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
[ 68, 90, 94, 63 ]
80
[ "94-90=4", "68/4=17", "63+17=80" ]
Current State: 80:[68, 90, 94, 63], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [68, 63, 4] Generated Node #2: [68, 63, 4] from Operation: 94-90=4 Current State: 80:[68, 63, 4], Operations: ['94-90=4'] Exploring Operation: 68/4=17, Resulting Numbers: [63, 17] Generated Node #3: [63, 17] from Operation: 68/4=17 Current State: 80:[63, 17], Operations: ['94-90=4', '68/4=17'] Exploring Operation: 63+17=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[68, 90, 94, 63], Operations: [] Exploring Operation: 68-63=5, Resulting Numbers: [90, 94, 5] Generated Node #0,0: 80:[90, 94, 5] Operation: 68-63=5 Moving to Node #0,0 Current State: 80:[90, 94, 5], Operations: ['68-63=5'] Exploring Operation: 94-90=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 80:[5, 4] Operation: 94-90=4 Moving to Node #0,0,0 Current State: 80:[5, 4], Operations: ['68-63=5', '94-90=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,80 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 4, 37, 88, 86 ]
66
[ "37-4=33", "88-86=2", "33*2=66" ]
Current State: 66:[4, 37, 88, 86], Operations: [] Exploring Operation: 37-4=33, Resulting Numbers: [88, 86, 33] Generated Node #2: [88, 86, 33] from Operation: 37-4=33 Current State: 66:[88, 86, 33], Operations: ['37-4=33'] Exploring Operation: 88-86=2, Resulting Numbers: [33, 2] Generated Node #3: [33, 2] from Operation: 88-86=2 Current State: 66:[33, 2], Operations: ['37-4=33', '88-86=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[4, 37, 88, 86], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [37, 86, 22] Generated Node #0,0: 66:[37, 86, 22] Operation: 88/4=22 Exploring Operation: 86-37=49, Resulting Numbers: [4, 88, 49] Generated Node #0,1: 66:[4, 88, 49] Operation: 86-37=49 Exploring Operation: 37-4=33, Resulting Numbers: [88, 86, 33] Generated Node #0,2: 66:[88, 86, 33] Operation: 37-4=33 Exploring Operation: 88-37=51, Resulting Numbers: [4, 86, 51] Generated Node #0,3: 66:[4, 86, 51] Operation: 88-37=51 Exploring Operation: 88-86=2, Resulting Numbers: [4, 37, 2] Generated Node #0,4: 66:[4, 37, 2] Operation: 88-86=2 Moving to Node #0,4 Current State: 66:[4, 37, 2], Operations: ['88-86=2'] Exploring Operation: 4+2=6, Resulting Numbers: [37, 6] Generated Node #0,4,0: 66:[37, 6] Operation: 4+2=6 Exploring Operation: 4/2=2, Resulting Numbers: [37, 2] Generated Node #0,4,1: 66:[37, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [37, 2] Generated Node #0,4,2: 66:[37, 2] Operation: 4-2=2 Exploring Operation: 37-4=33, Resulting Numbers: [2, 33] Generated Node #0,4,3: 66:[2, 33] Operation: 37-4=33 Exploring Operation: 37-2=35, Resulting Numbers: [4, 35] Generated Node #0,4,4: 66:[4, 35] Operation: 37-2=35 Moving to Node #0,0 Current State: 66:[37, 86, 22], Operations: ['88/4=22'] Exploring Operation: 86-22=64, Resulting Numbers: [37, 64] Generated Node #0,0,0: 66:[37, 64] Operation: 86-22=64 Exploring Operation: 37-22=15, Resulting Numbers: [86, 15] Generated Node #0,0,1: 66:[86, 15] Operation: 37-22=15 Exploring Operation: 86-37=49, Resulting Numbers: [22, 49] Generated Node #0,0,2: 66:[22, 49] Operation: 86-37=49 Exploring Operation: 86+22=108, Resulting Numbers: [37, 108] Generated Node #0,0,3: 66:[37, 108] Operation: 86+22=108 Exploring Operation: 37+22=59, Resulting Numbers: [86, 59] Generated Node #0,0,4: 66:[86, 59] Operation: 37+22=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[37, 64], Operations: ['88/4=22', '86-22=64'] Exploring Operation: 37+64=101, Resulting Numbers: [101] 101,66 unequal: No Solution Exploring Operation: 37*64=2368, Resulting Numbers: [2368] 2368,66 unequal: No Solution Exploring Operation: 64-37=27, Resulting Numbers: [27] 27,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 66:[22, 49], Operations: ['88/4=22', '86-37=49'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,66 unequal: No Solution Exploring Operation: 22*49=1078, Resulting Numbers: [1078] 1078,66 unequal: No Solution Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[86, 15], Operations: ['88/4=22', '37-22=15'] Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,66 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,66 unequal: No Solution Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 66:[86, 59], Operations: ['88/4=22', '37+22=59'] Exploring Operation: 86*59=5074, Resulting Numbers: [5074] 5074,66 unequal: No Solution Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,66 unequal: No Solution Exploring Operation: 86+59=145, Resulting Numbers: [145] 145,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[37, 108], Operations: ['88/4=22', '86+22=108'] Exploring Operation: 37+108=145, Resulting Numbers: [145] 145,66 unequal: No Solution Exploring Operation: 37*108=3996, Resulting Numbers: [3996] 3996,66 unequal: No Solution Exploring Operation: 108-37=71, Resulting Numbers: [71] 71,66 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: 66:[4, 86, 51], Operations: ['88-37=51'] Exploring Operation: 86-4=82, Resulting Numbers: [51, 82] Generated Node #0,3,0: 66:[51, 82] Operation: 86-4=82 Exploring Operation: 86-51=35, Resulting Numbers: [4, 35] Generated Node #0,3,1: 66:[4, 35] Operation: 86-51=35 Exploring Operation: 4+86=90, Resulting Numbers: [51, 90] Generated Node #0,3,2: 66:[51, 90] Operation: 4+86=90 Exploring Operation: 4+51=55, Resulting Numbers: [86, 55] Generated Node #0,3,3: 66:[86, 55] Operation: 4+51=55 Exploring Operation: 51-4=47, Resulting Numbers: [86, 47] Generated Node #0,3,4: 66:[86, 47] Operation: 51-4=47 Moving to Node #0,1 Current State: 66:[4, 88, 49], Operations: ['86-37=49'] Exploring Operation: 4+49=53, Resulting Numbers: [88, 53] Generated Node #0,1,0: 66:[88, 53] Operation: 4+49=53 Exploring Operation: 88-49=39, Resulting Numbers: [4, 39] Generated Node #0,1,1: 66:[4, 39] Operation: 88-49=39 Exploring Operation: 88-4=84, Resulting Numbers: [49, 84] Generated Node #0,1,2: 66:[49, 84] Operation: 88-4=84 Exploring Operation: 49-4=45, Resulting Numbers: [88, 45] Generated Node #0,1,3: 66:[88, 45] Operation: 49-4=45 Exploring Operation: 88/4=22, Resulting Numbers: [49, 22] Generated Node #0,1,4: 66:[49, 22] Operation: 88/4=22 Moving to Node #0,2 Current State: 66:[88, 86, 33], Operations: ['37-4=33'] Exploring Operation: 86-33=53, Resulting Numbers: [88, 53] Generated Node #0,2,0: 66:[88, 53] Operation: 86-33=53 Exploring Operation: 86+33=119, Resulting Numbers: [88, 119] Generated Node #0,2,1: 66:[88, 119] Operation: 86+33=119 Exploring Operation: 88+33=121, Resulting Numbers: [86, 121] Generated Node #0,2,2: 66:[86, 121] Operation: 88+33=121 Exploring Operation: 88-86=2, Resulting Numbers: [33, 2] Generated Node #0,2,3: 66:[33, 2] Operation: 88-86=2 Exploring Operation: 88-33=55, Resulting Numbers: [86, 55] Generated Node #0,2,4: 66:[86, 55] Operation: 88-33=55 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 66:[33, 2], Operations: ['37-4=33', '88-86=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,66 unequal: No Solution Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[4, 37, 88, 86], Operations: [] Exploring Operation: 37-4=33, Resulting Numbers: [88, 86, 33] Generated Node #0,2: 66:[88, 86, 33] Operation: 37-4=33 Moving to Node #0,2 Current State: 66:[88, 86, 33], Operations: ['37-4=33'] Exploring Operation: 88-86=2, Resulting Numbers: [33, 2] Generated Node #0,2,3: 66:[33, 2] Operation: 88-86=2 Moving to Node #0,2,3 Current State: 66:[33, 2], Operations: ['37-4=33', '88-86=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_5
sum_heuristic
[ 12, 66, 72, 4 ]
42
[ "72/12=6", "4*6=24", "66-24=42" ]
Current State: 42:[12, 66, 72, 4], Operations: [] Exploring Operation: 72/12=6, Resulting Numbers: [66, 4, 6] Generated Node #2: [66, 4, 6] from Operation: 72/12=6 Current State: 42:[66, 4, 6], Operations: ['72/12=6'] Exploring Operation: 4*6=24, Resulting Numbers: [66, 24] Generated Node #3: [66, 24] from Operation: 4*6=24 Current State: 42:[66, 24], Operations: ['72/12=6', '4*6=24'] Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[12, 66, 72, 4], Operations: [] Exploring Operation: 72/4=18, Resulting Numbers: [12, 66, 18] Generated Node #0,0: 42:[12, 66, 18] Operation: 72/4=18 Exploring Operation: 72-66=6, Resulting Numbers: [12, 4, 6] Generated Node #0,1: 42:[12, 4, 6] Operation: 72-66=6 Exploring Operation: 72-12=60, Resulting Numbers: [66, 4, 60] Generated Node #0,2: 42:[66, 4, 60] Operation: 72-12=60 Exploring Operation: 66-12=54, Resulting Numbers: [72, 4, 54] Generated Node #0,3: 42:[72, 4, 54] Operation: 66-12=54 Exploring Operation: 72/12=6, Resulting Numbers: [66, 4, 6] Generated Node #0,4: 42:[66, 4, 6] Operation: 72/12=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[12, 4, 6], Operations: ['72-66=6'] Exploring Operation: 12-6=6, Resulting Numbers: [4, 6] Generated Node #0,1,0: 42:[4, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 42:[4, 2] Operation: 12/6=2 Exploring Operation: 12+4=16, Resulting Numbers: [6, 16] Generated Node #0,1,2: 42:[6, 16] Operation: 12+4=16 Exploring Operation: 12-4=8, Resulting Numbers: [6, 8] Generated Node #0,1,3: 42:[6, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [6, 3] Generated Node #0,1,4: 42:[6, 3] Operation: 12/4=3 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 42:[6, 3], Operations: ['72-66=6', '12/4=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,42 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[4, 6], Operations: ['72-66=6', '12-6=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[4, 2], Operations: ['72-66=6', '12/6=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 42:[6, 8], Operations: ['72-66=6', '12-4=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[6, 16], Operations: ['72-66=6', '12+4=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 42:[66, 4, 6], Operations: ['72/12=6'] Exploring Operation: 4+6=10, Resulting Numbers: [66, 10] Generated Node #0,4,0: 42:[66, 10] Operation: 4+6=10 Exploring Operation: 66/6=11, Resulting Numbers: [4, 11] Generated Node #0,4,1: 42:[4, 11] Operation: 66/6=11 Exploring Operation: 66-6=60, Resulting Numbers: [4, 60] Generated Node #0,4,2: 42:[4, 60] Operation: 66-6=60 Exploring Operation: 6-4=2, Resulting Numbers: [66, 2] Generated Node #0,4,3: 42:[66, 2] Operation: 6-4=2 Exploring Operation: 66-4=62, Resulting Numbers: [6, 62] Generated Node #0,4,4: 42:[6, 62] Operation: 66-4=62 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 42:[4, 11], Operations: ['72/12=6', '66/6=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,42 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 42:[4, 60], Operations: ['72/12=6', '66-6=60'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 4*60=240, Resulting Numbers: [240] 240,42 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,42 unequal: No Solution Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 42:[6, 62], Operations: ['72/12=6', '66-4=62'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,42 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 42:[66, 2], Operations: ['72/12=6', '6-4=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,42 unequal: No Solution Exploring Operation: 66*2=132, Resulting Numbers: [132] 132,42 unequal: No Solution Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 42:[66, 10], Operations: ['72/12=6', '4+6=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,42 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 66*10=660, Resulting Numbers: [660] 660,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[12, 66, 18], Operations: ['72/4=18'] Exploring Operation: 66-18=48, Resulting Numbers: [12, 48] Generated Node #0,0,0: 42:[12, 48] Operation: 66-18=48 Exploring Operation: 12+66=78, Resulting Numbers: [18, 78] Generated Node #0,0,1: 42:[18, 78] Operation: 12+66=78 Exploring Operation: 12+18=30, Resulting Numbers: [66, 30] Generated Node #0,0,2: 42:[66, 30] Operation: 12+18=30 Exploring Operation: 18-12=6, Resulting Numbers: [66, 6] Generated Node #0,0,3: 42:[66, 6] Operation: 18-12=6 Exploring Operation: 66-12=54, Resulting Numbers: [18, 54] Generated Node #0,0,4: 42:[18, 54] Operation: 66-12=54 Moving to Node #0,0,0 Current State: 42:[12, 48], Operations: ['72/4=18', '66-18=48'] Exploring Operation: 12*48=576, Resulting Numbers: [576] 576,42 unequal: No Solution Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 12+48=60, Resulting Numbers: [60] 60,42 unequal: No Solution Moving to Node #0,0,4 Current State: 42:[18, 54], Operations: ['72/4=18', '66-12=54'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 18+54=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 18*54=972, Resulting Numbers: [972] 972,42 unequal: No Solution Moving to Node #0,0,3 Current State: 42:[66, 6], Operations: ['72/4=18', '18-12=6'] Exploring Operation: 66+6=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 66*6=396, Resulting Numbers: [396] 396,42 unequal: No Solution Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,42 unequal: No Solution Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[66, 30], Operations: ['72/4=18', '12+18=30'] Exploring Operation: 66+30=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 66-30=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 66*30=1980, Resulting Numbers: [1980] 1980,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[18, 78], Operations: ['72/4=18', '12+66=78'] Exploring Operation: 18*78=1404, Resulting Numbers: [1404] 1404,42 unequal: No Solution Exploring Operation: 18+78=96, Resulting Numbers: [96] 96,42 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[66, 4, 60], Operations: ['72-12=60'] Exploring Operation: 60/4=15, Resulting Numbers: [66, 15] Generated Node #0,2,0: 42:[66, 15] Operation: 60/4=15 Exploring Operation: 66+4=70, Resulting Numbers: [60, 70] Generated Node #0,2,1: 42:[60, 70] Operation: 66+4=70 Exploring Operation: 66-4=62, Resulting Numbers: [60, 62] Generated Node #0,2,2: 42:[60, 62] Operation: 66-4=62 Exploring Operation: 66-60=6, Resulting Numbers: [4, 6] Generated Node #0,2,3: 42:[4, 6] Operation: 66-60=6 Exploring Operation: 60-4=56, Resulting Numbers: [66, 56] Generated Node #0,2,4: 42:[66, 56] Operation: 60-4=56 Moving to Node #0,2,3 Current State: 42:[4, 6], Operations: ['72-12=60', '66-60=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,42 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[66, 15], Operations: ['72-12=60', '60/4=15'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 66+15=81, Resulting Numbers: [81] 81,42 unequal: No Solution Exploring Operation: 66*15=990, Resulting Numbers: [990] 990,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[60, 62], Operations: ['72-12=60', '66-4=62'] Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,42 unequal: No Solution Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,42 unequal: No Solution Moving to Node #0,2,4 Current State: 42:[66, 56], Operations: ['72-12=60', '60-4=56'] Exploring Operation: 66*56=3696, Resulting Numbers: [3696] 3696,42 unequal: No Solution Exploring Operation: 66+56=122, Resulting Numbers: [122] 122,42 unequal: No Solution Exploring Operation: 66-56=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[60, 70], Operations: ['72-12=60', '66+4=70'] Exploring Operation: 70-60=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 60*70=4200, Resulting Numbers: [4200] 4200,42 unequal: No Solution Exploring Operation: 60+70=130, Resulting Numbers: [130] 130,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[72, 4, 54], Operations: ['66-12=54'] Exploring Operation: 72-4=68, Resulting Numbers: [54, 68] Generated Node #0,3,0: 42:[54, 68] Operation: 72-4=68 Exploring Operation: 54-4=50, Resulting Numbers: [72, 50] Generated Node #0,3,1: 42:[72, 50] Operation: 54-4=50 Exploring Operation: 72+4=76, Resulting Numbers: [54, 76] Generated Node #0,3,2: 42:[54, 76] Operation: 72+4=76 Exploring Operation: 72-54=18, Resulting Numbers: [4, 18] Generated Node #0,3,3: 42:[4, 18] Operation: 72-54=18 Exploring Operation: 72/4=18, Resulting Numbers: [54, 18] Generated Node #0,3,4: 42:[54, 18] Operation: 72/4=18 Moving to Node #0,3,3 Current State: 42:[4, 18], Operations: ['66-12=54', '72-54=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,42 unequal: No Solution Moving to Node #0,3,4 Current State: 42:[54, 18], Operations: ['66-12=54', '72/4=18'] Exploring Operation: 54*18=972, Resulting Numbers: [972] 972,42 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[54, 68], Operations: ['66-12=54', '72-4=68'] Exploring Operation: 54*68=3672, Resulting Numbers: [3672] 3672,42 unequal: No Solution Exploring Operation: 68-54=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 54+68=122, Resulting Numbers: [122] 122,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[72, 50], Operations: ['66-12=54', '54-4=50'] Exploring Operation: 72+50=122, Resulting Numbers: [122] 122,42 unequal: No Solution Exploring Operation: 72-50=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 72*50=3600, Resulting Numbers: [3600] 3600,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[54, 76], Operations: ['66-12=54', '72+4=76'] Exploring Operation: 54+76=130, Resulting Numbers: [130] 130,42 unequal: No Solution Exploring Operation: 76-54=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 54*76=4104, Resulting Numbers: [4104] 4104,42 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
[ 2, 32, 22, 36 ]
36
[ "36/2=18", "32+22=54", "54-18=36" ]
Current State: 36:[2, 32, 22, 36], Operations: [] Exploring Operation: 36/2=18, Resulting Numbers: [32, 22, 18] Generated Node #2: [32, 22, 18] from Operation: 36/2=18 Current State: 36:[32, 22, 18], Operations: ['36/2=18'] Exploring Operation: 32+22=54, Resulting Numbers: [18, 54] Generated Node #3: [18, 54] from Operation: 32+22=54 Current State: 36:[18, 54], Operations: ['36/2=18', '32+22=54'] Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[2, 32, 22, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [2, 22, 4] Generated Node #0,0: 36:[2, 22, 4] Operation: 36-32=4 Exploring Operation: 32-22=10, Resulting Numbers: [2, 36, 10] Generated Node #0,1: 36:[2, 36, 10] Operation: 32-22=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[2, 36, 10], Operations: ['32-22=10'] Exploring Operation: 36/2=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 36:[10, 18] Operation: 36/2=18 Exploring Operation: 2+10=12, Resulting Numbers: [36, 12] Generated Node #0,1,1: 36:[36, 12] Operation: 2+10=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 36:[36, 12], Operations: ['32-22=10', '2+10=12'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,36 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 36:[10, 18], Operations: ['32-22=10', '36/2=18'] Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,36 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: 36:[2, 22, 4], Operations: ['36-32=4'] Exploring Operation: 22/2=11, Resulting Numbers: [4, 11] Generated Node #0,0,0: 36:[4, 11] Operation: 22/2=11 Exploring Operation: 22-4=18, Resulting Numbers: [2, 18] Generated Node #0,0,1: 36:[2, 18] Operation: 22-4=18 Moving to Node #0,0,1 Current State: 36:[2, 18], Operations: ['36-32=4', '22-4=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[2, 32, 22, 36], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [2, 22, 4] Generated Node #0,0: 36:[2, 22, 4] Operation: 36-32=4 Moving to Node #0,0 Current State: 36:[2, 22, 4], Operations: ['36-32=4'] Exploring Operation: 22-4=18, Resulting Numbers: [2, 18] Generated Node #0,0,1: 36:[2, 18] Operation: 22-4=18 Moving to Node #0,0,1 Current State: 36:[2, 18], Operations: ['36-32=4', '22-4=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 15, 65, 51, 13 ]
71
[ "15+51=66", "65/13=5", "66+5=71" ]
Current State: 71:[15, 65, 51, 13], Operations: [] Exploring Operation: 15+51=66, Resulting Numbers: [65, 13, 66] Generated Node #2: [65, 13, 66] from Operation: 15+51=66 Current State: 71:[65, 13, 66], Operations: ['15+51=66'] Exploring Operation: 65/13=5, Resulting Numbers: [66, 5] Generated Node #3: [66, 5] from Operation: 65/13=5 Current State: 71:[66, 5], Operations: ['15+51=66', '65/13=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[15, 65, 51, 13], Operations: [] Exploring Operation: 15+65=80, Resulting Numbers: [51, 13, 80] Generated Node #0,0: 71:[51, 13, 80] Operation: 15+65=80 Exploring Operation: 15+51=66, Resulting Numbers: [65, 13, 66] Generated Node #0,1: 71:[65, 13, 66] Operation: 15+51=66 Exploring Operation: 51+13=64, Resulting Numbers: [15, 65, 64] Generated Node #0,2: 71:[15, 65, 64] Operation: 51+13=64 Exploring Operation: 15+13=28, Resulting Numbers: [65, 51, 28] Generated Node #0,3: 71:[65, 51, 28] Operation: 15+13=28 Exploring Operation: 65+13=78, Resulting Numbers: [15, 51, 78] Generated Node #0,4: 71:[15, 51, 78] Operation: 65+13=78 Moving to Node #0,1 Current State: 71:[65, 13, 66], Operations: ['15+51=66'] Exploring Operation: 65/13=5, Resulting Numbers: [66, 5] Generated Node #0,1,0: 71:[66, 5] Operation: 65/13=5 Exploring Operation: 13+66=79, Resulting Numbers: [65, 79] Generated Node #0,1,1: 71:[65, 79] Operation: 13+66=79 Exploring Operation: 66-13=53, Resulting Numbers: [65, 53] Generated Node #0,1,2: 71:[65, 53] Operation: 66-13=53 Exploring Operation: 65+13=78, Resulting Numbers: [66, 78] Generated Node #0,1,3: 71:[66, 78] Operation: 65+13=78 Exploring Operation: 65-13=52, Resulting Numbers: [66, 52] Generated Node #0,1,4: 71:[66, 52] Operation: 65-13=52 Moving to Node #0,3 Current State: 71:[65, 51, 28], Operations: ['15+13=28'] Exploring Operation: 65+51=116, Resulting Numbers: [28, 116] Generated Node #0,3,0: 71:[28, 116] Operation: 65+51=116 Exploring Operation: 51+28=79, Resulting Numbers: [65, 79] Generated Node #0,3,1: 71:[65, 79] Operation: 51+28=79 Exploring Operation: 65-28=37, Resulting Numbers: [51, 37] Generated Node #0,3,2: 71:[51, 37] Operation: 65-28=37 Exploring Operation: 51-28=23, Resulting Numbers: [65, 23] Generated Node #0,3,3: 71:[65, 23] Operation: 51-28=23 Exploring Operation: 65+28=93, Resulting Numbers: [51, 93] Generated Node #0,3,4: 71:[51, 93] Operation: 65+28=93 Moving to Node #0,2 Current State: 71:[15, 65, 64], Operations: ['51+13=64'] Exploring Operation: 64-15=49, Resulting Numbers: [65, 49] Generated Node #0,2,0: 71:[65, 49] Operation: 64-15=49 Exploring Operation: 65-15=50, Resulting Numbers: [64, 50] Generated Node #0,2,1: 71:[64, 50] Operation: 65-15=50 Exploring Operation: 15+64=79, Resulting Numbers: [65, 79] Generated Node #0,2,2: 71:[65, 79] Operation: 15+64=79 Exploring Operation: 15+65=80, Resulting Numbers: [64, 80] Generated Node #0,2,3: 71:[64, 80] Operation: 15+65=80 Exploring Operation: 65+64=129, Resulting Numbers: [15, 129] Generated Node #0,2,4: 71:[15, 129] Operation: 65+64=129 Moving to Node #0,4 Current State: 71:[15, 51, 78], Operations: ['65+13=78'] Exploring Operation: 78-51=27, Resulting Numbers: [15, 27] Generated Node #0,4,0: 71:[15, 27] Operation: 78-51=27 Exploring Operation: 15+51=66, Resulting Numbers: [78, 66] Generated Node #0,4,1: 71:[78, 66] Operation: 15+51=66 Exploring Operation: 15+78=93, Resulting Numbers: [51, 93] Generated Node #0,4,2: 71:[51, 93] Operation: 15+78=93 Exploring Operation: 78-15=63, Resulting Numbers: [51, 63] Generated Node #0,4,3: 71:[51, 63] Operation: 78-15=63 Exploring Operation: 51-15=36, Resulting Numbers: [78, 36] Generated Node #0,4,4: 71:[78, 36] Operation: 51-15=36 Moving to Node #0,0 Current State: 71:[51, 13, 80], Operations: ['15+65=80'] Exploring Operation: 80-13=67, Resulting Numbers: [51, 67] Generated Node #0,0,0: 71:[51, 67] Operation: 80-13=67 Exploring Operation: 51+13=64, Resulting Numbers: [80, 64] Generated Node #0,0,1: 71:[80, 64] Operation: 51+13=64 Exploring Operation: 51-13=38, Resulting Numbers: [80, 38] Generated Node #0,0,2: 71:[80, 38] Operation: 51-13=38 Exploring Operation: 80-51=29, Resulting Numbers: [13, 29] Generated Node #0,0,3: 71:[13, 29] Operation: 80-51=29 Exploring Operation: 13+80=93, Resulting Numbers: [51, 93] Generated Node #0,0,4: 71:[51, 93] Operation: 13+80=93 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[80, 64], Operations: ['15+65=80', '51+13=64'] Exploring Operation: 80*64=5120, Resulting Numbers: [5120] 5120,71 unequal: No Solution Exploring Operation: 80+64=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,71 unequal: No Solution No 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: 71:[51, 67], Operations: ['15+65=80', '80-13=67'] Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 51+67=118, Resulting Numbers: [118] 118,71 unequal: No Solution Exploring Operation: 51*67=3417, Resulting Numbers: [3417] 3417,71 unequal: No Solution No 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: 71:[80, 38], Operations: ['15+65=80', '51-13=38'] Exploring Operation: 80+38=118, Resulting Numbers: [118] 118,71 unequal: No Solution Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 80*38=3040, Resulting Numbers: [3040] 3040,71 unequal: No Solution No 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: 71:[51, 93], Operations: ['15+65=80', '13+80=93'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,71 unequal: No Solution No 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: 71:[13, 29], Operations: ['15+65=80', '80-51=29'] Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,71 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,71 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: 71:[66, 78], Operations: ['15+51=66', '65+13=78'] Exploring Operation: 66*78=5148, Resulting Numbers: [5148] 5148,71 unequal: No Solution Exploring Operation: 66+78=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,4,1 Current State: 71:[78, 66], Operations: ['65+13=78', '15+51=66'] Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 78+66=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 78*66=5148, Resulting Numbers: [5148] 5148,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[65, 79], Operations: ['15+13=28', '51+28=79'] Exploring Operation: 65+79=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 65*79=5135, Resulting Numbers: [5135] 5135,71 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[65, 79], Operations: ['51+13=64', '15+64=79'] Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 65*79=5135, Resulting Numbers: [5135] 5135,71 unequal: No Solution Exploring Operation: 65+79=144, Resulting Numbers: [144] 144,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[65, 79], Operations: ['15+51=66', '13+66=79'] Exploring Operation: 65*79=5135, Resulting Numbers: [5135] 5135,71 unequal: No Solution Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 65+79=144, Resulting Numbers: [144] 144,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[64, 80], Operations: ['51+13=64', '15+65=80'] Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 64*80=5120, Resulting Numbers: [5120] 5120,71 unequal: No Solution Exploring Operation: 64+80=144, Resulting Numbers: [144] 144,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[65, 53], Operations: ['15+51=66', '66-13=53'] Exploring Operation: 65+53=118, Resulting Numbers: [118] 118,71 unequal: No Solution Exploring Operation: 65*53=3445, Resulting Numbers: [3445] 3445,71 unequal: No Solution Exploring Operation: 65-53=12, Resulting Numbers: [12] 12,71 unequal: No Solution Moving to Node #0,1,4 Current State: 71:[66, 52], Operations: ['15+51=66', '65-13=52'] Exploring Operation: 66-52=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 66*52=3432, Resulting Numbers: [3432] 3432,71 unequal: No Solution Exploring Operation: 66+52=118, Resulting Numbers: [118] 118,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[64, 50], Operations: ['51+13=64', '65-15=50'] Exploring Operation: 64+50=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 64*50=3200, Resulting Numbers: [3200] 3200,71 unequal: No Solution Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[65, 49], Operations: ['51+13=64', '64-15=49'] Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 65*49=3185, Resulting Numbers: [3185] 3185,71 unequal: No Solution Exploring Operation: 65+49=114, Resulting Numbers: [114] 114,71 unequal: No Solution Moving to Node #0,4,3 Current State: 71:[51, 63], Operations: ['65+13=78', '78-15=63'] Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,71 unequal: No Solution Exploring Operation: 51+63=114, Resulting Numbers: [114] 114,71 unequal: No Solution Exploring Operation: 51*63=3213, Resulting Numbers: [3213] 3213,71 unequal: No Solution Moving to Node #0,3,4 Current State: 71:[51, 93], Operations: ['15+13=28', '65+28=93'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,71 unequal: No Solution Moving to Node #0,4,4 Current State: 71:[78, 36], Operations: ['65+13=78', '51-15=36'] Exploring Operation: 78*36=2808, Resulting Numbers: [2808] 2808,71 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 78+36=114, Resulting Numbers: [114] 114,71 unequal: No Solution Moving to Node #0,4,2 Current State: 71:[51, 93], Operations: ['65+13=78', '15+78=93'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[65, 23], Operations: ['15+13=28', '51-28=23'] Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,71 unequal: No Solution Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,71 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[51, 37], Operations: ['15+13=28', '65-28=37'] Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 51*37=1887, Resulting Numbers: [1887] 1887,71 unequal: No Solution Exploring Operation: 51+37=88, Resulting Numbers: [88] 88,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[66, 5], Operations: ['15+51=66', '65/13=5'] Exploring Operation: 66*5=330, Resulting Numbers: [330] 330,71 unequal: No Solution Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[15, 65, 51, 13], Operations: [] Exploring Operation: 15+51=66, Resulting Numbers: [65, 13, 66] Generated Node #0,1: 71:[65, 13, 66] Operation: 15+51=66 Moving to Node #0,1 Current State: 71:[65, 13, 66], Operations: ['15+51=66'] Exploring Operation: 65/13=5, Resulting Numbers: [66, 5] Generated Node #0,1,0: 71:[66, 5] Operation: 65/13=5 Moving to Node #0,1,0 Current State: 71:[66, 5], Operations: ['15+51=66', '65/13=5'] Exploring Operation: 66+5=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
0.914063
hs_5
mult_heuristic
[ 78, 29, 11, 15 ]
53
[ "78-29=49", "15-11=4", "49+4=53" ]
Current State: 53:[78, 29, 11, 15], Operations: [] Exploring Operation: 78-29=49, Resulting Numbers: [11, 15, 49] Generated Node #2: [11, 15, 49] from Operation: 78-29=49 Current State: 53:[11, 15, 49], Operations: ['78-29=49'] Exploring Operation: 15-11=4, Resulting Numbers: [49, 4] Generated Node #3: [49, 4] from Operation: 15-11=4 Current State: 53:[49, 4], Operations: ['78-29=49', '15-11=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[78, 29, 11, 15], Operations: [] Exploring Operation: 78-15=63, Resulting Numbers: [29, 11, 63] Generated Node #0,0: 53:[29, 11, 63] Operation: 78-15=63 Exploring Operation: 78-11=67, Resulting Numbers: [29, 15, 67] Generated Node #0,1: 53:[29, 15, 67] Operation: 78-11=67 Moving to Node #0,0 Current State: 53:[29, 11, 63], Operations: ['78-15=63'] Exploring Operation: 29+11=40, Resulting Numbers: [63, 40] Generated Node #0,0,0: 53:[63, 40] Operation: 29+11=40 Exploring Operation: 63-11=52, Resulting Numbers: [29, 52] Generated Node #0,0,1: 53:[29, 52] Operation: 63-11=52 Moving to Node #0,1 Current State: 53:[29, 15, 67], Operations: ['78-11=67'] Exploring Operation: 29+15=44, Resulting Numbers: [67, 44] Generated Node #0,1,0: 53:[67, 44] Operation: 29+15=44 Exploring Operation: 67-15=52, Resulting Numbers: [29, 52] Generated Node #0,1,1: 53:[29, 52] Operation: 67-15=52 Moving to Node #0,0,0 Current State: 53:[63, 40], Operations: ['78-15=63', '29+11=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,53 unequal: No Solution Exploring Operation: 63+40=103, Resulting Numbers: [103] 103,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[67, 44], Operations: ['78-11=67', '29+15=44'] Exploring Operation: 67+44=111, Resulting Numbers: [111] 111,53 unequal: No Solution Exploring Operation: 67-44=23, Resulting Numbers: [23] 23,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[29, 52], Operations: ['78-15=63', '63-11=52'] Exploring Operation: 29+52=81, Resulting Numbers: [81] 81,53 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[29, 52], Operations: ['78-11=67', '67-15=52'] Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,53 unequal: No Solution Exploring Operation: 29+52=81, Resulting Numbers: [81] 81,53 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 96, 55, 98, 27 ]
56
[ "98-96=2", "55-27=28", "2*28=56" ]
Current State: 56:[96, 55, 98, 27], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [55, 27, 2] Generated Node #2: [55, 27, 2] from Operation: 98-96=2 Current State: 56:[55, 27, 2], Operations: ['98-96=2'] Exploring Operation: 55-27=28, Resulting Numbers: [2, 28] Generated Node #3: [2, 28] from Operation: 55-27=28 Current State: 56:[2, 28], Operations: ['98-96=2', '55-27=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[96, 55, 98, 27], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [55, 27, 2] Generated Node #0,0: 56:[55, 27, 2] Operation: 98-96=2 Exploring Operation: 98-55=43, Resulting Numbers: [96, 27, 43] Generated Node #0,1: 56:[96, 27, 43] Operation: 98-55=43 Moving to Node #0,0 Current State: 56:[55, 27, 2], Operations: ['98-96=2'] Exploring Operation: 55-27=28, Resulting Numbers: [2, 28] Generated Node #0,0,0: 56:[2, 28] Operation: 55-27=28 Exploring Operation: 55+2=57, Resulting Numbers: [27, 57] Generated Node #0,0,1: 56:[27, 57] Operation: 55+2=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[2, 28], Operations: ['98-96=2', '55-27=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[96, 55, 98, 27], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [55, 27, 2] Generated Node #0,0: 56:[55, 27, 2] Operation: 98-96=2 Moving to Node #0,0 Current State: 56:[55, 27, 2], Operations: ['98-96=2'] Exploring Operation: 55-27=28, Resulting Numbers: [2, 28] Generated Node #0,0,0: 56:[2, 28] Operation: 55-27=28 Moving to Node #0,0,0 Current State: 56:[2, 28], Operations: ['98-96=2', '55-27=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 46, 47, 2, 96 ]
52
[ "96-47=49", "2*49=98", "98-46=52" ]
Current State: 52:[46, 47, 2, 96], Operations: [] Exploring Operation: 96-47=49, Resulting Numbers: [46, 2, 49] Generated Node #2: [46, 2, 49] from Operation: 96-47=49 Current State: 52:[46, 2, 49], Operations: ['96-47=49'] Exploring Operation: 2*49=98, Resulting Numbers: [46, 98] Generated Node #3: [46, 98] from Operation: 2*49=98 Current State: 52:[46, 98], Operations: ['96-47=49', '2*49=98'] Exploring Operation: 98-46=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[46, 47, 2, 96], Operations: [] Exploring Operation: 96-46=50, Resulting Numbers: [47, 2, 50] Generated Node #0,0: 52:[47, 2, 50] Operation: 96-46=50 Moving to Node #0,0 Current State: 52:[47, 2, 50], Operations: ['96-46=50'] Exploring Operation: 50-47=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 52:[2, 3] Operation: 50-47=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[2, 3], Operations: ['96-46=50', '50-47=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 50, 21, 72, 53 ]
65
[ "53-50=3", "21/3=7", "72-7=65" ]
Current State: 65:[50, 21, 72, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [21, 72, 3] Generated Node #2: [21, 72, 3] from Operation: 53-50=3 Current State: 65:[21, 72, 3], Operations: ['53-50=3'] Exploring Operation: 21/3=7, Resulting Numbers: [72, 7] Generated Node #3: [72, 7] from Operation: 21/3=7 Current State: 65:[72, 7], Operations: ['53-50=3', '21/3=7'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[50, 21, 72, 53], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [21, 53, 22] Generated Node #0,0: 65:[21, 53, 22] Operation: 72-50=22 Exploring Operation: 53-50=3, Resulting Numbers: [21, 72, 3] Generated Node #0,1: 65:[21, 72, 3] Operation: 53-50=3 Exploring Operation: 21+53=74, Resulting Numbers: [50, 72, 74] Generated Node #0,2: 65:[50, 72, 74] Operation: 21+53=74 Exploring Operation: 72-53=19, Resulting Numbers: [50, 21, 19] Generated Node #0,3: 65:[50, 21, 19] Operation: 72-53=19 Exploring Operation: 50+21=71, Resulting Numbers: [72, 53, 71] Generated Node #0,4: 65:[72, 53, 71] Operation: 50+21=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[21, 72, 3], Operations: ['53-50=3'] Exploring Operation: 21-3=18, Resulting Numbers: [72, 18] Generated Node #0,1,0: 65:[72, 18] Operation: 21-3=18 Exploring Operation: 72-21=51, Resulting Numbers: [3, 51] Generated Node #0,1,1: 65:[3, 51] Operation: 72-21=51 Exploring Operation: 72-3=69, Resulting Numbers: [21, 69] Generated Node #0,1,2: 65:[21, 69] Operation: 72-3=69 Exploring Operation: 21/3=7, Resulting Numbers: [72, 7] Generated Node #0,1,3: 65:[72, 7] Operation: 21/3=7 Exploring Operation: 21*3=63, Resulting Numbers: [72, 63] Generated Node #0,1,4: 65:[72, 63] Operation: 21*3=63 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 65:[72, 7], Operations: ['53-50=3', '21/3=7'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[50, 21, 72, 53], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [21, 72, 3] Generated Node #0,1: 65:[21, 72, 3] Operation: 53-50=3 Moving to Node #0,1 Current State: 65:[21, 72, 3], Operations: ['53-50=3'] Exploring Operation: 21/3=7, Resulting Numbers: [72, 7] Generated Node #0,1,3: 65:[72, 7] Operation: 21/3=7 Moving to Node #0,1,3 Current State: 65:[72, 7], Operations: ['53-50=3', '21/3=7'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 14, 30, 16, 31 ]
46
[ "16-14=2", "30/2=15", "31+15=46" ]
Current State: 46:[14, 30, 16, 31], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [30, 31, 2] Generated Node #2: [30, 31, 2] from Operation: 16-14=2 Current State: 46:[30, 31, 2], Operations: ['16-14=2'] Exploring Operation: 30/2=15, Resulting Numbers: [31, 15] Generated Node #3: [31, 15] from Operation: 30/2=15 Current State: 46:[31, 15], Operations: ['16-14=2', '30/2=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[14, 30, 16, 31], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [30, 31, 2] Generated Node #0,0: 46:[30, 31, 2] Operation: 16-14=2 Exploring Operation: 30+16=46, Resulting Numbers: [14, 31, 46] Generated Node #0,1: 46:[14, 31, 46] Operation: 30+16=46 Exploring Operation: 14+30=44, Resulting Numbers: [16, 31, 44] Generated Node #0,2: 46:[16, 31, 44] Operation: 14+30=44 Exploring Operation: 14+31=45, Resulting Numbers: [30, 16, 45] Generated Node #0,3: 46:[30, 16, 45] Operation: 14+31=45 Exploring Operation: 31-30=1, Resulting Numbers: [14, 16, 1] Generated Node #0,4: 46:[14, 16, 1] Operation: 31-30=1 Moving to Node #0,0 Current State: 46:[30, 31, 2], Operations: ['16-14=2'] Exploring Operation: 31-30=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 46:[2, 1] Operation: 31-30=1 Exploring Operation: 30/2=15, Resulting Numbers: [31, 15] Generated Node #0,0,1: 46:[31, 15] Operation: 30/2=15 Exploring Operation: 30-2=28, Resulting Numbers: [31, 28] Generated Node #0,0,2: 46:[31, 28] Operation: 30-2=28 Exploring Operation: 31-2=29, Resulting Numbers: [30, 29] Generated Node #0,0,3: 46:[30, 29] Operation: 31-2=29 Exploring Operation: 30+31=61, Resulting Numbers: [2, 61] Generated Node #0,0,4: 46:[2, 61] Operation: 30+31=61 Moving to Node #0,3 Current State: 46:[30, 16, 45], Operations: ['14+31=45'] Exploring Operation: 30-16=14, Resulting Numbers: [45, 14] Generated Node #0,3,0: 46:[45, 14] Operation: 30-16=14 Exploring Operation: 45-16=29, Resulting Numbers: [30, 29] Generated Node #0,3,1: 46:[30, 29] Operation: 45-16=29 Exploring Operation: 45-30=15, Resulting Numbers: [16, 15] Generated Node #0,3,2: 46:[16, 15] Operation: 45-30=15 Exploring Operation: 30+16=46, Resulting Numbers: [45, 46] Generated Node #0,3,3: 46:[45, 46] Operation: 30+16=46 Exploring Operation: 16+45=61, Resulting Numbers: [30, 61] Generated Node #0,3,4: 46:[30, 61] Operation: 16+45=61 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 46:[45, 46], Operations: ['14+31=45', '30+16=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,46 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 46:[45, 14], Operations: ['14+31=45', '30-16=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 45*14=630, Resulting Numbers: [630] 630,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 46:[30, 29], Operations: ['14+31=45', '45-16=29'] Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,46 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 46:[16, 15], Operations: ['14+31=45', '45-30=15'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 16*15=240, Resulting Numbers: [240] 240,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 46:[30, 61], Operations: ['14+31=45', '16+45=61'] Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,46 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,46 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: 46:[14, 31, 46], Operations: ['30+16=46'] Exploring Operation: 14+46=60, Resulting Numbers: [31, 60] Generated Node #0,1,0: 46:[31, 60] Operation: 14+46=60 Exploring Operation: 46-14=32, Resulting Numbers: [31, 32] Generated Node #0,1,1: 46:[31, 32] Operation: 46-14=32 Exploring Operation: 14+31=45, Resulting Numbers: [46, 45] Generated Node #0,1,2: 46:[46, 45] Operation: 14+31=45 Exploring Operation: 46-31=15, Resulting Numbers: [14, 15] Generated Node #0,1,3: 46:[14, 15] Operation: 46-31=15 Exploring Operation: 31-14=17, Resulting Numbers: [46, 17] Generated Node #0,1,4: 46:[46, 17] Operation: 31-14=17 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[46, 45], Operations: ['30+16=46', '14+31=45'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 46+45=91, Resulting Numbers: [91] 91,46 unequal: No Solution Exploring Operation: 46*45=2070, Resulting Numbers: [2070] 2070,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 46:[46, 17], Operations: ['30+16=46', '31-14=17'] Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,46 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[31, 32], Operations: ['30+16=46', '46-14=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,46 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,46 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 46:[14, 15], Operations: ['30+16=46', '46-31=15'] Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,46 unequal: No Solution Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[31, 60], Operations: ['30+16=46', '14+46=60'] Exploring Operation: 31*60=1860, Resulting Numbers: [1860] 1860,46 unequal: No Solution Exploring Operation: 31+60=91, Resulting Numbers: [91] 91,46 unequal: No Solution Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,46 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: 46:[16, 31, 44], Operations: ['14+30=44'] Exploring Operation: 16+31=47, Resulting Numbers: [44, 47] Generated Node #0,2,0: 46:[44, 47] Operation: 16+31=47 Exploring Operation: 31-16=15, Resulting Numbers: [44, 15] Generated Node #0,2,1: 46:[44, 15] Operation: 31-16=15 Exploring Operation: 44-16=28, Resulting Numbers: [31, 28] Generated Node #0,2,2: 46:[31, 28] Operation: 44-16=28 Exploring Operation: 16+44=60, Resulting Numbers: [31, 60] Generated Node #0,2,3: 46:[31, 60] Operation: 16+44=60 Exploring Operation: 44-31=13, Resulting Numbers: [16, 13] Generated Node #0,2,4: 46:[16, 13] Operation: 44-31=13 Moving to Node #0,4 Current State: 46:[14, 16, 1], Operations: ['31-30=1'] Exploring Operation: 16-14=2, Resulting Numbers: [1, 2] Generated Node #0,4,0: 46:[1, 2] Operation: 16-14=2 Exploring Operation: 14+16=30, Resulting Numbers: [1, 30] Generated Node #0,4,1: 46:[1, 30] Operation: 14+16=30 Exploring Operation: 14+1=15, Resulting Numbers: [16, 15] Generated Node #0,4,2: 46:[16, 15] Operation: 14+1=15 Exploring Operation: 14*1=14, Resulting Numbers: [16, 14] Generated Node #0,4,3: 46:[16, 14] Operation: 14*1=14 Exploring Operation: 16+1=17, Resulting Numbers: [14, 17] Generated Node #0,4,4: 46:[14, 17] Operation: 16+1=17 Moving to Node #0,0,0 Current State: 46:[2, 1], Operations: ['16-14=2', '31-30=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,4,0 Current State: 46:[1, 2], Operations: ['31-30=1', '16-14=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[44, 47], Operations: ['14+30=44', '16+31=47'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,46 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[1, 30], Operations: ['31-30=1', '14+16=30'] Exploring Operation: 1+30=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[44, 15], Operations: ['14+30=44', '31-16=15'] Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,46 unequal: No Solution Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[30, 29], Operations: ['16-14=2', '31-2=29'] Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 30+29=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 30*29=870, Resulting Numbers: [870] 870,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[31, 28], Operations: ['16-14=2', '30-2=28'] Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,46 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[31, 28], Operations: ['14+30=44', '44-16=28'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,46 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,46 unequal: No Solution Moving to Node #0,4,2 Current State: 46:[16, 15], Operations: ['31-30=1', '14+1=15'] Exploring Operation: 16*15=240, Resulting Numbers: [240] 240,46 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[14, 17], Operations: ['31-30=1', '16+1=17'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[2, 61], Operations: ['16-14=2', '30+31=61'] Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,46 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,46 unequal: No Solution Moving to Node #0,4,3 Current State: 46:[16, 14], Operations: ['31-30=1', '14*1=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,46 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[31, 15], Operations: ['16-14=2', '30/2=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,46 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[14, 30, 16, 31], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [30, 31, 2] Generated Node #0,0: 46:[30, 31, 2] Operation: 16-14=2 Moving to Node #0,0 Current State: 46:[30, 31, 2], Operations: ['16-14=2'] Exploring Operation: 30/2=15, Resulting Numbers: [31, 15] Generated Node #0,0,1: 46:[31, 15] Operation: 30/2=15 Moving to Node #0,0,1 Current State: 46:[31, 15], Operations: ['16-14=2', '30/2=15'] Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
0.907986
hs_5
mult_heuristic
[ 13, 40, 22, 32 ]
28
[ "13+22=35", "32*35=1120", "1120/40=28" ]
Current State: 28:[13, 40, 22, 32], Operations: [] Exploring Operation: 13+22=35, Resulting Numbers: [40, 32, 35] Generated Node #2: [40, 32, 35] from Operation: 13+22=35 Current State: 28:[40, 32, 35], Operations: ['13+22=35'] Exploring Operation: 32*35=1120, Resulting Numbers: [40, 1120] Generated Node #3: [40, 1120] from Operation: 32*35=1120 Current State: 28:[40, 1120], Operations: ['13+22=35', '32*35=1120'] Exploring Operation: 1120/40=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[13, 40, 22, 32], Operations: [] Exploring Operation: 32-22=10, Resulting Numbers: [13, 40, 10] Generated Node #0,0: 28:[13, 40, 10] Operation: 32-22=10 Exploring Operation: 40-22=18, Resulting Numbers: [13, 32, 18] Generated Node #0,1: 28:[13, 32, 18] Operation: 40-22=18 Exploring Operation: 40-13=27, Resulting Numbers: [22, 32, 27] Generated Node #0,2: 28:[22, 32, 27] Operation: 40-13=27 Exploring Operation: 40-32=8, Resulting Numbers: [13, 22, 8] Generated Node #0,3: 28:[13, 22, 8] Operation: 40-32=8 Exploring Operation: 22-13=9, Resulting Numbers: [40, 32, 9] Generated Node #0,4: 28:[40, 32, 9] Operation: 22-13=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 28:[13, 22, 8], Operations: ['40-32=8'] Exploring Operation: 22+8=30, Resulting Numbers: [13, 30] Generated Node #0,3,0: 28:[13, 30] Operation: 22+8=30 Exploring Operation: 13+22=35, Resulting Numbers: [8, 35] Generated Node #0,3,1: 28:[8, 35] Operation: 13+22=35 Exploring Operation: 13-8=5, Resulting Numbers: [22, 5] Generated Node #0,3,2: 28:[22, 5] Operation: 13-8=5 Exploring Operation: 22-13=9, Resulting Numbers: [8, 9] Generated Node #0,3,3: 28:[8, 9] Operation: 22-13=9 Exploring Operation: 22-8=14, Resulting Numbers: [13, 14] Generated Node #0,3,4: 28:[13, 14] Operation: 22-8=14 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 28:[13, 14], Operations: ['40-32=8', '22-8=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,28 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 28:[13, 30], Operations: ['40-32=8', '22+8=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 28:[8, 9], Operations: ['40-32=8', '22-13=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 28:[22, 5], Operations: ['40-32=8', '13-8=5'] Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,28 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 28:[8, 35], Operations: ['40-32=8', '13+22=35'] Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,28 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[13, 32, 18], Operations: ['40-22=18'] Exploring Operation: 32-13=19, Resulting Numbers: [18, 19] Generated Node #0,1,0: 28:[18, 19] Operation: 32-13=19 Exploring Operation: 32-18=14, Resulting Numbers: [13, 14] Generated Node #0,1,1: 28:[13, 14] Operation: 32-18=14 Exploring Operation: 13+18=31, Resulting Numbers: [32, 31] Generated Node #0,1,2: 28:[32, 31] Operation: 13+18=31 Exploring Operation: 13+32=45, Resulting Numbers: [18, 45] Generated Node #0,1,3: 28:[18, 45] Operation: 13+32=45 Exploring Operation: 18-13=5, Resulting Numbers: [32, 5] Generated Node #0,1,4: 28:[32, 5] Operation: 18-13=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 28:[13, 14], Operations: ['40-22=18', '32-18=14'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,28 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 28:[32, 5], Operations: ['40-22=18', '18-13=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 28:[32, 31], Operations: ['40-22=18', '13+18=31'] Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,28 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[18, 19], Operations: ['40-22=18', '32-13=19'] Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,28 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 28:[18, 45], Operations: ['40-22=18', '13+32=45'] Exploring Operation: 18+45=63, Resulting Numbers: [63] 63,28 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 18*45=810, Resulting Numbers: [810] 810,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[22, 32, 27], Operations: ['40-13=27'] Exploring Operation: 32-27=5, Resulting Numbers: [22, 5] Generated Node #0,2,0: 28:[22, 5] Operation: 32-27=5 Exploring Operation: 27-22=5, Resulting Numbers: [32, 5] Generated Node #0,2,1: 28:[32, 5] Operation: 27-22=5 Exploring Operation: 32-22=10, Resulting Numbers: [27, 10] Generated Node #0,2,2: 28:[27, 10] Operation: 32-22=10 Exploring Operation: 22+32=54, Resulting Numbers: [27, 54] Generated Node #0,2,3: 28:[27, 54] Operation: 22+32=54 Exploring Operation: 22+27=49, Resulting Numbers: [32, 49] Generated Node #0,2,4: 28:[32, 49] Operation: 22+27=49 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[27, 10], Operations: ['40-13=27', '32-22=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[32, 5], Operations: ['40-13=27', '27-22=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,28 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,28 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 28:[22, 5], Operations: ['40-13=27', '32-27=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,28 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 28:[32, 49], Operations: ['40-13=27', '22+27=49'] Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,28 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 28:[27, 54], Operations: ['40-13=27', '22+32=54'] Exploring Operation: 27+54=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 27*54=1458, Resulting Numbers: [1458] 1458,28 unequal: No Solution Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[13, 40, 10], Operations: ['32-22=10'] Exploring Operation: 13+10=23, Resulting Numbers: [40, 23] Generated Node #0,0,0: 28:[40, 23] Operation: 13+10=23 Exploring Operation: 40/10=4, Resulting Numbers: [13, 4] Generated Node #0,0,1: 28:[13, 4] Operation: 40/10=4 Exploring Operation: 40-13=27, Resulting Numbers: [10, 27] Generated Node #0,0,2: 28:[10, 27] Operation: 40-13=27 Exploring Operation: 40-10=30, Resulting Numbers: [13, 30] Generated Node #0,0,3: 28:[13, 30] Operation: 40-10=30 Exploring Operation: 13-10=3, Resulting Numbers: [40, 3] Generated Node #0,0,4: 28:[40, 3] Operation: 13-10=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[13, 4], Operations: ['32-22=10', '40/10=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 28:[13, 30], Operations: ['32-22=10', '40-10=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 28:[10, 27], Operations: ['32-22=10', '40-13=27'] Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,28 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 28:[40, 3], Operations: ['32-22=10', '13-10=3'] Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,28 unequal: No Solution Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[40, 23], Operations: ['32-22=10', '13+10=23'] Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,28 unequal: No Solution Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 28:[40, 32, 9], Operations: ['22-13=9'] Exploring Operation: 40-9=31, Resulting Numbers: [32, 31] Generated Node #0,4,0: 28:[32, 31] Operation: 40-9=31 Exploring Operation: 40-32=8, Resulting Numbers: [9, 8] Generated Node #0,4,1: 28:[9, 8] Operation: 40-32=8 Exploring Operation: 40+9=49, Resulting Numbers: [32, 49] Generated Node #0,4,2: 28:[32, 49] Operation: 40+9=49 Exploring Operation: 32+9=41, Resulting Numbers: [40, 41] Generated Node #0,4,3: 28:[40, 41] Operation: 32+9=41 Exploring Operation: 32-9=23, Resulting Numbers: [40, 23] Generated Node #0,4,4: 28:[40, 23] Operation: 32-9=23 Moving to Node #0,4,1 Current State: 28:[9, 8], Operations: ['22-13=9', '40-32=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[32, 31], Operations: ['22-13=9', '40-9=31'] Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,28 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,28 unequal: No Solution Moving to Node #0,4,4 Current State: 28:[40, 23], Operations: ['22-13=9', '32-9=23'] Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,28 unequal: No Solution Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,28 unequal: No Solution Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,28 unequal: No Solution Moving to Node #0,4,2 Current State: 28:[32, 49], Operations: ['22-13=9', '40+9=49'] Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,28 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,28 unequal: No Solution Moving to Node #0,4,3 Current State: 28:[40, 41], Operations: ['22-13=9', '32+9=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,28 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,28 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
[ 48, 8, 40, 42 ]
47
[ "48/8=6", "42/6=7", "40+7=47" ]
Current State: 47:[48, 8, 40, 42], Operations: [] Exploring Operation: 48/8=6, Resulting Numbers: [40, 42, 6] Generated Node #2: [40, 42, 6] from Operation: 48/8=6 Current State: 47:[40, 42, 6], Operations: ['48/8=6'] Exploring Operation: 42/6=7, Resulting Numbers: [40, 7] Generated Node #3: [40, 7] from Operation: 42/6=7 Current State: 47:[40, 7], Operations: ['48/8=6', '42/6=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[48, 8, 40, 42], Operations: [] Exploring Operation: 8+40=48, Resulting Numbers: [48, 42, 48] Generated Node #0,0: 47:[48, 42, 48] Operation: 8+40=48 Moving to Node #0,0 Current State: 47:[48, 42, 48], Operations: ['8+40=48'] Exploring Operation: 48-42=6, Resulting Numbers: [48, 6] Generated Node #0,0,0: 47:[48, 6] Operation: 48-42=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[48, 6], Operations: ['8+40=48', '48-42=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,47 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, 67, 5, 65 ]
30
[ "86-67=19", "5*19=95", "95-65=30" ]
Current State: 30:[86, 67, 5, 65], Operations: [] Exploring Operation: 86-67=19, Resulting Numbers: [5, 65, 19] Generated Node #2: [5, 65, 19] from Operation: 86-67=19 Current State: 30:[5, 65, 19], Operations: ['86-67=19'] Exploring Operation: 5*19=95, Resulting Numbers: [65, 95] Generated Node #3: [65, 95] from Operation: 5*19=95 Current State: 30:[65, 95], Operations: ['86-67=19', '5*19=95'] Exploring Operation: 95-65=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[86, 67, 5, 65], Operations: [] Exploring Operation: 86-65=21, Resulting Numbers: [67, 5, 21] Generated Node #0,0: 30:[67, 5, 21] Operation: 86-65=21 Exploring Operation: 86-67=19, Resulting Numbers: [5, 65, 19] Generated Node #0,1: 30:[5, 65, 19] Operation: 86-67=19 Moving to Node #0,1 Current State: 30:[5, 65, 19], Operations: ['86-67=19'] Exploring Operation: 65-19=46, Resulting Numbers: [5, 46] Generated Node #0,1,0: 30:[5, 46] Operation: 65-19=46 Exploring Operation: 65/5=13, Resulting Numbers: [19, 13] Generated Node #0,1,1: 30:[19, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[19, 13], Operations: ['86-67=19', '65/5=13'] Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[5, 46], Operations: ['86-67=19', '65-19=46'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,30 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: 30:[67, 5, 21], Operations: ['86-65=21'] Exploring Operation: 67-5=62, Resulting Numbers: [21, 62] Generated Node #0,0,0: 30:[21, 62] Operation: 67-5=62 Exploring Operation: 67-21=46, Resulting Numbers: [5, 46] Generated Node #0,0,1: 30:[5, 46] Operation: 67-21=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[5, 46], Operations: ['86-65=21', '67-21=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,30 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[21, 62], Operations: ['86-65=21', '67-5=62'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 21+62=83, Resulting Numbers: [83] 83,30 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
[ 12, 58, 39, 24 ]
99
[ "24/12=2", "58+39=97", "2+97=99" ]
Current State: 99:[12, 58, 39, 24], Operations: [] Exploring Operation: 24/12=2, Resulting Numbers: [58, 39, 2] Generated Node #2: [58, 39, 2] from Operation: 24/12=2 Current State: 99:[58, 39, 2], Operations: ['24/12=2'] Exploring Operation: 58+39=97, Resulting Numbers: [2, 97] Generated Node #3: [2, 97] from Operation: 58+39=97 Current State: 99:[2, 97], Operations: ['24/12=2', '58+39=97'] Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[12, 58, 39, 24], Operations: [] Exploring Operation: 58+39=97, Resulting Numbers: [12, 24, 97] Generated Node #0,0: 99:[12, 24, 97] Operation: 58+39=97 Exploring Operation: 58-39=19, Resulting Numbers: [12, 24, 19] Generated Node #0,1: 99:[12, 24, 19] Operation: 58-39=19 Exploring Operation: 58-24=34, Resulting Numbers: [12, 39, 34] Generated Node #0,2: 99:[12, 39, 34] Operation: 58-24=34 Moving to Node #0,2 Current State: 99:[12, 39, 34], Operations: ['58-24=34'] Exploring Operation: 34-12=22, Resulting Numbers: [39, 22] Generated Node #0,2,0: 99:[39, 22] Operation: 34-12=22 Exploring Operation: 39-34=5, Resulting Numbers: [12, 5] Generated Node #0,2,1: 99:[12, 5] Operation: 39-34=5 Exploring Operation: 39-12=27, Resulting Numbers: [34, 27] Generated Node #0,2,2: 99:[34, 27] Operation: 39-12=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 99:[12, 5], Operations: ['58-24=34', '39-34=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,99 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[34, 27], Operations: ['58-24=34', '39-12=27'] Exploring Operation: 34*27=918, Resulting Numbers: [918] 918,99 unequal: No Solution Exploring Operation: 34+27=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[39, 22], Operations: ['58-24=34', '34-12=22'] Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,99 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 99:[12, 24, 97], Operations: ['58+39=97'] Exploring Operation: 12+24=36, Resulting Numbers: [97, 36] Generated Node #0,0,0: 99:[97, 36] Operation: 12+24=36 Exploring Operation: 24/12=2, Resulting Numbers: [97, 2] Generated Node #0,0,1: 99:[97, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [97, 12] Generated Node #0,0,2: 99:[97, 12] Operation: 24-12=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[97, 2], Operations: ['58+39=97', '24/12=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[12, 58, 39, 24], Operations: [] Exploring Operation: 58+39=97, Resulting Numbers: [12, 24, 97] Generated Node #0,0: 99:[12, 24, 97] Operation: 58+39=97 Moving to Node #0,0 Current State: 99:[12, 24, 97], Operations: ['58+39=97'] Exploring Operation: 24/12=2, Resulting Numbers: [97, 2] Generated Node #0,0,1: 99:[97, 2] Operation: 24/12=2 Moving to Node #0,0,1 Current State: 99:[97, 2], Operations: ['58+39=97', '24/12=2'] Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 86, 41, 98, 93 ]
40
[ "86-41=45", "98-93=5", "45-5=40" ]
Current State: 40:[86, 41, 98, 93], Operations: [] Exploring Operation: 86-41=45, Resulting Numbers: [98, 93, 45] Generated Node #2: [98, 93, 45] from Operation: 86-41=45 Current State: 40:[98, 93, 45], Operations: ['86-41=45'] Exploring Operation: 98-93=5, Resulting Numbers: [45, 5] Generated Node #3: [45, 5] from Operation: 98-93=5 Current State: 40:[45, 5], Operations: ['86-41=45', '98-93=5'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[86, 41, 98, 93], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [86, 41, 5] Generated Node #0,0: 40:[86, 41, 5] Operation: 98-93=5 Moving to Node #0,0 Current State: 40:[86, 41, 5], Operations: ['98-93=5'] Exploring Operation: 86-41=45, Resulting Numbers: [5, 45] Generated Node #0,0,0: 40:[5, 45] Operation: 86-41=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[5, 45], Operations: ['98-93=5', '86-41=45'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[86, 41, 98, 93], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [86, 41, 5] Generated Node #0,0: 40:[86, 41, 5] Operation: 98-93=5 Moving to Node #0,0 Current State: 40:[86, 41, 5], Operations: ['98-93=5'] Exploring Operation: 86-41=45, Resulting Numbers: [5, 45] Generated Node #0,0,0: 40:[5, 45] Operation: 86-41=45 Moving to Node #0,0,0 Current State: 40:[5, 45], Operations: ['98-93=5', '86-41=45'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 52, 24, 31, 24 ]
31
[ "24-24=0", "52*0=0", "31+0=31" ]
Current State: 31:[52, 24, 31, 24], Operations: [] Exploring Operation: 24-24=0, Resulting Numbers: [52, 31, 0] Generated Node #2: [52, 31, 0] from Operation: 24-24=0 Current State: 31:[52, 31, 0], Operations: ['24-24=0'] Exploring Operation: 52*0=0, Resulting Numbers: [31, 0] Generated Node #3: [31, 0] from Operation: 52*0=0 Current State: 31:[31, 0], Operations: ['24-24=0', '52*0=0'] Exploring Operation: 31+0=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[52, 24, 31, 24], Operations: [] Exploring Operation: 24+24=48, Resulting Numbers: [52, 31, 48] Generated Node #0,0: 31:[52, 31, 48] Operation: 24+24=48 Exploring Operation: 52-24=28, Resulting Numbers: [31, 24, 28] Generated Node #0,1: 31:[31, 24, 28] Operation: 52-24=28 Exploring Operation: 52-31=21, Resulting Numbers: [24, 24, 21] Generated Node #0,2: 31:[24, 24, 21] Operation: 52-31=21 Exploring Operation: 52-24=28, Resulting Numbers: [24, 31, 28] Generated Node #0,3: 31:[24, 31, 28] Operation: 52-24=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[31, 24, 28], Operations: ['52-24=28'] Exploring Operation: 28-24=4, Resulting Numbers: [31, 4] Generated Node #0,1,0: 31:[31, 4] Operation: 28-24=4 Exploring Operation: 31-24=7, Resulting Numbers: [28, 7] Generated Node #0,1,1: 31:[28, 7] Operation: 31-24=7 Exploring Operation: 24+28=52, Resulting Numbers: [31, 52] Generated Node #0,1,2: 31:[31, 52] Operation: 24+28=52 Exploring Operation: 31+24=55, Resulting Numbers: [28, 55] Generated Node #0,1,3: 31:[28, 55] Operation: 31+24=55 Moving to Node #0,1,2 Current State: 31:[31, 52], Operations: ['52-24=28', '24+28=52'] Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,31 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[28, 7], Operations: ['52-24=28', '31-24=7'] Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,31 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[31, 4], Operations: ['52-24=28', '28-24=4'] Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,31 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[28, 55], Operations: ['52-24=28', '31+24=55'] Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,31 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[24, 31, 28], Operations: ['52-24=28'] Exploring Operation: 24+28=52, Resulting Numbers: [31, 52] Generated Node #0,3,0: 31:[31, 52] Operation: 24+28=52 Exploring Operation: 28-24=4, Resulting Numbers: [31, 4] Generated Node #0,3,1: 31:[31, 4] Operation: 28-24=4 Exploring Operation: 24+31=55, Resulting Numbers: [28, 55] Generated Node #0,3,2: 31:[28, 55] Operation: 24+31=55 Exploring Operation: 31-24=7, Resulting Numbers: [28, 7] Generated Node #0,3,3: 31:[28, 7] Operation: 31-24=7 Moving to Node #0,3,0 Current State: 31:[31, 52], Operations: ['52-24=28', '24+28=52'] Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,31 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[28, 55], Operations: ['52-24=28', '24+31=55'] Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,31 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[31, 4], Operations: ['52-24=28', '28-24=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,31 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[28, 7], Operations: ['52-24=28', '31-24=7'] Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,31 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[24, 24, 21], Operations: ['52-31=21'] Exploring Operation: 24+21=45, Resulting Numbers: [24, 45] Generated Node #0,2,0: 31:[24, 45] Operation: 24+21=45 Exploring Operation: 24+21=45, Resulting Numbers: [24, 45] Generated Node #0,2,1: 31:[24, 45] Operation: 24+21=45 Exploring Operation: 24-21=3, Resulting Numbers: [24, 3] Generated Node #0,2,2: 31:[24, 3] Operation: 24-21=3 Exploring Operation: 24+24=48, Resulting Numbers: [21, 48] Generated Node #0,2,3: 31:[21, 48] Operation: 24+24=48 Moving to Node #0,2,0 Current State: 31:[24, 45], Operations: ['52-31=21', '24+21=45'] Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,31 unequal: No Solution Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[24, 45], Operations: ['52-31=21', '24+21=45'] Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,31 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[21, 48], Operations: ['52-31=21', '24+24=48'] Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,31 unequal: No Solution Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[24, 3], Operations: ['52-31=21', '24-21=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,31 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[52, 31, 48], Operations: ['24+24=48'] Exploring Operation: 52-48=4, Resulting Numbers: [31, 4] Generated Node #0,0,0: 31:[31, 4] Operation: 52-48=4 Exploring Operation: 52+31=83, Resulting Numbers: [48, 83] Generated Node #0,0,1: 31:[48, 83] Operation: 52+31=83 Exploring Operation: 48-31=17, Resulting Numbers: [52, 17] Generated Node #0,0,2: 31:[52, 17] Operation: 48-31=17 Exploring Operation: 52-31=21, Resulting Numbers: [48, 21] Generated Node #0,0,3: 31:[48, 21] Operation: 52-31=21 Moving to Node #0,0,0 Current State: 31:[31, 4], Operations: ['24+24=48', '52-48=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,31 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[48, 21], Operations: ['24+24=48', '52-31=21'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 48+21=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 48*21=1008, Resulting Numbers: [1008] 1008,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[52, 17], Operations: ['24+24=48', '48-31=17'] Exploring Operation: 52*17=884, Resulting Numbers: [884] 884,31 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[48, 83], Operations: ['24+24=48', '52+31=83'] Exploring Operation: 48+83=131, Resulting Numbers: [131] 131,31 unequal: No Solution Exploring Operation: 48*83=3984, Resulting Numbers: [3984] 3984,31 unequal: No Solution Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,31 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
[ 11, 39, 4, 9 ]
33
[ "11*39=429", "4+9=13", "429/13=33" ]
Current State: 33:[11, 39, 4, 9], Operations: [] Exploring Operation: 11*39=429, Resulting Numbers: [4, 9, 429] Generated Node #2: [4, 9, 429] from Operation: 11*39=429 Current State: 33:[4, 9, 429], Operations: ['11*39=429'] Exploring Operation: 4+9=13, Resulting Numbers: [429, 13] Generated Node #3: [429, 13] from Operation: 4+9=13 Current State: 33:[429, 13], Operations: ['11*39=429', '4+9=13'] Exploring Operation: 429/13=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[11, 39, 4, 9], Operations: [] Exploring Operation: 39-9=30, Resulting Numbers: [11, 4, 30] Generated Node #0,0: 33:[11, 4, 30] Operation: 39-9=30 Exploring Operation: 11-9=2, Resulting Numbers: [39, 4, 2] Generated Node #0,1: 33:[39, 4, 2] Operation: 11-9=2 Exploring Operation: 39-4=35, Resulting Numbers: [11, 9, 35] Generated Node #0,2: 33:[11, 9, 35] Operation: 39-4=35 Exploring Operation: 39-11=28, Resulting Numbers: [4, 9, 28] Generated Node #0,3: 33:[4, 9, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[11, 4, 30], Operations: ['39-9=30'] Exploring Operation: 4+30=34, Resulting Numbers: [11, 34] Generated Node #0,0,0: 33:[11, 34] Operation: 4+30=34 Exploring Operation: 30-4=26, Resulting Numbers: [11, 26] Generated Node #0,0,1: 33:[11, 26] Operation: 30-4=26 Exploring Operation: 11-4=7, Resulting Numbers: [30, 7] Generated Node #0,0,2: 33:[30, 7] Operation: 11-4=7 Exploring Operation: 11+4=15, Resulting Numbers: [30, 15] Generated Node #0,0,3: 33:[30, 15] Operation: 11+4=15 Moving to Node #0,0,0 Current State: 33:[11, 34], Operations: ['39-9=30', '4+30=34'] Exploring Operation: 11+34=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 11*34=374, Resulting Numbers: [374] 374,33 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,33 unequal: No Solution Moving to Node #0,0,2 Current State: 33:[30, 7], Operations: ['39-9=30', '11-4=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,33 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[11, 26], Operations: ['39-9=30', '30-4=26'] Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,33 unequal: No Solution Moving to Node #0,0,3 Current State: 33:[30, 15], Operations: ['39-9=30', '11+4=15'] Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,33 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[11, 9, 35], Operations: ['39-4=35'] Exploring Operation: 35-9=26, Resulting Numbers: [11, 26] Generated Node #0,2,0: 33:[11, 26] Operation: 35-9=26 Exploring Operation: 11+9=20, Resulting Numbers: [35, 20] Generated Node #0,2,1: 33:[35, 20] Operation: 11+9=20 Exploring Operation: 35-11=24, Resulting Numbers: [9, 24] Generated Node #0,2,2: 33:[9, 24] Operation: 35-11=24 Exploring Operation: 11-9=2, Resulting Numbers: [35, 2] Generated Node #0,2,3: 33:[35, 2] Operation: 11-9=2 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 33:[35, 2], Operations: ['39-4=35', '11-9=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,33 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[11, 39, 4, 9], Operations: [] Exploring Operation: 39-4=35, Resulting Numbers: [11, 9, 35] Generated Node #0,2: 33:[11, 9, 35] Operation: 39-4=35 Moving to Node #0,2 Current State: 33:[11, 9, 35], Operations: ['39-4=35'] Exploring Operation: 11-9=2, Resulting Numbers: [35, 2] Generated Node #0,2,3: 33:[35, 2] Operation: 11-9=2 Moving to Node #0,2,3 Current State: 33:[35, 2], Operations: ['39-4=35', '11-9=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 40, 91, 47, 45 ]
32
[ "47-40=7", "91/7=13", "45-13=32" ]
Current State: 32:[40, 91, 47, 45], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [91, 45, 7] Generated Node #2: [91, 45, 7] from Operation: 47-40=7 Current State: 32:[91, 45, 7], Operations: ['47-40=7'] Exploring Operation: 91/7=13, Resulting Numbers: [45, 13] Generated Node #3: [45, 13] from Operation: 91/7=13 Current State: 32:[45, 13], Operations: ['47-40=7', '91/7=13'] Exploring Operation: 45-13=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[40, 91, 47, 45], Operations: [] Exploring Operation: 91-45=46, Resulting Numbers: [40, 47, 46] Generated Node #0,0: 32:[40, 47, 46] Operation: 91-45=46 Exploring Operation: 91-40=51, Resulting Numbers: [47, 45, 51] Generated Node #0,1: 32:[47, 45, 51] Operation: 91-40=51 Exploring Operation: 91-47=44, Resulting Numbers: [40, 45, 44] Generated Node #0,2: 32:[40, 45, 44] Operation: 91-47=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[40, 45, 44], Operations: ['91-47=44'] Exploring Operation: 44-40=4, Resulting Numbers: [45, 4] Generated Node #0,2,0: 32:[45, 4] Operation: 44-40=4 Exploring Operation: 45-44=1, Resulting Numbers: [40, 1] Generated Node #0,2,1: 32:[40, 1] Operation: 45-44=1 Exploring Operation: 45-40=5, Resulting Numbers: [44, 5] Generated Node #0,2,2: 32:[44, 5] Operation: 45-40=5 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 32:[40, 1], Operations: ['91-47=44', '45-44=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[45, 4], Operations: ['91-47=44', '44-40=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 32:[44, 5], Operations: ['91-47=44', '45-40=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 44*5=220, Resulting Numbers: [220] 220,32 unequal: No Solution Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[40, 47, 46], Operations: ['91-45=46'] Exploring Operation: 46-40=6, Resulting Numbers: [47, 6] Generated Node #0,0,0: 32:[47, 6] Operation: 46-40=6 Exploring Operation: 47-46=1, Resulting Numbers: [40, 1] Generated Node #0,0,1: 32:[40, 1] Operation: 47-46=1 Exploring Operation: 47-40=7, Resulting Numbers: [46, 7] Generated Node #0,0,2: 32:[46, 7] Operation: 47-40=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[40, 1], Operations: ['91-45=46', '47-46=1'] Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,32 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[46, 7], Operations: ['91-45=46', '47-40=7'] Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,32 unequal: No Solution Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,32 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[47, 6], Operations: ['91-45=46', '46-40=6'] Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,32 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,32 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[47, 45, 51], Operations: ['91-40=51'] Exploring Operation: 51-45=6, Resulting Numbers: [47, 6] Generated Node #0,1,0: 32:[47, 6] Operation: 51-45=6 Exploring Operation: 47-45=2, Resulting Numbers: [51, 2] Generated Node #0,1,1: 32:[51, 2] Operation: 47-45=2 Exploring Operation: 51-47=4, Resulting Numbers: [45, 4] Generated Node #0,1,2: 32:[45, 4] Operation: 51-47=4 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 32:[45, 4], Operations: ['91-40=51', '51-47=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,32 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 32:[47, 6], Operations: ['91-40=51', '51-45=6'] Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,32 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[51, 2], Operations: ['91-40=51', '47-45=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,32 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 15, 59, 2, 72 ]
70
[ "15+59=74", "2*72=144", "144-74=70" ]
Current State: 70:[15, 59, 2, 72], Operations: [] Exploring Operation: 15+59=74, Resulting Numbers: [2, 72, 74] Generated Node #2: [2, 72, 74] from Operation: 15+59=74 Current State: 70:[2, 72, 74], Operations: ['15+59=74'] Exploring Operation: 2*72=144, Resulting Numbers: [74, 144] Generated Node #3: [74, 144] from Operation: 2*72=144 Current State: 70:[74, 144], Operations: ['15+59=74', '2*72=144'] Exploring Operation: 144-74=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[15, 59, 2, 72], Operations: [] Exploring Operation: 59+2=61, Resulting Numbers: [15, 72, 61] Generated Node #0,0: 70:[15, 72, 61] Operation: 59+2=61 Exploring Operation: 72-59=13, Resulting Numbers: [15, 2, 13] Generated Node #0,1: 70:[15, 2, 13] Operation: 72-59=13 Exploring Operation: 59-15=44, Resulting Numbers: [2, 72, 44] Generated Node #0,2: 70:[2, 72, 44] Operation: 59-15=44 Exploring Operation: 15+59=74, Resulting Numbers: [2, 72, 74] Generated Node #0,3: 70:[2, 72, 74] Operation: 15+59=74 Moving to Node #0,1 Current State: 70:[15, 2, 13], Operations: ['72-59=13'] Exploring Operation: 15-13=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 70:[2, 2] Operation: 15-13=2 Exploring Operation: 2+13=15, Resulting Numbers: [15, 15] Generated Node #0,1,1: 70:[15, 15] Operation: 2+13=15 Exploring Operation: 15-2=13, Resulting Numbers: [13, 13] Generated Node #0,1,2: 70:[13, 13] Operation: 15-2=13 Exploring Operation: 13-2=11, Resulting Numbers: [15, 11] Generated Node #0,1,3: 70:[15, 11] Operation: 13-2=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[2, 2], Operations: ['72-59=13', '15-13=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,70 unequal: No Solution No 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: 70:[15, 15], Operations: ['72-59=13', '2+13=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,70 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,70 unequal: No Solution No 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: 70:[13, 13], Operations: ['72-59=13', '15-2=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,70 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,70 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 13*13=169, Resulting Numbers: [169] 169,70 unequal: No Solution No 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: 70:[15, 11], Operations: ['72-59=13', '13-2=11'] Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,70 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,70 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: 70:[2, 72, 74], Operations: ['15+59=74'] Exploring Operation: 74-2=72, Resulting Numbers: [72, 72] Generated Node #0,3,0: 70:[72, 72] Operation: 74-2=72 Exploring Operation: 72-2=70, Resulting Numbers: [74, 70] Generated Node #0,3,1: 70:[74, 70] Operation: 72-2=70 Exploring Operation: 74-72=2, Resulting Numbers: [2, 2] Generated Node #0,3,2: 70:[2, 2] Operation: 74-72=2 Exploring Operation: 74/2=37, Resulting Numbers: [72, 37] Generated Node #0,3,3: 70:[72, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 70:[2, 2], Operations: ['15+59=74', '74-72=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,70 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,70 unequal: No Solution No 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: 70:[72, 72], Operations: ['15+59=74', '74-2=72'] Exploring Operation: 72*72=5184, Resulting Numbers: [5184] 5184,70 unequal: No Solution Exploring Operation: 72-72=0, Resulting Numbers: [0] 0,70 unequal: No Solution Exploring Operation: 72+72=144, Resulting Numbers: [144] 144,70 unequal: No Solution Exploring Operation: 72/72=1, Resulting Numbers: [1] 1,70 unequal: No Solution No 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: 70:[74, 70], Operations: ['15+59=74', '72-2=70'] Exploring Operation: 74*70=5180, Resulting Numbers: [5180] 5180,70 unequal: No Solution Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 74+70=144, Resulting Numbers: [144] 144,70 unequal: No Solution No 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: 70:[72, 37], Operations: ['15+59=74', '74/2=37'] Exploring Operation: 72-37=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 72+37=109, Resulting Numbers: [109] 109,70 unequal: No Solution Exploring Operation: 72*37=2664, Resulting Numbers: [2664] 2664,70 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: 70:[2, 72, 44], Operations: ['59-15=44'] Exploring Operation: 72-44=28, Resulting Numbers: [2, 28] Generated Node #0,2,0: 70:[2, 28] Operation: 72-44=28 Exploring Operation: 72-2=70, Resulting Numbers: [44, 70] Generated Node #0,2,1: 70:[44, 70] Operation: 72-2=70 Exploring Operation: 44-2=42, Resulting Numbers: [72, 42] Generated Node #0,2,2: 70:[72, 42] Operation: 44-2=42 Exploring Operation: 72/2=36, Resulting Numbers: [44, 36] Generated Node #0,2,3: 70:[44, 36] Operation: 72/2=36 Moving to Node #0,0 Current State: 70:[15, 72, 61], Operations: ['59+2=61'] Exploring Operation: 72-15=57, Resulting Numbers: [61, 57] Generated Node #0,0,0: 70:[61, 57] Operation: 72-15=57 Exploring Operation: 61-15=46, Resulting Numbers: [72, 46] Generated Node #0,0,1: 70:[72, 46] Operation: 61-15=46 Exploring Operation: 15+61=76, Resulting Numbers: [72, 76] Generated Node #0,0,2: 70:[72, 76] Operation: 15+61=76 Exploring Operation: 72-61=11, Resulting Numbers: [15, 11] Generated Node #0,0,3: 70:[15, 11] Operation: 72-61=11 Moving to Node #0,0,3 Current State: 70:[15, 11], Operations: ['59+2=61', '72-61=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,70 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[2, 28], Operations: ['59-15=44', '72-44=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,70 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,70 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[72, 76], Operations: ['59+2=61', '15+61=76'] Exploring Operation: 72+76=148, Resulting Numbers: [148] 148,70 unequal: No Solution Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 72*76=5472, Resulting Numbers: [5472] 5472,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[72, 42], Operations: ['59-15=44', '44-2=42'] Exploring Operation: 72+42=114, Resulting Numbers: [114] 114,70 unequal: No Solution Exploring Operation: 72*42=3024, Resulting Numbers: [3024] 3024,70 unequal: No Solution Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[44, 70], Operations: ['59-15=44', '72-2=70'] Exploring Operation: 70-44=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 44+70=114, Resulting Numbers: [114] 114,70 unequal: No Solution Exploring Operation: 44*70=3080, Resulting Numbers: [3080] 3080,70 unequal: No Solution Moving to Node #0,2,3 Current State: 70:[44, 36], Operations: ['59-15=44', '72/2=36'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,70 unequal: No Solution Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[72, 46], Operations: ['59+2=61', '61-15=46'] Exploring Operation: 72*46=3312, Resulting Numbers: [3312] 3312,70 unequal: No Solution Exploring Operation: 72+46=118, Resulting Numbers: [118] 118,70 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[61, 57], Operations: ['59+2=61', '72-15=57'] Exploring Operation: 61+57=118, Resulting Numbers: [118] 118,70 unequal: No Solution Exploring Operation: 61*57=3477, Resulting Numbers: [3477] 3477,70 unequal: No Solution Exploring Operation: 61-57=4, Resulting Numbers: [4] 4,70 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 59, 44, 4, 46 ]
65
[ "59-44=15", "4+46=50", "15+50=65" ]
Current State: 65:[59, 44, 4, 46], Operations: [] Exploring Operation: 59-44=15, Resulting Numbers: [4, 46, 15] Generated Node #2: [4, 46, 15] from Operation: 59-44=15 Current State: 65:[4, 46, 15], Operations: ['59-44=15'] Exploring Operation: 4+46=50, Resulting Numbers: [15, 50] Generated Node #3: [15, 50] from Operation: 4+46=50 Current State: 65:[15, 50], Operations: ['59-44=15', '4+46=50'] Exploring Operation: 15+50=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[59, 44, 4, 46], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [59, 4, 2] Generated Node #0,0: 65:[59, 4, 2] Operation: 46-44=2 Exploring Operation: 59-46=13, Resulting Numbers: [44, 4, 13] Generated Node #0,1: 65:[44, 4, 13] Operation: 59-46=13 Exploring Operation: 44/4=11, Resulting Numbers: [59, 46, 11] Generated Node #0,2: 65:[59, 46, 11] Operation: 44/4=11 Exploring Operation: 44+46=90, Resulting Numbers: [59, 4, 90] Generated Node #0,3: 65:[59, 4, 90] Operation: 44+46=90 Exploring Operation: 59-44=15, Resulting Numbers: [4, 46, 15] Generated Node #0,4: 65:[4, 46, 15] Operation: 59-44=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[59, 4, 2], Operations: ['46-44=2'] Exploring Operation: 59+2=61, Resulting Numbers: [4, 61] Generated Node #0,0,0: 65:[4, 61] Operation: 59+2=61 Exploring Operation: 59+4=63, Resulting Numbers: [2, 63] Generated Node #0,0,1: 65:[2, 63] Operation: 59+4=63 Exploring Operation: 59-2=57, Resulting Numbers: [4, 57] Generated Node #0,0,2: 65:[4, 57] Operation: 59-2=57 Exploring Operation: 4*2=8, Resulting Numbers: [59, 8] Generated Node #0,0,3: 65:[59, 8] Operation: 4*2=8 Exploring Operation: 4+2=6, Resulting Numbers: [59, 6] Generated Node #0,0,4: 65:[59, 6] Operation: 4+2=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[4, 61], Operations: ['46-44=2', '59+2=61'] Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[59, 44, 4, 46], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [59, 4, 2] Generated Node #0,0: 65:[59, 4, 2] Operation: 46-44=2 Moving to Node #0,0 Current State: 65:[59, 4, 2], Operations: ['46-44=2'] Exploring Operation: 59+2=61, Resulting Numbers: [4, 61] Generated Node #0,0,0: 65:[4, 61] Operation: 59+2=61 Moving to Node #0,0,0 Current State: 65:[4, 61], Operations: ['46-44=2', '59+2=61'] Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 15, 95, 51, 92 ]
69
[ "15+95=110", "92-51=41", "110-41=69" ]
Current State: 69:[15, 95, 51, 92], Operations: [] Exploring Operation: 15+95=110, Resulting Numbers: [51, 92, 110] Generated Node #2: [51, 92, 110] from Operation: 15+95=110 Current State: 69:[51, 92, 110], Operations: ['15+95=110'] Exploring Operation: 92-51=41, Resulting Numbers: [110, 41] Generated Node #3: [110, 41] from Operation: 92-51=41 Current State: 69:[110, 41], Operations: ['15+95=110', '92-51=41'] Exploring Operation: 110-41=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[15, 95, 51, 92], Operations: [] Exploring Operation: 95-15=80, Resulting Numbers: [51, 92, 80] Generated Node #0,0: 69:[51, 92, 80] Operation: 95-15=80 Exploring Operation: 95-92=3, Resulting Numbers: [15, 51, 3] Generated Node #0,1: 69:[15, 51, 3] Operation: 95-92=3 Exploring Operation: 15+51=66, Resulting Numbers: [95, 92, 66] Generated Node #0,2: 69:[95, 92, 66] Operation: 15+51=66 Exploring Operation: 92-15=77, Resulting Numbers: [95, 51, 77] Generated Node #0,3: 69:[95, 51, 77] Operation: 92-15=77 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[15, 51, 3], Operations: ['95-92=3'] Exploring Operation: 51-15=36, Resulting Numbers: [3, 36] Generated Node #0,1,0: 69:[3, 36] Operation: 51-15=36 Exploring Operation: 15/3=5, Resulting Numbers: [51, 5] Generated Node #0,1,1: 69:[51, 5] Operation: 15/3=5 Exploring Operation: 15+51=66, Resulting Numbers: [3, 66] Generated Node #0,1,2: 69:[3, 66] Operation: 15+51=66 Exploring Operation: 51/3=17, Resulting Numbers: [15, 17] Generated Node #0,1,3: 69:[15, 17] Operation: 51/3=17 Moving to Node #0,1,2 Current State: 69:[3, 66], Operations: ['95-92=3', '15+51=66'] Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 3+66=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[15, 95, 51, 92], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [15, 51, 3] Generated Node #0,1: 69:[15, 51, 3] Operation: 95-92=3 Moving to Node #0,1 Current State: 69:[15, 51, 3], Operations: ['95-92=3'] Exploring Operation: 15+51=66, Resulting Numbers: [3, 66] Generated Node #0,1,2: 69:[3, 66] Operation: 15+51=66 Moving to Node #0,1,2 Current State: 69:[3, 66], Operations: ['95-92=3', '15+51=66'] Exploring Operation: 3+66=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 55, 51, 26, 65 ]
15
[ "55+51=106", "26+65=91", "106-91=15" ]
Current State: 15:[55, 51, 26, 65], Operations: [] Exploring Operation: 55+51=106, Resulting Numbers: [26, 65, 106] Generated Node #2: [26, 65, 106] from Operation: 55+51=106 Current State: 15:[26, 65, 106], Operations: ['55+51=106'] Exploring Operation: 26+65=91, Resulting Numbers: [106, 91] Generated Node #3: [106, 91] from Operation: 26+65=91 Current State: 15:[106, 91], Operations: ['55+51=106', '26+65=91'] Exploring Operation: 106-91=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[55, 51, 26, 65], Operations: [] Exploring Operation: 65-55=10, Resulting Numbers: [51, 26, 10] Generated Node #0,0: 15:[51, 26, 10] Operation: 65-55=10 Exploring Operation: 51-26=25, Resulting Numbers: [55, 65, 25] Generated Node #0,1: 15:[55, 65, 25] Operation: 51-26=25 Exploring Operation: 55-51=4, Resulting Numbers: [26, 65, 4] Generated Node #0,2: 15:[26, 65, 4] Operation: 55-51=4 Exploring Operation: 65-51=14, Resulting Numbers: [55, 26, 14] Generated Node #0,3: 15:[55, 26, 14] Operation: 65-51=14 Exploring Operation: 55-26=29, Resulting Numbers: [51, 65, 29] Generated Node #0,4: 15:[51, 65, 29] Operation: 55-26=29 Moving to Node #0,0 Current State: 15:[51, 26, 10], Operations: ['65-55=10'] Exploring Operation: 26-10=16, Resulting Numbers: [51, 16] Generated Node #0,0,0: 15:[51, 16] Operation: 26-10=16 Exploring Operation: 51-26=25, Resulting Numbers: [10, 25] Generated Node #0,0,1: 15:[10, 25] Operation: 51-26=25 Exploring Operation: 51-10=41, Resulting Numbers: [26, 41] Generated Node #0,0,2: 15:[26, 41] Operation: 51-10=41 Exploring Operation: 51+10=61, Resulting Numbers: [26, 61] Generated Node #0,0,3: 15:[26, 61] Operation: 51+10=61 Exploring Operation: 26+10=36, Resulting Numbers: [51, 36] Generated Node #0,0,4: 15:[51, 36] Operation: 26+10=36 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[10, 25], Operations: ['65-55=10', '51-26=25'] Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,15 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[55, 51, 26, 65], Operations: [] Exploring Operation: 65-55=10, Resulting Numbers: [51, 26, 10] Generated Node #0,0: 15:[51, 26, 10] Operation: 65-55=10 Moving to Node #0,0 Current State: 15:[51, 26, 10], Operations: ['65-55=10'] Exploring Operation: 51-26=25, Resulting Numbers: [10, 25] Generated Node #0,0,1: 15:[10, 25] Operation: 51-26=25 Moving to Node #0,0,1 Current State: 15:[10, 25], Operations: ['65-55=10', '51-26=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 22, 90, 50, 10 ]
24
[ "90+10=100", "100/50=2", "22+2=24" ]
Current State: 24:[22, 90, 50, 10], Operations: [] Exploring Operation: 90+10=100, Resulting Numbers: [22, 50, 100] Generated Node #2: [22, 50, 100] from Operation: 90+10=100 Current State: 24:[22, 50, 100], Operations: ['90+10=100'] Exploring Operation: 100/50=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 100/50=2 Current State: 24:[22, 2], Operations: ['90+10=100', '100/50=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[22, 90, 50, 10], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [22, 90, 5] Generated Node #0,0: 24:[22, 90, 5] Operation: 50/10=5 Exploring Operation: 90-50=40, Resulting Numbers: [22, 10, 40] Generated Node #0,1: 24:[22, 10, 40] Operation: 90-50=40 Exploring Operation: 90/10=9, Resulting Numbers: [22, 50, 9] Generated Node #0,2: 24:[22, 50, 9] Operation: 90/10=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[22, 10, 40], Operations: ['90-50=40'] Exploring Operation: 40-10=30, Resulting Numbers: [22, 30] Generated Node #0,1,0: 24:[22, 30] Operation: 40-10=30 Exploring Operation: 40/10=4, Resulting Numbers: [22, 4] Generated Node #0,1,1: 24:[22, 4] Operation: 40/10=4 Exploring Operation: 40-22=18, Resulting Numbers: [10, 18] Generated Node #0,1,2: 24:[10, 18] Operation: 40-22=18 Moving to Node #0,1,1 Current State: 24:[22, 4], Operations: ['90-50=40', '40/10=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,24 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,24 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[22, 30], Operations: ['90-50=40', '40-10=30'] Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 22*30=660, Resulting Numbers: [660] 660,24 unequal: No Solution Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[10, 18], Operations: ['90-50=40', '40-22=18'] Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,24 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[22, 50, 9], Operations: ['90/10=9'] Exploring Operation: 22-9=13, Resulting Numbers: [50, 13] Generated Node #0,2,0: 24:[50, 13] Operation: 22-9=13 Exploring Operation: 50-22=28, Resulting Numbers: [9, 28] Generated Node #0,2,1: 24:[9, 28] Operation: 50-22=28 Exploring Operation: 50-9=41, Resulting Numbers: [22, 41] Generated Node #0,2,2: 24:[22, 41] Operation: 50-9=41 Moving to Node #0,2,1 Current State: 24:[9, 28], Operations: ['90/10=9', '50-22=28'] Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,24 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[22, 41], Operations: ['90/10=9', '50-9=41'] Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,24 unequal: No Solution Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,24 unequal: No Solution Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[50, 13], Operations: ['90/10=9', '22-9=13'] Exploring Operation: 50*13=650, Resulting Numbers: [650] 650,24 unequal: No Solution Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,24 unequal: No Solution Exploring Operation: 50+13=63, Resulting Numbers: [63] 63,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[22, 90, 5], Operations: ['50/10=5'] Exploring Operation: 90/5=18, Resulting Numbers: [22, 18] Generated Node #0,0,0: 24:[22, 18] Operation: 90/5=18 Exploring Operation: 90-22=68, Resulting Numbers: [5, 68] Generated Node #0,0,1: 24:[5, 68] Operation: 90-22=68 Exploring Operation: 90-5=85, Resulting Numbers: [22, 85] Generated Node #0,0,2: 24:[22, 85] Operation: 90-5=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[22, 18], Operations: ['50/10=5', '90/5=18'] Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,24 unequal: No Solution Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,24 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,24 unequal: No Solution No 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: 24:[5, 68], Operations: ['50/10=5', '90-22=68'] Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,24 unequal: No Solution Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,24 unequal: No Solution No 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: 24:[22, 85], Operations: ['50/10=5', '90-5=85'] Exploring Operation: 22+85=107, Resulting Numbers: [107] 107,24 unequal: No Solution Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 22*85=1870, Resulting Numbers: [1870] 1870,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 4, 36, 94, 93 ]
33
[ "36-4=32", "94-93=1", "32+1=33" ]
Current State: 33:[4, 36, 94, 93], Operations: [] Exploring Operation: 36-4=32, Resulting Numbers: [94, 93, 32] Generated Node #2: [94, 93, 32] from Operation: 36-4=32 Current State: 33:[94, 93, 32], Operations: ['36-4=32'] Exploring Operation: 94-93=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 94-93=1 Current State: 33:[32, 1], Operations: ['36-4=32', '94-93=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[4, 36, 94, 93], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [4, 36, 1] Generated Node #0,0: 33:[4, 36, 1] Operation: 94-93=1 Exploring Operation: 93-36=57, Resulting Numbers: [4, 94, 57] Generated Node #0,1: 33:[4, 94, 57] Operation: 93-36=57 Exploring Operation: 94-4=90, Resulting Numbers: [36, 93, 90] Generated Node #0,2: 33:[36, 93, 90] Operation: 94-4=90 Exploring Operation: 93-4=89, Resulting Numbers: [36, 94, 89] Generated Node #0,3: 33:[36, 94, 89] Operation: 93-4=89 Exploring Operation: 94-36=58, Resulting Numbers: [4, 93, 58] Generated Node #0,4: 33:[4, 93, 58] Operation: 94-36=58 Moving to Node #0,0 Current State: 33:[4, 36, 1], Operations: ['94-93=1'] Exploring Operation: 36-1=35, Resulting Numbers: [4, 35] Generated Node #0,0,0: 33:[4, 35] Operation: 36-1=35 Exploring Operation: 36/4=9, Resulting Numbers: [1, 9] Generated Node #0,0,1: 33:[1, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [1, 32] Generated Node #0,0,2: 33:[1, 32] Operation: 36-4=32 Exploring Operation: 4-1=3, Resulting Numbers: [36, 3] Generated Node #0,0,3: 33:[36, 3] Operation: 4-1=3 Exploring Operation: 4*1=4, Resulting Numbers: [36, 4] Generated Node #0,0,4: 33:[36, 4] Operation: 4*1=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[4, 35], Operations: ['94-93=1', '36-1=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,33 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[1, 32], Operations: ['94-93=1', '36-4=32'] Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[4, 36, 94, 93], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [4, 36, 1] Generated Node #0,0: 33:[4, 36, 1] Operation: 94-93=1 Moving to Node #0,0 Current State: 33:[4, 36, 1], Operations: ['94-93=1'] Exploring Operation: 36-4=32, Resulting Numbers: [1, 32] Generated Node #0,0,2: 33:[1, 32] Operation: 36-4=32 Moving to Node #0,0,2 Current State: 33:[1, 32], Operations: ['94-93=1', '36-4=32'] Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 75, 2, 65, 54 ]
98
[ "75-65=10", "2*54=108", "108-10=98" ]
Current State: 98:[75, 2, 65, 54], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [2, 54, 10] Generated Node #2: [2, 54, 10] from Operation: 75-65=10 Current State: 98:[2, 54, 10], Operations: ['75-65=10'] Exploring Operation: 2*54=108, Resulting Numbers: [10, 108] Generated Node #3: [10, 108] from Operation: 2*54=108 Current State: 98:[10, 108], Operations: ['75-65=10', '2*54=108'] Exploring Operation: 108-10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[75, 2, 65, 54], Operations: [] Exploring Operation: 75+2=77, Resulting Numbers: [65, 54, 77] Generated Node #0,0: 98:[65, 54, 77] Operation: 75+2=77 Exploring Operation: 75-54=21, Resulting Numbers: [2, 65, 21] Generated Node #0,1: 98:[2, 65, 21] Operation: 75-54=21 Exploring Operation: 75-65=10, Resulting Numbers: [2, 54, 10] Generated Node #0,2: 98:[2, 54, 10] Operation: 75-65=10 Exploring Operation: 65-54=11, Resulting Numbers: [75, 2, 11] Generated Node #0,3: 98:[75, 2, 11] Operation: 65-54=11 Moving to Node #0,2 Current State: 98:[2, 54, 10], Operations: ['75-65=10'] Exploring Operation: 54-2=52, Resulting Numbers: [10, 52] Generated Node #0,2,0: 98:[10, 52] Operation: 54-2=52 Exploring Operation: 54-10=44, Resulting Numbers: [2, 44] Generated Node #0,2,1: 98:[2, 44] Operation: 54-10=44 Exploring Operation: 2+10=12, Resulting Numbers: [54, 12] Generated Node #0,2,2: 98:[54, 12] Operation: 2+10=12 Exploring Operation: 10-2=8, Resulting Numbers: [54, 8] Generated Node #0,2,3: 98:[54, 8] Operation: 10-2=8 Moving to Node #0,1 Current State: 98:[2, 65, 21], Operations: ['75-54=21'] Exploring Operation: 65+21=86, Resulting Numbers: [2, 86] Generated Node #0,1,0: 98:[2, 86] Operation: 65+21=86 Exploring Operation: 65-2=63, Resulting Numbers: [21, 63] Generated Node #0,1,1: 98:[21, 63] Operation: 65-2=63 Exploring Operation: 21-2=19, Resulting Numbers: [65, 19] Generated Node #0,1,2: 98:[65, 19] Operation: 21-2=19 Exploring Operation: 65-21=44, Resulting Numbers: [2, 44] Generated Node #0,1,3: 98:[2, 44] Operation: 65-21=44 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 98:[2, 44], Operations: ['75-54=21', '65-21=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,98 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[2, 86], Operations: ['75-54=21', '65+21=86'] Exploring Operation: 2*86=172, Resulting Numbers: [172] 172,98 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[21, 63], Operations: ['75-54=21', '65-2=63'] Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,98 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[65, 19], Operations: ['75-54=21', '21-2=19'] Exploring Operation: 65+19=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 65*19=1235, Resulting Numbers: [1235] 1235,98 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,98 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: 98:[75, 2, 11], Operations: ['65-54=11'] Exploring Operation: 75+2=77, Resulting Numbers: [11, 77] Generated Node #0,3,0: 98:[11, 77] Operation: 75+2=77 Exploring Operation: 2+11=13, Resulting Numbers: [75, 13] Generated Node #0,3,1: 98:[75, 13] Operation: 2+11=13 Exploring Operation: 75+11=86, Resulting Numbers: [2, 86] Generated Node #0,3,2: 98:[2, 86] Operation: 75+11=86 Exploring Operation: 75-11=64, Resulting Numbers: [2, 64] Generated Node #0,3,3: 98:[2, 64] Operation: 75-11=64 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 98:[2, 86], Operations: ['65-54=11', '75+11=86'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,98 unequal: No Solution Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,98 unequal: No Solution Exploring Operation: 2*86=172, Resulting Numbers: [172] 172,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[2, 64], Operations: ['65-54=11', '75-11=64'] Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,98 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,98 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 98:[11, 77], Operations: ['65-54=11', '75+2=77'] Exploring Operation: 11*77=847, Resulting Numbers: [847] 847,98 unequal: No Solution Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,98 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 11+77=88, Resulting Numbers: [88] 88,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 98:[75, 13], Operations: ['65-54=11', '2+11=13'] Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,98 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,98 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: 98:[65, 54, 77], Operations: ['75+2=77'] Exploring Operation: 65+54=119, Resulting Numbers: [77, 119] Generated Node #0,0,0: 98:[77, 119] Operation: 65+54=119 Exploring Operation: 65-54=11, Resulting Numbers: [77, 11] Generated Node #0,0,1: 98:[77, 11] Operation: 65-54=11 Exploring Operation: 77-54=23, Resulting Numbers: [65, 23] Generated Node #0,0,2: 98:[65, 23] Operation: 77-54=23 Exploring Operation: 77-65=12, Resulting Numbers: [54, 12] Generated Node #0,0,3: 98:[54, 12] Operation: 77-65=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 98:[54, 12], Operations: ['75+2=77', '77-65=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,98 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[77, 11], Operations: ['75+2=77', '65-54=11'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,98 unequal: No Solution Exploring Operation: 77+11=88, Resulting Numbers: [88] 88,98 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 77*11=847, Resulting Numbers: [847] 847,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[65, 23], Operations: ['75+2=77', '77-54=23'] Exploring Operation: 65*23=1495, Resulting Numbers: [1495] 1495,98 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 65+23=88, Resulting Numbers: [88] 88,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[77, 119], Operations: ['75+2=77', '65+54=119'] Exploring Operation: 119-77=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 77*119=9163, Resulting Numbers: [9163] 9163,98 unequal: No Solution Exploring Operation: 77+119=196, Resulting Numbers: [196] 196,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 98:[2, 44], Operations: ['75-65=10', '54-10=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,98 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[54, 8], Operations: ['75-65=10', '10-2=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,98 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,98 unequal: No Solution Moving to Node #0,2,0 Current State: 98:[10, 52], Operations: ['75-65=10', '54-2=52'] Exploring Operation: 10*52=520, Resulting Numbers: [520] 520,98 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[54, 12], Operations: ['75-65=10', '2+10=12'] Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,98 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,98 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 70, 91, 11, 62 ]
10
[ "70-62=8", "91-11=80", "80/8=10" ]
Current State: 10:[70, 91, 11, 62], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [91, 11, 8] Generated Node #2: [91, 11, 8] from Operation: 70-62=8 Current State: 10:[91, 11, 8], Operations: ['70-62=8'] Exploring Operation: 91-11=80, Resulting Numbers: [8, 80] Generated Node #3: [8, 80] from Operation: 91-11=80 Current State: 10:[8, 80], Operations: ['70-62=8', '91-11=80'] Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[70, 91, 11, 62], Operations: [] Exploring Operation: 91-62=29, Resulting Numbers: [70, 11, 29] Generated Node #0,0: 10:[70, 11, 29] Operation: 91-62=29 Exploring Operation: 91-70=21, Resulting Numbers: [11, 62, 21] Generated Node #0,1: 10:[11, 62, 21] Operation: 91-70=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[11, 62, 21], Operations: ['91-70=21'] Exploring Operation: 62-11=51, Resulting Numbers: [21, 51] Generated Node #0,1,0: 10:[21, 51] Operation: 62-11=51 Exploring Operation: 62-21=41, Resulting Numbers: [11, 41] Generated Node #0,1,1: 10:[11, 41] Operation: 62-21=41 Moving to Node #0,1,1 Current State: 10:[11, 41], Operations: ['91-70=21', '62-21=41'] Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,10 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[21, 51], Operations: ['91-70=21', '62-11=51'] Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,10 unequal: No Solution Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,10 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 #0,0 Current State: 10:[70, 11, 29], Operations: ['91-62=29'] Exploring Operation: 70-29=41, Resulting Numbers: [11, 41] Generated Node #0,0,0: 10:[11, 41] Operation: 70-29=41 Exploring Operation: 70-11=59, Resulting Numbers: [29, 59] Generated Node #0,0,1: 10:[29, 59] Operation: 70-11=59 Moving to Node #0,0,0 Current State: 10:[11, 41], Operations: ['91-62=29', '70-29=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,10 unequal: No Solution Exploring Operation: 11+41=52, Resulting Numbers: [52] 52,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[29, 59], Operations: ['91-62=29', '70-11=59'] Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,10 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,10 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
[ 66, 95, 45, 5 ]
94
[ "95+45=140", "140/5=28", "66+28=94" ]
Current State: 94:[66, 95, 45, 5], Operations: [] Exploring Operation: 95+45=140, Resulting Numbers: [66, 5, 140] Generated Node #2: [66, 5, 140] from Operation: 95+45=140 Current State: 94:[66, 5, 140], Operations: ['95+45=140'] Exploring Operation: 140/5=28, Resulting Numbers: [66, 28] Generated Node #3: [66, 28] from Operation: 140/5=28 Current State: 94:[66, 28], Operations: ['95+45=140', '140/5=28'] Exploring Operation: 66+28=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[66, 95, 45, 5], Operations: [] Exploring Operation: 66+45=111, Resulting Numbers: [95, 5, 111] Generated Node #0,0: 94:[95, 5, 111] Operation: 66+45=111 Exploring Operation: 66-5=61, Resulting Numbers: [95, 45, 61] Generated Node #0,1: 94:[95, 45, 61] Operation: 66-5=61 Moving to Node #0,1 Current State: 94:[95, 45, 61], Operations: ['66-5=61'] Exploring Operation: 95-61=34, Resulting Numbers: [45, 34] Generated Node #0,1,0: 94:[45, 34] Operation: 95-61=34 Exploring Operation: 45+61=106, Resulting Numbers: [95, 106] Generated Node #0,1,1: 94:[95, 106] Operation: 45+61=106 Moving to Node #0,0 Current State: 94:[95, 5, 111], Operations: ['66+45=111'] Exploring Operation: 111-5=106, Resulting Numbers: [95, 106] Generated Node #0,0,0: 94:[95, 106] Operation: 111-5=106 Exploring Operation: 111-95=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 94:[5, 16] Operation: 111-95=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[95, 106], Operations: ['66+45=111', '111-5=106'] Exploring Operation: 95+106=201, Resulting Numbers: [201] 201,94 unequal: No Solution Exploring Operation: 106-95=11, Resulting Numbers: [11] 11,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[5, 16], Operations: ['66+45=111', '111-95=16'] Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 94:[95, 106], Operations: ['66-5=61', '45+61=106'] Exploring Operation: 106-95=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 95+106=201, Resulting Numbers: [201] 201,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[45, 34], Operations: ['66-5=61', '95-61=34'] Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 76, 31, 38, 93 ]
52
[ "76+31=107", "93-38=55", "107-55=52" ]
Current State: 52:[76, 31, 38, 93], Operations: [] Exploring Operation: 76+31=107, Resulting Numbers: [38, 93, 107] Generated Node #2: [38, 93, 107] from Operation: 76+31=107 Current State: 52:[38, 93, 107], Operations: ['76+31=107'] Exploring Operation: 93-38=55, Resulting Numbers: [107, 55] Generated Node #3: [107, 55] from Operation: 93-38=55 Current State: 52:[107, 55], Operations: ['76+31=107', '93-38=55'] Exploring Operation: 107-55=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[76, 31, 38, 93], Operations: [] Exploring Operation: 93-38=55, Resulting Numbers: [76, 31, 55] Generated Node #0,0: 52:[76, 31, 55] Operation: 93-38=55 Exploring Operation: 93-76=17, Resulting Numbers: [31, 38, 17] Generated Node #0,1: 52:[31, 38, 17] Operation: 93-76=17 Moving to Node #0,1 Current State: 52:[31, 38, 17], Operations: ['93-76=17'] Exploring Operation: 38+17=55, Resulting Numbers: [31, 55] Generated Node #0,1,0: 52:[31, 55] Operation: 38+17=55 Exploring Operation: 38-31=7, Resulting Numbers: [17, 7] Generated Node #0,1,1: 52:[17, 7] Operation: 38-31=7 Moving to Node #0,0 Current State: 52:[76, 31, 55], Operations: ['93-38=55'] Exploring Operation: 76-55=21, Resulting Numbers: [31, 21] Generated Node #0,0,0: 52:[31, 21] Operation: 76-55=21 Exploring Operation: 76-31=45, Resulting Numbers: [55, 45] Generated Node #0,0,1: 52:[55, 45] Operation: 76-31=45 Moving to Node #0,1,1 Current State: 52:[17, 7], Operations: ['93-76=17', '38-31=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[31, 55], Operations: ['93-76=17', '38+17=55'] Exploring Operation: 31+55=86, Resulting Numbers: [86] 86,52 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[55, 45], Operations: ['93-38=55', '76-31=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,52 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[31, 21], Operations: ['93-38=55', '76-55=21'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[76, 31, 38, 93], Operations: [] Exploring Operation: 93-38=55, Resulting Numbers: [76, 31, 55] Generated Node #0,0: 52:[76, 31, 55] Operation: 93-38=55 Moving to Node #0,0 Current State: 52:[76, 31, 55], Operations: ['93-38=55'] Exploring Operation: 76-55=21, Resulting Numbers: [31, 21] Generated Node #0,0,0: 52:[31, 21] Operation: 76-55=21 Moving to Node #0,0,0 Current State: 52:[31, 21], Operations: ['93-38=55', '76-55=21'] Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 98, 98, 38, 49 ]
78
[ "98*38=3724", "98+3724=3822", "3822/49=78" ]
Current State: 78:[98, 98, 38, 49], Operations: [] Exploring Operation: 98*38=3724, Resulting Numbers: [49, 3724] Generated Node #2: [49, 3724] from Operation: 98*38=3724 Current State: 78:[49, 3724], Operations: ['98*38=3724'] Exploring Operation: 98+3724=3822, Resulting Numbers: [49, 3822] Generated Node #3: [49, 3822] from Operation: 98+3724=3822 Current State: 78:[49, 3822], Operations: ['98*38=3724', '98+3724=3822'] Exploring Operation: 3822/49=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[98, 98, 38, 49], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [38, 49, 0] Generated Node #0,0: 78:[38, 49, 0] Operation: 98-98=0 Exploring Operation: 98/98=1, Resulting Numbers: [38, 49, 1] Generated Node #0,1: 78:[38, 49, 1] Operation: 98/98=1 Moving to Node #0,1 Current State: 78:[38, 49, 1], Operations: ['98/98=1'] Exploring Operation: 38+49=87, Resulting Numbers: [1, 87] Generated Node #0,1,0: 78:[1, 87] Operation: 38+49=87 Exploring Operation: 49-38=11, Resulting Numbers: [1, 11] Generated Node #0,1,1: 78:[1, 11] Operation: 49-38=11 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[1, 11], Operations: ['98/98=1', '49-38=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 1*11=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 #0,1,0 Current State: 78:[1, 87], Operations: ['98/98=1', '38+49=87'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,78 unequal: No Solution Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,78 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:[38, 49, 0], Operations: ['98-98=0'] Exploring Operation: 49-38=11, Resulting Numbers: [0, 11] Generated Node #0,0,0: 78:[0, 11] Operation: 49-38=11 Exploring Operation: 49*0=0, Resulting Numbers: [38, 0] Generated Node #0,0,1: 78:[38, 0] Operation: 49*0=0 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[38, 0], Operations: ['98-98=0', '49*0=0'] Exploring Operation: 38+0=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 38-0=38, Resulting Numbers: [38] 38,78 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:[0, 11], Operations: ['98-98=0', '49-38=11'] Exploring Operation: 0*11=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 0+11=11, Resulting Numbers: [11] 11,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 83, 2, 48, 7 ]
77
[ "83-48=35", "2*35=70", "7+70=77" ]
Current State: 77:[83, 2, 48, 7], Operations: [] Exploring Operation: 83-48=35, Resulting Numbers: [2, 7, 35] Generated Node #2: [2, 7, 35] from Operation: 83-48=35 Current State: 77:[2, 7, 35], Operations: ['83-48=35'] Exploring Operation: 2*35=70, Resulting Numbers: [7, 70] Generated Node #3: [7, 70] from Operation: 2*35=70 Current State: 77:[7, 70], Operations: ['83-48=35', '2*35=70'] Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[83, 2, 48, 7], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [83, 7, 24] Generated Node #0,0: 77:[83, 7, 24] Operation: 48/2=24 Exploring Operation: 2*48=96, Resulting Numbers: [83, 7, 96] Generated Node #0,1: 77:[83, 7, 96] Operation: 2*48=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[83, 7, 24], Operations: ['48/2=24'] Exploring Operation: 83-7=76, Resulting Numbers: [24, 76] Generated Node #0,0,0: 77:[24, 76] Operation: 83-7=76 Exploring Operation: 24-7=17, Resulting Numbers: [83, 17] Generated Node #0,0,1: 77:[83, 17] Operation: 24-7=17 Moving to Node #0,0,1 Current State: 77:[83, 17], Operations: ['48/2=24', '24-7=17'] Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,77 unequal: No Solution Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[24, 76], Operations: ['48/2=24', '83-7=76'] Exploring Operation: 24+76=100, Resulting Numbers: [100] 100,77 unequal: No Solution Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[83, 7, 96], Operations: ['2*48=96'] Exploring Operation: 96-83=13, Resulting Numbers: [7, 13] Generated Node #0,1,0: 77:[7, 13] Operation: 96-83=13 Exploring Operation: 96-7=89, Resulting Numbers: [83, 89] Generated Node #0,1,1: 77:[83, 89] Operation: 96-7=89 Moving to Node #0,1,0 Current State: 77:[7, 13], Operations: ['2*48=96', '96-83=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[83, 89], Operations: ['2*48=96', '96-7=89'] Exploring Operation: 83+89=172, Resulting Numbers: [172] 172,77 unequal: No Solution Exploring Operation: 89-83=6, Resulting Numbers: [6] 6,77 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
[ 10, 85, 67, 57 ]
29
[ "10+85=95", "67+57=124", "124-95=29" ]
Current State: 29:[10, 85, 67, 57], Operations: [] Exploring Operation: 10+85=95, Resulting Numbers: [67, 57, 95] Generated Node #2: [67, 57, 95] from Operation: 10+85=95 Current State: 29:[67, 57, 95], Operations: ['10+85=95'] Exploring Operation: 67+57=124, Resulting Numbers: [95, 124] Generated Node #3: [95, 124] from Operation: 67+57=124 Current State: 29:[95, 124], Operations: ['10+85=95', '67+57=124'] Exploring Operation: 124-95=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[10, 85, 67, 57], Operations: [] Exploring Operation: 67-57=10, Resulting Numbers: [10, 85, 10] Generated Node #0,0: 29:[10, 85, 10] Operation: 67-57=10 Exploring Operation: 85-57=28, Resulting Numbers: [10, 67, 28] Generated Node #0,1: 29:[10, 67, 28] Operation: 85-57=28 Exploring Operation: 85-10=75, Resulting Numbers: [67, 57, 75] Generated Node #0,2: 29:[67, 57, 75] Operation: 85-10=75 Exploring Operation: 85-67=18, Resulting Numbers: [10, 57, 18] Generated Node #0,3: 29:[10, 57, 18] Operation: 85-67=18 Moving to Node #0,1 Current State: 29:[10, 67, 28], Operations: ['85-57=28'] Exploring Operation: 67-28=39, Resulting Numbers: [10, 39] Generated Node #0,1,0: 29:[10, 39] Operation: 67-28=39 Exploring Operation: 67-10=57, Resulting Numbers: [28, 57] Generated Node #0,1,1: 29:[28, 57] Operation: 67-10=57 Exploring Operation: 10+28=38, Resulting Numbers: [67, 38] Generated Node #0,1,2: 29:[67, 38] Operation: 10+28=38 Exploring Operation: 10+67=77, Resulting Numbers: [28, 77] Generated Node #0,1,3: 29:[28, 77] Operation: 10+67=77 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[10, 39], Operations: ['85-57=28', '67-28=39'] Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,29 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,29 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[10, 85, 67, 57], Operations: [] Exploring Operation: 85-57=28, Resulting Numbers: [10, 67, 28] Generated Node #0,1: 29:[10, 67, 28] Operation: 85-57=28 Moving to Node #0,1 Current State: 29:[10, 67, 28], Operations: ['85-57=28'] Exploring Operation: 67-28=39, Resulting Numbers: [10, 39] Generated Node #0,1,0: 29:[10, 39] Operation: 67-28=39 Moving to Node #0,1,0 Current State: 29:[10, 39], Operations: ['85-57=28', '67-28=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 49, 5, 69, 21 ]
13
[ "49+69=118", "5*21=105", "118-105=13" ]
Current State: 13:[49, 5, 69, 21], Operations: [] Exploring Operation: 49+69=118, Resulting Numbers: [5, 21, 118] Generated Node #2: [5, 21, 118] from Operation: 49+69=118 Current State: 13:[5, 21, 118], Operations: ['49+69=118'] Exploring Operation: 5*21=105, Resulting Numbers: [118, 105] Generated Node #3: [118, 105] from Operation: 5*21=105 Current State: 13:[118, 105], Operations: ['49+69=118', '5*21=105'] Exploring Operation: 118-105=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[49, 5, 69, 21], Operations: [] Exploring Operation: 69-49=20, Resulting Numbers: [5, 21, 20] Generated Node #0,0: 13:[5, 21, 20] Operation: 69-49=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[5, 21, 20], Operations: ['69-49=20'] Exploring Operation: 21-5=16, Resulting Numbers: [20, 16] Generated Node #0,0,0: 13:[20, 16] Operation: 21-5=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[20, 16], Operations: ['69-49=20', '21-5=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 71, 62, 64, 53 ]
20
[ "71-62=9", "64-53=11", "9+11=20" ]
Current State: 20:[71, 62, 64, 53], Operations: [] Exploring Operation: 71-62=9, Resulting Numbers: [64, 53, 9] Generated Node #2: [64, 53, 9] from Operation: 71-62=9 Current State: 20:[64, 53, 9], Operations: ['71-62=9'] Exploring Operation: 64-53=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 64-53=11 Current State: 20:[9, 11], Operations: ['71-62=9', '64-53=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[71, 62, 64, 53], Operations: [] Exploring Operation: 71-62=9, Resulting Numbers: [64, 53, 9] Generated Node #0,0: 20:[64, 53, 9] Operation: 71-62=9 Exploring Operation: 71-64=7, Resulting Numbers: [62, 53, 7] Generated Node #0,1: 20:[62, 53, 7] Operation: 71-64=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[62, 53, 7], Operations: ['71-64=7'] Exploring Operation: 62-53=9, Resulting Numbers: [7, 9] Generated Node #0,1,0: 20:[7, 9] Operation: 62-53=9 Exploring Operation: 62-7=55, Resulting Numbers: [53, 55] Generated Node #0,1,1: 20:[53, 55] Operation: 62-7=55 Moving to Node #0,1,0 Current State: 20:[7, 9], Operations: ['71-64=7', '62-53=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[53, 55], Operations: ['71-64=7', '62-7=55'] Exploring Operation: 53+55=108, Resulting Numbers: [108] 108,20 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[64, 53, 9], Operations: ['71-62=9'] Exploring Operation: 64-9=55, Resulting Numbers: [53, 55] Generated Node #0,0,0: 20:[53, 55] Operation: 64-9=55 Exploring Operation: 64-53=11, Resulting Numbers: [9, 11] Generated Node #0,0,1: 20:[9, 11] Operation: 64-53=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[9, 11], Operations: ['71-62=9', '64-53=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[71, 62, 64, 53], Operations: [] Exploring Operation: 71-62=9, Resulting Numbers: [64, 53, 9] Generated Node #0,0: 20:[64, 53, 9] Operation: 71-62=9 Moving to Node #0,0 Current State: 20:[64, 53, 9], Operations: ['71-62=9'] Exploring Operation: 64-53=11, Resulting Numbers: [9, 11] Generated Node #0,0,1: 20:[9, 11] Operation: 64-53=11 Moving to Node #0,0,1 Current State: 20:[9, 11], Operations: ['71-62=9', '64-53=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 18, 44, 39, 42 ]
60
[ "44-42=2", "39*2=78", "78-18=60" ]
Current State: 60:[18, 44, 39, 42], Operations: [] Exploring Operation: 44-42=2, Resulting Numbers: [18, 39, 2] Generated Node #2: [18, 39, 2] from Operation: 44-42=2 Current State: 60:[18, 39, 2], Operations: ['44-42=2'] Exploring Operation: 39*2=78, Resulting Numbers: [18, 78] Generated Node #3: [18, 78] from Operation: 39*2=78 Current State: 60:[18, 78], Operations: ['44-42=2', '39*2=78'] Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[18, 44, 39, 42], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [18, 44, 3] Generated Node #0,0: 60:[18, 44, 3] Operation: 42-39=3 Exploring Operation: 44-42=2, Resulting Numbers: [18, 39, 2] Generated Node #0,1: 60:[18, 39, 2] Operation: 44-42=2 Exploring Operation: 18+44=62, Resulting Numbers: [39, 42, 62] Generated Node #0,2: 60:[39, 42, 62] Operation: 18+44=62 Exploring Operation: 44-39=5, Resulting Numbers: [18, 42, 5] Generated Node #0,3: 60:[18, 42, 5] Operation: 44-39=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[18, 39, 2], Operations: ['44-42=2'] Exploring Operation: 39-18=21, Resulting Numbers: [2, 21] Generated Node #0,1,0: 60:[2, 21] Operation: 39-18=21 Exploring Operation: 18+39=57, Resulting Numbers: [2, 57] Generated Node #0,1,1: 60:[2, 57] Operation: 18+39=57 Exploring Operation: 18+2=20, Resulting Numbers: [39, 20] Generated Node #0,1,2: 60:[39, 20] Operation: 18+2=20 Exploring Operation: 39-2=37, Resulting Numbers: [18, 37] Generated Node #0,1,3: 60:[18, 37] Operation: 39-2=37 Moving to Node #0,1,0 Current State: 60:[2, 21], Operations: ['44-42=2', '39-18=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[2, 57], Operations: ['44-42=2', '18+39=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[18, 37], Operations: ['44-42=2', '39-2=37'] Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[39, 20], Operations: ['44-42=2', '18+2=20'] Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,60 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 60:[18, 42, 5], Operations: ['44-39=5'] Exploring Operation: 18+42=60, Resulting Numbers: [5, 60] Generated Node #0,3,0: 60:[5, 60] Operation: 18+42=60 Exploring Operation: 18-5=13, Resulting Numbers: [42, 13] Generated Node #0,3,1: 60:[42, 13] Operation: 18-5=13 Exploring Operation: 42-5=37, Resulting Numbers: [18, 37] Generated Node #0,3,2: 60:[18, 37] Operation: 42-5=37 Exploring Operation: 42-18=24, Resulting Numbers: [5, 24] Generated Node #0,3,3: 60:[5, 24] Operation: 42-18=24 Moving to Node #0,3,0 Current State: 60:[5, 60], Operations: ['44-39=5', '18+42=60'] Exploring Operation: 5+60=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 5*60=300, Resulting Numbers: [300] 300,60 unequal: No Solution Moving to Node #0,3,3 Current State: 60:[5, 24], Operations: ['44-39=5', '42-18=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[18, 37], Operations: ['44-39=5', '42-5=37'] Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[42, 13], Operations: ['44-39=5', '18-5=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,60 unequal: No Solution Exploring Operation: 42*13=546, Resulting Numbers: [546] 546,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[18, 44, 3], Operations: ['42-39=3'] Exploring Operation: 44-18=26, Resulting Numbers: [3, 26] Generated Node #0,0,0: 60:[3, 26] Operation: 44-18=26 Exploring Operation: 18-3=15, Resulting Numbers: [44, 15] Generated Node #0,0,1: 60:[44, 15] Operation: 18-3=15 Exploring Operation: 44-3=41, Resulting Numbers: [18, 41] Generated Node #0,0,2: 60:[18, 41] Operation: 44-3=41 Exploring Operation: 18+44=62, Resulting Numbers: [3, 62] Generated Node #0,0,3: 60:[3, 62] Operation: 18+44=62 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 60:[3, 62], Operations: ['42-39=3', '18+44=62'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,60 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[3, 26], Operations: ['42-39=3', '44-18=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,60 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 60:[18, 41], Operations: ['42-39=3', '44-3=41'] Exploring Operation: 18+41=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 18*41=738, Resulting Numbers: [738] 738,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 60:[44, 15], Operations: ['42-39=3', '18-3=15'] Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[39, 42, 62], Operations: ['18+44=62'] Exploring Operation: 39+42=81, Resulting Numbers: [62, 81] Generated Node #0,2,0: 60:[62, 81] Operation: 39+42=81 Exploring Operation: 42-39=3, Resulting Numbers: [62, 3] Generated Node #0,2,1: 60:[62, 3] Operation: 42-39=3 Exploring Operation: 62-42=20, Resulting Numbers: [39, 20] Generated Node #0,2,2: 60:[39, 20] Operation: 62-42=20 Exploring Operation: 62-39=23, Resulting Numbers: [42, 23] Generated Node #0,2,3: 60:[42, 23] Operation: 62-39=23 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 60:[62, 3], Operations: ['18+44=62', '42-39=3'] Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,60 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 60:[39, 20], Operations: ['18+44=62', '62-42=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 60:[42, 23], Operations: ['18+44=62', '62-39=23'] Exploring Operation: 42*23=966, Resulting Numbers: [966] 966,60 unequal: No Solution Exploring Operation: 42+23=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 60:[62, 81], Operations: ['18+44=62', '39+42=81'] Exploring Operation: 62+81=143, Resulting Numbers: [143] 143,60 unequal: No Solution Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,60 unequal: No Solution Exploring Operation: 62*81=5022, Resulting Numbers: [5022] 5022,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 4, 52, 25, 62 ]
46
[ "52-25=27", "4*27=108", "108-62=46" ]
Current State: 46:[4, 52, 25, 62], Operations: [] Exploring Operation: 52-25=27, Resulting Numbers: [4, 62, 27] Generated Node #2: [4, 62, 27] from Operation: 52-25=27 Current State: 46:[4, 62, 27], Operations: ['52-25=27'] Exploring Operation: 4*27=108, Resulting Numbers: [62, 108] Generated Node #3: [62, 108] from Operation: 4*27=108 Current State: 46:[62, 108], Operations: ['52-25=27', '4*27=108'] Exploring Operation: 108-62=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[4, 52, 25, 62], Operations: [] Exploring Operation: 62-25=37, Resulting Numbers: [4, 52, 37] Generated Node #0,0: 46:[4, 52, 37] Operation: 62-25=37 Exploring Operation: 52-4=48, Resulting Numbers: [25, 62, 48] Generated Node #0,1: 46:[25, 62, 48] Operation: 52-4=48 Exploring Operation: 62-52=10, Resulting Numbers: [4, 25, 10] Generated Node #0,2: 46:[4, 25, 10] Operation: 62-52=10 Exploring Operation: 62-4=58, Resulting Numbers: [52, 25, 58] Generated Node #0,3: 46:[52, 25, 58] Operation: 62-4=58 Moving to Node #0,2 Current State: 46:[4, 25, 10], Operations: ['62-52=10'] Exploring Operation: 25-4=21, Resulting Numbers: [10, 21] Generated Node #0,2,0: 46:[10, 21] Operation: 25-4=21 Exploring Operation: 10-4=6, Resulting Numbers: [25, 6] Generated Node #0,2,1: 46:[25, 6] Operation: 10-4=6 Exploring Operation: 25-10=15, Resulting Numbers: [4, 15] Generated Node #0,2,2: 46:[4, 15] Operation: 25-10=15 Exploring Operation: 4*10=40, Resulting Numbers: [25, 40] Generated Node #0,2,3: 46:[25, 40] Operation: 4*10=40 Moving to Node #0,0 Current State: 46:[4, 52, 37], Operations: ['62-25=37'] Exploring Operation: 4+37=41, Resulting Numbers: [52, 41] Generated Node #0,0,0: 46:[52, 41] Operation: 4+37=41 Exploring Operation: 52-4=48, Resulting Numbers: [37, 48] Generated Node #0,0,1: 46:[37, 48] Operation: 52-4=48 Exploring Operation: 52-37=15, Resulting Numbers: [4, 15] Generated Node #0,0,2: 46:[4, 15] Operation: 52-37=15 Exploring Operation: 37-4=33, Resulting Numbers: [52, 33] Generated Node #0,0,3: 46:[52, 33] Operation: 37-4=33 Moving to Node #0,3 Current State: 46:[52, 25, 58], Operations: ['62-4=58'] Exploring Operation: 52+25=77, Resulting Numbers: [58, 77] Generated Node #0,3,0: 46:[58, 77] Operation: 52+25=77 Exploring Operation: 58-25=33, Resulting Numbers: [52, 33] Generated Node #0,3,1: 46:[52, 33] Operation: 58-25=33 Exploring Operation: 58-52=6, Resulting Numbers: [25, 6] Generated Node #0,3,2: 46:[25, 6] Operation: 58-52=6 Exploring Operation: 52-25=27, Resulting Numbers: [58, 27] Generated Node #0,3,3: 46:[58, 27] Operation: 52-25=27 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 46:[25, 6], Operations: ['62-4=58', '58-52=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 46:[52, 33], Operations: ['62-4=58', '58-25=33'] Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 46:[58, 27], Operations: ['62-4=58', '52-25=27'] Exploring Operation: 58+27=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 58*27=1566, Resulting Numbers: [1566] 1566,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 46:[58, 77], Operations: ['62-4=58', '52+25=77'] Exploring Operation: 58*77=4466, Resulting Numbers: [4466] 4466,46 unequal: No Solution Exploring Operation: 77-58=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 58+77=135, Resulting Numbers: [135] 135,46 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: 46:[25, 62, 48], Operations: ['52-4=48'] Exploring Operation: 62-48=14, Resulting Numbers: [25, 14] Generated Node #0,1,0: 46:[25, 14] Operation: 62-48=14 Exploring Operation: 62-25=37, Resulting Numbers: [48, 37] Generated Node #0,1,1: 46:[48, 37] Operation: 62-25=37 Exploring Operation: 25+62=87, Resulting Numbers: [48, 87] Generated Node #0,1,2: 46:[48, 87] Operation: 25+62=87 Exploring Operation: 48-25=23, Resulting Numbers: [62, 23] Generated Node #0,1,3: 46:[62, 23] Operation: 48-25=23 Moving to Node #0,2,1 Current State: 46:[25, 6], Operations: ['62-52=10', '10-4=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[25, 40], Operations: ['62-52=10', '4*10=40'] Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[10, 21], Operations: ['62-52=10', '25-4=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[4, 15], Operations: ['62-25=37', '52-37=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[4, 15], Operations: ['62-52=10', '25-10=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[37, 48], Operations: ['62-25=37', '52-4=48'] Exploring Operation: 37*48=1776, Resulting Numbers: [1776] 1776,46 unequal: No Solution Exploring Operation: 37+48=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[52, 41], Operations: ['62-25=37', '4+37=41'] Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,46 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 52*41=2132, Resulting Numbers: [2132] 2132,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[48, 37], Operations: ['52-4=48', '62-25=37'] Exploring Operation: 48*37=1776, Resulting Numbers: [1776] 1776,46 unequal: No Solution Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 48+37=85, Resulting Numbers: [85] 85,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[25, 14], Operations: ['52-4=48', '62-48=14'] Exploring Operation: 25*14=350, Resulting Numbers: [350] 350,46 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 25+14=39, Resulting Numbers: [39] 39,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[52, 33], Operations: ['62-25=37', '37-4=33'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,46 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,46 unequal: No Solution Moving to Node #0,1,3 Current State: 46:[62, 23], Operations: ['52-4=48', '48-25=23'] Exploring Operation: 62-23=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 62*23=1426, Resulting Numbers: [1426] 1426,46 unequal: No Solution Exploring Operation: 62+23=85, Resulting Numbers: [85] 85,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[48, 87], Operations: ['52-4=48', '25+62=87'] Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 48*87=4176, Resulting Numbers: [4176] 4176,46 unequal: No Solution Exploring Operation: 48+87=135, Resulting Numbers: [135] 135,46 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 26, 32, 27, 24 ]
43
[ "26-24=2", "32/2=16", "27+16=43" ]
Current State: 43:[26, 32, 27, 24], Operations: [] Exploring Operation: 26-24=2, Resulting Numbers: [32, 27, 2] Generated Node #2: [32, 27, 2] from Operation: 26-24=2 Current State: 43:[32, 27, 2], Operations: ['26-24=2'] Exploring Operation: 32/2=16, Resulting Numbers: [27, 16] Generated Node #3: [27, 16] from Operation: 32/2=16 Current State: 43:[27, 16], Operations: ['26-24=2', '32/2=16'] Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[26, 32, 27, 24], Operations: [] Exploring Operation: 27+24=51, Resulting Numbers: [26, 32, 51] Generated Node #0,0: 43:[26, 32, 51] Operation: 27+24=51 Exploring Operation: 26+24=50, Resulting Numbers: [32, 27, 50] Generated Node #0,1: 43:[32, 27, 50] Operation: 26+24=50 Exploring Operation: 26+32=58, Resulting Numbers: [27, 24, 58] Generated Node #0,2: 43:[27, 24, 58] Operation: 26+32=58 Exploring Operation: 32+24=56, Resulting Numbers: [26, 27, 56] Generated Node #0,3: 43:[26, 27, 56] Operation: 32+24=56 Exploring Operation: 26+27=53, Resulting Numbers: [32, 24, 53] Generated Node #0,4: 43:[32, 24, 53] Operation: 26+27=53 Moving to Node #0,1 Current State: 43:[32, 27, 50], Operations: ['26+24=50'] Exploring Operation: 32-27=5, Resulting Numbers: [50, 5] Generated Node #0,1,0: 43:[50, 5] Operation: 32-27=5 Exploring Operation: 50-27=23, Resulting Numbers: [32, 23] Generated Node #0,1,1: 43:[32, 23] Operation: 50-27=23 Exploring Operation: 27+50=77, Resulting Numbers: [32, 77] Generated Node #0,1,2: 43:[32, 77] Operation: 27+50=77 Exploring Operation: 50-32=18, Resulting Numbers: [27, 18] Generated Node #0,1,3: 43:[27, 18] Operation: 50-32=18 Exploring Operation: 32+27=59, Resulting Numbers: [50, 59] Generated Node #0,1,4: 43:[50, 59] Operation: 32+27=59 Moving to Node #0,0 Current State: 43:[26, 32, 51], Operations: ['27+24=51'] Exploring Operation: 51-32=19, Resulting Numbers: [26, 19] Generated Node #0,0,0: 43:[26, 19] Operation: 51-32=19 Exploring Operation: 51-26=25, Resulting Numbers: [32, 25] Generated Node #0,0,1: 43:[32, 25] Operation: 51-26=25 Exploring Operation: 26+32=58, Resulting Numbers: [51, 58] Generated Node #0,0,2: 43:[51, 58] Operation: 26+32=58 Exploring Operation: 26+51=77, Resulting Numbers: [32, 77] Generated Node #0,0,3: 43:[32, 77] Operation: 26+51=77 Exploring Operation: 32-26=6, Resulting Numbers: [51, 6] Generated Node #0,0,4: 43:[51, 6] Operation: 32-26=6 Moving to Node #0,4 Current State: 43:[32, 24, 53], Operations: ['26+27=53'] Exploring Operation: 24+53=77, Resulting Numbers: [32, 77] Generated Node #0,4,0: 43:[32, 77] Operation: 24+53=77 Exploring Operation: 32+24=56, Resulting Numbers: [53, 56] Generated Node #0,4,1: 43:[53, 56] Operation: 32+24=56 Exploring Operation: 53-32=21, Resulting Numbers: [24, 21] Generated Node #0,4,2: 43:[24, 21] Operation: 53-32=21 Exploring Operation: 32-24=8, Resulting Numbers: [53, 8] Generated Node #0,4,3: 43:[53, 8] Operation: 32-24=8 Exploring Operation: 53-24=29, Resulting Numbers: [32, 29] Generated Node #0,4,4: 43:[32, 29] Operation: 53-24=29 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 43:[53, 56], Operations: ['26+27=53', '32+24=56'] Exploring Operation: 53*56=2968, Resulting Numbers: [2968] 2968,43 unequal: No Solution Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 53+56=109, Resulting Numbers: [109] 109,43 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 #0,4,4 Current State: 43:[32, 29], Operations: ['26+27=53', '53-24=29'] Exploring Operation: 32*29=928, Resulting Numbers: [928] 928,43 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 32+29=61, Resulting Numbers: [61] 61,43 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 #0,4,2 Current State: 43:[24, 21], Operations: ['26+27=53', '53-32=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,43 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,43 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 #0,4,0 Current State: 43:[32, 77], Operations: ['26+27=53', '24+53=77'] Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 32+77=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 32*77=2464, Resulting Numbers: [2464] 2464,43 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 #0,4,3 Current State: 43:[53, 8], Operations: ['26+27=53', '32-24=8'] Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,43 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,43 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: 43:[26, 27, 56], Operations: ['32+24=56'] Exploring Operation: 26+56=82, Resulting Numbers: [27, 82] Generated Node #0,3,0: 43:[27, 82] Operation: 26+56=82 Exploring Operation: 26+27=53, Resulting Numbers: [56, 53] Generated Node #0,3,1: 43:[56, 53] Operation: 26+27=53 Exploring Operation: 56-27=29, Resulting Numbers: [26, 29] Generated Node #0,3,2: 43:[26, 29] Operation: 56-27=29 Exploring Operation: 56-26=30, Resulting Numbers: [27, 30] Generated Node #0,3,3: 43:[27, 30] Operation: 56-26=30 Exploring Operation: 27-26=1, Resulting Numbers: [56, 1] Generated Node #0,3,4: 43:[56, 1] Operation: 27-26=1 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 43:[56, 53], Operations: ['32+24=56', '26+27=53'] Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 56*53=2968, Resulting Numbers: [2968] 2968,43 unequal: No Solution Exploring Operation: 56+53=109, Resulting Numbers: [109] 109,43 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 #0,3,3 Current State: 43:[27, 30], Operations: ['32+24=56', '56-26=30'] Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,43 unequal: No Solution Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,43 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:[26, 29], Operations: ['32+24=56', '56-27=29'] Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,43 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,43 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:[27, 82], Operations: ['32+24=56', '26+56=82'] Exploring Operation: 27*82=2214, Resulting Numbers: [2214] 2214,43 unequal: No Solution Exploring Operation: 27+82=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,43 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 #0,3,4 Current State: 43:[56, 1], Operations: ['32+24=56', '27-26=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,43 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,43 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:[27, 24, 58], Operations: ['26+32=58'] Exploring Operation: 27+24=51, Resulting Numbers: [58, 51] Generated Node #0,2,0: 43:[58, 51] Operation: 27+24=51 Exploring Operation: 58-24=34, Resulting Numbers: [27, 34] Generated Node #0,2,1: 43:[27, 34] Operation: 58-24=34 Exploring Operation: 24+58=82, Resulting Numbers: [27, 82] Generated Node #0,2,2: 43:[27, 82] Operation: 24+58=82 Exploring Operation: 27-24=3, Resulting Numbers: [58, 3] Generated Node #0,2,3: 43:[58, 3] Operation: 27-24=3 Exploring Operation: 58-27=31, Resulting Numbers: [24, 31] Generated Node #0,2,4: 43:[24, 31] Operation: 58-27=31 Moving to Node #0,1,4 Current State: 43:[50, 59], Operations: ['26+24=50', '32+27=59'] Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 50+59=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 50*59=2950, Resulting Numbers: [2950] 2950,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[51, 58], Operations: ['27+24=51', '26+32=58'] Exploring Operation: 58-51=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 51*58=2958, Resulting Numbers: [2958] 2958,43 unequal: No Solution Exploring Operation: 51+58=109, Resulting Numbers: [109] 109,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[58, 51], Operations: ['26+32=58', '27+24=51'] Exploring Operation: 58-51=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 58*51=2958, Resulting Numbers: [2958] 2958,43 unequal: No Solution Exploring Operation: 58+51=109, Resulting Numbers: [109] 109,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[27, 34], Operations: ['26+32=58', '58-24=34'] Exploring Operation: 27+34=61, Resulting Numbers: [61] 61,43 unequal: No Solution Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 27*34=918, Resulting Numbers: [918] 918,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[32, 25], Operations: ['27+24=51', '51-26=25'] Exploring Operation: 32+25=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 32*25=800, Resulting Numbers: [800] 800,43 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,43 unequal: No Solution Moving to Node #0,2,4 Current State: 43:[24, 31], Operations: ['26+32=58', '58-27=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[32, 23], Operations: ['26+24=50', '50-27=23'] Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 32+23=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 32*23=736, Resulting Numbers: [736] 736,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[27, 18], Operations: ['26+24=50', '50-32=18'] Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[26, 19], Operations: ['27+24=51', '51-32=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,43 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[51, 6], Operations: ['27+24=51', '32-26=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,43 unequal: No Solution Exploring Operation: 51*6=306, Resulting Numbers: [306] 306,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[32, 77], Operations: ['26+24=50', '27+50=77'] Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 32+77=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 32*77=2464, Resulting Numbers: [2464] 2464,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[50, 5], Operations: ['26+24=50', '32-27=5'] Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,43 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,43 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[32, 77], Operations: ['27+24=51', '26+51=77'] Exploring Operation: 32*77=2464, Resulting Numbers: [2464] 2464,43 unequal: No Solution Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 32+77=109, Resulting Numbers: [109] 109,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[58, 3], Operations: ['26+32=58', '27-24=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,43 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,43 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[27, 82], Operations: ['26+32=58', '24+58=82'] Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 27*82=2214, Resulting Numbers: [2214] 2214,43 unequal: No Solution Exploring Operation: 27+82=109, Resulting Numbers: [109] 109,43 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 33, 24, 19, 58 ]
86
[ "33-24=9", "19+58=77", "9+77=86" ]
Current State: 86:[33, 24, 19, 58], Operations: [] Exploring Operation: 33-24=9, Resulting Numbers: [19, 58, 9] Generated Node #2: [19, 58, 9] from Operation: 33-24=9 Current State: 86:[19, 58, 9], Operations: ['33-24=9'] Exploring Operation: 19+58=77, Resulting Numbers: [9, 77] Generated Node #3: [9, 77] from Operation: 19+58=77 Current State: 86:[9, 77], Operations: ['33-24=9', '19+58=77'] Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[33, 24, 19, 58], Operations: [] Exploring Operation: 24+58=82, Resulting Numbers: [33, 19, 82] Generated Node #0,0: 86:[33, 19, 82] Operation: 24+58=82 Exploring Operation: 24-19=5, Resulting Numbers: [33, 58, 5] Generated Node #0,1: 86:[33, 58, 5] Operation: 24-19=5 Exploring Operation: 58-19=39, Resulting Numbers: [33, 24, 39] Generated Node #0,2: 86:[33, 24, 39] Operation: 58-19=39 Exploring Operation: 58-24=34, Resulting Numbers: [33, 19, 34] Generated Node #0,3: 86:[33, 19, 34] Operation: 58-24=34 Exploring Operation: 24+19=43, Resulting Numbers: [33, 58, 43] Generated Node #0,4: 86:[33, 58, 43] Operation: 24+19=43 Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[33, 58, 43], Operations: ['24+19=43'] Exploring Operation: 58-33=25, Resulting Numbers: [43, 25] Generated Node #0,4,0: 86:[43, 25] Operation: 58-33=25 Exploring Operation: 33+58=91, Resulting Numbers: [43, 91] Generated Node #0,4,1: 86:[43, 91] Operation: 33+58=91 Exploring Operation: 58-43=15, Resulting Numbers: [33, 15] Generated Node #0,4,2: 86:[33, 15] Operation: 58-43=15 Exploring Operation: 33+43=76, Resulting Numbers: [58, 76] Generated Node #0,4,3: 86:[58, 76] Operation: 33+43=76 Exploring Operation: 43-33=10, Resulting Numbers: [58, 10] Generated Node #0,4,4: 86:[58, 10] Operation: 43-33=10 Moving to Node #0,4,1 Current State: 86:[43, 91], Operations: ['24+19=43', '33+58=91'] Exploring Operation: 43+91=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 43*91=3913, Resulting Numbers: [3913] 3913,86 unequal: No Solution Exploring Operation: 91-43=48, Resulting Numbers: [48] 48,86 unequal: No Solution Moving to Node #0,4,0 Current State: 86:[43, 25], Operations: ['24+19=43', '58-33=25'] Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 43+25=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 43*25=1075, Resulting Numbers: [1075] 1075,86 unequal: No Solution Moving to Node #0,4,2 Current State: 86:[33, 15], Operations: ['24+19=43', '58-43=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,86 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,86 unequal: No Solution Moving to Node #0,4,4 Current State: 86:[58, 10], Operations: ['24+19=43', '43-33=10'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,86 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,86 unequal: No Solution Moving to Node #0,4,3 Current State: 86:[58, 76], Operations: ['24+19=43', '33+43=76'] Exploring Operation: 58+76=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 58*76=4408, Resulting Numbers: [4408] 4408,86 unequal: No Solution Exploring Operation: 76-58=18, Resulting Numbers: [18] 18,86 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 #0,1 Current State: 86:[33, 58, 5], Operations: ['24-19=5'] Exploring Operation: 33-5=28, Resulting Numbers: [58, 28] Generated Node #0,1,0: 86:[58, 28] Operation: 33-5=28 Exploring Operation: 33+5=38, Resulting Numbers: [58, 38] Generated Node #0,1,1: 86:[58, 38] Operation: 33+5=38 Exploring Operation: 58-33=25, Resulting Numbers: [5, 25] Generated Node #0,1,2: 86:[5, 25] Operation: 58-33=25 Exploring Operation: 58-5=53, Resulting Numbers: [33, 53] Generated Node #0,1,3: 86:[33, 53] Operation: 58-5=53 Exploring Operation: 33+58=91, Resulting Numbers: [5, 91] Generated Node #0,1,4: 86:[5, 91] Operation: 33+58=91 Moving to Node #0,1,4 Current State: 86:[5, 91], Operations: ['24-19=5', '33+58=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[33, 24, 19, 58], Operations: [] Exploring Operation: 24-19=5, Resulting Numbers: [33, 58, 5] Generated Node #0,1: 86:[33, 58, 5] Operation: 24-19=5 Moving to Node #0,1 Current State: 86:[33, 58, 5], Operations: ['24-19=5'] Exploring Operation: 33+58=91, Resulting Numbers: [5, 91] Generated Node #0,1,4: 86:[5, 91] Operation: 33+58=91 Moving to Node #0,1,4 Current State: 86:[5, 91], Operations: ['24-19=5', '33+58=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 17, 55, 24, 78 ]
18
[ "17+55=72", "78-24=54", "72-54=18" ]
Current State: 18:[17, 55, 24, 78], Operations: [] Exploring Operation: 17+55=72, Resulting Numbers: [24, 78, 72] Generated Node #2: [24, 78, 72] from Operation: 17+55=72 Current State: 18:[24, 78, 72], Operations: ['17+55=72'] Exploring Operation: 78-24=54, Resulting Numbers: [72, 54] Generated Node #3: [72, 54] from Operation: 78-24=54 Current State: 18:[72, 54], Operations: ['17+55=72', '78-24=54'] Exploring Operation: 72-54=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[17, 55, 24, 78], Operations: [] Exploring Operation: 55-24=31, Resulting Numbers: [17, 78, 31] Generated Node #0,0: 18:[17, 78, 31] Operation: 55-24=31 Exploring Operation: 78-24=54, Resulting Numbers: [17, 55, 54] Generated Node #0,1: 18:[17, 55, 54] Operation: 78-24=54 Exploring Operation: 78-55=23, Resulting Numbers: [17, 24, 23] Generated Node #0,2: 18:[17, 24, 23] Operation: 78-55=23 Moving to Node #0,2 Current State: 18:[17, 24, 23], Operations: ['78-55=23'] Exploring Operation: 23-17=6, Resulting Numbers: [24, 6] Generated Node #0,2,0: 18:[24, 6] Operation: 23-17=6 Exploring Operation: 24-17=7, Resulting Numbers: [23, 7] Generated Node #0,2,1: 18:[23, 7] Operation: 24-17=7 Exploring Operation: 24-23=1, Resulting Numbers: [17, 1] Generated Node #0,2,2: 18:[17, 1] Operation: 24-23=1 Moving to Node #0,0 Current State: 18:[17, 78, 31], Operations: ['55-24=31'] Exploring Operation: 31-17=14, Resulting Numbers: [78, 14] Generated Node #0,0,0: 18:[78, 14] Operation: 31-17=14 Exploring Operation: 78-31=47, Resulting Numbers: [17, 47] Generated Node #0,0,1: 18:[17, 47] Operation: 78-31=47 Exploring Operation: 78-17=61, Resulting Numbers: [31, 61] Generated Node #0,0,2: 18:[31, 61] Operation: 78-17=61 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[17, 47], Operations: ['55-24=31', '78-31=47'] Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[31, 61], Operations: ['55-24=31', '78-17=61'] Exploring Operation: 31*61=1891, Resulting Numbers: [1891] 1891,18 unequal: No Solution Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[78, 14], Operations: ['55-24=31', '31-17=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,18 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,18 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: 18:[17, 55, 54], Operations: ['78-24=54'] Exploring Operation: 54-17=37, Resulting Numbers: [55, 37] Generated Node #0,1,0: 18:[55, 37] Operation: 54-17=37 Exploring Operation: 55-54=1, Resulting Numbers: [17, 1] Generated Node #0,1,1: 18:[17, 1] Operation: 55-54=1 Exploring Operation: 55-17=38, Resulting Numbers: [54, 38] Generated Node #0,1,2: 18:[54, 38] Operation: 55-17=38 Moving to Node #0,2,2 Current State: 18:[17, 1], Operations: ['78-55=23', '24-23=1'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[17, 55, 24, 78], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [17, 24, 23] Generated Node #0,2: 18:[17, 24, 23] Operation: 78-55=23 Moving to Node #0,2 Current State: 18:[17, 24, 23], Operations: ['78-55=23'] Exploring Operation: 24-23=1, Resulting Numbers: [17, 1] Generated Node #0,2,2: 18:[17, 1] Operation: 24-23=1 Moving to Node #0,2,2 Current State: 18:[17, 1], Operations: ['78-55=23', '24-23=1'] Exploring Operation: 17+1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.975694
hs_3
sum_heuristic
[ 27, 8, 62, 9 ]
72
[ "27-8=19", "62-9=53", "19+53=72" ]
Current State: 72:[27, 8, 62, 9], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [62, 9, 19] Generated Node #2: [62, 9, 19] from Operation: 27-8=19 Current State: 72:[62, 9, 19], Operations: ['27-8=19'] Exploring Operation: 62-9=53, Resulting Numbers: [19, 53] Generated Node #3: [19, 53] from Operation: 62-9=53 Current State: 72:[19, 53], Operations: ['27-8=19', '62-9=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[27, 8, 62, 9], Operations: [] Exploring Operation: 62+9=71, Resulting Numbers: [27, 8, 71] Generated Node #0,0: 72:[27, 8, 71] Operation: 62+9=71 Exploring Operation: 62-27=35, Resulting Numbers: [8, 9, 35] Generated Node #0,1: 72:[8, 9, 35] Operation: 62-27=35 Exploring Operation: 8+62=70, Resulting Numbers: [27, 9, 70] Generated Node #0,2: 72:[27, 9, 70] Operation: 8+62=70 Moving to Node #0,1 Current State: 72:[8, 9, 35], Operations: ['62-27=35'] Exploring Operation: 9-8=1, Resulting Numbers: [35, 1] Generated Node #0,1,0: 72:[35, 1] Operation: 9-8=1 Exploring Operation: 8+9=17, Resulting Numbers: [35, 17] Generated Node #0,1,1: 72:[35, 17] Operation: 8+9=17 Exploring Operation: 8*9=72, Resulting Numbers: [35, 72] Generated Node #0,1,2: 72:[35, 72] Operation: 8*9=72 Moving to Node #0,0 Current State: 72:[27, 8, 71], Operations: ['62+9=71'] Exploring Operation: 71-27=44, Resulting Numbers: [8, 44] Generated Node #0,0,0: 72:[8, 44] Operation: 71-27=44 Exploring Operation: 27-8=19, Resulting Numbers: [71, 19] Generated Node #0,0,1: 72:[71, 19] Operation: 27-8=19 Exploring Operation: 27+8=35, Resulting Numbers: [71, 35] Generated Node #0,0,2: 72:[71, 35] Operation: 27+8=35 Moving to Node #0,2 Current State: 72:[27, 9, 70], Operations: ['8+62=70'] Exploring Operation: 27/9=3, Resulting Numbers: [70, 3] Generated Node #0,2,0: 72:[70, 3] Operation: 27/9=3 Exploring Operation: 27-9=18, Resulting Numbers: [70, 18] Generated Node #0,2,1: 72:[70, 18] Operation: 27-9=18 Exploring Operation: 27+9=36, Resulting Numbers: [70, 36] Generated Node #0,2,2: 72:[70, 36] Operation: 27+9=36 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[70, 3], Operations: ['8+62=70', '27/9=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 70*3=210, Resulting Numbers: [210] 210,72 unequal: No Solution Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[70, 18], Operations: ['8+62=70', '27-9=18'] Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,72 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[70, 36], Operations: ['8+62=70', '27+9=36'] Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,72 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 72:[35, 72], Operations: ['62-27=35', '8*9=72'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 35+72=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 35*72=2520, Resulting Numbers: [2520] 2520,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[35, 17], Operations: ['62-27=35', '8+9=17'] Exploring Operation: 35-17=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 35*17=595, Resulting Numbers: [595] 595,72 unequal: No Solution Exploring Operation: 35+17=52, Resulting Numbers: [52] 52,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[35, 1], Operations: ['62-27=35', '9-8=1'] Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,72 unequal: No Solution Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,72 unequal: No Solution Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[71, 19], Operations: ['62+9=71', '27-8=19'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 71*19=1349, Resulting Numbers: [1349] 1349,72 unequal: No Solution Exploring Operation: 71+19=90, Resulting Numbers: [90] 90,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[71, 35], Operations: ['62+9=71', '27+8=35'] Exploring Operation: 71+35=106, Resulting Numbers: [106] 106,72 unequal: No Solution Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 71*35=2485, Resulting Numbers: [2485] 2485,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[8, 44], Operations: ['62+9=71', '71-27=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,72 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,72 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 37, 2, 44, 54 ]
57
[ "54-44=10", "2*10=20", "37+20=57" ]
Current State: 57:[37, 2, 44, 54], Operations: [] Exploring Operation: 54-44=10, Resulting Numbers: [37, 2, 10] Generated Node #2: [37, 2, 10] from Operation: 54-44=10 Current State: 57:[37, 2, 10], Operations: ['54-44=10'] Exploring Operation: 2*10=20, Resulting Numbers: [37, 20] Generated Node #3: [37, 20] from Operation: 2*10=20 Current State: 57:[37, 20], Operations: ['54-44=10', '2*10=20'] Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[37, 2, 44, 54], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [2, 54, 7] Generated Node #0,0: 57:[2, 54, 7] Operation: 44-37=7 Exploring Operation: 44/2=22, Resulting Numbers: [37, 54, 22] Generated Node #0,1: 57:[37, 54, 22] Operation: 44/2=22 Exploring Operation: 54-37=17, Resulting Numbers: [2, 44, 17] Generated Node #0,2: 57:[2, 44, 17] Operation: 54-37=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[2, 54, 7], Operations: ['44-37=7'] Exploring Operation: 2+54=56, Resulting Numbers: [7, 56] Generated Node #0,0,0: 57:[7, 56] Operation: 2+54=56 Exploring Operation: 54+7=61, Resulting Numbers: [2, 61] Generated Node #0,0,1: 57:[2, 61] Operation: 54+7=61 Exploring Operation: 7-2=5, Resulting Numbers: [54, 5] Generated Node #0,0,2: 57:[54, 5] Operation: 7-2=5 Moving to Node #0,0,0 Current State: 57:[7, 56], Operations: ['44-37=7', '2+54=56'] Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[2, 61], Operations: ['44-37=7', '54+7=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,57 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,57 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[54, 5], Operations: ['44-37=7', '7-2=5'] Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,57 unequal: No Solution Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,57 unequal: No Solution Exploring Operation: 54*5=270, Resulting Numbers: [270] 270,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[2, 44, 17], Operations: ['54-37=17'] Exploring Operation: 44+17=61, Resulting Numbers: [2, 61] Generated Node #0,2,0: 57:[2, 61] Operation: 44+17=61 Exploring Operation: 44/2=22, Resulting Numbers: [17, 22] Generated Node #0,2,1: 57:[17, 22] Operation: 44/2=22 Exploring Operation: 44-17=27, Resulting Numbers: [2, 27] Generated Node #0,2,2: 57:[2, 27] Operation: 44-17=27 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 57:[2, 61], Operations: ['54-37=17', '44+17=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,57 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,57 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,57 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 #0,2,1 Current State: 57:[17, 22], Operations: ['54-37=17', '44/2=22'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,57 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 #0,2,2 Current State: 57:[2, 27], Operations: ['54-37=17', '44-17=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,57 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,57 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: 57:[37, 54, 22], Operations: ['44/2=22'] Exploring Operation: 37+22=59, Resulting Numbers: [54, 59] Generated Node #0,1,0: 57:[54, 59] Operation: 37+22=59 Exploring Operation: 54-37=17, Resulting Numbers: [22, 17] Generated Node #0,1,1: 57:[22, 17] Operation: 54-37=17 Exploring Operation: 37-22=15, Resulting Numbers: [54, 15] Generated Node #0,1,2: 57:[54, 15] Operation: 37-22=15 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[54, 59], Operations: ['44/2=22', '37+22=59'] Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,57 unequal: No Solution Exploring Operation: 54*59=3186, Resulting Numbers: [3186] 3186,57 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 #0,1,1 Current State: 57:[22, 17], Operations: ['44/2=22', '54-37=17'] Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,57 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,57 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 #0,1,2 Current State: 57:[54, 15], Operations: ['44/2=22', '37-22=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,57 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 85, 23, 21, 53 ]
76
[ "85+23=108", "53-21=32", "108-32=76" ]
Current State: 76:[85, 23, 21, 53], Operations: [] Exploring Operation: 85+23=108, Resulting Numbers: [21, 53, 108] Generated Node #2: [21, 53, 108] from Operation: 85+23=108 Current State: 76:[21, 53, 108], Operations: ['85+23=108'] Exploring Operation: 53-21=32, Resulting Numbers: [108, 32] Generated Node #3: [108, 32] from Operation: 53-21=32 Current State: 76:[108, 32], Operations: ['85+23=108', '53-21=32'] Exploring Operation: 108-32=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[85, 23, 21, 53], Operations: [] Exploring Operation: 53-23=30, Resulting Numbers: [85, 21, 30] Generated Node #0,0: 76:[85, 21, 30] Operation: 53-23=30 Exploring Operation: 23+53=76, Resulting Numbers: [85, 21, 76] Generated Node #0,1: 76:[85, 21, 76] Operation: 23+53=76 Exploring Operation: 85-53=32, Resulting Numbers: [23, 21, 32] Generated Node #0,2: 76:[23, 21, 32] Operation: 85-53=32 Exploring Operation: 21+53=74, Resulting Numbers: [85, 23, 74] Generated Node #0,3: 76:[85, 23, 74] Operation: 21+53=74 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[85, 21, 76], Operations: ['23+53=76'] Exploring Operation: 85-21=64, Resulting Numbers: [76, 64] Generated Node #0,1,0: 76:[76, 64] Operation: 85-21=64 Exploring Operation: 85+21=106, Resulting Numbers: [76, 106] Generated Node #0,1,1: 76:[76, 106] Operation: 85+21=106 Exploring Operation: 85-76=9, Resulting Numbers: [21, 9] Generated Node #0,1,2: 76:[21, 9] Operation: 85-76=9 Exploring Operation: 76-21=55, Resulting Numbers: [85, 55] Generated Node #0,1,3: 76:[85, 55] Operation: 76-21=55 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 76:[21, 9], Operations: ['23+53=76', '85-76=9'] Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,76 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[76, 64], Operations: ['23+53=76', '85-21=64'] Exploring Operation: 76+64=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 76-64=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 76*64=4864, Resulting Numbers: [4864] 4864,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[85, 55], Operations: ['23+53=76', '76-21=55'] Exploring Operation: 85+55=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 85-55=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 85*55=4675, Resulting Numbers: [4675] 4675,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[76, 106], Operations: ['23+53=76', '85+21=106'] Exploring Operation: 76*106=8056, Resulting Numbers: [8056] 8056,76 unequal: No Solution Exploring Operation: 76+106=182, Resulting Numbers: [182] 182,76 unequal: No Solution Exploring Operation: 106-76=30, Resulting Numbers: [30] 30,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[23, 21, 32], Operations: ['85-53=32'] Exploring Operation: 32-23=9, Resulting Numbers: [21, 9] Generated Node #0,2,0: 76:[21, 9] Operation: 32-23=9 Exploring Operation: 32-21=11, Resulting Numbers: [23, 11] Generated Node #0,2,1: 76:[23, 11] Operation: 32-21=11 Exploring Operation: 23+21=44, Resulting Numbers: [32, 44] Generated Node #0,2,2: 76:[32, 44] Operation: 23+21=44 Exploring Operation: 23-21=2, Resulting Numbers: [32, 2] Generated Node #0,2,3: 76:[32, 2] Operation: 23-21=2 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[32, 2], Operations: ['85-53=32', '23-21=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[21, 9], Operations: ['85-53=32', '32-23=9'] Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,76 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[23, 11], Operations: ['85-53=32', '32-21=11'] Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,76 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[32, 44], Operations: ['85-53=32', '23+21=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[85, 23, 21, 53], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [23, 21, 32] Generated Node #0,2: 76:[23, 21, 32] Operation: 85-53=32 Moving to Node #0,2 Current State: 76:[23, 21, 32], Operations: ['85-53=32'] Exploring Operation: 23+21=44, Resulting Numbers: [32, 44] Generated Node #0,2,2: 76:[32, 44] Operation: 23+21=44 Moving to Node #0,2,2 Current State: 76:[32, 44], Operations: ['85-53=32', '23+21=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 9, 61, 83, 55 ]
86
[ "61-9=52", "83+55=138", "138-52=86" ]
Current State: 86:[9, 61, 83, 55], Operations: [] Exploring Operation: 61-9=52, Resulting Numbers: [83, 55, 52] Generated Node #2: [83, 55, 52] from Operation: 61-9=52 Current State: 86:[83, 55, 52], Operations: ['61-9=52'] Exploring Operation: 83+55=138, Resulting Numbers: [52, 138] Generated Node #3: [52, 138] from Operation: 83+55=138 Current State: 86:[52, 138], Operations: ['61-9=52', '83+55=138'] Exploring Operation: 138-52=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[9, 61, 83, 55], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [9, 83, 6] Generated Node #0,0: 86:[9, 83, 6] Operation: 61-55=6 Moving to Node #0,0 Current State: 86:[9, 83, 6], Operations: ['61-55=6'] Exploring Operation: 9-6=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 9-6=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['61-55=6', '9-6=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[9, 61, 83, 55], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [9, 83, 6] Generated Node #0,0: 86:[9, 83, 6] Operation: 61-55=6 Moving to Node #0,0 Current State: 86:[9, 83, 6], Operations: ['61-55=6'] Exploring Operation: 9-6=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 9-6=3 Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['61-55=6', '9-6=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 46, 2, 36, 64 ]
84
[ "46-36=10", "2*10=20", "64+20=84" ]
Current State: 84:[46, 2, 36, 64], Operations: [] Exploring Operation: 46-36=10, Resulting Numbers: [2, 64, 10] Generated Node #2: [2, 64, 10] from Operation: 46-36=10 Current State: 84:[2, 64, 10], Operations: ['46-36=10'] Exploring Operation: 2*10=20, Resulting Numbers: [64, 20] Generated Node #3: [64, 20] from Operation: 2*10=20 Current State: 84:[64, 20], Operations: ['46-36=10', '2*10=20'] Exploring Operation: 64+20=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[46, 2, 36, 64], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [46, 36, 32] Generated Node #0,0: 84:[46, 36, 32] Operation: 64/2=32 Exploring Operation: 36+64=100, Resulting Numbers: [46, 2, 100] Generated Node #0,1: 84:[46, 2, 100] Operation: 36+64=100 Exploring Operation: 64-46=18, Resulting Numbers: [2, 36, 18] Generated Node #0,2: 84:[2, 36, 18] Operation: 64-46=18 Exploring Operation: 64-36=28, Resulting Numbers: [46, 2, 28] Generated Node #0,3: 84:[46, 2, 28] Operation: 64-36=28 Exploring Operation: 46+36=82, Resulting Numbers: [2, 64, 82] Generated Node #0,4: 84:[2, 64, 82] Operation: 46+36=82 Moving to Node #0,3 Current State: 84:[46, 2, 28], Operations: ['64-36=28'] Exploring Operation: 46/2=23, Resulting Numbers: [28, 23] Generated Node #0,3,0: 84:[28, 23] Operation: 46/2=23 Exploring Operation: 46-28=18, Resulting Numbers: [2, 18] Generated Node #0,3,1: 84:[2, 18] Operation: 46-28=18 Exploring Operation: 46+2=48, Resulting Numbers: [28, 48] Generated Node #0,3,2: 84:[28, 48] Operation: 46+2=48 Exploring Operation: 46-2=44, Resulting Numbers: [28, 44] Generated Node #0,3,3: 84:[28, 44] Operation: 46-2=44 Exploring Operation: 28/2=14, Resulting Numbers: [46, 14] Generated Node #0,3,4: 84:[46, 14] Operation: 28/2=14 Moving to Node #0,2 Current State: 84:[2, 36, 18], Operations: ['64-46=18'] Exploring Operation: 2+36=38, Resulting Numbers: [18, 38] Generated Node #0,2,0: 84:[18, 38] Operation: 2+36=38 Exploring Operation: 2+18=20, Resulting Numbers: [36, 20] Generated Node #0,2,1: 84:[36, 20] Operation: 2+18=20 Exploring Operation: 36-18=18, Resulting Numbers: [2, 18] Generated Node #0,2,2: 84:[2, 18] Operation: 36-18=18 Exploring Operation: 36/18=2, Resulting Numbers: [2, 2] Generated Node #0,2,3: 84:[2, 2] Operation: 36/18=2 Exploring Operation: 36/2=18, Resulting Numbers: [18, 18] Generated Node #0,2,4: 84:[18, 18] Operation: 36/2=18 Moving to Node #0,0 Current State: 84:[46, 36, 32], Operations: ['64/2=32'] Exploring Operation: 36-32=4, Resulting Numbers: [46, 4] Generated Node #0,0,0: 84:[46, 4] Operation: 36-32=4 Exploring Operation: 46+32=78, Resulting Numbers: [36, 78] Generated Node #0,0,1: 84:[36, 78] Operation: 46+32=78 Exploring Operation: 46-36=10, Resulting Numbers: [32, 10] Generated Node #0,0,2: 84:[32, 10] Operation: 46-36=10 Exploring Operation: 46-32=14, Resulting Numbers: [36, 14] Generated Node #0,0,3: 84:[36, 14] Operation: 46-32=14 Exploring Operation: 46+36=82, Resulting Numbers: [32, 82] Generated Node #0,0,4: 84:[32, 82] Operation: 46+36=82 Moving to Node #0,1 Current State: 84:[46, 2, 100], Operations: ['36+64=100'] Exploring Operation: 46-2=44, Resulting Numbers: [100, 44] Generated Node #0,1,0: 84:[100, 44] Operation: 46-2=44 Exploring Operation: 46/2=23, Resulting Numbers: [100, 23] Generated Node #0,1,1: 84:[100, 23] Operation: 46/2=23 Exploring Operation: 100/2=50, Resulting Numbers: [46, 50] Generated Node #0,1,2: 84:[46, 50] Operation: 100/2=50 Exploring Operation: 100-2=98, Resulting Numbers: [46, 98] Generated Node #0,1,3: 84:[46, 98] Operation: 100-2=98 Exploring Operation: 100-46=54, Resulting Numbers: [2, 54] Generated Node #0,1,4: 84:[2, 54] Operation: 100-46=54 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[46, 50], Operations: ['36+64=100', '100/2=50'] Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 46+50=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 46*50=2300, Resulting Numbers: [2300] 2300,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 84:[2, 54], Operations: ['36+64=100', '100-46=54'] Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,84 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,84 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[100, 44], Operations: ['36+64=100', '46-2=44'] Exploring Operation: 100+44=144, Resulting Numbers: [144] 144,84 unequal: No Solution Exploring Operation: 100-44=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 100*44=4400, Resulting Numbers: [4400] 4400,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[100, 23], Operations: ['36+64=100', '46/2=23'] Exploring Operation: 100+23=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 100*23=2300, Resulting Numbers: [2300] 2300,84 unequal: No Solution Exploring Operation: 100-23=77, Resulting Numbers: [77] 77,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[46, 98], Operations: ['36+64=100', '100-2=98'] Exploring Operation: 98-46=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 46*98=4508, Resulting Numbers: [4508] 4508,84 unequal: No Solution Exploring Operation: 46+98=144, Resulting Numbers: [144] 144,84 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: 84:[2, 64, 82], Operations: ['46+36=82'] Exploring Operation: 82/2=41, Resulting Numbers: [64, 41] Generated Node #0,4,0: 84:[64, 41] Operation: 82/2=41 Exploring Operation: 2+64=66, Resulting Numbers: [82, 66] Generated Node #0,4,1: 84:[82, 66] Operation: 2+64=66 Exploring Operation: 82-64=18, Resulting Numbers: [2, 18] Generated Node #0,4,2: 84:[2, 18] Operation: 82-64=18 Exploring Operation: 2+82=84, Resulting Numbers: [64, 84] Generated Node #0,4,3: 84:[64, 84] Operation: 2+82=84 Exploring Operation: 64/2=32, Resulting Numbers: [82, 32] Generated Node #0,4,4: 84:[82, 32] Operation: 64/2=32 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 84:[2, 18], Operations: ['46+36=82', '82-64=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 84:[82, 32], Operations: ['46+36=82', '64/2=32'] Exploring Operation: 82*32=2624, Resulting Numbers: [2624] 2624,84 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 82+32=114, Resulting Numbers: [114] 114,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 84:[82, 66], Operations: ['46+36=82', '2+64=66'] Exploring Operation: 82+66=148, Resulting Numbers: [148] 148,84 unequal: No Solution Exploring Operation: 82-66=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 82*66=5412, Resulting Numbers: [5412] 5412,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 84:[64, 84], Operations: ['46+36=82', '2+82=84'] Exploring Operation: 64+84=148, Resulting Numbers: [148] 148,84 unequal: No Solution Exploring Operation: 84-64=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 64*84=5376, Resulting Numbers: [5376] 5376,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 84:[64, 41], Operations: ['46+36=82', '82/2=41'] Exploring Operation: 64*41=2624, Resulting Numbers: [2624] 2624,84 unequal: No Solution Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 64+41=105, Resulting Numbers: [105] 105,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 84:[2, 2], Operations: ['64-46=18', '36/18=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[28, 23], Operations: ['64-36=28', '46/2=23'] Exploring Operation: 28*23=644, Resulting Numbers: [644] 644,84 unequal: No Solution Exploring Operation: 28+23=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[28, 44], Operations: ['64-36=28', '46-2=44'] Exploring Operation: 28*44=1232, Resulting Numbers: [1232] 1232,84 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 28+44=72, Resulting Numbers: [72] 72,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[2, 18], Operations: ['64-46=18', '36-18=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[2, 18], Operations: ['64-36=28', '46-28=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[46, 4], Operations: ['64/2=32', '36-32=4'] Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,84 unequal: No Solution Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,84 unequal: No Solution Moving to Node #0,3,4 Current State: 84:[46, 14], Operations: ['64-36=28', '28/2=14'] Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,84 unequal: No Solution Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,84 unequal: No Solution Moving to Node #0,0,4 Current State: 84:[32, 82], Operations: ['64/2=32', '46+36=82'] Exploring Operation: 32*82=2624, Resulting Numbers: [2624] 2624,84 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 32+82=114, Resulting Numbers: [114] 114,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[36, 14], Operations: ['64/2=32', '46-32=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 36*14=504, Resulting Numbers: [504] 504,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[32, 10], Operations: ['64/2=32', '46-36=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,84 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[28, 48], Operations: ['64-36=28', '46+2=48'] Exploring Operation: 28+48=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 28*48=1344, Resulting Numbers: [1344] 1344,84 unequal: No Solution Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,84 unequal: No Solution Moving to Node #0,2,4 Current State: 84:[18, 18], Operations: ['64-46=18', '36/2=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,84 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[18, 38], Operations: ['64-46=18', '2+36=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,84 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[36, 20], Operations: ['64-46=18', '2+18=20'] Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[36, 78], Operations: ['64/2=32', '46+32=78'] Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,84 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,84 unequal: No Solution Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,84 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 75, 85, 49, 36 ]
75
[ "75+85=160", "49+36=85", "160-85=75" ]
Current State: 75:[75, 85, 49, 36], Operations: [] Exploring Operation: 75+85=160, Resulting Numbers: [49, 36, 160] Generated Node #2: [49, 36, 160] from Operation: 75+85=160 Current State: 75:[49, 36, 160], Operations: ['75+85=160'] Exploring Operation: 49+36=85, Resulting Numbers: [160, 85] Generated Node #3: [160, 85] from Operation: 49+36=85 Current State: 75:[160, 85], Operations: ['75+85=160', '49+36=85'] Exploring Operation: 160-85=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[75, 85, 49, 36], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [75, 85, 13] Generated Node #0,0: 75:[75, 85, 13] Operation: 49-36=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[75, 85, 13], Operations: ['49-36=13'] Exploring Operation: 85-13=72, Resulting Numbers: [75, 72] Generated Node #0,0,0: 75:[75, 72] Operation: 85-13=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[75, 72], Operations: ['49-36=13', '85-13=72'] Exploring Operation: 75-72=3, Resulting Numbers: [3] 3,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 26, 58, 13, 80 ]
24
[ "26/13=2", "80-58=22", "2+22=24" ]
Current State: 24:[26, 58, 13, 80], Operations: [] Exploring Operation: 26/13=2, Resulting Numbers: [58, 80, 2] Generated Node #2: [58, 80, 2] from Operation: 26/13=2 Current State: 24:[58, 80, 2], Operations: ['26/13=2'] Exploring Operation: 80-58=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 80-58=22 Current State: 24:[2, 22], Operations: ['26/13=2', '80-58=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[26, 58, 13, 80], Operations: [] Exploring Operation: 58-26=32, Resulting Numbers: [13, 80, 32] Generated Node #0,0: 24:[13, 80, 32] Operation: 58-26=32 Exploring Operation: 80-58=22, Resulting Numbers: [26, 13, 22] Generated Node #0,1: 24:[26, 13, 22] Operation: 80-58=22 Moving to Node #0,1 Current State: 24:[26, 13, 22], Operations: ['80-58=22'] Exploring Operation: 26-22=4, Resulting Numbers: [13, 4] Generated Node #0,1,0: 24:[13, 4] Operation: 26-22=4 Exploring Operation: 26/13=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 24:[22, 2] Operation: 26/13=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[13, 4], Operations: ['80-58=22', '26-22=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[22, 2], Operations: ['80-58=22', '26/13=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[26, 58, 13, 80], Operations: [] Exploring Operation: 80-58=22, Resulting Numbers: [26, 13, 22] Generated Node #0,1: 24:[26, 13, 22] Operation: 80-58=22 Moving to Node #0,1 Current State: 24:[26, 13, 22], Operations: ['80-58=22'] Exploring Operation: 26/13=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 24:[22, 2] Operation: 26/13=2 Moving to Node #0,1,1 Current State: 24:[22, 2], Operations: ['80-58=22', '26/13=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 70, 78, 9, 85 ]
85
[ "78-70=8", "9-8=1", "85*1=85" ]
Current State: 85:[70, 78, 9, 85], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [9, 85, 8] Generated Node #2: [9, 85, 8] from Operation: 78-70=8 Current State: 85:[9, 85, 8], Operations: ['78-70=8'] Exploring Operation: 9-8=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 9-8=1 Current State: 85:[85, 1], Operations: ['78-70=8', '9-8=1'] Exploring Operation: 85*1=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[70, 78, 9, 85], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [9, 85, 8] Generated Node #0,0: 85:[9, 85, 8] Operation: 78-70=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[9, 85, 8], Operations: ['78-70=8'] Exploring Operation: 9+8=17, Resulting Numbers: [85, 17] Generated Node #0,0,0: 85:[85, 17] Operation: 9+8=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[85, 17], Operations: ['78-70=8', '9+8=17'] Exploring Operation: 85/17=5, Resulting Numbers: [5] 5,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 81, 87, 73, 69 ]
10
[ "87-81=6", "73-69=4", "6+4=10" ]
Current State: 10:[81, 87, 73, 69], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [73, 69, 6] Generated Node #2: [73, 69, 6] from Operation: 87-81=6 Current State: 10:[73, 69, 6], Operations: ['87-81=6'] Exploring Operation: 73-69=4, Resulting Numbers: [6, 4] Generated Node #3: [6, 4] from Operation: 73-69=4 Current State: 10:[6, 4], Operations: ['87-81=6', '73-69=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[81, 87, 73, 69], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [73, 69, 6] Generated Node #0,0: 10:[73, 69, 6] Operation: 87-81=6 Exploring Operation: 81-73=8, Resulting Numbers: [87, 69, 8] Generated Node #0,1: 10:[87, 69, 8] Operation: 81-73=8 Exploring Operation: 87-73=14, Resulting Numbers: [81, 69, 14] Generated Node #0,2: 10:[81, 69, 14] Operation: 87-73=14 Moving to Node #0,0 Current State: 10:[73, 69, 6], Operations: ['87-81=6'] Exploring Operation: 73-69=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 10:[6, 4] Operation: 73-69=4 Exploring Operation: 69-6=63, Resulting Numbers: [73, 63] Generated Node #0,0,1: 10:[73, 63] Operation: 69-6=63 Exploring Operation: 73-6=67, Resulting Numbers: [69, 67] Generated Node #0,0,2: 10:[69, 67] Operation: 73-6=67 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[6, 4], Operations: ['87-81=6', '73-69=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,10 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[81, 87, 73, 69], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [73, 69, 6] Generated Node #0,0: 10:[73, 69, 6] Operation: 87-81=6 Moving to Node #0,0 Current State: 10:[73, 69, 6], Operations: ['87-81=6'] Exploring Operation: 73-69=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 10:[6, 4] Operation: 73-69=4 Moving to Node #0,0,0 Current State: 10:[6, 4], Operations: ['87-81=6', '73-69=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 61, 38, 62, 97 ]
64
[ "61+38=99", "97-62=35", "99-35=64" ]
Current State: 64:[61, 38, 62, 97], Operations: [] Exploring Operation: 61+38=99, Resulting Numbers: [62, 97, 99] Generated Node #2: [62, 97, 99] from Operation: 61+38=99 Current State: 64:[62, 97, 99], Operations: ['61+38=99'] Exploring Operation: 97-62=35, Resulting Numbers: [99, 35] Generated Node #3: [99, 35] from Operation: 97-62=35 Current State: 64:[99, 35], Operations: ['61+38=99', '97-62=35'] Exploring Operation: 99-35=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[61, 38, 62, 97], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [38, 62, 36] Generated Node #0,0: 64:[38, 62, 36] Operation: 97-61=36 Exploring Operation: 97-38=59, Resulting Numbers: [61, 62, 59] Generated Node #0,1: 64:[61, 62, 59] Operation: 97-38=59 Moving to Node #0,1 Current State: 64:[61, 62, 59], Operations: ['97-38=59'] Exploring Operation: 62-59=3, Resulting Numbers: [61, 3] Generated Node #0,1,0: 64:[61, 3] Operation: 62-59=3 Exploring Operation: 61-59=2, Resulting Numbers: [62, 2] Generated Node #0,1,1: 64:[62, 2] Operation: 61-59=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[62, 2], Operations: ['97-38=59', '61-59=2'] Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[61, 38, 62, 97], Operations: [] Exploring Operation: 97-38=59, Resulting Numbers: [61, 62, 59] Generated Node #0,1: 64:[61, 62, 59] Operation: 97-38=59 Moving to Node #0,1 Current State: 64:[61, 62, 59], Operations: ['97-38=59'] Exploring Operation: 61-59=2, Resulting Numbers: [62, 2] Generated Node #0,1,1: 64:[62, 2] Operation: 61-59=2 Moving to Node #0,1,1 Current State: 64:[62, 2], Operations: ['97-38=59', '61-59=2'] Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 65, 7, 50, 57 ]
66
[ "7+50=57", "57/57=1", "65+1=66" ]
Current State: 66:[65, 7, 50, 57], Operations: [] Exploring Operation: 7+50=57, Resulting Numbers: [65, 57, 57] Generated Node #2: [65, 57, 57] from Operation: 7+50=57 Current State: 66:[65, 57, 57], Operations: ['7+50=57'] Exploring Operation: 57/57=1, Resulting Numbers: [65, 1] Generated Node #3: [65, 1] from Operation: 57/57=1 Current State: 66:[65, 1], Operations: ['7+50=57', '57/57=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[65, 7, 50, 57], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [65, 7, 7] Generated Node #0,0: 66:[65, 7, 7] Operation: 57-50=7 Moving to Node #0,0 Current State: 66:[65, 7, 7], Operations: ['57-50=7'] Exploring Operation: 7/7=1, Resulting Numbers: [65, 1] Generated Node #0,0,0: 66:[65, 1] Operation: 7/7=1 Moving to Node #0,0,0 Current State: 66:[65, 1], Operations: ['57-50=7', '7/7=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[65, 7, 50, 57], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [65, 7, 7] Generated Node #0,0: 66:[65, 7, 7] Operation: 57-50=7 Moving to Node #0,0 Current State: 66:[65, 7, 7], Operations: ['57-50=7'] Exploring Operation: 7/7=1, Resulting Numbers: [65, 1] Generated Node #0,0,0: 66:[65, 1] Operation: 7/7=1 Moving to Node #0,0,0 Current State: 66:[65, 1], Operations: ['57-50=7', '7/7=1'] Exploring Operation: 65+1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 4, 70, 7, 17 ]
76
[ "70-4=66", "17-7=10", "66+10=76" ]
Current State: 76:[4, 70, 7, 17], Operations: [] Exploring Operation: 70-4=66, Resulting Numbers: [7, 17, 66] Generated Node #2: [7, 17, 66] from Operation: 70-4=66 Current State: 76:[7, 17, 66], Operations: ['70-4=66'] Exploring Operation: 17-7=10, Resulting Numbers: [66, 10] Generated Node #3: [66, 10] from Operation: 17-7=10 Current State: 76:[66, 10], Operations: ['70-4=66', '17-7=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[4, 70, 7, 17], Operations: [] Exploring Operation: 70+7=77, Resulting Numbers: [4, 17, 77] Generated Node #0,0: 76:[4, 17, 77] Operation: 70+7=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[4, 17, 77], Operations: ['70+7=77'] Exploring Operation: 4+17=21, Resulting Numbers: [77, 21] Generated Node #0,0,0: 76:[77, 21] Operation: 4+17=21 Moving to Node #0,0,0 Current State: 76:[77, 21], Operations: ['70+7=77', '4+17=21'] Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,76 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
[ 96, 52, 71, 45 ]
72
[ "96-52=44", "71+45=116", "116-44=72" ]
Current State: 72:[96, 52, 71, 45], Operations: [] Exploring Operation: 96-52=44, Resulting Numbers: [71, 45, 44] Generated Node #2: [71, 45, 44] from Operation: 96-52=44 Current State: 72:[71, 45, 44], Operations: ['96-52=44'] Exploring Operation: 71+45=116, Resulting Numbers: [44, 116] Generated Node #3: [44, 116] from Operation: 71+45=116 Current State: 72:[44, 116], Operations: ['96-52=44', '71+45=116'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[96, 52, 71, 45], Operations: [] Exploring Operation: 96-45=51, Resulting Numbers: [52, 71, 51] Generated Node #0,0: 72:[52, 71, 51] Operation: 96-45=51 Exploring Operation: 52-45=7, Resulting Numbers: [96, 71, 7] Generated Node #0,1: 72:[96, 71, 7] Operation: 52-45=7 Exploring Operation: 96-52=44, Resulting Numbers: [71, 45, 44] Generated Node #0,2: 72:[71, 45, 44] Operation: 96-52=44 Exploring Operation: 71-52=19, Resulting Numbers: [96, 45, 19] Generated Node #0,3: 72:[96, 45, 19] Operation: 71-52=19 Exploring Operation: 96-71=25, Resulting Numbers: [52, 45, 25] Generated Node #0,4: 72:[52, 45, 25] Operation: 96-71=25 Moving to Node #0,2 Current State: 72:[71, 45, 44], Operations: ['96-52=44'] Exploring Operation: 71-44=27, Resulting Numbers: [45, 27] Generated Node #0,2,0: 72:[45, 27] Operation: 71-44=27 Exploring Operation: 45-44=1, Resulting Numbers: [71, 1] Generated Node #0,2,1: 72:[71, 1] Operation: 45-44=1 Exploring Operation: 45+44=89, Resulting Numbers: [71, 89] Generated Node #0,2,2: 72:[71, 89] Operation: 45+44=89 Exploring Operation: 71+45=116, Resulting Numbers: [44, 116] Generated Node #0,2,3: 72:[44, 116] Operation: 71+45=116 Exploring Operation: 71-45=26, Resulting Numbers: [44, 26] Generated Node #0,2,4: 72:[44, 26] Operation: 71-45=26 Moving to Node #0,4 Current State: 72:[52, 45, 25], Operations: ['96-71=25'] Exploring Operation: 52+25=77, Resulting Numbers: [45, 77] Generated Node #0,4,0: 72:[45, 77] Operation: 52+25=77 Exploring Operation: 52-25=27, Resulting Numbers: [45, 27] Generated Node #0,4,1: 72:[45, 27] Operation: 52-25=27 Exploring Operation: 52-45=7, Resulting Numbers: [25, 7] Generated Node #0,4,2: 72:[25, 7] Operation: 52-45=7 Exploring Operation: 45+25=70, Resulting Numbers: [52, 70] Generated Node #0,4,3: 72:[52, 70] Operation: 45+25=70 Exploring Operation: 45-25=20, Resulting Numbers: [52, 20] Generated Node #0,4,4: 72:[52, 20] Operation: 45-25=20 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 72:[25, 7], Operations: ['96-71=25', '52-45=7'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,72 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,72 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 #0,4,1 Current State: 72:[45, 27], Operations: ['96-71=25', '52-25=27'] Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[96, 52, 71, 45], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [52, 45, 25] Generated Node #0,4: 72:[52, 45, 25] Operation: 96-71=25 Moving to Node #0,4 Current State: 72:[52, 45, 25], Operations: ['96-71=25'] Exploring Operation: 52-25=27, Resulting Numbers: [45, 27] Generated Node #0,4,1: 72:[45, 27] Operation: 52-25=27 Moving to Node #0,4,1 Current State: 72:[45, 27], Operations: ['96-71=25', '52-25=27'] Exploring Operation: 45+27=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_5
sum_heuristic
[ 18, 7, 26, 97 ]
98
[ "18+7=25", "26+97=123", "123-25=98" ]
Current State: 98:[18, 7, 26, 97], Operations: [] Exploring Operation: 18+7=25, Resulting Numbers: [26, 97, 25] Generated Node #2: [26, 97, 25] from Operation: 18+7=25 Current State: 98:[26, 97, 25], Operations: ['18+7=25'] Exploring Operation: 26+97=123, Resulting Numbers: [25, 123] Generated Node #3: [25, 123] from Operation: 26+97=123 Current State: 98:[25, 123], Operations: ['18+7=25', '26+97=123'] Exploring Operation: 123-25=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[18, 7, 26, 97], Operations: [] Exploring Operation: 26-18=8, Resulting Numbers: [7, 97, 8] Generated Node #0,0: 98:[7, 97, 8] Operation: 26-18=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[7, 97, 8], Operations: ['26-18=8'] Exploring Operation: 7+8=15, Resulting Numbers: [97, 15] Generated Node #0,0,0: 98:[97, 15] Operation: 7+8=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[97, 15], Operations: ['26-18=8', '7+8=15'] Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 3, 19, 13, 6 ]
26
[ "3*13=39", "19-6=13", "39-13=26" ]
Current State: 26:[3, 19, 13, 6], Operations: [] Exploring Operation: 3*13=39, Resulting Numbers: [19, 6, 39] Generated Node #2: [19, 6, 39] from Operation: 3*13=39 Current State: 26:[19, 6, 39], Operations: ['3*13=39'] Exploring Operation: 19-6=13, Resulting Numbers: [39, 13] Generated Node #3: [39, 13] from Operation: 19-6=13 Current State: 26:[39, 13], Operations: ['3*13=39', '19-6=13'] Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[3, 19, 13, 6], Operations: [] Exploring Operation: 19-6=13, Resulting Numbers: [3, 13, 13] Generated Node #0,0: 26:[3, 13, 13] Operation: 19-6=13 Exploring Operation: 19+6=25, Resulting Numbers: [3, 13, 25] Generated Node #0,1: 26:[3, 13, 25] Operation: 19+6=25 Exploring Operation: 6/3=2, Resulting Numbers: [19, 13, 2] Generated Node #0,2: 26:[19, 13, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[3, 13, 13], Operations: ['19-6=13'] Exploring Operation: 13+13=26, Resulting Numbers: [3, 26] Generated Node #0,0,0: 26:[3, 26] Operation: 13+13=26 Exploring Operation: 13/13=1, Resulting Numbers: [3, 1] Generated Node #0,0,1: 26:[3, 1] Operation: 13/13=1 Exploring Operation: 3+13=16, Resulting Numbers: [13, 16] Generated Node #0,0,2: 26:[13, 16] Operation: 3+13=16 Moving to Node #0,0,0 Current State: 26:[3, 26], Operations: ['19-6=13', '13+13=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,26 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[3, 1], Operations: ['19-6=13', '13/13=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[13, 16], Operations: ['19-6=13', '3+13=16'] Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 13*16=208, Resulting Numbers: [208] 208,26 unequal: No Solution Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[3, 13, 25], Operations: ['19+6=25'] Exploring Operation: 3+25=28, Resulting Numbers: [13, 28] Generated Node #0,1,0: 26:[13, 28] Operation: 3+25=28 Exploring Operation: 3+13=16, Resulting Numbers: [25, 16] Generated Node #0,1,1: 26:[25, 16] Operation: 3+13=16 Exploring Operation: 25-13=12, Resulting Numbers: [3, 12] Generated Node #0,1,2: 26:[3, 12] Operation: 25-13=12 Moving to Node #0,1,0 Current State: 26:[13, 28], Operations: ['19+6=25', '3+25=28'] Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 13*28=364, Resulting Numbers: [364] 364,26 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[3, 12], Operations: ['19+6=25', '25-13=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[25, 16], Operations: ['19+6=25', '3+13=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,26 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,26 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[19, 13, 2], Operations: ['6/3=2'] Exploring Operation: 19+2=21, Resulting Numbers: [13, 21] Generated Node #0,2,0: 26:[13, 21] Operation: 19+2=21 Exploring Operation: 19-13=6, Resulting Numbers: [2, 6] Generated Node #0,2,1: 26:[2, 6] Operation: 19-13=6 Exploring Operation: 19-2=17, Resulting Numbers: [13, 17] Generated Node #0,2,2: 26:[13, 17] Operation: 19-2=17 Moving to Node #0,2,1 Current State: 26:[2, 6], Operations: ['6/3=2', '19-13=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[13, 17], Operations: ['6/3=2', '19-2=17'] Exploring Operation: 13*17=221, Resulting Numbers: [221] 221,26 unequal: No Solution Exploring Operation: 13+17=30, Resulting Numbers: [30] 30,26 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[13, 21], Operations: ['6/3=2', '19+2=21'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,26 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,26 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
[ 41, 65, 45, 10 ]
26
[ "45-41=4", "65*4=260", "260/10=26" ]
Current State: 26:[41, 65, 45, 10], Operations: [] Exploring Operation: 45-41=4, Resulting Numbers: [65, 10, 4] Generated Node #2: [65, 10, 4] from Operation: 45-41=4 Current State: 26:[65, 10, 4], Operations: ['45-41=4'] Exploring Operation: 65*4=260, Resulting Numbers: [10, 260] Generated Node #3: [10, 260] from Operation: 65*4=260 Current State: 26:[10, 260], Operations: ['45-41=4', '65*4=260'] Exploring Operation: 260/10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[41, 65, 45, 10], Operations: [] Exploring Operation: 65-41=24, Resulting Numbers: [45, 10, 24] Generated Node #0,0: 26:[45, 10, 24] Operation: 65-41=24 Exploring Operation: 65-45=20, Resulting Numbers: [41, 10, 20] Generated Node #0,1: 26:[41, 10, 20] Operation: 65-45=20 Moving to Node #0,0 Current State: 26:[45, 10, 24], Operations: ['65-41=24'] Exploring Operation: 45-10=35, Resulting Numbers: [24, 35] Generated Node #0,0,0: 26:[24, 35] Operation: 45-10=35 Exploring Operation: 45-24=21, Resulting Numbers: [10, 21] Generated Node #0,0,1: 26:[10, 21] Operation: 45-24=21 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[10, 21], Operations: ['65-41=24', '45-24=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[24, 35], Operations: ['65-41=24', '45-10=35'] Exploring Operation: 24+35=59, Resulting Numbers: [59] 59,26 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,26 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: 26:[41, 10, 20], Operations: ['65-45=20'] Exploring Operation: 41-10=31, Resulting Numbers: [20, 31] Generated Node #0,1,0: 26:[20, 31] Operation: 41-10=31 Exploring Operation: 41-20=21, Resulting Numbers: [10, 21] Generated Node #0,1,1: 26:[10, 21] Operation: 41-20=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[10, 21], Operations: ['65-45=20', '41-20=21'] Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,26 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[20, 31], Operations: ['65-45=20', '41-10=31'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,26 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
[ 99, 2, 56, 82 ]
11
[ "99-82=17", "56/2=28", "28-17=11" ]
Current State: 11:[99, 2, 56, 82], Operations: [] Exploring Operation: 99-82=17, Resulting Numbers: [2, 56, 17] Generated Node #2: [2, 56, 17] from Operation: 99-82=17 Current State: 11:[2, 56, 17], Operations: ['99-82=17'] Exploring Operation: 56/2=28, Resulting Numbers: [17, 28] Generated Node #3: [17, 28] from Operation: 56/2=28 Current State: 11:[17, 28], Operations: ['99-82=17', '56/2=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[99, 2, 56, 82], Operations: [] Exploring Operation: 99-82=17, Resulting Numbers: [2, 56, 17] Generated Node #0,0: 11:[2, 56, 17] Operation: 99-82=17 Exploring Operation: 99-56=43, Resulting Numbers: [2, 82, 43] Generated Node #0,1: 11:[2, 82, 43] Operation: 99-56=43 Exploring Operation: 56/2=28, Resulting Numbers: [99, 82, 28] Generated Node #0,2: 11:[99, 82, 28] Operation: 56/2=28 Exploring Operation: 82-56=26, Resulting Numbers: [99, 2, 26] Generated Node #0,3: 11:[99, 2, 26] Operation: 82-56=26 Exploring Operation: 82/2=41, Resulting Numbers: [99, 56, 41] Generated Node #0,4: 11:[99, 56, 41] Operation: 82/2=41 Moving to Node #0,0 Current State: 11:[2, 56, 17], Operations: ['99-82=17'] Exploring Operation: 56/2=28, Resulting Numbers: [17, 28] Generated Node #0,0,0: 11:[17, 28] Operation: 56/2=28 Exploring Operation: 56-2=54, Resulting Numbers: [17, 54] Generated Node #0,0,1: 11:[17, 54] Operation: 56-2=54 Exploring Operation: 17-2=15, Resulting Numbers: [56, 15] Generated Node #0,0,2: 11:[56, 15] Operation: 17-2=15 Exploring Operation: 56-17=39, Resulting Numbers: [2, 39] Generated Node #0,0,3: 11:[2, 39] Operation: 56-17=39 Exploring Operation: 2+56=58, Resulting Numbers: [17, 58] Generated Node #0,0,4: 11:[17, 58] Operation: 2+56=58 Moving to Node #0,3 Current State: 11:[99, 2, 26], Operations: ['82-56=26'] Exploring Operation: 99-26=73, Resulting Numbers: [2, 73] Generated Node #0,3,0: 11:[2, 73] Operation: 99-26=73 Exploring Operation: 26-2=24, Resulting Numbers: [99, 24] Generated Node #0,3,1: 11:[99, 24] Operation: 26-2=24 Exploring Operation: 99-2=97, Resulting Numbers: [26, 97] Generated Node #0,3,2: 11:[26, 97] Operation: 99-2=97 Exploring Operation: 99+2=101, Resulting Numbers: [26, 101] Generated Node #0,3,3: 11:[26, 101] Operation: 99+2=101 Exploring Operation: 26/2=13, Resulting Numbers: [99, 13] Generated Node #0,3,4: 11:[99, 13] Operation: 26/2=13 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[2, 73], Operations: ['82-56=26', '99-26=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 11:[99, 13], Operations: ['82-56=26', '26/2=13'] Exploring Operation: 99*13=1287, Resulting Numbers: [1287] 1287,11 unequal: No Solution Exploring Operation: 99+13=112, Resulting Numbers: [112] 112,11 unequal: No Solution Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[99, 24], Operations: ['82-56=26', '26-2=24'] Exploring Operation: 99+24=123, Resulting Numbers: [123] 123,11 unequal: No Solution Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,11 unequal: No Solution Exploring Operation: 99*24=2376, Resulting Numbers: [2376] 2376,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[26, 97], Operations: ['82-56=26', '99-2=97'] Exploring Operation: 26+97=123, Resulting Numbers: [123] 123,11 unequal: No Solution Exploring Operation: 97-26=71, Resulting Numbers: [71] 71,11 unequal: No Solution Exploring Operation: 26*97=2522, Resulting Numbers: [2522] 2522,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[26, 101], Operations: ['82-56=26', '99+2=101'] Exploring Operation: 26*101=2626, Resulting Numbers: [2626] 2626,11 unequal: No Solution Exploring Operation: 26+101=127, Resulting Numbers: [127] 127,11 unequal: No Solution Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 11:[2, 82, 43], Operations: ['99-56=43'] Exploring Operation: 82/2=41, Resulting Numbers: [43, 41] Generated Node #0,1,0: 11:[43, 41] Operation: 82/2=41 Exploring Operation: 43-2=41, Resulting Numbers: [82, 41] Generated Node #0,1,1: 11:[82, 41] Operation: 43-2=41 Exploring Operation: 82-43=39, Resulting Numbers: [2, 39] Generated Node #0,1,2: 11:[2, 39] Operation: 82-43=39 Exploring Operation: 2+82=84, Resulting Numbers: [43, 84] Generated Node #0,1,3: 11:[43, 84] Operation: 2+82=84 Exploring Operation: 82-2=80, Resulting Numbers: [43, 80] Generated Node #0,1,4: 11:[43, 80] Operation: 82-2=80 Moving to Node #0,4 Current State: 11:[99, 56, 41], Operations: ['82/2=41'] Exploring Operation: 99+56=155, Resulting Numbers: [41, 155] Generated Node #0,4,0: 11:[41, 155] Operation: 99+56=155 Exploring Operation: 56-41=15, Resulting Numbers: [99, 15] Generated Node #0,4,1: 11:[99, 15] Operation: 56-41=15 Exploring Operation: 99+41=140, Resulting Numbers: [56, 140] Generated Node #0,4,2: 11:[56, 140] Operation: 99+41=140 Exploring Operation: 99-41=58, Resulting Numbers: [56, 58] Generated Node #0,4,3: 11:[56, 58] Operation: 99-41=58 Exploring Operation: 99-56=43, Resulting Numbers: [41, 43] Generated Node #0,4,4: 11:[41, 43] Operation: 99-56=43 Moving to Node #0,2 Current State: 11:[99, 82, 28], Operations: ['56/2=28'] Exploring Operation: 99-28=71, Resulting Numbers: [82, 71] Generated Node #0,2,0: 11:[82, 71] Operation: 99-28=71 Exploring Operation: 99+82=181, Resulting Numbers: [28, 181] Generated Node #0,2,1: 11:[28, 181] Operation: 99+82=181 Exploring Operation: 99+28=127, Resulting Numbers: [82, 127] Generated Node #0,2,2: 11:[82, 127] Operation: 99+28=127 Exploring Operation: 99-82=17, Resulting Numbers: [28, 17] Generated Node #0,2,3: 11:[28, 17] Operation: 99-82=17 Exploring Operation: 82-28=54, Resulting Numbers: [99, 54] Generated Node #0,2,4: 11:[99, 54] Operation: 82-28=54 Moving to Node #0,0,0 Current State: 11:[17, 28], Operations: ['99-82=17', '56/2=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 17*28=476, Resulting Numbers: [476] 476,11 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[99, 2, 56, 82], Operations: [] Exploring Operation: 99-82=17, Resulting Numbers: [2, 56, 17] Generated Node #0,0: 11:[2, 56, 17] Operation: 99-82=17 Moving to Node #0,0 Current State: 11:[2, 56, 17], Operations: ['99-82=17'] Exploring Operation: 56/2=28, Resulting Numbers: [17, 28] Generated Node #0,0,0: 11:[17, 28] Operation: 56/2=28 Moving to Node #0,0,0 Current State: 11:[17, 28], Operations: ['99-82=17', '56/2=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
0.954861
hs_5
sum_heuristic
[ 60, 17, 29, 68 ]
85
[ "60+29=89", "68/17=4", "89-4=85" ]
Current State: 85:[60, 17, 29, 68], Operations: [] Exploring Operation: 60+29=89, Resulting Numbers: [17, 68, 89] Generated Node #2: [17, 68, 89] from Operation: 60+29=89 Current State: 85:[17, 68, 89], Operations: ['60+29=89'] Exploring Operation: 68/17=4, Resulting Numbers: [89, 4] Generated Node #3: [89, 4] from Operation: 68/17=4 Current State: 85:[89, 4], Operations: ['60+29=89', '68/17=4'] Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[60, 17, 29, 68], Operations: [] Exploring Operation: 60+29=89, Resulting Numbers: [17, 68, 89] Generated Node #0,0: 85:[17, 68, 89] Operation: 60+29=89 Exploring Operation: 60-29=31, Resulting Numbers: [17, 68, 31] Generated Node #0,1: 85:[17, 68, 31] Operation: 60-29=31 Exploring Operation: 68-60=8, Resulting Numbers: [17, 29, 8] Generated Node #0,2: 85:[17, 29, 8] Operation: 68-60=8 Exploring Operation: 60+17=77, Resulting Numbers: [29, 68, 77] Generated Node #0,3: 85:[29, 68, 77] Operation: 60+17=77 Exploring Operation: 17+68=85, Resulting Numbers: [60, 29, 85] Generated Node #0,4: 85:[60, 29, 85] Operation: 17+68=85 Moving to Node #0,2 Current State: 85:[17, 29, 8], Operations: ['68-60=8'] Exploring Operation: 29-17=12, Resulting Numbers: [8, 12] Generated Node #0,2,0: 85:[8, 12] Operation: 29-17=12 Exploring Operation: 29-8=21, Resulting Numbers: [17, 21] Generated Node #0,2,1: 85:[17, 21] Operation: 29-8=21 Exploring Operation: 29+8=37, Resulting Numbers: [17, 37] Generated Node #0,2,2: 85:[17, 37] Operation: 29+8=37 Exploring Operation: 17-8=9, Resulting Numbers: [29, 9] Generated Node #0,2,3: 85:[29, 9] Operation: 17-8=9 Exploring Operation: 17+8=25, Resulting Numbers: [29, 25] Generated Node #0,2,4: 85:[29, 25] Operation: 17+8=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[17, 21], Operations: ['68-60=8', '29-8=21'] Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,85 unequal: No Solution Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,85 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 #0,2,0 Current State: 85:[8, 12], Operations: ['68-60=8', '29-17=12'] Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,85 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 #0,2,3 Current State: 85:[29, 9], Operations: ['68-60=8', '17-8=9'] Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,85 unequal: No Solution Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,85 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:[17, 37], Operations: ['68-60=8', '29+8=37'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 17*37=629, Resulting Numbers: [629] 629,85 unequal: No Solution Exploring Operation: 17+37=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 85:[29, 25], Operations: ['68-60=8', '17+8=25'] Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,85 unequal: No Solution Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 85:[17, 68, 89], Operations: ['60+29=89'] Exploring Operation: 89-68=21, Resulting Numbers: [17, 21] Generated Node #0,0,0: 85:[17, 21] Operation: 89-68=21 Exploring Operation: 89-17=72, Resulting Numbers: [68, 72] Generated Node #0,0,1: 85:[68, 72] Operation: 89-17=72 Exploring Operation: 68-17=51, Resulting Numbers: [89, 51] Generated Node #0,0,2: 85:[89, 51] Operation: 68-17=51 Exploring Operation: 17+68=85, Resulting Numbers: [89, 85] Generated Node #0,0,3: 85:[89, 85] Operation: 17+68=85 Exploring Operation: 68/17=4, Resulting Numbers: [89, 4] Generated Node #0,0,4: 85:[89, 4] Operation: 68/17=4 Moving to Node #0,1 Current State: 85:[17, 68, 31], Operations: ['60-29=31'] Exploring Operation: 68/17=4, Resulting Numbers: [31, 4] Generated Node #0,1,0: 85:[31, 4] Operation: 68/17=4 Exploring Operation: 17+68=85, Resulting Numbers: [31, 85] Generated Node #0,1,1: 85:[31, 85] Operation: 17+68=85 Exploring Operation: 31-17=14, Resulting Numbers: [68, 14] Generated Node #0,1,2: 85:[68, 14] Operation: 31-17=14 Exploring Operation: 68-31=37, Resulting Numbers: [17, 37] Generated Node #0,1,3: 85:[17, 37] Operation: 68-31=37 Exploring Operation: 68+31=99, Resulting Numbers: [17, 99] Generated Node #0,1,4: 85:[17, 99] Operation: 68+31=99 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[31, 85], Operations: ['60-29=31', '17+68=85'] Exploring Operation: 31*85=2635, Resulting Numbers: [2635] 2635,85 unequal: No Solution Exploring Operation: 85-31=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 31+85=116, Resulting Numbers: [116] 116,85 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 #0,1,4 Current State: 85:[17, 99], Operations: ['60-29=31', '68+31=99'] Exploring Operation: 99-17=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 17*99=1683, Resulting Numbers: [1683] 1683,85 unequal: No Solution Exploring Operation: 17+99=116, Resulting Numbers: [116] 116,85 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:[31, 4], Operations: ['60-29=31', '68/17=4'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,85 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,85 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 85:[68, 14], Operations: ['60-29=31', '31-17=14'] Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 85:[17, 37], Operations: ['60-29=31', '68-31=37'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 17*37=629, Resulting Numbers: [629] 629,85 unequal: No Solution Exploring Operation: 17+37=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 85:[29, 68, 77], Operations: ['60+17=77'] Exploring Operation: 77-29=48, Resulting Numbers: [68, 48] Generated Node #0,3,0: 85:[68, 48] Operation: 77-29=48 Exploring Operation: 29+77=106, Resulting Numbers: [68, 106] Generated Node #0,3,1: 85:[68, 106] Operation: 29+77=106 Exploring Operation: 68-29=39, Resulting Numbers: [77, 39] Generated Node #0,3,2: 85:[77, 39] Operation: 68-29=39 Exploring Operation: 29+68=97, Resulting Numbers: [77, 97] Generated Node #0,3,3: 85:[77, 97] Operation: 29+68=97 Exploring Operation: 77-68=9, Resulting Numbers: [29, 9] Generated Node #0,3,4: 85:[29, 9] Operation: 77-68=9 Moving to Node #0,4 Current State: 85:[60, 29, 85], Operations: ['17+68=85'] Exploring Operation: 60+29=89, Resulting Numbers: [85, 89] Generated Node #0,4,0: 85:[85, 89] Operation: 60+29=89 Exploring Operation: 60-29=31, Resulting Numbers: [85, 31] Generated Node #0,4,1: 85:[85, 31] Operation: 60-29=31 Exploring Operation: 85-60=25, Resulting Numbers: [29, 25] Generated Node #0,4,2: 85:[29, 25] Operation: 85-60=25 Exploring Operation: 29+85=114, Resulting Numbers: [60, 114] Generated Node #0,4,3: 85:[60, 114] Operation: 29+85=114 Exploring Operation: 85-29=56, Resulting Numbers: [60, 56] Generated Node #0,4,4: 85:[60, 56] Operation: 85-29=56 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 85:[85, 89], Operations: ['17+68=85', '60+29=89'] Exploring Operation: 85*89=7565, Resulting Numbers: [7565] 7565,85 unequal: No Solution Exploring Operation: 89-85=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 85+89=174, Resulting Numbers: [174] 174,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 85:[85, 31], Operations: ['17+68=85', '60-29=31'] Exploring Operation: 85+31=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 85*31=2635, Resulting Numbers: [2635] 2635,85 unequal: No Solution Exploring Operation: 85-31=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 85:[29, 25], Operations: ['17+68=85', '85-60=25'] Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,85 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 85:[60, 114], Operations: ['17+68=85', '29+85=114'] Exploring Operation: 60+114=174, Resulting Numbers: [174] 174,85 unequal: No Solution Exploring Operation: 60*114=6840, Resulting Numbers: [6840] 6840,85 unequal: No Solution Exploring Operation: 114-60=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 85:[60, 56], Operations: ['17+68=85', '85-29=56'] Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 85:[17, 21], Operations: ['60+29=89', '89-68=21'] Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,85 unequal: No Solution Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,85 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[89, 85], Operations: ['60+29=89', '17+68=85'] Exploring Operation: 89*85=7565, Resulting Numbers: [7565] 7565,85 unequal: No Solution Exploring Operation: 89-85=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 89+85=174, Resulting Numbers: [174] 174,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[89, 4], Operations: ['60+29=89', '68/17=4'] Exploring Operation: 89+4=93, Resulting Numbers: [93] 93,85 unequal: No Solution Exploring Operation: 89*4=356, Resulting Numbers: [356] 356,85 unequal: No Solution Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[60, 17, 29, 68], Operations: [] Exploring Operation: 60+29=89, Resulting Numbers: [17, 68, 89] Generated Node #0,0: 85:[17, 68, 89] Operation: 60+29=89 Moving to Node #0,0 Current State: 85:[17, 68, 89], Operations: ['60+29=89'] Exploring Operation: 68/17=4, Resulting Numbers: [89, 4] Generated Node #0,0,4: 85:[89, 4] Operation: 68/17=4 Moving to Node #0,0,4 Current State: 85:[89, 4], Operations: ['60+29=89', '68/17=4'] Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.923611
hs_5
sum_heuristic
[ 13, 82, 41, 6 ]
25
[ "82/41=2", "6*2=12", "13+12=25" ]
Current State: 25:[13, 82, 41, 6], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [13, 6, 2] Generated Node #2: [13, 6, 2] from Operation: 82/41=2 Current State: 25:[13, 6, 2], Operations: ['82/41=2'] Exploring Operation: 6*2=12, Resulting Numbers: [13, 12] Generated Node #3: [13, 12] from Operation: 6*2=12 Current State: 25:[13, 12], Operations: ['82/41=2', '6*2=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[13, 82, 41, 6], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [13, 6, 2] Generated Node #0,0: 25:[13, 6, 2] Operation: 82/41=2 Moving to Node #0,0 Current State: 25:[13, 6, 2], Operations: ['82/41=2'] Exploring Operation: 13*2=26, Resulting Numbers: [6, 26] Generated Node #0,0,0: 25:[6, 26] Operation: 13*2=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[6, 26], Operations: ['82/41=2', '13*2=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,25 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
[ 55, 43, 42, 87 ]
57
[ "55-43=12", "87-42=45", "12+45=57" ]
Current State: 57:[55, 43, 42, 87], Operations: [] Exploring Operation: 55-43=12, Resulting Numbers: [42, 87, 12] Generated Node #2: [42, 87, 12] from Operation: 55-43=12 Current State: 57:[42, 87, 12], Operations: ['55-43=12'] Exploring Operation: 87-42=45, Resulting Numbers: [12, 45] Generated Node #3: [12, 45] from Operation: 87-42=45 Current State: 57:[12, 45], Operations: ['55-43=12', '87-42=45'] Exploring Operation: 12+45=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[55, 43, 42, 87], Operations: [] Exploring Operation: 87-42=45, Resulting Numbers: [55, 43, 45] Generated Node #0,0: 57:[55, 43, 45] Operation: 87-42=45 Exploring Operation: 87-43=44, Resulting Numbers: [55, 42, 44] Generated Node #0,1: 57:[55, 42, 44] Operation: 87-43=44 Exploring Operation: 43-42=1, Resulting Numbers: [55, 87, 1] Generated Node #0,2: 57:[55, 87, 1] Operation: 43-42=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[55, 43, 45], Operations: ['87-42=45'] Exploring Operation: 55-45=10, Resulting Numbers: [43, 10] Generated Node #0,0,0: 57:[43, 10] Operation: 55-45=10 Exploring Operation: 45-43=2, Resulting Numbers: [55, 2] Generated Node #0,0,1: 57:[55, 2] Operation: 45-43=2 Exploring Operation: 55-43=12, Resulting Numbers: [45, 12] Generated Node #0,0,2: 57:[45, 12] Operation: 55-43=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[55, 2], Operations: ['87-42=45', '45-43=2'] Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,57 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[55, 43, 42, 87], Operations: [] Exploring Operation: 87-42=45, Resulting Numbers: [55, 43, 45] Generated Node #0,0: 57:[55, 43, 45] Operation: 87-42=45 Moving to Node #0,0 Current State: 57:[55, 43, 45], Operations: ['87-42=45'] Exploring Operation: 45-43=2, Resulting Numbers: [55, 2] Generated Node #0,0,1: 57:[55, 2] Operation: 45-43=2 Moving to Node #0,0,1 Current State: 57:[55, 2], Operations: ['87-42=45', '45-43=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 76, 28, 14, 70 ]
43
[ "76-28=48", "70/14=5", "48-5=43" ]
Current State: 43:[76, 28, 14, 70], Operations: [] Exploring Operation: 76-28=48, Resulting Numbers: [14, 70, 48] Generated Node #2: [14, 70, 48] from Operation: 76-28=48 Current State: 43:[14, 70, 48], Operations: ['76-28=48'] Exploring Operation: 70/14=5, Resulting Numbers: [48, 5] Generated Node #3: [48, 5] from Operation: 70/14=5 Current State: 43:[48, 5], Operations: ['76-28=48', '70/14=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[76, 28, 14, 70], Operations: [] Exploring Operation: 28+14=42, Resulting Numbers: [76, 70, 42] Generated Node #0,0: 43:[76, 70, 42] Operation: 28+14=42 Exploring Operation: 76-14=62, Resulting Numbers: [28, 70, 62] Generated Node #0,1: 43:[28, 70, 62] Operation: 76-14=62 Exploring Operation: 76-28=48, Resulting Numbers: [14, 70, 48] Generated Node #0,2: 43:[14, 70, 48] Operation: 76-28=48 Moving to Node #0,0 Current State: 43:[76, 70, 42], Operations: ['28+14=42'] Exploring Operation: 70-42=28, Resulting Numbers: [76, 28] Generated Node #0,0,0: 43:[76, 28] Operation: 70-42=28 Exploring Operation: 76-70=6, Resulting Numbers: [42, 6] Generated Node #0,0,1: 43:[42, 6] Operation: 76-70=6 Exploring Operation: 76-42=34, Resulting Numbers: [70, 34] Generated Node #0,0,2: 43:[70, 34] Operation: 76-42=34 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 43:[70, 34], Operations: ['28+14=42', '76-42=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,43 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,43 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 #0,0,1 Current State: 43:[42, 6], Operations: ['28+14=42', '76-70=6'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,43 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 #0,0,0 Current State: 43:[76, 28], Operations: ['28+14=42', '70-42=28'] Exploring Operation: 76*28=2128, Resulting Numbers: [2128] 2128,43 unequal: No Solution Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,43 unequal: No Solution Exploring Operation: 76+28=104, Resulting Numbers: [104] 104,43 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:[28, 70, 62], Operations: ['76-14=62'] Exploring Operation: 70-62=8, Resulting Numbers: [28, 8] Generated Node #0,1,0: 43:[28, 8] Operation: 70-62=8 Exploring Operation: 62-28=34, Resulting Numbers: [70, 34] Generated Node #0,1,1: 43:[70, 34] Operation: 62-28=34 Exploring Operation: 70-28=42, Resulting Numbers: [62, 42] Generated Node #0,1,2: 43:[62, 42] Operation: 70-28=42 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[62, 42], Operations: ['76-14=62', '70-28=42'] Exploring Operation: 62+42=104, Resulting Numbers: [104] 104,43 unequal: No Solution Exploring Operation: 62-42=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 62*42=2604, Resulting Numbers: [2604] 2604,43 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 #0,1,1 Current State: 43:[70, 34], Operations: ['76-14=62', '62-28=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,43 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,43 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,43 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:[28, 8], Operations: ['76-14=62', '70-62=8'] Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,43 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:[14, 70, 48], Operations: ['76-28=48'] Exploring Operation: 70-14=56, Resulting Numbers: [48, 56] Generated Node #0,2,0: 43:[48, 56] Operation: 70-14=56 Exploring Operation: 70/14=5, Resulting Numbers: [48, 5] Generated Node #0,2,1: 43:[48, 5] Operation: 70/14=5 Exploring Operation: 48-14=34, Resulting Numbers: [70, 34] Generated Node #0,2,2: 43:[70, 34] Operation: 48-14=34 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[48, 56], Operations: ['76-28=48', '70-14=56'] Exploring Operation: 48+56=104, Resulting Numbers: [104] 104,43 unequal: No Solution Exploring Operation: 48*56=2688, Resulting Numbers: [2688] 2688,43 unequal: No Solution Exploring Operation: 56-48=8, Resulting Numbers: [8] 8,43 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 #0,2,2 Current State: 43:[70, 34], Operations: ['76-28=48', '48-14=34'] Exploring Operation: 70*34=2380, Resulting Numbers: [2380] 2380,43 unequal: No Solution Exploring Operation: 70-34=36, Resulting Numbers: [36] 36,43 unequal: No Solution Exploring Operation: 70+34=104, Resulting Numbers: [104] 104,43 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 #0,2,1 Current State: 43:[48, 5], Operations: ['76-28=48', '70/14=5'] Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,43 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,43 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[76, 28, 14, 70], Operations: [] Exploring Operation: 76-28=48, Resulting Numbers: [14, 70, 48] Generated Node #0,2: 43:[14, 70, 48] Operation: 76-28=48 Moving to Node #0,2 Current State: 43:[14, 70, 48], Operations: ['76-28=48'] Exploring Operation: 70/14=5, Resulting Numbers: [48, 5] Generated Node #0,2,1: 43:[48, 5] Operation: 70/14=5 Moving to Node #0,2,1 Current State: 43:[48, 5], Operations: ['76-28=48', '70/14=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_3
sum_heuristic
[ 56, 60, 76, 19 ]
71
[ "60*19=1140", "1140/76=15", "56+15=71" ]
Current State: 71:[56, 60, 76, 19], Operations: [] Exploring Operation: 60*19=1140, Resulting Numbers: [56, 76, 1140] Generated Node #2: [56, 76, 1140] from Operation: 60*19=1140 Current State: 71:[56, 76, 1140], Operations: ['60*19=1140'] Exploring Operation: 1140/76=15, Resulting Numbers: [56, 15] Generated Node #3: [56, 15] from Operation: 1140/76=15 Current State: 71:[56, 15], Operations: ['60*19=1140', '1140/76=15'] Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[56, 60, 76, 19], Operations: [] Exploring Operation: 56-19=37, Resulting Numbers: [60, 76, 37] Generated Node #0,0: 71:[60, 76, 37] Operation: 56-19=37 Exploring Operation: 60+19=79, Resulting Numbers: [56, 76, 79] Generated Node #0,1: 71:[56, 76, 79] Operation: 60+19=79 Exploring Operation: 60-19=41, Resulting Numbers: [56, 76, 41] Generated Node #0,2: 71:[56, 76, 41] Operation: 60-19=41 Exploring Operation: 76-19=57, Resulting Numbers: [56, 60, 57] Generated Node #0,3: 71:[56, 60, 57] Operation: 76-19=57 Exploring Operation: 56+19=75, Resulting Numbers: [60, 76, 75] Generated Node #0,4: 71:[60, 76, 75] Operation: 56+19=75 Start Sub Search at level 1: Moving to Node #0,4 Current State: 71:[60, 76, 75], Operations: ['56+19=75'] Exploring Operation: 76-60=16, Resulting Numbers: [75, 16] Generated Node #0,4,0: 71:[75, 16] Operation: 76-60=16 Exploring Operation: 60+75=135, Resulting Numbers: [76, 135] Generated Node #0,4,1: 71:[76, 135] Operation: 60+75=135 Exploring Operation: 60+76=136, Resulting Numbers: [75, 136] Generated Node #0,4,2: 71:[75, 136] Operation: 60+76=136 Exploring Operation: 76-75=1, Resulting Numbers: [60, 1] Generated Node #0,4,3: 71:[60, 1] Operation: 76-75=1 Exploring Operation: 75-60=15, Resulting Numbers: [76, 15] Generated Node #0,4,4: 71:[76, 15] Operation: 75-60=15 Moving to Node #0,4,0 Current State: 71:[75, 16], Operations: ['56+19=75', '76-60=16'] Exploring Operation: 75*16=1200, Resulting Numbers: [1200] 1200,71 unequal: No Solution Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 75+16=91, Resulting Numbers: [91] 91,71 unequal: No Solution Moving to Node #0,4,4 Current State: 71:[76, 15], Operations: ['56+19=75', '75-60=15'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 76+15=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 76*15=1140, Resulting Numbers: [1140] 1140,71 unequal: No Solution Moving to Node #0,4,1 Current State: 71:[76, 135], Operations: ['56+19=75', '60+75=135'] Exploring Operation: 76+135=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 76*135=10260, Resulting Numbers: [10260] 10260,71 unequal: No Solution Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,71 unequal: No Solution Moving to Node #0,4,2 Current State: 71:[75, 136], Operations: ['56+19=75', '60+76=136'] Exploring Operation: 75*136=10200, Resulting Numbers: [10200] 10200,71 unequal: No Solution Exploring Operation: 75+136=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 136-75=61, Resulting Numbers: [61] 61,71 unequal: No Solution Moving to Node #0,4,3 Current State: 71:[60, 1], Operations: ['56+19=75', '76-75=1'] Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,71 unequal: No Solution Exploring Operation: 60+1=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,71 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,71 unequal: No Solution No 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: 71:[56, 76, 79], Operations: ['60+19=79'] Exploring Operation: 76-56=20, Resulting Numbers: [79, 20] Generated Node #0,1,0: 71:[79, 20] Operation: 76-56=20 Exploring Operation: 56+76=132, Resulting Numbers: [79, 132] Generated Node #0,1,1: 71:[79, 132] Operation: 56+76=132 Exploring Operation: 79-76=3, Resulting Numbers: [56, 3] Generated Node #0,1,2: 71:[56, 3] Operation: 79-76=3 Exploring Operation: 79-56=23, Resulting Numbers: [76, 23] Generated Node #0,1,3: 71:[76, 23] Operation: 79-56=23 Exploring Operation: 56+79=135, Resulting Numbers: [76, 135] Generated Node #0,1,4: 71:[76, 135] Operation: 56+79=135 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 71:[76, 23], Operations: ['60+19=79', '79-56=23'] Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 76+23=99, Resulting Numbers: [99] 99,71 unequal: No Solution Exploring Operation: 76*23=1748, Resulting Numbers: [1748] 1748,71 unequal: No Solution No 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: 71:[79, 20], Operations: ['60+19=79', '76-56=20'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 79*20=1580, Resulting Numbers: [1580] 1580,71 unequal: No Solution Exploring Operation: 79+20=99, Resulting Numbers: [99] 99,71 unequal: No Solution No 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: 71:[79, 132], Operations: ['60+19=79', '56+76=132'] Exploring Operation: 79+132=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 79*132=10428, Resulting Numbers: [10428] 10428,71 unequal: No Solution Exploring Operation: 132-79=53, Resulting Numbers: [53] 53,71 unequal: No Solution No 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: 71:[76, 135], Operations: ['60+19=79', '56+79=135'] Exploring Operation: 76+135=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 76*135=10260, Resulting Numbers: [10260] 10260,71 unequal: No Solution No 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: 71:[56, 3], Operations: ['60+19=79', '79-76=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,71 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: 71:[56, 60, 57], Operations: ['76-19=57'] Exploring Operation: 60-56=4, Resulting Numbers: [57, 4] Generated Node #0,3,0: 71:[57, 4] Operation: 60-56=4 Exploring Operation: 60+57=117, Resulting Numbers: [56, 117] Generated Node #0,3,1: 71:[56, 117] Operation: 60+57=117 Exploring Operation: 56+60=116, Resulting Numbers: [57, 116] Generated Node #0,3,2: 71:[57, 116] Operation: 56+60=116 Exploring Operation: 56+57=113, Resulting Numbers: [60, 113] Generated Node #0,3,3: 71:[60, 113] Operation: 56+57=113 Exploring Operation: 57-56=1, Resulting Numbers: [60, 1] Generated Node #0,3,4: 71:[60, 1] Operation: 57-56=1 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 71:[60, 113], Operations: ['76-19=57', '56+57=113'] Exploring Operation: 60*113=6780, Resulting Numbers: [6780] 6780,71 unequal: No Solution Exploring Operation: 113-60=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 60+113=173, Resulting Numbers: [173] 173,71 unequal: No Solution No 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: 71:[57, 116], Operations: ['76-19=57', '56+60=116'] Exploring Operation: 116-57=59, Resulting Numbers: [59] 59,71 unequal: No Solution Exploring Operation: 57+116=173, Resulting Numbers: [173] 173,71 unequal: No Solution Exploring Operation: 57*116=6612, Resulting Numbers: [6612] 6612,71 unequal: No Solution No 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: 71:[56, 117], Operations: ['76-19=57', '60+57=117'] Exploring Operation: 56*117=6552, Resulting Numbers: [6552] 6552,71 unequal: No Solution Exploring Operation: 117-56=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 56+117=173, Resulting Numbers: [173] 173,71 unequal: No Solution No 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: 71:[57, 4], Operations: ['76-19=57', '60-56=4'] Exploring Operation: 57*4=228, Resulting Numbers: [228] 228,71 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,71 unequal: No Solution No 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: 71:[60, 1], Operations: ['76-19=57', '57-56=1'] Exploring Operation: 60+1=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,71 unequal: No Solution Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,71 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,71 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: 71:[60, 76, 37], Operations: ['56-19=37'] Exploring Operation: 60-37=23, Resulting Numbers: [76, 23] Generated Node #0,0,0: 71:[76, 23] Operation: 60-37=23 Exploring Operation: 76-37=39, Resulting Numbers: [60, 39] Generated Node #0,0,1: 71:[60, 39] Operation: 76-37=39 Exploring Operation: 76+37=113, Resulting Numbers: [60, 113] Generated Node #0,0,2: 71:[60, 113] Operation: 76+37=113 Exploring Operation: 60+37=97, Resulting Numbers: [76, 97] Generated Node #0,0,3: 71:[76, 97] Operation: 60+37=97 Exploring Operation: 76-60=16, Resulting Numbers: [37, 16] Generated Node #0,0,4: 71:[37, 16] Operation: 76-60=16 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[76, 97], Operations: ['56-19=37', '60+37=97'] Exploring Operation: 97-76=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 76*97=7372, Resulting Numbers: [7372] 7372,71 unequal: No Solution Exploring Operation: 76+97=173, Resulting Numbers: [173] 173,71 unequal: No Solution No 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: 71:[60, 39], Operations: ['56-19=37', '76-37=39'] Exploring Operation: 60*39=2340, Resulting Numbers: [2340] 2340,71 unequal: No Solution Exploring Operation: 60+39=99, Resulting Numbers: [99] 99,71 unequal: No Solution Exploring Operation: 60-39=21, Resulting Numbers: [21] 21,71 unequal: No Solution No 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: 71:[76, 23], Operations: ['56-19=37', '60-37=23'] Exploring Operation: 76+23=99, Resulting Numbers: [99] 99,71 unequal: No Solution Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 76*23=1748, Resulting Numbers: [1748] 1748,71 unequal: No Solution No 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: 71:[60, 113], Operations: ['56-19=37', '76+37=113'] Exploring Operation: 60+113=173, Resulting Numbers: [173] 173,71 unequal: No Solution Exploring Operation: 113-60=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 60*113=6780, Resulting Numbers: [6780] 6780,71 unequal: No Solution No 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: 71:[37, 16], Operations: ['56-19=37', '76-60=16'] Exploring Operation: 37+16=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 37*16=592, Resulting Numbers: [592] 592,71 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,71 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: 71:[56, 76, 41], Operations: ['60-19=41'] Exploring Operation: 76-56=20, Resulting Numbers: [41, 20] Generated Node #0,2,0: 71:[41, 20] Operation: 76-56=20 Exploring Operation: 56+41=97, Resulting Numbers: [76, 97] Generated Node #0,2,1: 71:[76, 97] Operation: 56+41=97 Exploring Operation: 76-41=35, Resulting Numbers: [56, 35] Generated Node #0,2,2: 71:[56, 35] Operation: 76-41=35 Exploring Operation: 56-41=15, Resulting Numbers: [76, 15] Generated Node #0,2,3: 71:[76, 15] Operation: 56-41=15 Exploring Operation: 76+41=117, Resulting Numbers: [56, 117] Generated Node #0,2,4: 71:[56, 117] Operation: 76+41=117 Moving to Node #0,2,1 Current State: 71:[76, 97], Operations: ['60-19=41', '56+41=97'] Exploring Operation: 97-76=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 76+97=173, Resulting Numbers: [173] 173,71 unequal: No Solution Exploring Operation: 76*97=7372, Resulting Numbers: [7372] 7372,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[56, 35], Operations: ['60-19=41', '76-41=35'] Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,71 unequal: No Solution Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[76, 15], Operations: ['60-19=41', '56-41=15'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 76+15=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 76*15=1140, Resulting Numbers: [1140] 1140,71 unequal: No Solution Moving to Node #0,2,4 Current State: 71:[56, 117], Operations: ['60-19=41', '76+41=117'] Exploring Operation: 56*117=6552, Resulting Numbers: [6552] 6552,71 unequal: No Solution Exploring Operation: 56+117=173, Resulting Numbers: [173] 173,71 unequal: No Solution Exploring Operation: 117-56=61, Resulting Numbers: [61] 61,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[41, 20], Operations: ['60-19=41', '76-56=20'] Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,71 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,71 unequal: No Solution Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 57, 23, 80, 81 ]
34
[ "57-23=34", "81-80=1", "34*1=34" ]
Current State: 34:[57, 23, 80, 81], Operations: [] Exploring Operation: 57-23=34, Resulting Numbers: [80, 81, 34] Generated Node #2: [80, 81, 34] from Operation: 57-23=34 Current State: 34:[80, 81, 34], Operations: ['57-23=34'] Exploring Operation: 81-80=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 81-80=1 Current State: 34:[34, 1], Operations: ['57-23=34', '81-80=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[57, 23, 80, 81], Operations: [] Exploring Operation: 57-23=34, Resulting Numbers: [80, 81, 34] Generated Node #0,0: 34:[80, 81, 34] Operation: 57-23=34 Exploring Operation: 81-80=1, Resulting Numbers: [57, 23, 1] Generated Node #0,1: 34:[57, 23, 1] Operation: 81-80=1 Exploring Operation: 80-23=57, Resulting Numbers: [57, 81, 57] Generated Node #0,2: 34:[57, 81, 57] Operation: 80-23=57 Exploring Operation: 81-57=24, Resulting Numbers: [23, 80, 24] Generated Node #0,3: 34:[23, 80, 24] Operation: 81-57=24 Exploring Operation: 80-57=23, Resulting Numbers: [23, 81, 23] Generated Node #0,4: 34:[23, 81, 23] Operation: 80-57=23 Moving to Node #0,1 Current State: 34:[57, 23, 1], Operations: ['81-80=1'] Exploring Operation: 57-1=56, Resulting Numbers: [23, 56] Generated Node #0,1,0: 34:[23, 56] Operation: 57-1=56 Exploring Operation: 57*1=57, Resulting Numbers: [23, 57] Generated Node #0,1,1: 34:[23, 57] Operation: 57*1=57 Exploring Operation: 57-23=34, Resulting Numbers: [1, 34] Generated Node #0,1,2: 34:[1, 34] Operation: 57-23=34 Exploring Operation: 23-1=22, Resulting Numbers: [57, 22] Generated Node #0,1,3: 34:[57, 22] Operation: 23-1=22 Exploring Operation: 57/1=57, Resulting Numbers: [23, 57] Generated Node #0,1,4: 34:[23, 57] Operation: 57/1=57 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 34:[1, 34], Operations: ['81-80=1', '57-23=34'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[57, 23, 80, 81], Operations: [] Exploring Operation: 81-80=1, Resulting Numbers: [57, 23, 1] Generated Node #0,1: 34:[57, 23, 1] Operation: 81-80=1 Moving to Node #0,1 Current State: 34:[57, 23, 1], Operations: ['81-80=1'] Exploring Operation: 57-23=34, Resulting Numbers: [1, 34] Generated Node #0,1,2: 34:[1, 34] Operation: 57-23=34 Moving to Node #0,1,2 Current State: 34:[1, 34], Operations: ['81-80=1', '57-23=34'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 91, 55, 39, 5 ]
37
[ "91+55=146", "39+146=185", "185/5=37" ]
Current State: 37:[91, 55, 39, 5], Operations: [] Exploring Operation: 91+55=146, Resulting Numbers: [39, 5, 146] Generated Node #2: [39, 5, 146] from Operation: 91+55=146 Current State: 37:[39, 5, 146], Operations: ['91+55=146'] Exploring Operation: 39+146=185, Resulting Numbers: [5, 185] Generated Node #3: [5, 185] from Operation: 39+146=185 Current State: 37:[5, 185], Operations: ['91+55=146', '39+146=185'] Exploring Operation: 185/5=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[91, 55, 39, 5], Operations: [] Exploring Operation: 91-39=52, Resulting Numbers: [55, 5, 52] Generated Node #0,0: 37:[55, 5, 52] Operation: 91-39=52 Exploring Operation: 91-55=36, Resulting Numbers: [39, 5, 36] Generated Node #0,1: 37:[39, 5, 36] Operation: 91-55=36 Moving to Node #0,1 Current State: 37:[39, 5, 36], Operations: ['91-55=36'] Exploring Operation: 5+36=41, Resulting Numbers: [39, 41] Generated Node #0,1,0: 37:[39, 41] Operation: 5+36=41 Exploring Operation: 39-5=34, Resulting Numbers: [36, 34] Generated Node #0,1,1: 37:[36, 34] Operation: 39-5=34 Moving to Node #0,0 Current State: 37:[55, 5, 52], Operations: ['91-39=52'] Exploring Operation: 52-5=47, Resulting Numbers: [55, 47] Generated Node #0,0,0: 37:[55, 47] Operation: 52-5=47 Exploring Operation: 55-5=50, Resulting Numbers: [52, 50] Generated Node #0,0,1: 37:[52, 50] Operation: 55-5=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[55, 47], Operations: ['91-39=52', '52-5=47'] Exploring Operation: 55-47=8, Resulting Numbers: [8] 8,37 unequal: No Solution Exploring Operation: 55+47=102, Resulting Numbers: [102] 102,37 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:[52, 50], Operations: ['91-39=52', '55-5=50'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 37:[36, 34], Operations: ['91-55=36', '39-5=34'] Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,37 unequal: No Solution Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[39, 41], Operations: ['91-55=36', '5+36=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,37 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,37 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 56, 94, 6, 54 ]
44
[ "56-54=2", "94-6=88", "88/2=44" ]
Current State: 44:[56, 94, 6, 54], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [94, 6, 2] Generated Node #2: [94, 6, 2] from Operation: 56-54=2 Current State: 44:[94, 6, 2], Operations: ['56-54=2'] Exploring Operation: 94-6=88, Resulting Numbers: [2, 88] Generated Node #3: [2, 88] from Operation: 94-6=88 Current State: 44:[2, 88], Operations: ['56-54=2', '94-6=88'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[56, 94, 6, 54], Operations: [] Exploring Operation: 94-56=38, Resulting Numbers: [6, 54, 38] Generated Node #0,0: 44:[6, 54, 38] Operation: 94-56=38 Exploring Operation: 54/6=9, Resulting Numbers: [56, 94, 9] Generated Node #0,1: 44:[56, 94, 9] Operation: 54/6=9 Exploring Operation: 94-54=40, Resulting Numbers: [56, 6, 40] Generated Node #0,2: 44:[56, 6, 40] Operation: 94-54=40 Exploring Operation: 56-54=2, Resulting Numbers: [94, 6, 2] Generated Node #0,3: 44:[94, 6, 2] Operation: 56-54=2 Moving to Node #0,0 Current State: 44:[6, 54, 38], Operations: ['94-56=38'] Exploring Operation: 6+38=44, Resulting Numbers: [54, 44] Generated Node #0,0,0: 44:[54, 44] Operation: 6+38=44 Exploring Operation: 54-38=16, Resulting Numbers: [6, 16] Generated Node #0,0,1: 44:[6, 16] Operation: 54-38=16 Exploring Operation: 54-6=48, Resulting Numbers: [38, 48] Generated Node #0,0,2: 44:[38, 48] Operation: 54-6=48 Exploring Operation: 54/6=9, Resulting Numbers: [38, 9] Generated Node #0,0,3: 44:[38, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[6, 16], Operations: ['94-56=38', '54-38=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,44 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,44 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 #0,0,3 Current State: 44:[38, 9], Operations: ['94-56=38', '54/6=9'] Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,44 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,44 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 #0,0,0 Current State: 44:[54, 44], Operations: ['94-56=38', '6+38=44'] Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,44 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,44 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 #0,0,2 Current State: 44:[38, 48], Operations: ['94-56=38', '54-6=48'] Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 38+48=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 38*48=1824, Resulting Numbers: [1824] 1824,44 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: 44:[56, 6, 40], Operations: ['94-54=40'] Exploring Operation: 56+6=62, Resulting Numbers: [40, 62] Generated Node #0,2,0: 44:[40, 62] Operation: 56+6=62 Exploring Operation: 56-40=16, Resulting Numbers: [6, 16] Generated Node #0,2,1: 44:[6, 16] Operation: 56-40=16 Exploring Operation: 56-6=50, Resulting Numbers: [40, 50] Generated Node #0,2,2: 44:[40, 50] Operation: 56-6=50 Exploring Operation: 6+40=46, Resulting Numbers: [56, 46] Generated Node #0,2,3: 44:[56, 46] Operation: 6+40=46 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[6, 16], Operations: ['94-54=40', '56-40=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,44 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,44 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 #0,2,2 Current State: 44:[40, 50], Operations: ['94-54=40', '56-6=50'] Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,44 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:[56, 46], Operations: ['94-54=40', '6+40=46'] Exploring Operation: 56+46=102, Resulting Numbers: [102] 102,44 unequal: No Solution Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 56*46=2576, Resulting Numbers: [2576] 2576,44 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:[40, 62], Operations: ['94-54=40', '56+6=62'] Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 40+62=102, Resulting Numbers: [102] 102,44 unequal: No Solution Exploring Operation: 40*62=2480, Resulting Numbers: [2480] 2480,44 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: 44:[94, 6, 2], Operations: ['56-54=2'] Exploring Operation: 94/2=47, Resulting Numbers: [6, 47] Generated Node #0,3,0: 44:[6, 47] Operation: 94/2=47 Exploring Operation: 94-2=92, Resulting Numbers: [6, 92] Generated Node #0,3,1: 44:[6, 92] Operation: 94-2=92 Exploring Operation: 94-6=88, Resulting Numbers: [2, 88] Generated Node #0,3,2: 44:[2, 88] Operation: 94-6=88 Exploring Operation: 6-2=4, Resulting Numbers: [94, 4] Generated Node #0,3,3: 44:[94, 4] Operation: 6-2=4 Moving to Node #0,1 Current State: 44:[56, 94, 9], Operations: ['54/6=9'] Exploring Operation: 56+9=65, Resulting Numbers: [94, 65] Generated Node #0,1,0: 44:[94, 65] Operation: 56+9=65 Exploring Operation: 94-9=85, Resulting Numbers: [56, 85] Generated Node #0,1,1: 44:[56, 85] Operation: 94-9=85 Exploring Operation: 94-56=38, Resulting Numbers: [9, 38] Generated Node #0,1,2: 44:[9, 38] Operation: 94-56=38 Exploring Operation: 56-9=47, Resulting Numbers: [94, 47] Generated Node #0,1,3: 44:[94, 47] Operation: 56-9=47 Moving to Node #0,3,0 Current State: 44:[6, 47], Operations: ['56-54=2', '94/2=47'] Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,44 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[9, 38], Operations: ['54/6=9', '94-56=38'] Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,44 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[2, 88], Operations: ['56-54=2', '94-6=88'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 2*88=176, Resulting Numbers: [176] 176,44 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[56, 94, 6, 54], Operations: [] Exploring Operation: 56-54=2, Resulting Numbers: [94, 6, 2] Generated Node #0,3: 44:[94, 6, 2] Operation: 56-54=2 Moving to Node #0,3 Current State: 44:[94, 6, 2], Operations: ['56-54=2'] Exploring Operation: 94-6=88, Resulting Numbers: [2, 88] Generated Node #0,3,2: 44:[2, 88] Operation: 94-6=88 Moving to Node #0,3,2 Current State: 44:[2, 88], Operations: ['56-54=2', '94-6=88'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.950521
hs_4
sum_heuristic
[ 92, 97, 26, 79 ]
95
[ "92-79=13", "26/13=2", "97-2=95" ]
Current State: 95:[92, 97, 26, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [97, 26, 13] Generated Node #2: [97, 26, 13] from Operation: 92-79=13 Current State: 95:[97, 26, 13], Operations: ['92-79=13'] Exploring Operation: 26/13=2, Resulting Numbers: [97, 2] Generated Node #3: [97, 2] from Operation: 26/13=2 Current State: 95:[97, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[92, 97, 26, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [97, 26, 13] Generated Node #0,0: 95:[97, 26, 13] Operation: 92-79=13 Exploring Operation: 26+79=105, Resulting Numbers: [92, 97, 105] Generated Node #0,1: 95:[92, 97, 105] Operation: 26+79=105 Exploring Operation: 79-26=53, Resulting Numbers: [92, 97, 53] Generated Node #0,2: 95:[92, 97, 53] Operation: 79-26=53 Exploring Operation: 97-92=5, Resulting Numbers: [26, 79, 5] Generated Node #0,3: 95:[26, 79, 5] Operation: 97-92=5 Exploring Operation: 97-79=18, Resulting Numbers: [92, 26, 18] Generated Node #0,4: 95:[92, 26, 18] Operation: 97-79=18 Start Sub Search at level 1: Moving to Node #0,4 Current State: 95:[92, 26, 18], Operations: ['97-79=18'] Exploring Operation: 26+18=44, Resulting Numbers: [92, 44] Generated Node #0,4,0: 95:[92, 44] Operation: 26+18=44 Exploring Operation: 92+18=110, Resulting Numbers: [26, 110] Generated Node #0,4,1: 95:[26, 110] Operation: 92+18=110 Exploring Operation: 92-18=74, Resulting Numbers: [26, 74] Generated Node #0,4,2: 95:[26, 74] Operation: 92-18=74 Exploring Operation: 26-18=8, Resulting Numbers: [92, 8] Generated Node #0,4,3: 95:[92, 8] Operation: 26-18=8 Exploring Operation: 92+26=118, Resulting Numbers: [18, 118] Generated Node #0,4,4: 95:[18, 118] Operation: 92+26=118 Moving to Node #0,4,3 Current State: 95:[92, 8], Operations: ['97-79=18', '26-18=8'] Exploring Operation: 92*8=736, Resulting Numbers: [736] 736,95 unequal: No Solution Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,95 unequal: No Solution Exploring Operation: 92+8=100, Resulting Numbers: [100] 100,95 unequal: No Solution Moving to Node #0,4,1 Current State: 95:[26, 110], Operations: ['97-79=18', '92+18=110'] Exploring Operation: 110-26=84, Resulting Numbers: [84] 84,95 unequal: No Solution Exploring Operation: 26+110=136, Resulting Numbers: [136] 136,95 unequal: No Solution Exploring Operation: 26*110=2860, Resulting Numbers: [2860] 2860,95 unequal: No Solution Moving to Node #0,4,4 Current State: 95:[18, 118], Operations: ['97-79=18', '92+26=118'] Exploring Operation: 118-18=100, Resulting Numbers: [100] 100,95 unequal: No Solution Exploring Operation: 18*118=2124, Resulting Numbers: [2124] 2124,95 unequal: No Solution Exploring Operation: 18+118=136, Resulting Numbers: [136] 136,95 unequal: No Solution Moving to Node #0,4,0 Current State: 95:[92, 44], Operations: ['97-79=18', '26+18=44'] Exploring Operation: 92*44=4048, Resulting Numbers: [4048] 4048,95 unequal: No Solution Exploring Operation: 92+44=136, Resulting Numbers: [136] 136,95 unequal: No Solution Exploring Operation: 92-44=48, Resulting Numbers: [48] 48,95 unequal: No Solution Moving to Node #0,4,2 Current State: 95:[26, 74], Operations: ['97-79=18', '92-18=74'] Exploring Operation: 26+74=100, Resulting Numbers: [100] 100,95 unequal: No Solution Exploring Operation: 74-26=48, Resulting Numbers: [48] 48,95 unequal: No Solution Exploring Operation: 26*74=1924, Resulting Numbers: [1924] 1924,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[97, 26, 13], Operations: ['92-79=13'] Exploring Operation: 26-13=13, Resulting Numbers: [97, 13] Generated Node #0,0,0: 95:[97, 13] Operation: 26-13=13 Exploring Operation: 26+13=39, Resulting Numbers: [97, 39] Generated Node #0,0,1: 95:[97, 39] Operation: 26+13=39 Exploring Operation: 97+13=110, Resulting Numbers: [26, 110] Generated Node #0,0,2: 95:[26, 110] Operation: 97+13=110 Exploring Operation: 97-13=84, Resulting Numbers: [26, 84] Generated Node #0,0,3: 95:[26, 84] Operation: 97-13=84 Exploring Operation: 26/13=2, Resulting Numbers: [97, 2] Generated Node #0,0,4: 95:[97, 2] Operation: 26/13=2 Moving to Node #0,0,4 Current State: 95:[97, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[92, 97, 26, 79], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [97, 26, 13] Generated Node #0,0: 95:[97, 26, 13] Operation: 92-79=13 Moving to Node #0,0 Current State: 95:[97, 26, 13], Operations: ['92-79=13'] Exploring Operation: 26/13=2, Resulting Numbers: [97, 2] Generated Node #0,0,4: 95:[97, 2] Operation: 26/13=2 Moving to Node #0,0,4 Current State: 95:[97, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 89, 38, 36, 36 ]
51
[ "89-38=51", "36-36=0", "51+0=51" ]
Current State: 51:[89, 38, 36, 36], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [36, 36, 51] Generated Node #2: [36, 36, 51] from Operation: 89-38=51 Current State: 51:[36, 36, 51], Operations: ['89-38=51'] Exploring Operation: 36-36=0, Resulting Numbers: [51, 0] Generated Node #3: [51, 0] from Operation: 36-36=0 Current State: 51:[51, 0], Operations: ['89-38=51', '36-36=0'] Exploring Operation: 51+0=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[89, 38, 36, 36], Operations: [] Exploring Operation: 89-36=53, Resulting Numbers: [38, 36, 53] Generated Node #0,0: 51:[38, 36, 53] Operation: 89-36=53 Exploring Operation: 89-38=51, Resulting Numbers: [36, 36, 51] Generated Node #0,1: 51:[36, 36, 51] Operation: 89-38=51 Exploring Operation: 89-36=53, Resulting Numbers: [38, 36, 53] Generated Node #0,2: 51:[38, 36, 53] Operation: 89-36=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[38, 36, 53], Operations: ['89-36=53'] Exploring Operation: 38-36=2, Resulting Numbers: [53, 2] Generated Node #0,0,0: 51:[53, 2] Operation: 38-36=2 Exploring Operation: 53-36=17, Resulting Numbers: [38, 17] Generated Node #0,0,1: 51:[38, 17] Operation: 53-36=17 Exploring Operation: 53-38=15, Resulting Numbers: [36, 15] Generated Node #0,0,2: 51:[36, 15] Operation: 53-38=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[53, 2], Operations: ['89-36=53', '38-36=2'] Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,51 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[89, 38, 36, 36], Operations: [] Exploring Operation: 89-36=53, Resulting Numbers: [38, 36, 53] Generated Node #0,0: 51:[38, 36, 53] Operation: 89-36=53 Moving to Node #0,0 Current State: 51:[38, 36, 53], Operations: ['89-36=53'] Exploring Operation: 38-36=2, Resulting Numbers: [53, 2] Generated Node #0,0,0: 51:[53, 2] Operation: 38-36=2 Moving to Node #0,0,0 Current State: 51:[53, 2], Operations: ['89-36=53', '38-36=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 83, 81, 37, 4 ]
94
[ "81-37=44", "44/4=11", "83+11=94" ]
Current State: 94:[83, 81, 37, 4], Operations: [] Exploring Operation: 81-37=44, Resulting Numbers: [83, 4, 44] Generated Node #2: [83, 4, 44] from Operation: 81-37=44 Current State: 94:[83, 4, 44], Operations: ['81-37=44'] Exploring Operation: 44/4=11, Resulting Numbers: [83, 11] Generated Node #3: [83, 11] from Operation: 44/4=11 Current State: 94:[83, 11], Operations: ['81-37=44', '44/4=11'] Exploring Operation: 83+11=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[83, 81, 37, 4], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [37, 4, 2] Generated Node #0,0: 94:[37, 4, 2] Operation: 83-81=2 Exploring Operation: 83-37=46, Resulting Numbers: [81, 4, 46] Generated Node #0,1: 94:[81, 4, 46] Operation: 83-37=46 Moving to Node #0,0 Current State: 94:[37, 4, 2], Operations: ['83-81=2'] Exploring Operation: 37+2=39, Resulting Numbers: [4, 39] Generated Node #0,0,0: 94:[4, 39] Operation: 37+2=39 Exploring Operation: 37+4=41, Resulting Numbers: [2, 41] Generated Node #0,0,1: 94:[2, 41] Operation: 37+4=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[2, 41], Operations: ['83-81=2', '37+4=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[4, 39], Operations: ['83-81=2', '37+2=39'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,94 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: 94:[81, 4, 46], Operations: ['83-37=46'] Exploring Operation: 81-46=35, Resulting Numbers: [4, 35] Generated Node #0,1,0: 94:[4, 35] Operation: 81-46=35 Exploring Operation: 81+4=85, Resulting Numbers: [46, 85] Generated Node #0,1,1: 94:[46, 85] Operation: 81+4=85 Moving to Node #0,1,1 Current State: 94:[46, 85], Operations: ['83-37=46', '81+4=85'] Exploring Operation: 46+85=131, Resulting Numbers: [131] 131,94 unequal: No Solution Exploring Operation: 85-46=39, Resulting Numbers: [39] 39,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[4, 35], Operations: ['83-37=46', '81-46=35'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,94 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,94 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 9, 72, 18 ]
17
[ "30-9=21", "72/18=4", "21-4=17" ]
Current State: 17:[30, 9, 72, 18], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [72, 18, 21] Generated Node #2: [72, 18, 21] from Operation: 30-9=21 Current State: 17:[72, 18, 21], Operations: ['30-9=21'] Exploring Operation: 72/18=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 72/18=4 Current State: 17:[21, 4], Operations: ['30-9=21', '72/18=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[30, 9, 72, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [30, 9, 4] Generated Node #0,0: 17:[30, 9, 4] Operation: 72/18=4 Exploring Operation: 72-30=42, Resulting Numbers: [9, 18, 42] Generated Node #0,1: 17:[9, 18, 42] Operation: 72-30=42 Exploring Operation: 72/9=8, Resulting Numbers: [30, 18, 8] Generated Node #0,2: 17:[30, 18, 8] Operation: 72/9=8 Exploring Operation: 72-18=54, Resulting Numbers: [30, 9, 54] Generated Node #0,3: 17:[30, 9, 54] Operation: 72-18=54 Exploring Operation: 30-9=21, Resulting Numbers: [72, 18, 21] Generated Node #0,4: 17:[72, 18, 21] Operation: 30-9=21 Moving to Node #0,2 Current State: 17:[30, 18, 8], Operations: ['72/9=8'] Exploring Operation: 30-8=22, Resulting Numbers: [18, 22] Generated Node #0,2,0: 17:[18, 22] Operation: 30-8=22 Exploring Operation: 18-8=10, Resulting Numbers: [30, 10] Generated Node #0,2,1: 17:[30, 10] Operation: 18-8=10 Exploring Operation: 18+8=26, Resulting Numbers: [30, 26] Generated Node #0,2,2: 17:[30, 26] Operation: 18+8=26 Exploring Operation: 30-18=12, Resulting Numbers: [8, 12] Generated Node #0,2,3: 17:[8, 12] Operation: 30-18=12 Exploring Operation: 30+8=38, Resulting Numbers: [18, 38] Generated Node #0,2,4: 17:[18, 38] Operation: 30+8=38 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[18, 22], Operations: ['72/9=8', '30-8=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,17 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 17:[8, 12], Operations: ['72/9=8', '30-18=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,17 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 17:[30, 10], Operations: ['72/9=8', '18-8=10'] Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,17 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,17 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 17:[30, 26], Operations: ['72/9=8', '18+8=26'] Exploring Operation: 30*26=780, Resulting Numbers: [780] 780,17 unequal: No Solution Exploring Operation: 30-26=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 17:[18, 38], Operations: ['72/9=8', '30+8=38'] Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,17 unequal: No Solution Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,17 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: 17:[9, 18, 42], Operations: ['72-30=42'] Exploring Operation: 18-9=9, Resulting Numbers: [42, 9] Generated Node #0,1,0: 17:[42, 9] Operation: 18-9=9 Exploring Operation: 42-18=24, Resulting Numbers: [9, 24] Generated Node #0,1,1: 17:[9, 24] Operation: 42-18=24 Exploring Operation: 9+42=51, Resulting Numbers: [18, 51] Generated Node #0,1,2: 17:[18, 51] Operation: 9+42=51 Exploring Operation: 42-9=33, Resulting Numbers: [18, 33] Generated Node #0,1,3: 17:[18, 33] Operation: 42-9=33 Exploring Operation: 9+18=27, Resulting Numbers: [42, 27] Generated Node #0,1,4: 17:[42, 27] Operation: 9+18=27 Moving to Node #0,0 Current State: 17:[30, 9, 4], Operations: ['72/18=4'] Exploring Operation: 30-9=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 30-9=21 Exploring Operation: 9+4=13, Resulting Numbers: [30, 13] Generated Node #0,0,1: 17:[30, 13] Operation: 9+4=13 Exploring Operation: 30-4=26, Resulting Numbers: [9, 26] Generated Node #0,0,2: 17:[9, 26] Operation: 30-4=26 Exploring Operation: 30+4=34, Resulting Numbers: [9, 34] Generated Node #0,0,3: 17:[9, 34] Operation: 30+4=34 Exploring Operation: 9-4=5, Resulting Numbers: [30, 5] Generated Node #0,0,4: 17:[30, 5] Operation: 9-4=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['72/18=4', '30-9=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[30, 9, 72, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [30, 9, 4] Generated Node #0,0: 17:[30, 9, 4] Operation: 72/18=4 Moving to Node #0,0 Current State: 17:[30, 9, 4], Operations: ['72/18=4'] Exploring Operation: 30-9=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 30-9=21 Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['72/18=4', '30-9=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 82, 3, 40, 85 ]
41
[ "82+3=85", "85/85=1", "40+1=41" ]
Current State: 41:[82, 3, 40, 85], Operations: [] Exploring Operation: 82+3=85, Resulting Numbers: [40, 85, 85] Generated Node #2: [40, 85, 85] from Operation: 82+3=85 Current State: 41:[40, 85, 85], Operations: ['82+3=85'] Exploring Operation: 85/85=1, Resulting Numbers: [40, 1] Generated Node #3: [40, 1] from Operation: 85/85=1 Current State: 41:[40, 1], Operations: ['82+3=85', '85/85=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[82, 3, 40, 85], Operations: [] Exploring Operation: 85-3=82, Resulting Numbers: [82, 40, 82] Generated Node #0,0: 41:[82, 40, 82] Operation: 85-3=82 Exploring Operation: 85-82=3, Resulting Numbers: [3, 40, 3] Generated Node #0,1: 41:[3, 40, 3] Operation: 85-82=3 Exploring Operation: 82-3=79, Resulting Numbers: [40, 85, 79] Generated Node #0,2: 41:[40, 85, 79] Operation: 82-3=79 Exploring Operation: 82-40=42, Resulting Numbers: [3, 85, 42] Generated Node #0,3: 41:[3, 85, 42] Operation: 82-40=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[3, 40, 3], Operations: ['85-82=3'] Exploring Operation: 3+40=43, Resulting Numbers: [3, 43] Generated Node #0,1,0: 41:[3, 43] Operation: 3+40=43 Exploring Operation: 40+3=43, Resulting Numbers: [3, 43] Generated Node #0,1,1: 41:[3, 43] Operation: 40+3=43 Exploring Operation: 3*3=9, Resulting Numbers: [40, 9] Generated Node #0,1,2: 41:[40, 9] Operation: 3*3=9 Exploring Operation: 3+3=6, Resulting Numbers: [40, 6] Generated Node #0,1,3: 41:[40, 6] Operation: 3+3=6 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[40, 9], Operations: ['85-82=3', '3*3=9'] Exploring Operation: 40+9=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 40*9=360, Resulting Numbers: [360] 360,41 unequal: No Solution No 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: 41:[40, 6], Operations: ['85-82=3', '3+3=6'] Exploring Operation: 40*6=240, Resulting Numbers: [240] 240,41 unequal: No Solution Exploring Operation: 40+6=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,41 unequal: No Solution No 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: 41:[3, 43], Operations: ['85-82=3', '3+40=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,41 unequal: No Solution No 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: 41:[3, 43], Operations: ['85-82=3', '40+3=43'] Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,41 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[82, 40, 82], Operations: ['85-3=82'] Exploring Operation: 82-82=0, Resulting Numbers: [40, 0] Generated Node #0,0,0: 41:[40, 0] Operation: 82-82=0 Exploring Operation: 82/82=1, Resulting Numbers: [40, 1] Generated Node #0,0,1: 41:[40, 1] Operation: 82/82=1 Exploring Operation: 82-40=42, Resulting Numbers: [82, 42] Generated Node #0,0,2: 41:[82, 42] Operation: 82-40=42 Exploring Operation: 82-40=42, Resulting Numbers: [82, 42] Generated Node #0,0,3: 41:[82, 42] Operation: 82-40=42 Moving to Node #0,0,1 Current State: 41:[40, 1], Operations: ['85-3=82', '82/82=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,41 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[82, 3, 40, 85], Operations: [] Exploring Operation: 85-3=82, Resulting Numbers: [82, 40, 82] Generated Node #0,0: 41:[82, 40, 82] Operation: 85-3=82 Moving to Node #0,0 Current State: 41:[82, 40, 82], Operations: ['85-3=82'] Exploring Operation: 82/82=1, Resulting Numbers: [40, 1] Generated Node #0,0,1: 41:[40, 1] Operation: 82/82=1 Moving to Node #0,0,1 Current State: 41:[40, 1], Operations: ['85-3=82', '82/82=1'] Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 33, 66, 68, 43 ]
20
[ "43-33=10", "68-66=2", "10*2=20" ]
Current State: 20:[33, 66, 68, 43], Operations: [] Exploring Operation: 43-33=10, Resulting Numbers: [66, 68, 10] Generated Node #2: [66, 68, 10] from Operation: 43-33=10 Current State: 20:[66, 68, 10], Operations: ['43-33=10'] Exploring Operation: 68-66=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 68-66=2 Current State: 20:[10, 2], Operations: ['43-33=10', '68-66=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[33, 66, 68, 43], Operations: [] Exploring Operation: 68-43=25, Resulting Numbers: [33, 66, 25] Generated Node #0,0: 20:[33, 66, 25] Operation: 68-43=25 Exploring Operation: 66-43=23, Resulting Numbers: [33, 68, 23] Generated Node #0,1: 20:[33, 68, 23] Operation: 66-43=23 Exploring Operation: 68-66=2, Resulting Numbers: [33, 43, 2] Generated Node #0,2: 20:[33, 43, 2] Operation: 68-66=2 Exploring Operation: 66/33=2, Resulting Numbers: [68, 43, 2] Generated Node #0,3: 20:[68, 43, 2] Operation: 66/33=2 Exploring Operation: 66-33=33, Resulting Numbers: [68, 43, 33] Generated Node #0,4: 20:[68, 43, 33] Operation: 66-33=33 Moving to Node #0,2 Current State: 20:[33, 43, 2], Operations: ['68-66=2'] Exploring Operation: 33+2=35, Resulting Numbers: [43, 35] Generated Node #0,2,0: 20:[43, 35] Operation: 33+2=35 Exploring Operation: 33-2=31, Resulting Numbers: [43, 31] Generated Node #0,2,1: 20:[43, 31] Operation: 33-2=31 Exploring Operation: 43+2=45, Resulting Numbers: [33, 45] Generated Node #0,2,2: 20:[33, 45] Operation: 43+2=45 Exploring Operation: 43-2=41, Resulting Numbers: [33, 41] Generated Node #0,2,3: 20:[33, 41] Operation: 43-2=41 Exploring Operation: 43-33=10, Resulting Numbers: [2, 10] Generated Node #0,2,4: 20:[2, 10] Operation: 43-33=10 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 20:[2, 10], Operations: ['68-66=2', '43-33=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[33, 66, 68, 43], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [33, 43, 2] Generated Node #0,2: 20:[33, 43, 2] Operation: 68-66=2 Moving to Node #0,2 Current State: 20:[33, 43, 2], Operations: ['68-66=2'] Exploring Operation: 43-33=10, Resulting Numbers: [2, 10] Generated Node #0,2,4: 20:[2, 10] Operation: 43-33=10 Moving to Node #0,2,4 Current State: 20:[2, 10], Operations: ['68-66=2', '43-33=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 27, 44, 20, 84 ]
33
[ "27+44=71", "20+84=104", "104-71=33" ]
Current State: 33:[27, 44, 20, 84], Operations: [] Exploring Operation: 27+44=71, Resulting Numbers: [20, 84, 71] Generated Node #2: [20, 84, 71] from Operation: 27+44=71 Current State: 33:[20, 84, 71], Operations: ['27+44=71'] Exploring Operation: 20+84=104, Resulting Numbers: [71, 104] Generated Node #3: [71, 104] from Operation: 20+84=104 Current State: 33:[71, 104], Operations: ['27+44=71', '20+84=104'] Exploring Operation: 104-71=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[27, 44, 20, 84], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [27, 20, 40] Generated Node #0,0: 33:[27, 20, 40] Operation: 84-44=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[27, 20, 40], Operations: ['84-44=40'] Exploring Operation: 40/20=2, Resulting Numbers: [27, 2] Generated Node #0,0,0: 33:[27, 2] Operation: 40/20=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[27, 2], Operations: ['84-44=40', '40/20=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,33 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 No solution found.
0
hs_1
sum_heuristic
[ 50, 6, 43, 27 ]
95
[ "50-27=23", "6*23=138", "138-43=95" ]
Current State: 95:[50, 6, 43, 27], Operations: [] Exploring Operation: 50-27=23, Resulting Numbers: [6, 43, 23] Generated Node #2: [6, 43, 23] from Operation: 50-27=23 Current State: 95:[6, 43, 23], Operations: ['50-27=23'] Exploring Operation: 6*23=138, Resulting Numbers: [43, 138] Generated Node #3: [43, 138] from Operation: 6*23=138 Current State: 95:[43, 138], Operations: ['50-27=23', '6*23=138'] Exploring Operation: 138-43=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[50, 6, 43, 27], Operations: [] Exploring Operation: 50-43=7, Resulting Numbers: [6, 27, 7] Generated Node #0,0: 95:[6, 27, 7] Operation: 50-43=7 Exploring Operation: 50+43=93, Resulting Numbers: [6, 27, 93] Generated Node #0,1: 95:[6, 27, 93] Operation: 50+43=93 Moving to Node #0,0 Current State: 95:[6, 27, 7], Operations: ['50-43=7'] Exploring Operation: 27-7=20, Resulting Numbers: [6, 20] Generated Node #0,0,0: 95:[6, 20] Operation: 27-7=20 Exploring Operation: 27-6=21, Resulting Numbers: [7, 21] Generated Node #0,0,1: 95:[7, 21] Operation: 27-6=21 Moving to Node #0,1 Current State: 95:[6, 27, 93], Operations: ['50+43=93'] Exploring Operation: 6+93=99, Resulting Numbers: [27, 99] Generated Node #0,1,0: 95:[27, 99] Operation: 6+93=99 Exploring Operation: 27-6=21, Resulting Numbers: [93, 21] Generated Node #0,1,1: 95:[93, 21] Operation: 27-6=21 Moving to Node #0,0,0 Current State: 95:[6, 20], Operations: ['50-43=7', '27-7=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,95 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[93, 21], Operations: ['50+43=93', '27-6=21'] Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,95 unequal: No Solution Exploring Operation: 93+21=114, Resulting Numbers: [114] 114,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[7, 21], Operations: ['50-43=7', '27-6=21'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[27, 99], Operations: ['50+43=93', '6+93=99'] Exploring Operation: 99-27=72, Resulting Numbers: [72] 72,95 unequal: No Solution Exploring Operation: 27+99=126, Resulting Numbers: [126] 126,95 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 35, 46, 81, 89 ]
90
[ "35+46=81", "81/81=1", "89+1=90" ]
Current State: 90:[35, 46, 81, 89], Operations: [] Exploring Operation: 35+46=81, Resulting Numbers: [81, 89, 81] Generated Node #2: [81, 89, 81] from Operation: 35+46=81 Current State: 90:[81, 89, 81], Operations: ['35+46=81'] Exploring Operation: 81/81=1, Resulting Numbers: [89, 1] Generated Node #3: [89, 1] from Operation: 81/81=1 Current State: 90:[89, 1], Operations: ['35+46=81', '81/81=1'] Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[35, 46, 81, 89], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [35, 46, 8] Generated Node #0,0: 90:[35, 46, 8] Operation: 89-81=8 Exploring Operation: 81-46=35, Resulting Numbers: [35, 89, 35] Generated Node #0,1: 90:[35, 89, 35] Operation: 81-46=35 Exploring Operation: 89-46=43, Resulting Numbers: [35, 81, 43] Generated Node #0,2: 90:[35, 81, 43] Operation: 89-46=43 Exploring Operation: 46-35=11, Resulting Numbers: [81, 89, 11] Generated Node #0,3: 90:[81, 89, 11] Operation: 46-35=11 Exploring Operation: 81-35=46, Resulting Numbers: [46, 89, 46] Generated Node #0,4: 90:[46, 89, 46] Operation: 81-35=46 Moving to Node #0,4 Current State: 90:[46, 89, 46], Operations: ['81-35=46'] Exploring Operation: 89-46=43, Resulting Numbers: [46, 43] Generated Node #0,4,0: 90:[46, 43] Operation: 89-46=43 Exploring Operation: 46-46=0, Resulting Numbers: [89, 0] Generated Node #0,4,1: 90:[89, 0] Operation: 46-46=0 Exploring Operation: 46/46=1, Resulting Numbers: [89, 1] Generated Node #0,4,2: 90:[89, 1] Operation: 46/46=1 Exploring Operation: 89-46=43, Resulting Numbers: [46, 43] Generated Node #0,4,3: 90:[46, 43] Operation: 89-46=43 Exploring Operation: 46+46=92, Resulting Numbers: [89, 92] Generated Node #0,4,4: 90:[89, 92] Operation: 46+46=92 Moving to Node #0,0 Current State: 90:[35, 46, 8], Operations: ['89-81=8'] Exploring Operation: 35+8=43, Resulting Numbers: [46, 43] Generated Node #0,0,0: 90:[46, 43] Operation: 35+8=43 Exploring Operation: 35+46=81, Resulting Numbers: [8, 81] Generated Node #0,0,1: 90:[8, 81] Operation: 35+46=81 Exploring Operation: 46-35=11, Resulting Numbers: [8, 11] Generated Node #0,0,2: 90:[8, 11] Operation: 46-35=11 Exploring Operation: 35-8=27, Resulting Numbers: [46, 27] Generated Node #0,0,3: 90:[46, 27] Operation: 35-8=27 Exploring Operation: 46-8=38, Resulting Numbers: [35, 38] Generated Node #0,0,4: 90:[35, 38] Operation: 46-8=38 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[8, 11], Operations: ['89-81=8', '46-35=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[46, 43], Operations: ['89-81=8', '35+8=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,90 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[46, 27], Operations: ['89-81=8', '35-8=27'] Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[8, 81], Operations: ['89-81=8', '35+46=81'] Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,90 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 90:[35, 38], Operations: ['89-81=8', '46-8=38'] Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 35*38=1330, Resulting Numbers: [1330] 1330,90 unequal: No Solution Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 90:[35, 89, 35], Operations: ['81-46=35'] Exploring Operation: 35+35=70, Resulting Numbers: [89, 70] Generated Node #0,1,0: 90:[89, 70] Operation: 35+35=70 Exploring Operation: 35-35=0, Resulting Numbers: [89, 0] Generated Node #0,1,1: 90:[89, 0] Operation: 35-35=0 Exploring Operation: 89-35=54, Resulting Numbers: [35, 54] Generated Node #0,1,2: 90:[35, 54] Operation: 89-35=54 Exploring Operation: 89-35=54, Resulting Numbers: [35, 54] Generated Node #0,1,3: 90:[35, 54] Operation: 89-35=54 Exploring Operation: 35/35=1, Resulting Numbers: [89, 1] Generated Node #0,1,4: 90:[89, 1] Operation: 35/35=1 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 90:[89, 1], Operations: ['81-46=35', '35/35=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,90 unequal: No Solution Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[35, 46, 81, 89], Operations: [] Exploring Operation: 81-46=35, Resulting Numbers: [35, 89, 35] Generated Node #0,1: 90:[35, 89, 35] Operation: 81-46=35 Moving to Node #0,1 Current State: 90:[35, 89, 35], Operations: ['81-46=35'] Exploring Operation: 35/35=1, Resulting Numbers: [89, 1] Generated Node #0,1,4: 90:[89, 1] Operation: 35/35=1 Moving to Node #0,1,4 Current State: 90:[89, 1], Operations: ['81-46=35', '35/35=1'] Exploring Operation: 89+1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 49, 92, 24, 36 ]
89
[ "92*36=3312", "3312/24=138", "138-49=89" ]
Current State: 89:[49, 92, 24, 36], Operations: [] Exploring Operation: 92*36=3312, Resulting Numbers: [49, 24, 3312] Generated Node #2: [49, 24, 3312] from Operation: 92*36=3312 Current State: 89:[49, 24, 3312], Operations: ['92*36=3312'] Exploring Operation: 3312/24=138, Resulting Numbers: [49, 138] Generated Node #3: [49, 138] from Operation: 3312/24=138 Current State: 89:[49, 138], Operations: ['92*36=3312', '3312/24=138'] Exploring Operation: 138-49=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[49, 92, 24, 36], Operations: [] Exploring Operation: 49+24=73, Resulting Numbers: [92, 36, 73] Generated Node #0,0: 89:[92, 36, 73] Operation: 49+24=73 Moving to Node #0,0 Current State: 89:[92, 36, 73], Operations: ['49+24=73'] Exploring Operation: 36+73=109, Resulting Numbers: [92, 109] Generated Node #0,0,0: 89:[92, 109] Operation: 36+73=109 Moving to Node #0,0,0 Current State: 89:[92, 109], Operations: ['49+24=73', '36+73=109'] Exploring Operation: 109-92=17, Resulting Numbers: [17] 17,89 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 14, 37, 71, 75 ]
92
[ "37-14=23", "75-71=4", "23*4=92" ]
Current State: 92:[14, 37, 71, 75], Operations: [] Exploring Operation: 37-14=23, Resulting Numbers: [71, 75, 23] Generated Node #2: [71, 75, 23] from Operation: 37-14=23 Current State: 92:[71, 75, 23], Operations: ['37-14=23'] Exploring Operation: 75-71=4, Resulting Numbers: [23, 4] Generated Node #3: [23, 4] from Operation: 75-71=4 Current State: 92:[23, 4], Operations: ['37-14=23', '75-71=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[14, 37, 71, 75], Operations: [] Exploring Operation: 14+71=85, Resulting Numbers: [37, 75, 85] Generated Node #0,0: 92:[37, 75, 85] Operation: 14+71=85 Exploring Operation: 14+75=89, Resulting Numbers: [37, 71, 89] Generated Node #0,1: 92:[37, 71, 89] Operation: 14+75=89 Exploring Operation: 75-71=4, Resulting Numbers: [14, 37, 4] Generated Node #0,2: 92:[14, 37, 4] Operation: 75-71=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[14, 37, 4], Operations: ['75-71=4'] Exploring Operation: 14+37=51, Resulting Numbers: [4, 51] Generated Node #0,2,0: 92:[4, 51] Operation: 14+37=51 Exploring Operation: 37-14=23, Resulting Numbers: [4, 23] Generated Node #0,2,1: 92:[4, 23] Operation: 37-14=23 Exploring Operation: 14+4=18, Resulting Numbers: [37, 18] Generated Node #0,2,2: 92:[37, 18] Operation: 14+4=18 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 92:[4, 23], Operations: ['75-71=4', '37-14=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[14, 37, 71, 75], Operations: [] Exploring Operation: 75-71=4, Resulting Numbers: [14, 37, 4] Generated Node #0,2: 92:[14, 37, 4] Operation: 75-71=4 Moving to Node #0,2 Current State: 92:[14, 37, 4], Operations: ['75-71=4'] Exploring Operation: 37-14=23, Resulting Numbers: [4, 23] Generated Node #0,2,1: 92:[4, 23] Operation: 37-14=23 Moving to Node #0,2,1 Current State: 92:[4, 23], Operations: ['75-71=4', '37-14=23'] Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 9, 38, 25, 45 ]
88
[ "45-38=7", "9*7=63", "25+63=88" ]
Current State: 88:[9, 38, 25, 45], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [9, 25, 7] Generated Node #2: [9, 25, 7] from Operation: 45-38=7 Current State: 88:[9, 25, 7], Operations: ['45-38=7'] Exploring Operation: 9*7=63, Resulting Numbers: [25, 63] Generated Node #3: [25, 63] from Operation: 9*7=63 Current State: 88:[25, 63], Operations: ['45-38=7', '9*7=63'] Exploring Operation: 25+63=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[9, 38, 25, 45], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [9, 25, 7] Generated Node #0,0: 88:[9, 25, 7] Operation: 45-38=7 Exploring Operation: 38+45=83, Resulting Numbers: [9, 25, 83] Generated Node #0,1: 88:[9, 25, 83] Operation: 38+45=83 Exploring Operation: 38-25=13, Resulting Numbers: [9, 45, 13] Generated Node #0,2: 88:[9, 45, 13] Operation: 38-25=13 Exploring Operation: 9+38=47, Resulting Numbers: [25, 45, 47] Generated Node #0,3: 88:[25, 45, 47] Operation: 9+38=47 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[9, 45, 13], Operations: ['38-25=13'] Exploring Operation: 13-9=4, Resulting Numbers: [45, 4] Generated Node #0,2,0: 88:[45, 4] Operation: 13-9=4 Exploring Operation: 45/9=5, Resulting Numbers: [13, 5] Generated Node #0,2,1: 88:[13, 5] Operation: 45/9=5 Exploring Operation: 45-9=36, Resulting Numbers: [13, 36] Generated Node #0,2,2: 88:[13, 36] Operation: 45-9=36 Exploring Operation: 9+13=22, Resulting Numbers: [45, 22] Generated Node #0,2,3: 88:[45, 22] Operation: 9+13=22 Moving to Node #0,2,0 Current State: 88:[45, 4], Operations: ['38-25=13', '13-9=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,88 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[45, 22], Operations: ['38-25=13', '9+13=22'] Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,88 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[13, 5], Operations: ['38-25=13', '45/9=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[13, 36], Operations: ['38-25=13', '45-9=36'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[9, 25, 7], Operations: ['45-38=7'] Exploring Operation: 9+7=16, Resulting Numbers: [25, 16] Generated Node #0,0,0: 88:[25, 16] Operation: 9+7=16 Exploring Operation: 9-7=2, Resulting Numbers: [25, 2] Generated Node #0,0,1: 88:[25, 2] Operation: 9-7=2 Exploring Operation: 25-7=18, Resulting Numbers: [9, 18] Generated Node #0,0,2: 88:[9, 18] Operation: 25-7=18 Exploring Operation: 25-9=16, Resulting Numbers: [7, 16] Generated Node #0,0,3: 88:[7, 16] Operation: 25-9=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[25, 2], Operations: ['45-38=7', '9-7=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[9, 18], Operations: ['45-38=7', '25-7=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,88 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[7, 16], Operations: ['45-38=7', '25-9=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[25, 16], Operations: ['45-38=7', '9+7=16'] Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[25, 45, 47], Operations: ['9+38=47'] Exploring Operation: 45-25=20, Resulting Numbers: [47, 20] Generated Node #0,3,0: 88:[47, 20] Operation: 45-25=20 Exploring Operation: 47-25=22, Resulting Numbers: [45, 22] Generated Node #0,3,1: 88:[45, 22] Operation: 47-25=22 Exploring Operation: 47-45=2, Resulting Numbers: [25, 2] Generated Node #0,3,2: 88:[25, 2] Operation: 47-45=2 Exploring Operation: 45+47=92, Resulting Numbers: [25, 92] Generated Node #0,3,3: 88:[25, 92] Operation: 45+47=92 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[45, 22], Operations: ['9+38=47', '47-25=22'] Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,88 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[25, 2], Operations: ['9+38=47', '47-45=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[47, 20], Operations: ['9+38=47', '45-25=20'] Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,88 unequal: No Solution Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[25, 92], Operations: ['9+38=47', '45+47=92'] Exploring Operation: 25*92=2300, Resulting Numbers: [2300] 2300,88 unequal: No Solution Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 25+92=117, Resulting Numbers: [117] 117,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[9, 25, 83], Operations: ['38+45=83'] Exploring Operation: 9+25=34, Resulting Numbers: [83, 34] Generated Node #0,1,0: 88:[83, 34] Operation: 9+25=34 Exploring Operation: 9+83=92, Resulting Numbers: [25, 92] Generated Node #0,1,1: 88:[25, 92] Operation: 9+83=92 Exploring Operation: 25-9=16, Resulting Numbers: [83, 16] Generated Node #0,1,2: 88:[83, 16] Operation: 25-9=16 Exploring Operation: 83-25=58, Resulting Numbers: [9, 58] Generated Node #0,1,3: 88:[9, 58] Operation: 83-25=58 Moving to Node #0,1,1 Current State: 88:[25, 92], Operations: ['38+45=83', '9+83=92'] Exploring Operation: 25+92=117, Resulting Numbers: [117] 117,88 unequal: No Solution Exploring Operation: 92-25=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 25*92=2300, Resulting Numbers: [2300] 2300,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[83, 16], Operations: ['38+45=83', '25-9=16'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 83+16=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 83*16=1328, Resulting Numbers: [1328] 1328,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[9, 58], Operations: ['38+45=83', '83-25=58'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 9+58=67, Resulting Numbers: [67] 67,88 unequal: No Solution Exploring Operation: 9*58=522, Resulting Numbers: [522] 522,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[83, 34], Operations: ['38+45=83', '9+25=34'] Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,88 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,88 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
[ 83, 39, 69, 78 ]
53
[ "83-39=44", "78-69=9", "44+9=53" ]
Current State: 53:[83, 39, 69, 78], Operations: [] Exploring Operation: 83-39=44, Resulting Numbers: [69, 78, 44] Generated Node #2: [69, 78, 44] from Operation: 83-39=44 Current State: 53:[69, 78, 44], Operations: ['83-39=44'] Exploring Operation: 78-69=9, Resulting Numbers: [44, 9] Generated Node #3: [44, 9] from Operation: 78-69=9 Current State: 53:[44, 9], Operations: ['83-39=44', '78-69=9'] Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[83, 39, 69, 78], Operations: [] Exploring Operation: 78-39=39, Resulting Numbers: [83, 69, 39] Generated Node #0,0: 53:[83, 69, 39] Operation: 78-39=39 Exploring Operation: 83-39=44, Resulting Numbers: [69, 78, 44] Generated Node #0,1: 53:[69, 78, 44] Operation: 83-39=44 Moving to Node #0,1 Current State: 53:[69, 78, 44], Operations: ['83-39=44'] Exploring Operation: 78-44=34, Resulting Numbers: [69, 34] Generated Node #0,1,0: 53:[69, 34] Operation: 78-44=34 Exploring Operation: 78-69=9, Resulting Numbers: [44, 9] Generated Node #0,1,1: 53:[44, 9] Operation: 78-69=9 Moving to Node #0,0 Current State: 53:[83, 69, 39], Operations: ['78-39=39'] Exploring Operation: 83-39=44, Resulting Numbers: [69, 44] Generated Node #0,0,0: 53:[69, 44] Operation: 83-39=44 Exploring Operation: 83-69=14, Resulting Numbers: [39, 14] Generated Node #0,0,1: 53:[39, 14] Operation: 83-69=14 Moving to Node #0,0,0 Current State: 53:[69, 44], Operations: ['78-39=39', '83-39=44'] Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,53 unequal: No Solution Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[69, 34], Operations: ['83-39=44', '78-44=34'] Exploring Operation: 69+34=103, Resulting Numbers: [103] 103,53 unequal: No Solution Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[44, 9], Operations: ['83-39=44', '78-69=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[83, 39, 69, 78], Operations: [] Exploring Operation: 83-39=44, Resulting Numbers: [69, 78, 44] Generated Node #0,1: 53:[69, 78, 44] Operation: 83-39=44 Moving to Node #0,1 Current State: 53:[69, 78, 44], Operations: ['83-39=44'] Exploring Operation: 78-69=9, Resulting Numbers: [44, 9] Generated Node #0,1,1: 53:[44, 9] Operation: 78-69=9 Moving to Node #0,1,1 Current State: 53:[44, 9], Operations: ['83-39=44', '78-69=9'] Exploring Operation: 44+9=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 6, 29, 15, 79 ]
99
[ "6+29=35", "79-15=64", "35+64=99" ]
Current State: 99:[6, 29, 15, 79], Operations: [] Exploring Operation: 6+29=35, Resulting Numbers: [15, 79, 35] Generated Node #2: [15, 79, 35] from Operation: 6+29=35 Current State: 99:[15, 79, 35], Operations: ['6+29=35'] Exploring Operation: 79-15=64, Resulting Numbers: [35, 64] Generated Node #3: [35, 64] from Operation: 79-15=64 Current State: 99:[35, 64], Operations: ['6+29=35', '79-15=64'] Exploring Operation: 35+64=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[6, 29, 15, 79], Operations: [] Exploring Operation: 15+79=94, Resulting Numbers: [6, 29, 94] Generated Node #0,0: 99:[6, 29, 94] Operation: 15+79=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[6, 29, 94], Operations: ['15+79=94'] Exploring Operation: 6+94=100, Resulting Numbers: [29, 100] Generated Node #0,0,0: 99:[29, 100] Operation: 6+94=100 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[29, 100], Operations: ['15+79=94', '6+94=100'] Exploring Operation: 100-29=71, Resulting Numbers: [71] 71,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 71, 73, 21, 41 ]
40
[ "73-71=2", "41-21=20", "2*20=40" ]
Current State: 40:[71, 73, 21, 41], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [21, 41, 2] Generated Node #2: [21, 41, 2] from Operation: 73-71=2 Current State: 40:[21, 41, 2], Operations: ['73-71=2'] Exploring Operation: 41-21=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 41-21=20 Current State: 40:[2, 20], Operations: ['73-71=2', '41-21=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[71, 73, 21, 41], Operations: [] Exploring Operation: 73-21=52, Resulting Numbers: [71, 41, 52] Generated Node #0,0: 40:[71, 41, 52] Operation: 73-21=52 Exploring Operation: 71-21=50, Resulting Numbers: [73, 41, 50] Generated Node #0,1: 40:[73, 41, 50] Operation: 71-21=50 Exploring Operation: 73-41=32, Resulting Numbers: [71, 21, 32] Generated Node #0,2: 40:[71, 21, 32] Operation: 73-41=32 Exploring Operation: 71-41=30, Resulting Numbers: [73, 21, 30] Generated Node #0,3: 40:[73, 21, 30] Operation: 71-41=30 Exploring Operation: 73-71=2, Resulting Numbers: [21, 41, 2] Generated Node #0,4: 40:[21, 41, 2] Operation: 73-71=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 40:[21, 41, 2], Operations: ['73-71=2'] Exploring Operation: 21*2=42, Resulting Numbers: [41, 42] Generated Node #0,4,0: 40:[41, 42] Operation: 21*2=42 Exploring Operation: 41-21=20, Resulting Numbers: [2, 20] Generated Node #0,4,1: 40:[2, 20] Operation: 41-21=20 Exploring Operation: 21-2=19, Resulting Numbers: [41, 19] Generated Node #0,4,2: 40:[41, 19] Operation: 21-2=19 Exploring Operation: 21+2=23, Resulting Numbers: [41, 23] Generated Node #0,4,3: 40:[41, 23] Operation: 21+2=23 Exploring Operation: 41-2=39, Resulting Numbers: [21, 39] Generated Node #0,4,4: 40:[21, 39] Operation: 41-2=39 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 40:[2, 20], Operations: ['73-71=2', '41-21=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,40 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[71, 73, 21, 41], Operations: [] Exploring Operation: 73-71=2, Resulting Numbers: [21, 41, 2] Generated Node #0,4: 40:[21, 41, 2] Operation: 73-71=2 Moving to Node #0,4 Current State: 40:[21, 41, 2], Operations: ['73-71=2'] Exploring Operation: 41-21=20, Resulting Numbers: [2, 20] Generated Node #0,4,1: 40:[2, 20] Operation: 41-21=20 Moving to Node #0,4,1 Current State: 40:[2, 20], Operations: ['73-71=2', '41-21=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
0.986111
hs_5
sum_heuristic
[ 90, 69, 27, 59 ]
18
[ "69-59=10", "90/10=9", "27-9=18" ]
Current State: 18:[90, 69, 27, 59], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [90, 27, 10] Generated Node #2: [90, 27, 10] from Operation: 69-59=10 Current State: 18:[90, 27, 10], Operations: ['69-59=10'] Exploring Operation: 90/10=9, Resulting Numbers: [27, 9] Generated Node #3: [27, 9] from Operation: 90/10=9 Current State: 18:[27, 9], Operations: ['69-59=10', '90/10=9'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 69, 27, 59], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [27, 59, 21] Generated Node #0,0: 18:[27, 59, 21] Operation: 90-69=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[27, 59, 21], Operations: ['90-69=21'] Exploring Operation: 59-27=32, Resulting Numbers: [21, 32] Generated Node #0,0,0: 18:[21, 32] Operation: 59-27=32 Moving to Node #0,0,0 Current State: 18:[21, 32], Operations: ['90-69=21', '59-27=32'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,18 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
[ 59, 5, 63, 97 ]
77
[ "63-59=4", "5*4=20", "97-20=77" ]
Current State: 77:[59, 5, 63, 97], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [5, 97, 4] Generated Node #2: [5, 97, 4] from Operation: 63-59=4 Current State: 77:[5, 97, 4], Operations: ['63-59=4'] Exploring Operation: 5*4=20, Resulting Numbers: [97, 20] Generated Node #3: [97, 20] from Operation: 5*4=20 Current State: 77:[97, 20], Operations: ['63-59=4', '5*4=20'] Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[59, 5, 63, 97], Operations: [] Exploring Operation: 59+5=64, Resulting Numbers: [63, 97, 64] Generated Node #0,0: 77:[63, 97, 64] Operation: 59+5=64 Exploring Operation: 97-63=34, Resulting Numbers: [59, 5, 34] Generated Node #0,1: 77:[59, 5, 34] Operation: 97-63=34 Exploring Operation: 97-59=38, Resulting Numbers: [5, 63, 38] Generated Node #0,2: 77:[5, 63, 38] Operation: 97-59=38 Exploring Operation: 63-59=4, Resulting Numbers: [5, 97, 4] Generated Node #0,3: 77:[5, 97, 4] Operation: 63-59=4 Moving to Node #0,3 Current State: 77:[5, 97, 4], Operations: ['63-59=4'] Exploring Operation: 5+4=9, Resulting Numbers: [97, 9] Generated Node #0,3,0: 77:[97, 9] Operation: 5+4=9 Exploring Operation: 97-4=93, Resulting Numbers: [5, 93] Generated Node #0,3,1: 77:[5, 93] Operation: 97-4=93 Exploring Operation: 5-4=1, Resulting Numbers: [97, 1] Generated Node #0,3,2: 77:[97, 1] Operation: 5-4=1 Exploring Operation: 97-5=92, Resulting Numbers: [4, 92] Generated Node #0,3,3: 77:[4, 92] Operation: 97-5=92 Moving to Node #0,2 Current State: 77:[5, 63, 38], Operations: ['97-59=38'] Exploring Operation: 63-38=25, Resulting Numbers: [5, 25] Generated Node #0,2,0: 77:[5, 25] Operation: 63-38=25 Exploring Operation: 38-5=33, Resulting Numbers: [63, 33] Generated Node #0,2,1: 77:[63, 33] Operation: 38-5=33 Exploring Operation: 5+63=68, Resulting Numbers: [38, 68] Generated Node #0,2,2: 77:[38, 68] Operation: 5+63=68 Exploring Operation: 63+38=101, Resulting Numbers: [5, 101] Generated Node #0,2,3: 77:[5, 101] Operation: 63+38=101 Moving to Node #0,1 Current State: 77:[59, 5, 34], Operations: ['97-63=34'] Exploring Operation: 59-34=25, Resulting Numbers: [5, 25] Generated Node #0,1,0: 77:[5, 25] Operation: 59-34=25 Exploring Operation: 59+34=93, Resulting Numbers: [5, 93] Generated Node #0,1,1: 77:[5, 93] Operation: 59+34=93 Exploring Operation: 34-5=29, Resulting Numbers: [59, 29] Generated Node #0,1,2: 77:[59, 29] Operation: 34-5=29 Exploring Operation: 59+5=64, Resulting Numbers: [34, 64] Generated Node #0,1,3: 77:[34, 64] Operation: 59+5=64 Moving to Node #0,0 Current State: 77:[63, 97, 64], Operations: ['59+5=64'] Exploring Operation: 97-64=33, Resulting Numbers: [63, 33] Generated Node #0,0,0: 77:[63, 33] Operation: 97-64=33 Exploring Operation: 64-63=1, Resulting Numbers: [97, 1] Generated Node #0,0,1: 77:[97, 1] Operation: 64-63=1 Exploring Operation: 63+64=127, Resulting Numbers: [97, 127] Generated Node #0,0,2: 77:[97, 127] Operation: 63+64=127 Exploring Operation: 97-63=34, Resulting Numbers: [64, 34] Generated Node #0,0,3: 77:[64, 34] Operation: 97-63=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[97, 1], Operations: ['59+5=64', '64-63=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 97*1=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 97/1=97, Resulting Numbers: [97] 97,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[63, 33], Operations: ['59+5=64', '97-64=33'] Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 63*33=2079, Resulting Numbers: [2079] 2079,77 unequal: No Solution Exploring Operation: 63+33=96, Resulting Numbers: [96] 96,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[64, 34], Operations: ['59+5=64', '97-63=34'] Exploring Operation: 64*34=2176, Resulting Numbers: [2176] 2176,77 unequal: No Solution Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 64+34=98, Resulting Numbers: [98] 98,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 77:[97, 127], Operations: ['59+5=64', '63+64=127'] Exploring Operation: 97+127=224, Resulting Numbers: [224] 224,77 unequal: No Solution Exploring Operation: 97*127=12319, Resulting Numbers: [12319] 12319,77 unequal: No Solution Exploring Operation: 127-97=30, Resulting Numbers: [30] 30,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 77:[5, 25], Operations: ['97-59=38', '63-38=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[5, 25], Operations: ['97-63=34', '59-34=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,77 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[4, 92], Operations: ['63-59=4', '97-5=92'] Exploring Operation: 4*92=368, Resulting Numbers: [368] 368,77 unequal: No Solution Exploring Operation: 4+92=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[5, 93], Operations: ['97-63=34', '59+34=93'] Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 5*93=465, Resulting Numbers: [465] 465,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[5, 93], Operations: ['63-59=4', '97-4=93'] Exploring Operation: 5*93=465, Resulting Numbers: [465] 465,77 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[97, 9], Operations: ['63-59=4', '5+4=9'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,77 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[5, 101], Operations: ['97-59=38', '63+38=101'] Exploring Operation: 101-5=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 5+101=106, Resulting Numbers: [106] 106,77 unequal: No Solution Exploring Operation: 5*101=505, Resulting Numbers: [505] 505,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[97, 1], Operations: ['63-59=4', '5-4=1'] Exploring Operation: 97+1=98, Resulting Numbers: [98] 98,77 unequal: No Solution Exploring Operation: 97/1=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 97*1=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[59, 29], Operations: ['97-63=34', '34-5=29'] Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,77 unequal: No Solution Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[63, 33], Operations: ['97-59=38', '38-5=33'] Exploring Operation: 63*33=2079, Resulting Numbers: [2079] 2079,77 unequal: No Solution Exploring Operation: 63+33=96, Resulting Numbers: [96] 96,77 unequal: No Solution Exploring Operation: 63-33=30, Resulting Numbers: [30] 30,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[34, 64], Operations: ['97-63=34', '59+5=64'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,77 unequal: No Solution Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[38, 68], Operations: ['97-59=38', '5+63=68'] Exploring Operation: 38+68=106, Resulting Numbers: [106] 106,77 unequal: No Solution Exploring Operation: 38*68=2584, Resulting Numbers: [2584] 2584,77 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,77 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 2, 99, 59, 73 ]
93
[ "99-59=40", "40/2=20", "73+20=93" ]
Current State: 93:[2, 99, 59, 73], Operations: [] Exploring Operation: 99-59=40, Resulting Numbers: [2, 73, 40] Generated Node #2: [2, 73, 40] from Operation: 99-59=40 Current State: 93:[2, 73, 40], Operations: ['99-59=40'] Exploring Operation: 40/2=20, Resulting Numbers: [73, 20] Generated Node #3: [73, 20] from Operation: 40/2=20 Current State: 93:[73, 20], Operations: ['99-59=40', '40/2=20'] Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[2, 99, 59, 73], Operations: [] Exploring Operation: 99-59=40, Resulting Numbers: [2, 73, 40] Generated Node #0,0: 93:[2, 73, 40] Operation: 99-59=40 Exploring Operation: 73-59=14, Resulting Numbers: [2, 99, 14] Generated Node #0,1: 93:[2, 99, 14] Operation: 73-59=14 Exploring Operation: 59+73=132, Resulting Numbers: [2, 99, 132] Generated Node #0,2: 93:[2, 99, 132] Operation: 59+73=132 Exploring Operation: 99-73=26, Resulting Numbers: [2, 59, 26] Generated Node #0,3: 93:[2, 59, 26] Operation: 99-73=26 Moving to Node #0,1 Current State: 93:[2, 99, 14], Operations: ['73-59=14'] Exploring Operation: 14/2=7, Resulting Numbers: [99, 7] Generated Node #0,1,0: 93:[99, 7] Operation: 14/2=7 Exploring Operation: 99-14=85, Resulting Numbers: [2, 85] Generated Node #0,1,1: 93:[2, 85] Operation: 99-14=85 Exploring Operation: 99-2=97, Resulting Numbers: [14, 97] Generated Node #0,1,2: 93:[14, 97] Operation: 99-2=97 Exploring Operation: 2*14=28, Resulting Numbers: [99, 28] Generated Node #0,1,3: 93:[99, 28] Operation: 2*14=28 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[2, 85], Operations: ['73-59=14', '99-14=85'] Exploring Operation: 2*85=170, Resulting Numbers: [170] 170,93 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 93:[99, 28], Operations: ['73-59=14', '2*14=28'] Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 99*28=2772, Resulting Numbers: [2772] 2772,93 unequal: No Solution Exploring Operation: 99+28=127, Resulting Numbers: [127] 127,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[99, 7], Operations: ['73-59=14', '14/2=7'] Exploring Operation: 99-7=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 99+7=106, Resulting Numbers: [106] 106,93 unequal: No Solution Exploring Operation: 99*7=693, Resulting Numbers: [693] 693,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 93:[14, 97], Operations: ['73-59=14', '99-2=97'] Exploring Operation: 97-14=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 14*97=1358, Resulting Numbers: [1358] 1358,93 unequal: No Solution Exploring Operation: 14+97=111, Resulting Numbers: [111] 111,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 93:[2, 73, 40], Operations: ['99-59=40'] Exploring Operation: 2+73=75, Resulting Numbers: [40, 75] Generated Node #0,0,0: 93:[40, 75] Operation: 2+73=75 Exploring Operation: 40-2=38, Resulting Numbers: [73, 38] Generated Node #0,0,1: 93:[73, 38] Operation: 40-2=38 Exploring Operation: 73-40=33, Resulting Numbers: [2, 33] Generated Node #0,0,2: 93:[2, 33] Operation: 73-40=33 Exploring Operation: 73+40=113, Resulting Numbers: [2, 113] Generated Node #0,0,3: 93:[2, 113] Operation: 73+40=113 Moving to Node #0,3 Current State: 93:[2, 59, 26], Operations: ['99-73=26'] Exploring Operation: 59-26=33, Resulting Numbers: [2, 33] Generated Node #0,3,0: 93:[2, 33] Operation: 59-26=33 Exploring Operation: 59-2=57, Resulting Numbers: [26, 57] Generated Node #0,3,1: 93:[26, 57] Operation: 59-2=57 Exploring Operation: 2*59=118, Resulting Numbers: [26, 118] Generated Node #0,3,2: 93:[26, 118] Operation: 2*59=118 Exploring Operation: 59+26=85, Resulting Numbers: [2, 85] Generated Node #0,3,3: 93:[2, 85] Operation: 59+26=85 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 93:[2, 33], Operations: ['99-73=26', '59-26=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,93 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 93:[2, 85], Operations: ['99-73=26', '59+26=85'] Exploring Operation: 2*85=170, Resulting Numbers: [170] 170,93 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 93:[26, 118], Operations: ['99-73=26', '2*59=118'] Exploring Operation: 118-26=92, Resulting Numbers: [92] 92,93 unequal: No Solution Exploring Operation: 26+118=144, Resulting Numbers: [144] 144,93 unequal: No Solution Exploring Operation: 26*118=3068, Resulting Numbers: [3068] 3068,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 93:[26, 57], Operations: ['99-73=26', '59-2=57'] Exploring Operation: 26*57=1482, Resulting Numbers: [1482] 1482,93 unequal: No Solution Exploring Operation: 26+57=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,93 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: 93:[2, 99, 132], Operations: ['59+73=132'] Exploring Operation: 99-2=97, Resulting Numbers: [132, 97] Generated Node #0,2,0: 93:[132, 97] Operation: 99-2=97 Exploring Operation: 132-99=33, Resulting Numbers: [2, 33] Generated Node #0,2,1: 93:[2, 33] Operation: 132-99=33 Exploring Operation: 132-2=130, Resulting Numbers: [99, 130] Generated Node #0,2,2: 93:[99, 130] Operation: 132-2=130 Exploring Operation: 132/2=66, Resulting Numbers: [99, 66] Generated Node #0,2,3: 93:[99, 66] Operation: 132/2=66 Moving to Node #0,0,2 Current State: 93:[2, 33], Operations: ['99-59=40', '73-40=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,93 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,93 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,93 unequal: No Solution Moving to Node #0,2,1 Current State: 93:[2, 33], Operations: ['59+73=132', '132-99=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,93 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[2, 113], Operations: ['99-59=40', '73+40=113'] Exploring Operation: 2+113=115, Resulting Numbers: [115] 115,93 unequal: No Solution Exploring Operation: 113-2=111, Resulting Numbers: [111] 111,93 unequal: No Solution Exploring Operation: 2*113=226, Resulting Numbers: [226] 226,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[40, 75], Operations: ['99-59=40', '2+73=75'] Exploring Operation: 40*75=3000, Resulting Numbers: [3000] 3000,93 unequal: No Solution Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 40+75=115, Resulting Numbers: [115] 115,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[73, 38], Operations: ['99-59=40', '40-2=38'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 73+38=111, Resulting Numbers: [111] 111,93 unequal: No Solution Exploring Operation: 73*38=2774, Resulting Numbers: [2774] 2774,93 unequal: No Solution Moving to Node #0,2,3 Current State: 93:[99, 66], Operations: ['59+73=132', '132/2=66'] Exploring Operation: 99-66=33, Resulting Numbers: [33] 33,93 unequal: No Solution Exploring Operation: 99+66=165, Resulting Numbers: [165] 165,93 unequal: No Solution Exploring Operation: 99*66=6534, Resulting Numbers: [6534] 6534,93 unequal: No Solution Moving to Node #0,2,0 Current State: 93:[132, 97], Operations: ['59+73=132', '99-2=97'] Exploring Operation: 132*97=12804, Resulting Numbers: [12804] 12804,93 unequal: No Solution Exploring Operation: 132-97=35, Resulting Numbers: [35] 35,93 unequal: No Solution Exploring Operation: 132+97=229, Resulting Numbers: [229] 229,93 unequal: No Solution Moving to Node #0,2,2 Current State: 93:[99, 130], Operations: ['59+73=132', '132-2=130'] Exploring Operation: 99+130=229, Resulting Numbers: [229] 229,93 unequal: No Solution Exploring Operation: 99*130=12870, Resulting Numbers: [12870] 12870,93 unequal: No Solution Exploring Operation: 130-99=31, Resulting Numbers: [31] 31,93 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 64, 3, 60, 67 ]
23
[ "67-64=3", "60/3=20", "3+20=23" ]
Current State: 23:[64, 3, 60, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [3, 60, 3] Generated Node #2: [3, 60, 3] from Operation: 67-64=3 Current State: 23:[3, 60, 3], Operations: ['67-64=3'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,23 equal: Goal Reached Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[64, 3, 60, 67], Operations: [] Exploring Operation: 64-3=61, Resulting Numbers: [60, 67, 61] Generated Node #0,0: 23:[60, 67, 61] Operation: 64-3=61 Exploring Operation: 67-60=7, Resulting Numbers: [64, 3, 7] Generated Node #0,1: 23:[64, 3, 7] Operation: 67-60=7 Exploring Operation: 64-60=4, Resulting Numbers: [3, 67, 4] Generated Node #0,2: 23:[3, 67, 4] Operation: 64-60=4 Exploring Operation: 60/3=20, Resulting Numbers: [64, 67, 20] Generated Node #0,3: 23:[64, 67, 20] Operation: 60/3=20 Exploring Operation: 67-64=3, Resulting Numbers: [3, 60, 3] Generated Node #0,4: 23:[3, 60, 3] Operation: 67-64=3 Moving to Node #0,1 Current State: 23:[64, 3, 7], Operations: ['67-60=7'] Exploring Operation: 3*7=21, Resulting Numbers: [64, 21] Generated Node #0,1,0: 23:[64, 21] Operation: 3*7=21 Exploring Operation: 64+3=67, Resulting Numbers: [7, 67] Generated Node #0,1,1: 23:[7, 67] Operation: 64+3=67 Exploring Operation: 64-7=57, Resulting Numbers: [3, 57] Generated Node #0,1,2: 23:[3, 57] Operation: 64-7=57 Exploring Operation: 3+7=10, Resulting Numbers: [64, 10] Generated Node #0,1,3: 23:[64, 10] Operation: 3+7=10 Exploring Operation: 64-3=61, Resulting Numbers: [7, 61] Generated Node #0,1,4: 23:[7, 61] Operation: 64-3=61 Moving to Node #0,4 Current State: 23:[3, 60, 3], Operations: ['67-64=3'] Exploring Operation: 60-3=57, Resulting Numbers: [3, 57] Generated Node #0,4,0: 23:[3, 57] Operation: 60-3=57 Exploring Operation: 3+3=6, Resulting Numbers: [60, 6] Generated Node #0,4,1: 23:[60, 6] Operation: 3+3=6 Exploring Operation: 60/3=20, Resulting Numbers: [3, 20] Generated Node #0,4,2: 23:[3, 20] Operation: 60/3=20 Exploring Operation: 60/3=20, Resulting Numbers: [3, 20] Generated Node #0,4,3: 23:[3, 20] Operation: 60/3=20 Exploring Operation: 3*3=9, Resulting Numbers: [60, 9] Generated Node #0,4,4: 23:[60, 9] Operation: 3*3=9 Moving to Node #0,2 Current State: 23:[3, 67, 4], Operations: ['64-60=4'] Exploring Operation: 3*4=12, Resulting Numbers: [67, 12] Generated Node #0,2,0: 23:[67, 12] Operation: 3*4=12 Exploring Operation: 67-4=63, Resulting Numbers: [3, 63] Generated Node #0,2,1: 23:[3, 63] Operation: 67-4=63 Exploring Operation: 3+67=70, Resulting Numbers: [4, 70] Generated Node #0,2,2: 23:[4, 70] Operation: 3+67=70 Exploring Operation: 3+4=7, Resulting Numbers: [67, 7] Generated Node #0,2,3: 23:[67, 7] Operation: 3+4=7 Exploring Operation: 67-3=64, Resulting Numbers: [4, 64] Generated Node #0,2,4: 23:[4, 64] Operation: 67-3=64 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[67, 12], Operations: ['64-60=4', '3*4=12'] Exploring Operation: 67+12=79, Resulting Numbers: [79] 79,23 unequal: No Solution Exploring Operation: 67*12=804, Resulting Numbers: [804] 804,23 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[3, 63], Operations: ['64-60=4', '67-4=63'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 3*63=189, Resulting Numbers: [189] 189,23 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[67, 7], Operations: ['64-60=4', '3+4=7'] Exploring Operation: 67-7=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 67+7=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 67*7=469, Resulting Numbers: [469] 469,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 23:[4, 64], Operations: ['64-60=4', '67-3=64'] Exploring Operation: 4*64=256, Resulting Numbers: [256] 256,23 unequal: No Solution Exploring Operation: 4+64=68, Resulting Numbers: [68] 68,23 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[4, 70], Operations: ['64-60=4', '3+67=70'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 4+70=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 4*70=280, Resulting Numbers: [280] 280,23 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: 23:[64, 67, 20], Operations: ['60/3=20'] Exploring Operation: 67-64=3, Resulting Numbers: [20, 3] Generated Node #0,3,0: 23:[20, 3] Operation: 67-64=3 Exploring Operation: 64+20=84, Resulting Numbers: [67, 84] Generated Node #0,3,1: 23:[67, 84] Operation: 64+20=84 Exploring Operation: 67-20=47, Resulting Numbers: [64, 47] Generated Node #0,3,2: 23:[64, 47] Operation: 67-20=47 Exploring Operation: 64-20=44, Resulting Numbers: [67, 44] Generated Node #0,3,3: 23:[67, 44] Operation: 64-20=44 Exploring Operation: 67+20=87, Resulting Numbers: [64, 87] Generated Node #0,3,4: 23:[64, 87] Operation: 67+20=87 Moving to Node #0,0 Current State: 23:[60, 67, 61], Operations: ['64-3=61'] Exploring Operation: 67-61=6, Resulting Numbers: [60, 6] Generated Node #0,0,0: 23:[60, 6] Operation: 67-61=6 Exploring Operation: 67-60=7, Resulting Numbers: [61, 7] Generated Node #0,0,1: 23:[61, 7] Operation: 67-60=7 Exploring Operation: 60+61=121, Resulting Numbers: [67, 121] Generated Node #0,0,2: 23:[67, 121] Operation: 60+61=121 Exploring Operation: 60+67=127, Resulting Numbers: [61, 127] Generated Node #0,0,3: 23:[61, 127] Operation: 60+67=127 Exploring Operation: 61-60=1, Resulting Numbers: [67, 1] Generated Node #0,0,4: 23:[67, 1] Operation: 61-60=1 Moving to Node #0,4,2 Current State: 23:[3, 20], Operations: ['67-64=3', '60/3=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[64, 3, 60, 67], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [3, 60, 3] Generated Node #0,4: 23:[3, 60, 3] Operation: 67-64=3 Moving to Node #0,4 Current State: 23:[3, 60, 3], Operations: ['67-64=3'] Exploring Operation: 60/3=20, Resulting Numbers: [3, 20] Generated Node #0,4,2: 23:[3, 20] Operation: 60/3=20 Moving to Node #0,4,2 Current State: 23:[3, 20], Operations: ['67-64=3', '60/3=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.953993
hs_5
mult_heuristic
[ 10, 40, 92, 27 ]
95
[ "40-10=30", "92-27=65", "30+65=95" ]
Current State: 95:[10, 40, 92, 27], Operations: [] Exploring Operation: 40-10=30, Resulting Numbers: [92, 27, 30] Generated Node #2: [92, 27, 30] from Operation: 40-10=30 Current State: 95:[92, 27, 30], Operations: ['40-10=30'] Exploring Operation: 92-27=65, Resulting Numbers: [30, 65] Generated Node #3: [30, 65] from Operation: 92-27=65 Current State: 95:[30, 65], Operations: ['40-10=30', '92-27=65'] Exploring Operation: 30+65=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[10, 40, 92, 27], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [10, 92, 13] Generated Node #0,0: 95:[10, 92, 13] Operation: 40-27=13 Exploring Operation: 40-10=30, Resulting Numbers: [92, 27, 30] Generated Node #0,1: 95:[92, 27, 30] Operation: 40-10=30 Exploring Operation: 40/10=4, Resulting Numbers: [92, 27, 4] Generated Node #0,2: 95:[92, 27, 4] Operation: 40/10=4 Exploring Operation: 27-10=17, Resulting Numbers: [40, 92, 17] Generated Node #0,3: 95:[40, 92, 17] Operation: 27-10=17 Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[92, 27, 4], Operations: ['40/10=4'] Exploring Operation: 92/4=23, Resulting Numbers: [27, 23] Generated Node #0,2,0: 95:[27, 23] Operation: 92/4=23 Exploring Operation: 92+4=96, Resulting Numbers: [27, 96] Generated Node #0,2,1: 95:[27, 96] Operation: 92+4=96 Exploring Operation: 27-4=23, Resulting Numbers: [92, 23] Generated Node #0,2,2: 95:[92, 23] Operation: 27-4=23 Exploring Operation: 92-4=88, Resulting Numbers: [27, 88] Generated Node #0,2,3: 95:[27, 88] Operation: 92-4=88 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 95:[92, 23], Operations: ['40/10=4', '27-4=23'] Exploring Operation: 92+23=115, Resulting Numbers: [115] 115,95 unequal: No Solution Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,95 unequal: No Solution Exploring Operation: 92*23=2116, Resulting Numbers: [2116] 2116,95 unequal: No Solution Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 95:[27, 96], Operations: ['40/10=4', '92+4=96'] Exploring Operation: 27*96=2592, Resulting Numbers: [2592] 2592,95 unequal: No Solution Exploring Operation: 27+96=123, Resulting Numbers: [123] 123,95 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 95:[27, 23], Operations: ['40/10=4', '92/4=23'] Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,95 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,95 unequal: No Solution Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 95:[27, 88], Operations: ['40/10=4', '92-4=88'] Exploring Operation: 27*88=2376, Resulting Numbers: [2376] 2376,95 unequal: No Solution Exploring Operation: 27+88=115, Resulting Numbers: [115] 115,95 unequal: No Solution Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[10, 92, 13], Operations: ['40-27=13'] Exploring Operation: 10+92=102, Resulting Numbers: [13, 102] Generated Node #0,0,0: 95:[13, 102] Operation: 10+92=102 Exploring Operation: 13-10=3, Resulting Numbers: [92, 3] Generated Node #0,0,1: 95:[92, 3] Operation: 13-10=3 Exploring Operation: 92+13=105, Resulting Numbers: [10, 105] Generated Node #0,0,2: 95:[10, 105] Operation: 92+13=105 Exploring Operation: 10+13=23, Resulting Numbers: [92, 23] Generated Node #0,0,3: 95:[92, 23] Operation: 10+13=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 95:[92, 3], Operations: ['40-27=13', '13-10=3'] Exploring Operation: 92*3=276, Resulting Numbers: [276] 276,95 unequal: No Solution Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[10, 40, 92, 27], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [10, 92, 13] Generated Node #0,0: 95:[10, 92, 13] Operation: 40-27=13 Moving to Node #0,0 Current State: 95:[10, 92, 13], Operations: ['40-27=13'] Exploring Operation: 13-10=3, Resulting Numbers: [92, 3] Generated Node #0,0,1: 95:[92, 3] Operation: 13-10=3 Moving to Node #0,0,1 Current State: 95:[92, 3], Operations: ['40-27=13', '13-10=3'] Exploring Operation: 92+3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 98, 4, 90, 88 ]
51
[ "98+4=102", "90-88=2", "102/2=51" ]
Current State: 51:[98, 4, 90, 88], Operations: [] Exploring Operation: 98+4=102, Resulting Numbers: [90, 88, 102] Generated Node #2: [90, 88, 102] from Operation: 98+4=102 Current State: 51:[90, 88, 102], Operations: ['98+4=102'] Exploring Operation: 90-88=2, Resulting Numbers: [102, 2] Generated Node #3: [102, 2] from Operation: 90-88=2 Current State: 51:[102, 2], Operations: ['98+4=102', '90-88=2'] Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[98, 4, 90, 88], Operations: [] Exploring Operation: 98-90=8, Resulting Numbers: [4, 88, 8] Generated Node #0,0: 51:[4, 88, 8] Operation: 98-90=8 Exploring Operation: 98-88=10, Resulting Numbers: [4, 90, 10] Generated Node #0,1: 51:[4, 90, 10] Operation: 98-88=10 Moving to Node #0,0 Current State: 51:[4, 88, 8], Operations: ['98-90=8'] Exploring Operation: 88/8=11, Resulting Numbers: [4, 11] Generated Node #0,0,0: 51:[4, 11] Operation: 88/8=11 Exploring Operation: 88/4=22, Resulting Numbers: [8, 22] Generated Node #0,0,1: 51:[8, 22] Operation: 88/4=22 Moving to Node #0,1 Current State: 51:[4, 90, 10], Operations: ['98-88=10'] Exploring Operation: 90/10=9, Resulting Numbers: [4, 9] Generated Node #0,1,0: 51:[4, 9] Operation: 90/10=9 Exploring Operation: 90-10=80, Resulting Numbers: [4, 80] Generated Node #0,1,1: 51:[4, 80] Operation: 90-10=80 Moving to Node #0,0,0 Current State: 51:[4, 11], Operations: ['98-90=8', '88/8=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,51 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[4, 9], Operations: ['98-88=10', '90/10=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[8, 22], Operations: ['98-90=8', '88/4=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,51 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[4, 80], Operations: ['98-88=10', '90-10=80'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,51 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,51 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 3, 81, 2, 1 ]
53
[ "81/3=27", "2*27=54", "54-1=53" ]
Current State: 53:[3, 81, 2, 1], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [2, 1, 27] Generated Node #2: [2, 1, 27] from Operation: 81/3=27 Current State: 53:[2, 1, 27], Operations: ['81/3=27'] Exploring Operation: 2*27=54, Resulting Numbers: [1, 54] Generated Node #3: [1, 54] from Operation: 2*27=54 Current State: 53:[1, 54], Operations: ['81/3=27', '2*27=54'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[3, 81, 2, 1], Operations: [] Exploring Operation: 3+1=4, Resulting Numbers: [81, 2, 4] Generated Node #0,0: 53:[81, 2, 4] Operation: 3+1=4 Exploring Operation: 81-3=78, Resulting Numbers: [2, 1, 78] Generated Node #0,1: 53:[2, 1, 78] Operation: 81-3=78 Exploring Operation: 3*2=6, Resulting Numbers: [81, 1, 6] Generated Node #0,2: 53:[81, 1, 6] Operation: 3*2=6 Exploring Operation: 3+2=5, Resulting Numbers: [81, 1, 5] Generated Node #0,3: 53:[81, 1, 5] Operation: 3+2=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[81, 1, 6], Operations: ['3*2=6'] Exploring Operation: 81-6=75, Resulting Numbers: [1, 75] Generated Node #0,2,0: 53:[1, 75] Operation: 81-6=75 Exploring Operation: 81*1=81, Resulting Numbers: [6, 81] Generated Node #0,2,1: 53:[6, 81] Operation: 81*1=81 Exploring Operation: 1+6=7, Resulting Numbers: [81, 7] Generated Node #0,2,2: 53:[81, 7] Operation: 1+6=7 Exploring Operation: 81-1=80, Resulting Numbers: [6, 80] Generated Node #0,2,3: 53:[6, 80] Operation: 81-1=80 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[1, 75], Operations: ['3*2=6', '81-6=75'] Exploring Operation: 1*75=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[81, 7], Operations: ['3*2=6', '1+6=7'] Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,53 unequal: No Solution Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[6, 80], Operations: ['3*2=6', '81-1=80'] Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,53 unequal: No Solution Exploring Operation: 6*80=480, Resulting Numbers: [480] 480,53 unequal: No Solution Exploring Operation: 6+80=86, Resulting Numbers: [86] 86,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[6, 81], Operations: ['3*2=6', '81*1=81'] Exploring Operation: 6+81=87, Resulting Numbers: [87] 87,53 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 6*81=486, Resulting Numbers: [486] 486,53 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: 53:[81, 2, 4], Operations: ['3+1=4'] Exploring Operation: 81-4=77, Resulting Numbers: [2, 77] Generated Node #0,0,0: 53:[2, 77] Operation: 81-4=77 Exploring Operation: 2+4=6, Resulting Numbers: [81, 6] Generated Node #0,0,1: 53:[81, 6] Operation: 2+4=6 Exploring Operation: 2*4=8, Resulting Numbers: [81, 8] Generated Node #0,0,2: 53:[81, 8] Operation: 2*4=8 Exploring Operation: 81-2=79, Resulting Numbers: [4, 79] Generated Node #0,0,3: 53:[4, 79] Operation: 81-2=79 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[81, 8], Operations: ['3+1=4', '2*4=8'] Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,53 unequal: No Solution Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,53 unequal: No Solution Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[2, 77], Operations: ['3+1=4', '81-4=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,53 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[81, 6], Operations: ['3+1=4', '2+4=6'] Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,53 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,53 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 53:[4, 79], Operations: ['3+1=4', '81-2=79'] Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,53 unequal: No Solution Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,53 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: 53:[2, 1, 78], Operations: ['81-3=78'] Exploring Operation: 78/2=39, Resulting Numbers: [1, 39] Generated Node #0,1,0: 53:[1, 39] Operation: 78/2=39 Exploring Operation: 78-2=76, Resulting Numbers: [1, 76] Generated Node #0,1,1: 53:[1, 76] Operation: 78-2=76 Exploring Operation: 2+1=3, Resulting Numbers: [78, 3] Generated Node #0,1,2: 53:[78, 3] Operation: 2+1=3 Exploring Operation: 78-1=77, Resulting Numbers: [2, 77] Generated Node #0,1,3: 53:[2, 77] Operation: 78-1=77 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[1, 39], Operations: ['81-3=78', '78/2=39'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,53 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,53 unequal: No Solution Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,53 unequal: No Solution Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[1, 76], Operations: ['81-3=78', '78-2=76'] Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 1*76=76, Resulting Numbers: [76] 76,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[78, 3], Operations: ['81-3=78', '2+1=3'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,53 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 78*3=234, Resulting Numbers: [234] 234,53 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[2, 77], Operations: ['81-3=78', '78-1=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,53 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,53 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: 53:[81, 1, 5], Operations: ['3+2=5'] Exploring Operation: 1+5=6, Resulting Numbers: [81, 6] Generated Node #0,3,0: 53:[81, 6] Operation: 1+5=6 Exploring Operation: 81-1=80, Resulting Numbers: [5, 80] Generated Node #0,3,1: 53:[5, 80] Operation: 81-1=80 Exploring Operation: 81*1=81, Resulting Numbers: [5, 81] Generated Node #0,3,2: 53:[5, 81] Operation: 81*1=81 Exploring Operation: 81-5=76, Resulting Numbers: [1, 76] Generated Node #0,3,3: 53:[1, 76] Operation: 81-5=76 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[81, 6], Operations: ['3+2=5', '1+5=6'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 81+6=87, Resulting Numbers: [87] 87,53 unequal: No Solution Exploring Operation: 81*6=486, Resulting Numbers: [486] 486,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[5, 80], Operations: ['3+2=5', '81-1=80'] Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,53 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,53 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[1, 76], Operations: ['3+2=5', '81-5=76'] Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,53 unequal: No Solution Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 1*76=76, Resulting Numbers: [76] 76,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[5, 81], Operations: ['3+2=5', '81*1=81'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 5*81=405, Resulting Numbers: [405] 405,53 unequal: No Solution Exploring Operation: 5+81=86, Resulting Numbers: [86] 86,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 93, 32, 73, 7 ]
84
[ "93-32=61", "73-61=12", "7*12=84" ]
Current State: 84:[93, 32, 73, 7], Operations: [] Exploring Operation: 93-32=61, Resulting Numbers: [73, 7, 61] Generated Node #2: [73, 7, 61] from Operation: 93-32=61 Current State: 84:[73, 7, 61], Operations: ['93-32=61'] Exploring Operation: 73-61=12, Resulting Numbers: [7, 12] Generated Node #3: [7, 12] from Operation: 73-61=12 Current State: 84:[7, 12], Operations: ['93-32=61', '73-61=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[93, 32, 73, 7], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [32, 7, 20] Generated Node #0,0: 84:[32, 7, 20] Operation: 93-73=20 Exploring Operation: 73-32=41, Resulting Numbers: [93, 7, 41] Generated Node #0,1: 84:[93, 7, 41] Operation: 73-32=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[32, 7, 20], Operations: ['93-73=20'] Exploring Operation: 32-20=12, Resulting Numbers: [7, 12] Generated Node #0,0,0: 84:[7, 12] Operation: 32-20=12 Exploring Operation: 32+7=39, Resulting Numbers: [20, 39] Generated Node #0,0,1: 84:[20, 39] Operation: 32+7=39 Moving to Node #0,0,0 Current State: 84:[7, 12], Operations: ['93-73=20', '32-20=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[93, 32, 73, 7], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [32, 7, 20] Generated Node #0,0: 84:[32, 7, 20] Operation: 93-73=20 Moving to Node #0,0 Current State: 84:[32, 7, 20], Operations: ['93-73=20'] Exploring Operation: 32-20=12, Resulting Numbers: [7, 12] Generated Node #0,0,0: 84:[7, 12] Operation: 32-20=12 Moving to Node #0,0,0 Current State: 84:[7, 12], Operations: ['93-73=20', '32-20=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 34, 5, 58, 47 ]
65
[ "34*5=170", "58+47=105", "170-105=65" ]
Current State: 65:[34, 5, 58, 47], Operations: [] Exploring Operation: 34*5=170, Resulting Numbers: [58, 47, 170] Generated Node #2: [58, 47, 170] from Operation: 34*5=170 Current State: 65:[58, 47, 170], Operations: ['34*5=170'] Exploring Operation: 58+47=105, Resulting Numbers: [170, 105] Generated Node #3: [170, 105] from Operation: 58+47=105 Current State: 65:[170, 105], Operations: ['34*5=170', '58+47=105'] Exploring Operation: 170-105=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[34, 5, 58, 47], Operations: [] Exploring Operation: 47-34=13, Resulting Numbers: [5, 58, 13] Generated Node #0,0: 65:[5, 58, 13] Operation: 47-34=13 Moving to Node #0,0 Current State: 65:[5, 58, 13], Operations: ['47-34=13'] Exploring Operation: 5+58=63, Resulting Numbers: [13, 63] Generated Node #0,0,0: 65:[13, 63] Operation: 5+58=63 Moving to Node #0,0,0 Current State: 65:[13, 63], Operations: ['47-34=13', '5+58=63'] Exploring Operation: 13+63=76, Resulting Numbers: [76] 76,65 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 96, 39, 46, 42 ]
47
[ "96+39=135", "46+42=88", "135-88=47" ]
Current State: 47:[96, 39, 46, 42], Operations: [] Exploring Operation: 96+39=135, Resulting Numbers: [46, 42, 135] Generated Node #2: [46, 42, 135] from Operation: 96+39=135 Current State: 47:[46, 42, 135], Operations: ['96+39=135'] Exploring Operation: 46+42=88, Resulting Numbers: [135, 88] Generated Node #3: [135, 88] from Operation: 46+42=88 Current State: 47:[135, 88], Operations: ['96+39=135', '46+42=88'] Exploring Operation: 135-88=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[96, 39, 46, 42], Operations: [] Exploring Operation: 96-42=54, Resulting Numbers: [39, 46, 54] Generated Node #0,0: 47:[39, 46, 54] Operation: 96-42=54 Exploring Operation: 96-39=57, Resulting Numbers: [46, 42, 57] Generated Node #0,1: 47:[46, 42, 57] Operation: 96-39=57 Exploring Operation: 96-46=50, Resulting Numbers: [39, 42, 50] Generated Node #0,2: 47:[39, 42, 50] Operation: 96-46=50 Moving to Node #0,0 Current State: 47:[39, 46, 54], Operations: ['96-42=54'] Exploring Operation: 46-39=7, Resulting Numbers: [54, 7] Generated Node #0,0,0: 47:[54, 7] Operation: 46-39=7 Exploring Operation: 39+46=85, Resulting Numbers: [54, 85] Generated Node #0,0,1: 47:[54, 85] Operation: 39+46=85 Exploring Operation: 54-39=15, Resulting Numbers: [46, 15] Generated Node #0,0,2: 47:[46, 15] Operation: 54-39=15 Moving to Node #0,1 Current State: 47:[46, 42, 57], Operations: ['96-39=57'] Exploring Operation: 57-42=15, Resulting Numbers: [46, 15] Generated Node #0,1,0: 47:[46, 15] Operation: 57-42=15 Exploring Operation: 46+42=88, Resulting Numbers: [57, 88] Generated Node #0,1,1: 47:[57, 88] Operation: 46+42=88 Exploring Operation: 57-46=11, Resulting Numbers: [42, 11] Generated Node #0,1,2: 47:[42, 11] Operation: 57-46=11 Moving to Node #0,2 Current State: 47:[39, 42, 50], Operations: ['96-46=50'] Exploring Operation: 42-39=3, Resulting Numbers: [50, 3] Generated Node #0,2,0: 47:[50, 3] Operation: 42-39=3 Exploring Operation: 39+42=81, Resulting Numbers: [50, 81] Generated Node #0,2,1: 47:[50, 81] Operation: 39+42=81 Exploring Operation: 50-39=11, Resulting Numbers: [42, 11] Generated Node #0,2,2: 47:[42, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[50, 81], Operations: ['96-46=50', '39+42=81'] Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 50+81=131, Resulting Numbers: [131] 131,47 unequal: No Solution Exploring Operation: 50*81=4050, Resulting Numbers: [4050] 4050,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[42, 11], Operations: ['96-46=50', '50-39=11'] Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[50, 3], Operations: ['96-46=50', '42-39=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[96, 39, 46, 42], Operations: [] Exploring Operation: 96-46=50, Resulting Numbers: [39, 42, 50] Generated Node #0,2: 47:[39, 42, 50] Operation: 96-46=50 Moving to Node #0,2 Current State: 47:[39, 42, 50], Operations: ['96-46=50'] Exploring Operation: 42-39=3, Resulting Numbers: [50, 3] Generated Node #0,2,0: 47:[50, 3] Operation: 42-39=3 Moving to Node #0,2,0 Current State: 47:[50, 3], Operations: ['96-46=50', '42-39=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 10, 90, 57, 90 ]
66
[ "10+57=67", "90/90=1", "67-1=66" ]
Current State: 66:[10, 90, 57, 90], Operations: [] Exploring Operation: 10+57=67, Resulting Numbers: [90, 90, 67] Generated Node #2: [90, 90, 67] from Operation: 10+57=67 Current State: 66:[90, 90, 67], Operations: ['10+57=67'] Exploring Operation: 90/90=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 90/90=1 Current State: 66:[67, 1], Operations: ['10+57=67', '90/90=1'] Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[10, 90, 57, 90], Operations: [] Exploring Operation: 90/10=9, Resulting Numbers: [57, 90, 9] Generated Node #0,0: 66:[57, 90, 9] Operation: 90/10=9 Exploring Operation: 90-57=33, Resulting Numbers: [10, 90, 33] Generated Node #0,1: 66:[10, 90, 33] Operation: 90-57=33 Exploring Operation: 90-57=33, Resulting Numbers: [10, 90, 33] Generated Node #0,2: 66:[10, 90, 33] Operation: 90-57=33 Exploring Operation: 90/90=1, Resulting Numbers: [10, 57, 1] Generated Node #0,3: 66:[10, 57, 1] Operation: 90/90=1 Exploring Operation: 90-90=0, Resulting Numbers: [10, 57, 0] Generated Node #0,4: 66:[10, 57, 0] Operation: 90-90=0 Start Sub Search at level 1: Moving to Node #0,3 Current State: 66:[10, 57, 1], Operations: ['90/90=1'] Exploring Operation: 10*1=10, Resulting Numbers: [57, 10] Generated Node #0,3,0: 66:[57, 10] Operation: 10*1=10 Exploring Operation: 57+1=58, Resulting Numbers: [10, 58] Generated Node #0,3,1: 66:[10, 58] Operation: 57+1=58 Exploring Operation: 10/1=10, Resulting Numbers: [57, 10] Generated Node #0,3,2: 66:[57, 10] Operation: 10/1=10 Exploring Operation: 10+57=67, Resulting Numbers: [1, 67] Generated Node #0,3,3: 66:[1, 67] Operation: 10+57=67 Exploring Operation: 10+1=11, Resulting Numbers: [57, 11] Generated Node #0,3,4: 66:[57, 11] Operation: 10+1=11 Moving to Node #0,3,3 Current State: 66:[1, 67], Operations: ['90/90=1', '10+57=67'] Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,66 unequal: No Solution Exploring Operation: 1+67=68, Resulting Numbers: [68] 68,66 unequal: No Solution Exploring Operation: 1*67=67, Resulting Numbers: [67] 67,66 unequal: No Solution Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[10, 90, 57, 90], Operations: [] Exploring Operation: 90/90=1, Resulting Numbers: [10, 57, 1] Generated Node #0,3: 66:[10, 57, 1] Operation: 90/90=1 Moving to Node #0,3 Current State: 66:[10, 57, 1], Operations: ['90/90=1'] Exploring Operation: 10+57=67, Resulting Numbers: [1, 67] Generated Node #0,3,3: 66:[1, 67] Operation: 10+57=67 Moving to Node #0,3,3 Current State: 66:[1, 67], Operations: ['90/90=1', '10+57=67'] Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 68, 72, 3, 62 ]
75
[ "68+72=140", "3+62=65", "140-65=75" ]
Current State: 75:[68, 72, 3, 62], Operations: [] Exploring Operation: 68+72=140, Resulting Numbers: [3, 62, 140] Generated Node #2: [3, 62, 140] from Operation: 68+72=140 Current State: 75:[3, 62, 140], Operations: ['68+72=140'] Exploring Operation: 3+62=65, Resulting Numbers: [140, 65] Generated Node #3: [140, 65] from Operation: 3+62=65 Current State: 75:[140, 65], Operations: ['68+72=140', '3+62=65'] Exploring Operation: 140-65=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[68, 72, 3, 62], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [68, 3, 10] Generated Node #0,0: 75:[68, 3, 10] Operation: 72-62=10 Exploring Operation: 72+3=75, Resulting Numbers: [68, 62, 75] Generated Node #0,1: 75:[68, 62, 75] Operation: 72+3=75 Exploring Operation: 68+3=71, Resulting Numbers: [72, 62, 71] Generated Node #0,2: 75:[72, 62, 71] Operation: 68+3=71 Exploring Operation: 72-68=4, Resulting Numbers: [3, 62, 4] Generated Node #0,3: 75:[3, 62, 4] Operation: 72-68=4 Exploring Operation: 68-62=6, Resulting Numbers: [72, 3, 6] Generated Node #0,4: 75:[72, 3, 6] Operation: 68-62=6 Start Sub Search at level 1: Moving to Node #0,4 Current State: 75:[72, 3, 6], Operations: ['68-62=6'] Exploring Operation: 72+3=75, Resulting Numbers: [6, 75] Generated Node #0,4,0: 75:[6, 75] Operation: 72+3=75 Exploring Operation: 6-3=3, Resulting Numbers: [72, 3] Generated Node #0,4,1: 75:[72, 3] Operation: 6-3=3 Exploring Operation: 72/3=24, Resulting Numbers: [6, 24] Generated Node #0,4,2: 75:[6, 24] Operation: 72/3=24 Exploring Operation: 72/6=12, Resulting Numbers: [3, 12] Generated Node #0,4,3: 75:[3, 12] Operation: 72/6=12 Exploring Operation: 72+6=78, Resulting Numbers: [3, 78] Generated Node #0,4,4: 75:[3, 78] Operation: 72+6=78 Moving to Node #0,4,0 Current State: 75:[6, 75], Operations: ['68-62=6', '72+3=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,75 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,75 unequal: No Solution Moving to Node #0,4,2 Current State: 75:[6, 24], Operations: ['68-62=6', '72/3=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,75 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,75 unequal: No Solution Moving to Node #0,4,1 Current State: 75:[72, 3], Operations: ['68-62=6', '6-3=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[68, 72, 3, 62], Operations: [] Exploring Operation: 68-62=6, Resulting Numbers: [72, 3, 6] Generated Node #0,4: 75:[72, 3, 6] Operation: 68-62=6 Moving to Node #0,4 Current State: 75:[72, 3, 6], Operations: ['68-62=6'] Exploring Operation: 6-3=3, Resulting Numbers: [72, 3] Generated Node #0,4,1: 75:[72, 3] Operation: 6-3=3 Moving to Node #0,4,1 Current State: 75:[72, 3], Operations: ['68-62=6', '6-3=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 62, 99, 31, 57 ]
21
[ "62/31=2", "99-57=42", "42/2=21" ]
Current State: 21:[62, 99, 31, 57], Operations: [] Exploring Operation: 62/31=2, Resulting Numbers: [99, 57, 2] Generated Node #2: [99, 57, 2] from Operation: 62/31=2 Current State: 21:[99, 57, 2], Operations: ['62/31=2'] Exploring Operation: 99-57=42, Resulting Numbers: [2, 42] Generated Node #3: [2, 42] from Operation: 99-57=42 Current State: 21:[2, 42], Operations: ['62/31=2', '99-57=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[62, 99, 31, 57], Operations: [] Exploring Operation: 99-62=37, Resulting Numbers: [31, 57, 37] Generated Node #0,0: 21:[31, 57, 37] Operation: 99-62=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[31, 57, 37], Operations: ['99-62=37'] Exploring Operation: 57-37=20, Resulting Numbers: [31, 20] Generated Node #0,0,0: 21:[31, 20] Operation: 57-37=20 Moving to Node #0,0,0 Current State: 21:[31, 20], Operations: ['99-62=37', '57-37=20'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 47, 47, 22, 8 ]
29
[ "47/47=1", "22+8=30", "30-1=29" ]
Current State: 29:[47, 47, 22, 8], Operations: [] Exploring Operation: 47/47=1, Resulting Numbers: [22, 8, 1] Generated Node #2: [22, 8, 1] from Operation: 47/47=1 Current State: 29:[22, 8, 1], Operations: ['47/47=1'] Exploring Operation: 22+8=30, Resulting Numbers: [1, 30] Generated Node #3: [1, 30] from Operation: 22+8=30 Current State: 29:[1, 30], Operations: ['47/47=1', '22+8=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[47, 47, 22, 8], Operations: [] Exploring Operation: 47-8=39, Resulting Numbers: [47, 22, 39] Generated Node #0,0: 29:[47, 22, 39] Operation: 47-8=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[47, 22, 39], Operations: ['47-8=39'] Exploring Operation: 47-22=25, Resulting Numbers: [39, 25] Generated Node #0,0,0: 29:[39, 25] Operation: 47-22=25 Moving to Node #0,0,0 Current State: 29:[39, 25], Operations: ['47-8=39', '47-22=25'] Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,29 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, 2, 49, 21 ]
27
[ "2-1=1", "49-21=28", "28-1=27" ]
Current State: 27:[1, 2, 49, 21], Operations: [] Exploring Operation: 2-1=1, Resulting Numbers: [49, 21, 1] Generated Node #2: [49, 21, 1] from Operation: 2-1=1 Current State: 27:[49, 21, 1], Operations: ['2-1=1'] Exploring Operation: 49-21=28, Resulting Numbers: [1, 28] Generated Node #3: [1, 28] from Operation: 49-21=28 Current State: 27:[1, 28], Operations: ['2-1=1', '49-21=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[1, 2, 49, 21], Operations: [] Exploring Operation: 49-21=28, Resulting Numbers: [1, 2, 28] Generated Node #0,0: 27:[1, 2, 28] Operation: 49-21=28 Exploring Operation: 1+2=3, Resulting Numbers: [49, 21, 3] Generated Node #0,1: 27:[49, 21, 3] Operation: 1+2=3 Exploring Operation: 49-1=48, Resulting Numbers: [2, 21, 48] Generated Node #0,2: 27:[2, 21, 48] Operation: 49-1=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[1, 2, 28], Operations: ['49-21=28'] Exploring Operation: 1*2=2, Resulting Numbers: [28, 2] Generated Node #0,0,0: 27:[28, 2] Operation: 1*2=2 Exploring Operation: 28-1=27, Resulting Numbers: [2, 27] Generated Node #0,0,1: 27:[2, 27] Operation: 28-1=27 Exploring Operation: 1+2=3, Resulting Numbers: [28, 3] Generated Node #0,0,2: 27:[28, 3] Operation: 1+2=3 Moving to Node #0,0,1 Current State: 27:[2, 27], Operations: ['49-21=28', '28-1=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[28, 3], Operations: ['49-21=28', '1+2=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,27 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,27 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[28, 2], Operations: ['49-21=28', '1*2=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,27 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,27 unequal: No Solution No 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: 27:[49, 21, 3], Operations: ['1+2=3'] Exploring Operation: 49-21=28, Resulting Numbers: [3, 28] Generated Node #0,1,0: 27:[3, 28] Operation: 49-21=28 Exploring Operation: 21/3=7, Resulting Numbers: [49, 7] Generated Node #0,1,1: 27:[49, 7] Operation: 21/3=7 Exploring Operation: 49-3=46, Resulting Numbers: [21, 46] Generated Node #0,1,2: 27:[21, 46] Operation: 49-3=46 Moving to Node #0,1,0 Current State: 27:[3, 28], Operations: ['1+2=3', '49-21=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,27 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[49, 7], Operations: ['1+2=3', '21/3=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,27 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[21, 46], Operations: ['1+2=3', '49-3=46'] Exploring Operation: 21*46=966, Resulting Numbers: [966] 966,27 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 21+46=67, Resulting Numbers: [67] 67,27 unequal: No Solution No 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: 27:[2, 21, 48], Operations: ['49-1=48'] Exploring Operation: 48/2=24, Resulting Numbers: [21, 24] Generated Node #0,2,0: 27:[21, 24] Operation: 48/2=24 Exploring Operation: 48-21=27, Resulting Numbers: [2, 27] Generated Node #0,2,1: 27:[2, 27] Operation: 48-21=27 Exploring Operation: 2+21=23, Resulting Numbers: [48, 23] Generated Node #0,2,2: 27:[48, 23] Operation: 2+21=23 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 27:[2, 27], Operations: ['49-1=48', '48-21=27'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,27 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 27:[21, 24], Operations: ['49-1=48', '48/2=24'] Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,27 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 27:[48, 23], Operations: ['49-1=48', '2+21=23'] Exploring Operation: 48*23=1104, Resulting Numbers: [1104] 1104,27 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 11, 85, 28, 18 ]
81
[ "18-11=7", "28/7=4", "85-4=81" ]
Current State: 81:[11, 85, 28, 18], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [85, 28, 7] Generated Node #2: [85, 28, 7] from Operation: 18-11=7 Current State: 81:[85, 28, 7], Operations: ['18-11=7'] Exploring Operation: 28/7=4, Resulting Numbers: [85, 4] Generated Node #3: [85, 4] from Operation: 28/7=4 Current State: 81:[85, 4], Operations: ['18-11=7', '28/7=4'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[11, 85, 28, 18], Operations: [] Exploring Operation: 11+18=29, Resulting Numbers: [85, 28, 29] Generated Node #0,0: 81:[85, 28, 29] Operation: 11+18=29 Exploring Operation: 85-11=74, Resulting Numbers: [28, 18, 74] Generated Node #0,1: 81:[28, 18, 74] Operation: 85-11=74 Exploring Operation: 28-18=10, Resulting Numbers: [11, 85, 10] Generated Node #0,2: 81:[11, 85, 10] Operation: 28-18=10 Exploring Operation: 85-18=67, Resulting Numbers: [11, 28, 67] Generated Node #0,3: 81:[11, 28, 67] Operation: 85-18=67 Exploring Operation: 18-11=7, Resulting Numbers: [85, 28, 7] Generated Node #0,4: 81:[85, 28, 7] Operation: 18-11=7 Moving to Node #0,0 Current State: 81:[85, 28, 29], Operations: ['11+18=29'] Exploring Operation: 29-28=1, Resulting Numbers: [85, 1] Generated Node #0,0,0: 81:[85, 1] Operation: 29-28=1 Exploring Operation: 85+28=113, Resulting Numbers: [29, 113] Generated Node #0,0,1: 81:[29, 113] Operation: 85+28=113 Exploring Operation: 28+29=57, Resulting Numbers: [85, 57] Generated Node #0,0,2: 81:[85, 57] Operation: 28+29=57 Exploring Operation: 85-29=56, Resulting Numbers: [28, 56] Generated Node #0,0,3: 81:[28, 56] Operation: 85-29=56 Exploring Operation: 85-28=57, Resulting Numbers: [29, 57] Generated Node #0,0,4: 81:[29, 57] Operation: 85-28=57 Moving to Node #0,4 Current State: 81:[85, 28, 7], Operations: ['18-11=7'] Exploring Operation: 28/7=4, Resulting Numbers: [85, 4] Generated Node #0,4,0: 81:[85, 4] Operation: 28/7=4 Exploring Operation: 85-7=78, Resulting Numbers: [28, 78] Generated Node #0,4,1: 81:[28, 78] Operation: 85-7=78 Exploring Operation: 28+7=35, Resulting Numbers: [85, 35] Generated Node #0,4,2: 81:[85, 35] Operation: 28+7=35 Exploring Operation: 28-7=21, Resulting Numbers: [85, 21] Generated Node #0,4,3: 81:[85, 21] Operation: 28-7=21 Exploring Operation: 85+7=92, Resulting Numbers: [28, 92] Generated Node #0,4,4: 81:[28, 92] Operation: 85+7=92 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 81:[28, 78], Operations: ['18-11=7', '85-7=78'] Exploring Operation: 28+78=106, Resulting Numbers: [106] 106,81 unequal: No Solution Exploring Operation: 28*78=2184, Resulting Numbers: [2184] 2184,81 unequal: No Solution Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,81 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 #0,4,0 Current State: 81:[85, 4], Operations: ['18-11=7', '28/7=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 85*4=340, Resulting Numbers: [340] 340,81 unequal: No Solution Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[11, 85, 28, 18], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [85, 28, 7] Generated Node #0,4: 81:[85, 28, 7] Operation: 18-11=7 Moving to Node #0,4 Current State: 81:[85, 28, 7], Operations: ['18-11=7'] Exploring Operation: 28/7=4, Resulting Numbers: [85, 4] Generated Node #0,4,0: 81:[85, 4] Operation: 28/7=4 Moving to Node #0,4,0 Current State: 81:[85, 4], Operations: ['18-11=7', '28/7=4'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 29, 16, 92, 5 ]
69
[ "29*5=145", "92-16=76", "145-76=69" ]
Current State: 69:[29, 16, 92, 5], Operations: [] Exploring Operation: 29*5=145, Resulting Numbers: [16, 92, 145] Generated Node #2: [16, 92, 145] from Operation: 29*5=145 Current State: 69:[16, 92, 145], Operations: ['29*5=145'] Exploring Operation: 92-16=76, Resulting Numbers: [145, 76] Generated Node #3: [145, 76] from Operation: 92-16=76 Current State: 69:[145, 76], Operations: ['29*5=145', '92-16=76'] Exploring Operation: 145-76=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[29, 16, 92, 5], Operations: [] Exploring Operation: 92-29=63, Resulting Numbers: [16, 5, 63] Generated Node #0,0: 69:[16, 5, 63] Operation: 92-29=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[16, 5, 63], Operations: ['92-29=63'] Exploring Operation: 16+5=21, Resulting Numbers: [63, 21] Generated Node #0,0,0: 69:[63, 21] Operation: 16+5=21 Moving to Node #0,0,0 Current State: 69:[63, 21], Operations: ['92-29=63', '16+5=21'] Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,69 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
[ 78, 75, 42, 73 ]
27
[ "78-73=5", "75/5=15", "42-15=27" ]
Current State: 27:[78, 75, 42, 73], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [75, 42, 5] Generated Node #2: [75, 42, 5] from Operation: 78-73=5 Current State: 27:[75, 42, 5], Operations: ['78-73=5'] Exploring Operation: 75/5=15, Resulting Numbers: [42, 15] Generated Node #3: [42, 15] from Operation: 75/5=15 Current State: 27:[42, 15], Operations: ['78-73=5', '75/5=15'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[78, 75, 42, 73], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [42, 73, 3] Generated Node #0,0: 27:[42, 73, 3] Operation: 78-75=3 Exploring Operation: 78-73=5, Resulting Numbers: [75, 42, 5] Generated Node #0,1: 27:[75, 42, 5] Operation: 78-73=5 Exploring Operation: 78-42=36, Resulting Numbers: [75, 73, 36] Generated Node #0,2: 27:[75, 73, 36] Operation: 78-42=36 Exploring Operation: 75-73=2, Resulting Numbers: [78, 42, 2] Generated Node #0,3: 27:[78, 42, 2] Operation: 75-73=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[42, 73, 3], Operations: ['78-75=3'] Exploring Operation: 73-3=70, Resulting Numbers: [42, 70] Generated Node #0,0,0: 27:[42, 70] Operation: 73-3=70 Exploring Operation: 42/3=14, Resulting Numbers: [73, 14] Generated Node #0,0,1: 27:[73, 14] Operation: 42/3=14 Exploring Operation: 42-3=39, Resulting Numbers: [73, 39] Generated Node #0,0,2: 27:[73, 39] Operation: 42-3=39 Exploring Operation: 73-42=31, Resulting Numbers: [3, 31] Generated Node #0,0,3: 27:[3, 31] Operation: 73-42=31 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 27:[3, 31], Operations: ['78-75=3', '73-42=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,27 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 27:[73, 14], Operations: ['78-75=3', '42/3=14'] Exploring Operation: 73*14=1022, Resulting Numbers: [1022] 1022,27 unequal: No Solution Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,27 unequal: No Solution Exploring Operation: 73+14=87, Resulting Numbers: [87] 87,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[42, 70], Operations: ['78-75=3', '73-3=70'] Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 42*70=2940, Resulting Numbers: [2940] 2940,27 unequal: No Solution Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 27:[73, 39], Operations: ['78-75=3', '42-3=39'] Exploring Operation: 73*39=2847, Resulting Numbers: [2847] 2847,27 unequal: No Solution Exploring Operation: 73+39=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 73-39=34, Resulting Numbers: [34] 34,27 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: 27:[75, 42, 5], Operations: ['78-73=5'] Exploring Operation: 75-42=33, Resulting Numbers: [5, 33] Generated Node #0,1,0: 27:[5, 33] Operation: 75-42=33 Exploring Operation: 75/5=15, Resulting Numbers: [42, 15] Generated Node #0,1,1: 27:[42, 15] Operation: 75/5=15 Exploring Operation: 75-5=70, Resulting Numbers: [42, 70] Generated Node #0,1,2: 27:[42, 70] Operation: 75-5=70 Exploring Operation: 42-5=37, Resulting Numbers: [75, 37] Generated Node #0,1,3: 27:[75, 37] Operation: 42-5=37 Moving to Node #0,1,0 Current State: 27:[5, 33], Operations: ['78-73=5', '75-42=33'] Exploring Operation: 5*33=165, Resulting Numbers: [165] 165,27 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[42, 15], Operations: ['78-73=5', '75/5=15'] Exploring Operation: 42*15=630, Resulting Numbers: [630] 630,27 unequal: No Solution Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[78, 75, 42, 73], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [75, 42, 5] Generated Node #0,1: 27:[75, 42, 5] Operation: 78-73=5 Moving to Node #0,1 Current State: 27:[75, 42, 5], Operations: ['78-73=5'] Exploring Operation: 75/5=15, Resulting Numbers: [42, 15] Generated Node #0,1,1: 27:[42, 15] Operation: 75/5=15 Moving to Node #0,1,1 Current State: 27:[42, 15], Operations: ['78-73=5', '75/5=15'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 26, 8, 71, 51 ]
38
[ "26-8=18", "71-51=20", "18+20=38" ]
Current State: 38:[26, 8, 71, 51], Operations: [] Exploring Operation: 26-8=18, Resulting Numbers: [71, 51, 18] Generated Node #2: [71, 51, 18] from Operation: 26-8=18 Current State: 38:[71, 51, 18], Operations: ['26-8=18'] Exploring Operation: 71-51=20, Resulting Numbers: [18, 20] Generated Node #3: [18, 20] from Operation: 71-51=20 Current State: 38:[18, 20], Operations: ['26-8=18', '71-51=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[26, 8, 71, 51], Operations: [] Exploring Operation: 71-51=20, Resulting Numbers: [26, 8, 20] Generated Node #0,0: 38:[26, 8, 20] Operation: 71-51=20 Exploring Operation: 71-26=45, Resulting Numbers: [8, 51, 45] Generated Node #0,1: 38:[8, 51, 45] Operation: 71-26=45 Exploring Operation: 51-26=25, Resulting Numbers: [8, 71, 25] Generated Node #0,2: 38:[8, 71, 25] Operation: 51-26=25 Exploring Operation: 71-8=63, Resulting Numbers: [26, 51, 63] Generated Node #0,3: 38:[26, 51, 63] Operation: 71-8=63 Moving to Node #0,0 Current State: 38:[26, 8, 20], Operations: ['71-51=20'] Exploring Operation: 26+8=34, Resulting Numbers: [20, 34] Generated Node #0,0,0: 38:[20, 34] Operation: 26+8=34 Exploring Operation: 26-20=6, Resulting Numbers: [8, 6] Generated Node #0,0,1: 38:[8, 6] Operation: 26-20=6 Exploring Operation: 26-8=18, Resulting Numbers: [20, 18] Generated Node #0,0,2: 38:[20, 18] Operation: 26-8=18 Exploring Operation: 26+20=46, Resulting Numbers: [8, 46] Generated Node #0,0,3: 38:[8, 46] Operation: 26+20=46 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[20, 18], Operations: ['71-51=20', '26-8=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[26, 8, 71, 51], Operations: [] Exploring Operation: 71-51=20, Resulting Numbers: [26, 8, 20] Generated Node #0,0: 38:[26, 8, 20] Operation: 71-51=20 Moving to Node #0,0 Current State: 38:[26, 8, 20], Operations: ['71-51=20'] Exploring Operation: 26-8=18, Resulting Numbers: [20, 18] Generated Node #0,0,2: 38:[20, 18] Operation: 26-8=18 Moving to Node #0,0,2 Current State: 38:[20, 18], Operations: ['71-51=20', '26-8=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 92, 99, 77, 81 ]
86
[ "92-81=11", "99/11=9", "77+9=86" ]
Current State: 86:[92, 99, 77, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [99, 77, 11] Generated Node #2: [99, 77, 11] from Operation: 92-81=11 Current State: 86:[99, 77, 11], Operations: ['92-81=11'] Exploring Operation: 99/11=9, Resulting Numbers: [77, 9] Generated Node #3: [77, 9] from Operation: 99/11=9 Current State: 86:[77, 9], Operations: ['92-81=11', '99/11=9'] Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[92, 99, 77, 81], Operations: [] Exploring Operation: 81-77=4, Resulting Numbers: [92, 99, 4] Generated Node #0,0: 86:[92, 99, 4] Operation: 81-77=4 Exploring Operation: 99-77=22, Resulting Numbers: [92, 81, 22] Generated Node #0,1: 86:[92, 81, 22] Operation: 99-77=22 Exploring Operation: 99-92=7, Resulting Numbers: [77, 81, 7] Generated Node #0,2: 86:[77, 81, 7] Operation: 99-92=7 Exploring Operation: 92-81=11, Resulting Numbers: [99, 77, 11] Generated Node #0,3: 86:[99, 77, 11] Operation: 92-81=11 Exploring Operation: 92-77=15, Resulting Numbers: [99, 81, 15] Generated Node #0,4: 86:[99, 81, 15] Operation: 92-77=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[77, 81, 7], Operations: ['99-92=7'] Exploring Operation: 81+7=88, Resulting Numbers: [77, 88] Generated Node #0,2,0: 86:[77, 88] Operation: 81+7=88 Exploring Operation: 77-7=70, Resulting Numbers: [81, 70] Generated Node #0,2,1: 86:[81, 70] Operation: 77-7=70 Exploring Operation: 77+7=84, Resulting Numbers: [81, 84] Generated Node #0,2,2: 86:[81, 84] Operation: 77+7=84 Exploring Operation: 81-77=4, Resulting Numbers: [7, 4] Generated Node #0,2,3: 86:[7, 4] Operation: 81-77=4 Exploring Operation: 77/7=11, Resulting Numbers: [81, 11] Generated Node #0,2,4: 86:[81, 11] Operation: 77/7=11 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 86:[81, 84], Operations: ['99-92=7', '77+7=84'] Exploring Operation: 84-81=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 81+84=165, Resulting Numbers: [165] 165,86 unequal: No Solution Exploring Operation: 81*84=6804, Resulting Numbers: [6804] 6804,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 86:[7, 4], Operations: ['99-92=7', '81-77=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 86:[77, 88], Operations: ['99-92=7', '81+7=88'] Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,86 unequal: No Solution Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 86:[81, 11], Operations: ['99-92=7', '77/7=11'] Exploring Operation: 81*11=891, Resulting Numbers: [891] 891,86 unequal: No Solution Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,86 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[81, 70], Operations: ['99-92=7', '77-7=70'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,86 unequal: No Solution Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[92, 99, 4], Operations: ['81-77=4'] Exploring Operation: 92+4=96, Resulting Numbers: [99, 96] Generated Node #0,0,0: 86:[99, 96] Operation: 92+4=96 Exploring Operation: 99-4=95, Resulting Numbers: [92, 95] Generated Node #0,0,1: 86:[92, 95] Operation: 99-4=95 Exploring Operation: 99+4=103, Resulting Numbers: [92, 103] Generated Node #0,0,2: 86:[92, 103] Operation: 99+4=103 Exploring Operation: 92-4=88, Resulting Numbers: [99, 88] Generated Node #0,0,3: 86:[99, 88] Operation: 92-4=88 Exploring Operation: 99-92=7, Resulting Numbers: [4, 7] Generated Node #0,0,4: 86:[4, 7] Operation: 99-92=7 Moving to Node #0,0,4 Current State: 86:[4, 7], Operations: ['81-77=4', '99-92=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[99, 88], Operations: ['81-77=4', '92-4=88'] Exploring Operation: 99+88=187, Resulting Numbers: [187] 187,86 unequal: No Solution Exploring Operation: 99*88=8712, Resulting Numbers: [8712] 8712,86 unequal: No Solution Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[92, 95], Operations: ['81-77=4', '99-4=95'] Exploring Operation: 95-92=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 92*95=8740, Resulting Numbers: [8740] 8740,86 unequal: No Solution Exploring Operation: 92+95=187, Resulting Numbers: [187] 187,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[99, 96], Operations: ['81-77=4', '92+4=96'] Exploring Operation: 99*96=9504, Resulting Numbers: [9504] 9504,86 unequal: No Solution Exploring Operation: 99+96=195, Resulting Numbers: [195] 195,86 unequal: No Solution Exploring Operation: 99-96=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[92, 103], Operations: ['81-77=4', '99+4=103'] Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,86 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,86 unequal: No Solution Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,86 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 #0,1 Current State: 86:[92, 81, 22], Operations: ['99-77=22'] Exploring Operation: 92+22=114, Resulting Numbers: [81, 114] Generated Node #0,1,0: 86:[81, 114] Operation: 92+22=114 Exploring Operation: 81-22=59, Resulting Numbers: [92, 59] Generated Node #0,1,1: 86:[92, 59] Operation: 81-22=59 Exploring Operation: 92-81=11, Resulting Numbers: [22, 11] Generated Node #0,1,2: 86:[22, 11] Operation: 92-81=11 Exploring Operation: 92-22=70, Resulting Numbers: [81, 70] Generated Node #0,1,3: 86:[81, 70] Operation: 92-22=70 Exploring Operation: 81+22=103, Resulting Numbers: [92, 103] Generated Node #0,1,4: 86:[92, 103] Operation: 81+22=103 Moving to Node #0,1,3 Current State: 86:[81, 70], Operations: ['99-77=22', '92-22=70'] Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,86 unequal: No Solution Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[92, 59], Operations: ['99-77=22', '81-22=59'] Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 92+59=151, Resulting Numbers: [151] 151,86 unequal: No Solution Exploring Operation: 92*59=5428, Resulting Numbers: [5428] 5428,86 unequal: No Solution Moving to Node #0,1,4 Current State: 86:[92, 103], Operations: ['99-77=22', '81+22=103'] Exploring Operation: 103-92=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 92*103=9476, Resulting Numbers: [9476] 9476,86 unequal: No Solution Exploring Operation: 92+103=195, Resulting Numbers: [195] 195,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[22, 11], Operations: ['99-77=22', '92-81=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,86 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,86 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[81, 114], Operations: ['99-77=22', '92+22=114'] Exploring Operation: 81*114=9234, Resulting Numbers: [9234] 9234,86 unequal: No Solution Exploring Operation: 81+114=195, Resulting Numbers: [195] 195,86 unequal: No Solution Exploring Operation: 114-81=33, Resulting Numbers: [33] 33,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[99, 77, 11], Operations: ['92-81=11'] Exploring Operation: 99-11=88, Resulting Numbers: [77, 88] Generated Node #0,3,0: 86:[77, 88] Operation: 99-11=88 Exploring Operation: 77+11=88, Resulting Numbers: [99, 88] Generated Node #0,3,1: 86:[99, 88] Operation: 77+11=88 Exploring Operation: 99-77=22, Resulting Numbers: [11, 22] Generated Node #0,3,2: 86:[11, 22] Operation: 99-77=22 Exploring Operation: 77/11=7, Resulting Numbers: [99, 7] Generated Node #0,3,3: 86:[99, 7] Operation: 77/11=7 Exploring Operation: 99/11=9, Resulting Numbers: [77, 9] Generated Node #0,3,4: 86:[77, 9] Operation: 99/11=9 Moving to Node #0,3,0 Current State: 86:[77, 88], Operations: ['92-81=11', '99-11=88'] Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,86 unequal: No Solution Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[99, 88], Operations: ['92-81=11', '77+11=88'] Exploring Operation: 99*88=8712, Resulting Numbers: [8712] 8712,86 unequal: No Solution Exploring Operation: 99-88=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 99+88=187, Resulting Numbers: [187] 187,86 unequal: No Solution Moving to Node #0,3,4 Current State: 86:[77, 9], Operations: ['92-81=11', '99/11=9'] Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,86 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[92, 99, 77, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [99, 77, 11] Generated Node #0,3: 86:[99, 77, 11] Operation: 92-81=11 Moving to Node #0,3 Current State: 86:[99, 77, 11], Operations: ['92-81=11'] Exploring Operation: 99/11=9, Resulting Numbers: [77, 9] Generated Node #0,3,4: 86:[77, 9] Operation: 99/11=9 Moving to Node #0,3,4 Current State: 86:[77, 9], Operations: ['92-81=11', '99/11=9'] Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.927083
hs_5
mult_heuristic
[ 64, 24, 40, 48 ]
32
[ "64-24=40", "48-40=8", "40-8=32" ]
Current State: 32:[64, 24, 40, 48], Operations: [] Exploring Operation: 64-24=40, Resulting Numbers: [40, 48, 40] Generated Node #2: [40, 48, 40] from Operation: 64-24=40 Current State: 32:[40, 48, 40], Operations: ['64-24=40'] Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,32 equal: Goal Reached Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[64, 24, 40, 48], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [64, 24, 8] Generated Node #0,0: 32:[64, 24, 8] Operation: 48-40=8 Exploring Operation: 64-48=16, Resulting Numbers: [24, 40, 16] Generated Node #0,1: 32:[24, 40, 16] Operation: 64-48=16 Exploring Operation: 64-40=24, Resulting Numbers: [24, 48, 24] Generated Node #0,2: 32:[24, 48, 24] Operation: 64-40=24 Exploring Operation: 48/24=2, Resulting Numbers: [64, 40, 2] Generated Node #0,3: 32:[64, 40, 2] Operation: 48/24=2 Exploring Operation: 64-24=40, Resulting Numbers: [40, 48, 40] Generated Node #0,4: 32:[40, 48, 40] Operation: 64-24=40 Moving to Node #0,1 Current State: 32:[24, 40, 16], Operations: ['64-48=16'] Exploring Operation: 24+40=64, Resulting Numbers: [16, 64] Generated Node #0,1,0: 32:[16, 64] Operation: 24+40=64 Exploring Operation: 40-16=24, Resulting Numbers: [24, 24] Generated Node #0,1,1: 32:[24, 24] Operation: 40-16=24 Exploring Operation: 24+16=40, Resulting Numbers: [40, 40] Generated Node #0,1,2: 32:[40, 40] Operation: 24+16=40 Exploring Operation: 24-16=8, Resulting Numbers: [40, 8] Generated Node #0,1,3: 32:[40, 8] Operation: 24-16=8 Exploring Operation: 40-24=16, Resulting Numbers: [16, 16] Generated Node #0,1,4: 32:[16, 16] Operation: 40-24=16 Moving to Node #0,4 Current State: 32:[40, 48, 40], Operations: ['64-24=40'] Exploring Operation: 40+48=88, Resulting Numbers: [40, 88] Generated Node #0,4,0: 32:[40, 88] Operation: 40+48=88 Exploring Operation: 40-40=0, Resulting Numbers: [48, 0] Generated Node #0,4,1: 32:[48, 0] Operation: 40-40=0 Exploring Operation: 40/40=1, Resulting Numbers: [48, 1] Generated Node #0,4,2: 32:[48, 1] Operation: 40/40=1 Exploring Operation: 48-40=8, Resulting Numbers: [40, 8] Generated Node #0,4,3: 32:[40, 8] Operation: 48-40=8 Exploring Operation: 48-40=8, Resulting Numbers: [40, 8] Generated Node #0,4,4: 32:[40, 8] Operation: 48-40=8 Moving to Node #0,2 Current State: 32:[24, 48, 24], Operations: ['64-40=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24, 24] Generated Node #0,2,0: 32:[24, 24] Operation: 48-24=24 Exploring Operation: 48-24=24, Resulting Numbers: [24, 24] Generated Node #0,2,1: 32:[24, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [24, 2] Generated Node #0,2,2: 32:[24, 2] Operation: 48/24=2 Exploring Operation: 48/24=2, Resulting Numbers: [24, 2] Generated Node #0,2,3: 32:[24, 2] Operation: 48/24=2 Exploring Operation: 24/24=1, Resulting Numbers: [48, 1] Generated Node #0,2,4: 32:[48, 1] Operation: 24/24=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 32:[24, 2], Operations: ['64-40=24', '48/24=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 32:[24, 2], Operations: ['64-40=24', '48/24=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[24, 24], Operations: ['64-40=24', '48-24=24'] Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,32 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,32 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[24, 24], Operations: ['64-40=24', '48-24=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,32 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,32 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 32:[48, 1], Operations: ['64-40=24', '24/24=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,32 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: 32:[64, 24, 8], Operations: ['48-40=8'] Exploring Operation: 64/8=8, Resulting Numbers: [24, 8] Generated Node #0,0,0: 32:[24, 8] Operation: 64/8=8 Exploring Operation: 24+8=32, Resulting Numbers: [64, 32] Generated Node #0,0,1: 32:[64, 32] Operation: 24+8=32 Exploring Operation: 64-8=56, Resulting Numbers: [24, 56] Generated Node #0,0,2: 32:[24, 56] Operation: 64-8=56 Exploring Operation: 64-24=40, Resulting Numbers: [8, 40] Generated Node #0,0,3: 32:[8, 40] Operation: 64-24=40 Exploring Operation: 24-8=16, Resulting Numbers: [64, 16] Generated Node #0,0,4: 32:[64, 16] Operation: 24-8=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[24, 8], Operations: ['48-40=8', '64/8=8'] Exploring Operation: 24/8=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 24*8=192, Resulting Numbers: [192] 192,32 unequal: No Solution Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[64, 24, 40, 48], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [64, 24, 8] Generated Node #0,0: 32:[64, 24, 8] Operation: 48-40=8 Moving to Node #0,0 Current State: 32:[64, 24, 8], Operations: ['48-40=8'] Exploring Operation: 64/8=8, Resulting Numbers: [24, 8] Generated Node #0,0,0: 32:[24, 8] Operation: 64/8=8 Moving to Node #0,0,0 Current State: 32:[24, 8], Operations: ['48-40=8', '64/8=8'] Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_5
mult_heuristic
[ 63, 90, 81, 51 ]
84
[ "63+90=153", "153/51=3", "81+3=84" ]
Current State: 84:[63, 90, 81, 51], Operations: [] Exploring Operation: 63+90=153, Resulting Numbers: [81, 51, 153] Generated Node #2: [81, 51, 153] from Operation: 63+90=153 Current State: 84:[81, 51, 153], Operations: ['63+90=153'] Exploring Operation: 153/51=3, Resulting Numbers: [81, 3] Generated Node #3: [81, 3] from Operation: 153/51=3 Current State: 84:[81, 3], Operations: ['63+90=153', '153/51=3'] Exploring Operation: 81+3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[63, 90, 81, 51], Operations: [] Exploring Operation: 63-51=12, Resulting Numbers: [90, 81, 12] Generated Node #0,0: 84:[90, 81, 12] Operation: 63-51=12 Exploring Operation: 90-63=27, Resulting Numbers: [81, 51, 27] Generated Node #0,1: 84:[81, 51, 27] Operation: 90-63=27 Exploring Operation: 81-63=18, Resulting Numbers: [90, 51, 18] Generated Node #0,2: 84:[90, 51, 18] Operation: 81-63=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[90, 81, 12], Operations: ['63-51=12'] Exploring Operation: 81+12=93, Resulting Numbers: [90, 93] Generated Node #0,0,0: 84:[90, 93] Operation: 81+12=93 Exploring Operation: 90-12=78, Resulting Numbers: [81, 78] Generated Node #0,0,1: 84:[81, 78] Operation: 90-12=78 Exploring Operation: 90-81=9, Resulting Numbers: [12, 9] Generated Node #0,0,2: 84:[12, 9] Operation: 90-81=9 Moving to Node #0,0,2 Current State: 84:[12, 9], Operations: ['63-51=12', '90-81=9'] Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,84 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[81, 78], Operations: ['63-51=12', '90-12=78'] Exploring Operation: 81+78=159, Resulting Numbers: [159] 159,84 unequal: No Solution Exploring Operation: 81*78=6318, Resulting Numbers: [6318] 6318,84 unequal: No Solution Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[90, 93], Operations: ['63-51=12', '81+12=93'] Exploring Operation: 90+93=183, Resulting Numbers: [183] 183,84 unequal: No Solution Exploring Operation: 90*93=8370, Resulting Numbers: [8370] 8370,84 unequal: No Solution Exploring Operation: 93-90=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 #0,1 Current State: 84:[81, 51, 27], Operations: ['90-63=27'] Exploring Operation: 81/27=3, Resulting Numbers: [51, 3] Generated Node #0,1,0: 84:[51, 3] Operation: 81/27=3 Exploring Operation: 81-51=30, Resulting Numbers: [27, 30] Generated Node #0,1,1: 84:[27, 30] Operation: 81-51=30 Exploring Operation: 51-27=24, Resulting Numbers: [81, 24] Generated Node #0,1,2: 84:[81, 24] Operation: 51-27=24 Moving to Node #0,1,1 Current State: 84:[27, 30], Operations: ['90-63=27', '81-51=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,84 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[81, 24], Operations: ['90-63=27', '51-27=24'] Exploring Operation: 81*24=1944, Resulting Numbers: [1944] 1944,84 unequal: No Solution Exploring Operation: 81+24=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[51, 3], Operations: ['90-63=27', '81/27=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[90, 51, 18], Operations: ['81-63=18'] Exploring Operation: 90/18=5, Resulting Numbers: [51, 5] Generated Node #0,2,0: 84:[51, 5] Operation: 90/18=5 Exploring Operation: 51-18=33, Resulting Numbers: [90, 33] Generated Node #0,2,1: 84:[90, 33] Operation: 51-18=33 Exploring Operation: 90-51=39, Resulting Numbers: [18, 39] Generated Node #0,2,2: 84:[18, 39] Operation: 90-51=39 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 84:[18, 39], Operations: ['81-63=18', '90-51=39'] Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,84 unequal: No Solution Exploring Operation: 18*39=702, Resulting Numbers: [702] 702,84 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,84 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 #0,2,0 Current State: 84:[51, 5], Operations: ['81-63=18', '90/18=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,84 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,84 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:[90, 33], Operations: ['81-63=18', '51-18=33'] Exploring Operation: 90+33=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 90*33=2970, Resulting Numbers: [2970] 2970,84 unequal: No Solution Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,84 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 No solution found.
0
hs_3
sum_heuristic