: [588] 588,72 unequal: No Solution Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[29, 48], Operations: ['60-24=36', '84-36=48'] Exploring Operation: 29+48=77, Resulting Numbers: [77] 77,72 unequal: No Solution Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 29*48=1392, Resulting Numbers: [1392] 1392,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 72:[36, 55], Operations: ['60-24=36', '84-29=55'] Exploring Operation: 36+55=91, Resulting Numbers: [91] 91,72 unequal: No Solution Exploring Operation: 36*55=1980, Resulting Numbers: [1980] 1980,72 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 72:[84, 65], Operations: ['60-24=36', '29+36=65'] Exploring Operation: 84-65=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 84*65=5460, Resulting Numbers: [5460] 5460,72 unequal: No Solution Exploring Operation: 84+65=149, Resulting Numbers: [149] 149,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[60, 84, 5], Operations: ['29-24=5'] Exploring Operation: 84-60=24, Resulting Numbers: [5, 24] Generated Node #0,0,0: 72:[5, 24] Operation: 84-60=24 Exploring Operation: 84-5=79, Resulting Numbers: [60, 79] Generated Node #0,0,1: 72:[60, 79] Operation: 84-5=79 Exploring Operation: 60+5=65, Resulting Numbers: [84, 65] Generated Node #0,0,2: 72:[84, 65] Operation: 60+5=65 Exploring Operation: 60/5=12, Resulting Numbers: [84, 12] Generated Node #0,0,3: 72:[84, 12] Operation: 60/5=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[5, 24], Operations: ['29-24=5', '84-60=24'] Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,72 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 72:[84, 12], Operations: ['29-24=5', '60/5=12'] Exploring Operation: 84/12=7, Resulting Numbers: [7] 7,72 unequal: No Solution Exploring Operation: 84-12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[29, 60, 24, 84], Operations: [] Exploring Operation: 29-24=5, Resulting Numbers: [60, 84, 5] Generated Node #0,0: 72:[60, 84, 5] Operation: 29-24=5 Moving to Node #0,0 Current State: 72:[60, 84, 5], Operations: ['29-24=5'] Exploring Operation: 60/5=12, Resulting Numbers: [84, 12] Generated Node #0,0,3: 72:[84, 12] Operation: 60/5=12 Moving to Node #0,0,3 Current State: 72:[84, 12], Operations: ['29-24=5', '60/5=12'] Exploring Operation: 84-12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.940972
hs_4
mult_heuristic
[ 12, 5, 9, 73 ]
47
[ "12+5=17", "73-9=64", "64-17=47" ]
Current State: 47:[12, 5, 9, 73], Operations: [] Exploring Operation: 12+5=17, Resulting Numbers: [9, 73, 17] Generated Node #2: [9, 73, 17] from Operation: 12+5=17 Current State: 47:[9, 73, 17], Operations: ['12+5=17'] Exploring Operation: 73-9=64, Resulting Numbers: [17, 64] Generated Node #3: [17, 64] from Operation: 73-9=64 Current State: 47:[17, 64], Operations: ['12+5=17', '73-9=64'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[12, 5, 9, 73], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [9, 73, 60] Generated Node #0,0: 47:[9, 73, 60] Operation: 12*5=60 Exploring Operation: 5*9=45, Resulting Numbers: [12, 73, 45] Generated Node #0,1: 47:[12, 73, 45] Operation: 5*9=45 Exploring Operation: 12+9=21, Resulting Numbers: [5, 73, 21] Generated Node #0,2: 47:[5, 73, 21] Operation: 12+9=21 Exploring Operation: 73-12=61, Resulting Numbers: [5, 9, 61] Generated Node #0,3: 47:[5, 9, 61] Operation: 73-12=61 Exploring Operation: 12+5=17, Resulting Numbers: [9, 73, 17] Generated Node #0,4: 47:[9, 73, 17] Operation: 12+5=17 Moving to Node #0,1 Current State: 47:[12, 73, 45], Operations: ['5*9=45'] Exploring Operation: 73-12=61, Resulting Numbers: [45, 61] Generated Node #0,1,0: 47:[45, 61] Operation: 73-12=61 Exploring Operation: 12+45=57, Resulting Numbers: [73, 57] Generated Node #0,1,1: 47:[73, 57] Operation: 12+45=57 Exploring Operation: 73-45=28, Resulting Numbers: [12, 28] Generated Node #0,1,2: 47:[12, 28] Operation: 73-45=28 Exploring Operation: 12+73=85, Resulting Numbers: [45, 85] Generated Node #0,1,3: 47:[45, 85] Operation: 12+73=85 Exploring Operation: 45-12=33, Resulting Numbers: [73, 33] Generated Node #0,1,4: 47:[73, 33] Operation: 45-12=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[45, 61], Operations: ['5*9=45', '73-12=61'] Exploring Operation: 45*61=2745, Resulting Numbers: [2745] 2745,47 unequal: No Solution Exploring Operation: 45+61=106, Resulting Numbers: [106] 106,47 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[73, 57], Operations: ['5*9=45', '12+45=57'] Exploring Operation: 73-57=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 73*57=4161, Resulting Numbers: [4161] 4161,47 unequal: No Solution Exploring Operation: 73+57=130, Resulting Numbers: [130] 130,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 47:[45, 85], Operations: ['5*9=45', '12+73=85'] Exploring Operation: 45*85=3825, Resulting Numbers: [3825] 3825,47 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,47 unequal: No Solution Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 47:[73, 33], Operations: ['5*9=45', '45-12=33'] Exploring Operation: 73*33=2409, Resulting Numbers: [2409] 2409,47 unequal: No Solution Exploring Operation: 73-33=40, Resulting Numbers: [40] 40,47 unequal: No Solution Exploring Operation: 73+33=106, Resulting Numbers: [106] 106,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[12, 28], Operations: ['5*9=45', '73-45=28'] Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,47 unequal: No Solution Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,47 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 47:[9, 73, 60], Operations: ['12*5=60'] Exploring Operation: 73-9=64, Resulting Numbers: [60, 64] Generated Node #0,0,0: 47:[60, 64] Operation: 73-9=64 Exploring Operation: 60-9=51, Resulting Numbers: [73, 51] Generated Node #0,0,1: 47:[73, 51] Operation: 60-9=51 Exploring Operation: 9+73=82, Resulting Numbers: [60, 82] Generated Node #0,0,2: 47:[60, 82] Operation: 9+73=82 Exploring Operation: 9+60=69, Resulting Numbers: [73, 69] Generated Node #0,0,3: 47:[73, 69] Operation: 9+60=69 Exploring Operation: 73-60=13, Resulting Numbers: [9, 13] Generated Node #0,0,4: 47:[9, 13] Operation: 73-60=13 Moving to Node #0,2 Current State: 47:[5, 73, 21], Operations: ['12+9=21'] Exploring Operation: 21-5=16, Resulting Numbers: [73, 16] Generated Node #0,2,0: 47:[73, 16] Operation: 21-5=16 Exploring Operation: 73-21=52, Resulting Numbers: [5, 52] Generated Node #0,2,1: 47:[5, 52] Operation: 73-21=52 Exploring Operation: 5+21=26, Resulting Numbers: [73, 26] Generated Node #0,2,2: 47:[73, 26] Operation: 5+21=26 Exploring Operation: 5+73=78, Resulting Numbers: [21, 78] Generated Node #0,2,3: 47:[21, 78] Operation: 5+73=78 Exploring Operation: 73-5=68, Resulting Numbers: [21, 68] Generated Node #0,2,4: 47:[21, 68] Operation: 73-5=68 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[5, 52], Operations: ['12+9=21', '73-21=52'] Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,47 unequal: No Solution Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[12, 5, 9, 73], Operations: [] Exploring Operation: 12+9=21, Resulting Numbers: [5, 73, 21] Generated Node #0,2: 47:[5, 73, 21] Operation: 12+9=21 Moving to Node #0,2 Current State: 47:[5, 73, 21], Operations: ['12+9=21'] Exploring Operation: 73-21=52, Resulting Numbers: [5, 52] Generated Node #0,2,1: 47:[5, 52] Operation: 73-21=52 Moving to Node #0,2,1 Current State: 47:[5, 52], Operations: ['12+9=21', '73-21=52'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 32, 45, 90, 11 ]
66
[ "45-32=13", "90-11=79", "79-13=66" ]
Current State: 66:[32, 45, 90, 11], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [90, 11, 13] Generated Node #2: [90, 11, 13] from Operation: 45-32=13 Current State: 66:[90, 11, 13], Operations: ['45-32=13'] Exploring Operation: 90-11=79, Resulting Numbers: [13, 79] Generated Node #3: [13, 79] from Operation: 90-11=79 Current State: 66:[13, 79], Operations: ['45-32=13', '90-11=79'] Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[32, 45, 90, 11], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [32, 11, 45] Generated Node #0,0: 66:[32, 11, 45] Operation: 90-45=45 Exploring Operation: 90/45=2, Resulting Numbers: [32, 11, 2] Generated Node #0,1: 66:[32, 11, 2] Operation: 90/45=2 Exploring Operation: 90-32=58, Resulting Numbers: [45, 11, 58] Generated Node #0,2: 66:[45, 11, 58] Operation: 90-32=58 Moving to Node #0,1 Current State: 66:[32, 11, 2], Operations: ['90/45=2'] Exploring Operation: 32+2=34, Resulting Numbers: [11, 34] Generated Node #0,1,0: 66:[11, 34] Operation: 32+2=34 Exploring Operation: 32-11=21, Resulting Numbers: [2, 21] Generated Node #0,1,1: 66:[2, 21] Operation: 32-11=21 Exploring Operation: 11*2=22, Resulting Numbers: [32, 22] Generated Node #0,1,2: 66:[32, 22] Operation: 11*2=22 Moving to Node #0,0 Current State: 66:[32, 11, 45], Operations: ['90-45=45'] Exploring Operation: 45-11=34, Resulting Numbers: [32, 34] Generated Node #0,0,0: 66:[32, 34] Operation: 45-11=34 Exploring Operation: 45-32=13, Resulting Numbers: [11, 13] Generated Node #0,0,1: 66:[11, 13] Operation: 45-32=13 Exploring Operation: 32+45=77, Resulting Numbers: [11, 77] Generated Node #0,0,2: 66:[11, 77] Operation: 32+45=77 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[32, 34], Operations: ['90-45=45', '45-11=34'] Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,66 unequal: No Solution Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,66 unequal: No Solution Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[32, 45, 90, 11], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [32, 11, 45] Generated Node #0,0: 66:[32, 11, 45] Operation: 90-45=45 Moving to Node #0,0 Current State: 66:[32, 11, 45], Operations: ['90-45=45'] Exploring Operation: 45-11=34, Resulting Numbers: [32, 34] Generated Node #0,0,0: 66:[32, 34] Operation: 45-11=34 Moving to Node #0,0,0 Current State: 66:[32, 34], Operations: ['90-45=45', '45-11=34'] Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 13, 97, 87, 5 ]
77
[ "13+87=100", "100/5=20", "97-20=77" ]
Current State: 77:[13, 97, 87, 5], Operations: [] Exploring Operation: 13+87=100, Resulting Numbers: [97, 5, 100] Generated Node #2: [97, 5, 100] from Operation: 13+87=100 Current State: 77:[97, 5, 100], Operations: ['13+87=100'] Exploring Operation: 100/5=20, Resulting Numbers: [97, 20] Generated Node #3: [97, 20] from Operation: 100/5=20 Current State: 77:[97, 20], Operations: ['13+87=100', '100/5=20'] Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[13, 97, 87, 5], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [13, 5, 10] Generated Node #0,0: 77:[13, 5, 10] Operation: 97-87=10 Moving to Node #0,0 Current State: 77:[13, 5, 10], Operations: ['97-87=10'] Exploring Operation: 13-5=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 77:[10, 8] Operation: 13-5=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[10, 8], Operations: ['97-87=10', '13-5=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 18, 7, 79, 24 ]
54
[ "79-7=72", "18*72=1296", "1296/24=54" ]
Current State: 54:[18, 7, 79, 24], Operations: [] Exploring Operation: 79-7=72, Resulting Numbers: [18, 24, 72] Generated Node #2: [18, 24, 72] from Operation: 79-7=72 Current State: 54:[18, 24, 72], Operations: ['79-7=72'] Exploring Operation: 18*72=1296, Resulting Numbers: [24, 1296] Generated Node #3: [24, 1296] from Operation: 18*72=1296 Current State: 54:[24, 1296], Operations: ['79-7=72', '18*72=1296'] Exploring Operation: 1296/24=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[18, 7, 79, 24], Operations: [] Exploring Operation: 79-24=55, Resulting Numbers: [18, 7, 55] Generated Node #0,0: 54:[18, 7, 55] Operation: 79-24=55 Exploring Operation: 79-18=61, Resulting Numbers: [7, 24, 61] Generated Node #0,1: 54:[7, 24, 61] Operation: 79-18=61 Exploring Operation: 79-7=72, Resulting Numbers: [18, 24, 72] Generated Node #0,2: 54:[18, 24, 72] Operation: 79-7=72 Moving to Node #0,0 Current State: 54:[18, 7, 55], Operations: ['79-24=55'] Exploring Operation: 18+7=25, Resulting Numbers: [55, 25] Generated Node #0,0,0: 54:[55, 25] Operation: 18+7=25 Exploring Operation: 55-7=48, Resulting Numbers: [18, 48] Generated Node #0,0,1: 54:[18, 48] Operation: 55-7=48 Exploring Operation: 18-7=11, Resulting Numbers: [55, 11] Generated Node #0,0,2: 54:[55, 11] Operation: 18-7=11 Moving to Node #0,1 Current State: 54:[7, 24, 61], Operations: ['79-18=61'] Exploring Operation: 61-7=54, Resulting Numbers: [24, 54] Generated Node #0,1,0: 54:[24, 54] Operation: 61-7=54 Exploring Operation: 7+24=31, Resulting Numbers: [61, 31] Generated Node #0,1,1: 54:[61, 31] Operation: 7+24=31 Exploring Operation: 24-7=17, Resulting Numbers: [61, 17] Generated Node #0,1,2: 54:[61, 17] Operation: 24-7=17 Moving to Node #0,2 Current State: 54:[18, 24, 72], Operations: ['79-7=72'] Exploring Operation: 72/24=3, Resulting Numbers: [18, 3] Generated Node #0,2,0: 54:[18, 3] Operation: 72/24=3 Exploring Operation: 72/18=4, Resulting Numbers: [24, 4] Generated Node #0,2,1: 54:[24, 4] Operation: 72/18=4 Exploring Operation: 72-18=54, Resulting Numbers: [24, 54] Generated Node #0,2,2: 54:[24, 54] Operation: 72-18=54 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[18, 3], Operations: ['79-7=72', '72/24=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[18, 7, 79, 24], Operations: [] Exploring Operation: 79-7=72, Resulting Numbers: [18, 24, 72] Generated Node #0,2: 54:[18, 24, 72] Operation: 79-7=72 Moving to Node #0,2 Current State: 54:[18, 24, 72], Operations: ['79-7=72'] Exploring Operation: 72/24=3, Resulting Numbers: [18, 3] Generated Node #0,2,0: 54:[18, 3] Operation: 72/24=3 Moving to Node #0,2,0 Current State: 54:[18, 3], Operations: ['79-7=72', '72/24=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 65, 63, 23, 30 ]
74
[ "30-23=7", "63/7=9", "65+9=74" ]
Current State: 74:[65, 63, 23, 30], Operations: [] Exploring Operation: 30-23=7, Resulting Numbers: [65, 63, 7] Generated Node #2: [65, 63, 7] from Operation: 30-23=7 Current State: 74:[65, 63, 7], Operations: ['30-23=7'] Exploring Operation: 63/7=9, Resulting Numbers: [65, 9] Generated Node #3: [65, 9] from Operation: 63/7=9 Current State: 74:[65, 9], Operations: ['30-23=7', '63/7=9'] Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[65, 63, 23, 30], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [23, 30, 2] Generated Node #0,0: 74:[23, 30, 2] Operation: 65-63=2 Exploring Operation: 63-23=40, Resulting Numbers: [65, 30, 40] Generated Node #0,1: 74:[65, 30, 40] Operation: 63-23=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[65, 30, 40], Operations: ['63-23=40'] Exploring Operation: 65-30=35, Resulting Numbers: [40, 35] Generated Node #0,1,0: 74:[40, 35] Operation: 65-30=35 Exploring Operation: 30+40=70, Resulting Numbers: [65, 70] Generated Node #0,1,1: 74:[65, 70] Operation: 30+40=70 Moving to Node #0,1,0 Current State: 74:[40, 35], Operations: ['63-23=40', '65-30=35'] Exploring Operation: 40+35=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[65, 70], Operations: ['63-23=40', '30+40=70'] Exploring Operation: 70-65=5, Resulting Numbers: [5] 5,74 unequal: No Solution Exploring Operation: 65+70=135, Resulting Numbers: [135] 135,74 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 #0,0 Current State: 74:[23, 30, 2], Operations: ['65-63=2'] Exploring Operation: 30-23=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 74:[2, 7] Operation: 30-23=7 Exploring Operation: 23+30=53, Resulting Numbers: [2, 53] Generated Node #0,0,1: 74:[2, 53] Operation: 23+30=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[2, 7], Operations: ['65-63=2', '30-23=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[2, 53], Operations: ['65-63=2', '23+30=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 50, 7, 3, 2 ]
35
[ "50/2=25", "7+3=10", "25+10=35" ]
Current State: 35:[50, 7, 3, 2], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [7, 3, 25] Generated Node #2: [7, 3, 25] from Operation: 50/2=25 Current State: 35:[7, 3, 25], Operations: ['50/2=25'] Exploring Operation: 7+3=10, Resulting Numbers: [25, 10] Generated Node #3: [25, 10] from Operation: 7+3=10 Current State: 35:[25, 10], Operations: ['50/2=25', '7+3=10'] Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[50, 7, 3, 2], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [7, 3, 25] Generated Node #0,0: 35:[7, 3, 25] Operation: 50/2=25 Moving to Node #0,0 Current State: 35:[7, 3, 25], Operations: ['50/2=25'] Exploring Operation: 7+25=32, Resulting Numbers: [3, 32] Generated Node #0,0,0: 35:[3, 32] Operation: 7+25=32 Moving to Node #0,0,0 Current State: 35:[3, 32], Operations: ['50/2=25', '7+25=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[50, 7, 3, 2], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [7, 3, 25] Generated Node #0,0: 35:[7, 3, 25] Operation: 50/2=25 Moving to Node #0,0 Current State: 35:[7, 3, 25], Operations: ['50/2=25'] Exploring Operation: 7+25=32, Resulting Numbers: [3, 32] Generated Node #0,0,0: 35:[3, 32] Operation: 7+25=32 Moving to Node #0,0,0 Current State: 35:[3, 32], Operations: ['50/2=25', '7+25=32'] Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 14, 20, 3, 5 ]
33
[ "20-14=6", "5+6=11", "3*11=33" ]
Current State: 33:[14, 20, 3, 5], Operations: [] Exploring Operation: 20-14=6, Resulting Numbers: [3, 5, 6] Generated Node #2: [3, 5, 6] from Operation: 20-14=6 Current State: 33:[3, 5, 6], Operations: ['20-14=6'] Exploring Operation: 5+6=11, Resulting Numbers: [3, 11] Generated Node #3: [3, 11] from Operation: 5+6=11 Current State: 33:[3, 11], Operations: ['20-14=6', '5+6=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[14, 20, 3, 5], Operations: [] Exploring Operation: 20/5=4, Resulting Numbers: [14, 3, 4] Generated Node #0,0: 33:[14, 3, 4] Operation: 20/5=4 Exploring Operation: 14+20=34, Resulting Numbers: [3, 5, 34] Generated Node #0,1: 33:[3, 5, 34] Operation: 14+20=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[3, 5, 34], Operations: ['14+20=34'] Exploring Operation: 3+5=8, Resulting Numbers: [34, 8] Generated Node #0,1,0: 33:[34, 8] Operation: 3+5=8 Exploring Operation: 5-3=2, Resulting Numbers: [34, 2] Generated Node #0,1,1: 33:[34, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 33:[34, 2], Operations: ['14+20=34', '5-3=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,33 unequal: No Solution No 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: 33:[34, 8], Operations: ['14+20=34', '3+5=8'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,33 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: 33:[14, 3, 4], Operations: ['20/5=4'] Exploring Operation: 14-4=10, Resulting Numbers: [3, 10] Generated Node #0,0,0: 33:[3, 10] Operation: 14-4=10 Exploring Operation: 14-3=11, Resulting Numbers: [4, 11] Generated Node #0,0,1: 33:[4, 11] Operation: 14-3=11 Moving to Node #0,0,0 Current State: 33:[3, 10], Operations: ['20/5=4', '14-4=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,33 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[4, 11], Operations: ['20/5=4', '14-3=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,33 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
[ 24, 2, 17, 19 ]
33
[ "24-17=7", "2*7=14", "19+14=33" ]
Current State: 33:[24, 2, 17, 19], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [2, 19, 7] Generated Node #2: [2, 19, 7] from Operation: 24-17=7 Current State: 33:[2, 19, 7], Operations: ['24-17=7'] Exploring Operation: 2*7=14, Resulting Numbers: [19, 14] Generated Node #3: [19, 14] from Operation: 2*7=14 Current State: 33:[19, 14], Operations: ['24-17=7', '2*7=14'] Exploring Operation: 19+14=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[24, 2, 17, 19], Operations: [] Exploring Operation: 19-17=2, Resulting Numbers: [24, 2, 2] Generated Node #0,0: 33:[24, 2, 2] Operation: 19-17=2 Exploring Operation: 24-19=5, Resulting Numbers: [2, 17, 5] Generated Node #0,1: 33:[2, 17, 5] Operation: 24-19=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[2, 17, 5], Operations: ['24-19=5'] Exploring Operation: 17-5=12, Resulting Numbers: [2, 12] Generated Node #0,1,0: 33:[2, 12] Operation: 17-5=12 Exploring Operation: 2*17=34, Resulting Numbers: [5, 34] Generated Node #0,1,1: 33:[5, 34] Operation: 2*17=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[2, 12], Operations: ['24-19=5', '17-5=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution No 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: 33:[5, 34], Operations: ['24-19=5', '2*17=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,33 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: 33:[24, 2, 2], Operations: ['19-17=2'] Exploring Operation: 24/2=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 33:[2, 12] Operation: 24/2=12 Exploring Operation: 24/2=12, Resulting Numbers: [2, 12] Generated Node #0,0,1: 33:[2, 12] Operation: 24/2=12 Moving to Node #0,0,0 Current State: 33:[2, 12], Operations: ['19-17=2', '24/2=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[2, 12], Operations: ['19-17=2', '24/2=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 43, 23, 6, 53 ]
79
[ "43-23=20", "6+53=59", "20+59=79" ]
Current State: 79:[43, 23, 6, 53], Operations: [] Exploring Operation: 43-23=20, Resulting Numbers: [6, 53, 20] Generated Node #2: [6, 53, 20] from Operation: 43-23=20 Current State: 79:[6, 53, 20], Operations: ['43-23=20'] Exploring Operation: 6+53=59, Resulting Numbers: [20, 59] Generated Node #3: [20, 59] from Operation: 6+53=59 Current State: 79:[20, 59], Operations: ['43-23=20', '6+53=59'] Exploring Operation: 20+59=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[43, 23, 6, 53], Operations: [] Exploring Operation: 43+23=66, Resulting Numbers: [6, 53, 66] Generated Node #0,0: 79:[6, 53, 66] Operation: 43+23=66 Moving to Node #0,0 Current State: 79:[6, 53, 66], Operations: ['43+23=66'] Exploring Operation: 6+53=59, Resulting Numbers: [66, 59] Generated Node #0,0,0: 79:[66, 59] Operation: 6+53=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[66, 59], Operations: ['43+23=66', '6+53=59'] Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 42, 63, 21, 39 ]
34
[ "42+63=105", "105/21=5", "39-5=34" ]
Current State: 34:[42, 63, 21, 39], Operations: [] Exploring Operation: 42+63=105, Resulting Numbers: [21, 39, 105] Generated Node #2: [21, 39, 105] from Operation: 42+63=105 Current State: 34:[21, 39, 105], Operations: ['42+63=105'] Exploring Operation: 105/21=5, Resulting Numbers: [39, 5] Generated Node #3: [39, 5] from Operation: 105/21=5 Current State: 34:[39, 5], Operations: ['42+63=105', '105/21=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[42, 63, 21, 39], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [42, 39, 3] Generated Node #0,0: 34:[42, 39, 3] Operation: 63/21=3 Exploring Operation: 63-39=24, Resulting Numbers: [42, 21, 24] Generated Node #0,1: 34:[42, 21, 24] Operation: 63-39=24 Exploring Operation: 63-42=21, Resulting Numbers: [21, 39, 21] Generated Node #0,2: 34:[21, 39, 21] Operation: 63-42=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[21, 39, 21], Operations: ['63-42=21'] Exploring Operation: 39-21=18, Resulting Numbers: [21, 18] Generated Node #0,2,0: 34:[21, 18] Operation: 39-21=18 Exploring Operation: 39-21=18, Resulting Numbers: [21, 18] Generated Node #0,2,1: 34:[21, 18] Operation: 39-21=18 Exploring Operation: 21/21=1, Resulting Numbers: [39, 1] Generated Node #0,2,2: 34:[39, 1] Operation: 21/21=1 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[21, 18], Operations: ['63-42=21', '39-21=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,34 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 34:[21, 18], Operations: ['63-42=21', '39-21=18'] Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[39, 1], Operations: ['63-42=21', '21/21=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[42, 39, 3], Operations: ['63/21=3'] Exploring Operation: 42/3=14, Resulting Numbers: [39, 14] Generated Node #0,0,0: 34:[39, 14] Operation: 42/3=14 Exploring Operation: 42-3=39, Resulting Numbers: [39, 39] Generated Node #0,0,1: 34:[39, 39] Operation: 42-3=39 Exploring Operation: 42-39=3, Resulting Numbers: [3, 3] Generated Node #0,0,2: 34:[3, 3] Operation: 42-39=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[3, 3], Operations: ['63/21=3', '42-39=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[39, 14], Operations: ['63/21=3', '42/3=14'] Exploring Operation: 39+14=53, Resulting Numbers: [53] 53,34 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,34 unequal: No Solution Exploring Operation: 39*14=546, Resulting Numbers: [546] 546,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 34:[39, 39], Operations: ['63/21=3', '42-3=39'] Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[42, 21, 24], Operations: ['63-39=24'] Exploring Operation: 42-24=18, Resulting Numbers: [21, 18] Generated Node #0,1,0: 34:[21, 18] Operation: 42-24=18 Exploring Operation: 24-21=3, Resulting Numbers: [42, 3] Generated Node #0,1,1: 34:[42, 3] Operation: 24-21=3 Exploring Operation: 42/21=2, Resulting Numbers: [24, 2] Generated Node #0,1,2: 34:[24, 2] Operation: 42/21=2 Moving to Node #0,1,0 Current State: 34:[21, 18], Operations: ['63-39=24', '42-24=18'] Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[24, 2], Operations: ['63-39=24', '42/21=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[42, 3], Operations: ['63-39=24', '24-21=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,34 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,34 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 19, 57, 24, 2 ]
67
[ "24-19=5", "2*5=10", "57+10=67" ]
Current State: 67:[19, 57, 24, 2], Operations: [] Exploring Operation: 24-19=5, Resulting Numbers: [57, 2, 5] Generated Node #2: [57, 2, 5] from Operation: 24-19=5 Current State: 67:[57, 2, 5], Operations: ['24-19=5'] Exploring Operation: 2*5=10, Resulting Numbers: [57, 10] Generated Node #3: [57, 10] from Operation: 2*5=10 Current State: 67:[57, 10], Operations: ['24-19=5', '2*5=10'] Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[19, 57, 24, 2], Operations: [] Exploring Operation: 24*2=48, Resulting Numbers: [19, 57, 48] Generated Node #0,0: 67:[19, 57, 48] Operation: 24*2=48 Exploring Operation: 19+24=43, Resulting Numbers: [57, 2, 43] Generated Node #0,1: 67:[57, 2, 43] Operation: 19+24=43 Exploring Operation: 19*2=38, Resulting Numbers: [57, 24, 38] Generated Node #0,2: 67:[57, 24, 38] Operation: 19*2=38 Moving to Node #0,0 Current State: 67:[19, 57, 48], Operations: ['24*2=48'] Exploring Operation: 19+57=76, Resulting Numbers: [48, 76] Generated Node #0,0,0: 67:[48, 76] Operation: 19+57=76 Exploring Operation: 19+48=67, Resulting Numbers: [57, 67] Generated Node #0,0,1: 67:[57, 67] Operation: 19+48=67 Exploring Operation: 57-19=38, Resulting Numbers: [48, 38] Generated Node #0,0,2: 67:[48, 38] Operation: 57-19=38 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[57, 67], Operations: ['24*2=48', '19+48=67'] Exploring Operation: 57*67=3819, Resulting Numbers: [3819] 3819,67 unequal: No Solution Exploring Operation: 57+67=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[48, 76], Operations: ['24*2=48', '19+57=76'] Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,67 unequal: No Solution Exploring Operation: 48+76=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 48*76=3648, Resulting Numbers: [3648] 3648,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[48, 38], Operations: ['24*2=48', '57-19=38'] Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,67 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,67 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: 67:[57, 24, 38], Operations: ['19*2=38'] Exploring Operation: 57-24=33, Resulting Numbers: [38, 33] Generated Node #0,2,0: 67:[38, 33] Operation: 57-24=33 Exploring Operation: 57+24=81, Resulting Numbers: [38, 81] Generated Node #0,2,1: 67:[38, 81] Operation: 57+24=81 Exploring Operation: 24+38=62, Resulting Numbers: [57, 62] Generated Node #0,2,2: 67:[57, 62] Operation: 24+38=62 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[57, 62], Operations: ['19*2=38', '24+38=62'] Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 57*62=3534, Resulting Numbers: [3534] 3534,67 unequal: No Solution Exploring Operation: 57+62=119, Resulting Numbers: [119] 119,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[38, 81], Operations: ['19*2=38', '57+24=81'] Exploring Operation: 38+81=119, Resulting Numbers: [119] 119,67 unequal: No Solution Exploring Operation: 38*81=3078, Resulting Numbers: [3078] 3078,67 unequal: No Solution Exploring Operation: 81-38=43, Resulting Numbers: [43] 43,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[38, 33], Operations: ['19*2=38', '57-24=33'] Exploring Operation: 38*33=1254, Resulting Numbers: [1254] 1254,67 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,67 unequal: No Solution Exploring Operation: 38+33=71, Resulting Numbers: [71] 71,67 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: 67:[57, 2, 43], Operations: ['19+24=43'] Exploring Operation: 57+2=59, Resulting Numbers: [43, 59] Generated Node #0,1,0: 67:[43, 59] Operation: 57+2=59 Exploring Operation: 2*43=86, Resulting Numbers: [57, 86] Generated Node #0,1,1: 67:[57, 86] Operation: 2*43=86 Exploring Operation: 2+43=45, Resulting Numbers: [57, 45] Generated Node #0,1,2: 67:[57, 45] Operation: 2+43=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[57, 86], Operations: ['19+24=43', '2*43=86'] Exploring Operation: 57*86=4902, Resulting Numbers: [4902] 4902,67 unequal: No Solution Exploring Operation: 57+86=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[43, 59], Operations: ['19+24=43', '57+2=59'] Exploring Operation: 43+59=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 43*59=2537, Resulting Numbers: [2537] 2537,67 unequal: No Solution Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[57, 45], Operations: ['19+24=43', '2+43=45'] Exploring Operation: 57+45=102, Resulting Numbers: [102] 102,67 unequal: No Solution Exploring Operation: 57*45=2565, Resulting Numbers: [2565] 2565,67 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,67 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
[ 22, 93, 90, 40 ]
88
[ "40-22=18", "90/18=5", "93-5=88" ]
Current State: 88:[22, 93, 90, 40], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [93, 90, 18] Generated Node #2: [93, 90, 18] from Operation: 40-22=18 Current State: 88:[93, 90, 18], Operations: ['40-22=18'] Exploring Operation: 90/18=5, Resulting Numbers: [93, 5] Generated Node #3: [93, 5] from Operation: 90/18=5 Current State: 88:[93, 5], Operations: ['40-22=18', '90/18=5'] Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[22, 93, 90, 40], Operations: [] Exploring Operation: 93-40=53, Resulting Numbers: [22, 90, 53] Generated Node #0,0: 88:[22, 90, 53] Operation: 93-40=53 Exploring Operation: 40-22=18, Resulting Numbers: [93, 90, 18] Generated Node #0,1: 88:[93, 90, 18] Operation: 40-22=18 Exploring Operation: 90-40=50, Resulting Numbers: [22, 93, 50] Generated Node #0,2: 88:[22, 93, 50] Operation: 90-40=50 Exploring Operation: 93-90=3, Resulting Numbers: [22, 40, 3] Generated Node #0,3: 88:[22, 40, 3] Operation: 93-90=3 Moving to Node #0,3 Current State: 88:[22, 40, 3], Operations: ['93-90=3'] Exploring Operation: 40-22=18, Resulting Numbers: [3, 18] Generated Node #0,3,0: 88:[3, 18] Operation: 40-22=18 Exploring Operation: 22-3=19, Resulting Numbers: [40, 19] Generated Node #0,3,1: 88:[40, 19] Operation: 22-3=19 Exploring Operation: 40+3=43, Resulting Numbers: [22, 43] Generated Node #0,3,2: 88:[22, 43] Operation: 40+3=43 Exploring Operation: 22+3=25, Resulting Numbers: [40, 25] Generated Node #0,3,3: 88:[40, 25] Operation: 22+3=25 Moving to Node #0,1 Current State: 88:[93, 90, 18], Operations: ['40-22=18'] Exploring Operation: 90/18=5, Resulting Numbers: [93, 5] Generated Node #0,1,0: 88:[93, 5] Operation: 90/18=5 Exploring Operation: 93-18=75, Resulting Numbers: [90, 75] Generated Node #0,1,1: 88:[90, 75] Operation: 93-18=75 Exploring Operation: 93-90=3, Resulting Numbers: [18, 3] Generated Node #0,1,2: 88:[18, 3] Operation: 93-90=3 Exploring Operation: 90-18=72, Resulting Numbers: [93, 72] Generated Node #0,1,3: 88:[93, 72] Operation: 90-18=72 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[18, 3], Operations: ['40-22=18', '93-90=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,88 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,88 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,88 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 #0,1,0 Current State: 88:[93, 5], Operations: ['40-22=18', '90/18=5'] Exploring Operation: 93*5=465, Resulting Numbers: [465] 465,88 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[22, 93, 90, 40], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [93, 90, 18] Generated Node #0,1: 88:[93, 90, 18] Operation: 40-22=18 Moving to Node #0,1 Current State: 88:[93, 90, 18], Operations: ['40-22=18'] Exploring Operation: 90/18=5, Resulting Numbers: [93, 5] Generated Node #0,1,0: 88:[93, 5] Operation: 90/18=5 Moving to Node #0,1,0 Current State: 88:[93, 5], Operations: ['40-22=18', '90/18=5'] Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 20, 54, 69, 7 ]
42
[ "54-20=34", "69+7=76", "76-34=42" ]
Current State: 42:[20, 54, 69, 7], Operations: [] Exploring Operation: 54-20=34, Resulting Numbers: [69, 7, 34] Generated Node #2: [69, 7, 34] from Operation: 54-20=34 Current State: 42:[69, 7, 34], Operations: ['54-20=34'] Exploring Operation: 69+7=76, Resulting Numbers: [34, 76] Generated Node #3: [34, 76] from Operation: 69+7=76 Current State: 42:[34, 76], Operations: ['54-20=34', '69+7=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[20, 54, 69, 7], Operations: [] Exploring Operation: 69-54=15, Resulting Numbers: [20, 7, 15] Generated Node #0,0: 42:[20, 7, 15] Operation: 69-54=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[20, 7, 15], Operations: ['69-54=15'] Exploring Operation: 20-15=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 42:[7, 5] Operation: 20-15=5 Moving to Node #0,0,0 Current State: 42:[7, 5], Operations: ['69-54=15', '20-15=5'] Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 48, 27, 98, 83 ]
60
[ "48+27=75", "98-83=15", "75-15=60" ]
Current State: 60:[48, 27, 98, 83], Operations: [] Exploring Operation: 48+27=75, Resulting Numbers: [98, 83, 75] Generated Node #2: [98, 83, 75] from Operation: 48+27=75 Current State: 60:[98, 83, 75], Operations: ['48+27=75'] Exploring Operation: 98-83=15, Resulting Numbers: [75, 15] Generated Node #3: [75, 15] from Operation: 98-83=15 Current State: 60:[75, 15], Operations: ['48+27=75', '98-83=15'] Exploring Operation: 75-15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[48, 27, 98, 83], Operations: [] Exploring Operation: 83-48=35, Resulting Numbers: [27, 98, 35] Generated Node #0,0: 60:[27, 98, 35] Operation: 83-48=35 Exploring Operation: 98-83=15, Resulting Numbers: [48, 27, 15] Generated Node #0,1: 60:[48, 27, 15] Operation: 98-83=15 Exploring Operation: 98-48=50, Resulting Numbers: [27, 83, 50] Generated Node #0,2: 60:[27, 83, 50] Operation: 98-48=50 Exploring Operation: 98-27=71, Resulting Numbers: [48, 83, 71] Generated Node #0,3: 60:[48, 83, 71] Operation: 98-27=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[48, 27, 15], Operations: ['98-83=15'] Exploring Operation: 27-15=12, Resulting Numbers: [48, 12] Generated Node #0,1,0: 60:[48, 12] Operation: 27-15=12 Exploring Operation: 48-15=33, Resulting Numbers: [27, 33] Generated Node #0,1,1: 60:[27, 33] Operation: 48-15=33 Exploring Operation: 48-27=21, Resulting Numbers: [15, 21] Generated Node #0,1,2: 60:[15, 21] Operation: 48-27=21 Exploring Operation: 48+15=63, Resulting Numbers: [27, 63] Generated Node #0,1,3: 60:[27, 63] Operation: 48+15=63 Moving to Node #0,1,2 Current State: 60:[15, 21], Operations: ['98-83=15', '48-27=21'] Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,60 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,60 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[27, 63], Operations: ['98-83=15', '48+15=63'] Exploring Operation: 27*63=1701, Resulting Numbers: [1701] 1701,60 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 27+63=90, Resulting Numbers: [90] 90,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[27, 33], Operations: ['98-83=15', '48-15=33'] Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[48, 27, 98, 83], Operations: [] Exploring Operation: 98-83=15, Resulting Numbers: [48, 27, 15] Generated Node #0,1: 60:[48, 27, 15] Operation: 98-83=15 Moving to Node #0,1 Current State: 60:[48, 27, 15], Operations: ['98-83=15'] Exploring Operation: 48-15=33, Resulting Numbers: [27, 33] Generated Node #0,1,1: 60:[27, 33] Operation: 48-15=33 Moving to Node #0,1,1 Current State: 60:[27, 33], Operations: ['98-83=15', '48-15=33'] Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 14, 29, 64, 61 ]
40
[ "14+29=43", "64-61=3", "43-3=40" ]
Current State: 40:[14, 29, 64, 61], Operations: [] Exploring Operation: 14+29=43, Resulting Numbers: [64, 61, 43] Generated Node #2: [64, 61, 43] from Operation: 14+29=43 Current State: 40:[64, 61, 43], Operations: ['14+29=43'] Exploring Operation: 64-61=3, Resulting Numbers: [43, 3] Generated Node #3: [43, 3] from Operation: 64-61=3 Current State: 40:[43, 3], Operations: ['14+29=43', '64-61=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[14, 29, 64, 61], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [14, 64, 32] Generated Node #0,0: 40:[14, 64, 32] Operation: 61-29=32 Exploring Operation: 64-61=3, Resulting Numbers: [14, 29, 3] Generated Node #0,1: 40:[14, 29, 3] Operation: 64-61=3 Exploring Operation: 64-29=35, Resulting Numbers: [14, 61, 35] Generated Node #0,2: 40:[14, 61, 35] Operation: 64-29=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[14, 29, 3], Operations: ['64-61=3'] Exploring Operation: 14-3=11, Resulting Numbers: [29, 11] Generated Node #0,1,0: 40:[29, 11] Operation: 14-3=11 Exploring Operation: 29-14=15, Resulting Numbers: [3, 15] Generated Node #0,1,1: 40:[3, 15] Operation: 29-14=15 Exploring Operation: 14+29=43, Resulting Numbers: [3, 43] Generated Node #0,1,2: 40:[3, 43] Operation: 14+29=43 Moving to Node #0,1,2 Current State: 40:[3, 43], Operations: ['64-61=3', '14+29=43'] Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,40 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[14, 29, 64, 61], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [14, 29, 3] Generated Node #0,1: 40:[14, 29, 3] Operation: 64-61=3 Moving to Node #0,1 Current State: 40:[14, 29, 3], Operations: ['64-61=3'] Exploring Operation: 14+29=43, Resulting Numbers: [3, 43] Generated Node #0,1,2: 40:[3, 43] Operation: 14+29=43 Moving to Node #0,1,2 Current State: 40:[3, 43], Operations: ['64-61=3', '14+29=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic