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
[ 5, 2, 98, 31 ]
59
[ "5*31=155", "98-2=96", "155-96=59" ]
Current State: 59:[5, 2, 98, 31], Operations: [] Exploring Operation: 5*31=155, Resulting Numbers: [2, 98, 155] Generated Node #2: [2, 98, 155] from Operation: 5*31=155 Current State: 59:[2, 98, 155], Operations: ['5*31=155'] Exploring Operation: 98-2=96, Resulting Numbers: [155, 96] Generated Node #3: [155, 96] from Operation: 98-2=96 Current State: 59:[155, 96], Operations: ['5*31=155', '98-2=96'] Exploring Operation: 155-96=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[5, 2, 98, 31], Operations: [] Exploring Operation: 98/2=49, Resulting Numbers: [5, 31, 49] Generated Node #0,0: 59:[5, 31, 49] Operation: 98/2=49 Moving to Node #0,0 Current State: 59:[5, 31, 49], Operations: ['98/2=49'] Exploring Operation: 5+31=36, Resulting Numbers: [49, 36] Generated Node #0,0,0: 59:[49, 36] Operation: 5+31=36 Moving to Node #0,0,0 Current State: 59:[49, 36], Operations: ['98/2=49', '5+31=36'] Exploring Operation: 49+36=85, Resulting Numbers: [85] 85,59 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 8, 24, 25, 35 ]
75
[ "8+24=32", "35-32=3", "25*3=75" ]
Current State: 75:[8, 24, 25, 35], Operations: [] Exploring Operation: 8+24=32, Resulting Numbers: [25, 35, 32] Generated Node #2: [25, 35, 32] from Operation: 8+24=32 Current State: 75:[25, 35, 32], Operations: ['8+24=32'] Exploring Operation: 35-32=3, Resulting Numbers: [25, 3] Generated Node #3: [25, 3] from Operation: 35-32=3 Current State: 75:[25, 3], Operations: ['8+24=32', '35-32=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[8, 24, 25, 35], Operations: [] Exploring Operation: 35-8=27, Resulting Numbers: [24, 25, 27] Generated Node #0,0: 75:[24, 25, 27] Operation: 35-8=27 Moving to Node #0,0 Current State: 75:[24, 25, 27], Operations: ['35-8=27'] Exploring Operation: 27-24=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 75:[25, 3] Operation: 27-24=3 Moving to Node #0,0,0 Current State: 75:[25, 3], Operations: ['35-8=27', '27-24=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[8, 24, 25, 35], Operations: [] Exploring Operation: 35-8=27, Resulting Numbers: [24, 25, 27] Generated Node #0,0: 75:[24, 25, 27] Operation: 35-8=27 Moving to Node #0,0 Current State: 75:[24, 25, 27], Operations: ['35-8=27'] Exploring Operation: 27-24=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 75:[25, 3] Operation: 27-24=3 Moving to Node #0,0,0 Current State: 75:[25, 3], Operations: ['35-8=27', '27-24=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 84, 1, 56, 51 ]
33
[ "56*51=2856", "2856/84=34", "34-1=33" ]
Current State: 33:[84, 1, 56, 51], Operations: [] Exploring Operation: 56*51=2856, Resulting Numbers: [84, 1, 2856] Generated Node #2: [84, 1, 2856] from Operation: 56*51=2856 Current State: 33:[84, 1, 2856], Operations: ['56*51=2856'] Exploring Operation: 2856/84=34, Resulting Numbers: [1, 34] Generated Node #3: [1, 34] from Operation: 2856/84=34 Current State: 33:[1, 34], Operations: ['56*51=2856', '2856/84=34'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[84, 1, 56, 51], Operations: [] Exploring Operation: 84-51=33, Resulting Numbers: [1, 56, 33] Generated Node #0,0: 33:[1, 56, 33] Operation: 84-51=33 Exploring Operation: 84-56=28, Resulting Numbers: [1, 51, 28] Generated Node #0,1: 33:[1, 51, 28] Operation: 84-56=28 Moving to Node #0,0 Current State: 33:[1, 56, 33], Operations: ['84-51=33'] Exploring Operation: 56-33=23, Resulting Numbers: [1, 23] Generated Node #0,0,0: 33:[1, 23] Operation: 56-33=23 Exploring Operation: 56-1=55, Resulting Numbers: [33, 55] Generated Node #0,0,1: 33:[33, 55] Operation: 56-1=55 Moving to Node #0,1 Current State: 33:[1, 51, 28], Operations: ['84-56=28'] Exploring Operation: 51-1=50, Resulting Numbers: [28, 50] Generated Node #0,1,0: 33:[28, 50] Operation: 51-1=50 Exploring Operation: 51-28=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 33:[1, 23] Operation: 51-28=23 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[1, 23], Operations: ['84-56=28', '51-28=23'] Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,33 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 #0,1,0 Current State: 33:[28, 50], Operations: ['84-56=28', '51-1=50'] Exploring Operation: 28+50=78, Resulting Numbers: [78] 78,33 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,33 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: 33:[1, 23], Operations: ['84-51=33', '56-33=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[33, 55], Operations: ['84-51=33', '56-1=55'] Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,33 unequal: No Solution Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,33 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 13, 14, 36 ]
59
[ "14-12=2", "36*2=72", "72-13=59" ]
Current State: 59:[12, 13, 14, 36], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [13, 36, 2] Generated Node #2: [13, 36, 2] from Operation: 14-12=2 Current State: 59:[13, 36, 2], Operations: ['14-12=2'] Exploring Operation: 36*2=72, Resulting Numbers: [13, 72] Generated Node #3: [13, 72] from Operation: 36*2=72 Current State: 59:[13, 72], Operations: ['14-12=2', '36*2=72'] Exploring Operation: 72-13=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[12, 13, 14, 36], Operations: [] Exploring Operation: 13+14=27, Resulting Numbers: [12, 36, 27] Generated Node #0,0: 59:[12, 36, 27] Operation: 13+14=27 Exploring Operation: 12+14=26, Resulting Numbers: [13, 36, 26] Generated Node #0,1: 59:[13, 36, 26] Operation: 12+14=26 Exploring Operation: 12+13=25, Resulting Numbers: [14, 36, 25] Generated Node #0,2: 59:[14, 36, 25] Operation: 12+13=25 Exploring Operation: 13+36=49, Resulting Numbers: [12, 14, 49] Generated Node #0,3: 59:[12, 14, 49] Operation: 13+36=49 Exploring Operation: 12+36=48, Resulting Numbers: [13, 14, 48] Generated Node #0,4: 59:[13, 14, 48] Operation: 12+36=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[12, 36, 27], Operations: ['13+14=27'] Exploring Operation: 12+27=39, Resulting Numbers: [36, 39] Generated Node #0,0,0: 59:[36, 39] Operation: 12+27=39 Exploring Operation: 36-12=24, Resulting Numbers: [27, 24] Generated Node #0,0,1: 59:[27, 24] Operation: 36-12=24 Exploring Operation: 12+36=48, Resulting Numbers: [27, 48] Generated Node #0,0,2: 59:[27, 48] Operation: 12+36=48 Exploring Operation: 36+27=63, Resulting Numbers: [12, 63] Generated Node #0,0,3: 59:[12, 63] Operation: 36+27=63 Exploring Operation: 27-12=15, Resulting Numbers: [36, 15] Generated Node #0,0,4: 59:[36, 15] Operation: 27-12=15 Moving to Node #0,0,0 Current State: 59:[36, 39], Operations: ['13+14=27', '12+27=39'] Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 36*39=1404, Resulting Numbers: [1404] 1404,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[27, 48], Operations: ['13+14=27', '12+36=48'] Exploring Operation: 27+48=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 27*48=1296, Resulting Numbers: [1296] 1296,59 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[12, 63], Operations: ['13+14=27', '36+27=63'] Exploring Operation: 12+63=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 12*63=756, Resulting Numbers: [756] 756,59 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[27, 24], Operations: ['13+14=27', '36-12=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,59 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[36, 15], Operations: ['13+14=27', '27-12=15'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,59 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[13, 36, 26], Operations: ['12+14=26'] Exploring Operation: 13+36=49, Resulting Numbers: [26, 49] Generated Node #0,1,0: 59:[26, 49] Operation: 13+36=49 Exploring Operation: 13+26=39, Resulting Numbers: [36, 39] Generated Node #0,1,1: 59:[36, 39] Operation: 13+26=39 Exploring Operation: 26-13=13, Resulting Numbers: [36, 13] Generated Node #0,1,2: 59:[36, 13] Operation: 26-13=13 Exploring Operation: 36+26=62, Resulting Numbers: [13, 62] Generated Node #0,1,3: 59:[13, 62] Operation: 36+26=62 Exploring Operation: 36-13=23, Resulting Numbers: [26, 23] Generated Node #0,1,4: 59:[26, 23] Operation: 36-13=23 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[26, 49], Operations: ['12+14=26', '13+36=49'] Exploring Operation: 26+49=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 26*49=1274, Resulting Numbers: [1274] 1274,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[36, 39], Operations: ['12+14=26', '13+26=39'] Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 36*39=1404, Resulting Numbers: [1404] 1404,59 unequal: No Solution Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 59:[13, 62], Operations: ['12+14=26', '36+26=62'] Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 13*62=806, Resulting Numbers: [806] 806,59 unequal: No Solution Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[36, 13], Operations: ['12+14=26', '26-13=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,59 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 59:[26, 23], Operations: ['12+14=26', '36-13=23'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,59 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[14, 36, 25], Operations: ['12+13=25'] Exploring Operation: 25-14=11, Resulting Numbers: [36, 11] Generated Node #0,2,0: 59:[36, 11] Operation: 25-14=11 Exploring Operation: 14+25=39, Resulting Numbers: [36, 39] Generated Node #0,2,1: 59:[36, 39] Operation: 14+25=39 Exploring Operation: 36+25=61, Resulting Numbers: [14, 61] Generated Node #0,2,2: 59:[14, 61] Operation: 36+25=61 Exploring Operation: 36-14=22, Resulting Numbers: [25, 22] Generated Node #0,2,3: 59:[25, 22] Operation: 36-14=22 Exploring Operation: 14+36=50, Resulting Numbers: [25, 50] Generated Node #0,2,4: 59:[25, 50] Operation: 14+36=50 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 59:[36, 39], Operations: ['12+13=25', '14+25=39'] Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 36*39=1404, Resulting Numbers: [1404] 1404,59 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 59:[25, 50], Operations: ['12+13=25', '14+36=50'] Exploring Operation: 25*50=1250, Resulting Numbers: [1250] 1250,59 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 25+50=75, Resulting Numbers: [75] 75,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 59:[14, 61], Operations: ['12+13=25', '36+25=61'] Exploring Operation: 14*61=854, Resulting Numbers: [854] 854,59 unequal: No Solution Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[36, 11], Operations: ['12+13=25', '25-14=11'] Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,59 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 59:[25, 22], Operations: ['12+13=25', '36-14=22'] Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,59 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[12, 14, 49], Operations: ['13+36=49'] Exploring Operation: 49-12=37, Resulting Numbers: [14, 37] Generated Node #0,3,0: 59:[14, 37] Operation: 49-12=37 Exploring Operation: 14-12=2, Resulting Numbers: [49, 2] Generated Node #0,3,1: 59:[49, 2] Operation: 14-12=2 Exploring Operation: 12+14=26, Resulting Numbers: [49, 26] Generated Node #0,3,2: 59:[49, 26] Operation: 12+14=26 Exploring Operation: 14+49=63, Resulting Numbers: [12, 63] Generated Node #0,3,3: 59:[12, 63] Operation: 14+49=63 Exploring Operation: 12+49=61, Resulting Numbers: [14, 61] Generated Node #0,3,4: 59:[14, 61] Operation: 12+49=61 Moving to Node #0,3,2 Current State: 59:[49, 26], Operations: ['13+36=49', '12+14=26'] Exploring Operation: 49*26=1274, Resulting Numbers: [1274] 1274,59 unequal: No Solution Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 49+26=75, Resulting Numbers: [75] 75,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[14, 61], Operations: ['13+36=49', '12+49=61'] Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 14*61=854, Resulting Numbers: [854] 854,59 unequal: No Solution Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[12, 63], Operations: ['13+36=49', '14+49=63'] Exploring Operation: 12*63=756, Resulting Numbers: [756] 756,59 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,59 unequal: No Solution Exploring Operation: 12+63=75, Resulting Numbers: [75] 75,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[14, 37], Operations: ['13+36=49', '49-12=37'] Exploring Operation: 14*37=518, Resulting Numbers: [518] 518,59 unequal: No Solution Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,59 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[49, 2], Operations: ['13+36=49', '14-12=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,59 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 59:[13, 14, 48], Operations: ['12+36=48'] Exploring Operation: 13+14=27, Resulting Numbers: [48, 27] Generated Node #0,4,0: 59:[48, 27] Operation: 13+14=27 Exploring Operation: 48-13=35, Resulting Numbers: [14, 35] Generated Node #0,4,1: 59:[14, 35] Operation: 48-13=35 Exploring Operation: 14-13=1, Resulting Numbers: [48, 1] Generated Node #0,4,2: 59:[48, 1] Operation: 14-13=1 Exploring Operation: 13+48=61, Resulting Numbers: [14, 61] Generated Node #0,4,3: 59:[14, 61] Operation: 13+48=61 Exploring Operation: 14+48=62, Resulting Numbers: [13, 62] Generated Node #0,4,4: 59:[13, 62] Operation: 14+48=62 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 59:[48, 27], Operations: ['12+36=48', '13+14=27'] Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,59 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 59:[14, 61], Operations: ['12+36=48', '13+48=61'] Exploring Operation: 14*61=854, Resulting Numbers: [854] 854,59 unequal: No Solution Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 59:[13, 62], Operations: ['12+36=48', '14+48=62'] Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 13*62=806, Resulting Numbers: [806] 806,59 unequal: No Solution Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 59:[14, 35], Operations: ['12+36=48', '48-13=35'] Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,59 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 59:[48, 1], Operations: ['12+36=48', '14-13=1'] Exploring Operation: 48+1=49, Resulting Numbers: [49] 49,59 unequal: No Solution Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,59 unequal: No Solution Exploring Operation: 48*1=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 48/1=48, Resulting Numbers: [48] 48,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 3, 2, 21, 37 ]
63
[ "3+2=5", "21+37=58", "5+58=63" ]
Current State: 63:[3, 2, 21, 37], Operations: [] Exploring Operation: 3+2=5, Resulting Numbers: [21, 37, 5] Generated Node #2: [21, 37, 5] from Operation: 3+2=5 Current State: 63:[21, 37, 5], Operations: ['3+2=5'] Exploring Operation: 21+37=58, Resulting Numbers: [5, 58] Generated Node #3: [5, 58] from Operation: 21+37=58 Current State: 63:[5, 58], Operations: ['3+2=5', '21+37=58'] Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[3, 2, 21, 37], Operations: [] Exploring Operation: 2*37=74, Resulting Numbers: [3, 21, 74] Generated Node #0,0: 63:[3, 21, 74] Operation: 2*37=74 Exploring Operation: 37-3=34, Resulting Numbers: [2, 21, 34] Generated Node #0,1: 63:[2, 21, 34] Operation: 37-3=34 Exploring Operation: 37-21=16, Resulting Numbers: [3, 2, 16] Generated Node #0,2: 63:[3, 2, 16] Operation: 37-21=16 Exploring Operation: 21+37=58, Resulting Numbers: [3, 2, 58] Generated Node #0,3: 63:[3, 2, 58] Operation: 21+37=58 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[3, 2, 16], Operations: ['37-21=16'] Exploring Operation: 2+16=18, Resulting Numbers: [3, 18] Generated Node #0,2,0: 63:[3, 18] Operation: 2+16=18 Exploring Operation: 16-3=13, Resulting Numbers: [2, 13] Generated Node #0,2,1: 63:[2, 13] Operation: 16-3=13 Exploring Operation: 16/2=8, Resulting Numbers: [3, 8] Generated Node #0,2,2: 63:[3, 8] Operation: 16/2=8 Exploring Operation: 3+16=19, Resulting Numbers: [2, 19] Generated Node #0,2,3: 63:[2, 19] Operation: 3+16=19 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[3, 8], Operations: ['37-21=16', '16/2=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,63 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,63 unequal: No Solution No 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: 63:[3, 18], Operations: ['37-21=16', '2+16=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,63 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,63 unequal: No Solution No 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: 63:[2, 19], Operations: ['37-21=16', '3+16=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,63 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,63 unequal: No Solution No 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: 63:[2, 13], Operations: ['37-21=16', '16-3=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,63 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,63 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: 63:[3, 2, 58], Operations: ['21+37=58'] Exploring Operation: 2+58=60, Resulting Numbers: [3, 60] Generated Node #0,3,0: 63:[3, 60] Operation: 2+58=60 Exploring Operation: 3+58=61, Resulting Numbers: [2, 61] Generated Node #0,3,1: 63:[2, 61] Operation: 3+58=61 Exploring Operation: 3+2=5, Resulting Numbers: [58, 5] Generated Node #0,3,2: 63:[58, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [58, 6] Generated Node #0,3,3: 63:[58, 6] Operation: 3*2=6 Moving to Node #0,3,0 Current State: 63:[3, 60], Operations: ['21+37=58', '2+58=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[3, 2, 21, 37], Operations: [] Exploring Operation: 21+37=58, Resulting Numbers: [3, 2, 58] Generated Node #0,3: 63:[3, 2, 58] Operation: 21+37=58 Moving to Node #0,3 Current State: 63:[3, 2, 58], Operations: ['21+37=58'] Exploring Operation: 2+58=60, Resulting Numbers: [3, 60] Generated Node #0,3,0: 63:[3, 60] Operation: 2+58=60 Moving to Node #0,3,0 Current State: 63:[3, 60], Operations: ['21+37=58', '2+58=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 2, 37, 83, 74 ]
60
[ "83-37=46", "74+46=120", "120/2=60" ]
Current State: 60:[2, 37, 83, 74], Operations: [] Exploring Operation: 83-37=46, Resulting Numbers: [2, 74, 46] Generated Node #2: [2, 74, 46] from Operation: 83-37=46 Current State: 60:[2, 74, 46], Operations: ['83-37=46'] Exploring Operation: 74+46=120, Resulting Numbers: [2, 120] Generated Node #3: [2, 120] from Operation: 74+46=120 Current State: 60:[2, 120], Operations: ['83-37=46', '74+46=120'] Exploring Operation: 120/2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[2, 37, 83, 74], Operations: [] Exploring Operation: 83-74=9, Resulting Numbers: [2, 37, 9] Generated Node #0,0: 60:[2, 37, 9] Operation: 83-74=9 Exploring Operation: 74/37=2, Resulting Numbers: [2, 83, 2] Generated Node #0,1: 60:[2, 83, 2] Operation: 74/37=2 Exploring Operation: 74-37=37, Resulting Numbers: [2, 83, 37] Generated Node #0,2: 60:[2, 83, 37] Operation: 74-37=37 Exploring Operation: 83-37=46, Resulting Numbers: [2, 74, 46] Generated Node #0,3: 60:[2, 74, 46] Operation: 83-37=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[2, 37, 9], Operations: ['83-74=9'] Exploring Operation: 2+9=11, Resulting Numbers: [37, 11] Generated Node #0,0,0: 60:[37, 11] Operation: 2+9=11 Exploring Operation: 9-2=7, Resulting Numbers: [37, 7] Generated Node #0,0,1: 60:[37, 7] Operation: 9-2=7 Exploring Operation: 37-9=28, Resulting Numbers: [2, 28] Generated Node #0,0,2: 60:[2, 28] Operation: 37-9=28 Exploring Operation: 37-2=35, Resulting Numbers: [9, 35] Generated Node #0,0,3: 60:[9, 35] Operation: 37-2=35 Moving to Node #0,0,2 Current State: 60:[2, 28], Operations: ['83-74=9', '37-9=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,60 unequal: No Solution Moving to Node #0,0,3 Current State: 60:[9, 35], Operations: ['83-74=9', '37-2=35'] Exploring Operation: 9*35=315, Resulting Numbers: [315] 315,60 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 9+35=44, Resulting Numbers: [44] 44,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[37, 7], Operations: ['83-74=9', '9-2=7'] Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,60 unequal: No Solution Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[37, 11], Operations: ['83-74=9', '2+9=11'] Exploring Operation: 37+11=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 37*11=407, Resulting Numbers: [407] 407,60 unequal: No Solution Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[2, 83, 2], Operations: ['74/37=2'] Exploring Operation: 83-2=81, Resulting Numbers: [2, 81] Generated Node #0,1,0: 60:[2, 81] Operation: 83-2=81 Exploring Operation: 2+2=4, Resulting Numbers: [83, 4] Generated Node #0,1,1: 60:[83, 4] Operation: 2+2=4 Exploring Operation: 2*2=4, Resulting Numbers: [83, 4] Generated Node #0,1,2: 60:[83, 4] Operation: 2*2=4 Exploring Operation: 83-2=81, Resulting Numbers: [2, 81] Generated Node #0,1,3: 60:[2, 81] Operation: 83-2=81 Moving to Node #0,1,0 Current State: 60:[2, 81], Operations: ['74/37=2', '83-2=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,60 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,60 unequal: No Solution Moving to Node #0,1,3 Current State: 60:[2, 81], Operations: ['74/37=2', '83-2=81'] Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,60 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[83, 4], Operations: ['74/37=2', '2*2=4'] Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,60 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,60 unequal: No Solution Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[83, 4], Operations: ['74/37=2', '2+2=4'] Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,60 unequal: No Solution Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,60 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,60 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:[2, 74, 46], Operations: ['83-37=46'] Exploring Operation: 46/2=23, Resulting Numbers: [74, 23] Generated Node #0,3,0: 60:[74, 23] Operation: 46/2=23 Exploring Operation: 74/2=37, Resulting Numbers: [46, 37] Generated Node #0,3,1: 60:[46, 37] Operation: 74/2=37 Exploring Operation: 74-2=72, Resulting Numbers: [46, 72] Generated Node #0,3,2: 60:[46, 72] Operation: 74-2=72 Exploring Operation: 74-46=28, Resulting Numbers: [2, 28] Generated Node #0,3,3: 60:[2, 28] Operation: 74-46=28 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 60:[2, 28], Operations: ['83-37=46', '74-46=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,60 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 60:[74, 23], Operations: ['83-37=46', '46/2=23'] Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,60 unequal: No Solution Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 60:[46, 37], Operations: ['83-37=46', '74/2=37'] Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,60 unequal: No Solution Exploring Operation: 46*37=1702, Resulting Numbers: [1702] 1702,60 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 60:[46, 72], Operations: ['83-37=46', '74-2=72'] Exploring Operation: 46*72=3312, Resulting Numbers: [3312] 3312,60 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 46+72=118, Resulting Numbers: [118] 118,60 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:[2, 83, 37], Operations: ['74-37=37'] Exploring Operation: 2+83=85, Resulting Numbers: [37, 85] Generated Node #0,2,0: 60:[37, 85] Operation: 2+83=85 Exploring Operation: 83-2=81, Resulting Numbers: [37, 81] Generated Node #0,2,1: 60:[37, 81] Operation: 83-2=81 Exploring Operation: 83-37=46, Resulting Numbers: [2, 46] Generated Node #0,2,2: 60:[2, 46] Operation: 83-37=46 Exploring Operation: 37-2=35, Resulting Numbers: [83, 35] Generated Node #0,2,3: 60:[83, 35] Operation: 37-2=35 Moving to Node #0,2,2 Current State: 60:[2, 46], Operations: ['74-37=37', '83-37=46'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,60 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[83, 35], Operations: ['74-37=37', '37-2=35'] Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 83*35=2905, Resulting Numbers: [2905] 2905,60 unequal: No Solution Exploring Operation: 83+35=118, Resulting Numbers: [118] 118,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[37, 81], Operations: ['74-37=37', '83-2=81'] Exploring Operation: 37*81=2997, Resulting Numbers: [2997] 2997,60 unequal: No Solution Exploring Operation: 81-37=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 37+81=118, Resulting Numbers: [118] 118,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[37, 85], Operations: ['74-37=37', '2+83=85'] Exploring Operation: 37*85=3145, Resulting Numbers: [3145] 3145,60 unequal: No Solution Exploring Operation: 37+85=122, Resulting Numbers: [122] 122,60 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,60 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
[ 87, 9, 19, 4 ]
80
[ "87+4=91", "9*19=171", "171-91=80" ]
Current State: 80:[87, 9, 19, 4], Operations: [] Exploring Operation: 87+4=91, Resulting Numbers: [9, 19, 91] Generated Node #2: [9, 19, 91] from Operation: 87+4=91 Current State: 80:[9, 19, 91], Operations: ['87+4=91'] Exploring Operation: 9*19=171, Resulting Numbers: [91, 171] Generated Node #3: [91, 171] from Operation: 9*19=171 Current State: 80:[91, 171], Operations: ['87+4=91', '9*19=171'] Exploring Operation: 171-91=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[87, 9, 19, 4], Operations: [] Exploring Operation: 87-4=83, Resulting Numbers: [9, 19, 83] Generated Node #0,0: 80:[9, 19, 83] Operation: 87-4=83 Exploring Operation: 19-9=10, Resulting Numbers: [87, 4, 10] Generated Node #0,1: 80:[87, 4, 10] Operation: 19-9=10 Exploring Operation: 87-9=78, Resulting Numbers: [19, 4, 78] Generated Node #0,2: 80:[19, 4, 78] Operation: 87-9=78 Moving to Node #0,2 Current State: 80:[19, 4, 78], Operations: ['87-9=78'] Exploring Operation: 19+4=23, Resulting Numbers: [78, 23] Generated Node #0,2,0: 80:[78, 23] Operation: 19+4=23 Exploring Operation: 19-4=15, Resulting Numbers: [78, 15] Generated Node #0,2,1: 80:[78, 15] Operation: 19-4=15 Exploring Operation: 4+78=82, Resulting Numbers: [19, 82] Generated Node #0,2,2: 80:[19, 82] Operation: 4+78=82 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[78, 15], Operations: ['87-9=78', '19-4=15'] Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,80 unequal: No Solution Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[19, 82], Operations: ['87-9=78', '4+78=82'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,80 unequal: No Solution Exploring Operation: 19*82=1558, Resulting Numbers: [1558] 1558,80 unequal: No Solution Exploring Operation: 19+82=101, Resulting Numbers: [101] 101,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[78, 23], Operations: ['87-9=78', '19+4=23'] Exploring Operation: 78+23=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 78*23=1794, Resulting Numbers: [1794] 1794,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 80:[9, 19, 83], Operations: ['87-4=83'] Exploring Operation: 19-9=10, Resulting Numbers: [83, 10] Generated Node #0,0,0: 80:[83, 10] Operation: 19-9=10 Exploring Operation: 9+19=28, Resulting Numbers: [83, 28] Generated Node #0,0,1: 80:[83, 28] Operation: 9+19=28 Exploring Operation: 83-9=74, Resulting Numbers: [19, 74] Generated Node #0,0,2: 80:[19, 74] Operation: 83-9=74 Moving to Node #0,1 Current State: 80:[87, 4, 10], Operations: ['19-9=10'] Exploring Operation: 4*10=40, Resulting Numbers: [87, 40] Generated Node #0,1,0: 80:[87, 40] Operation: 4*10=40 Exploring Operation: 87-4=83, Resulting Numbers: [10, 83] Generated Node #0,1,1: 80:[10, 83] Operation: 87-4=83 Exploring Operation: 87-10=77, Resulting Numbers: [4, 77] Generated Node #0,1,2: 80:[4, 77] Operation: 87-10=77 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[10, 83], Operations: ['19-9=10', '87-4=83'] Exploring Operation: 10*83=830, Resulting Numbers: [830] 830,80 unequal: No Solution Exploring Operation: 10+83=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[4, 77], Operations: ['19-9=10', '87-10=77'] Exploring Operation: 4+77=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 4*77=308, Resulting Numbers: [308] 308,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[87, 40], Operations: ['19-9=10', '4*10=40'] Exploring Operation: 87*40=3480, Resulting Numbers: [3480] 3480,80 unequal: No Solution Exploring Operation: 87+40=127, Resulting Numbers: [127] 127,80 unequal: No Solution Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,80 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: 80:[83, 10], Operations: ['87-4=83', '19-9=10'] Exploring Operation: 83*10=830, Resulting Numbers: [830] 830,80 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[19, 74], Operations: ['87-4=83', '83-9=74'] Exploring Operation: 19*74=1406, Resulting Numbers: [1406] 1406,80 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 19+74=93, Resulting Numbers: [93] 93,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[83, 28], Operations: ['87-4=83', '9+19=28'] Exploring Operation: 83+28=111, Resulting Numbers: [111] 111,80 unequal: No Solution Exploring Operation: 83*28=2324, Resulting Numbers: [2324] 2324,80 unequal: No Solution Exploring Operation: 83-28=55, Resulting Numbers: [55] 55,80 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 24, 60, 9, 96 ]
73
[ "96/24=4", "60+9=69", "4+69=73" ]
Current State: 73:[24, 60, 9, 96], Operations: [] Exploring Operation: 96/24=4, Resulting Numbers: [60, 9, 4] Generated Node #2: [60, 9, 4] from Operation: 96/24=4 Current State: 73:[60, 9, 4], Operations: ['96/24=4'] Exploring Operation: 60+9=69, Resulting Numbers: [4, 69] Generated Node #3: [4, 69] from Operation: 60+9=69 Current State: 73:[4, 69], Operations: ['96/24=4', '60+9=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[24, 60, 9, 96], Operations: [] Exploring Operation: 60+9=69, Resulting Numbers: [24, 96, 69] Generated Node #0,0: 73:[24, 96, 69] Operation: 60+9=69 Exploring Operation: 24+9=33, Resulting Numbers: [60, 96, 33] Generated Node #0,1: 73:[60, 96, 33] Operation: 24+9=33 Exploring Operation: 96-9=87, Resulting Numbers: [24, 60, 87] Generated Node #0,2: 73:[24, 60, 87] Operation: 96-9=87 Exploring Operation: 96-24=72, Resulting Numbers: [60, 9, 72] Generated Node #0,3: 73:[60, 9, 72] Operation: 96-24=72 Exploring Operation: 24-9=15, Resulting Numbers: [60, 96, 15] Generated Node #0,4: 73:[60, 96, 15] Operation: 24-9=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[24, 96, 69], Operations: ['60+9=69'] Exploring Operation: 96/24=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 73:[69, 4] Operation: 96/24=4 Exploring Operation: 24+69=93, Resulting Numbers: [96, 93] Generated Node #0,0,1: 73:[96, 93] Operation: 24+69=93 Exploring Operation: 96-24=72, Resulting Numbers: [69, 72] Generated Node #0,0,2: 73:[69, 72] Operation: 96-24=72 Exploring Operation: 24+96=120, Resulting Numbers: [69, 120] Generated Node #0,0,3: 73:[69, 120] Operation: 24+96=120 Exploring Operation: 69-24=45, Resulting Numbers: [96, 45] Generated Node #0,0,4: 73:[96, 45] Operation: 69-24=45 Moving to Node #0,0,2 Current State: 73:[69, 72], Operations: ['60+9=69', '96-24=72'] Exploring Operation: 72-69=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 69+72=141, Resulting Numbers: [141] 141,73 unequal: No Solution Exploring Operation: 69*72=4968, Resulting Numbers: [4968] 4968,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[96, 93], Operations: ['60+9=69', '24+69=93'] Exploring Operation: 96+93=189, Resulting Numbers: [189] 189,73 unequal: No Solution Exploring Operation: 96-93=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 96*93=8928, Resulting Numbers: [8928] 8928,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[69, 120], Operations: ['60+9=69', '24+96=120'] Exploring Operation: 69+120=189, Resulting Numbers: [189] 189,73 unequal: No Solution Exploring Operation: 120-69=51, Resulting Numbers: [51] 51,73 unequal: No Solution Exploring Operation: 69*120=8280, Resulting Numbers: [8280] 8280,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[96, 45], Operations: ['60+9=69', '69-24=45'] Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,73 unequal: No Solution Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,73 unequal: No Solution Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[69, 4], Operations: ['60+9=69', '96/24=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,73 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[24, 60, 9, 96], Operations: [] Exploring Operation: 60+9=69, Resulting Numbers: [24, 96, 69] Generated Node #0,0: 73:[24, 96, 69] Operation: 60+9=69 Moving to Node #0,0 Current State: 73:[24, 96, 69], Operations: ['60+9=69'] Exploring Operation: 96/24=4, Resulting Numbers: [69, 4] Generated Node #0,0,0: 73:[69, 4] Operation: 96/24=4 Moving to Node #0,0,0 Current State: 73:[69, 4], Operations: ['60+9=69', '96/24=4'] Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 55, 48, 99, 50 ]
11
[ "50-48=2", "55*2=110", "110-99=11" ]
Current State: 11:[55, 48, 99, 50], Operations: [] Exploring Operation: 50-48=2, Resulting Numbers: [55, 99, 2] Generated Node #2: [55, 99, 2] from Operation: 50-48=2 Current State: 11:[55, 99, 2], Operations: ['50-48=2'] Exploring Operation: 55*2=110, Resulting Numbers: [99, 110] Generated Node #3: [99, 110] from Operation: 55*2=110 Current State: 11:[99, 110], Operations: ['50-48=2', '55*2=110'] Exploring Operation: 110-99=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[55, 48, 99, 50], Operations: [] Exploring Operation: 99-48=51, Resulting Numbers: [55, 50, 51] Generated Node #0,0: 11:[55, 50, 51] Operation: 99-48=51 Exploring Operation: 99-50=49, Resulting Numbers: [55, 48, 49] Generated Node #0,1: 11:[55, 48, 49] Operation: 99-50=49 Exploring Operation: 55-48=7, Resulting Numbers: [99, 50, 7] Generated Node #0,2: 11:[99, 50, 7] Operation: 55-48=7 Exploring Operation: 99-55=44, Resulting Numbers: [48, 50, 44] Generated Node #0,3: 11:[48, 50, 44] Operation: 99-55=44 Start Sub Search at level 1: Moving to Node #0,3 Current State: 11:[48, 50, 44], Operations: ['99-55=44'] Exploring Operation: 48-44=4, Resulting Numbers: [50, 4] Generated Node #0,3,0: 11:[50, 4] Operation: 48-44=4 Exploring Operation: 50-48=2, Resulting Numbers: [44, 2] Generated Node #0,3,1: 11:[44, 2] Operation: 50-48=2 Exploring Operation: 50-44=6, Resulting Numbers: [48, 6] Generated Node #0,3,2: 11:[48, 6] Operation: 50-44=6 Exploring Operation: 48+50=98, Resulting Numbers: [44, 98] Generated Node #0,3,3: 11:[44, 98] Operation: 48+50=98 Moving to Node #0,3,1 Current State: 11:[44, 2], Operations: ['99-55=44', '50-48=2'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,11 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[48, 6], Operations: ['99-55=44', '50-44=6'] Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,11 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[50, 4], Operations: ['99-55=44', '48-44=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,11 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[44, 98], Operations: ['99-55=44', '48+50=98'] Exploring Operation: 98-44=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 44*98=4312, Resulting Numbers: [4312] 4312,11 unequal: No Solution Exploring Operation: 44+98=142, Resulting Numbers: [142] 142,11 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 #0,1 Current State: 11:[55, 48, 49], Operations: ['99-50=49'] Exploring Operation: 55+48=103, Resulting Numbers: [49, 103] Generated Node #0,1,0: 11:[49, 103] Operation: 55+48=103 Exploring Operation: 55-49=6, Resulting Numbers: [48, 6] Generated Node #0,1,1: 11:[48, 6] Operation: 55-49=6 Exploring Operation: 49-48=1, Resulting Numbers: [55, 1] Generated Node #0,1,2: 11:[55, 1] Operation: 49-48=1 Exploring Operation: 55-48=7, Resulting Numbers: [49, 7] Generated Node #0,1,3: 11:[49, 7] Operation: 55-48=7 Moving to Node #0,1,1 Current State: 11:[48, 6], Operations: ['99-50=49', '55-49=6'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[49, 7], Operations: ['99-50=49', '55-48=7'] Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 49*7=343, Resulting Numbers: [343] 343,11 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[55, 1], Operations: ['99-50=49', '49-48=1'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[49, 103], Operations: ['99-50=49', '55+48=103'] Exploring Operation: 49*103=5047, Resulting Numbers: [5047] 5047,11 unequal: No Solution Exploring Operation: 49+103=152, Resulting Numbers: [152] 152,11 unequal: No Solution Exploring Operation: 103-49=54, Resulting Numbers: [54] 54,11 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 #0,0 Current State: 11:[55, 50, 51], Operations: ['99-48=51'] Exploring Operation: 55-51=4, Resulting Numbers: [50, 4] Generated Node #0,0,0: 11:[50, 4] Operation: 55-51=4 Exploring Operation: 51-50=1, Resulting Numbers: [55, 1] Generated Node #0,0,1: 11:[55, 1] Operation: 51-50=1 Exploring Operation: 55+50=105, Resulting Numbers: [51, 105] Generated Node #0,0,2: 11:[51, 105] Operation: 55+50=105 Exploring Operation: 55-50=5, Resulting Numbers: [51, 5] Generated Node #0,0,3: 11:[51, 5] Operation: 55-50=5 Moving to Node #0,0,0 Current State: 11:[50, 4], Operations: ['99-48=51', '55-51=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,11 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[51, 5], Operations: ['99-48=51', '55-50=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[55, 1], Operations: ['99-48=51', '51-50=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,11 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[51, 105], Operations: ['99-48=51', '55+50=105'] Exploring Operation: 51*105=5355, Resulting Numbers: [5355] 5355,11 unequal: No Solution Exploring Operation: 105-51=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 51+105=156, Resulting Numbers: [156] 156,11 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 #0,2 Current State: 11:[99, 50, 7], Operations: ['55-48=7'] Exploring Operation: 99-7=92, Resulting Numbers: [50, 92] Generated Node #0,2,0: 11:[50, 92] Operation: 99-7=92 Exploring Operation: 99-50=49, Resulting Numbers: [7, 49] Generated Node #0,2,1: 11:[7, 49] Operation: 99-50=49 Exploring Operation: 50-7=43, Resulting Numbers: [99, 43] Generated Node #0,2,2: 11:[99, 43] Operation: 50-7=43 Exploring Operation: 99+7=106, Resulting Numbers: [50, 106] Generated Node #0,2,3: 11:[50, 106] Operation: 99+7=106 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 11:[7, 49], Operations: ['55-48=7', '99-50=49'] Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,11 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,11 unequal: No Solution No 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: 11:[50, 92], Operations: ['55-48=7', '99-7=92'] Exploring Operation: 50*92=4600, Resulting Numbers: [4600] 4600,11 unequal: No Solution Exploring Operation: 92-50=42, Resulting Numbers: [42] 42,11 unequal: No Solution Exploring Operation: 50+92=142, Resulting Numbers: [142] 142,11 unequal: No Solution No 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: 11:[99, 43], Operations: ['55-48=7', '50-7=43'] Exploring Operation: 99*43=4257, Resulting Numbers: [4257] 4257,11 unequal: No Solution Exploring Operation: 99-43=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 99+43=142, Resulting Numbers: [142] 142,11 unequal: No Solution No 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: 11:[50, 106], Operations: ['55-48=7', '99+7=106'] Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,11 unequal: No Solution Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,11 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,11 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
[ 94, 31, 50, 19 ]
93
[ "50-31=19", "19/19=1", "94-1=93" ]
Current State: 93:[94, 31, 50, 19], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [94, 19, 19] Generated Node #2: [94, 19, 19] from Operation: 50-31=19 Current State: 93:[94, 19, 19], Operations: ['50-31=19'] Exploring Operation: 19/19=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 19/19=1 Current State: 93:[94, 1], Operations: ['50-31=19', '19/19=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[94, 31, 50, 19], Operations: [] Exploring Operation: 50-19=31, Resulting Numbers: [94, 31, 31] Generated Node #0,0: 93:[94, 31, 31] Operation: 50-19=31 Exploring Operation: 94-50=44, Resulting Numbers: [31, 19, 44] Generated Node #0,1: 93:[31, 19, 44] Operation: 94-50=44 Exploring Operation: 50-31=19, Resulting Numbers: [94, 19, 19] Generated Node #0,2: 93:[94, 19, 19] Operation: 50-31=19 Exploring Operation: 31+50=81, Resulting Numbers: [94, 19, 81] Generated Node #0,3: 93:[94, 19, 81] Operation: 31+50=81 Moving to Node #0,0 Current State: 93:[94, 31, 31], Operations: ['50-19=31'] Exploring Operation: 31-31=0, Resulting Numbers: [94, 0] Generated Node #0,0,0: 93:[94, 0] Operation: 31-31=0 Exploring Operation: 31/31=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 31/31=1 Exploring Operation: 94-31=63, Resulting Numbers: [31, 63] Generated Node #0,0,2: 93:[31, 63] Operation: 94-31=63 Exploring Operation: 94-31=63, Resulting Numbers: [31, 63] Generated Node #0,0,3: 93:[31, 63] Operation: 94-31=63 Moving to Node #0,2 Current State: 93:[94, 19, 19], Operations: ['50-31=19'] Exploring Operation: 19+19=38, Resulting Numbers: [94, 38] Generated Node #0,2,0: 93:[94, 38] Operation: 19+19=38 Exploring Operation: 94-19=75, Resulting Numbers: [19, 75] Generated Node #0,2,1: 93:[19, 75] Operation: 94-19=75 Exploring Operation: 19/19=1, Resulting Numbers: [94, 1] Generated Node #0,2,2: 93:[94, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [94, 0] Generated Node #0,2,3: 93:[94, 0] Operation: 19-19=0 Moving to Node #0,1 Current State: 93:[31, 19, 44], Operations: ['94-50=44'] Exploring Operation: 44-19=25, Resulting Numbers: [31, 25] Generated Node #0,1,0: 93:[31, 25] Operation: 44-19=25 Exploring Operation: 31+44=75, Resulting Numbers: [19, 75] Generated Node #0,1,1: 93:[19, 75] Operation: 31+44=75 Exploring Operation: 31-19=12, Resulting Numbers: [44, 12] Generated Node #0,1,2: 93:[44, 12] Operation: 31-19=12 Exploring Operation: 44-31=13, Resulting Numbers: [19, 13] Generated Node #0,1,3: 93:[19, 13] Operation: 44-31=13 Moving to Node #0,3 Current State: 93:[94, 19, 81], Operations: ['31+50=81'] Exploring Operation: 94-81=13, Resulting Numbers: [19, 13] Generated Node #0,3,0: 93:[19, 13] Operation: 94-81=13 Exploring Operation: 19+81=100, Resulting Numbers: [94, 100] Generated Node #0,3,1: 93:[94, 100] Operation: 19+81=100 Exploring Operation: 94+19=113, Resulting Numbers: [81, 113] Generated Node #0,3,2: 93:[81, 113] Operation: 94+19=113 Exploring Operation: 94-19=75, Resulting Numbers: [81, 75] Generated Node #0,3,3: 93:[81, 75] Operation: 94-19=75 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 93:[94, 100], Operations: ['31+50=81', '19+81=100'] Exploring Operation: 94+100=194, Resulting Numbers: [194] 194,93 unequal: No Solution Exploring Operation: 100-94=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 94*100=9400, Resulting Numbers: [9400] 9400,93 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 #0,3,0 Current State: 93:[19, 13], Operations: ['31+50=81', '94-81=13'] Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,93 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 19*13=247, Resulting Numbers: [247] 247,93 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:[81, 75], Operations: ['31+50=81', '94-19=75'] Exploring Operation: 81+75=156, Resulting Numbers: [156] 156,93 unequal: No Solution Exploring Operation: 81-75=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 81*75=6075, Resulting Numbers: [6075] 6075,93 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:[81, 113], Operations: ['31+50=81', '94+19=113'] Exploring Operation: 81*113=9153, Resulting Numbers: [9153] 9153,93 unequal: No Solution Exploring Operation: 81+113=194, Resulting Numbers: [194] 194,93 unequal: No Solution Exploring Operation: 113-81=32, Resulting Numbers: [32] 32,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['50-19=31', '31/31=1'] Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,93 unequal: No Solution Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[94, 31, 50, 19], Operations: [] Exploring Operation: 50-19=31, Resulting Numbers: [94, 31, 31] Generated Node #0,0: 93:[94, 31, 31] Operation: 50-19=31 Moving to Node #0,0 Current State: 93:[94, 31, 31], Operations: ['50-19=31'] Exploring Operation: 31/31=1, Resulting Numbers: [94, 1] Generated Node #0,0,1: 93:[94, 1] Operation: 31/31=1 Moving to Node #0,0,1 Current State: 93:[94, 1], Operations: ['50-19=31', '31/31=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.967014
hs_4
sum_heuristic
[ 41, 6, 79, 44 ]
24
[ "41+79=120", "120/6=20", "44-20=24" ]
Current State: 24:[41, 6, 79, 44], Operations: [] Exploring Operation: 41+79=120, Resulting Numbers: [6, 44, 120] Generated Node #2: [6, 44, 120] from Operation: 41+79=120 Current State: 24:[6, 44, 120], Operations: ['41+79=120'] Exploring Operation: 120/6=20, Resulting Numbers: [44, 20] Generated Node #3: [44, 20] from Operation: 120/6=20 Current State: 24:[44, 20], Operations: ['41+79=120', '120/6=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[41, 6, 79, 44], Operations: [] Exploring Operation: 41-6=35, Resulting Numbers: [79, 44, 35] Generated Node #0,0: 24:[79, 44, 35] Operation: 41-6=35 Exploring Operation: 44-41=3, Resulting Numbers: [6, 79, 3] Generated Node #0,1: 24:[6, 79, 3] Operation: 44-41=3 Exploring Operation: 79-44=35, Resulting Numbers: [41, 6, 35] Generated Node #0,2: 24:[41, 6, 35] Operation: 79-44=35 Exploring Operation: 79-41=38, Resulting Numbers: [6, 44, 38] Generated Node #0,3: 24:[6, 44, 38] Operation: 79-41=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[41, 6, 35], Operations: ['79-44=35'] Exploring Operation: 41-6=35, Resulting Numbers: [35, 35] Generated Node #0,2,0: 24:[35, 35] Operation: 41-6=35 Exploring Operation: 41-35=6, Resulting Numbers: [6, 6] Generated Node #0,2,1: 24:[6, 6] Operation: 41-35=6 Exploring Operation: 35-6=29, Resulting Numbers: [41, 29] Generated Node #0,2,2: 24:[41, 29] Operation: 35-6=29 Exploring Operation: 41+6=47, Resulting Numbers: [35, 47] Generated Node #0,2,3: 24:[35, 47] Operation: 41+6=47 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[6, 6], Operations: ['79-44=35', '41-35=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,24 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 #0,2,0 Current State: 24:[35, 35], Operations: ['79-44=35', '41-6=35'] Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,24 unequal: No Solution Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,24 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,24 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 #0,2,2 Current State: 24:[41, 29], Operations: ['79-44=35', '35-6=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,24 unequal: No Solution Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,24 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,24 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 #0,2,3 Current State: 24:[35, 47], Operations: ['79-44=35', '41+6=47'] Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 35+47=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 35*47=1645, Resulting Numbers: [1645] 1645,24 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[6, 44, 38], Operations: ['79-41=38'] Exploring Operation: 6+44=50, Resulting Numbers: [38, 50] Generated Node #0,3,0: 24:[38, 50] Operation: 6+44=50 Exploring Operation: 44-38=6, Resulting Numbers: [6, 6] Generated Node #0,3,1: 24:[6, 6] Operation: 44-38=6 Exploring Operation: 38-6=32, Resulting Numbers: [44, 32] Generated Node #0,3,2: 24:[44, 32] Operation: 38-6=32 Exploring Operation: 44-6=38, Resulting Numbers: [38, 38] Generated Node #0,3,3: 24:[38, 38] Operation: 44-6=38 Moving to Node #0,3,1 Current State: 24:[6, 6], Operations: ['79-41=38', '44-38=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[38, 38], Operations: ['79-41=38', '44-6=38'] Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,24 unequal: No Solution Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 38*38=1444, Resulting Numbers: [1444] 1444,24 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[44, 32], Operations: ['79-41=38', '38-6=32'] Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,24 unequal: No Solution Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,24 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[38, 50], Operations: ['79-41=38', '6+44=50'] Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 38+50=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 38*50=1900, Resulting Numbers: [1900] 1900,24 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 Current State: 24:[6, 79, 3], Operations: ['44-41=3'] Exploring Operation: 79-3=76, Resulting Numbers: [6, 76] Generated Node #0,1,0: 24:[6, 76] Operation: 79-3=76 Exploring Operation: 6-3=3, Resulting Numbers: [79, 3] Generated Node #0,1,1: 24:[79, 3] Operation: 6-3=3 Exploring Operation: 79-6=73, Resulting Numbers: [3, 73] Generated Node #0,1,2: 24:[3, 73] Operation: 79-6=73 Exploring Operation: 6/3=2, Resulting Numbers: [79, 2] Generated Node #0,1,3: 24:[79, 2] Operation: 6/3=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[3, 73], Operations: ['44-41=3', '79-6=73'] Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,24 unequal: No Solution Exploring Operation: 3*73=219, Resulting Numbers: [219] 219,24 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,24 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 #0,1,0 Current State: 24:[6, 76], Operations: ['44-41=3', '79-3=76'] Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,24 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,24 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 #0,1,1 Current State: 24:[79, 3], Operations: ['44-41=3', '6-3=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,24 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,24 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,24 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 #0,1,3 Current State: 24:[79, 2], Operations: ['44-41=3', '6/3=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,24 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,24 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[79, 44, 35], Operations: ['41-6=35'] Exploring Operation: 79-35=44, Resulting Numbers: [44, 44] Generated Node #0,0,0: 24:[44, 44] Operation: 79-35=44 Exploring Operation: 44-35=9, Resulting Numbers: [79, 9] Generated Node #0,0,1: 24:[79, 9] Operation: 44-35=9 Exploring Operation: 79+44=123, Resulting Numbers: [35, 123] Generated Node #0,0,2: 24:[35, 123] Operation: 79+44=123 Exploring Operation: 79-44=35, Resulting Numbers: [35, 35] Generated Node #0,0,3: 24:[35, 35] Operation: 79-44=35 Moving to Node #0,0,3 Current State: 24:[35, 35], Operations: ['41-6=35', '79-44=35'] Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,24 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[44, 44], Operations: ['41-6=35', '79-35=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,24 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[79, 9], Operations: ['41-6=35', '44-35=9'] Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,24 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,24 unequal: No Solution Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[35, 123], Operations: ['41-6=35', '79+44=123'] Exploring Operation: 35*123=4305, Resulting Numbers: [4305] 4305,24 unequal: No Solution Exploring Operation: 35+123=158, Resulting Numbers: [158] 158,24 unequal: No Solution Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,24 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
[ 37, 2, 58, 15 ]
23
[ "37+15=52", "58/2=29", "52-29=23" ]
Current State: 23:[37, 2, 58, 15], Operations: [] Exploring Operation: 37+15=52, Resulting Numbers: [2, 58, 52] Generated Node #2: [2, 58, 52] from Operation: 37+15=52 Current State: 23:[2, 58, 52], Operations: ['37+15=52'] Exploring Operation: 58/2=29, Resulting Numbers: [52, 29] Generated Node #3: [52, 29] from Operation: 58/2=29 Current State: 23:[52, 29], Operations: ['37+15=52', '58/2=29'] Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[37, 2, 58, 15], Operations: [] Exploring Operation: 58/2=29, Resulting Numbers: [37, 15, 29] Generated Node #0,0: 23:[37, 15, 29] Operation: 58/2=29 Exploring Operation: 58-37=21, Resulting Numbers: [2, 15, 21] Generated Node #0,1: 23:[2, 15, 21] Operation: 58-37=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[37, 15, 29], Operations: ['58/2=29'] Exploring Operation: 37-15=22, Resulting Numbers: [29, 22] Generated Node #0,0,0: 23:[29, 22] Operation: 37-15=22 Exploring Operation: 37-29=8, Resulting Numbers: [15, 8] Generated Node #0,0,1: 23:[15, 8] Operation: 37-29=8 Moving to Node #0,0,0 Current State: 23:[29, 22], Operations: ['58/2=29', '37-15=22'] Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[15, 8], Operations: ['58/2=29', '37-29=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[37, 2, 58, 15], Operations: [] Exploring Operation: 58/2=29, Resulting Numbers: [37, 15, 29] Generated Node #0,0: 23:[37, 15, 29] Operation: 58/2=29 Moving to Node #0,0 Current State: 23:[37, 15, 29], Operations: ['58/2=29'] Exploring Operation: 37-29=8, Resulting Numbers: [15, 8] Generated Node #0,0,1: 23:[15, 8] Operation: 37-29=8 Moving to Node #0,0,1 Current State: 23:[15, 8], Operations: ['58/2=29', '37-29=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 13, 45, 46, 69 ]
83
[ "45-13=32", "46+69=115", "115-32=83" ]
Current State: 83:[13, 45, 46, 69], Operations: [] Exploring Operation: 45-13=32, Resulting Numbers: [46, 69, 32] Generated Node #2: [46, 69, 32] from Operation: 45-13=32 Current State: 83:[46, 69, 32], Operations: ['45-13=32'] Exploring Operation: 46+69=115, Resulting Numbers: [32, 115] Generated Node #3: [32, 115] from Operation: 46+69=115 Current State: 83:[32, 115], Operations: ['45-13=32', '46+69=115'] Exploring Operation: 115-32=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[13, 45, 46, 69], Operations: [] Exploring Operation: 13+45=58, Resulting Numbers: [46, 69, 58] Generated Node #0,0: 83:[46, 69, 58] Operation: 13+45=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[46, 69, 58], Operations: ['13+45=58'] Exploring Operation: 46+58=104, Resulting Numbers: [69, 104] Generated Node #0,0,0: 83:[69, 104] Operation: 46+58=104 Moving to Node #0,0,0 Current State: 83:[69, 104], Operations: ['13+45=58', '46+58=104'] Exploring Operation: 104-69=35, Resulting Numbers: [35] 35,83 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
[ 43, 97, 4, 35 ]
93
[ "97-43=54", "4+35=39", "54+39=93" ]
Current State: 93:[43, 97, 4, 35], Operations: [] Exploring Operation: 97-43=54, Resulting Numbers: [4, 35, 54] Generated Node #2: [4, 35, 54] from Operation: 97-43=54 Current State: 93:[4, 35, 54], Operations: ['97-43=54'] Exploring Operation: 4+35=39, Resulting Numbers: [54, 39] Generated Node #3: [54, 39] from Operation: 4+35=39 Current State: 93:[54, 39], Operations: ['97-43=54', '4+35=39'] Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[43, 97, 4, 35], Operations: [] Exploring Operation: 43-4=39, Resulting Numbers: [97, 35, 39] Generated Node #0,0: 93:[97, 35, 39] Operation: 43-4=39 Exploring Operation: 43-35=8, Resulting Numbers: [97, 4, 8] Generated Node #0,1: 93:[97, 4, 8] Operation: 43-35=8 Moving to Node #0,1 Current State: 93:[97, 4, 8], Operations: ['43-35=8'] Exploring Operation: 97-8=89, Resulting Numbers: [4, 89] Generated Node #0,1,0: 93:[4, 89] Operation: 97-8=89 Exploring Operation: 97-4=93, Resulting Numbers: [8, 93] Generated Node #0,1,1: 93:[8, 93] Operation: 97-4=93 Moving to Node #0,0 Current State: 93:[97, 35, 39], Operations: ['43-4=39'] Exploring Operation: 39-35=4, Resulting Numbers: [97, 4] Generated Node #0,0,0: 93:[97, 4] Operation: 39-35=4 Exploring Operation: 35+39=74, Resulting Numbers: [97, 74] Generated Node #0,0,1: 93:[97, 74] Operation: 35+39=74 Moving to Node #0,1,0 Current State: 93:[4, 89], Operations: ['43-35=8', '97-8=89'] Exploring Operation: 4+89=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[43, 97, 4, 35], Operations: [] Exploring Operation: 43-35=8, Resulting Numbers: [97, 4, 8] Generated Node #0,1: 93:[97, 4, 8] Operation: 43-35=8 Moving to Node #0,1 Current State: 93:[97, 4, 8], Operations: ['43-35=8'] Exploring Operation: 97-8=89, Resulting Numbers: [4, 89] Generated Node #0,1,0: 93:[4, 89] Operation: 97-8=89 Moving to Node #0,1,0 Current State: 93:[4, 89], Operations: ['43-35=8', '97-8=89'] Exploring Operation: 4+89=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 68, 42, 25, 23 ]
16
[ "25-23=2", "42*2=84", "84-68=16" ]
Current State: 16:[68, 42, 25, 23], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [68, 42, 2] Generated Node #2: [68, 42, 2] from Operation: 25-23=2 Current State: 16:[68, 42, 2], Operations: ['25-23=2'] Exploring Operation: 42*2=84, Resulting Numbers: [68, 84] Generated Node #3: [68, 84] from Operation: 42*2=84 Current State: 16:[68, 84], Operations: ['25-23=2', '42*2=84'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[68, 42, 25, 23], Operations: [] Exploring Operation: 68-23=45, Resulting Numbers: [42, 25, 45] Generated Node #0,0: 16:[42, 25, 45] Operation: 68-23=45 Exploring Operation: 68-42=26, Resulting Numbers: [25, 23, 26] Generated Node #0,1: 16:[25, 23, 26] Operation: 68-42=26 Exploring Operation: 42-25=17, Resulting Numbers: [68, 23, 17] Generated Node #0,2: 16:[68, 23, 17] Operation: 42-25=17 Exploring Operation: 68-25=43, Resulting Numbers: [42, 23, 43] Generated Node #0,3: 16:[42, 23, 43] Operation: 68-25=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[25, 23, 26], Operations: ['68-42=26'] Exploring Operation: 26-25=1, Resulting Numbers: [23, 1] Generated Node #0,1,0: 16:[23, 1] Operation: 26-25=1 Exploring Operation: 26-23=3, Resulting Numbers: [25, 3] Generated Node #0,1,1: 16:[25, 3] Operation: 26-23=3 Exploring Operation: 25-23=2, Resulting Numbers: [26, 2] Generated Node #0,1,2: 16:[26, 2] Operation: 25-23=2 Exploring Operation: 25+23=48, Resulting Numbers: [26, 48] Generated Node #0,1,3: 16:[26, 48] Operation: 25+23=48 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[23, 1], Operations: ['68-42=26', '26-25=1'] Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[25, 3], Operations: ['68-42=26', '26-23=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[26, 2], Operations: ['68-42=26', '25-23=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[26, 48], Operations: ['68-42=26', '25+23=48'] Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 26+48=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 26*48=1248, Resulting Numbers: [1248] 1248,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[68, 23, 17], Operations: ['42-25=17'] Exploring Operation: 68/17=4, Resulting Numbers: [23, 4] Generated Node #0,2,0: 16:[23, 4] Operation: 68/17=4 Exploring Operation: 23-17=6, Resulting Numbers: [68, 6] Generated Node #0,2,1: 16:[68, 6] Operation: 23-17=6 Exploring Operation: 68-17=51, Resulting Numbers: [23, 51] Generated Node #0,2,2: 16:[23, 51] Operation: 68-17=51 Exploring Operation: 68-23=45, Resulting Numbers: [17, 45] Generated Node #0,2,3: 16:[17, 45] Operation: 68-23=45 Moving to Node #0,2,0 Current State: 16:[23, 4], Operations: ['42-25=17', '68/17=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,16 unequal: No Solution Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,16 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[17, 45], Operations: ['42-25=17', '68-23=45'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 17*45=765, Resulting Numbers: [765] 765,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[23, 51], Operations: ['42-25=17', '68-17=51'] Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,16 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[68, 6], Operations: ['42-25=17', '23-17=6'] Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,16 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,16 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[42, 23, 43], Operations: ['68-25=43'] Exploring Operation: 43-42=1, Resulting Numbers: [23, 1] Generated Node #0,3,0: 16:[23, 1] Operation: 43-42=1 Exploring Operation: 43-23=20, Resulting Numbers: [42, 20] Generated Node #0,3,1: 16:[42, 20] Operation: 43-23=20 Exploring Operation: 42-23=19, Resulting Numbers: [43, 19] Generated Node #0,3,2: 16:[43, 19] Operation: 42-23=19 Exploring Operation: 42+23=65, Resulting Numbers: [43, 65] Generated Node #0,3,3: 16:[43, 65] Operation: 42+23=65 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 16:[23, 1], Operations: ['68-25=43', '43-42=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 16:[42, 20], Operations: ['68-25=43', '43-23=20'] Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,16 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 16:[43, 19], Operations: ['68-25=43', '42-23=19'] Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 43*19=817, Resulting Numbers: [817] 817,16 unequal: No Solution Exploring Operation: 43+19=62, Resulting Numbers: [62] 62,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 16:[43, 65], Operations: ['68-25=43', '42+23=65'] Exploring Operation: 43*65=2795, Resulting Numbers: [2795] 2795,16 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 43+65=108, Resulting Numbers: [108] 108,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[42, 25, 45], Operations: ['68-23=45'] Exploring Operation: 42-25=17, Resulting Numbers: [45, 17] Generated Node #0,0,0: 16:[45, 17] Operation: 42-25=17 Exploring Operation: 42+25=67, Resulting Numbers: [45, 67] Generated Node #0,0,1: 16:[45, 67] Operation: 42+25=67 Exploring Operation: 45-25=20, Resulting Numbers: [42, 20] Generated Node #0,0,2: 16:[42, 20] Operation: 45-25=20 Exploring Operation: 45-42=3, Resulting Numbers: [25, 3] Generated Node #0,0,3: 16:[25, 3] Operation: 45-42=3 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 16:[25, 3], Operations: ['68-23=45', '45-42=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[45, 17], Operations: ['68-23=45', '42-25=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[42, 20], Operations: ['68-23=45', '45-25=20'] Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,16 unequal: No Solution Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,16 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[45, 67], Operations: ['68-23=45', '42+25=67'] Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,16 unequal: No Solution Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 37, 46, 5, 28 ]
57
[ "37+46=83", "5*28=140", "140-83=57" ]
Current State: 57:[37, 46, 5, 28], Operations: [] Exploring Operation: 37+46=83, Resulting Numbers: [5, 28, 83] Generated Node #2: [5, 28, 83] from Operation: 37+46=83 Current State: 57:[5, 28, 83], Operations: ['37+46=83'] Exploring Operation: 5*28=140, Resulting Numbers: [83, 140] Generated Node #3: [83, 140] from Operation: 5*28=140 Current State: 57:[83, 140], Operations: ['37+46=83', '5*28=140'] Exploring Operation: 140-83=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[37, 46, 5, 28], Operations: [] Exploring Operation: 37+28=65, Resulting Numbers: [46, 5, 65] Generated Node #0,0: 57:[46, 5, 65] Operation: 37+28=65 Exploring Operation: 37-28=9, Resulting Numbers: [46, 5, 9] Generated Node #0,1: 57:[46, 5, 9] Operation: 37-28=9 Exploring Operation: 46-37=9, Resulting Numbers: [5, 28, 9] Generated Node #0,2: 57:[5, 28, 9] Operation: 46-37=9 Moving to Node #0,2 Current State: 57:[5, 28, 9], Operations: ['46-37=9'] Exploring Operation: 9-5=4, Resulting Numbers: [28, 4] Generated Node #0,2,0: 57:[28, 4] Operation: 9-5=4 Exploring Operation: 28-9=19, Resulting Numbers: [5, 19] Generated Node #0,2,1: 57:[5, 19] Operation: 28-9=19 Exploring Operation: 28-5=23, Resulting Numbers: [9, 23] Generated Node #0,2,2: 57:[9, 23] Operation: 28-5=23 Moving to Node #0,1 Current State: 57:[46, 5, 9], Operations: ['37-28=9'] Exploring Operation: 46+5=51, Resulting Numbers: [9, 51] Generated Node #0,1,0: 57:[9, 51] Operation: 46+5=51 Exploring Operation: 9-5=4, Resulting Numbers: [46, 4] Generated Node #0,1,1: 57:[46, 4] Operation: 9-5=4 Exploring Operation: 46+9=55, Resulting Numbers: [5, 55] Generated Node #0,1,2: 57:[5, 55] Operation: 46+9=55 Moving to Node #0,0 Current State: 57:[46, 5, 65], Operations: ['37+28=65'] Exploring Operation: 65-5=60, Resulting Numbers: [46, 60] Generated Node #0,0,0: 57:[46, 60] Operation: 65-5=60 Exploring Operation: 65-46=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 57:[5, 19] Operation: 65-46=19 Exploring Operation: 46+5=51, Resulting Numbers: [65, 51] Generated Node #0,0,2: 57:[65, 51] Operation: 46+5=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[5, 19], Operations: ['37+28=65', '65-46=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[46, 60], Operations: ['37+28=65', '65-5=60'] Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,57 unequal: No Solution Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[65, 51], Operations: ['37+28=65', '46+5=51'] Exploring Operation: 65*51=3315, Resulting Numbers: [3315] 3315,57 unequal: No Solution Exploring Operation: 65+51=116, Resulting Numbers: [116] 116,57 unequal: No Solution Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 57:[5, 19], Operations: ['46-37=9', '28-9=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[5, 55], Operations: ['37-28=9', '46+9=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,57 unequal: No Solution Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[9, 23], Operations: ['46-37=9', '28-5=23'] Exploring Operation: 9*23=207, Resulting Numbers: [207] 207,57 unequal: No Solution Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[28, 4], Operations: ['46-37=9', '9-5=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,57 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[46, 4], Operations: ['37-28=9', '9-5=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,57 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,57 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[9, 51], Operations: ['37-28=9', '46+5=51'] Exploring Operation: 9*51=459, Resulting Numbers: [459] 459,57 unequal: No Solution Exploring Operation: 9+51=60, Resulting Numbers: [60] 60,57 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,57 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 6, 34, 99, 98 ]
29
[ "34-6=28", "99-98=1", "28+1=29" ]
Current State: 29:[6, 34, 99, 98], Operations: [] Exploring Operation: 34-6=28, Resulting Numbers: [99, 98, 28] Generated Node #2: [99, 98, 28] from Operation: 34-6=28 Current State: 29:[99, 98, 28], Operations: ['34-6=28'] Exploring Operation: 99-98=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 99-98=1 Current State: 29:[28, 1], Operations: ['34-6=28', '99-98=1'] Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[6, 34, 99, 98], Operations: [] Exploring Operation: 98-34=64, Resulting Numbers: [6, 99, 64] Generated Node #0,0: 29:[6, 99, 64] Operation: 98-34=64 Exploring Operation: 99-34=65, Resulting Numbers: [6, 98, 65] Generated Node #0,1: 29:[6, 98, 65] Operation: 99-34=65 Exploring Operation: 99-6=93, Resulting Numbers: [34, 98, 93] Generated Node #0,2: 29:[34, 98, 93] Operation: 99-6=93 Exploring Operation: 99-98=1, Resulting Numbers: [6, 34, 1] Generated Node #0,3: 29:[6, 34, 1] Operation: 99-98=1 Exploring Operation: 98-6=92, Resulting Numbers: [34, 99, 92] Generated Node #0,4: 29:[34, 99, 92] Operation: 98-6=92 Moving to Node #0,3 Current State: 29:[6, 34, 1], Operations: ['99-98=1'] Exploring Operation: 34*1=34, Resulting Numbers: [6, 34] Generated Node #0,3,0: 29:[6, 34] Operation: 34*1=34 Exploring Operation: 6+1=7, Resulting Numbers: [34, 7] Generated Node #0,3,1: 29:[34, 7] Operation: 6+1=7 Exploring Operation: 6/1=6, Resulting Numbers: [34, 6] Generated Node #0,3,2: 29:[34, 6] Operation: 6/1=6 Exploring Operation: 34-1=33, Resulting Numbers: [6, 33] Generated Node #0,3,3: 29:[6, 33] Operation: 34-1=33 Exploring Operation: 6*1=6, Resulting Numbers: [34, 6] Generated Node #0,3,4: 29:[34, 6] Operation: 6*1=6 Moving to Node #0,1 Current State: 29:[6, 98, 65], Operations: ['99-34=65'] Exploring Operation: 65-6=59, Resulting Numbers: [98, 59] Generated Node #0,1,0: 29:[98, 59] Operation: 65-6=59 Exploring Operation: 6+65=71, Resulting Numbers: [98, 71] Generated Node #0,1,1: 29:[98, 71] Operation: 6+65=71 Exploring Operation: 6+98=104, Resulting Numbers: [65, 104] Generated Node #0,1,2: 29:[65, 104] Operation: 6+98=104 Exploring Operation: 98-6=92, Resulting Numbers: [65, 92] Generated Node #0,1,3: 29:[65, 92] Operation: 98-6=92 Exploring Operation: 98-65=33, Resulting Numbers: [6, 33] Generated Node #0,1,4: 29:[6, 33] Operation: 98-65=33 Moving to Node #0,0 Current State: 29:[6, 99, 64], Operations: ['98-34=64'] Exploring Operation: 6+99=105, Resulting Numbers: [64, 105] Generated Node #0,0,0: 29:[64, 105] Operation: 6+99=105 Exploring Operation: 64-6=58, Resulting Numbers: [99, 58] Generated Node #0,0,1: 29:[99, 58] Operation: 64-6=58 Exploring Operation: 6+64=70, Resulting Numbers: [99, 70] Generated Node #0,0,2: 29:[99, 70] Operation: 6+64=70 Exploring Operation: 99-6=93, Resulting Numbers: [64, 93] Generated Node #0,0,3: 29:[64, 93] Operation: 99-6=93 Exploring Operation: 99-64=35, Resulting Numbers: [6, 35] Generated Node #0,0,4: 29:[6, 35] Operation: 99-64=35 Moving to Node #0,2 Current State: 29:[34, 98, 93], Operations: ['99-6=93'] Exploring Operation: 34+93=127, Resulting Numbers: [98, 127] Generated Node #0,2,0: 29:[98, 127] Operation: 34+93=127 Exploring Operation: 93-34=59, Resulting Numbers: [98, 59] Generated Node #0,2,1: 29:[98, 59] Operation: 93-34=59 Exploring Operation: 98-93=5, Resulting Numbers: [34, 5] Generated Node #0,2,2: 29:[34, 5] Operation: 98-93=5 Exploring Operation: 98-34=64, Resulting Numbers: [93, 64] Generated Node #0,2,3: 29:[93, 64] Operation: 98-34=64 Exploring Operation: 34+98=132, Resulting Numbers: [93, 132] Generated Node #0,2,4: 29:[93, 132] Operation: 34+98=132 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[34, 5], Operations: ['99-6=93', '98-93=5'] Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,29 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[6, 34, 99, 98], Operations: [] Exploring Operation: 99-6=93, Resulting Numbers: [34, 98, 93] Generated Node #0,2: 29:[34, 98, 93] Operation: 99-6=93 Moving to Node #0,2 Current State: 29:[34, 98, 93], Operations: ['99-6=93'] Exploring Operation: 98-93=5, Resulting Numbers: [34, 5] Generated Node #0,2,2: 29:[34, 5] Operation: 98-93=5 Moving to Node #0,2,2 Current State: 29:[34, 5], Operations: ['99-6=93', '98-93=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_5
sum_heuristic
[ 68, 87, 15, 95 ]
20
[ "87-68=19", "95/19=5", "15+5=20" ]
Current State: 20:[68, 87, 15, 95], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [15, 95, 19] Generated Node #2: [15, 95, 19] from Operation: 87-68=19 Current State: 20:[15, 95, 19], Operations: ['87-68=19'] Exploring Operation: 95/19=5, Resulting Numbers: [15, 5] Generated Node #3: [15, 5] from Operation: 95/19=5 Current State: 20:[15, 5], Operations: ['87-68=19', '95/19=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[68, 87, 15, 95], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [68, 15, 8] Generated Node #0,0: 20:[68, 15, 8] Operation: 95-87=8 Exploring Operation: 95-68=27, Resulting Numbers: [87, 15, 27] Generated Node #0,1: 20:[87, 15, 27] Operation: 95-68=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[68, 15, 8], Operations: ['95-87=8'] Exploring Operation: 68-15=53, Resulting Numbers: [8, 53] Generated Node #0,0,0: 20:[8, 53] Operation: 68-15=53 Exploring Operation: 68-8=60, Resulting Numbers: [15, 60] Generated Node #0,0,1: 20:[15, 60] Operation: 68-8=60 Moving to Node #0,0,0 Current State: 20:[8, 53], Operations: ['95-87=8', '68-15=53'] Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,20 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[15, 60], Operations: ['95-87=8', '68-8=60'] Exploring Operation: 60-15=45, Resulting Numbers: [45] 45,20 unequal: No Solution Exploring Operation: 60/15=4, Resulting Numbers: [4] 4,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[87, 15, 27], Operations: ['95-68=27'] Exploring Operation: 87-27=60, Resulting Numbers: [15, 60] Generated Node #0,1,0: 20:[15, 60] Operation: 87-27=60 Exploring Operation: 87-15=72, Resulting Numbers: [27, 72] Generated Node #0,1,1: 20:[27, 72] Operation: 87-15=72 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[15, 60], Operations: ['95-68=27', '87-27=60'] Exploring Operation: 60/15=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 60-15=45, Resulting Numbers: [45] 45,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[27, 72], Operations: ['95-68=27', '87-15=72'] Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,20 unequal: No Solution Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 55, 4, 73, 82 ]
91
[ "82-73=9", "4*9=36", "55+36=91" ]
Current State: 91:[55, 4, 73, 82], Operations: [] Exploring Operation: 82-73=9, Resulting Numbers: [55, 4, 9] Generated Node #2: [55, 4, 9] from Operation: 82-73=9 Current State: 91:[55, 4, 9], Operations: ['82-73=9'] Exploring Operation: 4*9=36, Resulting Numbers: [55, 36] Generated Node #3: [55, 36] from Operation: 4*9=36 Current State: 91:[55, 36], Operations: ['82-73=9', '4*9=36'] Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[55, 4, 73, 82], Operations: [] Exploring Operation: 55+73=128, Resulting Numbers: [4, 82, 128] Generated Node #0,0: 91:[4, 82, 128] Operation: 55+73=128 Exploring Operation: 82-55=27, Resulting Numbers: [4, 73, 27] Generated Node #0,1: 91:[4, 73, 27] Operation: 82-55=27 Exploring Operation: 55+4=59, Resulting Numbers: [73, 82, 59] Generated Node #0,2: 91:[73, 82, 59] Operation: 55+4=59 Exploring Operation: 82-73=9, Resulting Numbers: [55, 4, 9] Generated Node #0,3: 91:[55, 4, 9] Operation: 82-73=9 Exploring Operation: 73-55=18, Resulting Numbers: [4, 82, 18] Generated Node #0,4: 91:[4, 82, 18] Operation: 73-55=18 Start Sub Search at level 1: Moving to Node #0,4 Current State: 91:[4, 82, 18], Operations: ['73-55=18'] Exploring Operation: 82+18=100, Resulting Numbers: [4, 100] Generated Node #0,4,0: 91:[4, 100] Operation: 82+18=100 Exploring Operation: 82-4=78, Resulting Numbers: [18, 78] Generated Node #0,4,1: 91:[18, 78] Operation: 82-4=78 Exploring Operation: 4+18=22, Resulting Numbers: [82, 22] Generated Node #0,4,2: 91:[82, 22] Operation: 4+18=22 Exploring Operation: 18-4=14, Resulting Numbers: [82, 14] Generated Node #0,4,3: 91:[82, 14] Operation: 18-4=14 Exploring Operation: 4+82=86, Resulting Numbers: [18, 86] Generated Node #0,4,4: 91:[18, 86] Operation: 4+82=86 Moving to Node #0,4,3 Current State: 91:[82, 14], Operations: ['73-55=18', '18-4=14'] Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 82*14=1148, Resulting Numbers: [1148] 1148,91 unequal: No Solution Moving to Node #0,4,4 Current State: 91:[18, 86], Operations: ['73-55=18', '4+82=86'] Exploring Operation: 18*86=1548, Resulting Numbers: [1548] 1548,91 unequal: No Solution Exploring Operation: 18+86=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,91 unequal: No Solution Moving to Node #0,4,0 Current State: 91:[4, 100], Operations: ['73-55=18', '82+18=100'] Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 4*100=400, Resulting Numbers: [400] 400,91 unequal: No Solution Exploring Operation: 4+100=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,91 unequal: No Solution Moving to Node #0,4,1 Current State: 91:[18, 78], Operations: ['73-55=18', '82-4=78'] Exploring Operation: 18+78=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 18*78=1404, Resulting Numbers: [1404] 1404,91 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,91 unequal: No Solution Moving to Node #0,4,2 Current State: 91:[82, 22], Operations: ['73-55=18', '4+18=22'] Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,91 unequal: No Solution Exploring Operation: 82+22=104, Resulting Numbers: [104] 104,91 unequal: No Solution Exploring Operation: 82*22=1804, Resulting Numbers: [1804] 1804,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[4, 73, 27], Operations: ['82-55=27'] Exploring Operation: 73-4=69, Resulting Numbers: [27, 69] Generated Node #0,1,0: 91:[27, 69] Operation: 73-4=69 Exploring Operation: 73+27=100, Resulting Numbers: [4, 100] Generated Node #0,1,1: 91:[4, 100] Operation: 73+27=100 Exploring Operation: 4+73=77, Resulting Numbers: [27, 77] Generated Node #0,1,2: 91:[27, 77] Operation: 4+73=77 Exploring Operation: 27-4=23, Resulting Numbers: [73, 23] Generated Node #0,1,3: 91:[73, 23] Operation: 27-4=23 Exploring Operation: 4*27=108, Resulting Numbers: [73, 108] Generated Node #0,1,4: 91:[73, 108] Operation: 4*27=108 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[4, 100], Operations: ['82-55=27', '73+27=100'] Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,91 unequal: No Solution Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 4*100=400, Resulting Numbers: [400] 400,91 unequal: No Solution Exploring Operation: 4+100=104, Resulting Numbers: [104] 104,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[27, 77], Operations: ['82-55=27', '4+73=77'] Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 27*77=2079, Resulting Numbers: [2079] 2079,91 unequal: No Solution Exploring Operation: 27+77=104, Resulting Numbers: [104] 104,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 91:[73, 23], Operations: ['82-55=27', '27-4=23'] Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 73*23=1679, Resulting Numbers: [1679] 1679,91 unequal: No Solution Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 91:[73, 108], Operations: ['82-55=27', '4*27=108'] Exploring Operation: 108-73=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 73*108=7884, Resulting Numbers: [7884] 7884,91 unequal: No Solution Exploring Operation: 73+108=181, Resulting Numbers: [181] 181,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[27, 69], Operations: ['82-55=27', '73-4=69'] Exploring Operation: 27*69=1863, Resulting Numbers: [1863] 1863,91 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 27+69=96, Resulting Numbers: [96] 96,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[55, 4, 9], Operations: ['82-73=9'] Exploring Operation: 55+4=59, Resulting Numbers: [9, 59] Generated Node #0,3,0: 91:[9, 59] Operation: 55+4=59 Exploring Operation: 9-4=5, Resulting Numbers: [55, 5] Generated Node #0,3,1: 91:[55, 5] Operation: 9-4=5 Exploring Operation: 55-9=46, Resulting Numbers: [4, 46] Generated Node #0,3,2: 91:[4, 46] Operation: 55-9=46 Exploring Operation: 4+9=13, Resulting Numbers: [55, 13] Generated Node #0,3,3: 91:[55, 13] Operation: 4+9=13 Exploring Operation: 55+9=64, Resulting Numbers: [4, 64] Generated Node #0,3,4: 91:[4, 64] Operation: 55+9=64 Moving to Node #0,3,4 Current State: 91:[4, 64], Operations: ['82-73=9', '55+9=64'] Exploring Operation: 4*64=256, Resulting Numbers: [256] 256,91 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 4+64=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,91 unequal: No Solution Moving to Node #0,3,0 Current State: 91:[9, 59], Operations: ['82-73=9', '55+4=59'] Exploring Operation: 9*59=531, Resulting Numbers: [531] 531,91 unequal: No Solution Exploring Operation: 9+59=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[4, 46], Operations: ['82-73=9', '55-9=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,91 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[55, 13], Operations: ['82-73=9', '4+9=13'] Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,91 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[55, 5], Operations: ['82-73=9', '9-4=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,91 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 55*5=275, Resulting Numbers: [275] 275,91 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[4, 82, 128], Operations: ['55+73=128'] Exploring Operation: 82-4=78, Resulting Numbers: [128, 78] Generated Node #0,0,0: 91:[128, 78] Operation: 82-4=78 Exploring Operation: 4+82=86, Resulting Numbers: [128, 86] Generated Node #0,0,1: 91:[128, 86] Operation: 4+82=86 Exploring Operation: 128/4=32, Resulting Numbers: [82, 32] Generated Node #0,0,2: 91:[82, 32] Operation: 128/4=32 Exploring Operation: 128-82=46, Resulting Numbers: [4, 46] Generated Node #0,0,3: 91:[4, 46] Operation: 128-82=46 Exploring Operation: 128-4=124, Resulting Numbers: [82, 124] Generated Node #0,0,4: 91:[82, 124] Operation: 128-4=124 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[82, 32], Operations: ['55+73=128', '128/4=32'] Exploring Operation: 82*32=2624, Resulting Numbers: [2624] 2624,91 unequal: No Solution Exploring Operation: 82+32=114, Resulting Numbers: [114] 114,91 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 91:[4, 46], Operations: ['55+73=128', '128-82=46'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[128, 86], Operations: ['55+73=128', '4+82=86'] Exploring Operation: 128-86=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 128+86=214, Resulting Numbers: [214] 214,91 unequal: No Solution Exploring Operation: 128*86=11008, Resulting Numbers: [11008] 11008,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 91:[82, 124], Operations: ['55+73=128', '128-4=124'] Exploring Operation: 82+124=206, Resulting Numbers: [206] 206,91 unequal: No Solution Exploring Operation: 124-82=42, Resulting Numbers: [42] 42,91 unequal: No Solution Exploring Operation: 82*124=10168, Resulting Numbers: [10168] 10168,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[128, 78], Operations: ['55+73=128', '82-4=78'] Exploring Operation: 128*78=9984, Resulting Numbers: [9984] 9984,91 unequal: No Solution Exploring Operation: 128+78=206, Resulting Numbers: [206] 206,91 unequal: No Solution Exploring Operation: 128-78=50, Resulting Numbers: [50] 50,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[73, 82, 59], Operations: ['55+4=59'] Exploring Operation: 82-59=23, Resulting Numbers: [73, 23] Generated Node #0,2,0: 91:[73, 23] Operation: 82-59=23 Exploring Operation: 73+59=132, Resulting Numbers: [82, 132] Generated Node #0,2,1: 91:[82, 132] Operation: 73+59=132 Exploring Operation: 82+59=141, Resulting Numbers: [73, 141] Generated Node #0,2,2: 91:[73, 141] Operation: 82+59=141 Exploring Operation: 82-73=9, Resulting Numbers: [59, 9] Generated Node #0,2,3: 91:[59, 9] Operation: 82-73=9 Exploring Operation: 73-59=14, Resulting Numbers: [82, 14] Generated Node #0,2,4: 91:[82, 14] Operation: 73-59=14 Moving to Node #0,2,4 Current State: 91:[82, 14], Operations: ['55+4=59', '73-59=14'] Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,91 unequal: No Solution Exploring Operation: 82*14=1148, Resulting Numbers: [1148] 1148,91 unequal: No Solution Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[73, 23], Operations: ['55+4=59', '82-59=23'] Exploring Operation: 73*23=1679, Resulting Numbers: [1679] 1679,91 unequal: No Solution Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[59, 9], Operations: ['55+4=59', '82-73=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 59*9=531, Resulting Numbers: [531] 531,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[82, 132], Operations: ['55+4=59', '73+59=132'] Exploring Operation: 132-82=50, Resulting Numbers: [50] 50,91 unequal: No Solution Exploring Operation: 82*132=10824, Resulting Numbers: [10824] 10824,91 unequal: No Solution Exploring Operation: 82+132=214, Resulting Numbers: [214] 214,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[73, 141], Operations: ['55+4=59', '82+59=141'] Exploring Operation: 73+141=214, Resulting Numbers: [214] 214,91 unequal: No Solution Exploring Operation: 73*141=10293, Resulting Numbers: [10293] 10293,91 unequal: No Solution Exploring Operation: 141-73=68, Resulting Numbers: [68] 68,91 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
[ 33, 80, 41, 36 ]
49
[ "41-36=5", "80/5=16", "33+16=49" ]
Current State: 49:[33, 80, 41, 36], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [33, 80, 5] Generated Node #2: [33, 80, 5] from Operation: 41-36=5 Current State: 49:[33, 80, 5], Operations: ['41-36=5'] Exploring Operation: 80/5=16, Resulting Numbers: [33, 16] Generated Node #3: [33, 16] from Operation: 80/5=16 Current State: 49:[33, 16], Operations: ['41-36=5', '80/5=16'] Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[33, 80, 41, 36], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [80, 36, 8] Generated Node #0,0: 49:[80, 36, 8] Operation: 41-33=8 Exploring Operation: 80-33=47, Resulting Numbers: [41, 36, 47] Generated Node #0,1: 49:[41, 36, 47] Operation: 80-33=47 Exploring Operation: 80-36=44, Resulting Numbers: [33, 41, 44] Generated Node #0,2: 49:[33, 41, 44] Operation: 80-36=44 Exploring Operation: 80-41=39, Resulting Numbers: [33, 36, 39] Generated Node #0,3: 49:[33, 36, 39] Operation: 80-41=39 Exploring Operation: 36-33=3, Resulting Numbers: [80, 41, 3] Generated Node #0,4: 49:[80, 41, 3] Operation: 36-33=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[41, 36, 47], Operations: ['80-33=47'] Exploring Operation: 47-36=11, Resulting Numbers: [41, 11] Generated Node #0,1,0: 49:[41, 11] Operation: 47-36=11 Exploring Operation: 41-36=5, Resulting Numbers: [47, 5] Generated Node #0,1,1: 49:[47, 5] Operation: 41-36=5 Exploring Operation: 41+36=77, Resulting Numbers: [47, 77] Generated Node #0,1,2: 49:[47, 77] Operation: 41+36=77 Exploring Operation: 36+47=83, Resulting Numbers: [41, 83] Generated Node #0,1,3: 49:[41, 83] Operation: 36+47=83 Exploring Operation: 47-41=6, Resulting Numbers: [36, 6] Generated Node #0,1,4: 49:[36, 6] Operation: 47-41=6 Moving to Node #0,1,1 Current State: 49:[47, 5], Operations: ['80-33=47', '41-36=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[41, 11], Operations: ['80-33=47', '47-36=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,49 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,49 unequal: No Solution Moving to Node #0,1,4 Current State: 49:[36, 6], Operations: ['80-33=47', '47-41=6'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,49 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[47, 77], Operations: ['80-33=47', '41+36=77'] Exploring Operation: 47+77=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 47*77=3619, Resulting Numbers: [3619] 3619,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[41, 83], Operations: ['80-33=47', '36+47=83'] Exploring Operation: 41+83=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 41*83=3403, Resulting Numbers: [3403] 3403,49 unequal: No Solution Exploring Operation: 83-41=42, Resulting Numbers: [42] 42,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[33, 41, 44], Operations: ['80-36=44'] Exploring Operation: 44-33=11, Resulting Numbers: [41, 11] Generated Node #0,2,0: 49:[41, 11] Operation: 44-33=11 Exploring Operation: 33+44=77, Resulting Numbers: [41, 77] Generated Node #0,2,1: 49:[41, 77] Operation: 33+44=77 Exploring Operation: 41-33=8, Resulting Numbers: [44, 8] Generated Node #0,2,2: 49:[44, 8] Operation: 41-33=8 Exploring Operation: 44-41=3, Resulting Numbers: [33, 3] Generated Node #0,2,3: 49:[33, 3] Operation: 44-41=3 Exploring Operation: 33+41=74, Resulting Numbers: [44, 74] Generated Node #0,2,4: 49:[44, 74] Operation: 33+41=74 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 49:[44, 8], Operations: ['80-36=44', '41-33=8'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 44+8=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 44*8=352, Resulting Numbers: [352] 352,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[41, 11], Operations: ['80-36=44', '44-33=11'] Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 49:[33, 3], Operations: ['80-36=44', '44-41=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 49:[44, 74], Operations: ['80-36=44', '33+41=74'] Exploring Operation: 44*74=3256, Resulting Numbers: [3256] 3256,49 unequal: No Solution Exploring Operation: 44+74=118, Resulting Numbers: [118] 118,49 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[41, 77], Operations: ['80-36=44', '33+44=77'] Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,49 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[33, 36, 39], Operations: ['80-41=39'] Exploring Operation: 39-33=6, Resulting Numbers: [36, 6] Generated Node #0,3,0: 49:[36, 6] Operation: 39-33=6 Exploring Operation: 39-36=3, Resulting Numbers: [33, 3] Generated Node #0,3,1: 49:[33, 3] Operation: 39-36=3 Exploring Operation: 33+39=72, Resulting Numbers: [36, 72] Generated Node #0,3,2: 49:[36, 72] Operation: 33+39=72 Exploring Operation: 33+36=69, Resulting Numbers: [39, 69] Generated Node #0,3,3: 49:[39, 69] Operation: 33+36=69 Exploring Operation: 36-33=3, Resulting Numbers: [39, 3] Generated Node #0,3,4: 49:[39, 3] Operation: 36-33=3 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 49:[36, 6], Operations: ['80-41=39', '39-33=6'] Exploring Operation: 36*6=216, Resulting Numbers: [216] 216,49 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 49:[39, 3], Operations: ['80-41=39', '36-33=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 39*3=117, Resulting Numbers: [117] 117,49 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 49:[33, 3], Operations: ['80-41=39', '39-36=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,49 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,49 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 49:[39, 69], Operations: ['80-41=39', '33+36=69'] Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,49 unequal: No Solution Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,49 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 49:[36, 72], Operations: ['80-41=39', '33+39=72'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,49 unequal: No Solution Exploring Operation: 36*72=2592, Resulting Numbers: [2592] 2592,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[80, 41, 3], Operations: ['36-33=3'] Exploring Operation: 80-41=39, Resulting Numbers: [3, 39] Generated Node #0,4,0: 49:[3, 39] Operation: 80-41=39 Exploring Operation: 80+3=83, Resulting Numbers: [41, 83] Generated Node #0,4,1: 49:[41, 83] Operation: 80+3=83 Exploring Operation: 41+3=44, Resulting Numbers: [80, 44] Generated Node #0,4,2: 49:[80, 44] Operation: 41+3=44 Exploring Operation: 80-3=77, Resulting Numbers: [41, 77] Generated Node #0,4,3: 49:[41, 77] Operation: 80-3=77 Exploring Operation: 41-3=38, Resulting Numbers: [80, 38] Generated Node #0,4,4: 49:[80, 38] Operation: 41-3=38 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 49:[3, 39], Operations: ['36-33=3', '80-41=39'] Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,49 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 49:[80, 44], Operations: ['36-33=3', '41+3=44'] Exploring Operation: 80+44=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 80*44=3520, Resulting Numbers: [3520] 3520,49 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 49:[41, 77], Operations: ['36-33=3', '80-3=77'] Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,49 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 49:[41, 83], Operations: ['36-33=3', '80+3=83'] Exploring Operation: 41*83=3403, Resulting Numbers: [3403] 3403,49 unequal: No Solution Exploring Operation: 83-41=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 41+83=124, Resulting Numbers: [124] 124,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 49:[80, 38], Operations: ['36-33=3', '41-3=38'] Exploring Operation: 80*38=3040, Resulting Numbers: [3040] 3040,49 unequal: No Solution Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,49 unequal: No Solution Exploring Operation: 80+38=118, Resulting Numbers: [118] 118,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[80, 36, 8], Operations: ['41-33=8'] Exploring Operation: 36+8=44, Resulting Numbers: [80, 44] Generated Node #0,0,0: 49:[80, 44] Operation: 36+8=44 Exploring Operation: 80/8=10, Resulting Numbers: [36, 10] Generated Node #0,0,1: 49:[36, 10] Operation: 80/8=10 Exploring Operation: 80-8=72, Resulting Numbers: [36, 72] Generated Node #0,0,2: 49:[36, 72] Operation: 80-8=72 Exploring Operation: 80-36=44, Resulting Numbers: [8, 44] Generated Node #0,0,3: 49:[8, 44] Operation: 80-36=44 Exploring Operation: 80+8=88, Resulting Numbers: [36, 88] Generated Node #0,0,4: 49:[36, 88] Operation: 80+8=88 Moving to Node #0,0,3 Current State: 49:[8, 44], Operations: ['41-33=8', '80-36=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[36, 10], Operations: ['41-33=8', '80/8=10'] Exploring Operation: 36*10=360, Resulting Numbers: [360] 360,49 unequal: No Solution Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,49 unequal: No Solution Moving to Node #0,0,0 Current State: 49:[80, 44], Operations: ['41-33=8', '36+8=44'] Exploring Operation: 80+44=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 80*44=3520, Resulting Numbers: [3520] 3520,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[36, 72], Operations: ['41-33=8', '80-8=72'] Exploring Operation: 36*72=2592, Resulting Numbers: [2592] 2592,49 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,49 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,49 unequal: No Solution Moving to Node #0,0,4 Current State: 49:[36, 88], Operations: ['41-33=8', '80+8=88'] Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,49 unequal: No Solution Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,49 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
[ 12, 19, 20, 23 ]
15
[ "23-20=3", "12/3=4", "19-4=15" ]
Current State: 15:[12, 19, 20, 23], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [12, 19, 3] Generated Node #2: [12, 19, 3] from Operation: 23-20=3 Current State: 15:[12, 19, 3], Operations: ['23-20=3'] Exploring Operation: 12/3=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 12/3=4 Current State: 15:[19, 4], Operations: ['23-20=3', '12/3=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[12, 19, 20, 23], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [12, 19, 3] Generated Node #0,0: 15:[12, 19, 3] Operation: 23-20=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[12, 19, 3], Operations: ['23-20=3'] Exploring Operation: 19-12=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 15:[3, 7] Operation: 19-12=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[3, 7], Operations: ['23-20=3', '19-12=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 25, 2, 5, 93 ]
29
[ "93-25=68", "68/2=34", "34-5=29" ]
Current State: 29:[25, 2, 5, 93], Operations: [] Exploring Operation: 93-25=68, Resulting Numbers: [2, 5, 68] Generated Node #2: [2, 5, 68] from Operation: 93-25=68 Current State: 29:[2, 5, 68], Operations: ['93-25=68'] Exploring Operation: 68/2=34, Resulting Numbers: [5, 34] Generated Node #3: [5, 34] from Operation: 68/2=34 Current State: 29:[5, 34], Operations: ['93-25=68', '68/2=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[25, 2, 5, 93], Operations: [] Exploring Operation: 25+2=27, Resulting Numbers: [5, 93, 27] Generated Node #0,0: 29:[5, 93, 27] Operation: 25+2=27 Exploring Operation: 2*5=10, Resulting Numbers: [25, 93, 10] Generated Node #0,1: 29:[25, 93, 10] Operation: 2*5=10 Exploring Operation: 93-25=68, Resulting Numbers: [2, 5, 68] Generated Node #0,2: 29:[2, 5, 68] Operation: 93-25=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[25, 93, 10], Operations: ['2*5=10'] Exploring Operation: 93-10=83, Resulting Numbers: [25, 83] Generated Node #0,1,0: 29:[25, 83] Operation: 93-10=83 Exploring Operation: 25+10=35, Resulting Numbers: [93, 35] Generated Node #0,1,1: 29:[93, 35] Operation: 25+10=35 Exploring Operation: 93-25=68, Resulting Numbers: [10, 68] Generated Node #0,1,2: 29:[10, 68] Operation: 93-25=68 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[25, 83], Operations: ['2*5=10', '93-10=83'] Exploring Operation: 25+83=108, Resulting Numbers: [108] 108,29 unequal: No Solution Exploring Operation: 25*83=2075, Resulting Numbers: [2075] 2075,29 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 29:[10, 68], Operations: ['2*5=10', '93-25=68'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 10*68=680, Resulting Numbers: [680] 680,29 unequal: No Solution Exploring Operation: 10+68=78, Resulting Numbers: [78] 78,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[93, 35], Operations: ['2*5=10', '25+10=35'] Exploring Operation: 93*35=3255, Resulting Numbers: [3255] 3255,29 unequal: No Solution Exploring Operation: 93-35=58, Resulting Numbers: [58] 58,29 unequal: No Solution Exploring Operation: 93+35=128, Resulting Numbers: [128] 128,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[5, 93, 27], Operations: ['25+2=27'] Exploring Operation: 5+27=32, Resulting Numbers: [93, 32] Generated Node #0,0,0: 29:[93, 32] Operation: 5+27=32 Exploring Operation: 93-5=88, Resulting Numbers: [27, 88] Generated Node #0,0,1: 29:[27, 88] Operation: 93-5=88 Exploring Operation: 93-27=66, Resulting Numbers: [5, 66] Generated Node #0,0,2: 29:[5, 66] Operation: 93-27=66 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[27, 88], Operations: ['25+2=27', '93-5=88'] Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 27*88=2376, Resulting Numbers: [2376] 2376,29 unequal: No Solution Exploring Operation: 27+88=115, Resulting Numbers: [115] 115,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 29:[5, 66], Operations: ['25+2=27', '93-27=66'] Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[93, 32], Operations: ['25+2=27', '5+27=32'] Exploring Operation: 93-32=61, Resulting Numbers: [61] 61,29 unequal: No Solution Exploring Operation: 93*32=2976, Resulting Numbers: [2976] 2976,29 unequal: No Solution Exploring Operation: 93+32=125, Resulting Numbers: [125] 125,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[2, 5, 68], Operations: ['93-25=68'] Exploring Operation: 2*5=10, Resulting Numbers: [68, 10] Generated Node #0,2,0: 29:[68, 10] Operation: 2*5=10 Exploring Operation: 68/2=34, Resulting Numbers: [5, 34] Generated Node #0,2,1: 29:[5, 34] Operation: 68/2=34 Exploring Operation: 2+5=7, Resulting Numbers: [68, 7] Generated Node #0,2,2: 29:[68, 7] Operation: 2+5=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 29:[5, 34], Operations: ['93-25=68', '68/2=34'] Exploring Operation: 5*34=170, Resulting Numbers: [170] 170,29 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[25, 2, 5, 93], Operations: [] Exploring Operation: 93-25=68, Resulting Numbers: [2, 5, 68] Generated Node #0,2: 29:[2, 5, 68] Operation: 93-25=68 Moving to Node #0,2 Current State: 29:[2, 5, 68], Operations: ['93-25=68'] Exploring Operation: 68/2=34, Resulting Numbers: [5, 34] Generated Node #0,2,1: 29:[5, 34] Operation: 68/2=34 Moving to Node #0,2,1 Current State: 29:[5, 34], Operations: ['93-25=68', '68/2=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 31, 29, 30, 20 ]
80
[ "31-29=2", "30*2=60", "20+60=80" ]
Current State: 80:[31, 29, 30, 20], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [30, 20, 2] Generated Node #2: [30, 20, 2] from Operation: 31-29=2 Current State: 80:[30, 20, 2], Operations: ['31-29=2'] Exploring Operation: 30*2=60, Resulting Numbers: [20, 60] Generated Node #3: [20, 60] from Operation: 30*2=60 Current State: 80:[20, 60], Operations: ['31-29=2', '30*2=60'] Exploring Operation: 20+60=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[31, 29, 30, 20], Operations: [] Exploring Operation: 30-29=1, Resulting Numbers: [31, 20, 1] Generated Node #0,0: 80:[31, 20, 1] Operation: 30-29=1 Exploring Operation: 31-30=1, Resulting Numbers: [29, 20, 1] Generated Node #0,1: 80:[29, 20, 1] Operation: 31-30=1 Exploring Operation: 30-20=10, Resulting Numbers: [31, 29, 10] Generated Node #0,2: 80:[31, 29, 10] Operation: 30-20=10 Exploring Operation: 31-29=2, Resulting Numbers: [30, 20, 2] Generated Node #0,3: 80:[30, 20, 2] Operation: 31-29=2 Exploring Operation: 31-20=11, Resulting Numbers: [29, 30, 11] Generated Node #0,4: 80:[29, 30, 11] Operation: 31-20=11 Moving to Node #0,0 Current State: 80:[31, 20, 1], Operations: ['30-29=1'] Exploring Operation: 31-20=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 80:[1, 11] Operation: 31-20=11 Exploring Operation: 31+1=32, Resulting Numbers: [20, 32] Generated Node #0,0,1: 80:[20, 32] Operation: 31+1=32 Exploring Operation: 20*1=20, Resulting Numbers: [31, 20] Generated Node #0,0,2: 80:[31, 20] Operation: 20*1=20 Exploring Operation: 31*1=31, Resulting Numbers: [20, 31] Generated Node #0,0,3: 80:[20, 31] Operation: 31*1=31 Exploring Operation: 31/1=31, Resulting Numbers: [20, 31] Generated Node #0,0,4: 80:[20, 31] Operation: 31/1=31 Moving to Node #0,3 Current State: 80:[30, 20, 2], Operations: ['31-29=2'] Exploring Operation: 30-20=10, Resulting Numbers: [2, 10] Generated Node #0,3,0: 80:[2, 10] Operation: 30-20=10 Exploring Operation: 30-2=28, Resulting Numbers: [20, 28] Generated Node #0,3,1: 80:[20, 28] Operation: 30-2=28 Exploring Operation: 30/2=15, Resulting Numbers: [20, 15] Generated Node #0,3,2: 80:[20, 15] Operation: 30/2=15 Exploring Operation: 30+20=50, Resulting Numbers: [2, 50] Generated Node #0,3,3: 80:[2, 50] Operation: 30+20=50 Exploring Operation: 30+2=32, Resulting Numbers: [20, 32] Generated Node #0,3,4: 80:[20, 32] Operation: 30+2=32 Moving to Node #0,1 Current State: 80:[29, 20, 1], Operations: ['31-30=1'] Exploring Operation: 29-20=9, Resulting Numbers: [1, 9] Generated Node #0,1,0: 80:[1, 9] Operation: 29-20=9 Exploring Operation: 29-1=28, Resulting Numbers: [20, 28] Generated Node #0,1,1: 80:[20, 28] Operation: 29-1=28 Exploring Operation: 29/1=29, Resulting Numbers: [20, 29] Generated Node #0,1,2: 80:[20, 29] Operation: 29/1=29 Exploring Operation: 29*1=29, Resulting Numbers: [20, 29] Generated Node #0,1,3: 80:[20, 29] Operation: 29*1=29 Exploring Operation: 20*1=20, Resulting Numbers: [29, 20] Generated Node #0,1,4: 80:[29, 20] Operation: 20*1=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[1, 9], Operations: ['31-30=1', '29-20=9'] Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[20, 28], Operations: ['31-30=1', '29-1=28'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[20, 29], Operations: ['31-30=1', '29/1=29'] Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,80 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[20, 29], Operations: ['31-30=1', '29*1=29'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,80 unequal: No Solution Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 80:[29, 20], Operations: ['31-30=1', '20*1=20'] Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,80 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: 80:[31, 29, 10], Operations: ['30-20=10'] Exploring Operation: 29+10=39, Resulting Numbers: [31, 39] Generated Node #0,2,0: 80:[31, 39] Operation: 29+10=39 Exploring Operation: 31+10=41, Resulting Numbers: [29, 41] Generated Node #0,2,1: 80:[29, 41] Operation: 31+10=41 Exploring Operation: 31-10=21, Resulting Numbers: [29, 21] Generated Node #0,2,2: 80:[29, 21] Operation: 31-10=21 Exploring Operation: 31-29=2, Resulting Numbers: [10, 2] Generated Node #0,2,3: 80:[10, 2] Operation: 31-29=2 Exploring Operation: 29-10=19, Resulting Numbers: [31, 19] Generated Node #0,2,4: 80:[31, 19] Operation: 29-10=19 Moving to Node #0,4 Current State: 80:[29, 30, 11], Operations: ['31-20=11'] Exploring Operation: 29-11=18, Resulting Numbers: [30, 18] Generated Node #0,4,0: 80:[30, 18] Operation: 29-11=18 Exploring Operation: 29+11=40, Resulting Numbers: [30, 40] Generated Node #0,4,1: 80:[30, 40] Operation: 29+11=40 Exploring Operation: 30-29=1, Resulting Numbers: [11, 1] Generated Node #0,4,2: 80:[11, 1] Operation: 30-29=1 Exploring Operation: 30+11=41, Resulting Numbers: [29, 41] Generated Node #0,4,3: 80:[29, 41] Operation: 30+11=41 Exploring Operation: 30-11=19, Resulting Numbers: [29, 19] Generated Node #0,4,4: 80:[29, 19] Operation: 30-11=19 Moving to Node #0,3,0 Current State: 80:[2, 10], Operations: ['31-29=2', '30-20=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[10, 2], Operations: ['30-20=10', '31-29=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[20, 15], Operations: ['31-29=2', '30/2=15'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,80 unequal: No Solution Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[1, 11], Operations: ['30-29=1', '31-20=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[11, 1], Operations: ['31-20=11', '30-29=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[20, 32], Operations: ['30-29=1', '31+1=32'] Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,80 unequal: No Solution Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,80 unequal: No Solution Moving to Node #0,3,4 Current State: 80:[20, 32], Operations: ['31-29=2', '30+2=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[20, 28], Operations: ['31-29=2', '30-2=28'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[31, 20], Operations: ['30-29=1', '20*1=20'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,80 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,80 unequal: No Solution Moving to Node #0,0,4 Current State: 80:[20, 31], Operations: ['30-29=1', '31/1=31'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,80 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[20, 31], Operations: ['30-29=1', '31*1=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,80 unequal: No Solution Moving to Node #0,2,4 Current State: 80:[31, 19], Operations: ['30-20=10', '29-10=19'] Exploring Operation: 31*19=589, Resulting Numbers: [589] 589,80 unequal: No Solution Exploring Operation: 31-19=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 31+19=50, Resulting Numbers: [50] 50,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[29, 41], Operations: ['31-20=11', '30+11=41'] Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,80 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[29, 21], Operations: ['30-20=10', '31-10=21'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[31, 39], Operations: ['30-20=10', '29+10=39'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,80 unequal: No Solution Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[29, 41], Operations: ['30-20=10', '31+10=41'] Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[30, 40], Operations: ['31-20=11', '29+11=40'] Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,80 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[29, 19], Operations: ['31-20=11', '30-11=19'] Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,80 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[2, 50], Operations: ['31-29=2', '30+20=50'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,80 unequal: No Solution Moving to Node #0,4,0 Current State: 80:[30, 18], Operations: ['31-20=11', '29-11=18'] Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,80 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 82, 88, 69, 32 ]
31
[ "88-82=6", "69-32=37", "37-6=31" ]
Current State: 31:[82, 88, 69, 32], Operations: [] Exploring Operation: 88-82=6, Resulting Numbers: [69, 32, 6] Generated Node #2: [69, 32, 6] from Operation: 88-82=6 Current State: 31:[69, 32, 6], Operations: ['88-82=6'] Exploring Operation: 69-32=37, Resulting Numbers: [6, 37] Generated Node #3: [6, 37] from Operation: 69-32=37 Current State: 31:[6, 37], Operations: ['88-82=6', '69-32=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[82, 88, 69, 32], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [82, 32, 19] Generated Node #0,0: 31:[82, 32, 19] Operation: 88-69=19 Exploring Operation: 88-32=56, Resulting Numbers: [82, 69, 56] Generated Node #0,1: 31:[82, 69, 56] Operation: 88-32=56 Exploring Operation: 88-82=6, Resulting Numbers: [69, 32, 6] Generated Node #0,2: 31:[69, 32, 6] Operation: 88-82=6 Exploring Operation: 82-69=13, Resulting Numbers: [88, 32, 13] Generated Node #0,3: 31:[88, 32, 13] Operation: 82-69=13 Exploring Operation: 82-32=50, Resulting Numbers: [88, 69, 50] Generated Node #0,4: 31:[88, 69, 50] Operation: 82-32=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[82, 32, 19], Operations: ['88-69=19'] Exploring Operation: 82-19=63, Resulting Numbers: [32, 63] Generated Node #0,0,0: 31:[32, 63] Operation: 82-19=63 Exploring Operation: 32-19=13, Resulting Numbers: [82, 13] Generated Node #0,0,1: 31:[82, 13] Operation: 32-19=13 Exploring Operation: 32+19=51, Resulting Numbers: [82, 51] Generated Node #0,0,2: 31:[82, 51] Operation: 32+19=51 Exploring Operation: 82-32=50, Resulting Numbers: [19, 50] Generated Node #0,0,3: 31:[19, 50] Operation: 82-32=50 Exploring Operation: 82+19=101, Resulting Numbers: [32, 101] Generated Node #0,0,4: 31:[32, 101] Operation: 82+19=101 Moving to Node #0,0,3 Current State: 31:[19, 50], Operations: ['88-69=19', '82-32=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,31 unequal: No Solution Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,31 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[82, 88, 69, 32], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [82, 32, 19] Generated Node #0,0: 31:[82, 32, 19] Operation: 88-69=19 Moving to Node #0,0 Current State: 31:[82, 32, 19], Operations: ['88-69=19'] Exploring Operation: 82-32=50, Resulting Numbers: [19, 50] Generated Node #0,0,3: 31:[19, 50] Operation: 82-32=50 Moving to Node #0,0,3 Current State: 31:[19, 50], Operations: ['88-69=19', '82-32=50'] Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 33, 28, 58, 27 ]
25
[ "58-33=25", "28-27=1", "25*1=25" ]
Current State: 25:[33, 28, 58, 27], Operations: [] Exploring Operation: 58-33=25, Resulting Numbers: [28, 27, 25] Generated Node #2: [28, 27, 25] from Operation: 58-33=25 Current State: 25:[28, 27, 25], Operations: ['58-33=25'] Exploring Operation: 28-27=1, Resulting Numbers: [25, 1] Generated Node #3: [25, 1] from Operation: 28-27=1 Current State: 25:[25, 1], Operations: ['58-33=25', '28-27=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[33, 28, 58, 27], Operations: [] Exploring Operation: 58-28=30, Resulting Numbers: [33, 27, 30] Generated Node #0,0: 25:[33, 27, 30] Operation: 58-28=30 Exploring Operation: 33-27=6, Resulting Numbers: [28, 58, 6] Generated Node #0,1: 25:[28, 58, 6] Operation: 33-27=6 Exploring Operation: 58-33=25, Resulting Numbers: [28, 27, 25] Generated Node #0,2: 25:[28, 27, 25] Operation: 58-33=25 Exploring Operation: 33-28=5, Resulting Numbers: [58, 27, 5] Generated Node #0,3: 25:[58, 27, 5] Operation: 33-28=5 Exploring Operation: 58-27=31, Resulting Numbers: [33, 28, 31] Generated Node #0,4: 25:[33, 28, 31] Operation: 58-27=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[28, 27, 25], Operations: ['58-33=25'] Exploring Operation: 28-27=1, Resulting Numbers: [25, 1] Generated Node #0,2,0: 25:[25, 1] Operation: 28-27=1 Exploring Operation: 27-25=2, Resulting Numbers: [28, 2] Generated Node #0,2,1: 25:[28, 2] Operation: 27-25=2 Exploring Operation: 28+25=53, Resulting Numbers: [27, 53] Generated Node #0,2,2: 25:[27, 53] Operation: 28+25=53 Exploring Operation: 28-25=3, Resulting Numbers: [27, 3] Generated Node #0,2,3: 25:[27, 3] Operation: 28-25=3 Exploring Operation: 28+27=55, Resulting Numbers: [25, 55] Generated Node #0,2,4: 25:[25, 55] Operation: 28+27=55 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[25, 1], Operations: ['58-33=25', '28-27=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[33, 28, 58, 27], Operations: [] Exploring Operation: 58-33=25, Resulting Numbers: [28, 27, 25] Generated Node #0,2: 25:[28, 27, 25] Operation: 58-33=25 Moving to Node #0,2 Current State: 25:[28, 27, 25], Operations: ['58-33=25'] Exploring Operation: 28-27=1, Resulting Numbers: [25, 1] Generated Node #0,2,0: 25:[25, 1] Operation: 28-27=1 Moving to Node #0,2,0 Current State: 25:[25, 1], Operations: ['58-33=25', '28-27=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 53, 28, 84, 4 ]
19
[ "53+4=57", "84/28=3", "57/3=19" ]
Current State: 19:[53, 28, 84, 4], Operations: [] Exploring Operation: 53+4=57, Resulting Numbers: [28, 84, 57] Generated Node #2: [28, 84, 57] from Operation: 53+4=57 Current State: 19:[28, 84, 57], Operations: ['53+4=57'] Exploring Operation: 84/28=3, Resulting Numbers: [57, 3] Generated Node #3: [57, 3] from Operation: 84/28=3 Current State: 19:[57, 3], Operations: ['53+4=57', '84/28=3'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[53, 28, 84, 4], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [53, 4, 3] Generated Node #0,0: 19:[53, 4, 3] Operation: 84/28=3 Exploring Operation: 84-28=56, Resulting Numbers: [53, 4, 56] Generated Node #0,1: 19:[53, 4, 56] Operation: 84-28=56 Exploring Operation: 84-53=31, Resulting Numbers: [28, 4, 31] Generated Node #0,2: 19:[28, 4, 31] Operation: 84-53=31 Exploring Operation: 53-28=25, Resulting Numbers: [84, 4, 25] Generated Node #0,3: 19:[84, 4, 25] Operation: 53-28=25 Exploring Operation: 84/4=21, Resulting Numbers: [53, 28, 21] Generated Node #0,4: 19:[53, 28, 21] Operation: 84/4=21 Moving to Node #0,2 Current State: 19:[28, 4, 31], Operations: ['84-53=31'] Exploring Operation: 28/4=7, Resulting Numbers: [31, 7] Generated Node #0,2,0: 19:[31, 7] Operation: 28/4=7 Exploring Operation: 4+31=35, Resulting Numbers: [28, 35] Generated Node #0,2,1: 19:[28, 35] Operation: 4+31=35 Exploring Operation: 28-4=24, Resulting Numbers: [31, 24] Generated Node #0,2,2: 19:[31, 24] Operation: 28-4=24 Exploring Operation: 31-4=27, Resulting Numbers: [28, 27] Generated Node #0,2,3: 19:[28, 27] Operation: 31-4=27 Exploring Operation: 28+4=32, Resulting Numbers: [31, 32] Generated Node #0,2,4: 19:[31, 32] Operation: 28+4=32 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 19:[31, 24], Operations: ['84-53=31', '28-4=24'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,19 unequal: No Solution No 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: 19:[28, 27], Operations: ['84-53=31', '31-4=27'] Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 28+27=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 28*27=756, Resulting Numbers: [756] 756,19 unequal: No Solution No 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: 19:[31, 7], Operations: ['84-53=31', '28/4=7'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,19 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,19 unequal: No Solution Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,19 unequal: No Solution No 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: 19:[28, 35], Operations: ['84-53=31', '4+31=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,19 unequal: No Solution No 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: 19:[31, 32], Operations: ['84-53=31', '28+4=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,19 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,19 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: 19:[53, 28, 21], Operations: ['84/4=21'] Exploring Operation: 53-28=25, Resulting Numbers: [21, 25] Generated Node #0,4,0: 19:[21, 25] Operation: 53-28=25 Exploring Operation: 53-21=32, Resulting Numbers: [28, 32] Generated Node #0,4,1: 19:[28, 32] Operation: 53-21=32 Exploring Operation: 53+28=81, Resulting Numbers: [21, 81] Generated Node #0,4,2: 19:[21, 81] Operation: 53+28=81 Exploring Operation: 28-21=7, Resulting Numbers: [53, 7] Generated Node #0,4,3: 19:[53, 7] Operation: 28-21=7 Exploring Operation: 53+21=74, Resulting Numbers: [28, 74] Generated Node #0,4,4: 19:[28, 74] Operation: 53+21=74 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 19:[21, 25], Operations: ['84/4=21', '53-28=25'] Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,19 unequal: No Solution Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,19 unequal: No Solution No 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: 19:[28, 32], Operations: ['84/4=21', '53-21=32'] Exploring Operation: 28*32=896, Resulting Numbers: [896] 896,19 unequal: No Solution Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,19 unequal: No Solution No 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: 19:[53, 7], Operations: ['84/4=21', '28-21=7'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,19 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,19 unequal: No Solution No 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: 19:[21, 81], Operations: ['84/4=21', '53+28=81'] Exploring Operation: 21*81=1701, Resulting Numbers: [1701] 1701,19 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 21+81=102, Resulting Numbers: [102] 102,19 unequal: No Solution No 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: 19:[28, 74], Operations: ['84/4=21', '53+21=74'] Exploring Operation: 74-28=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 28*74=2072, Resulting Numbers: [2072] 2072,19 unequal: No Solution Exploring Operation: 28+74=102, Resulting Numbers: [102] 102,19 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: 19:[53, 4, 3], Operations: ['84/28=3'] Exploring Operation: 53+3=56, Resulting Numbers: [4, 56] Generated Node #0,0,0: 19:[4, 56] Operation: 53+3=56 Exploring Operation: 4+3=7, Resulting Numbers: [53, 7] Generated Node #0,0,1: 19:[53, 7] Operation: 4+3=7 Exploring Operation: 53-3=50, Resulting Numbers: [4, 50] Generated Node #0,0,2: 19:[4, 50] Operation: 53-3=50 Exploring Operation: 53-4=49, Resulting Numbers: [3, 49] Generated Node #0,0,3: 19:[3, 49] Operation: 53-4=49 Exploring Operation: 4*3=12, Resulting Numbers: [53, 12] Generated Node #0,0,4: 19:[53, 12] Operation: 4*3=12 Moving to Node #0,1 Current State: 19:[53, 4, 56], Operations: ['84-28=56'] Exploring Operation: 56-53=3, Resulting Numbers: [4, 3] Generated Node #0,1,0: 19:[4, 3] Operation: 56-53=3 Exploring Operation: 56/4=14, Resulting Numbers: [53, 14] Generated Node #0,1,1: 19:[53, 14] Operation: 56/4=14 Exploring Operation: 56-4=52, Resulting Numbers: [53, 52] Generated Node #0,1,2: 19:[53, 52] Operation: 56-4=52 Exploring Operation: 53-4=49, Resulting Numbers: [56, 49] Generated Node #0,1,3: 19:[56, 49] Operation: 53-4=49 Exploring Operation: 53+4=57, Resulting Numbers: [56, 57] Generated Node #0,1,4: 19:[56, 57] Operation: 53+4=57 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[4, 3], Operations: ['84-28=56', '56-53=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,19 unequal: No Solution No 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: 19:[53, 14], Operations: ['84-28=56', '56/4=14'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,19 unequal: No Solution Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,19 unequal: No Solution Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,19 unequal: No Solution No 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: 19:[53, 52], Operations: ['84-28=56', '56-4=52'] Exploring Operation: 53*52=2756, Resulting Numbers: [2756] 2756,19 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 53+52=105, Resulting Numbers: [105] 105,19 unequal: No Solution No 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: 19:[56, 49], Operations: ['84-28=56', '53-4=49'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,19 unequal: No Solution Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,19 unequal: No Solution No 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: 19:[56, 57], Operations: ['84-28=56', '53+4=57'] Exploring Operation: 57-56=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 56+57=113, Resulting Numbers: [113] 113,19 unequal: No Solution Exploring Operation: 56*57=3192, Resulting Numbers: [3192] 3192,19 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: 19:[84, 4, 25], Operations: ['53-28=25'] Exploring Operation: 25-4=21, Resulting Numbers: [84, 21] Generated Node #0,3,0: 19:[84, 21] Operation: 25-4=21 Exploring Operation: 84/4=21, Resulting Numbers: [25, 21] Generated Node #0,3,1: 19:[25, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [25, 80] Generated Node #0,3,2: 19:[25, 80] Operation: 84-4=80 Exploring Operation: 84-25=59, Resulting Numbers: [4, 59] Generated Node #0,3,3: 19:[4, 59] Operation: 84-25=59 Exploring Operation: 84+4=88, Resulting Numbers: [25, 88] Generated Node #0,3,4: 19:[25, 88] Operation: 84+4=88 Moving to Node #0,3,1 Current State: 19:[25, 21], Operations: ['53-28=25', '84/4=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,19 unequal: No Solution Moving to Node #0,0,4 Current State: 19:[53, 12], Operations: ['84/28=3', '4*3=12'] Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,19 unequal: No Solution Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,19 unequal: No Solution Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[4, 50], Operations: ['84/28=3', '53-3=50'] Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,19 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[53, 7], Operations: ['84/28=3', '4+3=7'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,19 unequal: No Solution Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,19 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[3, 49], Operations: ['84/28=3', '53-4=49'] Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,19 unequal: No Solution Exploring Operation: 3*49=147, Resulting Numbers: [147] 147,19 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[4, 56], Operations: ['84/28=3', '53+3=56'] Exploring Operation: 4*56=224, Resulting Numbers: [224] 224,19 unequal: No Solution Exploring Operation: 56-4=52, Resulting Numbers: [52] 52,19 unequal: No Solution Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,19 unequal: No Solution Exploring Operation: 4+56=60, Resulting Numbers: [60] 60,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[4, 59], Operations: ['53-28=25', '84-25=59'] Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[25, 80], Operations: ['53-28=25', '84-4=80'] Exploring Operation: 25*80=2000, Resulting Numbers: [2000] 2000,19 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 25+80=105, Resulting Numbers: [105] 105,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[84, 21], Operations: ['53-28=25', '25-4=21'] Exploring Operation: 84*21=1764, Resulting Numbers: [1764] 1764,19 unequal: No Solution Exploring Operation: 84-21=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 84/21=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 84+21=105, Resulting Numbers: [105] 105,19 unequal: No Solution Moving to Node #0,3,4 Current State: 19:[25, 88], Operations: ['53-28=25', '84+4=88'] Exploring Operation: 25*88=2200, Resulting Numbers: [2200] 2200,19 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,19 unequal: No Solution Exploring Operation: 25+88=113, Resulting Numbers: [113] 113,19 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 78, 41, 26, 17 ]
61
[ "78/26=3", "41+17=58", "3+58=61" ]
Current State: 61:[78, 41, 26, 17], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [41, 17, 3] Generated Node #2: [41, 17, 3] from Operation: 78/26=3 Current State: 61:[41, 17, 3], Operations: ['78/26=3'] Exploring Operation: 41+17=58, Resulting Numbers: [3, 58] Generated Node #3: [3, 58] from Operation: 41+17=58 Current State: 61:[3, 58], Operations: ['78/26=3', '41+17=58'] Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[78, 41, 26, 17], Operations: [] Exploring Operation: 26+17=43, Resulting Numbers: [78, 41, 43] Generated Node #0,0: 61:[78, 41, 43] Operation: 26+17=43 Exploring Operation: 78-26=52, Resulting Numbers: [41, 17, 52] Generated Node #0,1: 61:[41, 17, 52] Operation: 78-26=52 Exploring Operation: 78-17=61, Resulting Numbers: [41, 26, 61] Generated Node #0,2: 61:[41, 26, 61] Operation: 78-17=61 Exploring Operation: 41+17=58, Resulting Numbers: [78, 26, 58] Generated Node #0,3: 61:[78, 26, 58] Operation: 41+17=58 Exploring Operation: 41+26=67, Resulting Numbers: [78, 17, 67] Generated Node #0,4: 61:[78, 17, 67] Operation: 41+26=67 Moving to Node #0,0 Current State: 61:[78, 41, 43], Operations: ['26+17=43'] Exploring Operation: 78+41=119, Resulting Numbers: [43, 119] Generated Node #0,0,0: 61:[43, 119] Operation: 78+41=119 Exploring Operation: 41+43=84, Resulting Numbers: [78, 84] Generated Node #0,0,1: 61:[78, 84] Operation: 41+43=84 Exploring Operation: 78-41=37, Resulting Numbers: [43, 37] Generated Node #0,0,2: 61:[43, 37] Operation: 78-41=37 Exploring Operation: 43-41=2, Resulting Numbers: [78, 2] Generated Node #0,0,3: 61:[78, 2] Operation: 43-41=2 Exploring Operation: 78-43=35, Resulting Numbers: [41, 35] Generated Node #0,0,4: 61:[41, 35] Operation: 78-43=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[78, 84], Operations: ['26+17=43', '41+43=84'] Exploring Operation: 78*84=6552, Resulting Numbers: [6552] 6552,61 unequal: No Solution Exploring Operation: 78+84=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 84-78=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[43, 37], Operations: ['26+17=43', '78-41=37'] Exploring Operation: 43*37=1591, Resulting Numbers: [1591] 1591,61 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 61:[41, 35], Operations: ['26+17=43', '78-43=35'] Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,61 unequal: No Solution Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[43, 119], Operations: ['26+17=43', '78+41=119'] Exploring Operation: 119-43=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 43+119=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 43*119=5117, Resulting Numbers: [5117] 5117,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[78, 2], Operations: ['26+17=43', '43-41=2'] Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,61 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: 61:[78, 26, 58], Operations: ['41+17=58'] Exploring Operation: 78-26=52, Resulting Numbers: [58, 52] Generated Node #0,3,0: 61:[58, 52] Operation: 78-26=52 Exploring Operation: 78+26=104, Resulting Numbers: [58, 104] Generated Node #0,3,1: 61:[58, 104] Operation: 78+26=104 Exploring Operation: 78/26=3, Resulting Numbers: [58, 3] Generated Node #0,3,2: 61:[58, 3] Operation: 78/26=3 Exploring Operation: 58-26=32, Resulting Numbers: [78, 32] Generated Node #0,3,3: 61:[78, 32] Operation: 58-26=32 Exploring Operation: 26+58=84, Resulting Numbers: [78, 84] Generated Node #0,3,4: 61:[78, 84] Operation: 26+58=84 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 61:[58, 52], Operations: ['41+17=58', '78-26=52'] Exploring Operation: 58+52=110, Resulting Numbers: [110] 110,61 unequal: No Solution Exploring Operation: 58*52=3016, Resulting Numbers: [3016] 3016,61 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 61:[78, 84], Operations: ['41+17=58', '26+58=84'] Exploring Operation: 84-78=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 78+84=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 78*84=6552, Resulting Numbers: [6552] 6552,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 61:[58, 104], Operations: ['41+17=58', '78+26=104'] Exploring Operation: 58+104=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 58*104=6032, Resulting Numbers: [6032] 6032,61 unequal: No Solution Exploring Operation: 104-58=46, Resulting Numbers: [46] 46,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 61:[78, 32], Operations: ['41+17=58', '58-26=32'] Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,61 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 61:[58, 3], Operations: ['41+17=58', '78/26=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,61 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[78, 41, 26, 17], Operations: [] Exploring Operation: 41+17=58, Resulting Numbers: [78, 26, 58] Generated Node #0,3: 61:[78, 26, 58] Operation: 41+17=58 Moving to Node #0,3 Current State: 61:[78, 26, 58], Operations: ['41+17=58'] Exploring Operation: 78/26=3, Resulting Numbers: [58, 3] Generated Node #0,3,2: 61:[58, 3] Operation: 78/26=3 Moving to Node #0,3,2 Current State: 61:[58, 3], Operations: ['41+17=58', '78/26=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_5
mult_heuristic
[ 20, 10, 19, 39 ]
48
[ "20-10=10", "19+39=58", "58-10=48" ]
Current State: 48:[20, 10, 19, 39], Operations: [] Exploring Operation: 20-10=10, Resulting Numbers: [19, 39, 10] Generated Node #2: [19, 39, 10] from Operation: 20-10=10 Current State: 48:[19, 39, 10], Operations: ['20-10=10'] Exploring Operation: 19+39=58, Resulting Numbers: [10, 58] Generated Node #3: [10, 58] from Operation: 19+39=58 Current State: 48:[10, 58], Operations: ['20-10=10', '19+39=58'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[20, 10, 19, 39], Operations: [] Exploring Operation: 10+39=49, Resulting Numbers: [20, 19, 49] Generated Node #0,0: 48:[20, 19, 49] Operation: 10+39=49 Exploring Operation: 39-20=19, Resulting Numbers: [10, 19, 19] Generated Node #0,1: 48:[10, 19, 19] Operation: 39-20=19 Exploring Operation: 39-19=20, Resulting Numbers: [20, 10, 20] Generated Node #0,2: 48:[20, 10, 20] Operation: 39-19=20 Exploring Operation: 20/10=2, Resulting Numbers: [19, 39, 2] Generated Node #0,3: 48:[19, 39, 2] Operation: 20/10=2 Moving to Node #0,0 Current State: 48:[20, 19, 49], Operations: ['10+39=49'] Exploring Operation: 49-20=29, Resulting Numbers: [19, 29] Generated Node #0,0,0: 48:[19, 29] Operation: 49-20=29 Exploring Operation: 20-19=1, Resulting Numbers: [49, 1] Generated Node #0,0,1: 48:[49, 1] Operation: 20-19=1 Exploring Operation: 49-19=30, Resulting Numbers: [20, 30] Generated Node #0,0,2: 48:[20, 30] Operation: 49-19=30 Exploring Operation: 20+19=39, Resulting Numbers: [49, 39] Generated Node #0,0,3: 48:[49, 39] Operation: 20+19=39 Moving to Node #0,1 Current State: 48:[10, 19, 19], Operations: ['39-20=19'] Exploring Operation: 19-10=9, Resulting Numbers: [19, 9] Generated Node #0,1,0: 48:[19, 9] Operation: 19-10=9 Exploring Operation: 19/19=1, Resulting Numbers: [10, 1] Generated Node #0,1,1: 48:[10, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [10, 0] Generated Node #0,1,2: 48:[10, 0] Operation: 19-19=0 Exploring Operation: 19-10=9, Resulting Numbers: [19, 9] Generated Node #0,1,3: 48:[19, 9] Operation: 19-10=9 Moving to Node #0,2 Current State: 48:[20, 10, 20], Operations: ['39-19=20'] Exploring Operation: 20/10=2, Resulting Numbers: [20, 2] Generated Node #0,2,0: 48:[20, 2] Operation: 20/10=2 Exploring Operation: 20/10=2, Resulting Numbers: [20, 2] Generated Node #0,2,1: 48:[20, 2] Operation: 20/10=2 Exploring Operation: 20-20=0, Resulting Numbers: [10, 0] Generated Node #0,2,2: 48:[10, 0] Operation: 20-20=0 Exploring Operation: 20/20=1, Resulting Numbers: [10, 1] Generated Node #0,2,3: 48:[10, 1] Operation: 20/20=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 48:[10, 1], Operations: ['39-19=20', '20/20=1'] Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 48:[20, 2], Operations: ['39-19=20', '20/10=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[20, 2], Operations: ['39-19=20', '20/10=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,48 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[10, 0], Operations: ['39-19=20', '20-20=0'] Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,48 unequal: No Solution Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,48 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: 48:[19, 39, 2], Operations: ['20/10=2'] Exploring Operation: 39+2=41, Resulting Numbers: [19, 41] Generated Node #0,3,0: 48:[19, 41] Operation: 39+2=41 Exploring Operation: 39-19=20, Resulting Numbers: [2, 20] Generated Node #0,3,1: 48:[2, 20] Operation: 39-19=20 Exploring Operation: 19+39=58, Resulting Numbers: [2, 58] Generated Node #0,3,2: 48:[2, 58] Operation: 19+39=58 Exploring Operation: 19-2=17, Resulting Numbers: [39, 17] Generated Node #0,3,3: 48:[39, 17] Operation: 19-2=17 Moving to Node #0,0,1 Current State: 48:[49, 1], Operations: ['10+39=49', '20-19=1'] Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,48 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[20, 10, 19, 39], Operations: [] Exploring Operation: 10+39=49, Resulting Numbers: [20, 19, 49] Generated Node #0,0: 48:[20, 19, 49] Operation: 10+39=49 Moving to Node #0,0 Current State: 48:[20, 19, 49], Operations: ['10+39=49'] Exploring Operation: 20-19=1, Resulting Numbers: [49, 1] Generated Node #0,0,1: 48:[49, 1] Operation: 20-19=1 Moving to Node #0,0,1 Current State: 48:[49, 1], Operations: ['10+39=49', '20-19=1'] Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.963542
hs_4
mult_heuristic
[ 89, 89, 30, 43 ]
13
[ "89-89=0", "43-30=13", "0+13=13" ]
Current State: 13:[89, 89, 30, 43], Operations: [] Exploring Operation: 89-89=0, Resulting Numbers: [30, 43, 0] Generated Node #2: [30, 43, 0] from Operation: 89-89=0 Current State: 13:[30, 43, 0], Operations: ['89-89=0'] Exploring Operation: 43-30=13, Resulting Numbers: [0, 13] Generated Node #3: [0, 13] from Operation: 43-30=13 Current State: 13:[0, 13], Operations: ['89-89=0', '43-30=13'] Exploring Operation: 0+13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[89, 89, 30, 43], Operations: [] Exploring Operation: 89/89=1, Resulting Numbers: [30, 43, 1] Generated Node #0,0: 13:[30, 43, 1] Operation: 89/89=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[30, 43, 1], Operations: ['89/89=1'] Exploring Operation: 43-30=13, Resulting Numbers: [1, 13] Generated Node #0,0,0: 13:[1, 13] Operation: 43-30=13 Moving to Node #0,0,0 Current State: 13:[1, 13], Operations: ['89/89=1', '43-30=13'] Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[89, 89, 30, 43], Operations: [] Exploring Operation: 89/89=1, Resulting Numbers: [30, 43, 1] Generated Node #0,0: 13:[30, 43, 1] Operation: 89/89=1 Moving to Node #0,0 Current State: 13:[30, 43, 1], Operations: ['89/89=1'] Exploring Operation: 43-30=13, Resulting Numbers: [1, 13] Generated Node #0,0,0: 13:[1, 13] Operation: 43-30=13 Moving to Node #0,0,0 Current State: 13:[1, 13], Operations: ['89/89=1', '43-30=13'] Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 11, 71, 74, 3 ]
66
[ "74-71=3", "3+3=6", "11*6=66" ]
Current State: 66:[11, 71, 74, 3], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [11, 3, 3] Generated Node #2: [11, 3, 3] from Operation: 74-71=3 Current State: 66:[11, 3, 3], Operations: ['74-71=3'] Exploring Operation: 3+3=6, Resulting Numbers: [11, 6] Generated Node #3: [11, 6] from Operation: 3+3=6 Current State: 66:[11, 6], Operations: ['74-71=3', '3+3=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[11, 71, 74, 3], Operations: [] Exploring Operation: 71-3=68, Resulting Numbers: [11, 74, 68] Generated Node #0,0: 66:[11, 74, 68] Operation: 71-3=68 Exploring Operation: 74-11=63, Resulting Numbers: [71, 3, 63] Generated Node #0,1: 66:[71, 3, 63] Operation: 74-11=63 Exploring Operation: 74-71=3, Resulting Numbers: [11, 3, 3] Generated Node #0,2: 66:[11, 3, 3] Operation: 74-71=3 Moving to Node #0,2 Current State: 66:[11, 3, 3], Operations: ['74-71=3'] Exploring Operation: 3+3=6, Resulting Numbers: [11, 6] Generated Node #0,2,0: 66:[11, 6] Operation: 3+3=6 Exploring Operation: 11*3=33, Resulting Numbers: [3, 33] Generated Node #0,2,1: 66:[3, 33] Operation: 11*3=33 Exploring Operation: 11*3=33, Resulting Numbers: [3, 33] Generated Node #0,2,2: 66:[3, 33] Operation: 11*3=33 Moving to Node #0,1 Current State: 66:[71, 3, 63], Operations: ['74-11=63'] Exploring Operation: 71-63=8, Resulting Numbers: [3, 8] Generated Node #0,1,0: 66:[3, 8] Operation: 71-63=8 Exploring Operation: 71-3=68, Resulting Numbers: [63, 68] Generated Node #0,1,1: 66:[63, 68] Operation: 71-3=68 Exploring Operation: 3+63=66, Resulting Numbers: [71, 66] Generated Node #0,1,2: 66:[71, 66] Operation: 3+63=66 Moving to Node #0,0 Current State: 66:[11, 74, 68], Operations: ['71-3=68'] Exploring Operation: 74-68=6, Resulting Numbers: [11, 6] Generated Node #0,0,0: 66:[11, 6] Operation: 74-68=6 Exploring Operation: 74-11=63, Resulting Numbers: [68, 63] Generated Node #0,0,1: 66:[68, 63] Operation: 74-11=63 Exploring Operation: 68-11=57, Resulting Numbers: [74, 57] Generated Node #0,0,2: 66:[74, 57] Operation: 68-11=57 Moving to Node #0,2,0 Current State: 66:[11, 6], Operations: ['74-71=3', '3+3=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,66 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[11, 71, 74, 3], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [11, 3, 3] Generated Node #0,2: 66:[11, 3, 3] Operation: 74-71=3 Moving to Node #0,2 Current State: 66:[11, 3, 3], Operations: ['74-71=3'] Exploring Operation: 3+3=6, Resulting Numbers: [11, 6] Generated Node #0,2,0: 66:[11, 6] Operation: 3+3=6 Moving to Node #0,2,0 Current State: 66:[11, 6], Operations: ['74-71=3', '3+3=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
0.984375
hs_3
mult_heuristic
[ 27, 52, 63, 21 ]
82
[ "27+52=79", "63/21=3", "79+3=82" ]
Current State: 82:[27, 52, 63, 21], Operations: [] Exploring Operation: 27+52=79, Resulting Numbers: [63, 21, 79] Generated Node #2: [63, 21, 79] from Operation: 27+52=79 Current State: 82:[63, 21, 79], Operations: ['27+52=79'] Exploring Operation: 63/21=3, Resulting Numbers: [79, 3] Generated Node #3: [79, 3] from Operation: 63/21=3 Current State: 82:[79, 3], Operations: ['27+52=79', '63/21=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[27, 52, 63, 21], Operations: [] Exploring Operation: 63-21=42, Resulting Numbers: [27, 52, 42] Generated Node #0,0: 82:[27, 52, 42] Operation: 63-21=42 Exploring Operation: 63+21=84, Resulting Numbers: [27, 52, 84] Generated Node #0,1: 82:[27, 52, 84] Operation: 63+21=84 Exploring Operation: 63/21=3, Resulting Numbers: [27, 52, 3] Generated Node #0,2: 82:[27, 52, 3] Operation: 63/21=3 Moving to Node #0,0 Current State: 82:[27, 52, 42], Operations: ['63-21=42'] Exploring Operation: 52-27=25, Resulting Numbers: [42, 25] Generated Node #0,0,0: 82:[42, 25] Operation: 52-27=25 Exploring Operation: 52-42=10, Resulting Numbers: [27, 10] Generated Node #0,0,1: 82:[27, 10] Operation: 52-42=10 Exploring Operation: 27+52=79, Resulting Numbers: [42, 79] Generated Node #0,0,2: 82:[42, 79] Operation: 27+52=79 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 82:[42, 79], Operations: ['63-21=42', '27+52=79'] Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 42+79=121, Resulting Numbers: [121] 121,82 unequal: No Solution Exploring Operation: 42*79=3318, Resulting Numbers: [3318] 3318,82 unequal: No Solution No 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: 82:[42, 25], Operations: ['63-21=42', '52-27=25'] Exploring Operation: 42*25=1050, Resulting Numbers: [1050] 1050,82 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 42+25=67, Resulting Numbers: [67] 67,82 unequal: No Solution No 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: 82:[27, 10], Operations: ['63-21=42', '52-42=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,82 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: 82:[27, 52, 3], Operations: ['63/21=3'] Exploring Operation: 52-27=25, Resulting Numbers: [3, 25] Generated Node #0,2,0: 82:[3, 25] Operation: 52-27=25 Exploring Operation: 27+52=79, Resulting Numbers: [3, 79] Generated Node #0,2,1: 82:[3, 79] Operation: 27+52=79 Exploring Operation: 27*3=81, Resulting Numbers: [52, 81] Generated Node #0,2,2: 82:[52, 81] Operation: 27*3=81 Moving to Node #0,1 Current State: 82:[27, 52, 84], Operations: ['63+21=84'] Exploring Operation: 27+52=79, Resulting Numbers: [84, 79] Generated Node #0,1,0: 82:[84, 79] Operation: 27+52=79 Exploring Operation: 52-27=25, Resulting Numbers: [84, 25] Generated Node #0,1,1: 82:[84, 25] Operation: 52-27=25 Exploring Operation: 84-52=32, Resulting Numbers: [27, 32] Generated Node #0,1,2: 82:[27, 32] Operation: 84-52=32 Moving to Node #0,2,1 Current State: 82:[3, 79], Operations: ['63/21=3', '27+52=79'] Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,82 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[27, 52, 63, 21], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [27, 52, 3] Generated Node #0,2: 82:[27, 52, 3] Operation: 63/21=3 Moving to Node #0,2 Current State: 82:[27, 52, 3], Operations: ['63/21=3'] Exploring Operation: 27+52=79, Resulting Numbers: [3, 79] Generated Node #0,2,1: 82:[3, 79] Operation: 27+52=79 Moving to Node #0,2,1 Current State: 82:[3, 79], Operations: ['63/21=3', '27+52=79'] Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 74, 79, 68, 28 ]
57
[ "74+79=153", "68+28=96", "153-96=57" ]
Current State: 57:[74, 79, 68, 28], Operations: [] Exploring Operation: 74+79=153, Resulting Numbers: [68, 28, 153] Generated Node #2: [68, 28, 153] from Operation: 74+79=153 Current State: 57:[68, 28, 153], Operations: ['74+79=153'] Exploring Operation: 68+28=96, Resulting Numbers: [153, 96] Generated Node #3: [153, 96] from Operation: 68+28=96 Current State: 57:[153, 96], Operations: ['74+79=153', '68+28=96'] Exploring Operation: 153-96=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[74, 79, 68, 28], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [68, 28, 5] Generated Node #0,0: 57:[68, 28, 5] Operation: 79-74=5 Exploring Operation: 74-68=6, Resulting Numbers: [79, 28, 6] Generated Node #0,1: 57:[79, 28, 6] Operation: 74-68=6 Exploring Operation: 74-28=46, Resulting Numbers: [79, 68, 46] Generated Node #0,2: 57:[79, 68, 46] Operation: 74-28=46 Exploring Operation: 79-28=51, Resulting Numbers: [74, 68, 51] Generated Node #0,3: 57:[74, 68, 51] Operation: 79-28=51 Exploring Operation: 79-68=11, Resulting Numbers: [74, 28, 11] Generated Node #0,4: 57:[74, 28, 11] Operation: 79-68=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[68, 28, 5], Operations: ['79-74=5'] Exploring Operation: 68-28=40, Resulting Numbers: [5, 40] Generated Node #0,0,0: 57:[5, 40] Operation: 68-28=40 Exploring Operation: 28-5=23, Resulting Numbers: [68, 23] Generated Node #0,0,1: 57:[68, 23] Operation: 28-5=23 Exploring Operation: 68+5=73, Resulting Numbers: [28, 73] Generated Node #0,0,2: 57:[28, 73] Operation: 68+5=73 Exploring Operation: 28+5=33, Resulting Numbers: [68, 33] Generated Node #0,0,3: 57:[68, 33] Operation: 28+5=33 Exploring Operation: 68-5=63, Resulting Numbers: [28, 63] Generated Node #0,0,4: 57:[28, 63] Operation: 68-5=63 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[68, 23], Operations: ['79-74=5', '28-5=23'] Exploring Operation: 68*23=1564, Resulting Numbers: [1564] 1564,57 unequal: No Solution Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 68+23=91, Resulting Numbers: [91] 91,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 57:[28, 63], Operations: ['79-74=5', '68-5=63'] Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,57 unequal: No Solution Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 28*63=1764, Resulting Numbers: [1764] 1764,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[5, 40], Operations: ['79-74=5', '68-28=40'] Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 57:[28, 73], Operations: ['79-74=5', '68+5=73'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 28*73=2044, Resulting Numbers: [2044] 2044,57 unequal: No Solution Exploring Operation: 28+73=101, Resulting Numbers: [101] 101,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 57:[68, 33], Operations: ['79-74=5', '28+5=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 68+33=101, Resulting Numbers: [101] 101,57 unequal: No Solution Exploring Operation: 68*33=2244, Resulting Numbers: [2244] 2244,57 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:[79, 28, 6], Operations: ['74-68=6'] Exploring Operation: 79-6=73, Resulting Numbers: [28, 73] Generated Node #0,1,0: 57:[28, 73] Operation: 79-6=73 Exploring Operation: 79+6=85, Resulting Numbers: [28, 85] Generated Node #0,1,1: 57:[28, 85] Operation: 79+6=85 Exploring Operation: 28+6=34, Resulting Numbers: [79, 34] Generated Node #0,1,2: 57:[79, 34] Operation: 28+6=34 Exploring Operation: 28-6=22, Resulting Numbers: [79, 22] Generated Node #0,1,3: 57:[79, 22] Operation: 28-6=22 Exploring Operation: 79-28=51, Resulting Numbers: [6, 51] Generated Node #0,1,4: 57:[6, 51] Operation: 79-28=51 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 57:[6, 51], Operations: ['74-68=6', '79-28=51'] Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[74, 79, 68, 28], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [79, 28, 6] Generated Node #0,1: 57:[79, 28, 6] Operation: 74-68=6 Moving to Node #0,1 Current State: 57:[79, 28, 6], Operations: ['74-68=6'] Exploring Operation: 79-28=51, Resulting Numbers: [6, 51] Generated Node #0,1,4: 57:[6, 51] Operation: 79-28=51 Moving to Node #0,1,4 Current State: 57:[6, 51], Operations: ['74-68=6', '79-28=51'] Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 28, 72, 38, 30 ]
91
[ "30-28=2", "38/2=19", "72+19=91" ]
Current State: 91:[28, 72, 38, 30], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [72, 38, 2] Generated Node #2: [72, 38, 2] from Operation: 30-28=2 Current State: 91:[72, 38, 2], Operations: ['30-28=2'] Exploring Operation: 38/2=19, Resulting Numbers: [72, 19] Generated Node #3: [72, 19] from Operation: 38/2=19 Current State: 91:[72, 19], Operations: ['30-28=2', '38/2=19'] Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[28, 72, 38, 30], Operations: [] Exploring Operation: 38-28=10, Resulting Numbers: [72, 30, 10] Generated Node #0,0: 91:[72, 30, 10] Operation: 38-28=10 Exploring Operation: 38-30=8, Resulting Numbers: [28, 72, 8] Generated Node #0,1: 91:[28, 72, 8] Operation: 38-30=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[28, 72, 8], Operations: ['38-30=8'] Exploring Operation: 72/8=9, Resulting Numbers: [28, 9] Generated Node #0,1,0: 91:[28, 9] Operation: 72/8=9 Exploring Operation: 28+72=100, Resulting Numbers: [8, 100] Generated Node #0,1,1: 91:[8, 100] Operation: 28+72=100 Moving to Node #0,1,1 Current State: 91:[8, 100], Operations: ['38-30=8', '28+72=100'] Exploring Operation: 8+100=108, Resulting Numbers: [108] 108,91 unequal: No Solution Exploring Operation: 100-8=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[28, 9], Operations: ['38-30=8', '72/8=9'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,91 unequal: No Solution Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[72, 30, 10], Operations: ['38-28=10'] Exploring Operation: 72+30=102, Resulting Numbers: [10, 102] Generated Node #0,0,0: 91:[10, 102] Operation: 72+30=102 Exploring Operation: 30/10=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 91:[72, 3] Operation: 30/10=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[10, 102], Operations: ['38-28=10', '72+30=102'] Exploring Operation: 102-10=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 10+102=112, Resulting Numbers: [112] 112,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[72, 3], Operations: ['38-28=10', '30/10=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 78, 18, 49 ]
75
[ "6*78=468", "468/18=26", "49+26=75" ]
Current State: 75:[6, 78, 18, 49], Operations: [] Exploring Operation: 6*78=468, Resulting Numbers: [18, 49, 468] Generated Node #2: [18, 49, 468] from Operation: 6*78=468 Current State: 75:[18, 49, 468], Operations: ['6*78=468'] Exploring Operation: 468/18=26, Resulting Numbers: [49, 26] Generated Node #3: [49, 26] from Operation: 468/18=26 Current State: 75:[49, 26], Operations: ['6*78=468', '468/18=26'] Exploring Operation: 49+26=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[6, 78, 18, 49], Operations: [] Exploring Operation: 49-18=31, Resulting Numbers: [6, 78, 31] Generated Node #0,0: 75:[6, 78, 31] Operation: 49-18=31 Exploring Operation: 78-49=29, Resulting Numbers: [6, 18, 29] Generated Node #0,1: 75:[6, 18, 29] Operation: 78-49=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[6, 18, 29], Operations: ['78-49=29'] Exploring Operation: 6+18=24, Resulting Numbers: [29, 24] Generated Node #0,1,0: 75:[29, 24] Operation: 6+18=24 Exploring Operation: 18/6=3, Resulting Numbers: [29, 3] Generated Node #0,1,1: 75:[29, 3] Operation: 18/6=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[29, 3], Operations: ['78-49=29', '18/6=3'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[29, 24], Operations: ['78-49=29', '6+18=24'] Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[6, 78, 31], Operations: ['49-18=31'] Exploring Operation: 78/6=13, Resulting Numbers: [31, 13] Generated Node #0,0,0: 75:[31, 13] Operation: 78/6=13 Exploring Operation: 31-6=25, Resulting Numbers: [78, 25] Generated Node #0,0,1: 75:[78, 25] Operation: 31-6=25 Moving to Node #0,0,1 Current State: 75:[78, 25], Operations: ['49-18=31', '31-6=25'] Exploring Operation: 78+25=103, Resulting Numbers: [103] 103,75 unequal: No Solution Exploring Operation: 78-25=53, Resulting Numbers: [53] 53,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[31, 13], Operations: ['49-18=31', '78/6=13'] Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,75 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 39, 36, 33, 68 ]
31
[ "39-36=3", "33*3=99", "99-68=31" ]
Current State: 31:[39, 36, 33, 68], Operations: [] Exploring Operation: 39-36=3, Resulting Numbers: [33, 68, 3] Generated Node #2: [33, 68, 3] from Operation: 39-36=3 Current State: 31:[33, 68, 3], Operations: ['39-36=3'] Exploring Operation: 33*3=99, Resulting Numbers: [68, 99] Generated Node #3: [68, 99] from Operation: 33*3=99 Current State: 31:[68, 99], Operations: ['39-36=3', '33*3=99'] Exploring Operation: 99-68=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[39, 36, 33, 68], Operations: [] Exploring Operation: 68-36=32, Resulting Numbers: [39, 33, 32] Generated Node #0,0: 31:[39, 33, 32] Operation: 68-36=32 Exploring Operation: 68-39=29, Resulting Numbers: [36, 33, 29] Generated Node #0,1: 31:[36, 33, 29] Operation: 68-39=29 Exploring Operation: 39-36=3, Resulting Numbers: [33, 68, 3] Generated Node #0,2: 31:[33, 68, 3] Operation: 39-36=3 Exploring Operation: 68-33=35, Resulting Numbers: [39, 36, 35] Generated Node #0,3: 31:[39, 36, 35] Operation: 68-33=35 Exploring Operation: 39-33=6, Resulting Numbers: [36, 68, 6] Generated Node #0,4: 31:[36, 68, 6] Operation: 39-33=6 Moving to Node #0,1 Current State: 31:[36, 33, 29], Operations: ['68-39=29'] Exploring Operation: 33+29=62, Resulting Numbers: [36, 62] Generated Node #0,1,0: 31:[36, 62] Operation: 33+29=62 Exploring Operation: 36-33=3, Resulting Numbers: [29, 3] Generated Node #0,1,1: 31:[29, 3] Operation: 36-33=3 Exploring Operation: 36-29=7, Resulting Numbers: [33, 7] Generated Node #0,1,2: 31:[33, 7] Operation: 36-29=7 Exploring Operation: 33-29=4, Resulting Numbers: [36, 4] Generated Node #0,1,3: 31:[36, 4] Operation: 33-29=4 Exploring Operation: 36+29=65, Resulting Numbers: [33, 65] Generated Node #0,1,4: 31:[33, 65] Operation: 36+29=65 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[33, 7], Operations: ['68-39=29', '36-29=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,31 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,31 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 #0,1,1 Current State: 31:[29, 3], Operations: ['68-39=29', '36-33=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,31 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,31 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 #0,1,3 Current State: 31:[36, 4], Operations: ['68-39=29', '33-29=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,31 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,31 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 #0,1,0 Current State: 31:[36, 62], Operations: ['68-39=29', '33+29=62'] Exploring Operation: 36*62=2232, Resulting Numbers: [2232] 2232,31 unequal: No Solution Exploring Operation: 36+62=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,31 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 #0,1,4 Current State: 31:[33, 65], Operations: ['68-39=29', '36+29=65'] Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,31 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: 31:[39, 33, 32], Operations: ['68-36=32'] Exploring Operation: 39+33=72, Resulting Numbers: [32, 72] Generated Node #0,0,0: 31:[32, 72] Operation: 39+33=72 Exploring Operation: 39-33=6, Resulting Numbers: [32, 6] Generated Node #0,0,1: 31:[32, 6] Operation: 39-33=6 Exploring Operation: 33-32=1, Resulting Numbers: [39, 1] Generated Node #0,0,2: 31:[39, 1] Operation: 33-32=1 Exploring Operation: 39+32=71, Resulting Numbers: [33, 71] Generated Node #0,0,3: 31:[33, 71] Operation: 39+32=71 Exploring Operation: 39-32=7, Resulting Numbers: [33, 7] Generated Node #0,0,4: 31:[33, 7] Operation: 39-32=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[32, 6], Operations: ['68-36=32', '39-33=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,31 unequal: No Solution Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,31 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 #0,0,4 Current State: 31:[33, 7], Operations: ['68-36=32', '39-32=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,31 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,31 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 #0,0,2 Current State: 31:[39, 1], Operations: ['68-36=32', '33-32=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,31 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 #0,0,0 Current State: 31:[32, 72], Operations: ['68-36=32', '39+33=72'] Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,31 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 #0,0,3 Current State: 31:[33, 71], Operations: ['68-36=32', '39+32=71'] Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,31 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: 31:[39, 36, 35], Operations: ['68-33=35'] Exploring Operation: 36-35=1, Resulting Numbers: [39, 1] Generated Node #0,3,0: 31:[39, 1] Operation: 36-35=1 Exploring Operation: 39-36=3, Resulting Numbers: [35, 3] Generated Node #0,3,1: 31:[35, 3] Operation: 39-36=3 Exploring Operation: 39-35=4, Resulting Numbers: [36, 4] Generated Node #0,3,2: 31:[36, 4] Operation: 39-35=4 Exploring Operation: 39+35=74, Resulting Numbers: [36, 74] Generated Node #0,3,3: 31:[36, 74] Operation: 39+35=74 Exploring Operation: 39+36=75, Resulting Numbers: [35, 75] Generated Node #0,3,4: 31:[35, 75] Operation: 39+36=75 Moving to Node #0,2 Current State: 31:[33, 68, 3], Operations: ['39-36=3'] Exploring Operation: 68-33=35, Resulting Numbers: [3, 35] Generated Node #0,2,0: 31:[3, 35] Operation: 68-33=35 Exploring Operation: 68+3=71, Resulting Numbers: [33, 71] Generated Node #0,2,1: 31:[33, 71] Operation: 68+3=71 Exploring Operation: 33-3=30, Resulting Numbers: [68, 30] Generated Node #0,2,2: 31:[68, 30] Operation: 33-3=30 Exploring Operation: 33+3=36, Resulting Numbers: [68, 36] Generated Node #0,2,3: 31:[68, 36] Operation: 33+3=36 Exploring Operation: 68-3=65, Resulting Numbers: [33, 65] Generated Node #0,2,4: 31:[33, 65] Operation: 68-3=65 Moving to Node #0,4 Current State: 31:[36, 68, 6], Operations: ['39-33=6'] Exploring Operation: 68+6=74, Resulting Numbers: [36, 74] Generated Node #0,4,0: 31:[36, 74] Operation: 68+6=74 Exploring Operation: 68-6=62, Resulting Numbers: [36, 62] Generated Node #0,4,1: 31:[36, 62] Operation: 68-6=62 Exploring Operation: 68-36=32, Resulting Numbers: [6, 32] Generated Node #0,4,2: 31:[6, 32] Operation: 68-36=32 Exploring Operation: 36+6=42, Resulting Numbers: [68, 42] Generated Node #0,4,3: 31:[68, 42] Operation: 36+6=42 Exploring Operation: 36-6=30, Resulting Numbers: [68, 30] Generated Node #0,4,4: 31:[68, 30] Operation: 36-6=30 Moving to Node #0,4,2 Current State: 31:[6, 32], Operations: ['39-33=6', '68-36=32'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 6*32=192, Resulting Numbers: [192] 192,31 unequal: No Solution Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[3, 35], Operations: ['39-36=3', '68-33=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[35, 3], Operations: ['68-33=35', '39-36=3'] Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,31 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[36, 4], Operations: ['68-33=35', '39-35=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,31 unequal: No Solution Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[33, 65], Operations: ['39-36=3', '68-3=65'] Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,31 unequal: No Solution Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[36, 62], Operations: ['39-33=6', '68-6=62'] Exploring Operation: 36+62=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 36*62=2232, Resulting Numbers: [2232] 2232,31 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[39, 1], Operations: ['68-33=35', '36-35=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[68, 30], Operations: ['39-36=3', '33-3=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,31 unequal: No Solution Moving to Node #0,4,4 Current State: 31:[68, 30], Operations: ['39-33=6', '36-6=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,31 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,31 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[68, 36], Operations: ['39-36=3', '33+3=36'] Exploring Operation: 68*36=2448, Resulting Numbers: [2448] 2448,31 unequal: No Solution Exploring Operation: 68+36=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[33, 71], Operations: ['39-36=3', '68+3=71'] Exploring Operation: 33*71=2343, Resulting Numbers: [2343] 2343,31 unequal: No Solution Exploring Operation: 33+71=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 71-33=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,4,0 Current State: 31:[36, 74], Operations: ['39-33=6', '68+6=74'] Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,31 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,31 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[68, 42], Operations: ['39-33=6', '36+6=42'] Exploring Operation: 68*42=2856, Resulting Numbers: [2856] 2856,31 unequal: No Solution Exploring Operation: 68+42=110, Resulting Numbers: [110] 110,31 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[36, 74], Operations: ['68-33=35', '39+35=74'] Exploring Operation: 36+74=110, Resulting Numbers: [110] 110,31 unequal: No Solution Exploring Operation: 36*74=2664, Resulting Numbers: [2664] 2664,31 unequal: No Solution Exploring Operation: 74-36=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,3,4 Current State: 31:[35, 75], Operations: ['68-33=35', '39+36=75'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 35*75=2625, Resulting Numbers: [2625] 2625,31 unequal: No Solution Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,31 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 24, 43, 13, 68 ]
13
[ "24+43=67", "68-67=1", "13*1=13" ]
Current State: 13:[24, 43, 13, 68], Operations: [] Exploring Operation: 24+43=67, Resulting Numbers: [13, 68, 67] Generated Node #2: [13, 68, 67] from Operation: 24+43=67 Current State: 13:[13, 68, 67], Operations: ['24+43=67'] Exploring Operation: 68-67=1, Resulting Numbers: [13, 1] Generated Node #3: [13, 1] from Operation: 68-67=1 Current State: 13:[13, 1], Operations: ['24+43=67', '68-67=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[24, 43, 13, 68], Operations: [] Exploring Operation: 43-13=30, Resulting Numbers: [24, 68, 30] Generated Node #0,0: 13:[24, 68, 30] Operation: 43-13=30 Exploring Operation: 43-24=19, Resulting Numbers: [13, 68, 19] Generated Node #0,1: 13:[13, 68, 19] Operation: 43-24=19 Exploring Operation: 68-43=25, Resulting Numbers: [24, 13, 25] Generated Node #0,2: 13:[24, 13, 25] Operation: 68-43=25 Exploring Operation: 68-24=44, Resulting Numbers: [43, 13, 44] Generated Node #0,3: 13:[43, 13, 44] Operation: 68-24=44 Moving to Node #0,2 Current State: 13:[24, 13, 25], Operations: ['68-43=25'] Exploring Operation: 25-24=1, Resulting Numbers: [13, 1] Generated Node #0,2,0: 13:[13, 1] Operation: 25-24=1 Exploring Operation: 24+13=37, Resulting Numbers: [25, 37] Generated Node #0,2,1: 13:[25, 37] Operation: 24+13=37 Exploring Operation: 25-13=12, Resulting Numbers: [24, 12] Generated Node #0,2,2: 13:[24, 12] Operation: 25-13=12 Exploring Operation: 24-13=11, Resulting Numbers: [25, 11] Generated Node #0,2,3: 13:[25, 11] Operation: 24-13=11 Moving to Node #0,3 Current State: 13:[43, 13, 44], Operations: ['68-24=44'] Exploring Operation: 43+13=56, Resulting Numbers: [44, 56] Generated Node #0,3,0: 13:[44, 56] Operation: 43+13=56 Exploring Operation: 44-43=1, Resulting Numbers: [13, 1] Generated Node #0,3,1: 13:[13, 1] Operation: 44-43=1 Exploring Operation: 43-13=30, Resulting Numbers: [44, 30] Generated Node #0,3,2: 13:[44, 30] Operation: 43-13=30 Exploring Operation: 44-13=31, Resulting Numbers: [43, 31] Generated Node #0,3,3: 13:[43, 31] Operation: 44-13=31 Moving to Node #0,1 Current State: 13:[13, 68, 19], Operations: ['43-24=19'] Exploring Operation: 19-13=6, Resulting Numbers: [68, 6] Generated Node #0,1,0: 13:[68, 6] Operation: 19-13=6 Exploring Operation: 68-13=55, Resulting Numbers: [19, 55] Generated Node #0,1,1: 13:[19, 55] Operation: 68-13=55 Exploring Operation: 68-19=49, Resulting Numbers: [13, 49] Generated Node #0,1,2: 13:[13, 49] Operation: 68-19=49 Exploring Operation: 13+68=81, Resulting Numbers: [19, 81] Generated Node #0,1,3: 13:[19, 81] Operation: 13+68=81 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 13:[13, 49], Operations: ['43-24=19', '68-19=49'] Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 13*49=637, Resulting Numbers: [637] 637,13 unequal: No Solution Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[19, 55], Operations: ['43-24=19', '68-13=55'] Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,13 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[68, 6], Operations: ['43-24=19', '19-13=6'] Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,13 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 13:[19, 81], Operations: ['43-24=19', '13+68=81'] Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,13 unequal: No Solution Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,13 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,13 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: 13:[24, 68, 30], Operations: ['43-13=30'] Exploring Operation: 68-24=44, Resulting Numbers: [30, 44] Generated Node #0,0,0: 13:[30, 44] Operation: 68-24=44 Exploring Operation: 68-30=38, Resulting Numbers: [24, 38] Generated Node #0,0,1: 13:[24, 38] Operation: 68-30=38 Exploring Operation: 30-24=6, Resulting Numbers: [68, 6] Generated Node #0,0,2: 13:[68, 6] Operation: 30-24=6 Exploring Operation: 24+68=92, Resulting Numbers: [30, 92] Generated Node #0,0,3: 13:[30, 92] Operation: 24+68=92 Moving to Node #0,2,0 Current State: 13:[13, 1], Operations: ['68-43=25', '25-24=1'] Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[24, 43, 13, 68], Operations: [] Exploring Operation: 68-43=25, Resulting Numbers: [24, 13, 25] Generated Node #0,2: 13:[24, 13, 25] Operation: 68-43=25 Moving to Node #0,2 Current State: 13:[24, 13, 25], Operations: ['68-43=25'] Exploring Operation: 25-24=1, Resulting Numbers: [13, 1] Generated Node #0,2,0: 13:[13, 1] Operation: 25-24=1 Moving to Node #0,2,0 Current State: 13:[13, 1], Operations: ['68-43=25', '25-24=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 10, 55, 30, 28 ]
13
[ "55-10=45", "30+28=58", "58-45=13" ]
Current State: 13:[10, 55, 30, 28], Operations: [] Exploring Operation: 55-10=45, Resulting Numbers: [30, 28, 45] Generated Node #2: [30, 28, 45] from Operation: 55-10=45 Current State: 13:[30, 28, 45], Operations: ['55-10=45'] Exploring Operation: 30+28=58, Resulting Numbers: [45, 58] Generated Node #3: [45, 58] from Operation: 30+28=58 Current State: 13:[45, 58], Operations: ['55-10=45', '30+28=58'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[10, 55, 30, 28], Operations: [] Exploring Operation: 55-28=27, Resulting Numbers: [10, 30, 27] Generated Node #0,0: 13:[10, 30, 27] Operation: 55-28=27 Exploring Operation: 30-28=2, Resulting Numbers: [10, 55, 2] Generated Node #0,1: 13:[10, 55, 2] Operation: 30-28=2 Exploring Operation: 55-30=25, Resulting Numbers: [10, 28, 25] Generated Node #0,2: 13:[10, 28, 25] Operation: 55-30=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[10, 28, 25], Operations: ['55-30=25'] Exploring Operation: 28-10=18, Resulting Numbers: [25, 18] Generated Node #0,2,0: 13:[25, 18] Operation: 28-10=18 Exploring Operation: 25-10=15, Resulting Numbers: [28, 15] Generated Node #0,2,1: 13:[28, 15] Operation: 25-10=15 Exploring Operation: 28-25=3, Resulting Numbers: [10, 3] Generated Node #0,2,2: 13:[10, 3] Operation: 28-25=3 Moving to Node #0,2,2 Current State: 13:[10, 3], Operations: ['55-30=25', '28-25=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[10, 55, 30, 28], Operations: [] Exploring Operation: 55-30=25, Resulting Numbers: [10, 28, 25] Generated Node #0,2: 13:[10, 28, 25] Operation: 55-30=25 Moving to Node #0,2 Current State: 13:[10, 28, 25], Operations: ['55-30=25'] Exploring Operation: 28-25=3, Resulting Numbers: [10, 3] Generated Node #0,2,2: 13:[10, 3] Operation: 28-25=3 Moving to Node #0,2,2 Current State: 13:[10, 3], Operations: ['55-30=25', '28-25=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 74, 82, 73, 78 ]
75
[ "74+82=156", "156/78=2", "73+2=75" ]
Current State: 75:[74, 82, 73, 78], Operations: [] Exploring Operation: 74+82=156, Resulting Numbers: [73, 78, 156] Generated Node #2: [73, 78, 156] from Operation: 74+82=156 Current State: 75:[73, 78, 156], Operations: ['74+82=156'] Exploring Operation: 156/78=2, Resulting Numbers: [73, 2] Generated Node #3: [73, 2] from Operation: 156/78=2 Current State: 75:[73, 2], Operations: ['74+82=156', '156/78=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[74, 82, 73, 78], Operations: [] Exploring Operation: 82-74=8, Resulting Numbers: [73, 78, 8] Generated Node #0,0: 75:[73, 78, 8] Operation: 82-74=8 Exploring Operation: 82-73=9, Resulting Numbers: [74, 78, 9] Generated Node #0,1: 75:[74, 78, 9] Operation: 82-73=9 Exploring Operation: 82-78=4, Resulting Numbers: [74, 73, 4] Generated Node #0,2: 75:[74, 73, 4] Operation: 82-78=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[74, 73, 4], Operations: ['82-78=4'] Exploring Operation: 74+4=78, Resulting Numbers: [73, 78] Generated Node #0,2,0: 75:[73, 78] Operation: 74+4=78 Exploring Operation: 74-73=1, Resulting Numbers: [4, 1] Generated Node #0,2,1: 75:[4, 1] Operation: 74-73=1 Exploring Operation: 73+4=77, Resulting Numbers: [74, 77] Generated Node #0,2,2: 75:[74, 77] Operation: 73+4=77 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 75:[4, 1], Operations: ['82-78=4', '74-73=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 75:[74, 77], Operations: ['82-78=4', '73+4=77'] Exploring Operation: 74*77=5698, Resulting Numbers: [5698] 5698,75 unequal: No Solution Exploring Operation: 77-74=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 74+77=151, Resulting Numbers: [151] 151,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[73, 78], Operations: ['82-78=4', '74+4=78'] Exploring Operation: 78-73=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 73*78=5694, Resulting Numbers: [5694] 5694,75 unequal: No Solution Exploring Operation: 73+78=151, Resulting Numbers: [151] 151,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[73, 78, 8], Operations: ['82-74=8'] Exploring Operation: 78-8=70, Resulting Numbers: [73, 70] Generated Node #0,0,0: 75:[73, 70] Operation: 78-8=70 Exploring Operation: 73+8=81, Resulting Numbers: [78, 81] Generated Node #0,0,1: 75:[78, 81] Operation: 73+8=81 Exploring Operation: 78-73=5, Resulting Numbers: [8, 5] Generated Node #0,0,2: 75:[8, 5] Operation: 78-73=5 Moving to Node #0,0,2 Current State: 75:[8, 5], Operations: ['82-74=8', '78-73=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[73, 70], Operations: ['82-74=8', '78-8=70'] Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,75 unequal: No Solution Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,75 unequal: No Solution Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[78, 81], Operations: ['82-74=8', '73+8=81'] Exploring Operation: 78*81=6318, Resulting Numbers: [6318] 6318,75 unequal: No Solution Exploring Operation: 78+81=159, Resulting Numbers: [159] 159,75 unequal: No Solution Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[74, 78, 9], Operations: ['82-73=9'] Exploring Operation: 78-74=4, Resulting Numbers: [9, 4] Generated Node #0,1,0: 75:[9, 4] Operation: 78-74=4 Exploring Operation: 78-9=69, Resulting Numbers: [74, 69] Generated Node #0,1,1: 75:[74, 69] Operation: 78-9=69 Exploring Operation: 74+9=83, Resulting Numbers: [78, 83] Generated Node #0,1,2: 75:[78, 83] Operation: 74+9=83 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[9, 4], Operations: ['82-73=9', '78-74=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[74, 69], Operations: ['82-73=9', '78-9=69'] Exploring Operation: 74+69=143, Resulting Numbers: [143] 143,75 unequal: No Solution Exploring Operation: 74*69=5106, Resulting Numbers: [5106] 5106,75 unequal: No Solution Exploring Operation: 74-69=5, Resulting Numbers: [5] 5,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 75:[78, 83], Operations: ['82-73=9', '74+9=83'] Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,75 unequal: No Solution Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,75 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_3
mult_heuristic
[ 14, 10, 16, 25 ]
76
[ "25-16=9", "10*9=90", "90-14=76" ]
Current State: 76:[14, 10, 16, 25], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [14, 10, 9] Generated Node #2: [14, 10, 9] from Operation: 25-16=9 Current State: 76:[14, 10, 9], Operations: ['25-16=9'] Exploring Operation: 10*9=90, Resulting Numbers: [14, 90] Generated Node #3: [14, 90] from Operation: 10*9=90 Current State: 76:[14, 90], Operations: ['25-16=9', '10*9=90'] Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[14, 10, 16, 25], Operations: [] Exploring Operation: 14-10=4, Resulting Numbers: [16, 25, 4] Generated Node #0,0: 76:[16, 25, 4] Operation: 14-10=4 Moving to Node #0,0 Current State: 76:[16, 25, 4], Operations: ['14-10=4'] Exploring Operation: 16+25=41, Resulting Numbers: [4, 41] Generated Node #0,0,0: 76:[4, 41] Operation: 16+25=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[4, 41], Operations: ['14-10=4', '16+25=41'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,76 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
[ 69, 13, 21, 54 ]
17
[ "69*13=897", "21+897=918", "918/54=17" ]
Current State: 17:[69, 13, 21, 54], Operations: [] Exploring Operation: 69*13=897, Resulting Numbers: [21, 54, 897] Generated Node #2: [21, 54, 897] from Operation: 69*13=897 Current State: 17:[21, 54, 897], Operations: ['69*13=897'] Exploring Operation: 21+897=918, Resulting Numbers: [54, 918] Generated Node #3: [54, 918] from Operation: 21+897=918 Current State: 17:[54, 918], Operations: ['69*13=897', '21+897=918'] Exploring Operation: 918/54=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[69, 13, 21, 54], Operations: [] Exploring Operation: 54-21=33, Resulting Numbers: [69, 13, 33] Generated Node #0,0: 17:[69, 13, 33] Operation: 54-21=33 Exploring Operation: 69-21=48, Resulting Numbers: [13, 54, 48] Generated Node #0,1: 17:[13, 54, 48] Operation: 69-21=48 Exploring Operation: 69-54=15, Resulting Numbers: [13, 21, 15] Generated Node #0,2: 17:[13, 21, 15] Operation: 69-54=15 Moving to Node #0,2 Current State: 17:[13, 21, 15], Operations: ['69-54=15'] Exploring Operation: 21-13=8, Resulting Numbers: [15, 8] Generated Node #0,2,0: 17:[15, 8] Operation: 21-13=8 Exploring Operation: 13+15=28, Resulting Numbers: [21, 28] Generated Node #0,2,1: 17:[21, 28] Operation: 13+15=28 Exploring Operation: 21-15=6, Resulting Numbers: [13, 6] Generated Node #0,2,2: 17:[13, 6] Operation: 21-15=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[15, 8], Operations: ['69-54=15', '21-13=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,17 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,17 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,17 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:[21, 28], Operations: ['69-54=15', '13+15=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,17 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:[13, 6], Operations: ['69-54=15', '21-15=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,17 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 17:[69, 13, 33], Operations: ['54-21=33'] Exploring Operation: 69-13=56, Resulting Numbers: [33, 56] Generated Node #0,0,0: 17:[33, 56] Operation: 69-13=56 Exploring Operation: 33-13=20, Resulting Numbers: [69, 20] Generated Node #0,0,1: 17:[69, 20] Operation: 33-13=20 Exploring Operation: 69-33=36, Resulting Numbers: [13, 36] Generated Node #0,0,2: 17:[13, 36] Operation: 69-33=36 Moving to Node #0,1 Current State: 17:[13, 54, 48], Operations: ['69-21=48'] Exploring Operation: 48-13=35, Resulting Numbers: [54, 35] Generated Node #0,1,0: 17:[54, 35] Operation: 48-13=35 Exploring Operation: 54-48=6, Resulting Numbers: [13, 6] Generated Node #0,1,1: 17:[13, 6] Operation: 54-48=6 Exploring Operation: 54-13=41, Resulting Numbers: [48, 41] Generated Node #0,1,2: 17:[48, 41] Operation: 54-13=41 Moving to Node #0,1,1 Current State: 17:[13, 6], Operations: ['69-21=48', '54-48=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[13, 36], Operations: ['54-21=33', '69-33=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 13*36=468, Resulting Numbers: [468] 468,17 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[69, 20], Operations: ['54-21=33', '33-13=20'] Exploring Operation: 69*20=1380, Resulting Numbers: [1380] 1380,17 unequal: No Solution Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 69+20=89, Resulting Numbers: [89] 89,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[48, 41], Operations: ['69-21=48', '54-13=41'] Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 48+41=89, Resulting Numbers: [89] 89,17 unequal: No Solution Exploring Operation: 48*41=1968, Resulting Numbers: [1968] 1968,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[54, 35], Operations: ['69-21=48', '48-13=35'] Exploring Operation: 54*35=1890, Resulting Numbers: [1890] 1890,17 unequal: No Solution Exploring Operation: 54-35=19, Resulting Numbers: [19] 19,17 unequal: No Solution Exploring Operation: 54+35=89, Resulting Numbers: [89] 89,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[33, 56], Operations: ['54-21=33', '69-13=56'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,17 unequal: No Solution Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,17 unequal: No Solution Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,17 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 67, 51, 9, 29 ]
53
[ "67-9=58", "58/29=2", "51+2=53" ]
Current State: 53:[67, 51, 9, 29], Operations: [] Exploring Operation: 67-9=58, Resulting Numbers: [51, 29, 58] Generated Node #2: [51, 29, 58] from Operation: 67-9=58 Current State: 53:[51, 29, 58], Operations: ['67-9=58'] Exploring Operation: 58/29=2, Resulting Numbers: [51, 2] Generated Node #3: [51, 2] from Operation: 58/29=2 Current State: 53:[51, 2], Operations: ['67-9=58', '58/29=2'] Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[67, 51, 9, 29], Operations: [] Exploring Operation: 67-9=58, Resulting Numbers: [51, 29, 58] Generated Node #0,0: 53:[51, 29, 58] Operation: 67-9=58 Exploring Operation: 67+9=76, Resulting Numbers: [51, 29, 76] Generated Node #0,1: 53:[51, 29, 76] Operation: 67+9=76 Exploring Operation: 9+29=38, Resulting Numbers: [67, 51, 38] Generated Node #0,2: 53:[67, 51, 38] Operation: 9+29=38 Exploring Operation: 51+9=60, Resulting Numbers: [67, 29, 60] Generated Node #0,3: 53:[67, 29, 60] Operation: 51+9=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[51, 29, 58], Operations: ['67-9=58'] Exploring Operation: 51+29=80, Resulting Numbers: [58, 80] Generated Node #0,0,0: 53:[58, 80] Operation: 51+29=80 Exploring Operation: 58-29=29, Resulting Numbers: [51, 29] Generated Node #0,0,1: 53:[51, 29] Operation: 58-29=29 Exploring Operation: 29+58=87, Resulting Numbers: [51, 87] Generated Node #0,0,2: 53:[51, 87] Operation: 29+58=87 Exploring Operation: 51-29=22, Resulting Numbers: [58, 22] Generated Node #0,0,3: 53:[58, 22] Operation: 51-29=22 Moving to Node #0,0,1 Current State: 53:[51, 29], Operations: ['67-9=58', '58-29=29'] Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 51*29=1479, Resulting Numbers: [1479] 1479,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[58, 80], Operations: ['67-9=58', '51+29=80'] Exploring Operation: 58+80=138, Resulting Numbers: [138] 138,53 unequal: No Solution Exploring Operation: 58*80=4640, Resulting Numbers: [4640] 4640,53 unequal: No Solution Exploring Operation: 80-58=22, Resulting Numbers: [22] 22,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[58, 22], Operations: ['67-9=58', '51-29=22'] Exploring Operation: 58*22=1276, Resulting Numbers: [1276] 1276,53 unequal: No Solution Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 58+22=80, Resulting Numbers: [80] 80,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[51, 87], Operations: ['67-9=58', '29+58=87'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,53 unequal: No Solution Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 53:[67, 51, 38], Operations: ['9+29=38'] Exploring Operation: 51+38=89, Resulting Numbers: [67, 89] Generated Node #0,2,0: 53:[67, 89] Operation: 51+38=89 Exploring Operation: 67+38=105, Resulting Numbers: [51, 105] Generated Node #0,2,1: 53:[51, 105] Operation: 67+38=105 Exploring Operation: 67-38=29, Resulting Numbers: [51, 29] Generated Node #0,2,2: 53:[51, 29] Operation: 67-38=29 Exploring Operation: 67-51=16, Resulting Numbers: [38, 16] Generated Node #0,2,3: 53:[38, 16] Operation: 67-51=16 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[51, 29], Operations: ['9+29=38', '67-38=29'] Exploring Operation: 51*29=1479, Resulting Numbers: [1479] 1479,53 unequal: No Solution Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 51+29=80, Resulting Numbers: [80] 80,53 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 #0,2,0 Current State: 53:[67, 89], Operations: ['9+29=38', '51+38=89'] Exploring Operation: 89-67=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 67+89=156, Resulting Numbers: [156] 156,53 unequal: No Solution Exploring Operation: 67*89=5963, Resulting Numbers: [5963] 5963,53 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:[38, 16], Operations: ['9+29=38', '67-51=16'] Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,53 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,53 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:[51, 105], Operations: ['9+29=38', '67+38=105'] Exploring Operation: 51+105=156, Resulting Numbers: [156] 156,53 unequal: No Solution Exploring Operation: 51*105=5355, Resulting Numbers: [5355] 5355,53 unequal: No Solution Exploring Operation: 105-51=54, Resulting Numbers: [54] 54,53 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:[67, 29, 60], Operations: ['51+9=60'] Exploring Operation: 60-29=31, Resulting Numbers: [67, 31] Generated Node #0,3,0: 53:[67, 31] Operation: 60-29=31 Exploring Operation: 67-29=38, Resulting Numbers: [60, 38] Generated Node #0,3,1: 53:[60, 38] Operation: 67-29=38 Exploring Operation: 29+60=89, Resulting Numbers: [67, 89] Generated Node #0,3,2: 53:[67, 89] Operation: 29+60=89 Exploring Operation: 67+29=96, Resulting Numbers: [60, 96] Generated Node #0,3,3: 53:[60, 96] Operation: 67+29=96 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[60, 38], Operations: ['51+9=60', '67-29=38'] Exploring Operation: 60+38=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 60*38=2280, Resulting Numbers: [2280] 2280,53 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 #0,3,0 Current State: 53:[67, 31], Operations: ['51+9=60', '60-29=31'] Exploring Operation: 67*31=2077, Resulting Numbers: [2077] 2077,53 unequal: No Solution Exploring Operation: 67+31=98, Resulting Numbers: [98] 98,53 unequal: No Solution Exploring Operation: 67-31=36, Resulting Numbers: [36] 36,53 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:[67, 89], Operations: ['51+9=60', '29+60=89'] Exploring Operation: 67+89=156, Resulting Numbers: [156] 156,53 unequal: No Solution Exploring Operation: 89-67=22, Resulting Numbers: [22] 22,53 unequal: No Solution Exploring Operation: 67*89=5963, Resulting Numbers: [5963] 5963,53 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:[60, 96], Operations: ['51+9=60', '67+29=96'] Exploring Operation: 60*96=5760, Resulting Numbers: [5760] 5760,53 unequal: No Solution Exploring Operation: 60+96=156, Resulting Numbers: [156] 156,53 unequal: No Solution Exploring Operation: 96-60=36, Resulting Numbers: [36] 36,53 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:[51, 29, 76], Operations: ['67+9=76'] Exploring Operation: 76-29=47, Resulting Numbers: [51, 47] Generated Node #0,1,0: 53:[51, 47] Operation: 76-29=47 Exploring Operation: 51-29=22, Resulting Numbers: [76, 22] Generated Node #0,1,1: 53:[76, 22] Operation: 51-29=22 Exploring Operation: 76-51=25, Resulting Numbers: [29, 25] Generated Node #0,1,2: 53:[29, 25] Operation: 76-51=25 Exploring Operation: 51+29=80, Resulting Numbers: [76, 80] Generated Node #0,1,3: 53:[76, 80] Operation: 51+29=80 Moving to Node #0,1,0 Current State: 53:[51, 47], Operations: ['67+9=76', '76-29=47'] Exploring Operation: 51*47=2397, Resulting Numbers: [2397] 2397,53 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 51+47=98, Resulting Numbers: [98] 98,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[76, 80], Operations: ['67+9=76', '51+29=80'] Exploring Operation: 76+80=156, Resulting Numbers: [156] 156,53 unequal: No Solution Exploring Operation: 76*80=6080, Resulting Numbers: [6080] 6080,53 unequal: No Solution Exploring Operation: 80-76=4, Resulting Numbers: [4] 4,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[29, 25], Operations: ['67+9=76', '76-51=25'] Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,53 unequal: No Solution Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,53 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[76, 22], Operations: ['67+9=76', '51-29=22'] Exploring Operation: 76*22=1672, Resulting Numbers: [1672] 1672,53 unequal: No Solution Exploring Operation: 76-22=54, Resulting Numbers: [54] 54,53 unequal: No Solution Exploring Operation: 76+22=98, Resulting Numbers: [98] 98,53 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
[ 36, 73, 37, 86 ]
86
[ "73-36=37", "37+86=123", "123-37=86" ]
Current State: 86:[36, 73, 37, 86], Operations: [] Exploring Operation: 73-36=37, Resulting Numbers: [37, 86, 37] Generated Node #2: [37, 86, 37] from Operation: 73-36=37 Current State: 86:[37, 86, 37], Operations: ['73-36=37'] Exploring Operation: 37+86=123, Resulting Numbers: [123] 123,86 equal: Goal Reached Exploring Operation: 123-37=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[36, 73, 37, 86], Operations: [] Exploring Operation: 86-73=13, Resulting Numbers: [36, 37, 13] Generated Node #0,0: 86:[36, 37, 13] Operation: 86-73=13 Exploring Operation: 73-37=36, Resulting Numbers: [36, 86, 36] Generated Node #0,1: 86:[36, 86, 36] Operation: 73-37=36 Exploring Operation: 36+37=73, Resulting Numbers: [73, 86, 73] Generated Node #0,2: 86:[73, 86, 73] Operation: 36+37=73 Exploring Operation: 37-36=1, Resulting Numbers: [73, 86, 1] Generated Node #0,3: 86:[73, 86, 1] Operation: 37-36=1 Exploring Operation: 73-36=37, Resulting Numbers: [37, 86, 37] Generated Node #0,4: 86:[37, 86, 37] Operation: 73-36=37 Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[37, 86, 37], Operations: ['73-36=37'] Exploring Operation: 37+37=74, Resulting Numbers: [86, 74] Generated Node #0,4,0: 86:[86, 74] Operation: 37+37=74 Exploring Operation: 86-37=49, Resulting Numbers: [37, 49] Generated Node #0,4,1: 86:[37, 49] Operation: 86-37=49 Exploring Operation: 37/37=1, Resulting Numbers: [86, 1] Generated Node #0,4,2: 86:[86, 1] Operation: 37/37=1 Exploring Operation: 86-37=49, Resulting Numbers: [37, 49] Generated Node #0,4,3: 86:[37, 49] Operation: 86-37=49 Exploring Operation: 37-37=0, Resulting Numbers: [86, 0] Generated Node #0,4,4: 86:[86, 0] Operation: 37-37=0 Moving to Node #0,4,2 Current State: 86:[86, 1], Operations: ['73-36=37', '37/37=1'] Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[36, 73, 37, 86], Operations: [] Exploring Operation: 73-36=37, Resulting Numbers: [37, 86, 37] Generated Node #0,4: 86:[37, 86, 37] Operation: 73-36=37 Moving to Node #0,4 Current State: 86:[37, 86, 37], Operations: ['73-36=37'] Exploring Operation: 37/37=1, Resulting Numbers: [86, 1] Generated Node #0,4,2: 86:[86, 1] Operation: 37/37=1 Moving to Node #0,4,2 Current State: 86:[86, 1], Operations: ['73-36=37', '37/37=1'] Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 21, 93, 78, 66 ]
30
[ "21+93=114", "78+66=144", "144-114=30" ]
Current State: 30:[21, 93, 78, 66], Operations: [] Exploring Operation: 21+93=114, Resulting Numbers: [78, 66, 114] Generated Node #2: [78, 66, 114] from Operation: 21+93=114 Current State: 30:[78, 66, 114], Operations: ['21+93=114'] Exploring Operation: 78+66=144, Resulting Numbers: [114, 144] Generated Node #3: [114, 144] from Operation: 78+66=144 Current State: 30:[114, 144], Operations: ['21+93=114', '78+66=144'] Exploring Operation: 144-114=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[21, 93, 78, 66], Operations: [] Exploring Operation: 93-21=72, Resulting Numbers: [78, 66, 72] Generated Node #0,0: 30:[78, 66, 72] Operation: 93-21=72 Exploring Operation: 93-66=27, Resulting Numbers: [21, 78, 27] Generated Node #0,1: 30:[21, 78, 27] Operation: 93-66=27 Exploring Operation: 78-66=12, Resulting Numbers: [21, 93, 12] Generated Node #0,2: 30:[21, 93, 12] Operation: 78-66=12 Exploring Operation: 93-78=15, Resulting Numbers: [21, 66, 15] Generated Node #0,3: 30:[21, 66, 15] Operation: 93-78=15 Exploring Operation: 78-21=57, Resulting Numbers: [93, 66, 57] Generated Node #0,4: 30:[93, 66, 57] Operation: 78-21=57 Moving to Node #0,3 Current State: 30:[21, 66, 15], Operations: ['93-78=15'] Exploring Operation: 21+66=87, Resulting Numbers: [15, 87] Generated Node #0,3,0: 30:[15, 87] Operation: 21+66=87 Exploring Operation: 21+15=36, Resulting Numbers: [66, 36] Generated Node #0,3,1: 30:[66, 36] Operation: 21+15=36 Exploring Operation: 21-15=6, Resulting Numbers: [66, 6] Generated Node #0,3,2: 30:[66, 6] Operation: 21-15=6 Exploring Operation: 66-15=51, Resulting Numbers: [21, 51] Generated Node #0,3,3: 30:[21, 51] Operation: 66-15=51 Exploring Operation: 66-21=45, Resulting Numbers: [15, 45] Generated Node #0,3,4: 30:[15, 45] Operation: 66-21=45 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[15, 45], Operations: ['93-78=15', '66-21=45'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[21, 93, 78, 66], Operations: [] Exploring Operation: 93-78=15, Resulting Numbers: [21, 66, 15] Generated Node #0,3: 30:[21, 66, 15] Operation: 93-78=15 Moving to Node #0,3 Current State: 30:[21, 66, 15], Operations: ['93-78=15'] Exploring Operation: 66-21=45, Resulting Numbers: [15, 45] Generated Node #0,3,4: 30:[15, 45] Operation: 66-21=45 Moving to Node #0,3,4 Current State: 30:[15, 45], Operations: ['93-78=15', '66-21=45'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 62, 22, 12, 25 ]
18
[ "62+22=84", "84/12=7", "25-7=18" ]
Current State: 18:[62, 22, 12, 25], Operations: [] Exploring Operation: 62+22=84, Resulting Numbers: [12, 25, 84] Generated Node #2: [12, 25, 84] from Operation: 62+22=84 Current State: 18:[12, 25, 84], Operations: ['62+22=84'] Exploring Operation: 84/12=7, Resulting Numbers: [25, 7] Generated Node #3: [25, 7] from Operation: 84/12=7 Current State: 18:[25, 7], Operations: ['62+22=84', '84/12=7'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[62, 22, 12, 25], Operations: [] Exploring Operation: 62-22=40, Resulting Numbers: [12, 25, 40] Generated Node #0,0: 18:[12, 25, 40] Operation: 62-22=40 Exploring Operation: 62-12=50, Resulting Numbers: [22, 25, 50] Generated Node #0,1: 18:[22, 25, 50] Operation: 62-12=50 Exploring Operation: 62-25=37, Resulting Numbers: [22, 12, 37] Generated Node #0,2: 18:[22, 12, 37] Operation: 62-25=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[22, 12, 37], Operations: ['62-25=37'] Exploring Operation: 22-12=10, Resulting Numbers: [37, 10] Generated Node #0,2,0: 18:[37, 10] Operation: 22-12=10 Exploring Operation: 37-12=25, Resulting Numbers: [22, 25] Generated Node #0,2,1: 18:[22, 25] Operation: 37-12=25 Exploring Operation: 37-22=15, Resulting Numbers: [12, 15] Generated Node #0,2,2: 18:[12, 15] Operation: 37-22=15 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 18:[12, 15], Operations: ['62-25=37', '37-22=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,18 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,18 unequal: No Solution No 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: 18:[22, 25], Operations: ['62-25=37', '37-12=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,18 unequal: No Solution No 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: 18:[37, 10], Operations: ['62-25=37', '22-12=10'] Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,18 unequal: No Solution Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,18 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: 18:[12, 25, 40], Operations: ['62-22=40'] Exploring Operation: 40-25=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 18:[12, 15] Operation: 40-25=15 Exploring Operation: 40-12=28, Resulting Numbers: [25, 28] Generated Node #0,0,1: 18:[25, 28] Operation: 40-12=28 Exploring Operation: 25-12=13, Resulting Numbers: [40, 13] Generated Node #0,0,2: 18:[40, 13] Operation: 25-12=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[12, 15], Operations: ['62-22=40', '40-25=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,18 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,18 unequal: No Solution No 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: 18:[25, 28], Operations: ['62-22=40', '40-12=28'] Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,18 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,18 unequal: No Solution No 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: 18:[40, 13], Operations: ['62-22=40', '25-12=13'] Exploring Operation: 40*13=520, Resulting Numbers: [520] 520,18 unequal: No Solution Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,18 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: 18:[22, 25, 50], Operations: ['62-12=50'] Exploring Operation: 50-22=28, Resulting Numbers: [25, 28] Generated Node #0,1,0: 18:[25, 28] Operation: 50-22=28 Exploring Operation: 50/25=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 18:[22, 2] Operation: 50/25=2 Exploring Operation: 50-25=25, Resulting Numbers: [22, 25] Generated Node #0,1,2: 18:[22, 25] Operation: 50-25=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 18:[22, 2], Operations: ['62-12=50', '50/25=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,18 unequal: No Solution No 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: 18:[22, 25], Operations: ['62-12=50', '50-25=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,18 unequal: No Solution No 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: 18:[25, 28], Operations: ['62-12=50', '50-22=28'] Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,18 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
[ 46, 11, 7, 3 ]
53
[ "46+11=57", "7-3=4", "57-4=53" ]
Current State: 53:[46, 11, 7, 3], Operations: [] Exploring Operation: 46+11=57, Resulting Numbers: [7, 3, 57] Generated Node #2: [7, 3, 57] from Operation: 46+11=57 Current State: 53:[7, 3, 57], Operations: ['46+11=57'] Exploring Operation: 7-3=4, Resulting Numbers: [57, 4] Generated Node #3: [57, 4] from Operation: 7-3=4 Current State: 53:[57, 4], Operations: ['46+11=57', '7-3=4'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[46, 11, 7, 3], Operations: [] Exploring Operation: 11*3=33, Resulting Numbers: [46, 7, 33] Generated Node #0,0: 53:[46, 7, 33] Operation: 11*3=33 Exploring Operation: 11*7=77, Resulting Numbers: [46, 3, 77] Generated Node #0,1: 53:[46, 3, 77] Operation: 11*7=77 Moving to Node #0,0 Current State: 53:[46, 7, 33], Operations: ['11*3=33'] Exploring Operation: 46+7=53, Resulting Numbers: [33, 53] Generated Node #0,0,0: 53:[33, 53] Operation: 46+7=53 Exploring Operation: 7+33=40, Resulting Numbers: [46, 40] Generated Node #0,0,1: 53:[46, 40] Operation: 7+33=40 Moving to Node #0,1 Current State: 53:[46, 3, 77], Operations: ['11*7=77'] Exploring Operation: 46+3=49, Resulting Numbers: [77, 49] Generated Node #0,1,0: 53:[77, 49] Operation: 46+3=49 Exploring Operation: 77-3=74, Resulting Numbers: [46, 74] Generated Node #0,1,1: 53:[46, 74] Operation: 77-3=74 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[77, 49], Operations: ['11*7=77', '46+3=49'] Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 77+49=126, Resulting Numbers: [126] 126,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[46, 74], Operations: ['11*7=77', '77-3=74'] Exploring Operation: 46+74=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,53 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: 53:[33, 53], Operations: ['11*3=33', '46+7=53'] Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[46, 40], Operations: ['11*3=33', '7+33=40'] Exploring Operation: 46+40=86, Resulting Numbers: [86] 86,53 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,53 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 14, 95, 57 ]
35
[ "14-11=3", "95-57=38", "38-3=35" ]
Current State: 35:[11, 14, 95, 57], Operations: [] Exploring Operation: 14-11=3, Resulting Numbers: [95, 57, 3] Generated Node #2: [95, 57, 3] from Operation: 14-11=3 Current State: 35:[95, 57, 3], Operations: ['14-11=3'] Exploring Operation: 95-57=38, Resulting Numbers: [3, 38] Generated Node #3: [3, 38] from Operation: 95-57=38 Current State: 35:[3, 38], Operations: ['14-11=3', '95-57=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[11, 14, 95, 57], Operations: [] Exploring Operation: 57-14=43, Resulting Numbers: [11, 95, 43] Generated Node #0,0: 35:[11, 95, 43] Operation: 57-14=43 Exploring Operation: 95-57=38, Resulting Numbers: [11, 14, 38] Generated Node #0,1: 35:[11, 14, 38] Operation: 95-57=38 Exploring Operation: 95-14=81, Resulting Numbers: [11, 57, 81] Generated Node #0,2: 35:[11, 57, 81] Operation: 95-14=81 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[11, 14, 38], Operations: ['95-57=38'] Exploring Operation: 11+14=25, Resulting Numbers: [38, 25] Generated Node #0,1,0: 35:[38, 25] Operation: 11+14=25 Exploring Operation: 14-11=3, Resulting Numbers: [38, 3] Generated Node #0,1,1: 35:[38, 3] Operation: 14-11=3 Exploring Operation: 38-11=27, Resulting Numbers: [14, 27] Generated Node #0,1,2: 35:[14, 27] Operation: 38-11=27 Moving to Node #0,1,1 Current State: 35:[38, 3], Operations: ['95-57=38', '14-11=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[11, 14, 95, 57], Operations: [] Exploring Operation: 95-57=38, Resulting Numbers: [11, 14, 38] Generated Node #0,1: 35:[11, 14, 38] Operation: 95-57=38 Moving to Node #0,1 Current State: 35:[11, 14, 38], Operations: ['95-57=38'] Exploring Operation: 14-11=3, Resulting Numbers: [38, 3] Generated Node #0,1,1: 35:[38, 3] Operation: 14-11=3 Moving to Node #0,1,1 Current State: 35:[38, 3], Operations: ['95-57=38', '14-11=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 52, 14, 46, 3 ]
48
[ "52-46=6", "14*3=42", "6+42=48" ]
Current State: 48:[52, 14, 46, 3], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [14, 3, 6] Generated Node #2: [14, 3, 6] from Operation: 52-46=6 Current State: 48:[14, 3, 6], Operations: ['52-46=6'] Exploring Operation: 14*3=42, Resulting Numbers: [6, 42] Generated Node #3: [6, 42] from Operation: 14*3=42 Current State: 48:[6, 42], Operations: ['52-46=6', '14*3=42'] Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[52, 14, 46, 3], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [14, 3, 6] Generated Node #0,0: 48:[14, 3, 6] Operation: 52-46=6 Moving to Node #0,0 Current State: 48:[14, 3, 6], Operations: ['52-46=6'] Exploring Operation: 14-6=8, Resulting Numbers: [3, 8] Generated Node #0,0,0: 48:[3, 8] Operation: 14-6=8 Moving to Node #0,0,0 Current State: 48:[3, 8], Operations: ['52-46=6', '14-6=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,48 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 74, 23, 39, 70 ]
46
[ "74-39=35", "23*70=1610", "1610/35=46" ]
Current State: 46:[74, 23, 39, 70], Operations: [] Exploring Operation: 74-39=35, Resulting Numbers: [23, 70, 35] Generated Node #2: [23, 70, 35] from Operation: 74-39=35 Current State: 46:[23, 70, 35], Operations: ['74-39=35'] Exploring Operation: 23*70=1610, Resulting Numbers: [35, 1610] Generated Node #3: [35, 1610] from Operation: 23*70=1610 Current State: 46:[35, 1610], Operations: ['74-39=35', '23*70=1610'] Exploring Operation: 1610/35=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[74, 23, 39, 70], Operations: [] Exploring Operation: 74-23=51, Resulting Numbers: [39, 70, 51] Generated Node #0,0: 46:[39, 70, 51] Operation: 74-23=51 Exploring Operation: 70-23=47, Resulting Numbers: [74, 39, 47] Generated Node #0,1: 46:[74, 39, 47] Operation: 70-23=47 Exploring Operation: 74-39=35, Resulting Numbers: [23, 70, 35] Generated Node #0,2: 46:[23, 70, 35] Operation: 74-39=35 Exploring Operation: 74-70=4, Resulting Numbers: [23, 39, 4] Generated Node #0,3: 46:[23, 39, 4] Operation: 74-70=4 Moving to Node #0,3 Current State: 46:[23, 39, 4], Operations: ['74-70=4'] Exploring Operation: 23+4=27, Resulting Numbers: [39, 27] Generated Node #0,3,0: 46:[39, 27] Operation: 23+4=27 Exploring Operation: 23-4=19, Resulting Numbers: [39, 19] Generated Node #0,3,1: 46:[39, 19] Operation: 23-4=19 Exploring Operation: 39-23=16, Resulting Numbers: [4, 16] Generated Node #0,3,2: 46:[4, 16] Operation: 39-23=16 Exploring Operation: 39+4=43, Resulting Numbers: [23, 43] Generated Node #0,3,3: 46:[23, 43] Operation: 39+4=43 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 46:[23, 43], Operations: ['74-70=4', '39+4=43'] Exploring Operation: 23*43=989, Resulting Numbers: [989] 989,46 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,46 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:[4, 16], Operations: ['74-70=4', '39-23=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,46 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 46:[39, 27], Operations: ['74-70=4', '23+4=27'] Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 39+27=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 39*27=1053, Resulting Numbers: [1053] 1053,46 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:[39, 19], Operations: ['74-70=4', '23-4=19'] Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,46 unequal: No Solution Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,46 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,46 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:[23, 70, 35], Operations: ['74-39=35'] Exploring Operation: 35-23=12, Resulting Numbers: [70, 12] Generated Node #0,2,0: 46:[70, 12] Operation: 35-23=12 Exploring Operation: 70/35=2, Resulting Numbers: [23, 2] Generated Node #0,2,1: 46:[23, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [23, 35] Generated Node #0,2,2: 46:[23, 35] Operation: 70-35=35 Exploring Operation: 70-23=47, Resulting Numbers: [35, 47] Generated Node #0,2,3: 46:[35, 47] Operation: 70-23=47 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 46:[23, 2], Operations: ['74-39=35', '70/35=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[74, 23, 39, 70], Operations: [] Exploring Operation: 74-39=35, Resulting Numbers: [23, 70, 35] Generated Node #0,2: 46:[23, 70, 35] Operation: 74-39=35 Moving to Node #0,2 Current State: 46:[23, 70, 35], Operations: ['74-39=35'] Exploring Operation: 70/35=2, Resulting Numbers: [23, 2] Generated Node #0,2,1: 46:[23, 2] Operation: 70/35=2 Moving to Node #0,2,1 Current State: 46:[23, 2], Operations: ['74-39=35', '70/35=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 73, 76, 19, 94 ]
73
[ "76+19=95", "95-94=1", "73*1=73" ]
Current State: 73:[73, 76, 19, 94], Operations: [] Exploring Operation: 76+19=95, Resulting Numbers: [73, 94, 95] Generated Node #2: [73, 94, 95] from Operation: 76+19=95 Current State: 73:[73, 94, 95], Operations: ['76+19=95'] Exploring Operation: 95-94=1, Resulting Numbers: [73, 1] Generated Node #3: [73, 1] from Operation: 95-94=1 Current State: 73:[73, 1], Operations: ['76+19=95', '95-94=1'] Exploring Operation: 73*1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[73, 76, 19, 94], Operations: [] Exploring Operation: 76-19=57, Resulting Numbers: [73, 94, 57] Generated Node #0,0: 73:[73, 94, 57] Operation: 76-19=57 Exploring Operation: 94-19=75, Resulting Numbers: [73, 76, 75] Generated Node #0,1: 73:[73, 76, 75] Operation: 94-19=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[73, 76, 75], Operations: ['94-19=75'] Exploring Operation: 76-75=1, Resulting Numbers: [73, 1] Generated Node #0,1,0: 73:[73, 1] Operation: 76-75=1 Exploring Operation: 76-73=3, Resulting Numbers: [75, 3] Generated Node #0,1,1: 73:[75, 3] Operation: 76-73=3 Moving to Node #0,1,0 Current State: 73:[73, 1], Operations: ['94-19=75', '76-75=1'] Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[73, 76, 19, 94], Operations: [] Exploring Operation: 94-19=75, Resulting Numbers: [73, 76, 75] Generated Node #0,1: 73:[73, 76, 75] Operation: 94-19=75 Moving to Node #0,1 Current State: 73:[73, 76, 75], Operations: ['94-19=75'] Exploring Operation: 76-75=1, Resulting Numbers: [73, 1] Generated Node #0,1,0: 73:[73, 1] Operation: 76-75=1 Moving to Node #0,1,0 Current State: 73:[73, 1], Operations: ['94-19=75', '76-75=1'] Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 16, 65, 5, 8 ]
23
[ "16*5=80", "65-8=57", "80-57=23" ]
Current State: 23:[16, 65, 5, 8], Operations: [] Exploring Operation: 16*5=80, Resulting Numbers: [65, 8, 80] Generated Node #2: [65, 8, 80] from Operation: 16*5=80 Current State: 23:[65, 8, 80], Operations: ['16*5=80'] Exploring Operation: 65-8=57, Resulting Numbers: [80, 57] Generated Node #3: [80, 57] from Operation: 65-8=57 Current State: 23:[80, 57], Operations: ['16*5=80', '65-8=57'] Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[16, 65, 5, 8], Operations: [] Exploring Operation: 65-16=49, Resulting Numbers: [5, 8, 49] Generated Node #0,0: 23:[5, 8, 49] Operation: 65-16=49 Exploring Operation: 16+5=21, Resulting Numbers: [65, 8, 21] Generated Node #0,1: 23:[65, 8, 21] Operation: 16+5=21 Exploring Operation: 65/5=13, Resulting Numbers: [16, 8, 13] Generated Node #0,2: 23:[16, 8, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[16, 8, 13], Operations: ['65/5=13'] Exploring Operation: 16+8=24, Resulting Numbers: [13, 24] Generated Node #0,2,0: 23:[13, 24] Operation: 16+8=24 Exploring Operation: 16+13=29, Resulting Numbers: [8, 29] Generated Node #0,2,1: 23:[8, 29] Operation: 16+13=29 Exploring Operation: 8+13=21, Resulting Numbers: [16, 21] Generated Node #0,2,2: 23:[16, 21] Operation: 8+13=21 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[16, 21], Operations: ['65/5=13', '8+13=21'] Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,23 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,23 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 23:[13, 24], Operations: ['65/5=13', '16+8=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,23 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 23:[8, 29], Operations: ['65/5=13', '16+13=29'] Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,23 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[5, 8, 49], Operations: ['65-16=49'] Exploring Operation: 5+8=13, Resulting Numbers: [49, 13] Generated Node #0,0,0: 23:[49, 13] Operation: 5+8=13 Exploring Operation: 49-8=41, Resulting Numbers: [5, 41] Generated Node #0,0,1: 23:[5, 41] Operation: 49-8=41 Exploring Operation: 49-5=44, Resulting Numbers: [8, 44] Generated Node #0,0,2: 23:[8, 44] Operation: 49-5=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[49, 13], Operations: ['65-16=49', '5+8=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,23 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[5, 41], Operations: ['65-16=49', '49-8=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,23 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 5*41=205, Resulting Numbers: [205] 205,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[8, 44], Operations: ['65-16=49', '49-5=44'] Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,23 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[65, 8, 21], Operations: ['16+5=21'] Exploring Operation: 8+21=29, Resulting Numbers: [65, 29] Generated Node #0,1,0: 23:[65, 29] Operation: 8+21=29 Exploring Operation: 65-8=57, Resulting Numbers: [21, 57] Generated Node #0,1,1: 23:[21, 57] Operation: 65-8=57 Exploring Operation: 65-21=44, Resulting Numbers: [8, 44] Generated Node #0,1,2: 23:[8, 44] Operation: 65-21=44 Moving to Node #0,1,1 Current State: 23:[21, 57], Operations: ['16+5=21', '65-8=57'] Exploring Operation: 21*57=1197, Resulting Numbers: [1197] 1197,23 unequal: No Solution Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,23 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[8, 44], Operations: ['16+5=21', '65-21=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,23 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[65, 29], Operations: ['16+5=21', '8+21=29'] Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,23 unequal: No Solution Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 13, 60, 8, 67 ]
83
[ "67-60=7", "13*7=91", "91-8=83" ]
Current State: 83:[13, 60, 8, 67], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [13, 8, 7] Generated Node #2: [13, 8, 7] from Operation: 67-60=7 Current State: 83:[13, 8, 7], Operations: ['67-60=7'] Exploring Operation: 13*7=91, Resulting Numbers: [8, 91] Generated Node #3: [8, 91] from Operation: 13*7=91 Current State: 83:[8, 91], Operations: ['67-60=7', '13*7=91'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[13, 60, 8, 67], Operations: [] Exploring Operation: 13*8=104, Resulting Numbers: [60, 67, 104] Generated Node #0,0: 83:[60, 67, 104] Operation: 13*8=104 Moving to Node #0,0 Current State: 83:[60, 67, 104], Operations: ['13*8=104'] Exploring Operation: 104-60=44, Resulting Numbers: [67, 44] Generated Node #0,0,0: 83:[67, 44] Operation: 104-60=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[67, 44], Operations: ['13*8=104', '104-60=44'] Exploring Operation: 67+44=111, Resulting Numbers: [111] 111,83 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
[ 2, 44, 17, 32 ]
95
[ "2+44=46", "17+32=49", "46+49=95" ]
Current State: 95:[2, 44, 17, 32], Operations: [] Exploring Operation: 2+44=46, Resulting Numbers: [17, 32, 46] Generated Node #2: [17, 32, 46] from Operation: 2+44=46 Current State: 95:[17, 32, 46], Operations: ['2+44=46'] Exploring Operation: 17+32=49, Resulting Numbers: [46, 49] Generated Node #3: [46, 49] from Operation: 17+32=49 Current State: 95:[46, 49], Operations: ['2+44=46', '17+32=49'] Exploring Operation: 46+49=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[2, 44, 17, 32], Operations: [] Exploring Operation: 44/2=22, Resulting Numbers: [17, 32, 22] Generated Node #0,0: 95:[17, 32, 22] Operation: 44/2=22 Exploring Operation: 44-32=12, Resulting Numbers: [2, 17, 12] Generated Node #0,1: 95:[2, 17, 12] Operation: 44-32=12 Exploring Operation: 44-17=27, Resulting Numbers: [2, 32, 27] Generated Node #0,2: 95:[2, 32, 27] Operation: 44-17=27 Exploring Operation: 2*44=88, Resulting Numbers: [17, 32, 88] Generated Node #0,3: 95:[17, 32, 88] Operation: 2*44=88 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[2, 17, 12], Operations: ['44-32=12'] Exploring Operation: 17-12=5, Resulting Numbers: [2, 5] Generated Node #0,1,0: 95:[2, 5] Operation: 17-12=5 Exploring Operation: 2+17=19, Resulting Numbers: [12, 19] Generated Node #0,1,1: 95:[12, 19] Operation: 2+17=19 Exploring Operation: 2+12=14, Resulting Numbers: [17, 14] Generated Node #0,1,2: 95:[17, 14] Operation: 2+12=14 Exploring Operation: 12/2=6, Resulting Numbers: [17, 6] Generated Node #0,1,3: 95:[17, 6] Operation: 12/2=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[2, 5], Operations: ['44-32=12', '17-12=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,95 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 #0,1,3 Current State: 95:[17, 6], Operations: ['44-32=12', '12/2=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,95 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,95 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,95 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 #0,1,1 Current State: 95:[12, 19], Operations: ['44-32=12', '2+17=19'] Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,95 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,95 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 #0,1,2 Current State: 95:[17, 14], Operations: ['44-32=12', '2+12=14'] Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,95 unequal: No Solution Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,95 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,95 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:[17, 32, 22], Operations: ['44/2=22'] Exploring Operation: 32-17=15, Resulting Numbers: [22, 15] Generated Node #0,0,0: 95:[22, 15] Operation: 32-17=15 Exploring Operation: 22-17=5, Resulting Numbers: [32, 5] Generated Node #0,0,1: 95:[32, 5] Operation: 22-17=5 Exploring Operation: 17+32=49, Resulting Numbers: [22, 49] Generated Node #0,0,2: 95:[22, 49] Operation: 17+32=49 Exploring Operation: 32-22=10, Resulting Numbers: [17, 10] Generated Node #0,0,3: 95:[17, 10] Operation: 32-22=10 Moving to Node #0,0,0 Current State: 95:[22, 15], Operations: ['44/2=22', '32-17=15'] Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,95 unequal: No Solution Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,95 unequal: No Solution Moving to Node #0,0,3 Current State: 95:[17, 10], Operations: ['44/2=22', '32-22=10'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,95 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[32, 5], Operations: ['44/2=22', '22-17=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,95 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,95 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[22, 49], Operations: ['44/2=22', '17+32=49'] Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,95 unequal: No Solution Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,95 unequal: No Solution Exploring Operation: 22*49=1078, Resulting Numbers: [1078] 1078,95 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 #0,3 Current State: 95:[17, 32, 88], Operations: ['2*44=88'] Exploring Operation: 32-17=15, Resulting Numbers: [88, 15] Generated Node #0,3,0: 95:[88, 15] Operation: 32-17=15 Exploring Operation: 17+32=49, Resulting Numbers: [88, 49] Generated Node #0,3,1: 95:[88, 49] Operation: 17+32=49 Exploring Operation: 17+88=105, Resulting Numbers: [32, 105] Generated Node #0,3,2: 95:[32, 105] Operation: 17+88=105 Exploring Operation: 32+88=120, Resulting Numbers: [17, 120] Generated Node #0,3,3: 95:[17, 120] Operation: 32+88=120 Moving to Node #0,3,0 Current State: 95:[88, 15], Operations: ['2*44=88', '32-17=15'] Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,95 unequal: No Solution Exploring Operation: 88+15=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 88*15=1320, Resulting Numbers: [1320] 1320,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[32, 105], Operations: ['2*44=88', '17+88=105'] Exploring Operation: 32*105=3360, Resulting Numbers: [3360] 3360,95 unequal: No Solution Exploring Operation: 32+105=137, Resulting Numbers: [137] 137,95 unequal: No Solution Exploring Operation: 105-32=73, Resulting Numbers: [73] 73,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[17, 120], Operations: ['2*44=88', '32+88=120'] Exploring Operation: 120-17=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 17+120=137, Resulting Numbers: [137] 137,95 unequal: No Solution Exploring Operation: 17*120=2040, Resulting Numbers: [2040] 2040,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[88, 49], Operations: ['2*44=88', '17+32=49'] Exploring Operation: 88+49=137, Resulting Numbers: [137] 137,95 unequal: No Solution Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 88*49=4312, Resulting Numbers: [4312] 4312,95 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 #0,2 Current State: 95:[2, 32, 27], Operations: ['44-17=27'] Exploring Operation: 32-2=30, Resulting Numbers: [27, 30] Generated Node #0,2,0: 95:[27, 30] Operation: 32-2=30 Exploring Operation: 27-2=25, Resulting Numbers: [32, 25] Generated Node #0,2,1: 95:[32, 25] Operation: 27-2=25 Exploring Operation: 32/2=16, Resulting Numbers: [27, 16] Generated Node #0,2,2: 95:[27, 16] Operation: 32/2=16 Exploring Operation: 32-27=5, Resulting Numbers: [2, 5] Generated Node #0,2,3: 95:[2, 5] Operation: 32-27=5 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 95:[2, 5], Operations: ['44-17=27', '32-27=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,95 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 #0,2,2 Current State: 95:[27, 16], Operations: ['44-17=27', '32/2=16'] Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,95 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,95 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, 30], Operations: ['44-17=27', '32-2=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,95 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,95 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:[32, 25], Operations: ['44-17=27', '27-2=25'] Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,95 unequal: No Solution Exploring Operation: 32*25=800, Resulting Numbers: [800] 800,95 unequal: No Solution Exploring Operation: 32+25=57, Resulting Numbers: [57] 57,95 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 No solution found.
0
hs_4
mult_heuristic
[ 39, 97, 58, 82 ]
34
[ "97-39=58", "82-58=24", "58-24=34" ]
Current State: 34:[39, 97, 58, 82], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [58, 82, 58] Generated Node #2: [58, 82, 58] from Operation: 97-39=58 Current State: 34:[58, 82, 58], Operations: ['97-39=58'] Exploring Operation: 82-58=24, Resulting Numbers: [24] 24,34 equal: Goal Reached Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[39, 97, 58, 82], Operations: [] Exploring Operation: 82-58=24, Resulting Numbers: [39, 97, 24] Generated Node #0,0: 34:[39, 97, 24] Operation: 82-58=24 Exploring Operation: 82-39=43, Resulting Numbers: [97, 58, 43] Generated Node #0,1: 34:[97, 58, 43] Operation: 82-39=43 Exploring Operation: 97-58=39, Resulting Numbers: [39, 82, 39] Generated Node #0,2: 34:[39, 82, 39] Operation: 97-58=39 Exploring Operation: 97-82=15, Resulting Numbers: [39, 58, 15] Generated Node #0,3: 34:[39, 58, 15] Operation: 97-82=15 Exploring Operation: 97-39=58, Resulting Numbers: [58, 82, 58] Generated Node #0,4: 34:[58, 82, 58] Operation: 97-39=58 Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[39, 58, 15], Operations: ['97-82=15'] Exploring Operation: 39+15=54, Resulting Numbers: [58, 54] Generated Node #0,3,0: 34:[58, 54] Operation: 39+15=54 Exploring Operation: 58-39=19, Resulting Numbers: [15, 19] Generated Node #0,3,1: 34:[15, 19] Operation: 58-39=19 Exploring Operation: 58+15=73, Resulting Numbers: [39, 73] Generated Node #0,3,2: 34:[39, 73] Operation: 58+15=73 Exploring Operation: 58-15=43, Resulting Numbers: [39, 43] Generated Node #0,3,3: 34:[39, 43] Operation: 58-15=43 Exploring Operation: 39-15=24, Resulting Numbers: [58, 24] Generated Node #0,3,4: 34:[58, 24] Operation: 39-15=24 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 34:[15, 19], Operations: ['97-82=15', '58-39=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,34 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,34 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[39, 97, 58, 82], Operations: [] Exploring Operation: 97-82=15, Resulting Numbers: [39, 58, 15] Generated Node #0,3: 34:[39, 58, 15] Operation: 97-82=15 Moving to Node #0,3 Current State: 34:[39, 58, 15], Operations: ['97-82=15'] Exploring Operation: 58-39=19, Resulting Numbers: [15, 19] Generated Node #0,3,1: 34:[15, 19] Operation: 58-39=19 Moving to Node #0,3,1 Current State: 34:[15, 19], Operations: ['97-82=15', '58-39=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 38, 51, 84, 63 ]
87
[ "51+63=114", "114/38=3", "84+3=87" ]
Current State: 87:[38, 51, 84, 63], Operations: [] Exploring Operation: 51+63=114, Resulting Numbers: [38, 84, 114] Generated Node #2: [38, 84, 114] from Operation: 51+63=114 Current State: 87:[38, 84, 114], Operations: ['51+63=114'] Exploring Operation: 114/38=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 114/38=3 Current State: 87:[84, 3], Operations: ['51+63=114', '114/38=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[38, 51, 84, 63], Operations: [] Exploring Operation: 38+51=89, Resulting Numbers: [84, 63, 89] Generated Node #0,0: 87:[84, 63, 89] Operation: 38+51=89 Exploring Operation: 84-51=33, Resulting Numbers: [38, 63, 33] Generated Node #0,1: 87:[38, 63, 33] Operation: 84-51=33 Exploring Operation: 51-38=13, Resulting Numbers: [84, 63, 13] Generated Node #0,2: 87:[84, 63, 13] Operation: 51-38=13 Exploring Operation: 63-51=12, Resulting Numbers: [38, 84, 12] Generated Node #0,3: 87:[38, 84, 12] Operation: 63-51=12 Exploring Operation: 63-38=25, Resulting Numbers: [51, 84, 25] Generated Node #0,4: 87:[51, 84, 25] Operation: 63-38=25 Moving to Node #0,3 Current State: 87:[38, 84, 12], Operations: ['63-51=12'] Exploring Operation: 38-12=26, Resulting Numbers: [84, 26] Generated Node #0,3,0: 87:[84, 26] Operation: 38-12=26 Exploring Operation: 84/12=7, Resulting Numbers: [38, 7] Generated Node #0,3,1: 87:[38, 7] Operation: 84/12=7 Exploring Operation: 84+12=96, Resulting Numbers: [38, 96] Generated Node #0,3,2: 87:[38, 96] Operation: 84+12=96 Exploring Operation: 84-12=72, Resulting Numbers: [38, 72] Generated Node #0,3,3: 87:[38, 72] Operation: 84-12=72 Exploring Operation: 38+12=50, Resulting Numbers: [84, 50] Generated Node #0,3,4: 87:[84, 50] Operation: 38+12=50 Moving to Node #0,4 Current State: 87:[51, 84, 25], Operations: ['63-38=25'] Exploring Operation: 51+25=76, Resulting Numbers: [84, 76] Generated Node #0,4,0: 87:[84, 76] Operation: 51+25=76 Exploring Operation: 84-25=59, Resulting Numbers: [51, 59] Generated Node #0,4,1: 87:[51, 59] Operation: 84-25=59 Exploring Operation: 84-51=33, Resulting Numbers: [25, 33] Generated Node #0,4,2: 87:[25, 33] Operation: 84-51=33 Exploring Operation: 51-25=26, Resulting Numbers: [84, 26] Generated Node #0,4,3: 87:[84, 26] Operation: 51-25=26 Exploring Operation: 84+25=109, Resulting Numbers: [51, 109] Generated Node #0,4,4: 87:[51, 109] Operation: 84+25=109 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 87:[84, 26], Operations: ['63-38=25', '51-25=26'] Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 87:[25, 33], Operations: ['63-38=25', '84-51=33'] Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,87 unequal: No Solution Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 87:[84, 76], Operations: ['63-38=25', '51+25=76'] Exploring Operation: 84+76=160, Resulting Numbers: [160] 160,87 unequal: No Solution Exploring Operation: 84*76=6384, Resulting Numbers: [6384] 6384,87 unequal: No Solution Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 87:[51, 109], Operations: ['63-38=25', '84+25=109'] Exploring Operation: 109-51=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 51*109=5559, Resulting Numbers: [5559] 5559,87 unequal: No Solution Exploring Operation: 51+109=160, Resulting Numbers: [160] 160,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 87:[51, 59], Operations: ['63-38=25', '84-25=59'] Exploring Operation: 51*59=3009, Resulting Numbers: [3009] 3009,87 unequal: No Solution Exploring Operation: 51+59=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 87:[84, 63, 89], Operations: ['38+51=89'] Exploring Operation: 84+63=147, Resulting Numbers: [89, 147] Generated Node #0,0,0: 87:[89, 147] Operation: 84+63=147 Exploring Operation: 89-63=26, Resulting Numbers: [84, 26] Generated Node #0,0,1: 87:[84, 26] Operation: 89-63=26 Exploring Operation: 84-63=21, Resulting Numbers: [89, 21] Generated Node #0,0,2: 87:[89, 21] Operation: 84-63=21 Exploring Operation: 63+89=152, Resulting Numbers: [84, 152] Generated Node #0,0,3: 87:[84, 152] Operation: 63+89=152 Exploring Operation: 89-84=5, Resulting Numbers: [63, 5] Generated Node #0,0,4: 87:[63, 5] Operation: 89-84=5 Moving to Node #0,1 Current State: 87:[38, 63, 33], Operations: ['84-51=33'] Exploring Operation: 63+33=96, Resulting Numbers: [38, 96] Generated Node #0,1,0: 87:[38, 96] Operation: 63+33=96 Exploring Operation: 63-38=25, Resulting Numbers: [33, 25] Generated Node #0,1,1: 87:[33, 25] Operation: 63-38=25 Exploring Operation: 38+63=101, Resulting Numbers: [33, 101] Generated Node #0,1,2: 87:[33, 101] Operation: 38+63=101 Exploring Operation: 63-33=30, Resulting Numbers: [38, 30] Generated Node #0,1,3: 87:[38, 30] Operation: 63-33=30 Exploring Operation: 38-33=5, Resulting Numbers: [63, 5] Generated Node #0,1,4: 87:[63, 5] Operation: 38-33=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[33, 25], Operations: ['84-51=33', '63-38=25'] Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 33+25=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 33*25=825, Resulting Numbers: [825] 825,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[38, 30], Operations: ['84-51=33', '63-33=30'] Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 38+30=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 38*30=1140, Resulting Numbers: [1140] 1140,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[38, 96], Operations: ['84-51=33', '63+33=96'] Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 38+96=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 38*96=3648, Resulting Numbers: [3648] 3648,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[33, 101], Operations: ['84-51=33', '38+63=101'] Exploring Operation: 33*101=3333, Resulting Numbers: [3333] 3333,87 unequal: No Solution Exploring Operation: 33+101=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 101-33=68, Resulting Numbers: [68] 68,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 87:[63, 5], Operations: ['84-51=33', '38-33=5'] Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 87:[84, 63, 13], Operations: ['51-38=13'] Exploring Operation: 63-13=50, Resulting Numbers: [84, 50] Generated Node #0,2,0: 87:[84, 50] Operation: 63-13=50 Exploring Operation: 84-13=71, Resulting Numbers: [63, 71] Generated Node #0,2,1: 87:[63, 71] Operation: 84-13=71 Exploring Operation: 84+13=97, Resulting Numbers: [63, 97] Generated Node #0,2,2: 87:[63, 97] Operation: 84+13=97 Exploring Operation: 84-63=21, Resulting Numbers: [13, 21] Generated Node #0,2,3: 87:[13, 21] Operation: 84-63=21 Exploring Operation: 63+13=76, Resulting Numbers: [84, 76] Generated Node #0,2,4: 87:[84, 76] Operation: 63+13=76 Moving to Node #0,3,0 Current State: 87:[84, 26], Operations: ['63-51=12', '38-12=26'] Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,87 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[84, 26], Operations: ['38+51=89', '89-63=26'] Exploring Operation: 84+26=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 84*26=2184, Resulting Numbers: [2184] 2184,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[89, 21], Operations: ['38+51=89', '84-63=21'] Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 89+21=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 89*21=1869, Resulting Numbers: [1869] 1869,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[38, 7], Operations: ['63-51=12', '84/12=7'] Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,87 unequal: No Solution Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,87 unequal: No Solution Moving to Node #0,2,4 Current State: 87:[84, 76], Operations: ['51-38=13', '63+13=76'] Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 84*76=6384, Resulting Numbers: [6384] 6384,87 unequal: No Solution Exploring Operation: 84+76=160, Resulting Numbers: [160] 160,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[38, 96], Operations: ['63-51=12', '84+12=96'] Exploring Operation: 38*96=3648, Resulting Numbers: [3648] 3648,87 unequal: No Solution Exploring Operation: 38+96=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,87 unequal: No Solution Moving to Node #0,2,3 Current State: 87:[13, 21], Operations: ['51-38=13', '84-63=21'] Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,87 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,87 unequal: No Solution Moving to Node #0,3,4 Current State: 87:[84, 50], Operations: ['63-51=12', '38+12=50'] Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,87 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[84, 50], Operations: ['51-38=13', '63-13=50'] Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[38, 72], Operations: ['63-51=12', '84-12=72'] Exploring Operation: 38+72=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 38*72=2736, Resulting Numbers: [2736] 2736,87 unequal: No Solution Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,87 unequal: No Solution Moving to Node #0,0,4 Current State: 87:[63, 5], Operations: ['38+51=89', '89-84=5'] Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,87 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[63, 97], Operations: ['51-38=13', '84+13=97'] Exploring Operation: 63*97=6111, Resulting Numbers: [6111] 6111,87 unequal: No Solution Exploring Operation: 97-63=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 63+97=160, Resulting Numbers: [160] 160,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[63, 71], Operations: ['51-38=13', '84-13=71'] Exploring Operation: 63+71=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 71-63=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 63*71=4473, Resulting Numbers: [4473] 4473,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[89, 147], Operations: ['38+51=89', '84+63=147'] Exploring Operation: 147-89=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 89+147=236, Resulting Numbers: [236] 236,87 unequal: No Solution Exploring Operation: 89*147=13083, Resulting Numbers: [13083] 13083,87 unequal: No Solution Moving to Node #0,0,3 Current State: 87:[84, 152], Operations: ['38+51=89', '63+89=152'] Exploring Operation: 152-84=68, Resulting Numbers: [68] 68,87 unequal: No Solution Exploring Operation: 84*152=12768, Resulting Numbers: [12768] 12768,87 unequal: No Solution Exploring Operation: 84+152=236, Resulting Numbers: [236] 236,87 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 90, 19, 69, 27 ]
67
[ "90+19=109", "69-27=42", "109-42=67" ]
Current State: 67:[90, 19, 69, 27], Operations: [] Exploring Operation: 90+19=109, Resulting Numbers: [69, 27, 109] Generated Node #2: [69, 27, 109] from Operation: 90+19=109 Current State: 67:[69, 27, 109], Operations: ['90+19=109'] Exploring Operation: 69-27=42, Resulting Numbers: [109, 42] Generated Node #3: [109, 42] from Operation: 69-27=42 Current State: 67:[109, 42], Operations: ['90+19=109', '69-27=42'] Exploring Operation: 109-42=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[90, 19, 69, 27], Operations: [] Exploring Operation: 19+27=46, Resulting Numbers: [90, 69, 46] Generated Node #0,0: 67:[90, 69, 46] Operation: 19+27=46 Exploring Operation: 90-19=71, Resulting Numbers: [69, 27, 71] Generated Node #0,1: 67:[69, 27, 71] Operation: 90-19=71 Exploring Operation: 90-27=63, Resulting Numbers: [19, 69, 63] Generated Node #0,2: 67:[19, 69, 63] Operation: 90-27=63 Exploring Operation: 69-19=50, Resulting Numbers: [90, 27, 50] Generated Node #0,3: 67:[90, 27, 50] Operation: 69-19=50 Exploring Operation: 90+19=109, Resulting Numbers: [69, 27, 109] Generated Node #0,4: 67:[69, 27, 109] Operation: 90+19=109 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[90, 69, 46], Operations: ['19+27=46'] Exploring Operation: 69+46=115, Resulting Numbers: [90, 115] Generated Node #0,0,0: 67:[90, 115] Operation: 69+46=115 Exploring Operation: 69-46=23, Resulting Numbers: [90, 23] Generated Node #0,0,1: 67:[90, 23] Operation: 69-46=23 Exploring Operation: 90-46=44, Resulting Numbers: [69, 44] Generated Node #0,0,2: 67:[69, 44] Operation: 90-46=44 Exploring Operation: 90-69=21, Resulting Numbers: [46, 21] Generated Node #0,0,3: 67:[46, 21] Operation: 90-69=21 Exploring Operation: 90+46=136, Resulting Numbers: [69, 136] Generated Node #0,0,4: 67:[69, 136] Operation: 90+46=136 Moving to Node #0,0,2 Current State: 67:[69, 44], Operations: ['19+27=46', '90-46=44'] Exploring Operation: 69+44=113, Resulting Numbers: [113] 113,67 unequal: No Solution Exploring Operation: 69*44=3036, Resulting Numbers: [3036] 3036,67 unequal: No Solution Exploring Operation: 69-44=25, Resulting Numbers: [25] 25,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[46, 21], Operations: ['19+27=46', '90-69=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,67 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[90, 19, 69, 27], Operations: [] Exploring Operation: 19+27=46, Resulting Numbers: [90, 69, 46] Generated Node #0,0: 67:[90, 69, 46] Operation: 19+27=46 Moving to Node #0,0 Current State: 67:[90, 69, 46], Operations: ['19+27=46'] Exploring Operation: 90-69=21, Resulting Numbers: [46, 21] Generated Node #0,0,3: 67:[46, 21] Operation: 90-69=21 Moving to Node #0,0,3 Current State: 67:[46, 21], Operations: ['19+27=46', '90-69=21'] Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 16, 88, 14, 69 ]
80
[ "88-14=74", "74-69=5", "16*5=80" ]
Current State: 80:[16, 88, 14, 69], Operations: [] Exploring Operation: 88-14=74, Resulting Numbers: [16, 69, 74] Generated Node #2: [16, 69, 74] from Operation: 88-14=74 Current State: 80:[16, 69, 74], Operations: ['88-14=74'] Exploring Operation: 74-69=5, Resulting Numbers: [16, 5] Generated Node #3: [16, 5] from Operation: 74-69=5 Current State: 80:[16, 5], Operations: ['88-14=74', '74-69=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[16, 88, 14, 69], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [16, 14, 19] Generated Node #0,0: 80:[16, 14, 19] Operation: 88-69=19 Exploring Operation: 14+69=83, Resulting Numbers: [16, 88, 83] Generated Node #0,1: 80:[16, 88, 83] Operation: 14+69=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[16, 14, 19], Operations: ['88-69=19'] Exploring Operation: 19-14=5, Resulting Numbers: [16, 5] Generated Node #0,0,0: 80:[16, 5] Operation: 19-14=5 Exploring Operation: 16-14=2, Resulting Numbers: [19, 2] Generated Node #0,0,1: 80:[19, 2] Operation: 16-14=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[16, 5], Operations: ['88-69=19', '19-14=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[16, 88, 14, 69], Operations: [] Exploring Operation: 88-69=19, Resulting Numbers: [16, 14, 19] Generated Node #0,0: 80:[16, 14, 19] Operation: 88-69=19 Moving to Node #0,0 Current State: 80:[16, 14, 19], Operations: ['88-69=19'] Exploring Operation: 19-14=5, Resulting Numbers: [16, 5] Generated Node #0,0,0: 80:[16, 5] Operation: 19-14=5 Moving to Node #0,0,0 Current State: 80:[16, 5], Operations: ['88-69=19', '19-14=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 45, 43, 80, 28 ]
94
[ "45-43=2", "28/2=14", "80+14=94" ]
Current State: 94:[45, 43, 80, 28], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [80, 28, 2] Generated Node #2: [80, 28, 2] from Operation: 45-43=2 Current State: 94:[80, 28, 2], Operations: ['45-43=2'] Exploring Operation: 28/2=14, Resulting Numbers: [80, 14] Generated Node #3: [80, 14] from Operation: 28/2=14 Current State: 94:[80, 14], Operations: ['45-43=2', '28/2=14'] Exploring Operation: 80+14=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[45, 43, 80, 28], Operations: [] Exploring Operation: 80-28=52, Resulting Numbers: [45, 43, 52] Generated Node #0,0: 94:[45, 43, 52] Operation: 80-28=52 Exploring Operation: 80+28=108, Resulting Numbers: [45, 43, 108] Generated Node #0,1: 94:[45, 43, 108] Operation: 80+28=108 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[45, 43, 52], Operations: ['80-28=52'] Exploring Operation: 43+52=95, Resulting Numbers: [45, 95] Generated Node #0,0,0: 94:[45, 95] Operation: 43+52=95 Exploring Operation: 45-43=2, Resulting Numbers: [52, 2] Generated Node #0,0,1: 94:[52, 2] Operation: 45-43=2 Moving to Node #0,0,0 Current State: 94:[45, 95], Operations: ['80-28=52', '43+52=95'] Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 45+95=140, Resulting Numbers: [140] 140,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[52, 2], Operations: ['80-28=52', '45-43=2'] Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,94 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,94 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 #0,1 Current State: 94:[45, 43, 108], Operations: ['80+28=108'] Exploring Operation: 45+43=88, Resulting Numbers: [108, 88] Generated Node #0,1,0: 94:[108, 88] Operation: 45+43=88 Exploring Operation: 45-43=2, Resulting Numbers: [108, 2] Generated Node #0,1,1: 94:[108, 2] Operation: 45-43=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[108, 2], Operations: ['80+28=108', '45-43=2'] Exploring Operation: 108-2=106, Resulting Numbers: [106] 106,94 unequal: No Solution Exploring Operation: 108/2=54, Resulting Numbers: [54] 54,94 unequal: No Solution No 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: 94:[108, 88], Operations: ['80+28=108', '45+43=88'] Exploring Operation: 108+88=196, Resulting Numbers: [196] 196,94 unequal: No Solution Exploring Operation: 108-88=20, Resulting Numbers: [20] 20,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 18, 86, 75, 43 ]
95
[ "18+75=93", "86/43=2", "93+2=95" ]
Current State: 95:[18, 86, 75, 43], Operations: [] Exploring Operation: 18+75=93, Resulting Numbers: [86, 43, 93] Generated Node #2: [86, 43, 93] from Operation: 18+75=93 Current State: 95:[86, 43, 93], Operations: ['18+75=93'] Exploring Operation: 86/43=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 86/43=2 Current State: 95:[93, 2], Operations: ['18+75=93', '86/43=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[18, 86, 75, 43], Operations: [] Exploring Operation: 75-43=32, Resulting Numbers: [18, 86, 32] Generated Node #0,0: 95:[18, 86, 32] Operation: 75-43=32 Moving to Node #0,0 Current State: 95:[18, 86, 32], Operations: ['75-43=32'] Exploring Operation: 32-18=14, Resulting Numbers: [86, 14] Generated Node #0,0,0: 95:[86, 14] Operation: 32-18=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[86, 14], Operations: ['75-43=32', '32-18=14'] Exploring Operation: 86+14=100, Resulting Numbers: [100] 100,95 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
[ 3, 7, 13, 39 ]
97
[ "3*39=117", "7+13=20", "117-20=97" ]
Current State: 97:[3, 7, 13, 39], Operations: [] Exploring Operation: 3*39=117, Resulting Numbers: [7, 13, 117] Generated Node #2: [7, 13, 117] from Operation: 3*39=117 Current State: 97:[7, 13, 117], Operations: ['3*39=117'] Exploring Operation: 7+13=20, Resulting Numbers: [117, 20] Generated Node #3: [117, 20] from Operation: 7+13=20 Current State: 97:[117, 20], Operations: ['3*39=117', '7+13=20'] Exploring Operation: 117-20=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[3, 7, 13, 39], Operations: [] Exploring Operation: 3*13=39, Resulting Numbers: [7, 39, 39] Generated Node #0,0: 97:[7, 39, 39] Operation: 3*13=39 Exploring Operation: 3*39=117, Resulting Numbers: [7, 13, 117] Generated Node #0,1: 97:[7, 13, 117] Operation: 3*39=117 Exploring Operation: 7*13=91, Resulting Numbers: [3, 39, 91] Generated Node #0,2: 97:[3, 39, 91] Operation: 7*13=91 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[3, 39, 91], Operations: ['7*13=91'] Exploring Operation: 3+39=42, Resulting Numbers: [91, 42] Generated Node #0,2,0: 97:[91, 42] Operation: 3+39=42 Exploring Operation: 3*39=117, Resulting Numbers: [91, 117] Generated Node #0,2,1: 97:[91, 117] Operation: 3*39=117 Exploring Operation: 3+91=94, Resulting Numbers: [39, 94] Generated Node #0,2,2: 97:[39, 94] Operation: 3+91=94 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[91, 117], Operations: ['7*13=91', '3*39=117'] Exploring Operation: 91+117=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 91*117=10647, Resulting Numbers: [10647] 10647,97 unequal: No Solution Exploring Operation: 117-91=26, Resulting Numbers: [26] 26,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[91, 42], Operations: ['7*13=91', '3+39=42'] Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,97 unequal: No Solution Exploring Operation: 91*42=3822, Resulting Numbers: [3822] 3822,97 unequal: No Solution Exploring Operation: 91+42=133, Resulting Numbers: [133] 133,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[39, 94], Operations: ['7*13=91', '3+91=94'] Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 39+94=133, Resulting Numbers: [133] 133,97 unequal: No Solution Exploring Operation: 39*94=3666, Resulting Numbers: [3666] 3666,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[7, 13, 117], Operations: ['3*39=117'] Exploring Operation: 7+13=20, Resulting Numbers: [117, 20] Generated Node #0,1,0: 97:[117, 20] Operation: 7+13=20 Exploring Operation: 7*13=91, Resulting Numbers: [117, 91] Generated Node #0,1,1: 97:[117, 91] Operation: 7*13=91 Exploring Operation: 117-7=110, Resulting Numbers: [13, 110] Generated Node #0,1,2: 97:[13, 110] Operation: 117-7=110 Moving to Node #0,1,1 Current State: 97:[117, 91], Operations: ['3*39=117', '7*13=91'] Exploring Operation: 117-91=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 117*91=10647, Resulting Numbers: [10647] 10647,97 unequal: No Solution Exploring Operation: 117+91=208, Resulting Numbers: [208] 208,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[117, 20], Operations: ['3*39=117', '7+13=20'] Exploring Operation: 117+20=137, Resulting Numbers: [137] 137,97 unequal: No Solution Exploring Operation: 117-20=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[3, 7, 13, 39], Operations: [] Exploring Operation: 3*39=117, Resulting Numbers: [7, 13, 117] Generated Node #0,1: 97:[7, 13, 117] Operation: 3*39=117 Moving to Node #0,1 Current State: 97:[7, 13, 117], Operations: ['3*39=117'] Exploring Operation: 7+13=20, Resulting Numbers: [117, 20] Generated Node #0,1,0: 97:[117, 20] Operation: 7+13=20 Moving to Node #0,1,0 Current State: 97:[117, 20], Operations: ['3*39=117', '7+13=20'] Exploring Operation: 117-20=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 61, 6, 29, 59 ]
85
[ "61-6=55", "59-29=30", "55+30=85" ]
Current State: 85:[61, 6, 29, 59], Operations: [] Exploring Operation: 61-6=55, Resulting Numbers: [29, 59, 55] Generated Node #2: [29, 59, 55] from Operation: 61-6=55 Current State: 85:[29, 59, 55], Operations: ['61-6=55'] Exploring Operation: 59-29=30, Resulting Numbers: [55, 30] Generated Node #3: [55, 30] from Operation: 59-29=30 Current State: 85:[55, 30], Operations: ['61-6=55', '59-29=30'] Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[61, 6, 29, 59], Operations: [] Exploring Operation: 61-59=2, Resulting Numbers: [6, 29, 2] Generated Node #0,0: 85:[6, 29, 2] Operation: 61-59=2 Moving to Node #0,0 Current State: 85:[6, 29, 2], Operations: ['61-59=2'] Exploring Operation: 29-6=23, Resulting Numbers: [2, 23] Generated Node #0,0,0: 85:[2, 23] Operation: 29-6=23 Moving to Node #0,0,0 Current State: 85:[2, 23], Operations: ['61-59=2', '29-6=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,85 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 26, 85, 6, 18 ]
47
[ "85-26=59", "18-6=12", "59-12=47" ]
Current State: 47:[26, 85, 6, 18], Operations: [] Exploring Operation: 85-26=59, Resulting Numbers: [6, 18, 59] Generated Node #2: [6, 18, 59] from Operation: 85-26=59 Current State: 47:[6, 18, 59], Operations: ['85-26=59'] Exploring Operation: 18-6=12, Resulting Numbers: [59, 12] Generated Node #3: [59, 12] from Operation: 18-6=12 Current State: 47:[59, 12], Operations: ['85-26=59', '18-6=12'] Exploring Operation: 59-12=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[26, 85, 6, 18], Operations: [] Exploring Operation: 26+6=32, Resulting Numbers: [85, 18, 32] Generated Node #0,0: 47:[85, 18, 32] Operation: 26+6=32 Exploring Operation: 85-6=79, Resulting Numbers: [26, 18, 79] Generated Node #0,1: 47:[26, 18, 79] Operation: 85-6=79 Exploring Operation: 26+18=44, Resulting Numbers: [85, 6, 44] Generated Node #0,2: 47:[85, 6, 44] Operation: 26+18=44 Exploring Operation: 85-18=67, Resulting Numbers: [26, 6, 67] Generated Node #0,3: 47:[26, 6, 67] Operation: 85-18=67 Exploring Operation: 85-26=59, Resulting Numbers: [6, 18, 59] Generated Node #0,4: 47:[6, 18, 59] Operation: 85-26=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[85, 18, 32], Operations: ['26+6=32'] Exploring Operation: 85-18=67, Resulting Numbers: [32, 67] Generated Node #0,0,0: 47:[32, 67] Operation: 85-18=67 Exploring Operation: 32-18=14, Resulting Numbers: [85, 14] Generated Node #0,0,1: 47:[85, 14] Operation: 32-18=14 Exploring Operation: 18+32=50, Resulting Numbers: [85, 50] Generated Node #0,0,2: 47:[85, 50] Operation: 18+32=50 Exploring Operation: 85-32=53, Resulting Numbers: [18, 53] Generated Node #0,0,3: 47:[18, 53] Operation: 85-32=53 Exploring Operation: 85+18=103, Resulting Numbers: [32, 103] Generated Node #0,0,4: 47:[32, 103] Operation: 85+18=103 Moving to Node #0,0,0 Current State: 47:[32, 67], Operations: ['26+6=32', '85-18=67'] Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 32+67=99, Resulting Numbers: [99] 99,47 unequal: No Solution Exploring Operation: 32*67=2144, Resulting Numbers: [2144] 2144,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[18, 53], Operations: ['26+6=32', '85-32=53'] Exploring Operation: 18+53=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 18*53=954, Resulting Numbers: [954] 954,47 unequal: No Solution Exploring Operation: 53-18=35, Resulting Numbers: [35] 35,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[85, 50], Operations: ['26+6=32', '18+32=50'] Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,47 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[85, 14], Operations: ['26+6=32', '32-18=14'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,47 unequal: No Solution Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,47 unequal: No Solution Moving to Node #0,0,4 Current State: 47:[32, 103], Operations: ['26+6=32', '85+18=103'] Exploring Operation: 32*103=3296, Resulting Numbers: [3296] 3296,47 unequal: No Solution Exploring Operation: 103-32=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 32+103=135, Resulting Numbers: [135] 135,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[26, 18, 79], Operations: ['85-6=79'] Exploring Operation: 26+18=44, Resulting Numbers: [79, 44] Generated Node #0,1,0: 47:[79, 44] Operation: 26+18=44 Exploring Operation: 18+79=97, Resulting Numbers: [26, 97] Generated Node #0,1,1: 47:[26, 97] Operation: 18+79=97 Exploring Operation: 79-18=61, Resulting Numbers: [26, 61] Generated Node #0,1,2: 47:[26, 61] Operation: 79-18=61 Exploring Operation: 26-18=8, Resulting Numbers: [79, 8] Generated Node #0,1,3: 47:[79, 8] Operation: 26-18=8 Exploring Operation: 79-26=53, Resulting Numbers: [18, 53] Generated Node #0,1,4: 47:[18, 53] Operation: 79-26=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[79, 44], Operations: ['85-6=79', '26+18=44'] Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 47:[26, 61], Operations: ['85-6=79', '79-18=61'] Exploring Operation: 26*61=1586, Resulting Numbers: [1586] 1586,47 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 47:[18, 53], Operations: ['85-6=79', '79-26=53'] Exploring Operation: 18*53=954, Resulting Numbers: [954] 954,47 unequal: No Solution Exploring Operation: 18+53=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 53-18=35, Resulting Numbers: [35] 35,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[26, 97], Operations: ['85-6=79', '18+79=97'] Exploring Operation: 26*97=2522, Resulting Numbers: [2522] 2522,47 unequal: No Solution Exploring Operation: 26+97=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 97-26=71, Resulting Numbers: [71] 71,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 47:[79, 8], Operations: ['85-6=79', '26-18=8'] Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 79+8=87, Resulting Numbers: [87] 87,47 unequal: No Solution Exploring Operation: 79*8=632, Resulting Numbers: [632] 632,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[85, 6, 44], Operations: ['26+18=44'] Exploring Operation: 6+44=50, Resulting Numbers: [85, 50] Generated Node #0,2,0: 47:[85, 50] Operation: 6+44=50 Exploring Operation: 85+6=91, Resulting Numbers: [44, 91] Generated Node #0,2,1: 47:[44, 91] Operation: 85+6=91 Exploring Operation: 85-44=41, Resulting Numbers: [6, 41] Generated Node #0,2,2: 47:[6, 41] Operation: 85-44=41 Exploring Operation: 85-6=79, Resulting Numbers: [44, 79] Generated Node #0,2,3: 47:[44, 79] Operation: 85-6=79 Exploring Operation: 44-6=38, Resulting Numbers: [85, 38] Generated Node #0,2,4: 47:[85, 38] Operation: 44-6=38 Moving to Node #0,2,3 Current State: 47:[44, 79], Operations: ['26+18=44', '85-6=79'] Exploring Operation: 44+79=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 44*79=3476, Resulting Numbers: [3476] 3476,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[85, 50], Operations: ['26+18=44', '6+44=50'] Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,47 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[44, 91], Operations: ['26+18=44', '85+6=91'] Exploring Operation: 44*91=4004, Resulting Numbers: [4004] 4004,47 unequal: No Solution Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[26, 85, 6, 18], Operations: [] Exploring Operation: 26+18=44, Resulting Numbers: [85, 6, 44] Generated Node #0,2: 47:[85, 6, 44] Operation: 26+18=44 Moving to Node #0,2 Current State: 47:[85, 6, 44], Operations: ['26+18=44'] Exploring Operation: 85+6=91, Resulting Numbers: [44, 91] Generated Node #0,2,1: 47:[44, 91] Operation: 85+6=91 Moving to Node #0,2,1 Current State: 47:[44, 91], Operations: ['26+18=44', '85+6=91'] Exploring Operation: 91-44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
sum_heuristic
[ 44, 89, 46, 10 ]
94
[ "46-44=2", "10/2=5", "89+5=94" ]
Current State: 94:[44, 89, 46, 10], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [89, 10, 2] Generated Node #2: [89, 10, 2] from Operation: 46-44=2 Current State: 94:[89, 10, 2], Operations: ['46-44=2'] Exploring Operation: 10/2=5, Resulting Numbers: [89, 5] Generated Node #3: [89, 5] from Operation: 10/2=5 Current State: 94:[89, 5], Operations: ['46-44=2', '10/2=5'] Exploring Operation: 89+5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[44, 89, 46, 10], Operations: [] Exploring Operation: 89+10=99, Resulting Numbers: [44, 46, 99] Generated Node #0,0: 94:[44, 46, 99] Operation: 89+10=99 Moving to Node #0,0 Current State: 94:[44, 46, 99], Operations: ['89+10=99'] Exploring Operation: 46-44=2, Resulting Numbers: [99, 2] Generated Node #0,0,0: 94:[99, 2] Operation: 46-44=2 Moving to Node #0,0,0 Current State: 94:[99, 2], Operations: ['89+10=99', '46-44=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,94 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 47, 69, 19, 50 ]
46
[ "69-19=50", "50/50=1", "47-1=46" ]
Current State: 46:[47, 69, 19, 50], Operations: [] Exploring Operation: 69-19=50, Resulting Numbers: [47, 50, 50] Generated Node #2: [47, 50, 50] from Operation: 69-19=50 Current State: 46:[47, 50, 50], Operations: ['69-19=50'] Exploring Operation: 50/50=1, Resulting Numbers: [47, 1] Generated Node #3: [47, 1] from Operation: 50/50=1 Current State: 46:[47, 1], Operations: ['69-19=50', '50/50=1'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[47, 69, 19, 50], Operations: [] Exploring Operation: 69-47=22, Resulting Numbers: [19, 50, 22] Generated Node #0,0: 46:[19, 50, 22] Operation: 69-47=22 Moving to Node #0,0 Current State: 46:[19, 50, 22], Operations: ['69-47=22'] Exploring Operation: 22-19=3, Resulting Numbers: [50, 3] Generated Node #0,0,0: 46:[50, 3] Operation: 22-19=3 Moving to Node #0,0,0 Current State: 46:[50, 3], Operations: ['69-47=22', '22-19=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,46 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 31, 56, 49, 65 ]
27
[ "31+56=87", "49+65=114", "114-87=27" ]
Current State: 27:[31, 56, 49, 65], Operations: [] Exploring Operation: 31+56=87, Resulting Numbers: [49, 65, 87] Generated Node #2: [49, 65, 87] from Operation: 31+56=87 Current State: 27:[49, 65, 87], Operations: ['31+56=87'] Exploring Operation: 49+65=114, Resulting Numbers: [87, 114] Generated Node #3: [87, 114] from Operation: 49+65=114 Current State: 27:[87, 114], Operations: ['31+56=87', '49+65=114'] Exploring Operation: 114-87=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[31, 56, 49, 65], Operations: [] Exploring Operation: 56-49=7, Resulting Numbers: [31, 65, 7] Generated Node #0,0: 27:[31, 65, 7] Operation: 56-49=7 Exploring Operation: 65-49=16, Resulting Numbers: [31, 56, 16] Generated Node #0,1: 27:[31, 56, 16] Operation: 65-49=16 Exploring Operation: 65-31=34, Resulting Numbers: [56, 49, 34] Generated Node #0,2: 27:[56, 49, 34] Operation: 65-31=34 Exploring Operation: 65-56=9, Resulting Numbers: [31, 49, 9] Generated Node #0,3: 27:[31, 49, 9] Operation: 65-56=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[31, 49, 9], Operations: ['65-56=9'] Exploring Operation: 31+9=40, Resulting Numbers: [49, 40] Generated Node #0,3,0: 27:[49, 40] Operation: 31+9=40 Exploring Operation: 49-9=40, Resulting Numbers: [31, 40] Generated Node #0,3,1: 27:[31, 40] Operation: 49-9=40 Exploring Operation: 31-9=22, Resulting Numbers: [49, 22] Generated Node #0,3,2: 27:[49, 22] Operation: 31-9=22 Exploring Operation: 49-31=18, Resulting Numbers: [9, 18] Generated Node #0,3,3: 27:[9, 18] Operation: 49-31=18 Moving to Node #0,3,3 Current State: 27:[9, 18], Operations: ['65-56=9', '49-31=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[31, 56, 49, 65], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [31, 49, 9] Generated Node #0,3: 27:[31, 49, 9] Operation: 65-56=9 Moving to Node #0,3 Current State: 27:[31, 49, 9], Operations: ['65-56=9'] Exploring Operation: 49-31=18, Resulting Numbers: [9, 18] Generated Node #0,3,3: 27:[9, 18] Operation: 49-31=18 Moving to Node #0,3,3 Current State: 27:[9, 18], Operations: ['65-56=9', '49-31=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 87, 69, 58, 78 ]
17
[ "58*78=4524", "4524/87=52", "69-52=17" ]
Current State: 17:[87, 69, 58, 78], Operations: [] Exploring Operation: 58*78=4524, Resulting Numbers: [87, 69, 4524] Generated Node #2: [87, 69, 4524] from Operation: 58*78=4524 Current State: 17:[87, 69, 4524], Operations: ['58*78=4524'] Exploring Operation: 4524/87=52, Resulting Numbers: [69, 52] Generated Node #3: [69, 52] from Operation: 4524/87=52 Current State: 17:[69, 52], Operations: ['58*78=4524', '4524/87=52'] Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[87, 69, 58, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [69, 58, 9] Generated Node #0,0: 17:[69, 58, 9] Operation: 87-78=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[69, 58, 9], Operations: ['87-78=9'] Exploring Operation: 69-58=11, Resulting Numbers: [9, 11] Generated Node #0,0,0: 17:[9, 11] Operation: 69-58=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[9, 11], Operations: ['87-78=9', '69-58=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,17 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, 13, 91, 65 ]
69
[ "91-65=26", "26/13=2", "71-2=69" ]
Current State: 69:[71, 13, 91, 65], Operations: [] Exploring Operation: 91-65=26, Resulting Numbers: [71, 13, 26] Generated Node #2: [71, 13, 26] from Operation: 91-65=26 Current State: 69:[71, 13, 26], Operations: ['91-65=26'] Exploring Operation: 26/13=2, Resulting Numbers: [71, 2] Generated Node #3: [71, 2] from Operation: 26/13=2 Current State: 69:[71, 2], Operations: ['91-65=26', '26/13=2'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[71, 13, 91, 65], Operations: [] Exploring Operation: 91/13=7, Resulting Numbers: [71, 65, 7] Generated Node #0,0: 69:[71, 65, 7] Operation: 91/13=7 Moving to Node #0,0 Current State: 69:[71, 65, 7], Operations: ['91/13=7'] Exploring Operation: 65+7=72, Resulting Numbers: [71, 72] Generated Node #0,0,0: 69:[71, 72] Operation: 65+7=72 Moving to Node #0,0,0 Current State: 69:[71, 72], Operations: ['91/13=7', '65+7=72'] Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,69 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 86, 61, 49, 74 ]
50
[ "86-61=25", "74-49=25", "25+25=50" ]
Current State: 50:[86, 61, 49, 74], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [49, 74, 25] Generated Node #2: [49, 74, 25] from Operation: 86-61=25 Current State: 50:[49, 74, 25], Operations: ['86-61=25'] Exploring Operation: 74-49=25, Resulting Numbers: [25, 25] Generated Node #3: [25, 25] from Operation: 74-49=25 Current State: 50:[25, 25], Operations: ['86-61=25', '74-49=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[86, 61, 49, 74], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [49, 74, 25] Generated Node #0,0: 50:[49, 74, 25] Operation: 86-61=25 Exploring Operation: 74-61=13, Resulting Numbers: [86, 49, 13] Generated Node #0,1: 50:[86, 49, 13] Operation: 74-61=13 Exploring Operation: 86-74=12, Resulting Numbers: [61, 49, 12] Generated Node #0,2: 50:[61, 49, 12] Operation: 86-74=12 Exploring Operation: 86-49=37, Resulting Numbers: [61, 74, 37] Generated Node #0,3: 50:[61, 74, 37] Operation: 86-49=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[61, 49, 12], Operations: ['86-74=12'] Exploring Operation: 61-49=12, Resulting Numbers: [12, 12] Generated Node #0,2,0: 50:[12, 12] Operation: 61-49=12 Exploring Operation: 61-12=49, Resulting Numbers: [49, 49] Generated Node #0,2,1: 50:[49, 49] Operation: 61-12=49 Exploring Operation: 49+12=61, Resulting Numbers: [61, 61] Generated Node #0,2,2: 50:[61, 61] Operation: 49+12=61 Exploring Operation: 49-12=37, Resulting Numbers: [61, 37] Generated Node #0,2,3: 50:[61, 37] Operation: 49-12=37 Moving to Node #0,2,1 Current State: 50:[49, 49], Operations: ['86-74=12', '61-12=49'] Exploring Operation: 49*49=2401, Resulting Numbers: [2401] 2401,50 unequal: No Solution Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,50 unequal: No Solution Exploring Operation: 49-49=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 49/49=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[12, 12], Operations: ['86-74=12', '61-49=12'] Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,50 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[61, 61], Operations: ['86-74=12', '49+12=61'] Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,50 unequal: No Solution Exploring Operation: 61*61=3721, Resulting Numbers: [3721] 3721,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[61, 37], Operations: ['86-74=12', '49-12=37'] Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,50 unequal: No Solution Exploring Operation: 61*37=2257, Resulting Numbers: [2257] 2257,50 unequal: No Solution Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[49, 74, 25], Operations: ['86-61=25'] Exploring Operation: 74-25=49, Resulting Numbers: [49, 49] Generated Node #0,0,0: 50:[49, 49] Operation: 74-25=49 Exploring Operation: 74-49=25, Resulting Numbers: [25, 25] Generated Node #0,0,1: 50:[25, 25] Operation: 74-49=25 Exploring Operation: 49+25=74, Resulting Numbers: [74, 74] Generated Node #0,0,2: 50:[74, 74] Operation: 49+25=74 Exploring Operation: 49-25=24, Resulting Numbers: [74, 24] Generated Node #0,0,3: 50:[74, 24] Operation: 49-25=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[25, 25], Operations: ['86-61=25', '74-49=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[86, 61, 49, 74], Operations: [] Exploring Operation: 86-61=25, Resulting Numbers: [49, 74, 25] Generated Node #0,0: 50:[49, 74, 25] Operation: 86-61=25 Moving to Node #0,0 Current State: 50:[49, 74, 25], Operations: ['86-61=25'] Exploring Operation: 74-49=25, Resulting Numbers: [25, 25] Generated Node #0,0,1: 50:[25, 25] Operation: 74-49=25 Moving to Node #0,0,1 Current State: 50:[25, 25], Operations: ['86-61=25', '74-49=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 42, 16, 16, 4 ]
37
[ "42-4=38", "16/16=1", "38-1=37" ]
Current State: 37:[42, 16, 16, 4], Operations: [] Exploring Operation: 42-4=38, Resulting Numbers: [16, 16, 38] Generated Node #2: [16, 16, 38] from Operation: 42-4=38 Current State: 37:[16, 16, 38], Operations: ['42-4=38'] Exploring Operation: 16/16=1, Resulting Numbers: [38, 1] Generated Node #3: [38, 1] from Operation: 16/16=1 Current State: 37:[38, 1], Operations: ['42-4=38', '16/16=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[42, 16, 16, 4], Operations: [] Exploring Operation: 42-4=38, Resulting Numbers: [16, 16, 38] Generated Node #0,0: 37:[16, 16, 38] Operation: 42-4=38 Exploring Operation: 16+16=32, Resulting Numbers: [42, 4, 32] Generated Node #0,1: 37:[42, 4, 32] Operation: 16+16=32 Exploring Operation: 16+4=20, Resulting Numbers: [42, 16, 20] Generated Node #0,2: 37:[42, 16, 20] Operation: 16+4=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[16, 16, 38], Operations: ['42-4=38'] Exploring Operation: 16+16=32, Resulting Numbers: [38, 32] Generated Node #0,0,0: 37:[38, 32] Operation: 16+16=32 Exploring Operation: 38-16=22, Resulting Numbers: [16, 22] Generated Node #0,0,1: 37:[16, 22] Operation: 38-16=22 Exploring Operation: 38-16=22, Resulting Numbers: [16, 22] Generated Node #0,0,2: 37:[16, 22] Operation: 38-16=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[38, 32], Operations: ['42-4=38', '16+16=32'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,37 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[16, 22], Operations: ['42-4=38', '38-16=22'] Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,37 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 37:[16, 22], Operations: ['42-4=38', '38-16=22'] Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,37 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,37 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: 37:[42, 4, 32], Operations: ['16+16=32'] Exploring Operation: 42-4=38, Resulting Numbers: [32, 38] Generated Node #0,1,0: 37:[32, 38] Operation: 42-4=38 Exploring Operation: 4+32=36, Resulting Numbers: [42, 36] Generated Node #0,1,1: 37:[42, 36] Operation: 4+32=36 Exploring Operation: 42+4=46, Resulting Numbers: [32, 46] Generated Node #0,1,2: 37:[32, 46] Operation: 42+4=46 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[32, 38], Operations: ['16+16=32', '42-4=38'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,37 unequal: No Solution Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[42, 36], Operations: ['16+16=32', '4+32=36'] Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,37 unequal: No Solution Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[32, 46], Operations: ['16+16=32', '42+4=46'] Exploring Operation: 32+46=78, Resulting Numbers: [78] 78,37 unequal: No Solution Exploring Operation: 32*46=1472, Resulting Numbers: [1472] 1472,37 unequal: No Solution Exploring Operation: 46-32=14, Resulting Numbers: [14] 14,37 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: 37:[42, 16, 20], Operations: ['16+4=20'] Exploring Operation: 42-16=26, Resulting Numbers: [20, 26] Generated Node #0,2,0: 37:[20, 26] Operation: 42-16=26 Exploring Operation: 42-20=22, Resulting Numbers: [16, 22] Generated Node #0,2,1: 37:[16, 22] Operation: 42-20=22 Exploring Operation: 16+20=36, Resulting Numbers: [42, 36] Generated Node #0,2,2: 37:[42, 36] Operation: 16+20=36 Moving to Node #0,2,2 Current State: 37:[42, 36], Operations: ['16+4=20', '16+20=36'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,37 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[20, 26], Operations: ['16+4=20', '42-16=26'] Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,37 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,37 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[16, 22], Operations: ['16+4=20', '42-20=22'] Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,37 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,37 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 37, 39, 44, 81 ]
39
[ "37+39=76", "81-44=37", "76-37=39" ]
Current State: 39:[37, 39, 44, 81], Operations: [] Exploring Operation: 37+39=76, Resulting Numbers: [44, 81, 76] Generated Node #2: [44, 81, 76] from Operation: 37+39=76 Current State: 39:[44, 81, 76], Operations: ['37+39=76'] Exploring Operation: 81-44=37, Resulting Numbers: [76, 37] Generated Node #3: [76, 37] from Operation: 81-44=37 Current State: 39:[76, 37], Operations: ['37+39=76', '81-44=37'] Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[37, 39, 44, 81], Operations: [] Exploring Operation: 81-44=37, Resulting Numbers: [37, 39, 37] Generated Node #0,0: 39:[37, 39, 37] Operation: 81-44=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[37, 39, 37], Operations: ['81-44=37'] Exploring Operation: 37/37=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 39:[39, 1] Operation: 37/37=1 Moving to Node #0,0,0 Current State: 39:[39, 1], Operations: ['81-44=37', '37/37=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[37, 39, 44, 81], Operations: [] Exploring Operation: 81-44=37, Resulting Numbers: [37, 39, 37] Generated Node #0,0: 39:[37, 39, 37] Operation: 81-44=37 Moving to Node #0,0 Current State: 39:[37, 39, 37], Operations: ['81-44=37'] Exploring Operation: 37/37=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 39:[39, 1] Operation: 37/37=1 Moving to Node #0,0,0 Current State: 39:[39, 1], Operations: ['81-44=37', '37/37=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 36, 57, 82, 6 ]
48
[ "82-6=76", "36*76=2736", "2736/57=48" ]
Current State: 48:[36, 57, 82, 6], Operations: [] Exploring Operation: 82-6=76, Resulting Numbers: [36, 57, 76] Generated Node #2: [36, 57, 76] from Operation: 82-6=76 Current State: 48:[36, 57, 76], Operations: ['82-6=76'] Exploring Operation: 36*76=2736, Resulting Numbers: [57, 2736] Generated Node #3: [57, 2736] from Operation: 36*76=2736 Current State: 48:[57, 2736], Operations: ['82-6=76', '36*76=2736'] Exploring Operation: 2736/57=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[36, 57, 82, 6], Operations: [] Exploring Operation: 57-36=21, Resulting Numbers: [82, 6, 21] Generated Node #0,0: 48:[82, 6, 21] Operation: 57-36=21 Exploring Operation: 82-36=46, Resulting Numbers: [57, 6, 46] Generated Node #0,1: 48:[57, 6, 46] Operation: 82-36=46 Exploring Operation: 82-57=25, Resulting Numbers: [36, 6, 25] Generated Node #0,2: 48:[36, 6, 25] Operation: 82-57=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[57, 6, 46], Operations: ['82-36=46'] Exploring Operation: 57-46=11, Resulting Numbers: [6, 11] Generated Node #0,1,0: 48:[6, 11] Operation: 57-46=11 Exploring Operation: 57-6=51, Resulting Numbers: [46, 51] Generated Node #0,1,1: 48:[46, 51] Operation: 57-6=51 Exploring Operation: 6+46=52, Resulting Numbers: [57, 52] Generated Node #0,1,2: 48:[57, 52] Operation: 6+46=52 Moving to Node #0,1,0 Current State: 48:[6, 11], Operations: ['82-36=46', '57-46=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,48 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[46, 51], Operations: ['82-36=46', '57-6=51'] Exploring Operation: 46+51=97, Resulting Numbers: [97] 97,48 unequal: No Solution Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,48 unequal: No Solution Exploring Operation: 46*51=2346, Resulting Numbers: [2346] 2346,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[57, 52], Operations: ['82-36=46', '6+46=52'] Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,48 unequal: No Solution Exploring Operation: 57*52=2964, Resulting Numbers: [2964] 2964,48 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[36, 6, 25], Operations: ['82-57=25'] Exploring Operation: 36-25=11, Resulting Numbers: [6, 11] Generated Node #0,2,0: 48:[6, 11] Operation: 36-25=11 Exploring Operation: 36/6=6, Resulting Numbers: [25, 6] Generated Node #0,2,1: 48:[25, 6] Operation: 36/6=6 Exploring Operation: 36+6=42, Resulting Numbers: [25, 42] Generated Node #0,2,2: 48:[25, 42] Operation: 36+6=42 Moving to Node #0,2,0 Current State: 48:[6, 11], Operations: ['82-57=25', '36-25=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,48 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[25, 6], Operations: ['82-57=25', '36/6=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,48 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[25, 42], Operations: ['82-57=25', '36+6=42'] Exploring Operation: 25*42=1050, Resulting Numbers: [1050] 1050,48 unequal: No Solution Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[82, 6, 21], Operations: ['57-36=21'] Exploring Operation: 21-6=15, Resulting Numbers: [82, 15] Generated Node #0,0,0: 48:[82, 15] Operation: 21-6=15 Exploring Operation: 82-21=61, Resulting Numbers: [6, 61] Generated Node #0,0,1: 48:[6, 61] Operation: 82-21=61 Exploring Operation: 82-6=76, Resulting Numbers: [21, 76] Generated Node #0,0,2: 48:[21, 76] Operation: 82-6=76 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[6, 61], Operations: ['57-36=21', '82-21=61'] Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,48 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 48:[21, 76], Operations: ['57-36=21', '82-6=76'] Exploring Operation: 21*76=1596, Resulting Numbers: [1596] 1596,48 unequal: No Solution Exploring Operation: 21+76=97, Resulting Numbers: [97] 97,48 unequal: No Solution Exploring Operation: 76-21=55, Resulting Numbers: [55] 55,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[82, 15], Operations: ['57-36=21', '21-6=15'] Exploring Operation: 82*15=1230, Resulting Numbers: [1230] 1230,48 unequal: No Solution Exploring Operation: 82-15=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 82+15=97, Resulting Numbers: [97] 97,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 14, 50, 99, 47 ]
47
[ "47-14=33", "99/33=3", "50-3=47" ]
Current State: 47:[14, 50, 99, 47], Operations: [] Exploring Operation: 47-14=33, Resulting Numbers: [50, 99, 33] Generated Node #2: [50, 99, 33] from Operation: 47-14=33 Current State: 47:[50, 99, 33], Operations: ['47-14=33'] Exploring Operation: 99/33=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 99/33=3 Current State: 47:[50, 3], Operations: ['47-14=33', '99/33=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[14, 50, 99, 47], Operations: [] Exploring Operation: 99-50=49, Resulting Numbers: [14, 47, 49] Generated Node #0,0: 47:[14, 47, 49] Operation: 99-50=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[14, 47, 49], Operations: ['99-50=49'] Exploring Operation: 49-14=35, Resulting Numbers: [47, 35] Generated Node #0,0,0: 47:[47, 35] Operation: 49-14=35 Moving to Node #0,0,0 Current State: 47:[47, 35], Operations: ['99-50=49', '49-14=35'] Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,47 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
[ 42, 60, 35, 33 ]
83
[ "60*35=2100", "2100/42=50", "33+50=83" ]
Current State: 83:[42, 60, 35, 33], Operations: [] Exploring Operation: 60*35=2100, Resulting Numbers: [42, 33, 2100] Generated Node #2: [42, 33, 2100] from Operation: 60*35=2100 Current State: 83:[42, 33, 2100], Operations: ['60*35=2100'] Exploring Operation: 2100/42=50, Resulting Numbers: [33, 50] Generated Node #3: [33, 50] from Operation: 2100/42=50 Current State: 83:[33, 50], Operations: ['60*35=2100', '2100/42=50'] Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[42, 60, 35, 33], Operations: [] Exploring Operation: 42+35=77, Resulting Numbers: [60, 33, 77] Generated Node #0,0: 83:[60, 33, 77] Operation: 42+35=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[60, 33, 77], Operations: ['42+35=77'] Exploring Operation: 60+33=93, Resulting Numbers: [77, 93] Generated Node #0,0,0: 83:[77, 93] Operation: 60+33=93 Moving to Node #0,0,0 Current State: 83:[77, 93], Operations: ['42+35=77', '60+33=93'] Exploring Operation: 93-77=16, Resulting Numbers: [16] 16,83 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, 26, 45, 21 ]
50
[ "1*26=26", "45-21=24", "26+24=50" ]
Current State: 50:[1, 26, 45, 21], Operations: [] Exploring Operation: 1*26=26, Resulting Numbers: [45, 21, 26] Generated Node #2: [45, 21, 26] from Operation: 1*26=26 Current State: 50:[45, 21, 26], Operations: ['1*26=26'] Exploring Operation: 45-21=24, Resulting Numbers: [26, 24] Generated Node #3: [26, 24] from Operation: 45-21=24 Current State: 50:[26, 24], Operations: ['1*26=26', '45-21=24'] Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[1, 26, 45, 21], Operations: [] Exploring Operation: 26-21=5, Resulting Numbers: [1, 45, 5] Generated Node #0,0: 50:[1, 45, 5] Operation: 26-21=5 Exploring Operation: 45-21=24, Resulting Numbers: [1, 26, 24] Generated Node #0,1: 50:[1, 26, 24] Operation: 45-21=24 Exploring Operation: 26-1=25, Resulting Numbers: [45, 21, 25] Generated Node #0,2: 50:[45, 21, 25] Operation: 26-1=25 Moving to Node #0,1 Current State: 50:[1, 26, 24], Operations: ['45-21=24'] Exploring Operation: 26+24=50, Resulting Numbers: [1, 50] Generated Node #0,1,0: 50:[1, 50] Operation: 26+24=50 Exploring Operation: 1+24=25, Resulting Numbers: [26, 25] Generated Node #0,1,1: 50:[26, 25] Operation: 1+24=25 Exploring Operation: 26-1=25, Resulting Numbers: [24, 25] Generated Node #0,1,2: 50:[24, 25] Operation: 26-1=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[1, 50], Operations: ['45-21=24', '26+24=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[1, 26, 45, 21], Operations: [] Exploring Operation: 45-21=24, Resulting Numbers: [1, 26, 24] Generated Node #0,1: 50:[1, 26, 24] Operation: 45-21=24 Moving to Node #0,1 Current State: 50:[1, 26, 24], Operations: ['45-21=24'] Exploring Operation: 26+24=50, Resulting Numbers: [1, 50] Generated Node #0,1,0: 50:[1, 50] Operation: 26+24=50 Moving to Node #0,1,0 Current State: 50:[1, 50], Operations: ['45-21=24', '26+24=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 43, 15, 95, 28 ]
96
[ "43-15=28", "28/28=1", "95+1=96" ]
Current State: 96:[43, 15, 95, 28], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [95, 28, 28] Generated Node #2: [95, 28, 28] from Operation: 43-15=28 Current State: 96:[95, 28, 28], Operations: ['43-15=28'] Exploring Operation: 28/28=1, Resulting Numbers: [95, 1] Generated Node #3: [95, 1] from Operation: 28/28=1 Current State: 96:[95, 1], Operations: ['43-15=28', '28/28=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[43, 15, 95, 28], Operations: [] Exploring Operation: 43-28=15, Resulting Numbers: [15, 95, 15] Generated Node #0,0: 96:[15, 95, 15] Operation: 43-28=15 Moving to Node #0,0 Current State: 96:[15, 95, 15], Operations: ['43-28=15'] Exploring Operation: 15/15=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 96:[95, 1] Operation: 15/15=1 Moving to Node #0,0,0 Current State: 96:[95, 1], Operations: ['43-28=15', '15/15=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[43, 15, 95, 28], Operations: [] Exploring Operation: 43-28=15, Resulting Numbers: [15, 95, 15] Generated Node #0,0: 96:[15, 95, 15] Operation: 43-28=15 Moving to Node #0,0 Current State: 96:[15, 95, 15], Operations: ['43-28=15'] Exploring Operation: 15/15=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 96:[95, 1] Operation: 15/15=1 Moving to Node #0,0,0 Current State: 96:[95, 1], Operations: ['43-28=15', '15/15=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 77, 82, 69, 58 ]
32
[ "77+82=159", "69+58=127", "159-127=32" ]
Current State: 32:[77, 82, 69, 58], Operations: [] Exploring Operation: 77+82=159, Resulting Numbers: [69, 58, 159] Generated Node #2: [69, 58, 159] from Operation: 77+82=159 Current State: 32:[69, 58, 159], Operations: ['77+82=159'] Exploring Operation: 69+58=127, Resulting Numbers: [159, 127] Generated Node #3: [159, 127] from Operation: 69+58=127 Current State: 32:[159, 127], Operations: ['77+82=159', '69+58=127'] Exploring Operation: 159-127=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[77, 82, 69, 58], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [77, 58, 13] Generated Node #0,0: 32:[77, 58, 13] Operation: 82-69=13 Exploring Operation: 82-77=5, Resulting Numbers: [69, 58, 5] Generated Node #0,1: 32:[69, 58, 5] Operation: 82-77=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[69, 58, 5], Operations: ['82-77=5'] Exploring Operation: 69-5=64, Resulting Numbers: [58, 64] Generated Node #0,1,0: 32:[58, 64] Operation: 69-5=64 Exploring Operation: 69-58=11, Resulting Numbers: [5, 11] Generated Node #0,1,1: 32:[5, 11] Operation: 69-58=11 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[5, 11], Operations: ['82-77=5', '69-58=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,32 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:[58, 64], Operations: ['82-77=5', '69-5=64'] Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 58+64=122, Resulting Numbers: [122] 122,32 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:[77, 58, 13], Operations: ['82-69=13'] Exploring Operation: 77-13=64, Resulting Numbers: [58, 64] Generated Node #0,0,0: 32:[58, 64] Operation: 77-13=64 Exploring Operation: 77-58=19, Resulting Numbers: [13, 19] Generated Node #0,0,1: 32:[13, 19] Operation: 77-58=19 Moving to Node #0,0,1 Current State: 32:[13, 19], Operations: ['82-69=13', '77-58=19'] Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[77, 82, 69, 58], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [77, 58, 13] Generated Node #0,0: 32:[77, 58, 13] Operation: 82-69=13 Moving to Node #0,0 Current State: 32:[77, 58, 13], Operations: ['82-69=13'] Exploring Operation: 77-58=19, Resulting Numbers: [13, 19] Generated Node #0,0,1: 32:[13, 19] Operation: 77-58=19 Moving to Node #0,0,1 Current State: 32:[13, 19], Operations: ['82-69=13', '77-58=19'] Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 82, 68, 54, 16 ]
80
[ "82+68=150", "54+16=70", "150-70=80" ]
Current State: 80:[82, 68, 54, 16], Operations: [] Exploring Operation: 82+68=150, Resulting Numbers: [54, 16, 150] Generated Node #2: [54, 16, 150] from Operation: 82+68=150 Current State: 80:[54, 16, 150], Operations: ['82+68=150'] Exploring Operation: 54+16=70, Resulting Numbers: [150, 70] Generated Node #3: [150, 70] from Operation: 54+16=70 Current State: 80:[150, 70], Operations: ['82+68=150', '54+16=70'] Exploring Operation: 150-70=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[82, 68, 54, 16], Operations: [] Exploring Operation: 54-16=38, Resulting Numbers: [82, 68, 38] Generated Node #0,0: 80:[82, 68, 38] Operation: 54-16=38 Exploring Operation: 82-68=14, Resulting Numbers: [54, 16, 14] Generated Node #0,1: 80:[54, 16, 14] Operation: 82-68=14 Exploring Operation: 82-54=28, Resulting Numbers: [68, 16, 28] Generated Node #0,2: 80:[68, 16, 28] Operation: 82-54=28 Exploring Operation: 68+16=84, Resulting Numbers: [82, 54, 84] Generated Node #0,3: 80:[82, 54, 84] Operation: 68+16=84 Exploring Operation: 68-54=14, Resulting Numbers: [82, 16, 14] Generated Node #0,4: 80:[82, 16, 14] Operation: 68-54=14 Start Sub Search at level 1: Moving to Node #0,4 Current State: 80:[82, 16, 14], Operations: ['68-54=14'] Exploring Operation: 82+14=96, Resulting Numbers: [16, 96] Generated Node #0,4,0: 80:[16, 96] Operation: 82+14=96 Exploring Operation: 82-14=68, Resulting Numbers: [16, 68] Generated Node #0,4,1: 80:[16, 68] Operation: 82-14=68 Exploring Operation: 16-14=2, Resulting Numbers: [82, 2] Generated Node #0,4,2: 80:[82, 2] Operation: 16-14=2 Exploring Operation: 82-16=66, Resulting Numbers: [14, 66] Generated Node #0,4,3: 80:[14, 66] Operation: 82-16=66 Exploring Operation: 16+14=30, Resulting Numbers: [82, 30] Generated Node #0,4,4: 80:[82, 30] Operation: 16+14=30 Moving to Node #0,4,2 Current State: 80:[82, 2], Operations: ['68-54=14', '16-14=2'] Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[82, 68, 54, 16], Operations: [] Exploring Operation: 68-54=14, Resulting Numbers: [82, 16, 14] Generated Node #0,4: 80:[82, 16, 14] Operation: 68-54=14 Moving to Node #0,4 Current State: 80:[82, 16, 14], Operations: ['68-54=14'] Exploring Operation: 16-14=2, Resulting Numbers: [82, 2] Generated Node #0,4,2: 80:[82, 2] Operation: 16-14=2 Moving to Node #0,4,2 Current State: 80:[82, 2], Operations: ['68-54=14', '16-14=2'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 87, 15, 44, 13 ]
39
[ "87*13=1131", "44-15=29", "1131/29=39" ]
Current State: 39:[87, 15, 44, 13], Operations: [] Exploring Operation: 87*13=1131, Resulting Numbers: [15, 44, 1131] Generated Node #2: [15, 44, 1131] from Operation: 87*13=1131 Current State: 39:[15, 44, 1131], Operations: ['87*13=1131'] Exploring Operation: 44-15=29, Resulting Numbers: [1131, 29] Generated Node #3: [1131, 29] from Operation: 44-15=29 Current State: 39:[1131, 29], Operations: ['87*13=1131', '44-15=29'] Exploring Operation: 1131/29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[87, 15, 44, 13], Operations: [] Exploring Operation: 87-15=72, Resulting Numbers: [44, 13, 72] Generated Node #0,0: 39:[44, 13, 72] Operation: 87-15=72 Exploring Operation: 87-44=43, Resulting Numbers: [15, 13, 43] Generated Node #0,1: 39:[15, 13, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[15, 13, 43], Operations: ['87-44=43'] Exploring Operation: 15-13=2, Resulting Numbers: [43, 2] Generated Node #0,1,0: 39:[43, 2] Operation: 15-13=2 Exploring Operation: 43-15=28, Resulting Numbers: [13, 28] Generated Node #0,1,1: 39:[13, 28] Operation: 43-15=28 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[43, 2], Operations: ['87-44=43', '15-13=2'] Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,39 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[13, 28], Operations: ['87-44=43', '43-15=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[44, 13, 72], Operations: ['87-15=72'] Exploring Operation: 72-44=28, Resulting Numbers: [13, 28] Generated Node #0,0,0: 39:[13, 28] Operation: 72-44=28 Exploring Operation: 72-13=59, Resulting Numbers: [44, 59] Generated Node #0,0,1: 39:[44, 59] Operation: 72-13=59 Moving to Node #0,0,0 Current State: 39:[13, 28], Operations: ['87-15=72', '72-44=28'] Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[44, 59], Operations: ['87-15=72', '72-13=59'] Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,39 unequal: No Solution Exploring Operation: 44+59=103, Resulting Numbers: [103] 103,39 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
[ 2, 21, 84, 23 ]
15
[ "2*84=168", "168/21=8", "23-8=15" ]
Current State: 15:[2, 21, 84, 23], Operations: [] Exploring Operation: 2*84=168, Resulting Numbers: [21, 23, 168] Generated Node #2: [21, 23, 168] from Operation: 2*84=168 Current State: 15:[21, 23, 168], Operations: ['2*84=168'] Exploring Operation: 168/21=8, Resulting Numbers: [23, 8] Generated Node #3: [23, 8] from Operation: 168/21=8 Current State: 15:[23, 8], Operations: ['2*84=168', '168/21=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[2, 21, 84, 23], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [21, 23, 42] Generated Node #0,0: 15:[21, 23, 42] Operation: 84/2=42 Exploring Operation: 84-23=61, Resulting Numbers: [2, 21, 61] Generated Node #0,1: 15:[2, 21, 61] Operation: 84-23=61 Exploring Operation: 84/21=4, Resulting Numbers: [2, 23, 4] Generated Node #0,2: 15:[2, 23, 4] Operation: 84/21=4 Exploring Operation: 23-21=2, Resulting Numbers: [2, 84, 2] Generated Node #0,3: 15:[2, 84, 2] Operation: 23-21=2 Exploring Operation: 84-21=63, Resulting Numbers: [2, 23, 63] Generated Node #0,4: 15:[2, 23, 63] Operation: 84-21=63 Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[2, 23, 4], Operations: ['84/21=4'] Exploring Operation: 2+4=6, Resulting Numbers: [23, 6] Generated Node #0,2,0: 15:[23, 6] Operation: 2+4=6 Exploring Operation: 23-2=21, Resulting Numbers: [4, 21] Generated Node #0,2,1: 15:[4, 21] Operation: 23-2=21 Exploring Operation: 23-4=19, Resulting Numbers: [2, 19] Generated Node #0,2,2: 15:[2, 19] Operation: 23-4=19 Exploring Operation: 4/2=2, Resulting Numbers: [23, 2] Generated Node #0,2,3: 15:[23, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [23, 2] Generated Node #0,2,4: 15:[23, 2] Operation: 4-2=2 Moving to Node #0,2,2 Current State: 15:[2, 19], Operations: ['84/21=4', '23-4=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[4, 21], Operations: ['84/21=4', '23-2=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[23, 6], Operations: ['84/21=4', '2+4=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,15 unequal: No Solution Moving to Node #0,2,3 Current State: 15:[23, 2], Operations: ['84/21=4', '4/2=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,15 unequal: No Solution Moving to Node #0,2,4 Current State: 15:[23, 2], Operations: ['84/21=4', '4-2=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[21, 23, 42], Operations: ['84/2=42'] Exploring Operation: 21+23=44, Resulting Numbers: [42, 44] Generated Node #0,0,0: 15:[42, 44] Operation: 21+23=44 Exploring Operation: 23-21=2, Resulting Numbers: [42, 2] Generated Node #0,0,1: 15:[42, 2] Operation: 23-21=2 Exploring Operation: 42/21=2, Resulting Numbers: [23, 2] Generated Node #0,0,2: 15:[23, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [23, 21] Generated Node #0,0,3: 15:[23, 21] Operation: 42-21=21 Exploring Operation: 42-23=19, Resulting Numbers: [21, 19] Generated Node #0,0,4: 15:[21, 19] Operation: 42-23=19 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 15:[23, 2], Operations: ['84/2=42', '42/21=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 15:[21, 19], Operations: ['84/2=42', '42-23=19'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 21+19=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 21*19=399, Resulting Numbers: [399] 399,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 15:[23, 21], Operations: ['84/2=42', '42-21=21'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,15 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[42, 2], Operations: ['84/2=42', '23-21=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,15 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[42, 44], Operations: ['84/2=42', '21+23=44'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,15 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[2, 21, 61], Operations: ['84-23=61'] Exploring Operation: 2+61=63, Resulting Numbers: [21, 63] Generated Node #0,1,0: 15:[21, 63] Operation: 2+61=63 Exploring Operation: 2+21=23, Resulting Numbers: [61, 23] Generated Node #0,1,1: 15:[61, 23] Operation: 2+21=23 Exploring Operation: 61-2=59, Resulting Numbers: [21, 59] Generated Node #0,1,2: 15:[21, 59] Operation: 61-2=59 Exploring Operation: 61-21=40, Resulting Numbers: [2, 40] Generated Node #0,1,3: 15:[2, 40] Operation: 61-21=40 Exploring Operation: 21-2=19, Resulting Numbers: [61, 19] Generated Node #0,1,4: 15:[61, 19] Operation: 21-2=19 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 15:[2, 40], Operations: ['84-23=61', '61-21=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 15:[21, 59], Operations: ['84-23=61', '61-2=59'] Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,15 unequal: No Solution Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 15:[61, 19], Operations: ['84-23=61', '21-2=19'] Exploring Operation: 61*19=1159, Resulting Numbers: [1159] 1159,15 unequal: No Solution Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 61+19=80, Resulting Numbers: [80] 80,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[21, 63], Operations: ['84-23=61', '2+61=63'] Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,15 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 15:[61, 23], Operations: ['84-23=61', '2+21=23'] Exploring Operation: 61+23=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 61*23=1403, Resulting Numbers: [1403] 1403,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 15:[2, 23, 63], Operations: ['84-21=63'] Exploring Operation: 2+63=65, Resulting Numbers: [23, 65] Generated Node #0,4,0: 15:[23, 65] Operation: 2+63=65 Exploring Operation: 2+23=25, Resulting Numbers: [63, 25] Generated Node #0,4,1: 15:[63, 25] Operation: 2+23=25 Exploring Operation: 63-23=40, Resulting Numbers: [2, 40] Generated Node #0,4,2: 15:[2, 40] Operation: 63-23=40 Exploring Operation: 23-2=21, Resulting Numbers: [63, 21] Generated Node #0,4,3: 15:[63, 21] Operation: 23-2=21 Exploring Operation: 63-2=61, Resulting Numbers: [23, 61] Generated Node #0,4,4: 15:[23, 61] Operation: 63-2=61 Moving to Node #0,4,2 Current State: 15:[2, 40], Operations: ['84-21=63', '63-23=40'] Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,4,4 Current State: 15:[23, 61], Operations: ['84-21=63', '63-2=61'] Exploring Operation: 61-23=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 23*61=1403, Resulting Numbers: [1403] 1403,15 unequal: No Solution Exploring Operation: 23+61=84, Resulting Numbers: [84] 84,15 unequal: No Solution Moving to Node #0,4,3 Current State: 15:[63, 21], Operations: ['84-21=63', '23-2=21'] Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 63*21=1323, Resulting Numbers: [1323] 1323,15 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 63+21=84, Resulting Numbers: [84] 84,15 unequal: No Solution Moving to Node #0,4,0 Current State: 15:[23, 65], Operations: ['84-21=63', '2+63=65'] Exploring Operation: 23*65=1495, Resulting Numbers: [1495] 1495,15 unequal: No Solution Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 23+65=88, Resulting Numbers: [88] 88,15 unequal: No Solution Moving to Node #0,4,1 Current State: 15:[63, 25], Operations: ['84-21=63', '2+23=25'] Exploring Operation: 63*25=1575, Resulting Numbers: [1575] 1575,15 unequal: No Solution Exploring Operation: 63+25=88, Resulting Numbers: [88] 88,15 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 15:[2, 84, 2], Operations: ['23-21=2'] Exploring Operation: 2+2=4, Resulting Numbers: [84, 4] Generated Node #0,3,0: 15:[84, 4] Operation: 2+2=4 Exploring Operation: 84-2=82, Resulting Numbers: [2, 82] Generated Node #0,3,1: 15:[2, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [2, 42] Generated Node #0,3,2: 15:[2, 42] Operation: 84/2=42 Exploring Operation: 84/2=42, Resulting Numbers: [2, 42] Generated Node #0,3,3: 15:[2, 42] Operation: 84/2=42 Exploring Operation: 84-2=82, Resulting Numbers: [2, 82] Generated Node #0,3,4: 15:[2, 82] Operation: 84-2=82 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 15:[2, 42], Operations: ['23-21=2', '84/2=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,15 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 15:[2, 42], Operations: ['23-21=2', '84/2=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,15 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 15:[2, 82], Operations: ['23-21=2', '84-2=82'] Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,15 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 15:[2, 82], Operations: ['23-21=2', '84-2=82'] Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,15 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,15 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 15:[84, 4], Operations: ['23-21=2', '2+2=4'] Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,15 unequal: No Solution Exploring Operation: 84*4=336, Resulting Numbers: [336] 336,15 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 69, 82, 66, 6 ]
73
[ "82-69=13", "66-6=60", "13+60=73" ]
Current State: 73:[69, 82, 66, 6], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [66, 6, 13] Generated Node #2: [66, 6, 13] from Operation: 82-69=13 Current State: 73:[66, 6, 13], Operations: ['82-69=13'] Exploring Operation: 66-6=60, Resulting Numbers: [13, 60] Generated Node #3: [13, 60] from Operation: 66-6=60 Current State: 73:[13, 60], Operations: ['82-69=13', '66-6=60'] Exploring Operation: 13+60=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[69, 82, 66, 6], Operations: [] Exploring Operation: 82-6=76, Resulting Numbers: [69, 66, 76] Generated Node #0,0: 73:[69, 66, 76] Operation: 82-6=76 Moving to Node #0,0 Current State: 73:[69, 66, 76], Operations: ['82-6=76'] Exploring Operation: 69+66=135, Resulting Numbers: [76, 135] Generated Node #0,0,0: 73:[76, 135] Operation: 69+66=135 Moving to Node #0,0,0 Current State: 73:[76, 135], Operations: ['82-6=76', '69+66=135'] Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,73 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 12, 20, 48, 43 ]
59
[ "12+20=32", "48+43=91", "91-32=59" ]
Current State: 59:[12, 20, 48, 43], Operations: [] Exploring Operation: 12+20=32, Resulting Numbers: [48, 43, 32] Generated Node #2: [48, 43, 32] from Operation: 12+20=32 Current State: 59:[48, 43, 32], Operations: ['12+20=32'] Exploring Operation: 48+43=91, Resulting Numbers: [32, 91] Generated Node #3: [32, 91] from Operation: 48+43=91 Current State: 59:[32, 91], Operations: ['12+20=32', '48+43=91'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[12, 20, 48, 43], Operations: [] Exploring Operation: 12+43=55, Resulting Numbers: [20, 48, 55] Generated Node #0,0: 59:[20, 48, 55] Operation: 12+43=55 Exploring Operation: 12+20=32, Resulting Numbers: [48, 43, 32] Generated Node #0,1: 59:[48, 43, 32] Operation: 12+20=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[20, 48, 55], Operations: ['12+43=55'] Exploring Operation: 20+48=68, Resulting Numbers: [55, 68] Generated Node #0,0,0: 59:[55, 68] Operation: 20+48=68 Exploring Operation: 20+55=75, Resulting Numbers: [48, 75] Generated Node #0,0,1: 59:[48, 75] Operation: 20+55=75 Moving to Node #0,0,0 Current State: 59:[55, 68], Operations: ['12+43=55', '20+48=68'] Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,59 unequal: No Solution Exploring Operation: 55+68=123, Resulting Numbers: [123] 123,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[48, 75], Operations: ['12+43=55', '20+55=75'] Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,59 unequal: No Solution Exploring Operation: 48+75=123, Resulting Numbers: [123] 123,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[48, 43, 32], Operations: ['12+20=32'] Exploring Operation: 48+32=80, Resulting Numbers: [43, 80] Generated Node #0,1,0: 59:[43, 80] Operation: 48+32=80 Exploring Operation: 43+32=75, Resulting Numbers: [48, 75] Generated Node #0,1,1: 59:[48, 75] Operation: 43+32=75 Moving to Node #0,1,1 Current State: 59:[48, 75], Operations: ['12+20=32', '43+32=75'] Exploring Operation: 48+75=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[43, 80], Operations: ['12+20=32', '48+32=80'] Exploring Operation: 43+80=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 80-43=37, Resulting Numbers: [37] 37,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 90, 11, 67, 90 ]
11
[ "90-90=0", "67*0=0", "11+0=11" ]
Current State: 11:[90, 11, 67, 90], Operations: [] Exploring Operation: 90-90=0, Resulting Numbers: [11, 67, 0] Generated Node #2: [11, 67, 0] from Operation: 90-90=0 Current State: 11:[11, 67, 0], Operations: ['90-90=0'] Exploring Operation: 67*0=0, Resulting Numbers: [11, 0] Generated Node #3: [11, 0] from Operation: 67*0=0 Current State: 11:[11, 0], Operations: ['90-90=0', '67*0=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[90, 11, 67, 90], Operations: [] Exploring Operation: 90/90=1, Resulting Numbers: [11, 67, 1] Generated Node #0,0: 11:[11, 67, 1] Operation: 90/90=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[11, 67, 1], Operations: ['90/90=1'] Exploring Operation: 67-11=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 11:[1, 56] Operation: 67-11=56 Moving to Node #0,0,0 Current State: 11:[1, 56], Operations: ['90/90=1', '67-11=56'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,11 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
[ 2, 43, 24, 83 ]
75
[ "43+24=67", "83+67=150", "150/2=75" ]
Current State: 75:[2, 43, 24, 83], Operations: [] Exploring Operation: 43+24=67, Resulting Numbers: [2, 83, 67] Generated Node #2: [2, 83, 67] from Operation: 43+24=67 Current State: 75:[2, 83, 67], Operations: ['43+24=67'] Exploring Operation: 83+67=150, Resulting Numbers: [2, 150] Generated Node #3: [2, 150] from Operation: 83+67=150 Current State: 75:[2, 150], Operations: ['43+24=67', '83+67=150'] Exploring Operation: 150/2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[2, 43, 24, 83], Operations: [] Exploring Operation: 43+24=67, Resulting Numbers: [2, 83, 67] Generated Node #0,0: 75:[2, 83, 67] Operation: 43+24=67 Exploring Operation: 43-24=19, Resulting Numbers: [2, 83, 19] Generated Node #0,1: 75:[2, 83, 19] Operation: 43-24=19 Moving to Node #0,1 Current State: 75:[2, 83, 19], Operations: ['43-24=19'] Exploring Operation: 83-2=81, Resulting Numbers: [19, 81] Generated Node #0,1,0: 75:[19, 81] Operation: 83-2=81 Exploring Operation: 19-2=17, Resulting Numbers: [83, 17] Generated Node #0,1,1: 75:[83, 17] Operation: 19-2=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[19, 81], Operations: ['43-24=19', '83-2=81'] Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,75 unequal: No Solution Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[83, 17], Operations: ['43-24=19', '19-2=17'] Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,75 unequal: No Solution Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,75 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: 75:[2, 83, 67], Operations: ['43+24=67'] Exploring Operation: 83-67=16, Resulting Numbers: [2, 16] Generated Node #0,0,0: 75:[2, 16] Operation: 83-67=16 Exploring Operation: 83-2=81, Resulting Numbers: [67, 81] Generated Node #0,0,1: 75:[67, 81] Operation: 83-2=81 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[2, 16], Operations: ['43+24=67', '83-67=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,75 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[67, 81], Operations: ['43+24=67', '83-2=81'] Exploring Operation: 67+81=148, Resulting Numbers: [148] 148,75 unequal: No Solution Exploring Operation: 81-67=14, Resulting Numbers: [14] 14,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 57, 14, 59, 75 ]
91
[ "57-14=43", "59+75=134", "134-43=91" ]
Current State: 91:[57, 14, 59, 75], Operations: [] Exploring Operation: 57-14=43, Resulting Numbers: [59, 75, 43] Generated Node #2: [59, 75, 43] from Operation: 57-14=43 Current State: 91:[59, 75, 43], Operations: ['57-14=43'] Exploring Operation: 59+75=134, Resulting Numbers: [43, 134] Generated Node #3: [43, 134] from Operation: 59+75=134 Current State: 91:[43, 134], Operations: ['57-14=43', '59+75=134'] Exploring Operation: 134-43=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[57, 14, 59, 75], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [14, 75, 2] Generated Node #0,0: 91:[14, 75, 2] Operation: 59-57=2 Exploring Operation: 75-57=18, Resulting Numbers: [14, 59, 18] Generated Node #0,1: 91:[14, 59, 18] Operation: 75-57=18 Exploring Operation: 75-59=16, Resulting Numbers: [57, 14, 16] Generated Node #0,2: 91:[57, 14, 16] Operation: 75-59=16 Moving to Node #0,0 Current State: 91:[14, 75, 2], Operations: ['59-57=2'] Exploring Operation: 75+2=77, Resulting Numbers: [14, 77] Generated Node #0,0,0: 91:[14, 77] Operation: 75+2=77 Exploring Operation: 14+75=89, Resulting Numbers: [2, 89] Generated Node #0,0,1: 91:[2, 89] Operation: 14+75=89 Exploring Operation: 14/2=7, Resulting Numbers: [75, 7] Generated Node #0,0,2: 91:[75, 7] Operation: 14/2=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[2, 89], Operations: ['59-57=2', '14+75=89'] Exploring Operation: 2*89=178, Resulting Numbers: [178] 178,91 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,91 unequal: No Solution Exploring Operation: 2+89=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[57, 14, 59, 75], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [14, 75, 2] Generated Node #0,0: 91:[14, 75, 2] Operation: 59-57=2 Moving to Node #0,0 Current State: 91:[14, 75, 2], Operations: ['59-57=2'] Exploring Operation: 14+75=89, Resulting Numbers: [2, 89] Generated Node #0,0,1: 91:[2, 89] Operation: 14+75=89 Moving to Node #0,0,1 Current State: 91:[2, 89], Operations: ['59-57=2', '14+75=89'] Exploring Operation: 2+89=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 36, 16, 97, 50 ]
27
[ "36-16=20", "97-50=47", "47-20=27" ]
Current State: 27:[36, 16, 97, 50], Operations: [] Exploring Operation: 36-16=20, Resulting Numbers: [97, 50, 20] Generated Node #2: [97, 50, 20] from Operation: 36-16=20 Current State: 27:[97, 50, 20], Operations: ['36-16=20'] Exploring Operation: 97-50=47, Resulting Numbers: [20, 47] Generated Node #3: [20, 47] from Operation: 97-50=47 Current State: 27:[20, 47], Operations: ['36-16=20', '97-50=47'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[36, 16, 97, 50], Operations: [] Exploring Operation: 97-36=61, Resulting Numbers: [16, 50, 61] Generated Node #0,0: 27:[16, 50, 61] Operation: 97-36=61 Exploring Operation: 97-50=47, Resulting Numbers: [36, 16, 47] Generated Node #0,1: 27:[36, 16, 47] Operation: 97-50=47 Moving to Node #0,1 Current State: 27:[36, 16, 47], Operations: ['97-50=47'] Exploring Operation: 47-36=11, Resulting Numbers: [16, 11] Generated Node #0,1,0: 27:[16, 11] Operation: 47-36=11 Exploring Operation: 47-16=31, Resulting Numbers: [36, 31] Generated Node #0,1,1: 27:[36, 31] Operation: 47-16=31 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[16, 11], Operations: ['97-50=47', '47-36=11'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[36, 16, 97, 50], Operations: [] Exploring Operation: 97-50=47, Resulting Numbers: [36, 16, 47] Generated Node #0,1: 27:[36, 16, 47] Operation: 97-50=47 Moving to Node #0,1 Current State: 27:[36, 16, 47], Operations: ['97-50=47'] Exploring Operation: 47-36=11, Resulting Numbers: [16, 11] Generated Node #0,1,0: 27:[16, 11] Operation: 47-36=11 Moving to Node #0,1,0 Current State: 27:[16, 11], Operations: ['97-50=47', '47-36=11'] Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 8, 45, 16, 17 ]
53
[ "8+45=53", "17-16=1", "53*1=53" ]
Current State: 53:[8, 45, 16, 17], Operations: [] Exploring Operation: 8+45=53, Resulting Numbers: [16, 17, 53] Generated Node #2: [16, 17, 53] from Operation: 8+45=53 Current State: 53:[16, 17, 53], Operations: ['8+45=53'] Exploring Operation: 17-16=1, Resulting Numbers: [53, 1] Generated Node #3: [53, 1] from Operation: 17-16=1 Current State: 53:[53, 1], Operations: ['8+45=53', '17-16=1'] Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[8, 45, 16, 17], Operations: [] Exploring Operation: 8+17=25, Resulting Numbers: [45, 16, 25] Generated Node #0,0: 53:[45, 16, 25] Operation: 8+17=25 Exploring Operation: 8+45=53, Resulting Numbers: [16, 17, 53] Generated Node #0,1: 53:[16, 17, 53] Operation: 8+45=53 Exploring Operation: 8+16=24, Resulting Numbers: [45, 17, 24] Generated Node #0,2: 53:[45, 17, 24] Operation: 8+16=24 Moving to Node #0,0 Current State: 53:[45, 16, 25], Operations: ['8+17=25'] Exploring Operation: 45-16=29, Resulting Numbers: [25, 29] Generated Node #0,0,0: 53:[25, 29] Operation: 45-16=29 Exploring Operation: 45+16=61, Resulting Numbers: [25, 61] Generated Node #0,0,1: 53:[25, 61] Operation: 45+16=61 Exploring Operation: 16+25=41, Resulting Numbers: [45, 41] Generated Node #0,0,2: 53:[45, 41] Operation: 16+25=41 Moving to Node #0,1 Current State: 53:[16, 17, 53], Operations: ['8+45=53'] Exploring Operation: 16+53=69, Resulting Numbers: [17, 69] Generated Node #0,1,0: 53:[17, 69] Operation: 16+53=69 Exploring Operation: 17-16=1, Resulting Numbers: [53, 1] Generated Node #0,1,1: 53:[53, 1] Operation: 17-16=1 Exploring Operation: 16+17=33, Resulting Numbers: [53, 33] Generated Node #0,1,2: 53:[53, 33] Operation: 16+17=33 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[53, 33], Operations: ['8+45=53', '16+17=33'] Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,53 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,53 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[17, 69], Operations: ['8+45=53', '16+53=69'] Exploring Operation: 17*69=1173, Resulting Numbers: [1173] 1173,53 unequal: No Solution Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,53 unequal: No Solution Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[53, 1], Operations: ['8+45=53', '17-16=1'] Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[8, 45, 16, 17], Operations: [] Exploring Operation: 8+45=53, Resulting Numbers: [16, 17, 53] Generated Node #0,1: 53:[16, 17, 53] Operation: 8+45=53 Moving to Node #0,1 Current State: 53:[16, 17, 53], Operations: ['8+45=53'] Exploring Operation: 17-16=1, Resulting Numbers: [53, 1] Generated Node #0,1,1: 53:[53, 1] Operation: 17-16=1 Moving to Node #0,1,1 Current State: 53:[53, 1], Operations: ['8+45=53', '17-16=1'] Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
sum_heuristic
[ 62, 64, 4, 7 ]
14
[ "62+64=126", "126/7=18", "18-4=14" ]
Current State: 14:[62, 64, 4, 7], Operations: [] Exploring Operation: 62+64=126, Resulting Numbers: [4, 7, 126] Generated Node #2: [4, 7, 126] from Operation: 62+64=126 Current State: 14:[4, 7, 126], Operations: ['62+64=126'] Exploring Operation: 126/7=18, Resulting Numbers: [4, 18] Generated Node #3: [4, 18] from Operation: 126/7=18 Current State: 14:[4, 18], Operations: ['62+64=126', '126/7=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[62, 64, 4, 7], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [62, 7, 16] Generated Node #0,0: 14:[62, 7, 16] Operation: 64/4=16 Exploring Operation: 64-62=2, Resulting Numbers: [4, 7, 2] Generated Node #0,1: 14:[4, 7, 2] Operation: 64-62=2 Moving to Node #0,1 Current State: 14:[4, 7, 2], Operations: ['64-62=2'] Exploring Operation: 4/2=2, Resulting Numbers: [7, 2] Generated Node #0,1,0: 14:[7, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [7, 2] Generated Node #0,1,1: 14:[7, 2] Operation: 4-2=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[7, 2], Operations: ['64-62=2', '4/2=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,14 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[62, 64, 4, 7], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [4, 7, 2] Generated Node #0,1: 14:[4, 7, 2] Operation: 64-62=2 Moving to Node #0,1 Current State: 14:[4, 7, 2], Operations: ['64-62=2'] Exploring Operation: 4/2=2, Resulting Numbers: [7, 2] Generated Node #0,1,0: 14:[7, 2] Operation: 4/2=2 Moving to Node #0,1,0 Current State: 14:[7, 2], Operations: ['64-62=2', '4/2=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 54, 78, 52, 4 ]
75
[ "54-4=50", "78*50=3900", "3900/52=75" ]
Current State: 75:[54, 78, 52, 4], Operations: [] Exploring Operation: 54-4=50, Resulting Numbers: [78, 52, 50] Generated Node #2: [78, 52, 50] from Operation: 54-4=50 Current State: 75:[78, 52, 50], Operations: ['54-4=50'] Exploring Operation: 78*50=3900, Resulting Numbers: [52, 3900] Generated Node #3: [52, 3900] from Operation: 78*50=3900 Current State: 75:[52, 3900], Operations: ['54-4=50', '78*50=3900'] Exploring Operation: 3900/52=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[54, 78, 52, 4], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [78, 4, 2] Generated Node #0,0: 75:[78, 4, 2] Operation: 54-52=2 Moving to Node #0,0 Current State: 75:[78, 4, 2], Operations: ['54-52=2'] Exploring Operation: 78-4=74, Resulting Numbers: [2, 74] Generated Node #0,0,0: 75:[2, 74] Operation: 78-4=74 Moving to Node #0,0,0 Current State: 75:[2, 74], Operations: ['54-52=2', '78-4=74'] Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,75 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 63, 43, 86, 5 ]
13
[ "86/43=2", "63+2=65", "65/5=13" ]
Current State: 13:[63, 43, 86, 5], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [63, 5, 2] Generated Node #2: [63, 5, 2] from Operation: 86/43=2 Current State: 13:[63, 5, 2], Operations: ['86/43=2'] Exploring Operation: 63+2=65, Resulting Numbers: [5, 65] Generated Node #3: [5, 65] from Operation: 63+2=65 Current State: 13:[5, 65], Operations: ['86/43=2', '63+2=65'] Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[63, 43, 86, 5], Operations: [] Exploring Operation: 63-43=20, Resulting Numbers: [86, 5, 20] Generated Node #0,0: 13:[86, 5, 20] Operation: 63-43=20 Exploring Operation: 63-5=58, Resulting Numbers: [43, 86, 58] Generated Node #0,1: 13:[43, 86, 58] Operation: 63-5=58 Exploring Operation: 86/43=2, Resulting Numbers: [63, 5, 2] Generated Node #0,2: 13:[63, 5, 2] Operation: 86/43=2 Exploring Operation: 86-63=23, Resulting Numbers: [43, 5, 23] Generated Node #0,3: 13:[43, 5, 23] Operation: 86-63=23 Exploring Operation: 86-43=43, Resulting Numbers: [63, 5, 43] Generated Node #0,4: 13:[63, 5, 43] Operation: 86-43=43 Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[43, 5, 23], Operations: ['86-63=23'] Exploring Operation: 43+5=48, Resulting Numbers: [23, 48] Generated Node #0,3,0: 13:[23, 48] Operation: 43+5=48 Exploring Operation: 43-5=38, Resulting Numbers: [23, 38] Generated Node #0,3,1: 13:[23, 38] Operation: 43-5=38 Exploring Operation: 5+23=28, Resulting Numbers: [43, 28] Generated Node #0,3,2: 13:[43, 28] Operation: 5+23=28 Exploring Operation: 43-23=20, Resulting Numbers: [5, 20] Generated Node #0,3,3: 13:[5, 20] Operation: 43-23=20 Exploring Operation: 23-5=18, Resulting Numbers: [43, 18] Generated Node #0,3,4: 13:[43, 18] Operation: 23-5=18 Moving to Node #0,3,3 Current State: 13:[5, 20], Operations: ['86-63=23', '43-23=20'] Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,13 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,13 unequal: No Solution Moving to Node #0,3,4 Current State: 13:[43, 18], Operations: ['86-63=23', '23-5=18'] Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,13 unequal: No Solution Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,13 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[23, 38], Operations: ['86-63=23', '43-5=38'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,13 unequal: No Solution Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,13 unequal: No Solution Moving to Node #0,3,0 Current State: 13:[23, 48], Operations: ['86-63=23', '43+5=48'] Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,13 unequal: No Solution Exploring Operation: 23*48=1104, Resulting Numbers: [1104] 1104,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[43, 28], Operations: ['86-63=23', '5+23=28'] Exploring Operation: 43*28=1204, Resulting Numbers: [1204] 1204,13 unequal: No Solution Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,13 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[63, 5, 2], Operations: ['86/43=2'] Exploring Operation: 63-5=58, Resulting Numbers: [2, 58] Generated Node #0,2,0: 13:[2, 58] Operation: 63-5=58 Exploring Operation: 5+2=7, Resulting Numbers: [63, 7] Generated Node #0,2,1: 13:[63, 7] Operation: 5+2=7 Exploring Operation: 63+2=65, Resulting Numbers: [5, 65] Generated Node #0,2,2: 13:[5, 65] Operation: 63+2=65 Exploring Operation: 63-2=61, Resulting Numbers: [5, 61] Generated Node #0,2,3: 13:[5, 61] Operation: 63-2=61 Exploring Operation: 5*2=10, Resulting Numbers: [63, 10] Generated Node #0,2,4: 13:[63, 10] Operation: 5*2=10 Moving to Node #0,2,4 Current State: 13:[63, 10], Operations: ['86/43=2', '5*2=10'] Exploring Operation: 63*10=630, Resulting Numbers: [630] 630,13 unequal: No Solution Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,13 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[63, 7], Operations: ['86/43=2', '5+2=7'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,13 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[2, 58], Operations: ['86/43=2', '63-5=58'] Exploring Operation: 2*58=116, Resulting Numbers: [116] 116,13 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,13 unequal: No Solution Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,13 unequal: No Solution Moving to Node #0,2,3 Current State: 13:[5, 61], Operations: ['86/43=2', '63-2=61'] Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,13 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[5, 65], Operations: ['86/43=2', '63+2=65'] Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,13 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,13 unequal: No Solution Exploring Operation: 5*65=325, Resulting Numbers: [325] 325,13 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[63, 43, 86, 5], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [63, 5, 2] Generated Node #0,2: 13:[63, 5, 2] Operation: 86/43=2 Moving to Node #0,2 Current State: 13:[63, 5, 2], Operations: ['86/43=2'] Exploring Operation: 63+2=65, Resulting Numbers: [5, 65] Generated Node #0,2,2: 13:[5, 65] Operation: 63+2=65 Moving to Node #0,2,2 Current State: 13:[5, 65], Operations: ['86/43=2', '63+2=65'] Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_5
sum_heuristic
[ 17, 15, 3, 44 ]
72
[ "44-17=27", "15*3=45", "27+45=72" ]
Current State: 72:[17, 15, 3, 44], Operations: [] Exploring Operation: 44-17=27, Resulting Numbers: [15, 3, 27] Generated Node #2: [15, 3, 27] from Operation: 44-17=27 Current State: 72:[15, 3, 27], Operations: ['44-17=27'] Exploring Operation: 15*3=45, Resulting Numbers: [27, 45] Generated Node #3: [27, 45] from Operation: 15*3=45 Current State: 72:[27, 45], Operations: ['44-17=27', '15*3=45'] Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[17, 15, 3, 44], Operations: [] Exploring Operation: 17-15=2, Resulting Numbers: [3, 44, 2] Generated Node #0,0: 72:[3, 44, 2] Operation: 17-15=2 Exploring Operation: 15+3=18, Resulting Numbers: [17, 44, 18] Generated Node #0,1: 72:[17, 44, 18] Operation: 15+3=18 Exploring Operation: 44-15=29, Resulting Numbers: [17, 3, 29] Generated Node #0,2: 72:[17, 3, 29] Operation: 44-15=29 Exploring Operation: 44-17=27, Resulting Numbers: [15, 3, 27] Generated Node #0,3: 72:[15, 3, 27] Operation: 44-17=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[17, 3, 29], Operations: ['44-15=29'] Exploring Operation: 17+3=20, Resulting Numbers: [29, 20] Generated Node #0,2,0: 72:[29, 20] Operation: 17+3=20 Exploring Operation: 29-17=12, Resulting Numbers: [3, 12] Generated Node #0,2,1: 72:[3, 12] Operation: 29-17=12 Exploring Operation: 29-3=26, Resulting Numbers: [17, 26] Generated Node #0,2,2: 72:[17, 26] Operation: 29-3=26 Exploring Operation: 3+29=32, Resulting Numbers: [17, 32] Generated Node #0,2,3: 72:[17, 32] Operation: 3+29=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[3, 12], Operations: ['44-15=29', '29-17=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[17, 26], Operations: ['44-15=29', '29-3=26'] Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,72 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 72:[17, 32], Operations: ['44-15=29', '3+29=32'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 17*32=544, Resulting Numbers: [544] 544,72 unequal: No Solution Exploring Operation: 17+32=49, Resulting Numbers: [49] 49,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[29, 20], Operations: ['44-15=29', '17+3=20'] Exploring Operation: 29*20=580, Resulting Numbers: [580] 580,72 unequal: No Solution Exploring Operation: 29+20=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[15, 3, 27], Operations: ['44-17=27'] Exploring Operation: 15-3=12, Resulting Numbers: [27, 12] Generated Node #0,3,0: 72:[27, 12] Operation: 15-3=12 Exploring Operation: 27-3=24, Resulting Numbers: [15, 24] Generated Node #0,3,1: 72:[15, 24] Operation: 27-3=24 Exploring Operation: 15+3=18, Resulting Numbers: [27, 18] Generated Node #0,3,2: 72:[27, 18] Operation: 15+3=18 Exploring Operation: 27-15=12, Resulting Numbers: [3, 12] Generated Node #0,3,3: 72:[3, 12] Operation: 27-15=12 Moving to Node #0,3,3 Current State: 72:[3, 12], Operations: ['44-17=27', '27-15=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,72 unequal: No Solution Moving to Node #0,3,1 Current State: 72:[15, 24], Operations: ['44-17=27', '27-3=24'] Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[27, 12], Operations: ['44-17=27', '15-3=12'] Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,72 unequal: No Solution Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,3,2 Current State: 72:[27, 18], Operations: ['44-17=27', '15+3=18'] Exploring Operation: 27*18=486, Resulting Numbers: [486] 486,72 unequal: No Solution Exploring Operation: 27+18=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,72 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 #0,0 Current State: 72:[3, 44, 2], Operations: ['17-15=2'] Exploring Operation: 44-3=41, Resulting Numbers: [2, 41] Generated Node #0,0,0: 72:[2, 41] Operation: 44-3=41 Exploring Operation: 44-2=42, Resulting Numbers: [3, 42] Generated Node #0,0,1: 72:[3, 42] Operation: 44-2=42 Exploring Operation: 44/2=22, Resulting Numbers: [3, 22] Generated Node #0,0,2: 72:[3, 22] Operation: 44/2=22 Exploring Operation: 3*2=6, Resulting Numbers: [44, 6] Generated Node #0,0,3: 72:[44, 6] Operation: 3*2=6 Moving to Node #0,0,2 Current State: 72:[3, 22], Operations: ['17-15=2', '44/2=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[2, 41], Operations: ['17-15=2', '44-3=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[3, 42], Operations: ['17-15=2', '44-2=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[44, 6], Operations: ['17-15=2', '3*2=6'] Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,72 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[17, 44, 18], Operations: ['15+3=18'] Exploring Operation: 44-17=27, Resulting Numbers: [18, 27] Generated Node #0,1,0: 72:[18, 27] Operation: 44-17=27 Exploring Operation: 17+18=35, Resulting Numbers: [44, 35] Generated Node #0,1,1: 72:[44, 35] Operation: 17+18=35 Exploring Operation: 44-18=26, Resulting Numbers: [17, 26] Generated Node #0,1,2: 72:[17, 26] Operation: 44-18=26 Exploring Operation: 18-17=1, Resulting Numbers: [44, 1] Generated Node #0,1,3: 72:[44, 1] Operation: 18-17=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[18, 27], Operations: ['15+3=18', '44-17=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,72 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[17, 26], Operations: ['15+3=18', '44-18=26'] Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,72 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[44, 35], Operations: ['15+3=18', '17+18=35'] Exploring Operation: 44-35=9, Resulting Numbers: [9] 9,72 unequal: No Solution Exploring Operation: 44+35=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 44*35=1540, Resulting Numbers: [1540] 1540,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 72:[44, 1], Operations: ['15+3=18', '18-17=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,72 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,72 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,72 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 60, 34, 32, 20 ]
62
[ "60*32=1920", "1920/20=96", "96-34=62" ]
Current State: 62:[60, 34, 32, 20], Operations: [] Exploring Operation: 60*32=1920, Resulting Numbers: [34, 20, 1920] Generated Node #2: [34, 20, 1920] from Operation: 60*32=1920 Current State: 62:[34, 20, 1920], Operations: ['60*32=1920'] Exploring Operation: 1920/20=96, Resulting Numbers: [34, 96] Generated Node #3: [34, 96] from Operation: 1920/20=96 Current State: 62:[34, 96], Operations: ['60*32=1920', '1920/20=96'] Exploring Operation: 96-34=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[60, 34, 32, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [34, 32, 3] Generated Node #0,0: 62:[34, 32, 3] Operation: 60/20=3 Moving to Node #0,0 Current State: 62:[34, 32, 3], Operations: ['60/20=3'] Exploring Operation: 34-32=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 62:[3, 2] Operation: 34-32=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[3, 2], Operations: ['60/20=3', '34-32=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,62 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
[ 98, 41, 3, 69 ]
88
[ "98-41=57", "57/3=19", "69+19=88" ]
Current State: 88:[98, 41, 3, 69], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [3, 69, 57] Generated Node #2: [3, 69, 57] from Operation: 98-41=57 Current State: 88:[3, 69, 57], Operations: ['98-41=57'] Exploring Operation: 57/3=19, Resulting Numbers: [69, 19] Generated Node #3: [69, 19] from Operation: 57/3=19 Current State: 88:[69, 19], Operations: ['98-41=57', '57/3=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[98, 41, 3, 69], Operations: [] Exploring Operation: 69/3=23, Resulting Numbers: [98, 41, 23] Generated Node #0,0: 88:[98, 41, 23] Operation: 69/3=23 Exploring Operation: 98-69=29, Resulting Numbers: [41, 3, 29] Generated Node #0,1: 88:[41, 3, 29] Operation: 98-69=29 Moving to Node #0,1 Current State: 88:[41, 3, 29], Operations: ['98-69=29'] Exploring Operation: 41-29=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 88:[3, 12] Operation: 41-29=12 Exploring Operation: 3*29=87, Resulting Numbers: [41, 87] Generated Node #0,1,1: 88:[41, 87] Operation: 3*29=87 Moving to Node #0,0 Current State: 88:[98, 41, 23], Operations: ['69/3=23'] Exploring Operation: 98-41=57, Resulting Numbers: [23, 57] Generated Node #0,0,0: 88:[23, 57] Operation: 98-41=57 Exploring Operation: 41-23=18, Resulting Numbers: [98, 18] Generated Node #0,0,1: 88:[98, 18] Operation: 41-23=18 Moving to Node #0,1,0 Current State: 88:[3, 12], Operations: ['98-69=29', '41-29=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[41, 87], Operations: ['98-69=29', '3*29=87'] Exploring Operation: 41+87=128, Resulting Numbers: [128] 128,88 unequal: No Solution Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[98, 18], Operations: ['69/3=23', '41-23=18'] Exploring Operation: 98-18=80, Resulting Numbers: [80] 80,88 unequal: No Solution Exploring Operation: 98+18=116, Resulting Numbers: [116] 116,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[23, 57], Operations: ['69/3=23', '98-41=57'] Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,88 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,88 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 14, 47, 54, 41 ]
30
[ "47-41=6", "14*6=84", "84-54=30" ]
Current State: 30:[14, 47, 54, 41], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [14, 54, 6] Generated Node #2: [14, 54, 6] from Operation: 47-41=6 Current State: 30:[14, 54, 6], Operations: ['47-41=6'] Exploring Operation: 14*6=84, Resulting Numbers: [54, 84] Generated Node #3: [54, 84] from Operation: 14*6=84 Current State: 30:[54, 84], Operations: ['47-41=6', '14*6=84'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[14, 47, 54, 41], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [14, 47, 13] Generated Node #0,0: 30:[14, 47, 13] Operation: 54-41=13 Exploring Operation: 54-47=7, Resulting Numbers: [14, 41, 7] Generated Node #0,1: 30:[14, 41, 7] Operation: 54-47=7 Exploring Operation: 47-14=33, Resulting Numbers: [54, 41, 33] Generated Node #0,2: 30:[54, 41, 33] Operation: 47-14=33 Exploring Operation: 47-41=6, Resulting Numbers: [14, 54, 6] Generated Node #0,3: 30:[14, 54, 6] Operation: 47-41=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[14, 41, 7], Operations: ['54-47=7'] Exploring Operation: 41-7=34, Resulting Numbers: [14, 34] Generated Node #0,1,0: 30:[14, 34] Operation: 41-7=34 Exploring Operation: 41-14=27, Resulting Numbers: [7, 27] Generated Node #0,1,1: 30:[7, 27] Operation: 41-14=27 Exploring Operation: 14/7=2, Resulting Numbers: [41, 2] Generated Node #0,1,2: 30:[41, 2] Operation: 14/7=2 Exploring Operation: 14-7=7, Resulting Numbers: [41, 7] Generated Node #0,1,3: 30:[41, 7] Operation: 14-7=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[7, 27], Operations: ['54-47=7', '41-14=27'] Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[14, 34], Operations: ['54-47=7', '41-7=34'] Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,30 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 30:[41, 2], Operations: ['54-47=7', '14/7=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,30 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 30:[41, 7], Operations: ['54-47=7', '14-7=7'] Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,30 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[14, 47, 13], Operations: ['54-41=13'] Exploring Operation: 14-13=1, Resulting Numbers: [47, 1] Generated Node #0,0,0: 30:[47, 1] Operation: 14-13=1 Exploring Operation: 14+13=27, Resulting Numbers: [47, 27] Generated Node #0,0,1: 30:[47, 27] Operation: 14+13=27 Exploring Operation: 47-14=33, Resulting Numbers: [13, 33] Generated Node #0,0,2: 30:[13, 33] Operation: 47-14=33 Exploring Operation: 47-13=34, Resulting Numbers: [14, 34] Generated Node #0,0,3: 30:[14, 34] Operation: 47-13=34 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[13, 33], Operations: ['54-41=13', '47-14=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 30:[14, 34], Operations: ['54-41=13', '47-13=34'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,30 unequal: No Solution Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[47, 1], Operations: ['54-41=13', '14-13=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,30 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[47, 27], Operations: ['54-41=13', '14+13=27'] Exploring Operation: 47-27=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 47+27=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 47*27=1269, Resulting Numbers: [1269] 1269,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[14, 54, 6], Operations: ['47-41=6'] Exploring Operation: 14-6=8, Resulting Numbers: [54, 8] Generated Node #0,3,0: 30:[54, 8] Operation: 14-6=8 Exploring Operation: 54-14=40, Resulting Numbers: [6, 40] Generated Node #0,3,1: 30:[6, 40] Operation: 54-14=40 Exploring Operation: 54/6=9, Resulting Numbers: [14, 9] Generated Node #0,3,2: 30:[14, 9] Operation: 54/6=9 Exploring Operation: 54-6=48, Resulting Numbers: [14, 48] Generated Node #0,3,3: 30:[14, 48] Operation: 54-6=48 Moving to Node #0,3,2 Current State: 30:[14, 9], Operations: ['47-41=6', '54/6=9'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 14*9=126, Resulting Numbers: [126] 126,30 unequal: No Solution Exploring Operation: 14+9=23, Resulting Numbers: [23] 23,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[6, 40], Operations: ['47-41=6', '54-14=40'] Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,30 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[14, 48], Operations: ['47-41=6', '54-6=48'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 14*48=672, Resulting Numbers: [672] 672,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[54, 8], Operations: ['47-41=6', '14-6=8'] Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,30 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 #0,2 Current State: 30:[54, 41, 33], Operations: ['47-14=33'] Exploring Operation: 54+41=95, Resulting Numbers: [33, 95] Generated Node #0,2,0: 30:[33, 95] Operation: 54+41=95 Exploring Operation: 54-33=21, Resulting Numbers: [41, 21] Generated Node #0,2,1: 30:[41, 21] Operation: 54-33=21 Exploring Operation: 54-41=13, Resulting Numbers: [33, 13] Generated Node #0,2,2: 30:[33, 13] Operation: 54-41=13 Exploring Operation: 41-33=8, Resulting Numbers: [54, 8] Generated Node #0,2,3: 30:[54, 8] Operation: 41-33=8 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[33, 13], Operations: ['47-14=33', '54-41=13'] Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,30 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[41, 21], Operations: ['47-14=33', '54-33=21'] Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,30 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 30:[54, 8], Operations: ['47-14=33', '41-33=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,30 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,30 unequal: No Solution Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[33, 95], Operations: ['47-14=33', '54+41=95'] Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,30 unequal: No Solution Exploring Operation: 33+95=128, Resulting Numbers: [128] 128,30 unequal: No Solution Exploring Operation: 33*95=3135, Resulting Numbers: [3135] 3135,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 26, 59, 68, 89 ]
72
[ "26+59=85", "68+89=157", "157-85=72" ]
Current State: 72:[26, 59, 68, 89], Operations: [] Exploring Operation: 26+59=85, Resulting Numbers: [68, 89, 85] Generated Node #2: [68, 89, 85] from Operation: 26+59=85 Current State: 72:[68, 89, 85], Operations: ['26+59=85'] Exploring Operation: 68+89=157, Resulting Numbers: [85, 157] Generated Node #3: [85, 157] from Operation: 68+89=157 Current State: 72:[85, 157], Operations: ['26+59=85', '68+89=157'] Exploring Operation: 157-85=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[26, 59, 68, 89], Operations: [] Exploring Operation: 89-59=30, Resulting Numbers: [26, 68, 30] Generated Node #0,0: 72:[26, 68, 30] Operation: 89-59=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[26, 68, 30], Operations: ['89-59=30'] Exploring Operation: 30-26=4, Resulting Numbers: [68, 4] Generated Node #0,0,0: 72:[68, 4] Operation: 30-26=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[68, 4], Operations: ['89-59=30', '30-26=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[26, 59, 68, 89], Operations: [] Exploring Operation: 89-59=30, Resulting Numbers: [26, 68, 30] Generated Node #0,0: 72:[26, 68, 30] Operation: 89-59=30 Moving to Node #0,0 Current State: 72:[26, 68, 30], Operations: ['89-59=30'] Exploring Operation: 30-26=4, Resulting Numbers: [68, 4] Generated Node #0,0,0: 72:[68, 4] Operation: 30-26=4 Moving to Node #0,0,0 Current State: 72:[68, 4], Operations: ['89-59=30', '30-26=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 22, 12, 23, 94 ]
83
[ "22+12=34", "23+94=117", "117-34=83" ]
Current State: 83:[22, 12, 23, 94], Operations: [] Exploring Operation: 22+12=34, Resulting Numbers: [23, 94, 34] Generated Node #2: [23, 94, 34] from Operation: 22+12=34 Current State: 83:[23, 94, 34], Operations: ['22+12=34'] Exploring Operation: 23+94=117, Resulting Numbers: [34, 117] Generated Node #3: [34, 117] from Operation: 23+94=117 Current State: 83:[34, 117], Operations: ['22+12=34', '23+94=117'] Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[22, 12, 23, 94], Operations: [] Exploring Operation: 22+12=34, Resulting Numbers: [23, 94, 34] Generated Node #0,0: 83:[23, 94, 34] Operation: 22+12=34 Exploring Operation: 12+23=35, Resulting Numbers: [22, 94, 35] Generated Node #0,1: 83:[22, 94, 35] Operation: 12+23=35 Exploring Operation: 22+23=45, Resulting Numbers: [12, 94, 45] Generated Node #0,2: 83:[12, 94, 45] Operation: 22+23=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[23, 94, 34], Operations: ['22+12=34'] Exploring Operation: 23+34=57, Resulting Numbers: [94, 57] Generated Node #0,0,0: 83:[94, 57] Operation: 23+34=57 Exploring Operation: 94-23=71, Resulting Numbers: [34, 71] Generated Node #0,0,1: 83:[34, 71] Operation: 94-23=71 Exploring Operation: 23+94=117, Resulting Numbers: [34, 117] Generated Node #0,0,2: 83:[34, 117] Operation: 23+94=117 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[94, 57], Operations: ['22+12=34', '23+34=57'] Exploring Operation: 94*57=5358, Resulting Numbers: [5358] 5358,83 unequal: No Solution Exploring Operation: 94+57=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[34, 71], Operations: ['22+12=34', '94-23=71'] Exploring Operation: 34*71=2414, Resulting Numbers: [2414] 2414,83 unequal: No Solution Exploring Operation: 34+71=105, Resulting Numbers: [105] 105,83 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[34, 117], Operations: ['22+12=34', '23+94=117'] Exploring Operation: 34+117=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 34*117=3978, Resulting Numbers: [3978] 3978,83 unequal: No Solution Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[22, 12, 23, 94], Operations: [] Exploring Operation: 22+12=34, Resulting Numbers: [23, 94, 34] Generated Node #0,0: 83:[23, 94, 34] Operation: 22+12=34 Moving to Node #0,0 Current State: 83:[23, 94, 34], Operations: ['22+12=34'] Exploring Operation: 23+94=117, Resulting Numbers: [34, 117] Generated Node #0,0,2: 83:[34, 117] Operation: 23+94=117 Moving to Node #0,0,2 Current State: 83:[34, 117], Operations: ['22+12=34', '23+94=117'] Exploring Operation: 117-34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 19, 51, 28, 84 ]
29
[ "51-19=32", "84/28=3", "32-3=29" ]
Current State: 29:[19, 51, 28, 84], Operations: [] Exploring Operation: 51-19=32, Resulting Numbers: [28, 84, 32] Generated Node #2: [28, 84, 32] from Operation: 51-19=32 Current State: 29:[28, 84, 32], Operations: ['51-19=32'] Exploring Operation: 84/28=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 84/28=3 Current State: 29:[32, 3], Operations: ['51-19=32', '84/28=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[19, 51, 28, 84], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [19, 51, 3] Generated Node #0,0: 29:[19, 51, 3] Operation: 84/28=3 Exploring Operation: 84-51=33, Resulting Numbers: [19, 28, 33] Generated Node #0,1: 29:[19, 28, 33] Operation: 84-51=33 Exploring Operation: 51-19=32, Resulting Numbers: [28, 84, 32] Generated Node #0,2: 29:[28, 84, 32] Operation: 51-19=32 Moving to Node #0,1 Current State: 29:[19, 28, 33], Operations: ['84-51=33'] Exploring Operation: 28-19=9, Resulting Numbers: [33, 9] Generated Node #0,1,0: 29:[33, 9] Operation: 28-19=9 Exploring Operation: 19+28=47, Resulting Numbers: [33, 47] Generated Node #0,1,1: 29:[33, 47] Operation: 19+28=47 Exploring Operation: 33-19=14, Resulting Numbers: [28, 14] Generated Node #0,1,2: 29:[28, 14] Operation: 33-19=14 Moving to Node #0,0 Current State: 29:[19, 51, 3], Operations: ['84/28=3'] Exploring Operation: 19+3=22, Resulting Numbers: [51, 22] Generated Node #0,0,0: 29:[51, 22] Operation: 19+3=22 Exploring Operation: 51-19=32, Resulting Numbers: [3, 32] Generated Node #0,0,1: 29:[3, 32] Operation: 51-19=32 Exploring Operation: 51/3=17, Resulting Numbers: [19, 17] Generated Node #0,0,2: 29:[19, 17] Operation: 51/3=17 Moving to Node #0,2 Current State: 29:[28, 84, 32], Operations: ['51-19=32'] Exploring Operation: 84-32=52, Resulting Numbers: [28, 52] Generated Node #0,2,0: 29:[28, 52] Operation: 84-32=52 Exploring Operation: 84/28=3, Resulting Numbers: [32, 3] Generated Node #0,2,1: 29:[32, 3] Operation: 84/28=3 Exploring Operation: 84-28=56, Resulting Numbers: [32, 56] Generated Node #0,2,2: 29:[32, 56] Operation: 84-28=56 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[28, 52], Operations: ['51-19=32', '84-32=52'] Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,29 unequal: No Solution Exploring Operation: 28*52=1456, Resulting Numbers: [1456] 1456,29 unequal: No Solution Exploring Operation: 28+52=80, Resulting Numbers: [80] 80,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[32, 3], Operations: ['51-19=32', '84/28=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[19, 51, 28, 84], Operations: [] Exploring Operation: 51-19=32, Resulting Numbers: [28, 84, 32] Generated Node #0,2: 29:[28, 84, 32] Operation: 51-19=32 Moving to Node #0,2 Current State: 29:[28, 84, 32], Operations: ['51-19=32'] Exploring Operation: 84/28=3, Resulting Numbers: [32, 3] Generated Node #0,2,1: 29:[32, 3] Operation: 84/28=3 Moving to Node #0,2,1 Current State: 29:[32, 3], Operations: ['51-19=32', '84/28=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
mult_heuristic
[ 4, 12, 75, 41 ]
16
[ "12/4=3", "75/3=25", "41-25=16" ]
Current State: 16:[4, 12, 75, 41], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [75, 41, 3] Generated Node #2: [75, 41, 3] from Operation: 12/4=3 Current State: 16:[75, 41, 3], Operations: ['12/4=3'] Exploring Operation: 75/3=25, Resulting Numbers: [41, 25] Generated Node #3: [41, 25] from Operation: 75/3=25 Current State: 16:[41, 25], Operations: ['12/4=3', '75/3=25'] Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[4, 12, 75, 41], Operations: [] Exploring Operation: 75-41=34, Resulting Numbers: [4, 12, 34] Generated Node #0,0: 16:[4, 12, 34] Operation: 75-41=34 Moving to Node #0,0 Current State: 16:[4, 12, 34], Operations: ['75-41=34'] Exploring Operation: 34-12=22, Resulting Numbers: [4, 22] Generated Node #0,0,0: 16:[4, 22] Operation: 34-12=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[4, 22], Operations: ['75-41=34', '34-12=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,16 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
[ 66, 49, 99, 70 ]
37
[ "70-66=4", "49+99=148", "148/4=37" ]
Current State: 37:[66, 49, 99, 70], Operations: [] Exploring Operation: 70-66=4, Resulting Numbers: [49, 99, 4] Generated Node #2: [49, 99, 4] from Operation: 70-66=4 Current State: 37:[49, 99, 4], Operations: ['70-66=4'] Exploring Operation: 49+99=148, Resulting Numbers: [4, 148] Generated Node #3: [4, 148] from Operation: 49+99=148 Current State: 37:[4, 148], Operations: ['70-66=4', '49+99=148'] Exploring Operation: 148/4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[66, 49, 99, 70], Operations: [] Exploring Operation: 99-70=29, Resulting Numbers: [66, 49, 29] Generated Node #0,0: 37:[66, 49, 29] Operation: 99-70=29 Exploring Operation: 99-66=33, Resulting Numbers: [49, 70, 33] Generated Node #0,1: 37:[49, 70, 33] Operation: 99-66=33 Moving to Node #0,0 Current State: 37:[66, 49, 29], Operations: ['99-70=29'] Exploring Operation: 66-29=37, Resulting Numbers: [49, 37] Generated Node #0,0,0: 37:[49, 37] Operation: 66-29=37 Exploring Operation: 66-49=17, Resulting Numbers: [29, 17] Generated Node #0,0,1: 37:[29, 17] Operation: 66-49=17 Moving to Node #0,1 Current State: 37:[49, 70, 33], Operations: ['99-66=33'] Exploring Operation: 70-49=21, Resulting Numbers: [33, 21] Generated Node #0,1,0: 37:[33, 21] Operation: 70-49=21 Exploring Operation: 70-33=37, Resulting Numbers: [49, 37] Generated Node #0,1,1: 37:[49, 37] Operation: 70-33=37 Moving to Node #0,0,0 Current State: 37:[49, 37], Operations: ['99-70=29', '66-29=37'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[49, 37], Operations: ['99-66=33', '70-33=37'] Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,37 unequal: No Solution Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[33, 21], Operations: ['99-66=33', '70-49=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,37 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[29, 17], Operations: ['99-70=29', '66-49=17'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,37 unequal: No Solution Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,37 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 27, 7, 78, 18 ]
94
[ "27+7=34", "78-18=60", "34+60=94" ]
Current State: 94:[27, 7, 78, 18], Operations: [] Exploring Operation: 27+7=34, Resulting Numbers: [78, 18, 34] Generated Node #2: [78, 18, 34] from Operation: 27+7=34 Current State: 94:[78, 18, 34], Operations: ['27+7=34'] Exploring Operation: 78-18=60, Resulting Numbers: [34, 60] Generated Node #3: [34, 60] from Operation: 78-18=60 Current State: 94:[34, 60], Operations: ['27+7=34', '78-18=60'] Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[27, 7, 78, 18], Operations: [] Exploring Operation: 27+18=45, Resulting Numbers: [7, 78, 45] Generated Node #0,0: 94:[7, 78, 45] Operation: 27+18=45 Moving to Node #0,0 Current State: 94:[7, 78, 45], Operations: ['27+18=45'] Exploring Operation: 7+78=85, Resulting Numbers: [45, 85] Generated Node #0,0,0: 94:[45, 85] Operation: 7+78=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[45, 85], Operations: ['27+18=45', '7+78=85'] Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 60, 35, 85, 9 ]
18
[ "35+85=120", "120/60=2", "9*2=18" ]
Current State: 18:[60, 35, 85, 9], Operations: [] Exploring Operation: 35+85=120, Resulting Numbers: [60, 9, 120] Generated Node #2: [60, 9, 120] from Operation: 35+85=120 Current State: 18:[60, 9, 120], Operations: ['35+85=120'] Exploring Operation: 120/60=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 120/60=2 Current State: 18:[9, 2], Operations: ['35+85=120', '120/60=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[60, 35, 85, 9], Operations: [] Exploring Operation: 85-60=25, Resulting Numbers: [35, 9, 25] Generated Node #0,0: 18:[35, 9, 25] Operation: 85-60=25 Moving to Node #0,0 Current State: 18:[35, 9, 25], Operations: ['85-60=25'] Exploring Operation: 35-25=10, Resulting Numbers: [9, 10] Generated Node #0,0,0: 18:[9, 10] Operation: 35-25=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[9, 10], Operations: ['85-60=25', '35-25=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,18 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
[ 65, 24, 2, 20 ]
93
[ "65-20=45", "24*2=48", "45+48=93" ]
Current State: 93:[65, 24, 2, 20], Operations: [] Exploring Operation: 65-20=45, Resulting Numbers: [24, 2, 45] Generated Node #2: [24, 2, 45] from Operation: 65-20=45 Current State: 93:[24, 2, 45], Operations: ['65-20=45'] Exploring Operation: 24*2=48, Resulting Numbers: [45, 48] Generated Node #3: [45, 48] from Operation: 24*2=48 Current State: 93:[45, 48], Operations: ['65-20=45', '24*2=48'] Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[65, 24, 2, 20], Operations: [] Exploring Operation: 24-20=4, Resulting Numbers: [65, 2, 4] Generated Node #0,0: 93:[65, 2, 4] Operation: 24-20=4 Exploring Operation: 65-24=41, Resulting Numbers: [2, 20, 41] Generated Node #0,1: 93:[2, 20, 41] Operation: 65-24=41 Exploring Operation: 65+20=85, Resulting Numbers: [24, 2, 85] Generated Node #0,2: 93:[24, 2, 85] Operation: 65+20=85 Exploring Operation: 65+24=89, Resulting Numbers: [2, 20, 89] Generated Node #0,3: 93:[2, 20, 89] Operation: 65+24=89 Exploring Operation: 65-20=45, Resulting Numbers: [24, 2, 45] Generated Node #0,4: 93:[24, 2, 45] Operation: 65-20=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[24, 2, 85], Operations: ['65+20=85'] Exploring Operation: 24+85=109, Resulting Numbers: [2, 109] Generated Node #0,2,0: 93:[2, 109] Operation: 24+85=109 Exploring Operation: 24+2=26, Resulting Numbers: [85, 26] Generated Node #0,2,1: 93:[85, 26] Operation: 24+2=26 Exploring Operation: 2+85=87, Resulting Numbers: [24, 87] Generated Node #0,2,2: 93:[24, 87] Operation: 2+85=87 Exploring Operation: 24-2=22, Resulting Numbers: [85, 22] Generated Node #0,2,3: 93:[85, 22] Operation: 24-2=22 Exploring Operation: 24/2=12, Resulting Numbers: [85, 12] Generated Node #0,2,4: 93:[85, 12] Operation: 24/2=12 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[85, 26], Operations: ['65+20=85', '24+2=26'] Exploring Operation: 85*26=2210, Resulting Numbers: [2210] 2210,93 unequal: No Solution Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 85+26=111, Resulting Numbers: [111] 111,93 unequal: No Solution No 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: 93:[24, 87], Operations: ['65+20=85', '2+85=87'] Exploring Operation: 24+87=111, Resulting Numbers: [111] 111,93 unequal: No Solution Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 24*87=2088, Resulting Numbers: [2088] 2088,93 unequal: No Solution No 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: 93:[2, 109], Operations: ['65+20=85', '24+85=109'] Exploring Operation: 2*109=218, Resulting Numbers: [218] 218,93 unequal: No Solution Exploring Operation: 109-2=107, Resulting Numbers: [107] 107,93 unequal: No Solution Exploring Operation: 2+109=111, Resulting Numbers: [111] 111,93 unequal: No Solution No 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: 93:[85, 22], Operations: ['65+20=85', '24-2=22'] Exploring Operation: 85+22=107, Resulting Numbers: [107] 107,93 unequal: No Solution Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 85*22=1870, Resulting Numbers: [1870] 1870,93 unequal: No Solution No 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: 93:[85, 12], Operations: ['65+20=85', '24/2=12'] Exploring Operation: 85*12=1020, Resulting Numbers: [1020] 1020,93 unequal: No Solution Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,93 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: 93:[2, 20, 89], Operations: ['65+24=89'] Exploring Operation: 2*20=40, Resulting Numbers: [89, 40] Generated Node #0,3,0: 93:[89, 40] Operation: 2*20=40 Exploring Operation: 20-2=18, Resulting Numbers: [89, 18] Generated Node #0,3,1: 93:[89, 18] Operation: 20-2=18 Exploring Operation: 2+89=91, Resulting Numbers: [20, 91] Generated Node #0,3,2: 93:[20, 91] Operation: 2+89=91 Exploring Operation: 20/2=10, Resulting Numbers: [89, 10] Generated Node #0,3,3: 93:[89, 10] Operation: 20/2=10 Exploring Operation: 2+20=22, Resulting Numbers: [89, 22] Generated Node #0,3,4: 93:[89, 22] Operation: 2+20=22 Moving to Node #0,3,3 Current State: 93:[89, 10], Operations: ['65+24=89', '20/2=10'] Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,93 unequal: No Solution Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,93 unequal: No Solution Exploring Operation: 89*10=890, Resulting Numbers: [890] 890,93 unequal: No Solution Moving to Node #0,3,2 Current State: 93:[20, 91], Operations: ['65+24=89', '2+89=91'] Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 20+91=111, Resulting Numbers: [111] 111,93 unequal: No Solution Exploring Operation: 20*91=1820, Resulting Numbers: [1820] 1820,93 unequal: No Solution Moving to Node #0,3,0 Current State: 93:[89, 40], Operations: ['65+24=89', '2*20=40'] Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,93 unequal: No Solution Exploring Operation: 89*40=3560, Resulting Numbers: [3560] 3560,93 unequal: No Solution Exploring Operation: 89+40=129, Resulting Numbers: [129] 129,93 unequal: No Solution Moving to Node #0,3,4 Current State: 93:[89, 22], Operations: ['65+24=89', '2+20=22'] Exploring Operation: 89*22=1958, Resulting Numbers: [1958] 1958,93 unequal: No Solution Exploring Operation: 89+22=111, Resulting Numbers: [111] 111,93 unequal: No Solution Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[89, 18], Operations: ['65+24=89', '20-2=18'] Exploring Operation: 89*18=1602, Resulting Numbers: [1602] 1602,93 unequal: No Solution Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 89+18=107, Resulting Numbers: [107] 107,93 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 Current State: 93:[2, 20, 41], Operations: ['65-24=41'] Exploring Operation: 2+20=22, Resulting Numbers: [41, 22] Generated Node #0,1,0: 93:[41, 22] Operation: 2+20=22 Exploring Operation: 41-2=39, Resulting Numbers: [20, 39] Generated Node #0,1,1: 93:[20, 39] Operation: 41-2=39 Exploring Operation: 2*20=40, Resulting Numbers: [41, 40] Generated Node #0,1,2: 93:[41, 40] Operation: 2*20=40 Exploring Operation: 41-20=21, Resulting Numbers: [2, 21] Generated Node #0,1,3: 93:[2, 21] Operation: 41-20=21 Exploring Operation: 20/2=10, Resulting Numbers: [41, 10] Generated Node #0,1,4: 93:[41, 10] Operation: 20/2=10 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 93:[2, 21], Operations: ['65-24=41', '41-20=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,93 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,93 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,93 unequal: No Solution No 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: 93:[41, 10], Operations: ['65-24=41', '20/2=10'] Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,93 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,93 unequal: No Solution No 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: 93:[41, 22], Operations: ['65-24=41', '2+20=22'] Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,93 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,93 unequal: No Solution No 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: 93:[20, 39], Operations: ['65-24=41', '41-2=39'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,93 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 20*39=780, Resulting Numbers: [780] 780,93 unequal: No Solution No 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: 93:[41, 40], Operations: ['65-24=41', '2*20=40'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,93 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,93 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: 93:[24, 2, 45], Operations: ['65-20=45'] Exploring Operation: 45-24=21, Resulting Numbers: [2, 21] Generated Node #0,4,0: 93:[2, 21] Operation: 45-24=21 Exploring Operation: 45-2=43, Resulting Numbers: [24, 43] Generated Node #0,4,1: 93:[24, 43] Operation: 45-2=43 Exploring Operation: 24-2=22, Resulting Numbers: [45, 22] Generated Node #0,4,2: 93:[45, 22] Operation: 24-2=22 Exploring Operation: 2*45=90, Resulting Numbers: [24, 90] Generated Node #0,4,3: 93:[24, 90] Operation: 2*45=90 Exploring Operation: 24+2=26, Resulting Numbers: [45, 26] Generated Node #0,4,4: 93:[45, 26] Operation: 24+2=26 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 93:[24, 90], Operations: ['65-20=45', '2*45=90'] Exploring Operation: 90-24=66, Resulting Numbers: [66] 66,93 unequal: No Solution Exploring Operation: 24*90=2160, Resulting Numbers: [2160] 2160,93 unequal: No Solution Exploring Operation: 24+90=114, Resulting Numbers: [114] 114,93 unequal: No Solution No 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: 93:[2, 21], Operations: ['65-20=45', '45-24=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,93 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,93 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 93:[24, 43], Operations: ['65-20=45', '45-2=43'] Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,93 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,93 unequal: No Solution No 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: 93:[45, 26], Operations: ['65-20=45', '24+2=26'] Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,93 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,93 unequal: No Solution No 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: 93:[45, 22], Operations: ['65-20=45', '24-2=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,93 unequal: No Solution Exploring Operation: 45+22=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 45*22=990, Resulting Numbers: [990] 990,93 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: 93:[65, 2, 4], Operations: ['24-20=4'] Exploring Operation: 65-2=63, Resulting Numbers: [4, 63] Generated Node #0,0,0: 93:[4, 63] Operation: 65-2=63 Exploring Operation: 4/2=2, Resulting Numbers: [65, 2] Generated Node #0,0,1: 93:[65, 2] Operation: 4/2=2 Exploring Operation: 65+2=67, Resulting Numbers: [4, 67] Generated Node #0,0,2: 93:[4, 67] Operation: 65+2=67 Exploring Operation: 65+4=69, Resulting Numbers: [2, 69] Generated Node #0,0,3: 93:[2, 69] Operation: 65+4=69 Exploring Operation: 4-2=2, Resulting Numbers: [65, 2] Generated Node #0,0,4: 93:[65, 2] Operation: 4-2=2 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 93:[2, 69], Operations: ['24-20=4', '65+4=69'] Exploring Operation: 2+69=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 2*69=138, Resulting Numbers: [138] 138,93 unequal: No Solution Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,93 unequal: No Solution No 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: 93:[4, 67], Operations: ['24-20=4', '65+2=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,93 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,93 unequal: No Solution No 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: 93:[65, 2], Operations: ['24-20=4', '4/2=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,93 unequal: No Solution No 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: 93:[65, 2], Operations: ['24-20=4', '4-2=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 65*2=130, Resulting Numbers: [130] 130,93 unequal: No Solution No 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: 93:[4, 63], Operations: ['24-20=4', '65-2=63'] Exploring Operation: 4+63=67, Resulting Numbers: [67] 67,93 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 4*63=252, Resulting Numbers: [252] 252,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic