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
[ 45, 47, 46, 82 ]
37
[ "82-45=37", "47-46=1", "37*1=37" ]
Current State: 37:[45, 47, 46, 82], Operations: [] Exploring Operation: 82-45=37, Resulting Numbers: [47, 46, 37] Generated Node #2: [47, 46, 37] from Operation: 82-45=37 Current State: 37:[47, 46, 37], Operations: ['82-45=37'] Exploring Operation: 47-46=1, Resulting Numbers: [37, 1] Generated Node #3: [37, 1] from Operation: 47-46=1 Current State: 37:[37, 1], Operations: ['82-45=37', '47-46=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[45, 47, 46, 82], Operations: [] Exploring Operation: 82-47=35, Resulting Numbers: [45, 46, 35] Generated Node #0,0: 37:[45, 46, 35] Operation: 82-47=35 Exploring Operation: 82-45=37, Resulting Numbers: [47, 46, 37] Generated Node #0,1: 37:[47, 46, 37] Operation: 82-45=37 Exploring Operation: 82-46=36, Resulting Numbers: [45, 47, 36] Generated Node #0,2: 37:[45, 47, 36] Operation: 82-46=36 Moving to Node #0,0 Current State: 37:[45, 46, 35], Operations: ['82-47=35'] Exploring Operation: 45-35=10, Resulting Numbers: [46, 10] Generated Node #0,0,0: 37:[46, 10] Operation: 45-35=10 Exploring Operation: 46-45=1, Resulting Numbers: [35, 1] Generated Node #0,0,1: 37:[35, 1] Operation: 46-45=1 Exploring Operation: 46-35=11, Resulting Numbers: [45, 11] Generated Node #0,0,2: 37:[45, 11] Operation: 46-35=11 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[45, 11], Operations: ['82-47=35', '46-35=11'] Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,37 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,37 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[46, 10], Operations: ['82-47=35', '45-35=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,37 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[35, 1], Operations: ['82-47=35', '46-45=1'] Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 37:[47, 46, 37], Operations: ['82-45=37'] Exploring Operation: 47-46=1, Resulting Numbers: [37, 1] Generated Node #0,1,0: 37:[37, 1] Operation: 47-46=1 Exploring Operation: 47-37=10, Resulting Numbers: [46, 10] Generated Node #0,1,1: 37:[46, 10] Operation: 47-37=10 Exploring Operation: 46-37=9, Resulting Numbers: [47, 9] Generated Node #0,1,2: 37:[47, 9] Operation: 46-37=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[37, 1], Operations: ['82-45=37', '47-46=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[45, 47, 46, 82], Operations: [] Exploring Operation: 82-45=37, Resulting Numbers: [47, 46, 37] Generated Node #0,1: 37:[47, 46, 37] Operation: 82-45=37 Moving to Node #0,1 Current State: 37:[47, 46, 37], Operations: ['82-45=37'] Exploring Operation: 47-46=1, Resulting Numbers: [37, 1] Generated Node #0,1,0: 37:[37, 1] Operation: 47-46=1 Moving to Node #0,1,0 Current State: 37:[37, 1], Operations: ['82-45=37', '47-46=1'] Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 85, 32, 5, 45 ]
77
[ "85+32=117", "45-5=40", "117-40=77" ]
Current State: 77:[85, 32, 5, 45], Operations: [] Exploring Operation: 85+32=117, Resulting Numbers: [5, 45, 117] Generated Node #2: [5, 45, 117] from Operation: 85+32=117 Current State: 77:[5, 45, 117], Operations: ['85+32=117'] Exploring Operation: 45-5=40, Resulting Numbers: [117, 40] Generated Node #3: [117, 40] from Operation: 45-5=40 Current State: 77:[117, 40], Operations: ['85+32=117', '45-5=40'] Exploring Operation: 117-40=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[85, 32, 5, 45], Operations: [] Exploring Operation: 45/5=9, Resulting Numbers: [85, 32, 9] Generated Node #0,0: 77:[85, 32, 9] Operation: 45/5=9 Exploring Operation: 32+45=77, Resulting Numbers: [85, 5, 77] Generated Node #0,1: 77:[85, 5, 77] Operation: 32+45=77 Exploring Operation: 45-32=13, Resulting Numbers: [85, 5, 13] Generated Node #0,2: 77:[85, 5, 13] Operation: 45-32=13 Exploring Operation: 85-45=40, Resulting Numbers: [32, 5, 40] Generated Node #0,3: 77:[32, 5, 40] Operation: 85-45=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[85, 5, 77], Operations: ['32+45=77'] Exploring Operation: 85-77=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 77:[5, 8] Operation: 85-77=8 Exploring Operation: 85-5=80, Resulting Numbers: [77, 80] Generated Node #0,1,1: 77:[77, 80] Operation: 85-5=80 Exploring Operation: 85+5=90, Resulting Numbers: [77, 90] Generated Node #0,1,2: 77:[77, 90] Operation: 85+5=90 Exploring Operation: 85/5=17, Resulting Numbers: [77, 17] Generated Node #0,1,3: 77:[77, 17] Operation: 85/5=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[5, 8], Operations: ['32+45=77', '85-77=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,77 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,77 unequal: No Solution No 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: 77:[77, 80], Operations: ['32+45=77', '85-5=80'] Exploring Operation: 77+80=157, Resulting Numbers: [157] 157,77 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 77*80=6160, Resulting Numbers: [6160] 6160,77 unequal: No Solution No 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: 77:[77, 17], Operations: ['32+45=77', '85/5=17'] Exploring Operation: 77+17=94, Resulting Numbers: [94] 94,77 unequal: No Solution Exploring Operation: 77*17=1309, Resulting Numbers: [1309] 1309,77 unequal: No Solution Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,77 unequal: No Solution No 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: 77:[77, 90], Operations: ['32+45=77', '85+5=90'] Exploring Operation: 77*90=6930, Resulting Numbers: [6930] 6930,77 unequal: No Solution Exploring Operation: 77+90=167, Resulting Numbers: [167] 167,77 unequal: No Solution Exploring Operation: 90-77=13, Resulting Numbers: [13] 13,77 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: 77:[85, 5, 13], Operations: ['45-32=13'] Exploring Operation: 85-13=72, Resulting Numbers: [5, 72] Generated Node #0,2,0: 77:[5, 72] Operation: 85-13=72 Exploring Operation: 85-5=80, Resulting Numbers: [13, 80] Generated Node #0,2,1: 77:[13, 80] Operation: 85-5=80 Exploring Operation: 85/5=17, Resulting Numbers: [13, 17] Generated Node #0,2,2: 77:[13, 17] Operation: 85/5=17 Exploring Operation: 13-5=8, Resulting Numbers: [85, 8] Generated Node #0,2,3: 77:[85, 8] Operation: 13-5=8 Moving to Node #0,2,1 Current State: 77:[13, 80], Operations: ['45-32=13', '85-5=80'] Exploring Operation: 13*80=1040, Resulting Numbers: [1040] 1040,77 unequal: No Solution Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 13+80=93, Resulting Numbers: [93] 93,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[5, 72], Operations: ['45-32=13', '85-13=72'] Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,77 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[85, 32, 5, 45], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [85, 5, 13] Generated Node #0,2: 77:[85, 5, 13] Operation: 45-32=13 Moving to Node #0,2 Current State: 77:[85, 5, 13], Operations: ['45-32=13'] Exploring Operation: 85-13=72, Resulting Numbers: [5, 72] Generated Node #0,2,0: 77:[5, 72] Operation: 85-13=72 Moving to Node #0,2,0 Current State: 77:[5, 72], Operations: ['45-32=13', '85-13=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 68, 89, 95, 78 ]
60
[ "78-68=10", "95-89=6", "10*6=60" ]
Current State: 60:[68, 89, 95, 78], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [89, 95, 10] Generated Node #2: [89, 95, 10] from Operation: 78-68=10 Current State: 60:[89, 95, 10], Operations: ['78-68=10'] Exploring Operation: 95-89=6, Resulting Numbers: [10, 6] Generated Node #3: [10, 6] from Operation: 95-89=6 Current State: 60:[10, 6], Operations: ['78-68=10', '95-89=6'] Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[68, 89, 95, 78], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [68, 78, 6] Generated Node #0,0: 60:[68, 78, 6] Operation: 95-89=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[68, 78, 6], Operations: ['95-89=6'] Exploring Operation: 78-68=10, Resulting Numbers: [6, 10] Generated Node #0,0,0: 60:[6, 10] Operation: 78-68=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[6, 10], Operations: ['95-89=6', '78-68=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[68, 89, 95, 78], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [68, 78, 6] Generated Node #0,0: 60:[68, 78, 6] Operation: 95-89=6 Moving to Node #0,0 Current State: 60:[68, 78, 6], Operations: ['95-89=6'] Exploring Operation: 78-68=10, Resulting Numbers: [6, 10] Generated Node #0,0,0: 60:[6, 10] Operation: 78-68=10 Moving to Node #0,0,0 Current State: 60:[6, 10], Operations: ['95-89=6', '78-68=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 29, 6, 26, 31 ]
40
[ "29+6=35", "31-26=5", "35+5=40" ]
Current State: 40:[29, 6, 26, 31], Operations: [] Exploring Operation: 29+6=35, Resulting Numbers: [26, 31, 35] Generated Node #2: [26, 31, 35] from Operation: 29+6=35 Current State: 40:[26, 31, 35], Operations: ['29+6=35'] Exploring Operation: 31-26=5, Resulting Numbers: [35, 5] Generated Node #3: [35, 5] from Operation: 31-26=5 Current State: 40:[35, 5], Operations: ['29+6=35', '31-26=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[29, 6, 26, 31], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [6, 26, 2] Generated Node #0,0: 40:[6, 26, 2] Operation: 31-29=2 Moving to Node #0,0 Current State: 40:[6, 26, 2], Operations: ['31-29=2'] Exploring Operation: 26-6=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 40:[2, 20] Operation: 26-6=20 Moving to Node #0,0,0 Current State: 40:[2, 20], Operations: ['31-29=2', '26-6=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[29, 6, 26, 31], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [6, 26, 2] Generated Node #0,0: 40:[6, 26, 2] Operation: 31-29=2 Moving to Node #0,0 Current State: 40:[6, 26, 2], Operations: ['31-29=2'] Exploring Operation: 26-6=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 40:[2, 20] Operation: 26-6=20 Moving to Node #0,0,0 Current State: 40:[2, 20], Operations: ['31-29=2', '26-6=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 43, 75, 82, 32 ]
77
[ "43-32=11", "82-75=7", "11*7=77" ]
Current State: 77:[43, 75, 82, 32], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [75, 82, 11] Generated Node #2: [75, 82, 11] from Operation: 43-32=11 Current State: 77:[75, 82, 11], Operations: ['43-32=11'] Exploring Operation: 82-75=7, Resulting Numbers: [11, 7] Generated Node #3: [11, 7] from Operation: 82-75=7 Current State: 77:[11, 7], Operations: ['43-32=11', '82-75=7'] Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[43, 75, 82, 32], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [75, 82, 11] Generated Node #0,0: 77:[75, 82, 11] Operation: 43-32=11 Exploring Operation: 75-43=32, Resulting Numbers: [82, 32, 32] Generated Node #0,1: 77:[82, 32, 32] Operation: 75-43=32 Exploring Operation: 43+32=75, Resulting Numbers: [75, 82, 75] Generated Node #0,2: 77:[75, 82, 75] Operation: 43+32=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[75, 82, 11], Operations: ['43-32=11'] Exploring Operation: 82-75=7, Resulting Numbers: [11, 7] Generated Node #0,0,0: 77:[11, 7] Operation: 82-75=7 Exploring Operation: 82-11=71, Resulting Numbers: [75, 71] Generated Node #0,0,1: 77:[75, 71] Operation: 82-11=71 Exploring Operation: 75+11=86, Resulting Numbers: [82, 86] Generated Node #0,0,2: 77:[82, 86] Operation: 75+11=86 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[11, 7], Operations: ['43-32=11', '82-75=7'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[43, 75, 82, 32], Operations: [] Exploring Operation: 43-32=11, Resulting Numbers: [75, 82, 11] Generated Node #0,0: 77:[75, 82, 11] Operation: 43-32=11 Moving to Node #0,0 Current State: 77:[75, 82, 11], Operations: ['43-32=11'] Exploring Operation: 82-75=7, Resulting Numbers: [11, 7] Generated Node #0,0,0: 77:[11, 7] Operation: 82-75=7 Moving to Node #0,0,0 Current State: 77:[11, 7], Operations: ['43-32=11', '82-75=7'] Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 18, 29, 30, 51 ]
70
[ "29-18=11", "30+51=81", "81-11=70" ]
Current State: 70:[18, 29, 30, 51], Operations: [] Exploring Operation: 29-18=11, Resulting Numbers: [30, 51, 11] Generated Node #2: [30, 51, 11] from Operation: 29-18=11 Current State: 70:[30, 51, 11], Operations: ['29-18=11'] Exploring Operation: 30+51=81, Resulting Numbers: [11, 81] Generated Node #3: [11, 81] from Operation: 30+51=81 Current State: 70:[11, 81], Operations: ['29-18=11', '30+51=81'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[18, 29, 30, 51], Operations: [] Exploring Operation: 51-18=33, Resulting Numbers: [29, 30, 33] Generated Node #0,0: 70:[29, 30, 33] Operation: 51-18=33 Exploring Operation: 18+51=69, Resulting Numbers: [29, 30, 69] Generated Node #0,1: 70:[29, 30, 69] Operation: 18+51=69 Exploring Operation: 51-30=21, Resulting Numbers: [18, 29, 21] Generated Node #0,2: 70:[18, 29, 21] Operation: 51-30=21 Exploring Operation: 29+51=80, Resulting Numbers: [18, 30, 80] Generated Node #0,3: 70:[18, 30, 80] Operation: 29+51=80 Exploring Operation: 51-29=22, Resulting Numbers: [18, 30, 22] Generated Node #0,4: 70:[18, 30, 22] Operation: 51-29=22 Moving to Node #0,1 Current State: 70:[29, 30, 69], Operations: ['18+51=69'] Exploring Operation: 69-29=40, Resulting Numbers: [30, 40] Generated Node #0,1,0: 70:[30, 40] Operation: 69-29=40 Exploring Operation: 29+30=59, Resulting Numbers: [69, 59] Generated Node #0,1,1: 70:[69, 59] Operation: 29+30=59 Exploring Operation: 69-30=39, Resulting Numbers: [29, 39] Generated Node #0,1,2: 70:[29, 39] Operation: 69-30=39 Exploring Operation: 30-29=1, Resulting Numbers: [69, 1] Generated Node #0,1,3: 70:[69, 1] Operation: 30-29=1 Exploring Operation: 29+69=98, Resulting Numbers: [30, 98] Generated Node #0,1,4: 70:[30, 98] Operation: 29+69=98 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 70:[69, 1], Operations: ['18+51=69', '30-29=1'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,70 unequal: No Solution Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[18, 29, 30, 51], Operations: [] Exploring Operation: 18+51=69, Resulting Numbers: [29, 30, 69] Generated Node #0,1: 70:[29, 30, 69] Operation: 18+51=69 Moving to Node #0,1 Current State: 70:[29, 30, 69], Operations: ['18+51=69'] Exploring Operation: 30-29=1, Resulting Numbers: [69, 1] Generated Node #0,1,3: 70:[69, 1] Operation: 30-29=1 Moving to Node #0,1,3 Current State: 70:[69, 1], Operations: ['18+51=69', '30-29=1'] Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 82, 16, 76, 68 ]
28
[ "82-76=6", "16*6=96", "96-68=28" ]
Current State: 28:[82, 16, 76, 68], Operations: [] Exploring Operation: 82-76=6, Resulting Numbers: [16, 68, 6] Generated Node #2: [16, 68, 6] from Operation: 82-76=6 Current State: 28:[16, 68, 6], Operations: ['82-76=6'] Exploring Operation: 16*6=96, Resulting Numbers: [68, 96] Generated Node #3: [68, 96] from Operation: 16*6=96 Current State: 28:[68, 96], Operations: ['82-76=6', '16*6=96'] Exploring Operation: 96-68=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[82, 16, 76, 68], Operations: [] Exploring Operation: 76-68=8, Resulting Numbers: [82, 16, 8] Generated Node #0,0: 28:[82, 16, 8] Operation: 76-68=8 Exploring Operation: 76-16=60, Resulting Numbers: [82, 68, 60] Generated Node #0,1: 28:[82, 68, 60] Operation: 76-16=60 Exploring Operation: 82-16=66, Resulting Numbers: [76, 68, 66] Generated Node #0,2: 28:[76, 68, 66] Operation: 82-16=66 Exploring Operation: 82-76=6, Resulting Numbers: [16, 68, 6] Generated Node #0,3: 28:[16, 68, 6] Operation: 82-76=6 Exploring Operation: 82-68=14, Resulting Numbers: [16, 76, 14] Generated Node #0,4: 28:[16, 76, 14] Operation: 82-68=14 Moving to Node #0,3 Current State: 28:[16, 68, 6], Operations: ['82-76=6'] Exploring Operation: 16+6=22, Resulting Numbers: [68, 22] Generated Node #0,3,0: 28:[68, 22] Operation: 16+6=22 Exploring Operation: 68+6=74, Resulting Numbers: [16, 74] Generated Node #0,3,1: 28:[16, 74] Operation: 68+6=74 Exploring Operation: 16-6=10, Resulting Numbers: [68, 10] Generated Node #0,3,2: 28:[68, 10] Operation: 16-6=10 Exploring Operation: 68-6=62, Resulting Numbers: [16, 62] Generated Node #0,3,3: 28:[16, 62] Operation: 68-6=62 Exploring Operation: 68-16=52, Resulting Numbers: [6, 52] Generated Node #0,3,4: 28:[6, 52] Operation: 68-16=52 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 28:[6, 52], Operations: ['82-76=6', '68-16=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,28 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,28 unequal: No Solution No 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: 28:[16, 62], Operations: ['82-76=6', '68-6=62'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,28 unequal: No Solution Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,28 unequal: No Solution No 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: 28:[68, 10], Operations: ['82-76=6', '16-6=10'] Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,28 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,28 unequal: No Solution No 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: 28:[68, 22], Operations: ['82-76=6', '16+6=22'] Exploring Operation: 68+22=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 68*22=1496, Resulting Numbers: [1496] 1496,28 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,28 unequal: No Solution No 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: 28:[16, 74], Operations: ['82-76=6', '68+6=74'] Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,28 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: 28:[16, 76, 14], Operations: ['82-68=14'] Exploring Operation: 16-14=2, Resulting Numbers: [76, 2] Generated Node #0,4,0: 28:[76, 2] Operation: 16-14=2 Exploring Operation: 76-14=62, Resulting Numbers: [16, 62] Generated Node #0,4,1: 28:[16, 62] Operation: 76-14=62 Exploring Operation: 76-16=60, Resulting Numbers: [14, 60] Generated Node #0,4,2: 28:[14, 60] Operation: 76-16=60 Exploring Operation: 16+14=30, Resulting Numbers: [76, 30] Generated Node #0,4,3: 28:[76, 30] Operation: 16+14=30 Exploring Operation: 16+76=92, Resulting Numbers: [14, 92] Generated Node #0,4,4: 28:[14, 92] Operation: 16+76=92 Moving to Node #0,0 Current State: 28:[82, 16, 8], Operations: ['76-68=8'] Exploring Operation: 82-8=74, Resulting Numbers: [16, 74] Generated Node #0,0,0: 28:[16, 74] Operation: 82-8=74 Exploring Operation: 16+8=24, Resulting Numbers: [82, 24] Generated Node #0,0,1: 28:[82, 24] Operation: 16+8=24 Exploring Operation: 82-16=66, Resulting Numbers: [8, 66] Generated Node #0,0,2: 28:[8, 66] Operation: 82-16=66 Exploring Operation: 16-8=8, Resulting Numbers: [82, 8] Generated Node #0,0,3: 28:[82, 8] Operation: 16-8=8 Exploring Operation: 16/8=2, Resulting Numbers: [82, 2] Generated Node #0,0,4: 28:[82, 2] Operation: 16/8=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 28:[8, 66], Operations: ['76-68=8', '82-16=66'] Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 8*66=528, Resulting Numbers: [528] 528,28 unequal: No Solution No 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: 28:[16, 74], Operations: ['76-68=8', '82-8=74'] Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,28 unequal: No Solution No 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: 28:[82, 2], Operations: ['76-68=8', '16/8=2'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,28 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,28 unequal: No Solution Exploring Operation: 82*2=164, Resulting Numbers: [164] 164,28 unequal: No Solution No 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: 28:[82, 8], Operations: ['76-68=8', '16-8=8'] Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,28 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,28 unequal: No Solution No 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: 28:[82, 24], Operations: ['76-68=8', '16+8=24'] Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 82*24=1968, Resulting Numbers: [1968] 1968,28 unequal: No Solution Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 28:[82, 68, 60], Operations: ['76-16=60'] Exploring Operation: 82-60=22, Resulting Numbers: [68, 22] Generated Node #0,1,0: 28:[68, 22] Operation: 82-60=22 Exploring Operation: 68-60=8, Resulting Numbers: [82, 8] Generated Node #0,1,1: 28:[82, 8] Operation: 68-60=8 Exploring Operation: 82-68=14, Resulting Numbers: [60, 14] Generated Node #0,1,2: 28:[60, 14] Operation: 82-68=14 Exploring Operation: 82+68=150, Resulting Numbers: [60, 150] Generated Node #0,1,3: 28:[60, 150] Operation: 82+68=150 Exploring Operation: 82+60=142, Resulting Numbers: [68, 142] Generated Node #0,1,4: 28:[68, 142] Operation: 82+60=142 Moving to Node #0,2 Current State: 28:[76, 68, 66], Operations: ['82-16=66'] Exploring Operation: 68-66=2, Resulting Numbers: [76, 2] Generated Node #0,2,0: 28:[76, 2] Operation: 68-66=2 Exploring Operation: 76+68=144, Resulting Numbers: [66, 144] Generated Node #0,2,1: 28:[66, 144] Operation: 76+68=144 Exploring Operation: 76-68=8, Resulting Numbers: [66, 8] Generated Node #0,2,2: 28:[66, 8] Operation: 76-68=8 Exploring Operation: 76+66=142, Resulting Numbers: [68, 142] Generated Node #0,2,3: 28:[68, 142] Operation: 76+66=142 Exploring Operation: 76-66=10, Resulting Numbers: [68, 10] Generated Node #0,2,4: 28:[68, 10] Operation: 76-66=10 Moving to Node #0,4,2 Current State: 28:[14, 60], Operations: ['82-68=14', '76-16=60'] Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 14*60=840, Resulting Numbers: [840] 840,28 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[60, 14], Operations: ['76-16=60', '82-68=14'] Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,28 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,4,1 Current State: 28:[16, 62], Operations: ['82-68=14', '76-14=62'] Exploring Operation: 16+62=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 16*62=992, Resulting Numbers: [992] 992,28 unequal: No Solution Moving to Node #0,2,2 Current State: 28:[66, 8], Operations: ['82-16=66', '76-68=8'] Exploring Operation: 66*8=528, Resulting Numbers: [528] 528,28 unequal: No Solution Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,2,4 Current State: 28:[68, 10], Operations: ['82-16=66', '76-66=10'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,28 unequal: No Solution Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[68, 22], Operations: ['76-16=60', '82-60=22'] Exploring Operation: 68*22=1496, Resulting Numbers: [1496] 1496,28 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,28 unequal: No Solution Exploring Operation: 68+22=90, Resulting Numbers: [90] 90,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[76, 2], Operations: ['82-68=14', '16-14=2'] Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[76, 2], Operations: ['82-16=66', '68-66=2'] Exploring Operation: 76*2=152, Resulting Numbers: [152] 152,28 unequal: No Solution Exploring Operation: 76+2=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,28 unequal: No Solution Moving to Node #0,4,3 Current State: 28:[76, 30], Operations: ['82-68=14', '16+14=30'] Exploring Operation: 76*30=2280, Resulting Numbers: [2280] 2280,28 unequal: No Solution Exploring Operation: 76+30=106, Resulting Numbers: [106] 106,28 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[82, 8], Operations: ['76-16=60', '68-60=8'] Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,28 unequal: No Solution Moving to Node #0,4,4 Current State: 28:[14, 92], Operations: ['82-68=14', '16+76=92'] Exploring Operation: 14*92=1288, Resulting Numbers: [1288] 1288,28 unequal: No Solution Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 14+92=106, Resulting Numbers: [106] 106,28 unequal: No Solution Moving to Node #0,2,1 Current State: 28:[66, 144], Operations: ['82-16=66', '76+68=144'] Exploring Operation: 66*144=9504, Resulting Numbers: [9504] 9504,28 unequal: No Solution Exploring Operation: 144-66=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 66+144=210, Resulting Numbers: [210] 210,28 unequal: No Solution Moving to Node #0,1,4 Current State: 28:[68, 142], Operations: ['76-16=60', '82+60=142'] Exploring Operation: 68+142=210, Resulting Numbers: [210] 210,28 unequal: No Solution Exploring Operation: 68*142=9656, Resulting Numbers: [9656] 9656,28 unequal: No Solution Exploring Operation: 142-68=74, Resulting Numbers: [74] 74,28 unequal: No Solution Moving to Node #0,1,3 Current State: 28:[60, 150], Operations: ['76-16=60', '82+68=150'] Exploring Operation: 150-60=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 60+150=210, Resulting Numbers: [210] 210,28 unequal: No Solution Exploring Operation: 60*150=9000, Resulting Numbers: [9000] 9000,28 unequal: No Solution Moving to Node #0,2,3 Current State: 28:[68, 142], Operations: ['82-16=66', '76+66=142'] Exploring Operation: 68*142=9656, Resulting Numbers: [9656] 9656,28 unequal: No Solution Exploring Operation: 142-68=74, Resulting Numbers: [74] 74,28 unequal: No Solution Exploring Operation: 68+142=210, Resulting Numbers: [210] 210,28 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 44, 41, 69, 99 ]
56
[ "44-41=3", "69+99=168", "168/3=56" ]
Current State: 56:[44, 41, 69, 99], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [69, 99, 3] Generated Node #2: [69, 99, 3] from Operation: 44-41=3 Current State: 56:[69, 99, 3], Operations: ['44-41=3'] Exploring Operation: 69+99=168, Resulting Numbers: [3, 168] Generated Node #3: [3, 168] from Operation: 69+99=168 Current State: 56:[3, 168], Operations: ['44-41=3', '69+99=168'] Exploring Operation: 168/3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[44, 41, 69, 99], Operations: [] Exploring Operation: 99-44=55, Resulting Numbers: [41, 69, 55] Generated Node #0,0: 56:[41, 69, 55] Operation: 99-44=55 Exploring Operation: 99-69=30, Resulting Numbers: [44, 41, 30] Generated Node #0,1: 56:[44, 41, 30] Operation: 99-69=30 Exploring Operation: 99-41=58, Resulting Numbers: [44, 69, 58] Generated Node #0,2: 56:[44, 69, 58] Operation: 99-41=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[41, 69, 55], Operations: ['99-44=55'] Exploring Operation: 69-55=14, Resulting Numbers: [41, 14] Generated Node #0,0,0: 56:[41, 14] Operation: 69-55=14 Exploring Operation: 55-41=14, Resulting Numbers: [69, 14] Generated Node #0,0,1: 56:[69, 14] Operation: 55-41=14 Exploring Operation: 69-41=28, Resulting Numbers: [55, 28] Generated Node #0,0,2: 56:[55, 28] Operation: 69-41=28 Moving to Node #0,0,2 Current State: 56:[55, 28], Operations: ['99-44=55', '69-41=28'] Exploring Operation: 55*28=1540, Resulting Numbers: [1540] 1540,56 unequal: No Solution Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,56 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[41, 14], Operations: ['99-44=55', '69-55=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,56 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[69, 14], Operations: ['99-44=55', '55-41=14'] Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,56 unequal: No Solution Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,56 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[44, 41, 30], Operations: ['99-69=30'] Exploring Operation: 44-41=3, Resulting Numbers: [30, 3] Generated Node #0,1,0: 56:[30, 3] Operation: 44-41=3 Exploring Operation: 44-30=14, Resulting Numbers: [41, 14] Generated Node #0,1,1: 56:[41, 14] Operation: 44-30=14 Exploring Operation: 41-30=11, Resulting Numbers: [44, 11] Generated Node #0,1,2: 56:[44, 11] Operation: 41-30=11 Moving to Node #0,1,0 Current State: 56:[30, 3], Operations: ['99-69=30', '44-41=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,56 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[41, 14], Operations: ['99-69=30', '44-30=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,56 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[44, 11], Operations: ['99-69=30', '41-30=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[44, 69, 58], Operations: ['99-41=58'] Exploring Operation: 69-58=11, Resulting Numbers: [44, 11] Generated Node #0,2,0: 56:[44, 11] Operation: 69-58=11 Exploring Operation: 69-44=25, Resulting Numbers: [58, 25] Generated Node #0,2,1: 56:[58, 25] Operation: 69-44=25 Exploring Operation: 58-44=14, Resulting Numbers: [69, 14] Generated Node #0,2,2: 56:[69, 14] Operation: 58-44=14 Moving to Node #0,2,1 Current State: 56:[58, 25], Operations: ['99-41=58', '69-44=25'] Exploring Operation: 58+25=83, Resulting Numbers: [83] 83,56 unequal: No Solution Exploring Operation: 58-25=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 58*25=1450, Resulting Numbers: [1450] 1450,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[69, 14], Operations: ['99-41=58', '58-44=14'] Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,56 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[44, 11], Operations: ['99-41=58', '69-58=11'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 95, 75, 22, 69 ]
67
[ "95-75=20", "69-22=47", "20+47=67" ]
Current State: 67:[95, 75, 22, 69], Operations: [] Exploring Operation: 95-75=20, Resulting Numbers: [22, 69, 20] Generated Node #2: [22, 69, 20] from Operation: 95-75=20 Current State: 67:[22, 69, 20], Operations: ['95-75=20'] Exploring Operation: 69-22=47, Resulting Numbers: [20, 47] Generated Node #3: [20, 47] from Operation: 69-22=47 Current State: 67:[20, 47], Operations: ['95-75=20', '69-22=47'] Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[95, 75, 22, 69], Operations: [] Exploring Operation: 95-22=73, Resulting Numbers: [75, 69, 73] Generated Node #0,0: 67:[75, 69, 73] Operation: 95-22=73 Exploring Operation: 75-22=53, Resulting Numbers: [95, 69, 53] Generated Node #0,1: 67:[95, 69, 53] Operation: 75-22=53 Exploring Operation: 75+22=97, Resulting Numbers: [95, 69, 97] Generated Node #0,2: 67:[95, 69, 97] Operation: 75+22=97 Exploring Operation: 95+22=117, Resulting Numbers: [75, 69, 117] Generated Node #0,3: 67:[75, 69, 117] Operation: 95+22=117 Exploring Operation: 69-22=47, Resulting Numbers: [95, 75, 47] Generated Node #0,4: 67:[95, 75, 47] Operation: 69-22=47 Moving to Node #0,0 Current State: 67:[75, 69, 73], Operations: ['95-22=73'] Exploring Operation: 75+73=148, Resulting Numbers: [69, 148] Generated Node #0,0,0: 67:[69, 148] Operation: 75+73=148 Exploring Operation: 73-69=4, Resulting Numbers: [75, 4] Generated Node #0,0,1: 67:[75, 4] Operation: 73-69=4 Exploring Operation: 75+69=144, Resulting Numbers: [73, 144] Generated Node #0,0,2: 67:[73, 144] Operation: 75+69=144 Exploring Operation: 75-73=2, Resulting Numbers: [69, 2] Generated Node #0,0,3: 67:[69, 2] Operation: 75-73=2 Exploring Operation: 75-69=6, Resulting Numbers: [73, 6] Generated Node #0,0,4: 67:[73, 6] Operation: 75-69=6 Moving to Node #0,1 Current State: 67:[95, 69, 53], Operations: ['75-22=53'] Exploring Operation: 95-69=26, Resulting Numbers: [53, 26] Generated Node #0,1,0: 67:[53, 26] Operation: 95-69=26 Exploring Operation: 95-53=42, Resulting Numbers: [69, 42] Generated Node #0,1,1: 67:[69, 42] Operation: 95-53=42 Exploring Operation: 69-53=16, Resulting Numbers: [95, 16] Generated Node #0,1,2: 67:[95, 16] Operation: 69-53=16 Exploring Operation: 69+53=122, Resulting Numbers: [95, 122] Generated Node #0,1,3: 67:[95, 122] Operation: 69+53=122 Exploring Operation: 95+53=148, Resulting Numbers: [69, 148] Generated Node #0,1,4: 67:[69, 148] Operation: 95+53=148 Moving to Node #0,4 Current State: 67:[95, 75, 47], Operations: ['69-22=47'] Exploring Operation: 75-47=28, Resulting Numbers: [95, 28] Generated Node #0,4,0: 67:[95, 28] Operation: 75-47=28 Exploring Operation: 95-47=48, Resulting Numbers: [75, 48] Generated Node #0,4,1: 67:[75, 48] Operation: 95-47=48 Exploring Operation: 75+47=122, Resulting Numbers: [95, 122] Generated Node #0,4,2: 67:[95, 122] Operation: 75+47=122 Exploring Operation: 95+47=142, Resulting Numbers: [75, 142] Generated Node #0,4,3: 67:[75, 142] Operation: 95+47=142 Exploring Operation: 95-75=20, Resulting Numbers: [47, 20] Generated Node #0,4,4: 67:[47, 20] Operation: 95-75=20 Moving to Node #0,2 Current State: 67:[95, 69, 97], Operations: ['75+22=97'] Exploring Operation: 97-69=28, Resulting Numbers: [95, 28] Generated Node #0,2,0: 67:[95, 28] Operation: 97-69=28 Exploring Operation: 95-69=26, Resulting Numbers: [97, 26] Generated Node #0,2,1: 67:[97, 26] Operation: 95-69=26 Exploring Operation: 95+97=192, Resulting Numbers: [69, 192] Generated Node #0,2,2: 67:[69, 192] Operation: 95+97=192 Exploring Operation: 97-95=2, Resulting Numbers: [69, 2] Generated Node #0,2,3: 67:[69, 2] Operation: 97-95=2 Exploring Operation: 95+69=164, Resulting Numbers: [97, 164] Generated Node #0,2,4: 67:[97, 164] Operation: 95+69=164 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[95, 28], Operations: ['75+22=97', '97-69=28'] Exploring Operation: 95-28=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[95, 75, 22, 69], Operations: [] Exploring Operation: 75+22=97, Resulting Numbers: [95, 69, 97] Generated Node #0,2: 67:[95, 69, 97] Operation: 75+22=97 Moving to Node #0,2 Current State: 67:[95, 69, 97], Operations: ['75+22=97'] Exploring Operation: 97-69=28, Resulting Numbers: [95, 28] Generated Node #0,2,0: 67:[95, 28] Operation: 97-69=28 Moving to Node #0,2,0 Current State: 67:[95, 28], Operations: ['75+22=97', '97-69=28'] Exploring Operation: 95-28=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
mult_heuristic
[ 32, 53, 31, 73 ]
21
[ "53-32=21", "73-31=42", "42-21=21" ]
Current State: 21:[32, 53, 31, 73], Operations: [] Exploring Operation: 53-32=21, Resulting Numbers: [31, 73, 21] Generated Node #2: [31, 73, 21] from Operation: 53-32=21 Current State: 21:[31, 73, 21], Operations: ['53-32=21'] Exploring Operation: 73-31=42, Resulting Numbers: [21, 42] Generated Node #3: [21, 42] from Operation: 73-31=42 Current State: 21:[21, 42], Operations: ['53-32=21', '73-31=42'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[32, 53, 31, 73], Operations: [] Exploring Operation: 73-32=41, Resulting Numbers: [53, 31, 41] Generated Node #0,0: 21:[53, 31, 41] Operation: 73-32=41 Exploring Operation: 53-32=21, Resulting Numbers: [31, 73, 21] Generated Node #0,1: 21:[31, 73, 21] Operation: 53-32=21 Exploring Operation: 53-31=22, Resulting Numbers: [32, 73, 22] Generated Node #0,2: 21:[32, 73, 22] Operation: 53-31=22 Exploring Operation: 73-53=20, Resulting Numbers: [32, 31, 20] Generated Node #0,3: 21:[32, 31, 20] Operation: 73-53=20 Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[32, 31, 20], Operations: ['73-53=20'] Exploring Operation: 32-31=1, Resulting Numbers: [20, 1] Generated Node #0,3,0: 21:[20, 1] Operation: 32-31=1 Exploring Operation: 31-20=11, Resulting Numbers: [32, 11] Generated Node #0,3,1: 21:[32, 11] Operation: 31-20=11 Exploring Operation: 32+20=52, Resulting Numbers: [31, 52] Generated Node #0,3,2: 21:[31, 52] Operation: 32+20=52 Exploring Operation: 32-20=12, Resulting Numbers: [31, 12] Generated Node #0,3,3: 21:[31, 12] Operation: 32-20=12 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 21:[20, 1], Operations: ['73-53=20', '32-31=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[32, 53, 31, 73], Operations: [] Exploring Operation: 73-53=20, Resulting Numbers: [32, 31, 20] Generated Node #0,3: 21:[32, 31, 20] Operation: 73-53=20 Moving to Node #0,3 Current State: 21:[32, 31, 20], Operations: ['73-53=20'] Exploring Operation: 32-31=1, Resulting Numbers: [20, 1] Generated Node #0,3,0: 21:[20, 1] Operation: 32-31=1 Moving to Node #0,3,0 Current State: 21:[20, 1], Operations: ['73-53=20', '32-31=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 31, 70, 58, 56 ]
75
[ "70-31=39", "58+56=114", "114-39=75" ]
Current State: 75:[31, 70, 58, 56], Operations: [] Exploring Operation: 70-31=39, Resulting Numbers: [58, 56, 39] Generated Node #2: [58, 56, 39] from Operation: 70-31=39 Current State: 75:[58, 56, 39], Operations: ['70-31=39'] Exploring Operation: 58+56=114, Resulting Numbers: [39, 114] Generated Node #3: [39, 114] from Operation: 58+56=114 Current State: 75:[39, 114], Operations: ['70-31=39', '58+56=114'] Exploring Operation: 114-39=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[31, 70, 58, 56], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [31, 58, 14] Generated Node #0,0: 75:[31, 58, 14] Operation: 70-56=14 Exploring Operation: 58-56=2, Resulting Numbers: [31, 70, 2] Generated Node #0,1: 75:[31, 70, 2] Operation: 58-56=2 Exploring Operation: 56-31=25, Resulting Numbers: [70, 58, 25] Generated Node #0,2: 75:[70, 58, 25] Operation: 56-31=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[31, 70, 2], Operations: ['58-56=2'] Exploring Operation: 31+2=33, Resulting Numbers: [70, 33] Generated Node #0,1,0: 75:[70, 33] Operation: 31+2=33 Exploring Operation: 31-2=29, Resulting Numbers: [70, 29] Generated Node #0,1,1: 75:[70, 29] Operation: 31-2=29 Exploring Operation: 70+2=72, Resulting Numbers: [31, 72] Generated Node #0,1,2: 75:[31, 72] Operation: 70+2=72 Moving to Node #0,1,1 Current State: 75:[70, 29], Operations: ['58-56=2', '31-2=29'] Exploring Operation: 70*29=2030, Resulting Numbers: [2030] 2030,75 unequal: No Solution Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,75 unequal: No Solution Exploring Operation: 70+29=99, Resulting Numbers: [99] 99,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[31, 72], Operations: ['58-56=2', '70+2=72'] Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,75 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,75 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[70, 33], Operations: ['58-56=2', '31+2=33'] Exploring Operation: 70+33=103, Resulting Numbers: [103] 103,75 unequal: No Solution Exploring Operation: 70*33=2310, Resulting Numbers: [2310] 2310,75 unequal: No Solution Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[70, 58, 25], Operations: ['56-31=25'] Exploring Operation: 70-58=12, Resulting Numbers: [25, 12] Generated Node #0,2,0: 75:[25, 12] Operation: 70-58=12 Exploring Operation: 58-25=33, Resulting Numbers: [70, 33] Generated Node #0,2,1: 75:[70, 33] Operation: 58-25=33 Exploring Operation: 58+25=83, Resulting Numbers: [70, 83] Generated Node #0,2,2: 75:[70, 83] Operation: 58+25=83 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 75:[25, 12], Operations: ['56-31=25', '70-58=12'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,75 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,75 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 #0,2,1 Current State: 75:[70, 33], Operations: ['56-31=25', '58-25=33'] Exploring Operation: 70*33=2310, Resulting Numbers: [2310] 2310,75 unequal: No Solution Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 70+33=103, Resulting Numbers: [103] 103,75 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:[70, 83], Operations: ['56-31=25', '58+25=83'] Exploring Operation: 70*83=5810, Resulting Numbers: [5810] 5810,75 unequal: No Solution Exploring Operation: 70+83=153, Resulting Numbers: [153] 153,75 unequal: No Solution Exploring Operation: 83-70=13, Resulting Numbers: [13] 13,75 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:[31, 58, 14], Operations: ['70-56=14'] Exploring Operation: 58+14=72, Resulting Numbers: [31, 72] Generated Node #0,0,0: 75:[31, 72] Operation: 58+14=72 Exploring Operation: 31+58=89, Resulting Numbers: [14, 89] Generated Node #0,0,1: 75:[14, 89] Operation: 31+58=89 Exploring Operation: 58-31=27, Resulting Numbers: [14, 27] Generated Node #0,0,2: 75:[14, 27] Operation: 58-31=27 Moving to Node #0,0,2 Current State: 75:[14, 27], Operations: ['70-56=14', '58-31=27'] Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,75 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,75 unequal: No Solution Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[31, 72], Operations: ['70-56=14', '58+14=72'] Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,75 unequal: No Solution Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,75 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[14, 89], Operations: ['70-56=14', '31+58=89'] Exploring Operation: 14*89=1246, Resulting Numbers: [1246] 1246,75 unequal: No Solution Exploring Operation: 14+89=103, Resulting Numbers: [103] 103,75 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[31, 70, 58, 56], Operations: [] Exploring Operation: 70-56=14, Resulting Numbers: [31, 58, 14] Generated Node #0,0: 75:[31, 58, 14] Operation: 70-56=14 Moving to Node #0,0 Current State: 75:[31, 58, 14], Operations: ['70-56=14'] Exploring Operation: 31+58=89, Resulting Numbers: [14, 89] Generated Node #0,0,1: 75:[14, 89] Operation: 31+58=89 Moving to Node #0,0,1 Current State: 75:[14, 89], Operations: ['70-56=14', '31+58=89'] Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_3
mult_heuristic
[ 77, 89, 70, 10 ]
48
[ "89-77=12", "70-10=60", "60-12=48" ]
Current State: 48:[77, 89, 70, 10], Operations: [] Exploring Operation: 89-77=12, Resulting Numbers: [70, 10, 12] Generated Node #2: [70, 10, 12] from Operation: 89-77=12 Current State: 48:[70, 10, 12], Operations: ['89-77=12'] Exploring Operation: 70-10=60, Resulting Numbers: [12, 60] Generated Node #3: [12, 60] from Operation: 70-10=60 Current State: 48:[12, 60], Operations: ['89-77=12', '70-10=60'] Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[77, 89, 70, 10], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [77, 10, 19] Generated Node #0,0: 48:[77, 10, 19] Operation: 89-70=19 Exploring Operation: 89-77=12, Resulting Numbers: [70, 10, 12] Generated Node #0,1: 48:[70, 10, 12] Operation: 89-77=12 Moving to Node #0,1 Current State: 48:[70, 10, 12], Operations: ['89-77=12'] Exploring Operation: 70-10=60, Resulting Numbers: [12, 60] Generated Node #0,1,0: 48:[12, 60] Operation: 70-10=60 Exploring Operation: 70/10=7, Resulting Numbers: [12, 7] Generated Node #0,1,1: 48:[12, 7] Operation: 70/10=7 Moving to Node #0,0 Current State: 48:[77, 10, 19], Operations: ['89-70=19'] Exploring Operation: 77-19=58, Resulting Numbers: [10, 58] Generated Node #0,0,0: 48:[10, 58] Operation: 77-19=58 Exploring Operation: 77-10=67, Resulting Numbers: [19, 67] Generated Node #0,0,1: 48:[19, 67] Operation: 77-10=67 Moving to Node #0,1,1 Current State: 48:[12, 7], Operations: ['89-77=12', '70/10=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,48 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[10, 58], Operations: ['89-70=19', '77-19=58'] Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[77, 89, 70, 10], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [77, 10, 19] Generated Node #0,0: 48:[77, 10, 19] Operation: 89-70=19 Moving to Node #0,0 Current State: 48:[77, 10, 19], Operations: ['89-70=19'] Exploring Operation: 77-19=58, Resulting Numbers: [10, 58] Generated Node #0,0,0: 48:[10, 58] Operation: 77-19=58 Moving to Node #0,0,0 Current State: 48:[10, 58], Operations: ['89-70=19', '77-19=58'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.987847
hs_2
mult_heuristic
[ 22, 37, 26, 64 ]
23
[ "37-22=15", "64-26=38", "38-15=23" ]
Current State: 23:[22, 37, 26, 64], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [26, 64, 15] Generated Node #2: [26, 64, 15] from Operation: 37-22=15 Current State: 23:[26, 64, 15], Operations: ['37-22=15'] Exploring Operation: 64-26=38, Resulting Numbers: [15, 38] Generated Node #3: [15, 38] from Operation: 64-26=38 Current State: 23:[15, 38], Operations: ['37-22=15', '64-26=38'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[22, 37, 26, 64], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [22, 37, 38] Generated Node #0,0: 23:[22, 37, 38] Operation: 64-26=38 Exploring Operation: 64-37=27, Resulting Numbers: [22, 26, 27] Generated Node #0,1: 23:[22, 26, 27] Operation: 64-37=27 Moving to Node #0,1 Current State: 23:[22, 26, 27], Operations: ['64-37=27'] Exploring Operation: 26-22=4, Resulting Numbers: [27, 4] Generated Node #0,1,0: 23:[27, 4] Operation: 26-22=4 Exploring Operation: 27-22=5, Resulting Numbers: [26, 5] Generated Node #0,1,1: 23:[26, 5] Operation: 27-22=5 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[26, 5], Operations: ['64-37=27', '27-22=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[27, 4], Operations: ['64-37=27', '26-22=4'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[22, 37, 26, 64], Operations: [] Exploring Operation: 64-37=27, Resulting Numbers: [22, 26, 27] Generated Node #0,1: 23:[22, 26, 27] Operation: 64-37=27 Moving to Node #0,1 Current State: 23:[22, 26, 27], Operations: ['64-37=27'] Exploring Operation: 26-22=4, Resulting Numbers: [27, 4] Generated Node #0,1,0: 23:[27, 4] Operation: 26-22=4 Moving to Node #0,1,0 Current State: 23:[27, 4], Operations: ['64-37=27', '26-22=4'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 33, 4, 32, 22 ]
38
[ "33*4=132", "132/22=6", "32+6=38" ]
Current State: 38:[33, 4, 32, 22], Operations: [] Exploring Operation: 33*4=132, Resulting Numbers: [32, 22, 132] Generated Node #2: [32, 22, 132] from Operation: 33*4=132 Current State: 38:[32, 22, 132], Operations: ['33*4=132'] Exploring Operation: 132/22=6, Resulting Numbers: [32, 6] Generated Node #3: [32, 6] from Operation: 132/22=6 Current State: 38:[32, 6], Operations: ['33*4=132', '132/22=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[33, 4, 32, 22], Operations: [] Exploring Operation: 33+4=37, Resulting Numbers: [32, 22, 37] Generated Node #0,0: 38:[32, 22, 37] Operation: 33+4=37 Exploring Operation: 32/4=8, Resulting Numbers: [33, 22, 8] Generated Node #0,1: 38:[33, 22, 8] Operation: 32/4=8 Exploring Operation: 4+32=36, Resulting Numbers: [33, 22, 36] Generated Node #0,2: 38:[33, 22, 36] Operation: 4+32=36 Exploring Operation: 22-4=18, Resulting Numbers: [33, 32, 18] Generated Node #0,3: 38:[33, 32, 18] Operation: 22-4=18 Exploring Operation: 33-32=1, Resulting Numbers: [4, 22, 1] Generated Node #0,4: 38:[4, 22, 1] Operation: 33-32=1 Moving to Node #0,4 Current State: 38:[4, 22, 1], Operations: ['33-32=1'] Exploring Operation: 4/1=4, Resulting Numbers: [22, 4] Generated Node #0,4,0: 38:[22, 4] Operation: 4/1=4 Exploring Operation: 4-1=3, Resulting Numbers: [22, 3] Generated Node #0,4,1: 38:[22, 3] Operation: 4-1=3 Exploring Operation: 22-1=21, Resulting Numbers: [4, 21] Generated Node #0,4,2: 38:[4, 21] Operation: 22-1=21 Exploring Operation: 22-4=18, Resulting Numbers: [1, 18] Generated Node #0,4,3: 38:[1, 18] Operation: 22-4=18 Exploring Operation: 4*1=4, Resulting Numbers: [22, 4] Generated Node #0,4,4: 38:[22, 4] Operation: 4*1=4 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 38:[1, 18], Operations: ['33-32=1', '22-4=18'] Exploring Operation: 1+18=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 1*18=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 38:[22, 3], Operations: ['33-32=1', '4-1=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,38 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 38:[4, 21], Operations: ['33-32=1', '22-1=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,38 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 38:[22, 4], Operations: ['33-32=1', '4/1=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,38 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 38:[22, 4], Operations: ['33-32=1', '4*1=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,38 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,38 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: 38:[33, 22, 36], Operations: ['4+32=36'] Exploring Operation: 33+22=55, Resulting Numbers: [36, 55] Generated Node #0,2,0: 38:[36, 55] Operation: 33+22=55 Exploring Operation: 22+36=58, Resulting Numbers: [33, 58] Generated Node #0,2,1: 38:[33, 58] Operation: 22+36=58 Exploring Operation: 36-22=14, Resulting Numbers: [33, 14] Generated Node #0,2,2: 38:[33, 14] Operation: 36-22=14 Exploring Operation: 33-22=11, Resulting Numbers: [36, 11] Generated Node #0,2,3: 38:[36, 11] Operation: 33-22=11 Exploring Operation: 36-33=3, Resulting Numbers: [22, 3] Generated Node #0,2,4: 38:[22, 3] Operation: 36-33=3 Moving to Node #0,0 Current State: 38:[32, 22, 37], Operations: ['33+4=37'] Exploring Operation: 22+37=59, Resulting Numbers: [32, 59] Generated Node #0,0,0: 38:[32, 59] Operation: 22+37=59 Exploring Operation: 32+22=54, Resulting Numbers: [37, 54] Generated Node #0,0,1: 38:[37, 54] Operation: 32+22=54 Exploring Operation: 37-22=15, Resulting Numbers: [32, 15] Generated Node #0,0,2: 38:[32, 15] Operation: 37-22=15 Exploring Operation: 32-22=10, Resulting Numbers: [37, 10] Generated Node #0,0,3: 38:[37, 10] Operation: 32-22=10 Exploring Operation: 37-32=5, Resulting Numbers: [22, 5] Generated Node #0,0,4: 38:[22, 5] Operation: 37-32=5 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 38:[22, 5], Operations: ['33+4=37', '37-32=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,38 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 38:[37, 10], Operations: ['33+4=37', '32-22=10'] Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,38 unequal: No Solution Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[32, 15], Operations: ['33+4=37', '37-22=15'] Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,38 unequal: No Solution Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[37, 54], Operations: ['33+4=37', '32+22=54'] Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,38 unequal: No Solution Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[32, 59], Operations: ['33+4=37', '22+37=59'] Exploring Operation: 32*59=1888, Resulting Numbers: [1888] 1888,38 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 32+59=91, Resulting Numbers: [91] 91,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 38:[33, 32, 18], Operations: ['22-4=18'] Exploring Operation: 32-18=14, Resulting Numbers: [33, 14] Generated Node #0,3,0: 38:[33, 14] Operation: 32-18=14 Exploring Operation: 33-18=15, Resulting Numbers: [32, 15] Generated Node #0,3,1: 38:[32, 15] Operation: 33-18=15 Exploring Operation: 33-32=1, Resulting Numbers: [18, 1] Generated Node #0,3,2: 38:[18, 1] Operation: 33-32=1 Exploring Operation: 32+18=50, Resulting Numbers: [33, 50] Generated Node #0,3,3: 38:[33, 50] Operation: 32+18=50 Exploring Operation: 33+18=51, Resulting Numbers: [32, 51] Generated Node #0,3,4: 38:[32, 51] Operation: 33+18=51 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[18, 1], Operations: ['22-4=18', '33-32=1'] Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[33, 14], Operations: ['22-4=18', '32-18=14'] Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,38 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[32, 15], Operations: ['22-4=18', '33-18=15'] Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,38 unequal: No Solution Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[33, 50], Operations: ['22-4=18', '32+18=50'] Exploring Operation: 33+50=83, Resulting Numbers: [83] 83,38 unequal: No Solution Exploring Operation: 33*50=1650, Resulting Numbers: [1650] 1650,38 unequal: No Solution Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 38:[32, 51], Operations: ['22-4=18', '33+18=51'] Exploring Operation: 32+51=83, Resulting Numbers: [83] 83,38 unequal: No Solution Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 32*51=1632, Resulting Numbers: [1632] 1632,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 38:[33, 22, 8], Operations: ['32/4=8'] Exploring Operation: 33-8=25, Resulting Numbers: [22, 25] Generated Node #0,1,0: 38:[22, 25] Operation: 33-8=25 Exploring Operation: 22+8=30, Resulting Numbers: [33, 30] Generated Node #0,1,1: 38:[33, 30] Operation: 22+8=30 Exploring Operation: 22-8=14, Resulting Numbers: [33, 14] Generated Node #0,1,2: 38:[33, 14] Operation: 22-8=14 Exploring Operation: 33-22=11, Resulting Numbers: [8, 11] Generated Node #0,1,3: 38:[8, 11] Operation: 33-22=11 Exploring Operation: 33+8=41, Resulting Numbers: [22, 41] Generated Node #0,1,4: 38:[22, 41] Operation: 33+8=41 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 38:[22, 41], Operations: ['32/4=8', '33+8=41'] Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,38 unequal: No Solution Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[22, 25], Operations: ['32/4=8', '33-8=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 38:[33, 14], Operations: ['32/4=8', '22-8=14'] Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 38:[33, 30], Operations: ['32/4=8', '22+8=30'] Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 38:[8, 11], Operations: ['32/4=8', '33-22=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,38 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,4 Current State: 38:[22, 3], Operations: ['4+32=36', '36-33=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[36, 11], Operations: ['4+32=36', '33-22=11'] Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,38 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,38 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[33, 14], Operations: ['4+32=36', '36-22=14'] Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,38 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[36, 55], Operations: ['4+32=36', '33+22=55'] Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 36*55=1980, Resulting Numbers: [1980] 1980,38 unequal: No Solution Exploring Operation: 36+55=91, Resulting Numbers: [91] 91,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[33, 58], Operations: ['4+32=36', '22+36=58'] Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 33+58=91, Resulting Numbers: [91] 91,38 unequal: No Solution Exploring Operation: 33*58=1914, Resulting Numbers: [1914] 1914,38 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 45, 61, 56, 70 ]
31
[ "61-56=5", "70/5=14", "45-14=31" ]
Current State: 31:[45, 61, 56, 70], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [45, 70, 5] Generated Node #2: [45, 70, 5] from Operation: 61-56=5 Current State: 31:[45, 70, 5], Operations: ['61-56=5'] Exploring Operation: 70/5=14, Resulting Numbers: [45, 14] Generated Node #3: [45, 14] from Operation: 70/5=14 Current State: 31:[45, 14], Operations: ['61-56=5', '70/5=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[45, 61, 56, 70], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [56, 70, 16] Generated Node #0,0: 31:[56, 70, 16] Operation: 61-45=16 Exploring Operation: 70-61=9, Resulting Numbers: [45, 56, 9] Generated Node #0,1: 31:[45, 56, 9] Operation: 70-61=9 Exploring Operation: 70-56=14, Resulting Numbers: [45, 61, 14] Generated Node #0,2: 31:[45, 61, 14] Operation: 70-56=14 Exploring Operation: 70-45=25, Resulting Numbers: [61, 56, 25] Generated Node #0,3: 31:[61, 56, 25] Operation: 70-45=25 Moving to Node #0,1 Current State: 31:[45, 56, 9], Operations: ['70-61=9'] Exploring Operation: 45+9=54, Resulting Numbers: [56, 54] Generated Node #0,1,0: 31:[56, 54] Operation: 45+9=54 Exploring Operation: 56-45=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 31:[9, 11] Operation: 56-45=11 Exploring Operation: 45-9=36, Resulting Numbers: [56, 36] Generated Node #0,1,2: 31:[56, 36] Operation: 45-9=36 Exploring Operation: 56-9=47, Resulting Numbers: [45, 47] Generated Node #0,1,3: 31:[45, 47] Operation: 56-9=47 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[56, 36], Operations: ['70-61=9', '45-9=36'] Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,31 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:[45, 47], Operations: ['70-61=9', '56-9=47'] Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,31 unequal: No Solution Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,31 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:[9, 11], Operations: ['70-61=9', '56-45=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,31 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,31 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:[56, 54], Operations: ['70-61=9', '45+9=54'] Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,31 unequal: No Solution Exploring Operation: 56*54=3024, Resulting Numbers: [3024] 3024,31 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:[61, 56, 25], Operations: ['70-45=25'] Exploring Operation: 56-25=31, Resulting Numbers: [61, 31] Generated Node #0,3,0: 31:[61, 31] Operation: 56-25=31 Exploring Operation: 61-25=36, Resulting Numbers: [56, 36] Generated Node #0,3,1: 31:[56, 36] Operation: 61-25=36 Exploring Operation: 61+25=86, Resulting Numbers: [56, 86] Generated Node #0,3,2: 31:[56, 86] Operation: 61+25=86 Exploring Operation: 61-56=5, Resulting Numbers: [25, 5] Generated Node #0,3,3: 31:[25, 5] Operation: 61-56=5 Moving to Node #0,2 Current State: 31:[45, 61, 14], Operations: ['70-56=14'] Exploring Operation: 61-45=16, Resulting Numbers: [14, 16] Generated Node #0,2,0: 31:[14, 16] Operation: 61-45=16 Exploring Operation: 45-14=31, Resulting Numbers: [61, 31] Generated Node #0,2,1: 31:[61, 31] Operation: 45-14=31 Exploring Operation: 45+14=59, Resulting Numbers: [61, 59] Generated Node #0,2,2: 31:[61, 59] Operation: 45+14=59 Exploring Operation: 61-14=47, Resulting Numbers: [45, 47] Generated Node #0,2,3: 31:[45, 47] Operation: 61-14=47 Moving to Node #0,0 Current State: 31:[56, 70, 16], Operations: ['61-45=16'] Exploring Operation: 70-56=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 31:[16, 14] Operation: 70-56=14 Exploring Operation: 56-16=40, Resulting Numbers: [70, 40] Generated Node #0,0,1: 31:[70, 40] Operation: 56-16=40 Exploring Operation: 70-16=54, Resulting Numbers: [56, 54] Generated Node #0,0,2: 31:[56, 54] Operation: 70-16=54 Exploring Operation: 56+16=72, Resulting Numbers: [70, 72] Generated Node #0,0,3: 31:[70, 72] Operation: 56+16=72 Moving to Node #0,3,0 Current State: 31:[61, 31], Operations: ['70-45=25', '56-25=31'] Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,31 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[45, 47], Operations: ['70-56=14', '61-14=47'] Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,31 unequal: No Solution Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[56, 36], Operations: ['70-45=25', '61-25=36'] Exploring Operation: 56+36=92, Resulting Numbers: [92] 92,31 unequal: No Solution Exploring Operation: 56-36=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 56*36=2016, Resulting Numbers: [2016] 2016,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[61, 31], Operations: ['70-56=14', '45-14=31'] Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,31 unequal: No Solution Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,31 unequal: No Solution Moving to Node #0,2,0 Current State: 31:[14, 16], Operations: ['70-56=14', '61-45=16'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 14*16=224, Resulting Numbers: [224] 224,31 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[25, 5], Operations: ['70-45=25', '61-56=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,31 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[16, 14], Operations: ['61-45=16', '70-56=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,31 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[70, 40], Operations: ['61-45=16', '56-16=40'] Exploring Operation: 70*40=2800, Resulting Numbers: [2800] 2800,31 unequal: No Solution Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[56, 54], Operations: ['61-45=16', '70-16=54'] Exploring Operation: 56+54=110, Resulting Numbers: [110] 110,31 unequal: No Solution Exploring Operation: 56*54=3024, Resulting Numbers: [3024] 3024,31 unequal: No Solution Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[61, 59], Operations: ['70-56=14', '45+14=59'] Exploring Operation: 61*59=3599, Resulting Numbers: [3599] 3599,31 unequal: No Solution Exploring Operation: 61+59=120, Resulting Numbers: [120] 120,31 unequal: No Solution Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[56, 86], Operations: ['70-45=25', '61+25=86'] Exploring Operation: 56+86=142, Resulting Numbers: [142] 142,31 unequal: No Solution Exploring Operation: 56*86=4816, Resulting Numbers: [4816] 4816,31 unequal: No Solution Exploring Operation: 86-56=30, Resulting Numbers: [30] 30,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[70, 72], Operations: ['61-45=16', '56+16=72'] Exploring Operation: 70*72=5040, Resulting Numbers: [5040] 5040,31 unequal: No Solution Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 70+72=142, Resulting Numbers: [142] 142,31 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 62, 12, 21, 45 ]
50
[ "62+12=74", "45-21=24", "74-24=50" ]
Current State: 50:[62, 12, 21, 45], Operations: [] Exploring Operation: 62+12=74, Resulting Numbers: [21, 45, 74] Generated Node #2: [21, 45, 74] from Operation: 62+12=74 Current State: 50:[21, 45, 74], Operations: ['62+12=74'] Exploring Operation: 45-21=24, Resulting Numbers: [74, 24] Generated Node #3: [74, 24] from Operation: 45-21=24 Current State: 50:[74, 24], Operations: ['62+12=74', '45-21=24'] Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[62, 12, 21, 45], Operations: [] Exploring Operation: 62-12=50, Resulting Numbers: [21, 45, 50] Generated Node #0,0: 50:[21, 45, 50] Operation: 62-12=50 Exploring Operation: 45-21=24, Resulting Numbers: [62, 12, 24] Generated Node #0,1: 50:[62, 12, 24] Operation: 45-21=24 Exploring Operation: 62-21=41, Resulting Numbers: [12, 45, 41] Generated Node #0,2: 50:[12, 45, 41] Operation: 62-21=41 Exploring Operation: 62-45=17, Resulting Numbers: [12, 21, 17] Generated Node #0,3: 50:[12, 21, 17] Operation: 62-45=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[21, 45, 50], Operations: ['62-12=50'] Exploring Operation: 45-21=24, Resulting Numbers: [50, 24] Generated Node #0,0,0: 50:[50, 24] Operation: 45-21=24 Exploring Operation: 50-21=29, Resulting Numbers: [45, 29] Generated Node #0,0,1: 50:[45, 29] Operation: 50-21=29 Exploring Operation: 50-45=5, Resulting Numbers: [21, 5] Generated Node #0,0,2: 50:[21, 5] Operation: 50-45=5 Exploring Operation: 21+45=66, Resulting Numbers: [50, 66] Generated Node #0,0,3: 50:[50, 66] Operation: 21+45=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[50, 24], Operations: ['62-12=50', '45-21=24'] Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,50 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 50*24=1200, Resulting Numbers: [1200] 1200,50 unequal: No Solution No 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: 50:[21, 5], Operations: ['62-12=50', '50-45=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,50 unequal: No Solution No 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: 50:[45, 29], Operations: ['62-12=50', '50-21=29'] Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,50 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,50 unequal: No Solution No 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: 50:[50, 66], Operations: ['62-12=50', '21+45=66'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 50+66=116, Resulting Numbers: [116] 116,50 unequal: No Solution Exploring Operation: 50*66=3300, Resulting Numbers: [3300] 3300,50 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: 50:[12, 21, 17], Operations: ['62-45=17'] Exploring Operation: 17-12=5, Resulting Numbers: [21, 5] Generated Node #0,3,0: 50:[21, 5] Operation: 17-12=5 Exploring Operation: 21-17=4, Resulting Numbers: [12, 4] Generated Node #0,3,1: 50:[12, 4] Operation: 21-17=4 Exploring Operation: 21-12=9, Resulting Numbers: [17, 9] Generated Node #0,3,2: 50:[17, 9] Operation: 21-12=9 Exploring Operation: 12+17=29, Resulting Numbers: [21, 29] Generated Node #0,3,3: 50:[21, 29] Operation: 12+17=29 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 50:[12, 4], Operations: ['62-45=17', '21-17=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,50 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,50 unequal: No Solution No 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: 50:[21, 5], Operations: ['62-45=17', '17-12=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,50 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,50 unequal: No Solution No 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: 50:[17, 9], Operations: ['62-45=17', '21-12=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,50 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,50 unequal: No Solution No 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: 50:[21, 29], Operations: ['62-45=17', '12+17=29'] Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,50 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[62, 12, 21, 45], Operations: [] Exploring Operation: 62-45=17, Resulting Numbers: [12, 21, 17] Generated Node #0,3: 50:[12, 21, 17] Operation: 62-45=17 Moving to Node #0,3 Current State: 50:[12, 21, 17], Operations: ['62-45=17'] Exploring Operation: 12+17=29, Resulting Numbers: [21, 29] Generated Node #0,3,3: 50:[21, 29] Operation: 12+17=29 Moving to Node #0,3,3 Current State: 50:[21, 29], Operations: ['62-45=17', '12+17=29'] Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 83, 89, 96, 58 ]
44
[ "89-83=6", "96-58=38", "6+38=44" ]
Current State: 44:[83, 89, 96, 58], Operations: [] Exploring Operation: 89-83=6, Resulting Numbers: [96, 58, 6] Generated Node #2: [96, 58, 6] from Operation: 89-83=6 Current State: 44:[96, 58, 6], Operations: ['89-83=6'] Exploring Operation: 96-58=38, Resulting Numbers: [6, 38] Generated Node #3: [6, 38] from Operation: 96-58=38 Current State: 44:[6, 38], Operations: ['89-83=6', '96-58=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[83, 89, 96, 58], Operations: [] Exploring Operation: 96-83=13, Resulting Numbers: [89, 58, 13] Generated Node #0,0: 44:[89, 58, 13] Operation: 96-83=13 Exploring Operation: 96-89=7, Resulting Numbers: [83, 58, 7] Generated Node #0,1: 44:[83, 58, 7] Operation: 96-89=7 Moving to Node #0,1 Current State: 44:[83, 58, 7], Operations: ['96-89=7'] Exploring Operation: 83-7=76, Resulting Numbers: [58, 76] Generated Node #0,1,0: 44:[58, 76] Operation: 83-7=76 Exploring Operation: 83-58=25, Resulting Numbers: [7, 25] Generated Node #0,1,1: 44:[7, 25] Operation: 83-58=25 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[7, 25], Operations: ['96-89=7', '83-58=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[58, 76], Operations: ['96-89=7', '83-7=76'] Exploring Operation: 58+76=134, Resulting Numbers: [134] 134,44 unequal: No Solution Exploring Operation: 76-58=18, Resulting Numbers: [18] 18,44 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: 44:[89, 58, 13], Operations: ['96-83=13'] Exploring Operation: 89-13=76, Resulting Numbers: [58, 76] Generated Node #0,0,0: 44:[58, 76] Operation: 89-13=76 Exploring Operation: 89-58=31, Resulting Numbers: [13, 31] Generated Node #0,0,1: 44:[13, 31] Operation: 89-58=31 Moving to Node #0,0,1 Current State: 44:[13, 31], Operations: ['96-83=13', '89-58=31'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[83, 89, 96, 58], Operations: [] Exploring Operation: 96-83=13, Resulting Numbers: [89, 58, 13] Generated Node #0,0: 44:[89, 58, 13] Operation: 96-83=13 Moving to Node #0,0 Current State: 44:[89, 58, 13], Operations: ['96-83=13'] Exploring Operation: 89-58=31, Resulting Numbers: [13, 31] Generated Node #0,0,1: 44:[13, 31] Operation: 89-58=31 Moving to Node #0,0,1 Current State: 44:[13, 31], Operations: ['96-83=13', '89-58=31'] Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 33, 56, 2, 68 ]
19
[ "33+56=89", "2+68=70", "89-70=19" ]
Current State: 19:[33, 56, 2, 68], Operations: [] Exploring Operation: 33+56=89, Resulting Numbers: [2, 68, 89] Generated Node #2: [2, 68, 89] from Operation: 33+56=89 Current State: 19:[2, 68, 89], Operations: ['33+56=89'] Exploring Operation: 2+68=70, Resulting Numbers: [89, 70] Generated Node #3: [89, 70] from Operation: 2+68=70 Current State: 19:[89, 70], Operations: ['33+56=89', '2+68=70'] Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[33, 56, 2, 68], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [33, 2, 12] Generated Node #0,0: 19:[33, 2, 12] Operation: 68-56=12 Moving to Node #0,0 Current State: 19:[33, 2, 12], Operations: ['68-56=12'] Exploring Operation: 33-2=31, Resulting Numbers: [12, 31] Generated Node #0,0,0: 19:[12, 31] Operation: 33-2=31 Moving to Node #0,0,0 Current State: 19:[12, 31], Operations: ['68-56=12', '33-2=31'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[33, 56, 2, 68], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [33, 2, 12] Generated Node #0,0: 19:[33, 2, 12] Operation: 68-56=12 Moving to Node #0,0 Current State: 19:[33, 2, 12], Operations: ['68-56=12'] Exploring Operation: 33-2=31, Resulting Numbers: [12, 31] Generated Node #0,0,0: 19:[12, 31] Operation: 33-2=31 Moving to Node #0,0,0 Current State: 19:[12, 31], Operations: ['68-56=12', '33-2=31'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 75, 83, 2, 73 ]
79
[ "83-75=8", "73-2=71", "8+71=79" ]
Current State: 79:[75, 83, 2, 73], Operations: [] Exploring Operation: 83-75=8, Resulting Numbers: [2, 73, 8] Generated Node #2: [2, 73, 8] from Operation: 83-75=8 Current State: 79:[2, 73, 8], Operations: ['83-75=8'] Exploring Operation: 73-2=71, Resulting Numbers: [8, 71] Generated Node #3: [8, 71] from Operation: 73-2=71 Current State: 79:[8, 71], Operations: ['83-75=8', '73-2=71'] Exploring Operation: 8+71=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[75, 83, 2, 73], Operations: [] Exploring Operation: 2+73=75, Resulting Numbers: [75, 83, 75] Generated Node #0,0: 79:[75, 83, 75] Operation: 2+73=75 Exploring Operation: 83-2=81, Resulting Numbers: [75, 73, 81] Generated Node #0,1: 79:[75, 73, 81] Operation: 83-2=81 Exploring Operation: 75-2=73, Resulting Numbers: [83, 73, 73] Generated Node #0,2: 79:[83, 73, 73] Operation: 75-2=73 Exploring Operation: 75+2=77, Resulting Numbers: [83, 73, 77] Generated Node #0,3: 79:[83, 73, 77] Operation: 75+2=77 Moving to Node #0,0 Current State: 79:[75, 83, 75], Operations: ['2+73=75'] Exploring Operation: 83-75=8, Resulting Numbers: [75, 8] Generated Node #0,0,0: 79:[75, 8] Operation: 83-75=8 Exploring Operation: 83-75=8, Resulting Numbers: [75, 8] Generated Node #0,0,1: 79:[75, 8] Operation: 83-75=8 Exploring Operation: 75+75=150, Resulting Numbers: [83, 150] Generated Node #0,0,2: 79:[83, 150] Operation: 75+75=150 Exploring Operation: 75/75=1, Resulting Numbers: [83, 1] Generated Node #0,0,3: 79:[83, 1] Operation: 75/75=1 Moving to Node #0,3 Current State: 79:[83, 73, 77], Operations: ['75+2=77'] Exploring Operation: 83-77=6, Resulting Numbers: [73, 6] Generated Node #0,3,0: 79:[73, 6] Operation: 83-77=6 Exploring Operation: 83+73=156, Resulting Numbers: [77, 156] Generated Node #0,3,1: 79:[77, 156] Operation: 83+73=156 Exploring Operation: 83-73=10, Resulting Numbers: [77, 10] Generated Node #0,3,2: 79:[77, 10] Operation: 83-73=10 Exploring Operation: 73+77=150, Resulting Numbers: [83, 150] Generated Node #0,3,3: 79:[83, 150] Operation: 73+77=150 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[77, 10], Operations: ['75+2=77', '83-73=10'] Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,79 unequal: No Solution Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,79 unequal: No Solution Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[83, 150], Operations: ['75+2=77', '73+77=150'] Exploring Operation: 83*150=12450, Resulting Numbers: [12450] 12450,79 unequal: No Solution Exploring Operation: 83+150=233, Resulting Numbers: [233] 233,79 unequal: No Solution Exploring Operation: 150-83=67, Resulting Numbers: [67] 67,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[73, 6], Operations: ['75+2=77', '83-77=6'] Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,79 unequal: No Solution Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[75, 83, 2, 73], Operations: [] Exploring Operation: 75+2=77, Resulting Numbers: [83, 73, 77] Generated Node #0,3: 79:[83, 73, 77] Operation: 75+2=77 Moving to Node #0,3 Current State: 79:[83, 73, 77], Operations: ['75+2=77'] Exploring Operation: 83-77=6, Resulting Numbers: [73, 6] Generated Node #0,3,0: 79:[73, 6] Operation: 83-77=6 Moving to Node #0,3,0 Current State: 79:[73, 6], Operations: ['75+2=77', '83-77=6'] Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 30, 98, 76, 48 ]
40
[ "98-30=68", "76-48=28", "68-28=40" ]
Current State: 40:[30, 98, 76, 48], Operations: [] Exploring Operation: 98-30=68, Resulting Numbers: [76, 48, 68] Generated Node #2: [76, 48, 68] from Operation: 98-30=68 Current State: 40:[76, 48, 68], Operations: ['98-30=68'] Exploring Operation: 76-48=28, Resulting Numbers: [68, 28] Generated Node #3: [68, 28] from Operation: 76-48=28 Current State: 40:[68, 28], Operations: ['98-30=68', '76-48=28'] Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[30, 98, 76, 48], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [30, 98, 28] Generated Node #0,0: 40:[30, 98, 28] Operation: 76-48=28 Exploring Operation: 98-76=22, Resulting Numbers: [30, 48, 22] Generated Node #0,1: 40:[30, 48, 22] Operation: 98-76=22 Exploring Operation: 76-30=46, Resulting Numbers: [98, 48, 46] Generated Node #0,2: 40:[98, 48, 46] Operation: 76-30=46 Exploring Operation: 98-30=68, Resulting Numbers: [76, 48, 68] Generated Node #0,3: 40:[76, 48, 68] Operation: 98-30=68 Exploring Operation: 98-48=50, Resulting Numbers: [30, 76, 50] Generated Node #0,4: 40:[30, 76, 50] Operation: 98-48=50 Moving to Node #0,1 Current State: 40:[30, 48, 22], Operations: ['98-76=22'] Exploring Operation: 30+22=52, Resulting Numbers: [48, 52] Generated Node #0,1,0: 40:[48, 52] Operation: 30+22=52 Exploring Operation: 48-30=18, Resulting Numbers: [22, 18] Generated Node #0,1,1: 40:[22, 18] Operation: 48-30=18 Exploring Operation: 30+48=78, Resulting Numbers: [22, 78] Generated Node #0,1,2: 40:[22, 78] Operation: 30+48=78 Exploring Operation: 48-22=26, Resulting Numbers: [30, 26] Generated Node #0,1,3: 40:[30, 26] Operation: 48-22=26 Exploring Operation: 30-22=8, Resulting Numbers: [48, 8] Generated Node #0,1,4: 40:[48, 8] Operation: 30-22=8 Moving to Node #0,4 Current State: 40:[30, 76, 50], Operations: ['98-48=50'] Exploring Operation: 50-30=20, Resulting Numbers: [76, 20] Generated Node #0,4,0: 40:[76, 20] Operation: 50-30=20 Exploring Operation: 76-50=26, Resulting Numbers: [30, 26] Generated Node #0,4,1: 40:[30, 26] Operation: 76-50=26 Exploring Operation: 30+76=106, Resulting Numbers: [50, 106] Generated Node #0,4,2: 40:[50, 106] Operation: 30+76=106 Exploring Operation: 30+50=80, Resulting Numbers: [76, 80] Generated Node #0,4,3: 40:[76, 80] Operation: 30+50=80 Exploring Operation: 76-30=46, Resulting Numbers: [50, 46] Generated Node #0,4,4: 40:[50, 46] Operation: 76-30=46 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 40:[30, 26], Operations: ['98-48=50', '76-50=26'] Exploring Operation: 30-26=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 30*26=780, Resulting Numbers: [780] 780,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 40:[50, 46], Operations: ['98-48=50', '76-30=46'] Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 50*46=2300, Resulting Numbers: [2300] 2300,40 unequal: No Solution Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 40:[76, 20], Operations: ['98-48=50', '50-30=20'] Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 40:[50, 106], Operations: ['98-48=50', '30+76=106'] Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,40 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,40 unequal: No Solution Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 40:[76, 80], Operations: ['98-48=50', '30+50=80'] Exploring Operation: 80-76=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 76*80=6080, Resulting Numbers: [6080] 6080,40 unequal: No Solution Exploring Operation: 76+80=156, Resulting Numbers: [156] 156,40 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: 40:[98, 48, 46], Operations: ['76-30=46'] Exploring Operation: 98-46=52, Resulting Numbers: [48, 52] Generated Node #0,2,0: 40:[48, 52] Operation: 98-46=52 Exploring Operation: 48-46=2, Resulting Numbers: [98, 2] Generated Node #0,2,1: 40:[98, 2] Operation: 48-46=2 Exploring Operation: 98+46=144, Resulting Numbers: [48, 144] Generated Node #0,2,2: 40:[48, 144] Operation: 98+46=144 Exploring Operation: 98-48=50, Resulting Numbers: [46, 50] Generated Node #0,2,3: 40:[46, 50] Operation: 98-48=50 Exploring Operation: 98+48=146, Resulting Numbers: [46, 146] Generated Node #0,2,4: 40:[46, 146] Operation: 98+48=146 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 40:[46, 50], Operations: ['76-30=46', '98-48=50'] Exploring Operation: 46*50=2300, Resulting Numbers: [2300] 2300,40 unequal: No Solution Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 46+50=96, Resulting Numbers: [96] 96,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[48, 52], Operations: ['76-30=46', '98-46=52'] Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,40 unequal: No Solution Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,40 unequal: No Solution Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[98, 2], Operations: ['76-30=46', '48-46=2'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,40 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,40 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[48, 144], Operations: ['76-30=46', '98+46=144'] Exploring Operation: 144-48=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 144/48=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 48+144=192, Resulting Numbers: [192] 192,40 unequal: No Solution Exploring Operation: 48*144=6912, Resulting Numbers: [6912] 6912,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 40:[46, 146], Operations: ['76-30=46', '98+48=146'] Exploring Operation: 46+146=192, Resulting Numbers: [192] 192,40 unequal: No Solution Exploring Operation: 146-46=100, Resulting Numbers: [100] 100,40 unequal: No Solution Exploring Operation: 46*146=6716, Resulting Numbers: [6716] 6716,40 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: 40:[76, 48, 68], Operations: ['98-30=68'] Exploring Operation: 76-48=28, Resulting Numbers: [68, 28] Generated Node #0,3,0: 40:[68, 28] Operation: 76-48=28 Exploring Operation: 68-48=20, Resulting Numbers: [76, 20] Generated Node #0,3,1: 40:[76, 20] Operation: 68-48=20 Exploring Operation: 76-68=8, Resulting Numbers: [48, 8] Generated Node #0,3,2: 40:[48, 8] Operation: 76-68=8 Exploring Operation: 76+68=144, Resulting Numbers: [48, 144] Generated Node #0,3,3: 40:[48, 144] Operation: 76+68=144 Exploring Operation: 76+48=124, Resulting Numbers: [68, 124] Generated Node #0,3,4: 40:[68, 124] Operation: 76+48=124 Moving to Node #0,0 Current State: 40:[30, 98, 28], Operations: ['76-48=28'] Exploring Operation: 30-28=2, Resulting Numbers: [98, 2] Generated Node #0,0,0: 40:[98, 2] Operation: 30-28=2 Exploring Operation: 98-28=70, Resulting Numbers: [30, 70] Generated Node #0,0,1: 40:[30, 70] Operation: 98-28=70 Exploring Operation: 30+28=58, Resulting Numbers: [98, 58] Generated Node #0,0,2: 40:[98, 58] Operation: 30+28=58 Exploring Operation: 98-30=68, Resulting Numbers: [28, 68] Generated Node #0,0,3: 40:[28, 68] Operation: 98-30=68 Exploring Operation: 30+98=128, Resulting Numbers: [28, 128] Generated Node #0,0,4: 40:[28, 128] Operation: 30+98=128 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 40:[28, 68], Operations: ['76-48=28', '98-30=68'] Exploring Operation: 28*68=1904, Resulting Numbers: [1904] 1904,40 unequal: No Solution Exploring Operation: 28+68=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[30, 98, 76, 48], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [30, 98, 28] Generated Node #0,0: 40:[30, 98, 28] Operation: 76-48=28 Moving to Node #0,0 Current State: 40:[30, 98, 28], Operations: ['76-48=28'] Exploring Operation: 98-30=68, Resulting Numbers: [28, 68] Generated Node #0,0,3: 40:[28, 68] Operation: 98-30=68 Moving to Node #0,0,3 Current State: 40:[28, 68], Operations: ['76-48=28', '98-30=68'] Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_5
mult_heuristic
[ 89, 4, 2, 82 ]
20
[ "89-2=87", "87-82=5", "4*5=20" ]
Current State: 20:[89, 4, 2, 82], Operations: [] Exploring Operation: 89-2=87, Resulting Numbers: [4, 82, 87] Generated Node #2: [4, 82, 87] from Operation: 89-2=87 Current State: 20:[4, 82, 87], Operations: ['89-2=87'] Exploring Operation: 87-82=5, Resulting Numbers: [4, 5] Generated Node #3: [4, 5] from Operation: 87-82=5 Current State: 20:[4, 5], Operations: ['89-2=87', '87-82=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[89, 4, 2, 82], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [2, 82, 85] Generated Node #0,0: 20:[2, 82, 85] Operation: 89-4=85 Exploring Operation: 82-4=78, Resulting Numbers: [89, 2, 78] Generated Node #0,1: 20:[89, 2, 78] Operation: 82-4=78 Exploring Operation: 89-82=7, Resulting Numbers: [4, 2, 7] Generated Node #0,2: 20:[4, 2, 7] Operation: 89-82=7 Exploring Operation: 82/2=41, Resulting Numbers: [89, 4, 41] Generated Node #0,3: 20:[89, 4, 41] Operation: 82/2=41 Moving to Node #0,2 Current State: 20:[4, 2, 7], Operations: ['89-82=7'] Exploring Operation: 2+7=9, Resulting Numbers: [4, 9] Generated Node #0,2,0: 20:[4, 9] Operation: 2+7=9 Exploring Operation: 7-2=5, Resulting Numbers: [4, 5] Generated Node #0,2,1: 20:[4, 5] Operation: 7-2=5 Exploring Operation: 4+7=11, Resulting Numbers: [2, 11] Generated Node #0,2,2: 20:[2, 11] Operation: 4+7=11 Exploring Operation: 7-4=3, Resulting Numbers: [2, 3] Generated Node #0,2,3: 20:[2, 3] Operation: 7-4=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[4, 5], Operations: ['89-82=7', '7-2=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[89, 4, 2, 82], Operations: [] Exploring Operation: 89-82=7, Resulting Numbers: [4, 2, 7] Generated Node #0,2: 20:[4, 2, 7] Operation: 89-82=7 Moving to Node #0,2 Current State: 20:[4, 2, 7], Operations: ['89-82=7'] Exploring Operation: 7-2=5, Resulting Numbers: [4, 5] Generated Node #0,2,1: 20:[4, 5] Operation: 7-2=5 Moving to Node #0,2,1 Current State: 20:[4, 5], Operations: ['89-82=7', '7-2=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 86, 50, 54, 70 ]
48
[ "86+54=140", "140/70=2", "50-2=48" ]
Current State: 48:[86, 50, 54, 70], Operations: [] Exploring Operation: 86+54=140, Resulting Numbers: [50, 70, 140] Generated Node #2: [50, 70, 140] from Operation: 86+54=140 Current State: 48:[50, 70, 140], Operations: ['86+54=140'] Exploring Operation: 140/70=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 140/70=2 Current State: 48:[50, 2], Operations: ['86+54=140', '140/70=2'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[86, 50, 54, 70], Operations: [] Exploring Operation: 86-54=32, Resulting Numbers: [50, 70, 32] Generated Node #0,0: 48:[50, 70, 32] Operation: 86-54=32 Exploring Operation: 86-70=16, Resulting Numbers: [50, 54, 16] Generated Node #0,1: 48:[50, 54, 16] Operation: 86-70=16 Moving to Node #0,1 Current State: 48:[50, 54, 16], Operations: ['86-70=16'] Exploring Operation: 54-16=38, Resulting Numbers: [50, 38] Generated Node #0,1,0: 48:[50, 38] Operation: 54-16=38 Exploring Operation: 54-50=4, Resulting Numbers: [16, 4] Generated Node #0,1,1: 48:[16, 4] Operation: 54-50=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 48:[16, 4], Operations: ['86-70=16', '54-50=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,48 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[50, 38], Operations: ['86-70=16', '54-16=38'] Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 48:[50, 70, 32], Operations: ['86-54=32'] Exploring Operation: 70-32=38, Resulting Numbers: [50, 38] Generated Node #0,0,0: 48:[50, 38] Operation: 70-32=38 Exploring Operation: 70-50=20, Resulting Numbers: [32, 20] Generated Node #0,0,1: 48:[32, 20] Operation: 70-50=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[50, 38], Operations: ['86-54=32', '70-32=38'] Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,48 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,48 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 #0,0,1 Current State: 48:[32, 20], Operations: ['86-54=32', '70-50=20'] Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,48 unequal: No Solution Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 69, 24, 18, 29 ]
46
[ "69+24=93", "18+29=47", "93-47=46" ]
Current State: 46:[69, 24, 18, 29], Operations: [] Exploring Operation: 69+24=93, Resulting Numbers: [18, 29, 93] Generated Node #2: [18, 29, 93] from Operation: 69+24=93 Current State: 46:[18, 29, 93], Operations: ['69+24=93'] Exploring Operation: 18+29=47, Resulting Numbers: [93, 47] Generated Node #3: [93, 47] from Operation: 18+29=47 Current State: 46:[93, 47], Operations: ['69+24=93', '18+29=47'] Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[69, 24, 18, 29], Operations: [] Exploring Operation: 18+29=47, Resulting Numbers: [69, 24, 47] Generated Node #0,0: 46:[69, 24, 47] Operation: 18+29=47 Exploring Operation: 69-24=45, Resulting Numbers: [18, 29, 45] Generated Node #0,1: 46:[18, 29, 45] Operation: 69-24=45 Exploring Operation: 69-29=40, Resulting Numbers: [24, 18, 40] Generated Node #0,2: 46:[24, 18, 40] Operation: 69-29=40 Exploring Operation: 69-18=51, Resulting Numbers: [24, 29, 51] Generated Node #0,3: 46:[24, 29, 51] Operation: 69-18=51 Exploring Operation: 29-24=5, Resulting Numbers: [69, 18, 5] Generated Node #0,4: 46:[69, 18, 5] Operation: 29-24=5 Moving to Node #0,1 Current State: 46:[18, 29, 45], Operations: ['69-24=45'] Exploring Operation: 45-18=27, Resulting Numbers: [29, 27] Generated Node #0,1,0: 46:[29, 27] Operation: 45-18=27 Exploring Operation: 29-18=11, Resulting Numbers: [45, 11] Generated Node #0,1,1: 46:[45, 11] Operation: 29-18=11 Exploring Operation: 45-29=16, Resulting Numbers: [18, 16] Generated Node #0,1,2: 46:[18, 16] Operation: 45-29=16 Exploring Operation: 18+45=63, Resulting Numbers: [29, 63] Generated Node #0,1,3: 46:[29, 63] Operation: 18+45=63 Exploring Operation: 18+29=47, Resulting Numbers: [45, 47] Generated Node #0,1,4: 46:[45, 47] Operation: 18+29=47 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 46:[45, 47], Operations: ['69-24=45', '18+29=47'] Exploring Operation: 45+47=92, Resulting Numbers: [92] 92,46 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 45*47=2115, Resulting Numbers: [2115] 2115,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[29, 27], Operations: ['69-24=45', '45-18=27'] Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,46 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[45, 11], Operations: ['69-24=45', '29-18=11'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,46 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,46 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[18, 16], Operations: ['69-24=45', '45-29=16'] Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,46 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 46:[29, 63], Operations: ['69-24=45', '18+45=63'] Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,46 unequal: No Solution Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,46 unequal: No Solution Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,46 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: 46:[24, 29, 51], Operations: ['69-18=51'] Exploring Operation: 24+29=53, Resulting Numbers: [51, 53] Generated Node #0,3,0: 46:[51, 53] Operation: 24+29=53 Exploring Operation: 29-24=5, Resulting Numbers: [51, 5] Generated Node #0,3,1: 46:[51, 5] Operation: 29-24=5 Exploring Operation: 51-24=27, Resulting Numbers: [29, 27] Generated Node #0,3,2: 46:[29, 27] Operation: 51-24=27 Exploring Operation: 24+51=75, Resulting Numbers: [29, 75] Generated Node #0,3,3: 46:[29, 75] Operation: 24+51=75 Exploring Operation: 51-29=22, Resulting Numbers: [24, 22] Generated Node #0,3,4: 46:[24, 22] Operation: 51-29=22 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 46:[24, 22], Operations: ['69-18=51', '51-29=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,46 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[69, 24, 18, 29], Operations: [] Exploring Operation: 69-18=51, Resulting Numbers: [24, 29, 51] Generated Node #0,3: 46:[24, 29, 51] Operation: 69-18=51 Moving to Node #0,3 Current State: 46:[24, 29, 51], Operations: ['69-18=51'] Exploring Operation: 51-29=22, Resulting Numbers: [24, 22] Generated Node #0,3,4: 46:[24, 22] Operation: 51-29=22 Moving to Node #0,3,4 Current State: 46:[24, 22], Operations: ['69-18=51', '51-29=22'] Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 45, 44, 25, 67 ]
91
[ "45-44=1", "25+67=92", "92-1=91" ]
Current State: 91:[45, 44, 25, 67], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [25, 67, 1] Generated Node #2: [25, 67, 1] from Operation: 45-44=1 Current State: 91:[25, 67, 1], Operations: ['45-44=1'] Exploring Operation: 25+67=92, Resulting Numbers: [1, 92] Generated Node #3: [1, 92] from Operation: 25+67=92 Current State: 91:[1, 92], Operations: ['45-44=1', '25+67=92'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[45, 44, 25, 67], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [25, 67, 1] Generated Node #0,0: 91:[25, 67, 1] Operation: 45-44=1 Exploring Operation: 45+44=89, Resulting Numbers: [25, 67, 89] Generated Node #0,1: 91:[25, 67, 89] Operation: 45+44=89 Moving to Node #0,1 Current State: 91:[25, 67, 89], Operations: ['45+44=89'] Exploring Operation: 89-67=22, Resulting Numbers: [25, 22] Generated Node #0,1,0: 91:[25, 22] Operation: 89-67=22 Exploring Operation: 25+67=92, Resulting Numbers: [89, 92] Generated Node #0,1,1: 91:[89, 92] Operation: 25+67=92 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[89, 92], Operations: ['45+44=89', '25+67=92'] Exploring Operation: 92-89=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 89+92=181, Resulting Numbers: [181] 181,91 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 #0,1,0 Current State: 91:[25, 22], Operations: ['45+44=89', '89-67=22'] Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,91 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: 91:[25, 67, 1], Operations: ['45-44=1'] Exploring Operation: 25+67=92, Resulting Numbers: [1, 92] Generated Node #0,0,0: 91:[1, 92] Operation: 25+67=92 Exploring Operation: 67-25=42, Resulting Numbers: [1, 42] Generated Node #0,0,1: 91:[1, 42] Operation: 67-25=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[1, 92], Operations: ['45-44=1', '25+67=92'] Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[45, 44, 25, 67], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [25, 67, 1] Generated Node #0,0: 91:[25, 67, 1] Operation: 45-44=1 Moving to Node #0,0 Current State: 91:[25, 67, 1], Operations: ['45-44=1'] Exploring Operation: 25+67=92, Resulting Numbers: [1, 92] Generated Node #0,0,0: 91:[1, 92] Operation: 25+67=92 Moving to Node #0,0,0 Current State: 91:[1, 92], Operations: ['45-44=1', '25+67=92'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 12, 22, 21, 75 ]
66
[ "75-12=63", "22*63=1386", "1386/21=66" ]
Current State: 66:[12, 22, 21, 75], Operations: [] Exploring Operation: 75-12=63, Resulting Numbers: [22, 21, 63] Generated Node #2: [22, 21, 63] from Operation: 75-12=63 Current State: 66:[22, 21, 63], Operations: ['75-12=63'] Exploring Operation: 22*63=1386, Resulting Numbers: [21, 1386] Generated Node #3: [21, 1386] from Operation: 22*63=1386 Current State: 66:[21, 1386], Operations: ['75-12=63', '22*63=1386'] Exploring Operation: 1386/21=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[12, 22, 21, 75], Operations: [] Exploring Operation: 75-12=63, Resulting Numbers: [22, 21, 63] Generated Node #0,0: 66:[22, 21, 63] Operation: 75-12=63 Exploring Operation: 12+21=33, Resulting Numbers: [22, 75, 33] Generated Node #0,1: 66:[22, 75, 33] Operation: 12+21=33 Moving to Node #0,0 Current State: 66:[22, 21, 63], Operations: ['75-12=63'] Exploring Operation: 63/21=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 66:[22, 3] Operation: 63/21=3 Exploring Operation: 22-21=1, Resulting Numbers: [63, 1] Generated Node #0,0,1: 66:[63, 1] Operation: 22-21=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[22, 3], Operations: ['75-12=63', '63/21=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[12, 22, 21, 75], Operations: [] Exploring Operation: 75-12=63, Resulting Numbers: [22, 21, 63] Generated Node #0,0: 66:[22, 21, 63] Operation: 75-12=63 Moving to Node #0,0 Current State: 66:[22, 21, 63], Operations: ['75-12=63'] Exploring Operation: 63/21=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 66:[22, 3] Operation: 63/21=3 Moving to Node #0,0,0 Current State: 66:[22, 3], Operations: ['75-12=63', '63/21=3'] Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 6, 4, 38, 54 ]
82
[ "6+4=10", "38+54=92", "92-10=82" ]
Current State: 82:[6, 4, 38, 54], Operations: [] Exploring Operation: 6+4=10, Resulting Numbers: [38, 54, 10] Generated Node #2: [38, 54, 10] from Operation: 6+4=10 Current State: 82:[38, 54, 10], Operations: ['6+4=10'] Exploring Operation: 38+54=92, Resulting Numbers: [10, 92] Generated Node #3: [10, 92] from Operation: 38+54=92 Current State: 82:[10, 92], Operations: ['6+4=10', '38+54=92'] Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[6, 4, 38, 54], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [4, 38, 9] Generated Node #0,0: 82:[4, 38, 9] Operation: 54/6=9 Exploring Operation: 54-4=50, Resulting Numbers: [6, 38, 50] Generated Node #0,1: 82:[6, 38, 50] Operation: 54-4=50 Exploring Operation: 6-4=2, Resulting Numbers: [38, 54, 2] Generated Node #0,2: 82:[38, 54, 2] Operation: 6-4=2 Exploring Operation: 54-6=48, Resulting Numbers: [4, 38, 48] Generated Node #0,3: 82:[4, 38, 48] Operation: 54-6=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[4, 38, 9], Operations: ['54/6=9'] Exploring Operation: 4+38=42, Resulting Numbers: [9, 42] Generated Node #0,0,0: 82:[9, 42] Operation: 4+38=42 Exploring Operation: 4*9=36, Resulting Numbers: [38, 36] Generated Node #0,0,1: 82:[38, 36] Operation: 4*9=36 Exploring Operation: 9-4=5, Resulting Numbers: [38, 5] Generated Node #0,0,2: 82:[38, 5] Operation: 9-4=5 Exploring Operation: 38+9=47, Resulting Numbers: [4, 47] Generated Node #0,0,3: 82:[4, 47] Operation: 38+9=47 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[38, 5], Operations: ['54/6=9', '9-4=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,82 unequal: No Solution No 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: 82:[9, 42], Operations: ['54/6=9', '4+38=42'] Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,82 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,82 unequal: No Solution No 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: 82:[38, 36], Operations: ['54/6=9', '4*9=36'] Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,82 unequal: No Solution Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,82 unequal: No Solution No 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: 82:[4, 47], Operations: ['54/6=9', '38+9=47'] Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,82 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,82 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: 82:[4, 38, 48], Operations: ['54-6=48'] Exploring Operation: 4+38=42, Resulting Numbers: [48, 42] Generated Node #0,3,0: 82:[48, 42] Operation: 4+38=42 Exploring Operation: 38+48=86, Resulting Numbers: [4, 86] Generated Node #0,3,1: 82:[4, 86] Operation: 38+48=86 Exploring Operation: 48-38=10, Resulting Numbers: [4, 10] Generated Node #0,3,2: 82:[4, 10] Operation: 48-38=10 Exploring Operation: 48-4=44, Resulting Numbers: [38, 44] Generated Node #0,3,3: 82:[38, 44] Operation: 48-4=44 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[4, 86], Operations: ['54-6=48', '38+48=86'] Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,82 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,82 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[6, 4, 38, 54], Operations: [] Exploring Operation: 54-6=48, Resulting Numbers: [4, 38, 48] Generated Node #0,3: 82:[4, 38, 48] Operation: 54-6=48 Moving to Node #0,3 Current State: 82:[4, 38, 48], Operations: ['54-6=48'] Exploring Operation: 38+48=86, Resulting Numbers: [4, 86] Generated Node #0,3,1: 82:[4, 86] Operation: 38+48=86 Moving to Node #0,3,1 Current State: 82:[4, 86], Operations: ['54-6=48', '38+48=86'] Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 64, 86, 58, 6 ]
98
[ "64+86=150", "58-6=52", "150-52=98" ]
Current State: 98:[64, 86, 58, 6], Operations: [] Exploring Operation: 64+86=150, Resulting Numbers: [58, 6, 150] Generated Node #2: [58, 6, 150] from Operation: 64+86=150 Current State: 98:[58, 6, 150], Operations: ['64+86=150'] Exploring Operation: 58-6=52, Resulting Numbers: [150, 52] Generated Node #3: [150, 52] from Operation: 58-6=52 Current State: 98:[150, 52], Operations: ['64+86=150', '58-6=52'] Exploring Operation: 150-52=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[64, 86, 58, 6], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [86, 6, 6] Generated Node #0,0: 98:[86, 6, 6] Operation: 64-58=6 Exploring Operation: 86-64=22, Resulting Numbers: [58, 6, 22] Generated Node #0,1: 98:[58, 6, 22] Operation: 86-64=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[86, 6, 6], Operations: ['64-58=6'] Exploring Operation: 86+6=92, Resulting Numbers: [6, 92] Generated Node #0,0,0: 98:[6, 92] Operation: 86+6=92 Exploring Operation: 86+6=92, Resulting Numbers: [6, 92] Generated Node #0,0,1: 98:[6, 92] Operation: 86+6=92 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[6, 92], Operations: ['64-58=6', '86+6=92'] Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[64, 86, 58, 6], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [86, 6, 6] Generated Node #0,0: 98:[86, 6, 6] Operation: 64-58=6 Moving to Node #0,0 Current State: 98:[86, 6, 6], Operations: ['64-58=6'] Exploring Operation: 86+6=92, Resulting Numbers: [6, 92] Generated Node #0,0,0: 98:[6, 92] Operation: 86+6=92 Moving to Node #0,0,0 Current State: 98:[6, 92], Operations: ['64-58=6', '86+6=92'] Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 6, 68, 6, 87 ]
78
[ "6+68=74", "87-74=13", "6*13=78" ]
Current State: 78:[6, 68, 6, 87], Operations: [] Exploring Operation: 6+68=74, Resulting Numbers: [87, 74] Generated Node #2: [87, 74] from Operation: 6+68=74 Current State: 78:[87, 74], Operations: ['6+68=74'] Exploring Operation: 87-74=13, Resulting Numbers: [13] 13,78 equal: Goal Reached Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[6, 68, 6, 87], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [6, 6, 19] Generated Node #0,0: 78:[6, 6, 19] Operation: 87-68=19 Exploring Operation: 68+6=74, Resulting Numbers: [6, 87, 74] Generated Node #0,1: 78:[6, 87, 74] Operation: 68+6=74 Exploring Operation: 87-6=81, Resulting Numbers: [68, 6, 81] Generated Node #0,2: 78:[68, 6, 81] Operation: 87-6=81 Exploring Operation: 6+68=74, Resulting Numbers: [6, 87, 74] Generated Node #0,3: 78:[6, 87, 74] Operation: 6+68=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[6, 6, 19], Operations: ['87-68=19'] Exploring Operation: 6+19=25, Resulting Numbers: [6, 25] Generated Node #0,0,0: 78:[6, 25] Operation: 6+19=25 Exploring Operation: 19-6=13, Resulting Numbers: [6, 13] Generated Node #0,0,1: 78:[6, 13] Operation: 19-6=13 Exploring Operation: 6+19=25, Resulting Numbers: [6, 25] Generated Node #0,0,2: 78:[6, 25] Operation: 6+19=25 Exploring Operation: 19-6=13, Resulting Numbers: [6, 13] Generated Node #0,0,3: 78:[6, 13] Operation: 19-6=13 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[6, 13], Operations: ['87-68=19', '19-6=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,78 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[6, 68, 6, 87], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [6, 6, 19] Generated Node #0,0: 78:[6, 6, 19] Operation: 87-68=19 Moving to Node #0,0 Current State: 78:[6, 6, 19], Operations: ['87-68=19'] Exploring Operation: 19-6=13, Resulting Numbers: [6, 13] Generated Node #0,0,1: 78:[6, 13] Operation: 19-6=13 Moving to Node #0,0,1 Current State: 78:[6, 13], Operations: ['87-68=19', '19-6=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 76, 45, 19, 78 ]
71
[ "78-76=2", "45*2=90", "90-19=71" ]
Current State: 71:[76, 45, 19, 78], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [45, 19, 2] Generated Node #2: [45, 19, 2] from Operation: 78-76=2 Current State: 71:[45, 19, 2], Operations: ['78-76=2'] Exploring Operation: 45*2=90, Resulting Numbers: [19, 90] Generated Node #3: [19, 90] from Operation: 45*2=90 Current State: 71:[19, 90], Operations: ['78-76=2', '45*2=90'] Exploring Operation: 90-19=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[76, 45, 19, 78], Operations: [] Exploring Operation: 76-19=57, Resulting Numbers: [45, 78, 57] Generated Node #0,0: 71:[45, 78, 57] Operation: 76-19=57 Exploring Operation: 78-19=59, Resulting Numbers: [76, 45, 59] Generated Node #0,1: 71:[76, 45, 59] Operation: 78-19=59 Exploring Operation: 45+19=64, Resulting Numbers: [76, 78, 64] Generated Node #0,2: 71:[76, 78, 64] Operation: 45+19=64 Moving to Node #0,2 Current State: 71:[76, 78, 64], Operations: ['45+19=64'] Exploring Operation: 78-64=14, Resulting Numbers: [76, 14] Generated Node #0,2,0: 71:[76, 14] Operation: 78-64=14 Exploring Operation: 76-64=12, Resulting Numbers: [78, 12] Generated Node #0,2,1: 71:[78, 12] Operation: 76-64=12 Exploring Operation: 78-76=2, Resulting Numbers: [64, 2] Generated Node #0,2,2: 71:[64, 2] Operation: 78-76=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[76, 14], Operations: ['45+19=64', '78-64=14'] Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,71 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[78, 12], Operations: ['45+19=64', '76-64=12'] Exploring Operation: 78+12=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,71 unequal: No Solution Exploring Operation: 78*12=936, Resulting Numbers: [936] 936,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[64, 2], Operations: ['45+19=64', '78-76=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,71 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[76, 45, 59], Operations: ['78-19=59'] Exploring Operation: 45+59=104, Resulting Numbers: [76, 104] Generated Node #0,1,0: 71:[76, 104] Operation: 45+59=104 Exploring Operation: 76+45=121, Resulting Numbers: [59, 121] Generated Node #0,1,1: 71:[59, 121] Operation: 76+45=121 Exploring Operation: 76-45=31, Resulting Numbers: [59, 31] Generated Node #0,1,2: 71:[59, 31] Operation: 76-45=31 Moving to Node #0,0 Current State: 71:[45, 78, 57], Operations: ['76-19=57'] Exploring Operation: 45+57=102, Resulting Numbers: [78, 102] Generated Node #0,0,0: 71:[78, 102] Operation: 45+57=102 Exploring Operation: 45+78=123, Resulting Numbers: [57, 123] Generated Node #0,0,1: 71:[57, 123] Operation: 45+78=123 Exploring Operation: 78-45=33, Resulting Numbers: [57, 33] Generated Node #0,0,2: 71:[57, 33] Operation: 78-45=33 Moving to Node #0,1,0 Current State: 71:[76, 104], Operations: ['78-19=59', '45+59=104'] Exploring Operation: 76*104=7904, Resulting Numbers: [7904] 7904,71 unequal: No Solution Exploring Operation: 104-76=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 76+104=180, Resulting Numbers: [180] 180,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[78, 102], Operations: ['76-19=57', '45+57=102'] Exploring Operation: 102-78=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 78+102=180, Resulting Numbers: [180] 180,71 unequal: No Solution Exploring Operation: 78*102=7956, Resulting Numbers: [7956] 7956,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[57, 33], Operations: ['76-19=57', '78-45=33'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,71 unequal: No Solution Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 57*33=1881, Resulting Numbers: [1881] 1881,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[59, 31], Operations: ['78-19=59', '76-45=31'] Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,71 unequal: No Solution Exploring Operation: 59*31=1829, Resulting Numbers: [1829] 1829,71 unequal: No Solution Exploring Operation: 59+31=90, Resulting Numbers: [90] 90,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[59, 121], Operations: ['78-19=59', '76+45=121'] Exploring Operation: 121-59=62, Resulting Numbers: [62] 62,71 unequal: No Solution Exploring Operation: 59+121=180, Resulting Numbers: [180] 180,71 unequal: No Solution Exploring Operation: 59*121=7139, Resulting Numbers: [7139] 7139,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[57, 123], Operations: ['76-19=57', '45+78=123'] Exploring Operation: 57*123=7011, Resulting Numbers: [7011] 7011,71 unequal: No Solution Exploring Operation: 123-57=66, Resulting Numbers: [66] 66,71 unequal: No Solution Exploring Operation: 57+123=180, Resulting Numbers: [180] 180,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 38, 88, 77, 3 ]
52
[ "38+88=126", "77-3=74", "126-74=52" ]
Current State: 52:[38, 88, 77, 3], Operations: [] Exploring Operation: 38+88=126, Resulting Numbers: [77, 3, 126] Generated Node #2: [77, 3, 126] from Operation: 38+88=126 Current State: 52:[77, 3, 126], Operations: ['38+88=126'] Exploring Operation: 77-3=74, Resulting Numbers: [126, 74] Generated Node #3: [126, 74] from Operation: 77-3=74 Current State: 52:[126, 74], Operations: ['38+88=126', '77-3=74'] Exploring Operation: 126-74=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[38, 88, 77, 3], Operations: [] Exploring Operation: 88-77=11, Resulting Numbers: [38, 3, 11] Generated Node #0,0: 52:[38, 3, 11] Operation: 88-77=11 Exploring Operation: 88-38=50, Resulting Numbers: [77, 3, 50] Generated Node #0,1: 52:[77, 3, 50] Operation: 88-38=50 Exploring Operation: 77-38=39, Resulting Numbers: [88, 3, 39] Generated Node #0,2: 52:[88, 3, 39] Operation: 77-38=39 Moving to Node #0,0 Current State: 52:[38, 3, 11], Operations: ['88-77=11'] Exploring Operation: 38-3=35, Resulting Numbers: [11, 35] Generated Node #0,0,0: 52:[11, 35] Operation: 38-3=35 Exploring Operation: 38+11=49, Resulting Numbers: [3, 49] Generated Node #0,0,1: 52:[3, 49] Operation: 38+11=49 Exploring Operation: 38-11=27, Resulting Numbers: [3, 27] Generated Node #0,0,2: 52:[3, 27] Operation: 38-11=27 Moving to Node #0,1 Current State: 52:[77, 3, 50], Operations: ['88-38=50'] Exploring Operation: 3+50=53, Resulting Numbers: [77, 53] Generated Node #0,1,0: 52:[77, 53] Operation: 3+50=53 Exploring Operation: 77-3=74, Resulting Numbers: [50, 74] Generated Node #0,1,1: 52:[50, 74] Operation: 77-3=74 Exploring Operation: 77-50=27, Resulting Numbers: [3, 27] Generated Node #0,1,2: 52:[3, 27] Operation: 77-50=27 Moving to Node #0,2 Current State: 52:[88, 3, 39], Operations: ['77-38=39'] Exploring Operation: 88-39=49, Resulting Numbers: [3, 49] Generated Node #0,2,0: 52:[3, 49] Operation: 88-39=49 Exploring Operation: 88-3=85, Resulting Numbers: [39, 85] Generated Node #0,2,1: 52:[39, 85] Operation: 88-3=85 Exploring Operation: 39/3=13, Resulting Numbers: [88, 13] Generated Node #0,2,2: 52:[88, 13] Operation: 39/3=13 Moving to Node #0,0,2 Current State: 52:[3, 27], Operations: ['88-77=11', '38-11=27'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[3, 27], Operations: ['88-38=50', '77-50=27'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[3, 49], Operations: ['77-38=39', '88-39=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,52 unequal: No Solution Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[38, 88, 77, 3], Operations: [] Exploring Operation: 77-38=39, Resulting Numbers: [88, 3, 39] Generated Node #0,2: 52:[88, 3, 39] Operation: 77-38=39 Moving to Node #0,2 Current State: 52:[88, 3, 39], Operations: ['77-38=39'] Exploring Operation: 88-39=49, Resulting Numbers: [3, 49] Generated Node #0,2,0: 52:[3, 49] Operation: 88-39=49 Moving to Node #0,2,0 Current State: 52:[3, 49], Operations: ['77-38=39', '88-39=49'] Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.979167
hs_3
sum_heuristic
[ 2, 64, 7, 8 ]
75
[ "8/2=4", "64+7=71", "4+71=75" ]
Current State: 75:[2, 64, 7, 8], Operations: [] Exploring Operation: 8/2=4, Resulting Numbers: [64, 7, 4] Generated Node #2: [64, 7, 4] from Operation: 8/2=4 Current State: 75:[64, 7, 4], Operations: ['8/2=4'] Exploring Operation: 64+7=71, Resulting Numbers: [4, 71] Generated Node #3: [4, 71] from Operation: 64+7=71 Current State: 75:[4, 71], Operations: ['8/2=4', '64+7=71'] Exploring Operation: 4+71=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[2, 64, 7, 8], Operations: [] Exploring Operation: 64+8=72, Resulting Numbers: [2, 7, 72] Generated Node #0,0: 75:[2, 7, 72] Operation: 64+8=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[2, 7, 72], Operations: ['64+8=72'] Exploring Operation: 7-2=5, Resulting Numbers: [72, 5] Generated Node #0,0,0: 75:[72, 5] Operation: 7-2=5 Moving to Node #0,0,0 Current State: 75:[72, 5], Operations: ['64+8=72', '7-2=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,75 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
[ 40, 28, 7, 15 ]
29
[ "40-15=25", "28/7=4", "25+4=29" ]
Current State: 29:[40, 28, 7, 15], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [28, 7, 25] Generated Node #2: [28, 7, 25] from Operation: 40-15=25 Current State: 29:[28, 7, 25], Operations: ['40-15=25'] Exploring Operation: 28/7=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 28/7=4 Current State: 29:[25, 4], Operations: ['40-15=25', '28/7=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[40, 28, 7, 15], Operations: [] Exploring Operation: 7+15=22, Resulting Numbers: [40, 28, 22] Generated Node #0,0: 29:[40, 28, 22] Operation: 7+15=22 Exploring Operation: 40-7=33, Resulting Numbers: [28, 15, 33] Generated Node #0,1: 29:[28, 15, 33] Operation: 40-7=33 Exploring Operation: 40-15=25, Resulting Numbers: [28, 7, 25] Generated Node #0,2: 29:[28, 7, 25] Operation: 40-15=25 Moving to Node #0,0 Current State: 29:[40, 28, 22], Operations: ['7+15=22'] Exploring Operation: 40-28=12, Resulting Numbers: [22, 12] Generated Node #0,0,0: 29:[22, 12] Operation: 40-28=12 Exploring Operation: 28+22=50, Resulting Numbers: [40, 50] Generated Node #0,0,1: 29:[40, 50] Operation: 28+22=50 Exploring Operation: 40-22=18, Resulting Numbers: [28, 18] Generated Node #0,0,2: 29:[28, 18] Operation: 40-22=18 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[28, 18], Operations: ['7+15=22', '40-22=18'] Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,29 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,29 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 #0,0,0 Current State: 29:[22, 12], Operations: ['7+15=22', '40-28=12'] Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,29 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,29 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 #0,0,1 Current State: 29:[40, 50], Operations: ['7+15=22', '28+22=50'] Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,29 unequal: No Solution Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 29:[28, 15, 33], Operations: ['40-7=33'] Exploring Operation: 28+15=43, Resulting Numbers: [33, 43] Generated Node #0,1,0: 29:[33, 43] Operation: 28+15=43 Exploring Operation: 28-15=13, Resulting Numbers: [33, 13] Generated Node #0,1,1: 29:[33, 13] Operation: 28-15=13 Exploring Operation: 33-15=18, Resulting Numbers: [28, 18] Generated Node #0,1,2: 29:[28, 18] Operation: 33-15=18 Moving to Node #0,2 Current State: 29:[28, 7, 25], Operations: ['40-15=25'] Exploring Operation: 28+7=35, Resulting Numbers: [25, 35] Generated Node #0,2,0: 29:[25, 35] Operation: 28+7=35 Exploring Operation: 28-7=21, Resulting Numbers: [25, 21] Generated Node #0,2,1: 29:[25, 21] Operation: 28-7=21 Exploring Operation: 7+25=32, Resulting Numbers: [28, 32] Generated Node #0,2,2: 29:[28, 32] Operation: 7+25=32 Moving to Node #0,2,2 Current State: 29:[28, 32], Operations: ['40-15=25', '7+25=32'] Exploring Operation: 28*32=896, Resulting Numbers: [896] 896,29 unequal: No Solution Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[25, 35], Operations: ['40-15=25', '28+7=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,29 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[25, 21], Operations: ['40-15=25', '28-7=21'] Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,29 unequal: No Solution Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,29 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[28, 18], Operations: ['40-7=33', '33-15=18'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,29 unequal: No Solution Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[33, 43], Operations: ['40-7=33', '28+15=43'] Exploring Operation: 33*43=1419, Resulting Numbers: [1419] 1419,29 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 33+43=76, Resulting Numbers: [76] 76,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[33, 13], Operations: ['40-7=33', '28-15=13'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,29 unequal: No Solution Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,29 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 83, 33, 7, 73 ]
16
[ "83-33=50", "73-7=66", "66-50=16" ]
Current State: 16:[83, 33, 7, 73], Operations: [] Exploring Operation: 83-33=50, Resulting Numbers: [7, 73, 50] Generated Node #2: [7, 73, 50] from Operation: 83-33=50 Current State: 16:[7, 73, 50], Operations: ['83-33=50'] Exploring Operation: 73-7=66, Resulting Numbers: [50, 66] Generated Node #3: [50, 66] from Operation: 73-7=66 Current State: 16:[50, 66], Operations: ['83-33=50', '73-7=66'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[83, 33, 7, 73], Operations: [] Exploring Operation: 83-7=76, Resulting Numbers: [33, 73, 76] Generated Node #0,0: 16:[33, 73, 76] Operation: 83-7=76 Exploring Operation: 83-73=10, Resulting Numbers: [33, 7, 10] Generated Node #0,1: 16:[33, 7, 10] Operation: 83-73=10 Exploring Operation: 83-33=50, Resulting Numbers: [7, 73, 50] Generated Node #0,2: 16:[7, 73, 50] Operation: 83-33=50 Exploring Operation: 73-33=40, Resulting Numbers: [83, 7, 40] Generated Node #0,3: 16:[83, 7, 40] Operation: 73-33=40 Moving to Node #0,1 Current State: 16:[33, 7, 10], Operations: ['83-73=10'] Exploring Operation: 33-10=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 16:[7, 23] Operation: 33-10=23 Exploring Operation: 7+10=17, Resulting Numbers: [33, 17] Generated Node #0,1,1: 16:[33, 17] Operation: 7+10=17 Exploring Operation: 10-7=3, Resulting Numbers: [33, 3] Generated Node #0,1,2: 16:[33, 3] Operation: 10-7=3 Exploring Operation: 33-7=26, Resulting Numbers: [10, 26] Generated Node #0,1,3: 16:[10, 26] Operation: 33-7=26 Moving to Node #0,3 Current State: 16:[83, 7, 40], Operations: ['73-33=40'] Exploring Operation: 83+7=90, Resulting Numbers: [40, 90] Generated Node #0,3,0: 16:[40, 90] Operation: 83+7=90 Exploring Operation: 40-7=33, Resulting Numbers: [83, 33] Generated Node #0,3,1: 16:[83, 33] Operation: 40-7=33 Exploring Operation: 83-40=43, Resulting Numbers: [7, 43] Generated Node #0,3,2: 16:[7, 43] Operation: 83-40=43 Exploring Operation: 83-7=76, Resulting Numbers: [40, 76] Generated Node #0,3,3: 16:[40, 76] Operation: 83-7=76 Moving to Node #0,2 Current State: 16:[7, 73, 50], Operations: ['83-33=50'] Exploring Operation: 50-7=43, Resulting Numbers: [73, 43] Generated Node #0,2,0: 16:[73, 43] Operation: 50-7=43 Exploring Operation: 73-50=23, Resulting Numbers: [7, 23] Generated Node #0,2,1: 16:[7, 23] Operation: 73-50=23 Exploring Operation: 73-7=66, Resulting Numbers: [50, 66] Generated Node #0,2,2: 16:[50, 66] Operation: 73-7=66 Exploring Operation: 7+73=80, Resulting Numbers: [50, 80] Generated Node #0,2,3: 16:[50, 80] Operation: 7+73=80 Moving to Node #0,0 Current State: 16:[33, 73, 76], Operations: ['83-7=76'] Exploring Operation: 33+73=106, Resulting Numbers: [76, 106] Generated Node #0,0,0: 16:[76, 106] Operation: 33+73=106 Exploring Operation: 76-33=43, Resulting Numbers: [73, 43] Generated Node #0,0,1: 16:[73, 43] Operation: 76-33=43 Exploring Operation: 73-33=40, Resulting Numbers: [76, 40] Generated Node #0,0,2: 16:[76, 40] Operation: 73-33=40 Exploring Operation: 76-73=3, Resulting Numbers: [33, 3] Generated Node #0,0,3: 16:[33, 3] Operation: 76-73=3 Moving to Node #0,1,0 Current State: 16:[7, 23], Operations: ['83-73=10', '33-10=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[83, 33, 7, 73], Operations: [] Exploring Operation: 83-73=10, Resulting Numbers: [33, 7, 10] Generated Node #0,1: 16:[33, 7, 10] Operation: 83-73=10 Moving to Node #0,1 Current State: 16:[33, 7, 10], Operations: ['83-73=10'] Exploring Operation: 33-10=23, Resulting Numbers: [7, 23] Generated Node #0,1,0: 16:[7, 23] Operation: 33-10=23 Moving to Node #0,1,0 Current State: 16:[7, 23], Operations: ['83-73=10', '33-10=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.978299
hs_4
mult_heuristic
[ 75, 7, 57, 16 ]
71
[ "7+57=64", "64/16=4", "75-4=71" ]
Current State: 71:[75, 7, 57, 16], Operations: [] Exploring Operation: 7+57=64, Resulting Numbers: [75, 16, 64] Generated Node #2: [75, 16, 64] from Operation: 7+57=64 Current State: 71:[75, 16, 64], Operations: ['7+57=64'] Exploring Operation: 64/16=4, Resulting Numbers: [75, 4] Generated Node #3: [75, 4] from Operation: 64/16=4 Current State: 71:[75, 4], Operations: ['7+57=64', '64/16=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[75, 7, 57, 16], Operations: [] Exploring Operation: 7*16=112, Resulting Numbers: [75, 57, 112] Generated Node #0,0: 71:[75, 57, 112] Operation: 7*16=112 Exploring Operation: 57+16=73, Resulting Numbers: [75, 7, 73] Generated Node #0,1: 71:[75, 7, 73] Operation: 57+16=73 Exploring Operation: 7+16=23, Resulting Numbers: [75, 57, 23] Generated Node #0,2: 71:[75, 57, 23] Operation: 7+16=23 Exploring Operation: 7+57=64, Resulting Numbers: [75, 16, 64] Generated Node #0,3: 71:[75, 16, 64] Operation: 7+57=64 Moving to Node #0,0 Current State: 71:[75, 57, 112], Operations: ['7*16=112'] Exploring Operation: 75+57=132, Resulting Numbers: [112, 132] Generated Node #0,0,0: 71:[112, 132] Operation: 75+57=132 Exploring Operation: 112-57=55, Resulting Numbers: [75, 55] Generated Node #0,0,1: 71:[75, 55] Operation: 112-57=55 Exploring Operation: 112-75=37, Resulting Numbers: [57, 37] Generated Node #0,0,2: 71:[57, 37] Operation: 112-75=37 Exploring Operation: 75-57=18, Resulting Numbers: [112, 18] Generated Node #0,0,3: 71:[112, 18] Operation: 75-57=18 Moving to Node #0,3 Current State: 71:[75, 16, 64], Operations: ['7+57=64'] Exploring Operation: 75-16=59, Resulting Numbers: [64, 59] Generated Node #0,3,0: 71:[64, 59] Operation: 75-16=59 Exploring Operation: 64-16=48, Resulting Numbers: [75, 48] Generated Node #0,3,1: 71:[75, 48] Operation: 64-16=48 Exploring Operation: 75+16=91, Resulting Numbers: [64, 91] Generated Node #0,3,2: 71:[64, 91] Operation: 75+16=91 Exploring Operation: 16+64=80, Resulting Numbers: [75, 80] Generated Node #0,3,3: 71:[75, 80] Operation: 16+64=80 Moving to Node #0,2 Current State: 71:[75, 57, 23], Operations: ['7+16=23'] Exploring Operation: 75-23=52, Resulting Numbers: [57, 52] Generated Node #0,2,0: 71:[57, 52] Operation: 75-23=52 Exploring Operation: 75+23=98, Resulting Numbers: [57, 98] Generated Node #0,2,1: 71:[57, 98] Operation: 75+23=98 Exploring Operation: 57-23=34, Resulting Numbers: [75, 34] Generated Node #0,2,2: 71:[75, 34] Operation: 57-23=34 Exploring Operation: 57+23=80, Resulting Numbers: [75, 80] Generated Node #0,2,3: 71:[75, 80] Operation: 57+23=80 Moving to Node #0,1 Current State: 71:[75, 7, 73], Operations: ['57+16=73'] Exploring Operation: 73-7=66, Resulting Numbers: [75, 66] Generated Node #0,1,0: 71:[75, 66] Operation: 73-7=66 Exploring Operation: 7+73=80, Resulting Numbers: [75, 80] Generated Node #0,1,1: 71:[75, 80] Operation: 7+73=80 Exploring Operation: 75+7=82, Resulting Numbers: [73, 82] Generated Node #0,1,2: 71:[73, 82] Operation: 75+7=82 Exploring Operation: 75-7=68, Resulting Numbers: [73, 68] Generated Node #0,1,3: 71:[73, 68] Operation: 75-7=68 Moving to Node #0,1,3 Current State: 71:[73, 68], Operations: ['57+16=73', '75-7=68'] Exploring Operation: 73-68=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 73+68=141, Resulting Numbers: [141] 141,71 unequal: No Solution Exploring Operation: 73*68=4964, Resulting Numbers: [4964] 4964,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[75, 66], Operations: ['57+16=73', '73-7=66'] Exploring Operation: 75*66=4950, Resulting Numbers: [4950] 4950,71 unequal: No Solution Exploring Operation: 75+66=141, Resulting Numbers: [141] 141,71 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[75, 80], Operations: ['7+57=64', '16+64=80'] Exploring Operation: 75*80=6000, Resulting Numbers: [6000] 6000,71 unequal: No Solution Exploring Operation: 75+80=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 80-75=5, Resulting Numbers: [5] 5,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[75, 80], Operations: ['57+16=73', '7+73=80'] Exploring Operation: 75*80=6000, Resulting Numbers: [6000] 6000,71 unequal: No Solution Exploring Operation: 80-75=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 75+80=155, Resulting Numbers: [155] 155,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[75, 80], Operations: ['7+16=23', '57+23=80'] Exploring Operation: 75*80=6000, Resulting Numbers: [6000] 6000,71 unequal: No Solution Exploring Operation: 75+80=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 80-75=5, Resulting Numbers: [5] 5,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[73, 82], Operations: ['57+16=73', '75+7=82'] Exploring Operation: 73*82=5986, Resulting Numbers: [5986] 5986,71 unequal: No Solution Exploring Operation: 73+82=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 82-73=9, Resulting Numbers: [9] 9,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[64, 59], Operations: ['7+57=64', '75-16=59'] Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,71 unequal: No Solution Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[75, 55], Operations: ['7*16=112', '112-57=55'] Exploring Operation: 75*55=4125, Resulting Numbers: [4125] 4125,71 unequal: No Solution Exploring Operation: 75+55=130, Resulting Numbers: [130] 130,71 unequal: No Solution Exploring Operation: 75-55=20, Resulting Numbers: [20] 20,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[75, 48], Operations: ['7+57=64', '64-16=48'] Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 75*48=3600, Resulting Numbers: [3600] 3600,71 unequal: No Solution Exploring Operation: 75+48=123, Resulting Numbers: [123] 123,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[64, 91], Operations: ['7+57=64', '75+16=91'] Exploring Operation: 64*91=5824, Resulting Numbers: [5824] 5824,71 unequal: No Solution Exploring Operation: 91-64=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 64+91=155, Resulting Numbers: [155] 155,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[57, 52], Operations: ['7+16=23', '75-23=52'] Exploring Operation: 57+52=109, Resulting Numbers: [109] 109,71 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 57*52=2964, Resulting Numbers: [2964] 2964,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[57, 98], Operations: ['7+16=23', '75+23=98'] Exploring Operation: 57+98=155, Resulting Numbers: [155] 155,71 unequal: No Solution Exploring Operation: 98-57=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 57*98=5586, Resulting Numbers: [5586] 5586,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[75, 34], Operations: ['7+16=23', '57-23=34'] Exploring Operation: 75-34=41, Resulting Numbers: [41] 41,71 unequal: No Solution Exploring Operation: 75+34=109, Resulting Numbers: [109] 109,71 unequal: No Solution Exploring Operation: 75*34=2550, Resulting Numbers: [2550] 2550,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[57, 37], Operations: ['7*16=112', '112-75=37'] Exploring Operation: 57+37=94, Resulting Numbers: [94] 94,71 unequal: No Solution Exploring Operation: 57*37=2109, Resulting Numbers: [2109] 2109,71 unequal: No Solution Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[112, 18], Operations: ['7*16=112', '75-57=18'] Exploring Operation: 112-18=94, Resulting Numbers: [94] 94,71 unequal: No Solution Exploring Operation: 112+18=130, Resulting Numbers: [130] 130,71 unequal: No Solution Exploring Operation: 112*18=2016, Resulting Numbers: [2016] 2016,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[112, 132], Operations: ['7*16=112', '75+57=132'] Exploring Operation: 112*132=14784, Resulting Numbers: [14784] 14784,71 unequal: No Solution Exploring Operation: 112+132=244, Resulting Numbers: [244] 244,71 unequal: No Solution Exploring Operation: 132-112=20, Resulting Numbers: [20] 20,71 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 46, 6, 15, 91 ]
10
[ "46-15=31", "91-31=60", "60/6=10" ]
Current State: 10:[46, 6, 15, 91], Operations: [] Exploring Operation: 46-15=31, Resulting Numbers: [6, 91, 31] Generated Node #2: [6, 91, 31] from Operation: 46-15=31 Current State: 10:[6, 91, 31], Operations: ['46-15=31'] Exploring Operation: 91-31=60, Resulting Numbers: [6, 60] Generated Node #3: [6, 60] from Operation: 91-31=60 Current State: 10:[6, 60], Operations: ['46-15=31', '91-31=60'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[46, 6, 15, 91], Operations: [] Exploring Operation: 91-46=45, Resulting Numbers: [6, 15, 45] Generated Node #0,0: 10:[6, 15, 45] Operation: 91-46=45 Exploring Operation: 46-15=31, Resulting Numbers: [6, 91, 31] Generated Node #0,1: 10:[6, 91, 31] Operation: 46-15=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[6, 15, 45], Operations: ['91-46=45'] Exploring Operation: 45/15=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 10:[6, 3] Operation: 45/15=3 Exploring Operation: 45-15=30, Resulting Numbers: [6, 30] Generated Node #0,0,1: 10:[6, 30] Operation: 45-15=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[6, 3], Operations: ['91-46=45', '45/15=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[6, 30], Operations: ['91-46=45', '45-15=30'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,10 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[6, 91, 31], Operations: ['46-15=31'] Exploring Operation: 91-6=85, Resulting Numbers: [31, 85] Generated Node #0,1,0: 10:[31, 85] Operation: 91-6=85 Exploring Operation: 91-31=60, Resulting Numbers: [6, 60] Generated Node #0,1,1: 10:[6, 60] Operation: 91-31=60 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[6, 60], Operations: ['46-15=31', '91-31=60'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[46, 6, 15, 91], Operations: [] Exploring Operation: 46-15=31, Resulting Numbers: [6, 91, 31] Generated Node #0,1: 10:[6, 91, 31] Operation: 46-15=31 Moving to Node #0,1 Current State: 10:[6, 91, 31], Operations: ['46-15=31'] Exploring Operation: 91-31=60, Resulting Numbers: [6, 60] Generated Node #0,1,1: 10:[6, 60] Operation: 91-31=60 Moving to Node #0,1,1 Current State: 10:[6, 60], Operations: ['46-15=31', '91-31=60'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 42, 15, 48, 2 ]
21
[ "42*2=84", "15+48=63", "84-63=21" ]
Current State: 21:[42, 15, 48, 2], Operations: [] Exploring Operation: 42*2=84, Resulting Numbers: [15, 48, 84] Generated Node #2: [15, 48, 84] from Operation: 42*2=84 Current State: 21:[15, 48, 84], Operations: ['42*2=84'] Exploring Operation: 15+48=63, Resulting Numbers: [84, 63] Generated Node #3: [84, 63] from Operation: 15+48=63 Current State: 21:[84, 63], Operations: ['42*2=84', '15+48=63'] Exploring Operation: 84-63=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[42, 15, 48, 2], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [15, 2, 6] Generated Node #0,0: 21:[15, 2, 6] Operation: 48-42=6 Exploring Operation: 42-15=27, Resulting Numbers: [48, 2, 27] Generated Node #0,1: 21:[48, 2, 27] Operation: 42-15=27 Exploring Operation: 48-15=33, Resulting Numbers: [42, 2, 33] Generated Node #0,2: 21:[42, 2, 33] Operation: 48-15=33 Exploring Operation: 48/2=24, Resulting Numbers: [42, 15, 24] Generated Node #0,3: 21:[42, 15, 24] Operation: 48/2=24 Exploring Operation: 42/2=21, Resulting Numbers: [15, 48, 21] Generated Node #0,4: 21:[15, 48, 21] Operation: 42/2=21 Moving to Node #0,0 Current State: 21:[15, 2, 6], Operations: ['48-42=6'] Exploring Operation: 6/2=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 21:[15, 3] Operation: 6/2=3 Exploring Operation: 15+6=21, Resulting Numbers: [2, 21] Generated Node #0,0,1: 21:[2, 21] Operation: 15+6=21 Exploring Operation: 15-2=13, Resulting Numbers: [6, 13] Generated Node #0,0,2: 21:[6, 13] Operation: 15-2=13 Exploring Operation: 15+2=17, Resulting Numbers: [6, 17] Generated Node #0,0,3: 21:[6, 17] Operation: 15+2=17 Exploring Operation: 15-6=9, Resulting Numbers: [2, 9] Generated Node #0,0,4: 21:[2, 9] Operation: 15-6=9 Moving to Node #0,3 Current State: 21:[42, 15, 24], Operations: ['48/2=24'] Exploring Operation: 42-15=27, Resulting Numbers: [24, 27] Generated Node #0,3,0: 21:[24, 27] Operation: 42-15=27 Exploring Operation: 42+15=57, Resulting Numbers: [24, 57] Generated Node #0,3,1: 21:[24, 57] Operation: 42+15=57 Exploring Operation: 24-15=9, Resulting Numbers: [42, 9] Generated Node #0,3,2: 21:[42, 9] Operation: 24-15=9 Exploring Operation: 42-24=18, Resulting Numbers: [15, 18] Generated Node #0,3,3: 21:[15, 18] Operation: 42-24=18 Exploring Operation: 15+24=39, Resulting Numbers: [42, 39] Generated Node #0,3,4: 21:[42, 39] Operation: 15+24=39 Moving to Node #0,4 Current State: 21:[15, 48, 21], Operations: ['42/2=21'] Exploring Operation: 48-21=27, Resulting Numbers: [15, 27] Generated Node #0,4,0: 21:[15, 27] Operation: 48-21=27 Exploring Operation: 48-15=33, Resulting Numbers: [21, 33] Generated Node #0,4,1: 21:[21, 33] Operation: 48-15=33 Exploring Operation: 21-15=6, Resulting Numbers: [48, 6] Generated Node #0,4,2: 21:[48, 6] Operation: 21-15=6 Exploring Operation: 15+48=63, Resulting Numbers: [21, 63] Generated Node #0,4,3: 21:[21, 63] Operation: 15+48=63 Exploring Operation: 15+21=36, Resulting Numbers: [48, 36] Generated Node #0,4,4: 21:[48, 36] Operation: 15+21=36 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 21:[15, 27], Operations: ['42/2=21', '48-21=27'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 15*27=405, Resulting Numbers: [405] 405,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 21:[21, 33], Operations: ['42/2=21', '48-15=33'] Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,21 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 21:[48, 6], Operations: ['42/2=21', '21-15=6'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 48*6=288, Resulting Numbers: [288] 288,21 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,21 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 21:[21, 63], Operations: ['42/2=21', '15+48=63'] Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,21 unequal: No Solution Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 21:[48, 36], Operations: ['42/2=21', '15+21=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,21 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 21:[48, 2, 27], Operations: ['42-15=27'] Exploring Operation: 48-2=46, Resulting Numbers: [27, 46] Generated Node #0,1,0: 21:[27, 46] Operation: 48-2=46 Exploring Operation: 48-27=21, Resulting Numbers: [2, 21] Generated Node #0,1,1: 21:[2, 21] Operation: 48-27=21 Exploring Operation: 27-2=25, Resulting Numbers: [48, 25] Generated Node #0,1,2: 21:[48, 25] Operation: 27-2=25 Exploring Operation: 48/2=24, Resulting Numbers: [27, 24] Generated Node #0,1,3: 21:[27, 24] Operation: 48/2=24 Exploring Operation: 48+2=50, Resulting Numbers: [27, 50] Generated Node #0,1,4: 21:[27, 50] Operation: 48+2=50 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[2, 21], Operations: ['42-15=27', '48-27=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 21:[27, 24], Operations: ['42-15=27', '48/2=24'] Exploring Operation: 27+24=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 27*24=648, Resulting Numbers: [648] 648,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[27, 46], Operations: ['42-15=27', '48-2=46'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 27*46=1242, Resulting Numbers: [1242] 1242,21 unequal: No Solution Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[48, 25], Operations: ['42-15=27', '27-2=25'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 48*25=1200, Resulting Numbers: [1200] 1200,21 unequal: No Solution Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 21:[27, 50], Operations: ['42-15=27', '48+2=50'] Exploring Operation: 27*50=1350, Resulting Numbers: [1350] 1350,21 unequal: No Solution Exploring Operation: 27+50=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 50-27=23, Resulting Numbers: [23] 23,21 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: 21:[42, 2, 33], Operations: ['48-15=33'] Exploring Operation: 42-33=9, Resulting Numbers: [2, 9] Generated Node #0,2,0: 21:[2, 9] Operation: 42-33=9 Exploring Operation: 42-2=40, Resulting Numbers: [33, 40] Generated Node #0,2,1: 21:[33, 40] Operation: 42-2=40 Exploring Operation: 42/2=21, Resulting Numbers: [33, 21] Generated Node #0,2,2: 21:[33, 21] Operation: 42/2=21 Exploring Operation: 33-2=31, Resulting Numbers: [42, 31] Generated Node #0,2,3: 21:[42, 31] Operation: 33-2=31 Exploring Operation: 42+2=44, Resulting Numbers: [33, 44] Generated Node #0,2,4: 21:[33, 44] Operation: 42+2=44 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[2, 9], Operations: ['48-15=33', '42-33=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[33, 21], Operations: ['48-15=33', '42/2=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,21 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,21 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[33, 40], Operations: ['48-15=33', '42-2=40'] Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,21 unequal: No Solution Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,21 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[42, 31], Operations: ['48-15=33', '33-2=31'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,21 unequal: No Solution Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 21:[33, 44], Operations: ['48-15=33', '42+2=44'] Exploring Operation: 33+44=77, Resulting Numbers: [77] 77,21 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 33*44=1452, Resulting Numbers: [1452] 1452,21 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: 21:[2, 21], Operations: ['48-42=6', '15+6=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,21 unequal: No Solution Moving to Node #0,0,4 Current State: 21:[2, 9], Operations: ['48-42=6', '15-6=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[6, 17], Operations: ['48-42=6', '15+2=17'] Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[15, 3], Operations: ['48-42=6', '6/2=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[6, 13], Operations: ['48-42=6', '15-2=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,21 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,21 unequal: No Solution Moving to Node #0,3,3 Current State: 21:[15, 18], Operations: ['48/2=24', '42-24=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,21 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[24, 27], Operations: ['48/2=24', '42-15=27'] Exploring Operation: 24*27=648, Resulting Numbers: [648] 648,21 unequal: No Solution Exploring Operation: 27-24=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,3,2 Current State: 21:[42, 9], Operations: ['48/2=24', '24-15=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,21 unequal: No Solution Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,3,1 Current State: 21:[24, 57], Operations: ['48/2=24', '42+15=57'] Exploring Operation: 24*57=1368, Resulting Numbers: [1368] 1368,21 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 24+57=81, Resulting Numbers: [81] 81,21 unequal: No Solution Moving to Node #0,3,4 Current State: 21:[42, 39], Operations: ['48/2=24', '15+24=39'] Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 42*39=1638, Resulting Numbers: [1638] 1638,21 unequal: No Solution Exploring Operation: 42+39=81, Resulting Numbers: [81] 81,21 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 72, 10, 1, 73 ]
20
[ "72-1=71", "73-71=2", "10*2=20" ]
Current State: 20:[72, 10, 1, 73], Operations: [] Exploring Operation: 72-1=71, Resulting Numbers: [10, 73, 71] Generated Node #2: [10, 73, 71] from Operation: 72-1=71 Current State: 20:[10, 73, 71], Operations: ['72-1=71'] Exploring Operation: 73-71=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 73-71=2 Current State: 20:[10, 2], Operations: ['72-1=71', '73-71=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[72, 10, 1, 73], Operations: [] Exploring Operation: 73-72=1, Resulting Numbers: [10, 1, 1] Generated Node #0,0: 20:[10, 1, 1] Operation: 73-72=1 Exploring Operation: 72-10=62, Resulting Numbers: [1, 73, 62] Generated Node #0,1: 20:[1, 73, 62] Operation: 72-10=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[10, 1, 1], Operations: ['73-72=1'] Exploring Operation: 1+1=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 20:[10, 2] Operation: 1+1=2 Exploring Operation: 10*1=10, Resulting Numbers: [1, 10] Generated Node #0,0,1: 20:[1, 10] Operation: 10*1=10 Moving to Node #0,0,0 Current State: 20:[10, 2], Operations: ['73-72=1', '1+1=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[72, 10, 1, 73], Operations: [] Exploring Operation: 73-72=1, Resulting Numbers: [10, 1, 1] Generated Node #0,0: 20:[10, 1, 1] Operation: 73-72=1 Moving to Node #0,0 Current State: 20:[10, 1, 1], Operations: ['73-72=1'] Exploring Operation: 1+1=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 20:[10, 2] Operation: 1+1=2 Moving to Node #0,0,0 Current State: 20:[10, 2], Operations: ['73-72=1', '1+1=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 57, 37, 32, 35 ]
82
[ "37-35=2", "57*2=114", "114-32=82" ]
Current State: 82:[57, 37, 32, 35], Operations: [] Exploring Operation: 37-35=2, Resulting Numbers: [57, 32, 2] Generated Node #2: [57, 32, 2] from Operation: 37-35=2 Current State: 82:[57, 32, 2], Operations: ['37-35=2'] Exploring Operation: 57*2=114, Resulting Numbers: [32, 114] Generated Node #3: [32, 114] from Operation: 57*2=114 Current State: 82:[32, 114], Operations: ['37-35=2', '57*2=114'] Exploring Operation: 114-32=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[57, 37, 32, 35], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [57, 37, 3] Generated Node #0,0: 82:[57, 37, 3] Operation: 35-32=3 Exploring Operation: 57+32=89, Resulting Numbers: [37, 35, 89] Generated Node #0,1: 82:[37, 35, 89] Operation: 57+32=89 Exploring Operation: 57+35=92, Resulting Numbers: [37, 32, 92] Generated Node #0,2: 82:[37, 32, 92] Operation: 57+35=92 Moving to Node #0,1 Current State: 82:[37, 35, 89], Operations: ['57+32=89'] Exploring Operation: 37+35=72, Resulting Numbers: [89, 72] Generated Node #0,1,0: 82:[89, 72] Operation: 37+35=72 Exploring Operation: 89-37=52, Resulting Numbers: [35, 52] Generated Node #0,1,1: 82:[35, 52] Operation: 89-37=52 Exploring Operation: 37-35=2, Resulting Numbers: [89, 2] Generated Node #0,1,2: 82:[89, 2] Operation: 37-35=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 82:[89, 2], Operations: ['57+32=89', '37-35=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,82 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,82 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 #0,1,0 Current State: 82:[89, 72], Operations: ['57+32=89', '37+35=72'] Exploring Operation: 89+72=161, Resulting Numbers: [161] 161,82 unequal: No Solution Exploring Operation: 89*72=6408, Resulting Numbers: [6408] 6408,82 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,82 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 #0,1,1 Current State: 82:[35, 52], Operations: ['57+32=89', '89-37=52'] Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,82 unequal: No Solution Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,82 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: 82:[57, 37, 3], Operations: ['35-32=3'] Exploring Operation: 57-3=54, Resulting Numbers: [37, 54] Generated Node #0,0,0: 82:[37, 54] Operation: 57-3=54 Exploring Operation: 57+37=94, Resulting Numbers: [3, 94] Generated Node #0,0,1: 82:[3, 94] Operation: 57+37=94 Exploring Operation: 37+3=40, Resulting Numbers: [57, 40] Generated Node #0,0,2: 82:[57, 40] Operation: 37+3=40 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[3, 94], Operations: ['35-32=3', '57+37=94'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,82 unequal: No Solution Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,82 unequal: No Solution Exploring Operation: 3*94=282, Resulting Numbers: [282] 282,82 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:[37, 54], Operations: ['35-32=3', '57-3=54'] Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,82 unequal: No Solution Exploring Operation: 37*54=1998, Resulting Numbers: [1998] 1998,82 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 #0,0,2 Current State: 82:[57, 40], Operations: ['35-32=3', '37+3=40'] Exploring Operation: 57-40=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 57+40=97, Resulting Numbers: [97] 97,82 unequal: No Solution Exploring Operation: 57*40=2280, Resulting Numbers: [2280] 2280,82 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:[37, 32, 92], Operations: ['57+35=92'] Exploring Operation: 92-37=55, Resulting Numbers: [32, 55] Generated Node #0,2,0: 82:[32, 55] Operation: 92-37=55 Exploring Operation: 37+32=69, Resulting Numbers: [92, 69] Generated Node #0,2,1: 82:[92, 69] Operation: 37+32=69 Exploring Operation: 37-32=5, Resulting Numbers: [92, 5] Generated Node #0,2,2: 82:[92, 5] Operation: 37-32=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[92, 5], Operations: ['57+35=92', '37-32=5'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 92*5=460, Resulting Numbers: [460] 460,82 unequal: No Solution Exploring Operation: 92+5=97, Resulting Numbers: [97] 97,82 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 #0,2,0 Current State: 82:[32, 55], Operations: ['57+35=92', '92-37=55'] Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,82 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,82 unequal: No Solution Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,82 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 #0,2,1 Current State: 82:[92, 69], Operations: ['57+35=92', '37+32=69'] Exploring Operation: 92*69=6348, Resulting Numbers: [6348] 6348,82 unequal: No Solution Exploring Operation: 92-69=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 92+69=161, Resulting Numbers: [161] 161,82 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
[ 3, 72, 73, 92 ]
79
[ "72+73=145", "92+145=237", "237/3=79" ]
Current State: 79:[3, 72, 73, 92], Operations: [] Exploring Operation: 72+73=145, Resulting Numbers: [3, 92, 145] Generated Node #2: [3, 92, 145] from Operation: 72+73=145 Current State: 79:[3, 92, 145], Operations: ['72+73=145'] Exploring Operation: 92+145=237, Resulting Numbers: [3, 237] Generated Node #3: [3, 237] from Operation: 92+145=237 Current State: 79:[3, 237], Operations: ['72+73=145', '92+145=237'] Exploring Operation: 237/3=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[3, 72, 73, 92], Operations: [] Exploring Operation: 3+72=75, Resulting Numbers: [73, 92, 75] Generated Node #0,0: 79:[73, 92, 75] Operation: 3+72=75 Moving to Node #0,0 Current State: 79:[73, 92, 75], Operations: ['3+72=75'] Exploring Operation: 92-73=19, Resulting Numbers: [75, 19] Generated Node #0,0,0: 79:[75, 19] Operation: 92-73=19 Moving to Node #0,0,0 Current State: 79:[75, 19], Operations: ['3+72=75', '92-73=19'] Exploring Operation: 75+19=94, Resulting Numbers: [94] 94,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 11, 4, 95, 15 ]
40
[ "95+15=110", "110/11=10", "4*10=40" ]
Current State: 40:[11, 4, 95, 15], Operations: [] Exploring Operation: 95+15=110, Resulting Numbers: [11, 4, 110] Generated Node #2: [11, 4, 110] from Operation: 95+15=110 Current State: 40:[11, 4, 110], Operations: ['95+15=110'] Exploring Operation: 110/11=10, Resulting Numbers: [4, 10] Generated Node #3: [4, 10] from Operation: 110/11=10 Current State: 40:[4, 10], Operations: ['95+15=110', '110/11=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[11, 4, 95, 15], Operations: [] Exploring Operation: 95-11=84, Resulting Numbers: [4, 15, 84] Generated Node #0,0: 40:[4, 15, 84] Operation: 95-11=84 Exploring Operation: 95-15=80, Resulting Numbers: [11, 4, 80] Generated Node #0,1: 40:[11, 4, 80] Operation: 95-15=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[11, 4, 80], Operations: ['95-15=80'] Exploring Operation: 80/4=20, Resulting Numbers: [11, 20] Generated Node #0,1,0: 40:[11, 20] Operation: 80/4=20 Exploring Operation: 80-11=69, Resulting Numbers: [4, 69] Generated Node #0,1,1: 40:[4, 69] Operation: 80-11=69 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[11, 20], Operations: ['95-15=80', '80/4=20'] Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[4, 69], Operations: ['95-15=80', '80-11=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,40 unequal: No Solution Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,40 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: 40:[4, 15, 84], Operations: ['95-11=84'] Exploring Operation: 84/4=21, Resulting Numbers: [15, 21] Generated Node #0,0,0: 40:[15, 21] Operation: 84/4=21 Exploring Operation: 84-15=69, Resulting Numbers: [4, 69] Generated Node #0,0,1: 40:[4, 69] Operation: 84-15=69 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[15, 21], Operations: ['95-11=84', '84/4=21'] Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,40 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 40:[4, 69], Operations: ['95-11=84', '84-15=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,40 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,40 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
[ 11, 79, 19, 91 ]
18
[ "11+79=90", "91-19=72", "90-72=18" ]
Current State: 18:[11, 79, 19, 91], Operations: [] Exploring Operation: 11+79=90, Resulting Numbers: [19, 91, 90] Generated Node #2: [19, 91, 90] from Operation: 11+79=90 Current State: 18:[19, 91, 90], Operations: ['11+79=90'] Exploring Operation: 91-19=72, Resulting Numbers: [90, 72] Generated Node #3: [90, 72] from Operation: 91-19=72 Current State: 18:[90, 72], Operations: ['11+79=90', '91-19=72'] Exploring Operation: 90-72=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[11, 79, 19, 91], Operations: [] Exploring Operation: 79-19=60, Resulting Numbers: [11, 91, 60] Generated Node #0,0: 18:[11, 91, 60] Operation: 79-19=60 Exploring Operation: 79-11=68, Resulting Numbers: [19, 91, 68] Generated Node #0,1: 18:[19, 91, 68] Operation: 79-11=68 Exploring Operation: 91-79=12, Resulting Numbers: [11, 19, 12] Generated Node #0,2: 18:[11, 19, 12] Operation: 91-79=12 Exploring Operation: 91-11=80, Resulting Numbers: [79, 19, 80] Generated Node #0,3: 18:[79, 19, 80] Operation: 91-11=80 Exploring Operation: 91-19=72, Resulting Numbers: [11, 79, 72] Generated Node #0,4: 18:[11, 79, 72] Operation: 91-19=72 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[11, 19, 12], Operations: ['91-79=12'] Exploring Operation: 11+12=23, Resulting Numbers: [19, 23] Generated Node #0,2,0: 18:[19, 23] Operation: 11+12=23 Exploring Operation: 11+19=30, Resulting Numbers: [12, 30] Generated Node #0,2,1: 18:[12, 30] Operation: 11+19=30 Exploring Operation: 19-11=8, Resulting Numbers: [12, 8] Generated Node #0,2,2: 18:[12, 8] Operation: 19-11=8 Exploring Operation: 19-12=7, Resulting Numbers: [11, 7] Generated Node #0,2,3: 18:[11, 7] Operation: 19-12=7 Exploring Operation: 12-11=1, Resulting Numbers: [19, 1] Generated Node #0,2,4: 18:[19, 1] Operation: 12-11=1 Moving to Node #0,2,4 Current State: 18:[19, 1], Operations: ['91-79=12', '12-11=1'] Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[11, 79, 19, 91], Operations: [] Exploring Operation: 91-79=12, Resulting Numbers: [11, 19, 12] Generated Node #0,2: 18:[11, 19, 12] Operation: 91-79=12 Moving to Node #0,2 Current State: 18:[11, 19, 12], Operations: ['91-79=12'] Exploring Operation: 12-11=1, Resulting Numbers: [19, 1] Generated Node #0,2,4: 18:[19, 1] Operation: 12-11=1 Moving to Node #0,2,4 Current State: 18:[19, 1], Operations: ['91-79=12', '12-11=1'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 35, 30, 65, 63 ]
63
[ "35+30=65", "65+63=128", "128-65=63" ]
Current State: 63:[35, 30, 65, 63], Operations: [] Exploring Operation: 35+30=65, Resulting Numbers: [65, 63, 65] Generated Node #2: [65, 63, 65] from Operation: 35+30=65 Current State: 63:[65, 63, 65], Operations: ['35+30=65'] Exploring Operation: 65+63=128, Resulting Numbers: [128] 128,63 equal: Goal Reached Exploring Operation: 128-65=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[35, 30, 65, 63], Operations: [] Exploring Operation: 35+30=65, Resulting Numbers: [65, 63, 65] Generated Node #0,0: 63:[65, 63, 65] Operation: 35+30=65 Exploring Operation: 65-35=30, Resulting Numbers: [30, 63, 30] Generated Node #0,1: 63:[30, 63, 30] Operation: 65-35=30 Exploring Operation: 35-30=5, Resulting Numbers: [65, 63, 5] Generated Node #0,2: 63:[65, 63, 5] Operation: 35-30=5 Exploring Operation: 63-35=28, Resulting Numbers: [30, 65, 28] Generated Node #0,3: 63:[30, 65, 28] Operation: 63-35=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[65, 63, 65], Operations: ['35+30=65'] Exploring Operation: 65/65=1, Resulting Numbers: [63, 1] Generated Node #0,0,0: 63:[63, 1] Operation: 65/65=1 Exploring Operation: 65-65=0, Resulting Numbers: [63, 0] Generated Node #0,0,1: 63:[63, 0] Operation: 65-65=0 Exploring Operation: 65-63=2, Resulting Numbers: [65, 2] Generated Node #0,0,2: 63:[65, 2] Operation: 65-63=2 Exploring Operation: 65-63=2, Resulting Numbers: [65, 2] Generated Node #0,0,3: 63:[65, 2] Operation: 65-63=2 Moving to Node #0,0,0 Current State: 63:[63, 1], Operations: ['35+30=65', '65/65=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[35, 30, 65, 63], Operations: [] Exploring Operation: 35+30=65, Resulting Numbers: [65, 63, 65] Generated Node #0,0: 63:[65, 63, 65] Operation: 35+30=65 Moving to Node #0,0 Current State: 63:[65, 63, 65], Operations: ['35+30=65'] Exploring Operation: 65/65=1, Resulting Numbers: [63, 1] Generated Node #0,0,0: 63:[63, 1] Operation: 65/65=1 Moving to Node #0,0,0 Current State: 63:[63, 1], Operations: ['35+30=65', '65/65=1'] Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 63, 93, 84, 3 ]
52
[ "84-63=21", "93/3=31", "21+31=52" ]
Current State: 52:[63, 93, 84, 3], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [93, 3, 21] Generated Node #2: [93, 3, 21] from Operation: 84-63=21 Current State: 52:[93, 3, 21], Operations: ['84-63=21'] Exploring Operation: 93/3=31, Resulting Numbers: [21, 31] Generated Node #3: [21, 31] from Operation: 93/3=31 Current State: 52:[21, 31], Operations: ['84-63=21', '93/3=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[63, 93, 84, 3], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [93, 3, 21] Generated Node #0,0: 52:[93, 3, 21] Operation: 84-63=21 Exploring Operation: 93-84=9, Resulting Numbers: [63, 3, 9] Generated Node #0,1: 52:[63, 3, 9] Operation: 93-84=9 Exploring Operation: 84/3=28, Resulting Numbers: [63, 93, 28] Generated Node #0,2: 52:[63, 93, 28] Operation: 84/3=28 Exploring Operation: 93-63=30, Resulting Numbers: [84, 3, 30] Generated Node #0,3: 52:[84, 3, 30] Operation: 93-63=30 Exploring Operation: 93/3=31, Resulting Numbers: [63, 84, 31] Generated Node #0,4: 52:[63, 84, 31] Operation: 93/3=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[63, 3, 9], Operations: ['93-84=9'] Exploring Operation: 63-9=54, Resulting Numbers: [3, 54] Generated Node #0,1,0: 52:[3, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 52:[3, 7] Operation: 63/9=7 Exploring Operation: 63/3=21, Resulting Numbers: [9, 21] Generated Node #0,1,2: 52:[9, 21] Operation: 63/3=21 Exploring Operation: 63-3=60, Resulting Numbers: [9, 60] Generated Node #0,1,3: 52:[9, 60] Operation: 63-3=60 Exploring Operation: 3+9=12, Resulting Numbers: [63, 12] Generated Node #0,1,4: 52:[63, 12] Operation: 3+9=12 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[3, 54], Operations: ['93-84=9', '63-9=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[3, 7], Operations: ['93-84=9', '63/9=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,52 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[9, 21], Operations: ['93-84=9', '63/3=21'] Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,52 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[9, 60], Operations: ['93-84=9', '63-3=60'] Exploring Operation: 9*60=540, Resulting Numbers: [540] 540,52 unequal: No Solution Exploring Operation: 9+60=69, Resulting Numbers: [69] 69,52 unequal: No Solution Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 52:[63, 12], Operations: ['93-84=9', '3+9=12'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,52 unequal: No Solution Exploring Operation: 63*12=756, Resulting Numbers: [756] 756,52 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: 52:[84, 3, 30], Operations: ['93-63=30'] Exploring Operation: 84-30=54, Resulting Numbers: [3, 54] Generated Node #0,3,0: 52:[3, 54] Operation: 84-30=54 Exploring Operation: 84-3=81, Resulting Numbers: [30, 81] Generated Node #0,3,1: 52:[30, 81] Operation: 84-3=81 Exploring Operation: 84/3=28, Resulting Numbers: [30, 28] Generated Node #0,3,2: 52:[30, 28] Operation: 84/3=28 Exploring Operation: 30/3=10, Resulting Numbers: [84, 10] Generated Node #0,3,3: 52:[84, 10] Operation: 30/3=10 Exploring Operation: 30-3=27, Resulting Numbers: [84, 27] Generated Node #0,3,4: 52:[84, 27] Operation: 30-3=27 Moving to Node #0,3,0 Current State: 52:[3, 54], Operations: ['93-63=30', '84-30=54'] Exploring Operation: 3*54=162, Resulting Numbers: [162] 162,52 unequal: No Solution Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[30, 28], Operations: ['93-63=30', '84/3=28'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,52 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,52 unequal: No Solution Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[30, 81], Operations: ['93-63=30', '84-3=81'] Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 30*81=2430, Resulting Numbers: [2430] 2430,52 unequal: No Solution Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,52 unequal: No Solution Moving to Node #0,3,4 Current State: 52:[84, 27], Operations: ['93-63=30', '30-3=27'] Exploring Operation: 84+27=111, Resulting Numbers: [111] 111,52 unequal: No Solution Exploring Operation: 84-27=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 84*27=2268, Resulting Numbers: [2268] 2268,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[84, 10], Operations: ['93-63=30', '30/3=10'] Exploring Operation: 84-10=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 84+10=94, Resulting Numbers: [94] 94,52 unequal: No Solution Exploring Operation: 84*10=840, Resulting Numbers: [840] 840,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[93, 3, 21], Operations: ['84-63=21'] Exploring Operation: 3+21=24, Resulting Numbers: [93, 24] Generated Node #0,0,0: 52:[93, 24] Operation: 3+21=24 Exploring Operation: 93-3=90, Resulting Numbers: [21, 90] Generated Node #0,0,1: 52:[21, 90] Operation: 93-3=90 Exploring Operation: 93/3=31, Resulting Numbers: [21, 31] Generated Node #0,0,2: 52:[21, 31] Operation: 93/3=31 Exploring Operation: 21/3=7, Resulting Numbers: [93, 7] Generated Node #0,0,3: 52:[93, 7] Operation: 21/3=7 Exploring Operation: 93-21=72, Resulting Numbers: [3, 72] Generated Node #0,0,4: 52:[3, 72] Operation: 93-21=72 Moving to Node #0,0,2 Current State: 52:[21, 31], Operations: ['84-63=21', '93/3=31'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[63, 93, 84, 3], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [93, 3, 21] Generated Node #0,0: 52:[93, 3, 21] Operation: 84-63=21 Moving to Node #0,0 Current State: 52:[93, 3, 21], Operations: ['84-63=21'] Exploring Operation: 93/3=31, Resulting Numbers: [21, 31] Generated Node #0,0,2: 52:[21, 31] Operation: 93/3=31 Moving to Node #0,0,2 Current State: 52:[21, 31], Operations: ['84-63=21', '93/3=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
sum_heuristic
[ 22, 56, 42, 84 ]
17
[ "56-22=34", "84/42=2", "34/2=17" ]
Current State: 17:[22, 56, 42, 84], Operations: [] Exploring Operation: 56-22=34, Resulting Numbers: [42, 84, 34] Generated Node #2: [42, 84, 34] from Operation: 56-22=34 Current State: 17:[42, 84, 34], Operations: ['56-22=34'] Exploring Operation: 84/42=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 84/42=2 Current State: 17:[34, 2], Operations: ['56-22=34', '84/42=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[22, 56, 42, 84], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [22, 42, 28] Generated Node #0,0: 17:[22, 42, 28] Operation: 84-56=28 Exploring Operation: 84/42=2, Resulting Numbers: [22, 56, 2] Generated Node #0,1: 17:[22, 56, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[22, 42, 28], Operations: ['84-56=28'] Exploring Operation: 42-22=20, Resulting Numbers: [28, 20] Generated Node #0,0,0: 17:[28, 20] Operation: 42-22=20 Exploring Operation: 42-28=14, Resulting Numbers: [22, 14] Generated Node #0,0,1: 17:[22, 14] Operation: 42-28=14 Moving to Node #0,0,1 Current State: 17:[22, 14], Operations: ['84-56=28', '42-28=14'] Exploring Operation: 22+14=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[28, 20], Operations: ['84-56=28', '42-22=20'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,17 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 #0,1 Current State: 17:[22, 56, 2], Operations: ['84/42=2'] Exploring Operation: 56/2=28, Resulting Numbers: [22, 28] Generated Node #0,1,0: 17:[22, 28] Operation: 56/2=28 Exploring Operation: 56-22=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 17:[2, 34] Operation: 56-22=34 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[22, 28], Operations: ['84/42=2', '56/2=28'] Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,17 unequal: No Solution No 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: 17:[2, 34], Operations: ['84/42=2', '56-22=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[22, 56, 42, 84], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [22, 56, 2] Generated Node #0,1: 17:[22, 56, 2] Operation: 84/42=2 Moving to Node #0,1 Current State: 17:[22, 56, 2], Operations: ['84/42=2'] Exploring Operation: 56-22=34, Resulting Numbers: [2, 34] Generated Node #0,1,1: 17:[2, 34] Operation: 56-22=34 Moving to Node #0,1,1 Current State: 17:[2, 34], Operations: ['84/42=2', '56-22=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 58, 42, 28, 59 ]
70
[ "59-58=1", "42+28=70", "1*70=70" ]
Current State: 70:[58, 42, 28, 59], Operations: [] Exploring Operation: 59-58=1, Resulting Numbers: [42, 28, 1] Generated Node #2: [42, 28, 1] from Operation: 59-58=1 Current State: 70:[42, 28, 1], Operations: ['59-58=1'] Exploring Operation: 42+28=70, Resulting Numbers: [1, 70] Generated Node #3: [1, 70] from Operation: 42+28=70 Current State: 70:[1, 70], Operations: ['59-58=1', '42+28=70'] Exploring Operation: 1*70=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[58, 42, 28, 59], Operations: [] Exploring Operation: 59-58=1, Resulting Numbers: [42, 28, 1] Generated Node #0,0: 70:[42, 28, 1] Operation: 59-58=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[42, 28, 1], Operations: ['59-58=1'] Exploring Operation: 42+28=70, Resulting Numbers: [1, 70] Generated Node #0,0,0: 70:[1, 70] Operation: 42+28=70 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[1, 70], Operations: ['59-58=1', '42+28=70'] Exploring Operation: 1*70=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[58, 42, 28, 59], Operations: [] Exploring Operation: 59-58=1, Resulting Numbers: [42, 28, 1] Generated Node #0,0: 70:[42, 28, 1] Operation: 59-58=1 Moving to Node #0,0 Current State: 70:[42, 28, 1], Operations: ['59-58=1'] Exploring Operation: 42+28=70, Resulting Numbers: [1, 70] Generated Node #0,0,0: 70:[1, 70] Operation: 42+28=70 Moving to Node #0,0,0 Current State: 70:[1, 70], Operations: ['59-58=1', '42+28=70'] Exploring Operation: 1*70=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 32, 4, 3, 28 ]
80
[ "32+4=36", "3*36=108", "108-28=80" ]
Current State: 80:[32, 4, 3, 28], Operations: [] Exploring Operation: 32+4=36, Resulting Numbers: [3, 28, 36] Generated Node #2: [3, 28, 36] from Operation: 32+4=36 Current State: 80:[3, 28, 36], Operations: ['32+4=36'] Exploring Operation: 3*36=108, Resulting Numbers: [28, 108] Generated Node #3: [28, 108] from Operation: 3*36=108 Current State: 80:[28, 108], Operations: ['32+4=36', '3*36=108'] Exploring Operation: 108-28=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[32, 4, 3, 28], Operations: [] Exploring Operation: 3*28=84, Resulting Numbers: [32, 4, 84] Generated Node #0,0: 80:[32, 4, 84] Operation: 3*28=84 Exploring Operation: 32+4=36, Resulting Numbers: [3, 28, 36] Generated Node #0,1: 80:[3, 28, 36] Operation: 32+4=36 Exploring Operation: 28/4=7, Resulting Numbers: [32, 3, 7] Generated Node #0,2: 80:[32, 3, 7] Operation: 28/4=7 Exploring Operation: 32-28=4, Resulting Numbers: [4, 3, 4] Generated Node #0,3: 80:[4, 3, 4] Operation: 32-28=4 Exploring Operation: 32/4=8, Resulting Numbers: [3, 28, 8] Generated Node #0,4: 80:[3, 28, 8] Operation: 32/4=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 80:[4, 3, 4], Operations: ['32-28=4'] Exploring Operation: 4+3=7, Resulting Numbers: [4, 7] Generated Node #0,3,0: 80:[4, 7] Operation: 4+3=7 Exploring Operation: 4*4=16, Resulting Numbers: [3, 16] Generated Node #0,3,1: 80:[3, 16] Operation: 4*4=16 Exploring Operation: 4-3=1, Resulting Numbers: [4, 1] Generated Node #0,3,2: 80:[4, 1] Operation: 4-3=1 Exploring Operation: 3+4=7, Resulting Numbers: [4, 7] Generated Node #0,3,3: 80:[4, 7] Operation: 3+4=7 Exploring Operation: 4+4=8, Resulting Numbers: [3, 8] Generated Node #0,3,4: 80:[3, 8] Operation: 4+4=8 Moving to Node #0,3,0 Current State: 80:[4, 7], Operations: ['32-28=4', '4+3=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[4, 1], Operations: ['32-28=4', '4-3=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,80 unequal: No Solution Moving to Node #0,3,4 Current State: 80:[3, 8], Operations: ['32-28=4', '4+4=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[3, 16], Operations: ['32-28=4', '4*4=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[4, 7], Operations: ['32-28=4', '3+4=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,80 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 #0,4 Current State: 80:[3, 28, 8], Operations: ['32/4=8'] Exploring Operation: 28-8=20, Resulting Numbers: [3, 20] Generated Node #0,4,0: 80:[3, 20] Operation: 28-8=20 Exploring Operation: 28-3=25, Resulting Numbers: [8, 25] Generated Node #0,4,1: 80:[8, 25] Operation: 28-3=25 Exploring Operation: 28+8=36, Resulting Numbers: [3, 36] Generated Node #0,4,2: 80:[3, 36] Operation: 28+8=36 Exploring Operation: 8-3=5, Resulting Numbers: [28, 5] Generated Node #0,4,3: 80:[28, 5] Operation: 8-3=5 Exploring Operation: 3*28=84, Resulting Numbers: [8, 84] Generated Node #0,4,4: 80:[8, 84] Operation: 3*28=84 Moving to Node #0,4,0 Current State: 80:[3, 20], Operations: ['32/4=8', '28-8=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[8, 84], Operations: ['32/4=8', '3*28=84'] Exploring Operation: 8+84=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 8*84=672, Resulting Numbers: [672] 672,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[8, 25], Operations: ['32/4=8', '28-3=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,80 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[3, 36], Operations: ['32/4=8', '28+8=36'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,80 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[28, 5], Operations: ['32/4=8', '8-3=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,80 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,80 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 Current State: 80:[32, 3, 7], Operations: ['28/4=7'] Exploring Operation: 32-7=25, Resulting Numbers: [3, 25] Generated Node #0,2,0: 80:[3, 25] Operation: 32-7=25 Exploring Operation: 3+7=10, Resulting Numbers: [32, 10] Generated Node #0,2,1: 80:[32, 10] Operation: 3+7=10 Exploring Operation: 7-3=4, Resulting Numbers: [32, 4] Generated Node #0,2,2: 80:[32, 4] Operation: 7-3=4 Exploring Operation: 32+7=39, Resulting Numbers: [3, 39] Generated Node #0,2,3: 80:[3, 39] Operation: 32+7=39 Exploring Operation: 32+3=35, Resulting Numbers: [7, 35] Generated Node #0,2,4: 80:[7, 35] Operation: 32+3=35 Moving to Node #0,2,3 Current State: 80:[3, 39], Operations: ['28/4=7', '32+7=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 3*39=117, Resulting Numbers: [117] 117,80 unequal: No Solution Moving to Node #0,2,4 Current State: 80:[7, 35], Operations: ['28/4=7', '32+3=35'] Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,80 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[3, 25], Operations: ['28/4=7', '32-7=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[32, 10], Operations: ['28/4=7', '3+7=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,80 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,80 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[32, 4], Operations: ['28/4=7', '7-3=4'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,80 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,80 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,80 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 #0,0 Current State: 80:[32, 4, 84], Operations: ['3*28=84'] Exploring Operation: 84/4=21, Resulting Numbers: [32, 21] Generated Node #0,0,0: 80:[32, 21] Operation: 84/4=21 Exploring Operation: 32/4=8, Resulting Numbers: [84, 8] Generated Node #0,0,1: 80:[84, 8] Operation: 32/4=8 Exploring Operation: 32-4=28, Resulting Numbers: [84, 28] Generated Node #0,0,2: 80:[84, 28] Operation: 32-4=28 Exploring Operation: 32+4=36, Resulting Numbers: [84, 36] Generated Node #0,0,3: 80:[84, 36] Operation: 32+4=36 Exploring Operation: 84-4=80, Resulting Numbers: [32, 80] Generated Node #0,0,4: 80:[32, 80] Operation: 84-4=80 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[84, 8], Operations: ['3*28=84', '32/4=8'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 84+8=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 84*8=672, Resulting Numbers: [672] 672,80 unequal: No Solution No 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: 80:[84, 36], Operations: ['3*28=84', '32+4=36'] Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,80 unequal: No Solution No 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: 80:[32, 80], Operations: ['3*28=84', '84-4=80'] Exploring Operation: 32+80=112, Resulting Numbers: [112] 112,80 unequal: No Solution Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 32*80=2560, Resulting Numbers: [2560] 2560,80 unequal: No Solution No 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: 80:[32, 21], Operations: ['3*28=84', '84/4=21'] Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,80 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,80 unequal: No Solution No 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: 80:[84, 28], Operations: ['3*28=84', '32-4=28'] Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,80 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,80 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: 80:[3, 28, 36], Operations: ['32+4=36'] Exploring Operation: 36-28=8, Resulting Numbers: [3, 8] Generated Node #0,1,0: 80:[3, 8] Operation: 36-28=8 Exploring Operation: 3*28=84, Resulting Numbers: [36, 84] Generated Node #0,1,1: 80:[36, 84] Operation: 3*28=84 Exploring Operation: 3+36=39, Resulting Numbers: [28, 39] Generated Node #0,1,2: 80:[28, 39] Operation: 3+36=39 Exploring Operation: 36/3=12, Resulting Numbers: [28, 12] Generated Node #0,1,3: 80:[28, 12] Operation: 36/3=12 Exploring Operation: 28-3=25, Resulting Numbers: [36, 25] Generated Node #0,1,4: 80:[36, 25] Operation: 28-3=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[3, 8], Operations: ['32+4=36', '36-28=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,80 unequal: No Solution No 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: 80:[36, 84], Operations: ['32+4=36', '3*28=84'] Exploring Operation: 36*84=3024, Resulting Numbers: [3024] 3024,80 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 36+84=120, Resulting Numbers: [120] 120,80 unequal: No Solution No 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: 80:[28, 39], Operations: ['32+4=36', '3+36=39'] Exploring Operation: 28+39=67, Resulting Numbers: [67] 67,80 unequal: No Solution Exploring Operation: 28*39=1092, Resulting Numbers: [1092] 1092,80 unequal: No Solution Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,80 unequal: No Solution No 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: 80:[36, 25], Operations: ['32+4=36', '28-3=25'] Exploring Operation: 36*25=900, Resulting Numbers: [900] 900,80 unequal: No Solution Exploring Operation: 36+25=61, Resulting Numbers: [61] 61,80 unequal: No Solution Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,80 unequal: No Solution No 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: 80:[28, 12], Operations: ['32+4=36', '36/3=12'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,80 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
[ 24, 87, 32, 78 ]
17
[ "87-24=63", "78-32=46", "63-46=17" ]
Current State: 17:[24, 87, 32, 78], Operations: [] Exploring Operation: 87-24=63, Resulting Numbers: [32, 78, 63] Generated Node #2: [32, 78, 63] from Operation: 87-24=63 Current State: 17:[32, 78, 63], Operations: ['87-24=63'] Exploring Operation: 78-32=46, Resulting Numbers: [63, 46] Generated Node #3: [63, 46] from Operation: 78-32=46 Current State: 17:[63, 46], Operations: ['87-24=63', '78-32=46'] Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[24, 87, 32, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [24, 32, 9] Generated Node #0,0: 17:[24, 32, 9] Operation: 87-78=9 Exploring Operation: 78-32=46, Resulting Numbers: [24, 87, 46] Generated Node #0,1: 17:[24, 87, 46] Operation: 78-32=46 Exploring Operation: 87-32=55, Resulting Numbers: [24, 78, 55] Generated Node #0,2: 17:[24, 78, 55] Operation: 87-32=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[24, 32, 9], Operations: ['87-78=9'] Exploring Operation: 32-24=8, Resulting Numbers: [9, 8] Generated Node #0,0,0: 17:[9, 8] Operation: 32-24=8 Exploring Operation: 32-9=23, Resulting Numbers: [24, 23] Generated Node #0,0,1: 17:[24, 23] Operation: 32-9=23 Exploring Operation: 24-9=15, Resulting Numbers: [32, 15] Generated Node #0,0,2: 17:[32, 15] Operation: 24-9=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 17:[24, 23], Operations: ['87-78=9', '32-9=23'] Exploring Operation: 24*23=552, Resulting Numbers: [552] 552,17 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 24+23=47, Resulting Numbers: [47] 47,17 unequal: No Solution No 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: 17:[9, 8], Operations: ['87-78=9', '32-24=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[24, 87, 32, 78], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [24, 32, 9] Generated Node #0,0: 17:[24, 32, 9] Operation: 87-78=9 Moving to Node #0,0 Current State: 17:[24, 32, 9], Operations: ['87-78=9'] Exploring Operation: 32-24=8, Resulting Numbers: [9, 8] Generated Node #0,0,0: 17:[9, 8] Operation: 32-24=8 Moving to Node #0,0,0 Current State: 17:[9, 8], Operations: ['87-78=9', '32-24=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 56, 13, 41, 30 ]
28
[ "56-13=43", "41+30=71", "71-43=28" ]
Current State: 28:[56, 13, 41, 30], Operations: [] Exploring Operation: 56-13=43, Resulting Numbers: [41, 30, 43] Generated Node #2: [41, 30, 43] from Operation: 56-13=43 Current State: 28:[41, 30, 43], Operations: ['56-13=43'] Exploring Operation: 41+30=71, Resulting Numbers: [43, 71] Generated Node #3: [43, 71] from Operation: 41+30=71 Current State: 28:[43, 71], Operations: ['56-13=43', '41+30=71'] Exploring Operation: 71-43=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[56, 13, 41, 30], Operations: [] Exploring Operation: 56-41=15, Resulting Numbers: [13, 30, 15] Generated Node #0,0: 28:[13, 30, 15] Operation: 56-41=15 Exploring Operation: 56-30=26, Resulting Numbers: [13, 41, 26] Generated Node #0,1: 28:[13, 41, 26] Operation: 56-30=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[13, 30, 15], Operations: ['56-41=15'] Exploring Operation: 13+15=28, Resulting Numbers: [30, 28] Generated Node #0,0,0: 28:[30, 28] Operation: 13+15=28 Exploring Operation: 30/15=2, Resulting Numbers: [13, 2] Generated Node #0,0,1: 28:[13, 2] Operation: 30/15=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[13, 2], Operations: ['56-41=15', '30/15=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,28 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[30, 28], Operations: ['56-41=15', '13+15=28'] Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,28 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[13, 41, 26], Operations: ['56-30=26'] Exploring Operation: 41-26=15, Resulting Numbers: [13, 15] Generated Node #0,1,0: 28:[13, 15] Operation: 41-26=15 Exploring Operation: 41-13=28, Resulting Numbers: [26, 28] Generated Node #0,1,1: 28:[26, 28] Operation: 41-13=28 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[13, 15], Operations: ['56-30=26', '41-26=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[56, 13, 41, 30], Operations: [] Exploring Operation: 56-30=26, Resulting Numbers: [13, 41, 26] Generated Node #0,1: 28:[13, 41, 26] Operation: 56-30=26 Moving to Node #0,1 Current State: 28:[13, 41, 26], Operations: ['56-30=26'] Exploring Operation: 41-26=15, Resulting Numbers: [13, 15] Generated Node #0,1,0: 28:[13, 15] Operation: 41-26=15 Moving to Node #0,1,0 Current State: 28:[13, 15], Operations: ['56-30=26', '41-26=15'] Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 84, 91, 58, 28 ]
54
[ "91-84=7", "28/7=4", "58-4=54" ]
Current State: 54:[84, 91, 58, 28], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [58, 28, 7] Generated Node #2: [58, 28, 7] from Operation: 91-84=7 Current State: 54:[58, 28, 7], Operations: ['91-84=7'] Exploring Operation: 28/7=4, Resulting Numbers: [58, 4] Generated Node #3: [58, 4] from Operation: 28/7=4 Current State: 54:[58, 4], Operations: ['91-84=7', '28/7=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[84, 91, 58, 28], Operations: [] Exploring Operation: 84-28=56, Resulting Numbers: [91, 58, 56] Generated Node #0,0: 54:[91, 58, 56] Operation: 84-28=56 Exploring Operation: 84-58=26, Resulting Numbers: [91, 28, 26] Generated Node #0,1: 54:[91, 28, 26] Operation: 84-58=26 Exploring Operation: 84/28=3, Resulting Numbers: [91, 58, 3] Generated Node #0,2: 54:[91, 58, 3] Operation: 84/28=3 Exploring Operation: 91-58=33, Resulting Numbers: [84, 28, 33] Generated Node #0,3: 54:[84, 28, 33] Operation: 91-58=33 Exploring Operation: 91-84=7, Resulting Numbers: [58, 28, 7] Generated Node #0,4: 54:[58, 28, 7] Operation: 91-84=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 54:[58, 28, 7], Operations: ['91-84=7'] Exploring Operation: 58+7=65, Resulting Numbers: [28, 65] Generated Node #0,4,0: 54:[28, 65] Operation: 58+7=65 Exploring Operation: 28-7=21, Resulting Numbers: [58, 21] Generated Node #0,4,1: 54:[58, 21] Operation: 28-7=21 Exploring Operation: 28/7=4, Resulting Numbers: [58, 4] Generated Node #0,4,2: 54:[58, 4] Operation: 28/7=4 Exploring Operation: 58-28=30, Resulting Numbers: [7, 30] Generated Node #0,4,3: 54:[7, 30] Operation: 58-28=30 Exploring Operation: 58-7=51, Resulting Numbers: [28, 51] Generated Node #0,4,4: 54:[28, 51] Operation: 58-7=51 Moving to Node #0,4,3 Current State: 54:[7, 30], Operations: ['91-84=7', '58-28=30'] Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,54 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,54 unequal: No Solution Moving to Node #0,4,4 Current State: 54:[28, 51], Operations: ['91-84=7', '58-7=51'] Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,54 unequal: No Solution Exploring Operation: 28*51=1428, Resulting Numbers: [1428] 1428,54 unequal: No Solution Exploring Operation: 28+51=79, Resulting Numbers: [79] 79,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[58, 4], Operations: ['91-84=7', '28/7=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,54 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[84, 91, 58, 28], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [58, 28, 7] Generated Node #0,4: 54:[58, 28, 7] Operation: 91-84=7 Moving to Node #0,4 Current State: 54:[58, 28, 7], Operations: ['91-84=7'] Exploring Operation: 28/7=4, Resulting Numbers: [58, 4] Generated Node #0,4,2: 54:[58, 4] Operation: 28/7=4 Moving to Node #0,4,2 Current State: 54:[58, 4], Operations: ['91-84=7', '28/7=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 61, 62, 56, 32 ]
35
[ "61+62=123", "56+32=88", "123-88=35" ]
Current State: 35:[61, 62, 56, 32], Operations: [] Exploring Operation: 61+62=123, Resulting Numbers: [56, 32, 123] Generated Node #2: [56, 32, 123] from Operation: 61+62=123 Current State: 35:[56, 32, 123], Operations: ['61+62=123'] Exploring Operation: 56+32=88, Resulting Numbers: [123, 88] Generated Node #3: [123, 88] from Operation: 56+32=88 Current State: 35:[123, 88], Operations: ['61+62=123', '56+32=88'] Exploring Operation: 123-88=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[61, 62, 56, 32], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [56, 32, 1] Generated Node #0,0: 35:[56, 32, 1] Operation: 62-61=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[56, 32, 1], Operations: ['62-61=1'] Exploring Operation: 56-32=24, Resulting Numbers: [1, 24] Generated Node #0,0,0: 35:[1, 24] Operation: 56-32=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[1, 24], Operations: ['62-61=1', '56-32=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 33, 24, 8, 32 ]
61
[ "33+24=57", "32/8=4", "57+4=61" ]
Current State: 61:[33, 24, 8, 32], Operations: [] Exploring Operation: 33+24=57, Resulting Numbers: [8, 32, 57] Generated Node #2: [8, 32, 57] from Operation: 33+24=57 Current State: 61:[8, 32, 57], Operations: ['33+24=57'] Exploring Operation: 32/8=4, Resulting Numbers: [57, 4] Generated Node #3: [57, 4] from Operation: 32/8=4 Current State: 61:[57, 4], Operations: ['33+24=57', '32/8=4'] Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[33, 24, 8, 32], Operations: [] Exploring Operation: 33+24=57, Resulting Numbers: [8, 32, 57] Generated Node #0,0: 61:[8, 32, 57] Operation: 33+24=57 Exploring Operation: 33+8=41, Resulting Numbers: [24, 32, 41] Generated Node #0,1: 61:[24, 32, 41] Operation: 33+8=41 Exploring Operation: 24+32=56, Resulting Numbers: [33, 8, 56] Generated Node #0,2: 61:[33, 8, 56] Operation: 24+32=56 Exploring Operation: 24+8=32, Resulting Numbers: [33, 32, 32] Generated Node #0,3: 61:[33, 32, 32] Operation: 24+8=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[8, 32, 57], Operations: ['33+24=57'] Exploring Operation: 8+32=40, Resulting Numbers: [57, 40] Generated Node #0,0,0: 61:[57, 40] Operation: 8+32=40 Exploring Operation: 32-8=24, Resulting Numbers: [57, 24] Generated Node #0,0,1: 61:[57, 24] Operation: 32-8=24 Exploring Operation: 57-8=49, Resulting Numbers: [32, 49] Generated Node #0,0,2: 61:[32, 49] Operation: 57-8=49 Exploring Operation: 8+57=65, Resulting Numbers: [32, 65] Generated Node #0,0,3: 61:[32, 65] Operation: 8+57=65 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[57, 40], Operations: ['33+24=57', '8+32=40'] Exploring Operation: 57*40=2280, Resulting Numbers: [2280] 2280,61 unequal: No Solution Exploring Operation: 57+40=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 57-40=17, Resulting Numbers: [17] 17,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 61:[32, 65], Operations: ['33+24=57', '8+57=65'] Exploring Operation: 32+65=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 32*65=2080, Resulting Numbers: [2080] 2080,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[57, 24], Operations: ['33+24=57', '32-8=24'] Exploring Operation: 57*24=1368, Resulting Numbers: [1368] 1368,61 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[32, 49], Operations: ['33+24=57', '57-8=49'] Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,61 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,61 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[24, 32, 41], Operations: ['33+8=41'] Exploring Operation: 32-24=8, Resulting Numbers: [41, 8] Generated Node #0,1,0: 61:[41, 8] Operation: 32-24=8 Exploring Operation: 24+41=65, Resulting Numbers: [32, 65] Generated Node #0,1,1: 61:[32, 65] Operation: 24+41=65 Exploring Operation: 32+41=73, Resulting Numbers: [24, 73] Generated Node #0,1,2: 61:[24, 73] Operation: 32+41=73 Exploring Operation: 24+32=56, Resulting Numbers: [41, 56] Generated Node #0,1,3: 61:[41, 56] Operation: 24+32=56 Moving to Node #0,1,3 Current State: 61:[41, 56], Operations: ['33+8=41', '24+32=56'] Exploring Operation: 41*56=2296, Resulting Numbers: [2296] 2296,61 unequal: No Solution Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 41+56=97, Resulting Numbers: [97] 97,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[32, 65], Operations: ['33+8=41', '24+41=65'] Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 32*65=2080, Resulting Numbers: [2080] 2080,61 unequal: No Solution Exploring Operation: 32+65=97, Resulting Numbers: [97] 97,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[24, 73], Operations: ['33+8=41', '32+41=73'] Exploring Operation: 24+73=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 24*73=1752, Resulting Numbers: [1752] 1752,61 unequal: No Solution Exploring Operation: 73-24=49, Resulting Numbers: [49] 49,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[41, 8], Operations: ['33+8=41', '32-24=8'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,61 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 #0,2 Current State: 61:[33, 8, 56], Operations: ['24+32=56'] Exploring Operation: 33-8=25, Resulting Numbers: [56, 25] Generated Node #0,2,0: 61:[56, 25] Operation: 33-8=25 Exploring Operation: 56-8=48, Resulting Numbers: [33, 48] Generated Node #0,2,1: 61:[33, 48] Operation: 56-8=48 Exploring Operation: 33+8=41, Resulting Numbers: [56, 41] Generated Node #0,2,2: 61:[56, 41] Operation: 33+8=41 Exploring Operation: 8+56=64, Resulting Numbers: [33, 64] Generated Node #0,2,3: 61:[33, 64] Operation: 8+56=64 Moving to Node #0,2,2 Current State: 61:[56, 41], Operations: ['24+32=56', '33+8=41'] Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,61 unequal: No Solution Exploring Operation: 56*41=2296, Resulting Numbers: [2296] 2296,61 unequal: No Solution Exploring Operation: 56+41=97, Resulting Numbers: [97] 97,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[33, 64], Operations: ['24+32=56', '8+56=64'] Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,61 unequal: No Solution Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[33, 48], Operations: ['24+32=56', '56-8=48'] Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,61 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,61 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[56, 25], Operations: ['24+32=56', '33-8=25'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,61 unequal: No Solution Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,61 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 Current State: 61:[33, 32, 32], Operations: ['24+8=32'] Exploring Operation: 33+32=65, Resulting Numbers: [32, 65] Generated Node #0,3,0: 61:[32, 65] Operation: 33+32=65 Exploring Operation: 33+32=65, Resulting Numbers: [32, 65] Generated Node #0,3,1: 61:[32, 65] Operation: 33+32=65 Exploring Operation: 32/32=1, Resulting Numbers: [33, 1] Generated Node #0,3,2: 61:[33, 1] Operation: 32/32=1 Exploring Operation: 32+32=64, Resulting Numbers: [33, 64] Generated Node #0,3,3: 61:[33, 64] Operation: 32+32=64 Moving to Node #0,3,3 Current State: 61:[33, 64], Operations: ['24+8=32', '32+32=64'] Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,61 unequal: No Solution Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[32, 65], Operations: ['24+8=32', '33+32=65'] Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 32+65=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 32*65=2080, Resulting Numbers: [2080] 2080,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[32, 65], Operations: ['24+8=32', '33+32=65'] Exploring Operation: 32*65=2080, Resulting Numbers: [2080] 2080,61 unequal: No Solution Exploring Operation: 32+65=97, Resulting Numbers: [97] 97,61 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[33, 1], Operations: ['24+8=32', '32/32=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,61 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
[ 64, 97, 76, 83 ]
26
[ "97-64=33", "83-76=7", "33-7=26" ]
Current State: 26:[64, 97, 76, 83], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [76, 83, 33] Generated Node #2: [76, 83, 33] from Operation: 97-64=33 Current State: 26:[76, 83, 33], Operations: ['97-64=33'] Exploring Operation: 83-76=7, Resulting Numbers: [33, 7] Generated Node #3: [33, 7] from Operation: 83-76=7 Current State: 26:[33, 7], Operations: ['97-64=33', '83-76=7'] Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[64, 97, 76, 83], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [76, 83, 33] Generated Node #0,0: 26:[76, 83, 33] Operation: 97-64=33 Exploring Operation: 83-76=7, Resulting Numbers: [64, 97, 7] Generated Node #0,1: 26:[64, 97, 7] Operation: 83-76=7 Exploring Operation: 97-83=14, Resulting Numbers: [64, 76, 14] Generated Node #0,2: 26:[64, 76, 14] Operation: 97-83=14 Exploring Operation: 97-76=21, Resulting Numbers: [64, 83, 21] Generated Node #0,3: 26:[64, 83, 21] Operation: 97-76=21 Moving to Node #0,2 Current State: 26:[64, 76, 14], Operations: ['97-83=14'] Exploring Operation: 76-64=12, Resulting Numbers: [14, 12] Generated Node #0,2,0: 26:[14, 12] Operation: 76-64=12 Exploring Operation: 76-14=62, Resulting Numbers: [64, 62] Generated Node #0,2,1: 26:[64, 62] Operation: 76-14=62 Exploring Operation: 64-14=50, Resulting Numbers: [76, 50] Generated Node #0,2,2: 26:[76, 50] Operation: 64-14=50 Exploring Operation: 64+14=78, Resulting Numbers: [76, 78] Generated Node #0,2,3: 26:[76, 78] Operation: 64+14=78 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[14, 12], Operations: ['97-83=14', '76-64=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,26 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[64, 97, 76, 83], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [64, 76, 14] Generated Node #0,2: 26:[64, 76, 14] Operation: 97-83=14 Moving to Node #0,2 Current State: 26:[64, 76, 14], Operations: ['97-83=14'] Exploring Operation: 76-64=12, Resulting Numbers: [14, 12] Generated Node #0,2,0: 26:[14, 12] Operation: 76-64=12 Moving to Node #0,2,0 Current State: 26:[14, 12], Operations: ['97-83=14', '76-64=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 23, 15, 25, 5 ]
44
[ "23*15=345", "345/5=69", "69-25=44" ]
Current State: 44:[23, 15, 25, 5], Operations: [] Exploring Operation: 23*15=345, Resulting Numbers: [25, 5, 345] Generated Node #2: [25, 5, 345] from Operation: 23*15=345 Current State: 44:[25, 5, 345], Operations: ['23*15=345'] Exploring Operation: 345/5=69, Resulting Numbers: [25, 69] Generated Node #3: [25, 69] from Operation: 345/5=69 Current State: 44:[25, 69], Operations: ['23*15=345', '345/5=69'] Exploring Operation: 69-25=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[23, 15, 25, 5], Operations: [] Exploring Operation: 15/5=3, Resulting Numbers: [23, 25, 3] Generated Node #0,0: 44:[23, 25, 3] Operation: 15/5=3 Exploring Operation: 25-15=10, Resulting Numbers: [23, 5, 10] Generated Node #0,1: 44:[23, 5, 10] Operation: 25-15=10 Exploring Operation: 15+25=40, Resulting Numbers: [23, 5, 40] Generated Node #0,2: 44:[23, 5, 40] Operation: 15+25=40 Exploring Operation: 15-5=10, Resulting Numbers: [23, 25, 10] Generated Node #0,3: 44:[23, 25, 10] Operation: 15-5=10 Exploring Operation: 25-23=2, Resulting Numbers: [15, 5, 2] Generated Node #0,4: 44:[15, 5, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[23, 5, 10], Operations: ['25-15=10'] Exploring Operation: 23-5=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 44:[10, 18] Operation: 23-5=18 Exploring Operation: 23-10=13, Resulting Numbers: [5, 13] Generated Node #0,1,1: 44:[5, 13] Operation: 23-10=13 Exploring Operation: 10-5=5, Resulting Numbers: [23, 5] Generated Node #0,1,2: 44:[23, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [23, 2] Generated Node #0,1,3: 44:[23, 2] Operation: 10/5=2 Exploring Operation: 5+10=15, Resulting Numbers: [23, 15] Generated Node #0,1,4: 44:[23, 15] Operation: 5+10=15 Moving to Node #0,1,3 Current State: 44:[23, 2], Operations: ['25-15=10', '10/5=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,44 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[23, 5], Operations: ['25-15=10', '10-5=5'] Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,44 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[5, 13], Operations: ['25-15=10', '23-10=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[10, 18], Operations: ['25-15=10', '23-5=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,1,4 Current State: 44:[23, 15], Operations: ['25-15=10', '5+10=15'] Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[23, 25, 3], Operations: ['15/5=3'] Exploring Operation: 25-23=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 44:[3, 2] Operation: 25-23=2 Exploring Operation: 23+25=48, Resulting Numbers: [3, 48] Generated Node #0,0,1: 44:[3, 48] Operation: 23+25=48 Exploring Operation: 23-3=20, Resulting Numbers: [25, 20] Generated Node #0,0,2: 44:[25, 20] Operation: 23-3=20 Exploring Operation: 23+3=26, Resulting Numbers: [25, 26] Generated Node #0,0,3: 44:[25, 26] Operation: 23+3=26 Exploring Operation: 25-3=22, Resulting Numbers: [23, 22] Generated Node #0,0,4: 44:[23, 22] Operation: 25-3=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[3, 2], Operations: ['15/5=3', '25-23=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 44:[23, 22], Operations: ['15/5=3', '25-3=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,44 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[3, 48], Operations: ['15/5=3', '23+25=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,44 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,44 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[25, 20], Operations: ['15/5=3', '23-3=20'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,44 unequal: No Solution Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 44:[25, 26], Operations: ['15/5=3', '23+3=26'] Exploring Operation: 25*26=650, Resulting Numbers: [650] 650,44 unequal: No Solution Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,44 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[23, 25, 10], Operations: ['15-5=10'] Exploring Operation: 23-10=13, Resulting Numbers: [25, 13] Generated Node #0,3,0: 44:[25, 13] Operation: 23-10=13 Exploring Operation: 23+25=48, Resulting Numbers: [10, 48] Generated Node #0,3,1: 44:[10, 48] Operation: 23+25=48 Exploring Operation: 25-10=15, Resulting Numbers: [23, 15] Generated Node #0,3,2: 44:[23, 15] Operation: 25-10=15 Exploring Operation: 25+10=35, Resulting Numbers: [23, 35] Generated Node #0,3,3: 44:[23, 35] Operation: 25+10=35 Exploring Operation: 25-23=2, Resulting Numbers: [10, 2] Generated Node #0,3,4: 44:[10, 2] Operation: 25-23=2 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 44:[10, 2], Operations: ['15-5=10', '25-23=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 44:[25, 13], Operations: ['15-5=10', '23-10=13'] Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,44 unequal: No Solution Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 44:[10, 48], Operations: ['15-5=10', '23+25=48'] Exploring Operation: 10*48=480, Resulting Numbers: [480] 480,44 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 44:[23, 15], Operations: ['15-5=10', '25-10=15'] Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 23*15=345, Resulting Numbers: [345] 345,44 unequal: No Solution Exploring Operation: 23+15=38, Resulting Numbers: [38] 38,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 44:[23, 35], Operations: ['15-5=10', '25+10=35'] Exploring Operation: 23+35=58, Resulting Numbers: [58] 58,44 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 23*35=805, Resulting Numbers: [805] 805,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 44:[15, 5, 2], Operations: ['25-23=2'] Exploring Operation: 15/5=3, Resulting Numbers: [2, 3] Generated Node #0,4,0: 44:[2, 3] Operation: 15/5=3 Exploring Operation: 15-5=10, Resulting Numbers: [2, 10] Generated Node #0,4,1: 44:[2, 10] Operation: 15-5=10 Exploring Operation: 15-2=13, Resulting Numbers: [5, 13] Generated Node #0,4,2: 44:[5, 13] Operation: 15-2=13 Exploring Operation: 15+5=20, Resulting Numbers: [2, 20] Generated Node #0,4,3: 44:[2, 20] Operation: 15+5=20 Exploring Operation: 5*2=10, Resulting Numbers: [15, 10] Generated Node #0,4,4: 44:[15, 10] Operation: 5*2=10 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 44:[2, 3], Operations: ['25-23=2', '15/5=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 44:[2, 10], Operations: ['25-23=2', '15-5=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 44:[2, 20], Operations: ['25-23=2', '15+5=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,44 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 44:[5, 13], Operations: ['25-23=2', '15-2=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 44:[15, 10], Operations: ['25-23=2', '5*2=10'] Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,44 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[23, 5, 40], Operations: ['15+25=40'] Exploring Operation: 40/5=8, Resulting Numbers: [23, 8] Generated Node #0,2,0: 44:[23, 8] Operation: 40/5=8 Exploring Operation: 23+5=28, Resulting Numbers: [40, 28] Generated Node #0,2,1: 44:[40, 28] Operation: 23+5=28 Exploring Operation: 23-5=18, Resulting Numbers: [40, 18] Generated Node #0,2,2: 44:[40, 18] Operation: 23-5=18 Exploring Operation: 5+40=45, Resulting Numbers: [23, 45] Generated Node #0,2,3: 44:[23, 45] Operation: 5+40=45 Exploring Operation: 40-23=17, Resulting Numbers: [5, 17] Generated Node #0,2,4: 44:[5, 17] Operation: 40-23=17 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[23, 45], Operations: ['15+25=40', '5+40=45'] Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 23*45=1035, Resulting Numbers: [1035] 1035,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[23, 8], Operations: ['15+25=40', '40/5=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,44 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 44:[5, 17], Operations: ['15+25=40', '40-23=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,44 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[40, 18], Operations: ['15+25=40', '23-5=18'] Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,44 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,44 unequal: No Solution Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[40, 28], Operations: ['15+25=40', '23+5=28'] Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,44 unequal: No Solution Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 8, 68, 14, 36 ]
82
[ "68-8=60", "36-14=22", "60+22=82" ]
Current State: 82:[8, 68, 14, 36], Operations: [] Exploring Operation: 68-8=60, Resulting Numbers: [14, 36, 60] Generated Node #2: [14, 36, 60] from Operation: 68-8=60 Current State: 82:[14, 36, 60], Operations: ['68-8=60'] Exploring Operation: 36-14=22, Resulting Numbers: [60, 22] Generated Node #3: [60, 22] from Operation: 36-14=22 Current State: 82:[60, 22], Operations: ['68-8=60', '36-14=22'] Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[8, 68, 14, 36], Operations: [] Exploring Operation: 68+14=82, Resulting Numbers: [8, 36, 82] Generated Node #0,0: 82:[8, 36, 82] Operation: 68+14=82 Moving to Node #0,0 Current State: 82:[8, 36, 82], Operations: ['68+14=82'] Exploring Operation: 8+36=44, Resulting Numbers: [82, 44] Generated Node #0,0,0: 82:[82, 44] Operation: 8+36=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[82, 44], Operations: ['68+14=82', '8+36=44'] Exploring Operation: 82-44=38, Resulting Numbers: [38] 38,82 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
[ 14, 51, 26, 32 ]
80
[ "14+51=65", "32*65=2080", "2080/26=80" ]
Current State: 80:[14, 51, 26, 32], Operations: [] Exploring Operation: 14+51=65, Resulting Numbers: [26, 32, 65] Generated Node #2: [26, 32, 65] from Operation: 14+51=65 Current State: 80:[26, 32, 65], Operations: ['14+51=65'] Exploring Operation: 32*65=2080, Resulting Numbers: [26, 2080] Generated Node #3: [26, 2080] from Operation: 32*65=2080 Current State: 80:[26, 2080], Operations: ['14+51=65', '32*65=2080'] Exploring Operation: 2080/26=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[14, 51, 26, 32], Operations: [] Exploring Operation: 51-32=19, Resulting Numbers: [14, 26, 19] Generated Node #0,0: 80:[14, 26, 19] Operation: 51-32=19 Exploring Operation: 32-26=6, Resulting Numbers: [14, 51, 6] Generated Node #0,1: 80:[14, 51, 6] Operation: 32-26=6 Exploring Operation: 51+26=77, Resulting Numbers: [14, 32, 77] Generated Node #0,2: 80:[14, 32, 77] Operation: 51+26=77 Exploring Operation: 51+32=83, Resulting Numbers: [14, 26, 83] Generated Node #0,3: 80:[14, 26, 83] Operation: 51+32=83 Moving to Node #0,0 Current State: 80:[14, 26, 19], Operations: ['51-32=19'] Exploring Operation: 26-19=7, Resulting Numbers: [14, 7] Generated Node #0,0,0: 80:[14, 7] Operation: 26-19=7 Exploring Operation: 14+26=40, Resulting Numbers: [19, 40] Generated Node #0,0,1: 80:[19, 40] Operation: 14+26=40 Exploring Operation: 19-14=5, Resulting Numbers: [26, 5] Generated Node #0,0,2: 80:[26, 5] Operation: 19-14=5 Exploring Operation: 26-14=12, Resulting Numbers: [19, 12] Generated Node #0,0,3: 80:[19, 12] Operation: 26-14=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[19, 40], Operations: ['51-32=19', '14+26=40'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,80 unequal: No Solution Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,80 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 #0,0,0 Current State: 80:[14, 7], Operations: ['51-32=19', '26-19=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,80 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,80 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 #0,0,3 Current State: 80:[19, 12], Operations: ['51-32=19', '26-14=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,80 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 #0,0,2 Current State: 80:[26, 5], Operations: ['51-32=19', '19-14=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,80 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: 80:[14, 26, 83], Operations: ['51+32=83'] Exploring Operation: 14+26=40, Resulting Numbers: [83, 40] Generated Node #0,3,0: 80:[83, 40] Operation: 14+26=40 Exploring Operation: 83-26=57, Resulting Numbers: [14, 57] Generated Node #0,3,1: 80:[14, 57] Operation: 83-26=57 Exploring Operation: 26-14=12, Resulting Numbers: [83, 12] Generated Node #0,3,2: 80:[83, 12] Operation: 26-14=12 Exploring Operation: 83-14=69, Resulting Numbers: [26, 69] Generated Node #0,3,3: 80:[26, 69] Operation: 83-14=69 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[83, 40], Operations: ['51+32=83', '14+26=40'] Exploring Operation: 83*40=3320, Resulting Numbers: [3320] 3320,80 unequal: No Solution Exploring Operation: 83+40=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 83-40=43, Resulting Numbers: [43] 43,80 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 #0,3,2 Current State: 80:[83, 12], Operations: ['51+32=83', '26-14=12'] Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,80 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,80 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 #0,3,3 Current State: 80:[26, 69], Operations: ['51+32=83', '83-14=69'] Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 26+69=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 26*69=1794, Resulting Numbers: [1794] 1794,80 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 #0,3,1 Current State: 80:[14, 57], Operations: ['51+32=83', '83-26=57'] Exploring Operation: 14*57=798, Resulting Numbers: [798] 798,80 unequal: No Solution Exploring Operation: 14+57=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,80 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:[14, 32, 77], Operations: ['51+26=77'] Exploring Operation: 14+32=46, Resulting Numbers: [77, 46] Generated Node #0,2,0: 80:[77, 46] Operation: 14+32=46 Exploring Operation: 32-14=18, Resulting Numbers: [77, 18] Generated Node #0,2,1: 80:[77, 18] Operation: 32-14=18 Exploring Operation: 14+77=91, Resulting Numbers: [32, 91] Generated Node #0,2,2: 80:[32, 91] Operation: 14+77=91 Exploring Operation: 77-32=45, Resulting Numbers: [14, 45] Generated Node #0,2,3: 80:[14, 45] Operation: 77-32=45 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[77, 18], Operations: ['51+26=77', '32-14=18'] Exploring Operation: 77+18=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 77*18=1386, Resulting Numbers: [1386] 1386,80 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,80 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 #0,2,3 Current State: 80:[14, 45], Operations: ['51+26=77', '77-32=45'] Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,80 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,80 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:[77, 46], Operations: ['51+26=77', '14+32=46'] Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,80 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,80 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:[32, 91], Operations: ['51+26=77', '14+77=91'] Exploring Operation: 32*91=2912, Resulting Numbers: [2912] 2912,80 unequal: No Solution Exploring Operation: 32+91=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 80:[14, 51, 6], Operations: ['32-26=6'] Exploring Operation: 14-6=8, Resulting Numbers: [51, 8] Generated Node #0,1,0: 80:[51, 8] Operation: 14-6=8 Exploring Operation: 51-14=37, Resulting Numbers: [6, 37] Generated Node #0,1,1: 80:[6, 37] Operation: 51-14=37 Exploring Operation: 51-6=45, Resulting Numbers: [14, 45] Generated Node #0,1,2: 80:[14, 45] Operation: 51-6=45 Exploring Operation: 14+6=20, Resulting Numbers: [51, 20] Generated Node #0,1,3: 80:[51, 20] Operation: 14+6=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[6, 37], Operations: ['32-26=6', '51-14=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,80 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:[14, 45], Operations: ['32-26=6', '51-6=45'] Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,80 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,80 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:[51, 8], Operations: ['32-26=6', '14-6=8'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,80 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,80 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:[51, 20], Operations: ['32-26=6', '14+6=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,80 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,80 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, 13, 32, 28 ]
11
[ "36+13=49", "32+28=60", "60-49=11" ]
Current State: 11:[36, 13, 32, 28], Operations: [] Exploring Operation: 36+13=49, Resulting Numbers: [32, 28, 49] Generated Node #2: [32, 28, 49] from Operation: 36+13=49 Current State: 11:[32, 28, 49], Operations: ['36+13=49'] Exploring Operation: 32+28=60, Resulting Numbers: [49, 60] Generated Node #3: [49, 60] from Operation: 32+28=60 Current State: 11:[49, 60], Operations: ['36+13=49', '32+28=60'] Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[36, 13, 32, 28], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [13, 28, 4] Generated Node #0,0: 11:[13, 28, 4] Operation: 36-32=4 Exploring Operation: 32-28=4, Resulting Numbers: [36, 13, 4] Generated Node #0,1: 11:[36, 13, 4] Operation: 32-28=4 Exploring Operation: 32-13=19, Resulting Numbers: [36, 28, 19] Generated Node #0,2: 11:[36, 28, 19] Operation: 32-13=19 Exploring Operation: 36-28=8, Resulting Numbers: [13, 32, 8] Generated Node #0,3: 11:[13, 32, 8] Operation: 36-28=8 Exploring Operation: 36-13=23, Resulting Numbers: [32, 28, 23] Generated Node #0,4: 11:[32, 28, 23] Operation: 36-13=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[13, 28, 4], Operations: ['36-32=4'] Exploring Operation: 28/4=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 11:[13, 7] Operation: 28/4=7 Exploring Operation: 13-4=9, Resulting Numbers: [28, 9] Generated Node #0,0,1: 11:[28, 9] Operation: 13-4=9 Exploring Operation: 28-13=15, Resulting Numbers: [4, 15] Generated Node #0,0,2: 11:[4, 15] Operation: 28-13=15 Exploring Operation: 13+4=17, Resulting Numbers: [28, 17] Generated Node #0,0,3: 11:[28, 17] Operation: 13+4=17 Exploring Operation: 28-4=24, Resulting Numbers: [13, 24] Generated Node #0,0,4: 11:[13, 24] Operation: 28-4=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[13, 7], Operations: ['36-32=4', '28/4=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,11 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,11 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 #0,0,2 Current State: 11:[4, 15], Operations: ['36-32=4', '28-13=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,11 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[36, 13, 32, 28], Operations: [] Exploring Operation: 36-32=4, Resulting Numbers: [13, 28, 4] Generated Node #0,0: 11:[13, 28, 4] Operation: 36-32=4 Moving to Node #0,0 Current State: 11:[13, 28, 4], Operations: ['36-32=4'] Exploring Operation: 28-13=15, Resulting Numbers: [4, 15] Generated Node #0,0,2: 11:[4, 15] Operation: 28-13=15 Moving to Node #0,0,2 Current State: 11:[4, 15], Operations: ['36-32=4', '28-13=15'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 51, 27, 98, 41 ]
44
[ "41-27=14", "98/14=7", "51-7=44" ]
Current State: 44:[51, 27, 98, 41], Operations: [] Exploring Operation: 41-27=14, Resulting Numbers: [51, 98, 14] Generated Node #2: [51, 98, 14] from Operation: 41-27=14 Current State: 44:[51, 98, 14], Operations: ['41-27=14'] Exploring Operation: 98/14=7, Resulting Numbers: [51, 7] Generated Node #3: [51, 7] from Operation: 98/14=7 Current State: 44:[51, 7], Operations: ['41-27=14', '98/14=7'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[51, 27, 98, 41], Operations: [] Exploring Operation: 98-27=71, Resulting Numbers: [51, 41, 71] Generated Node #0,0: 44:[51, 41, 71] Operation: 98-27=71 Exploring Operation: 51-27=24, Resulting Numbers: [98, 41, 24] Generated Node #0,1: 44:[98, 41, 24] Operation: 51-27=24 Exploring Operation: 98-41=57, Resulting Numbers: [51, 27, 57] Generated Node #0,2: 44:[51, 27, 57] Operation: 98-41=57 Exploring Operation: 98-51=47, Resulting Numbers: [27, 41, 47] Generated Node #0,3: 44:[27, 41, 47] Operation: 98-51=47 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[27, 41, 47], Operations: ['98-51=47'] Exploring Operation: 41-27=14, Resulting Numbers: [47, 14] Generated Node #0,3,0: 44:[47, 14] Operation: 41-27=14 Exploring Operation: 47-27=20, Resulting Numbers: [41, 20] Generated Node #0,3,1: 44:[41, 20] Operation: 47-27=20 Exploring Operation: 27+41=68, Resulting Numbers: [47, 68] Generated Node #0,3,2: 44:[47, 68] Operation: 27+41=68 Exploring Operation: 47-41=6, Resulting Numbers: [27, 6] Generated Node #0,3,3: 44:[27, 6] Operation: 47-41=6 Moving to Node #0,3,1 Current State: 44:[41, 20], Operations: ['98-51=47', '47-27=20'] Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,44 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[47, 14], Operations: ['98-51=47', '41-27=14'] Exploring Operation: 47*14=658, Resulting Numbers: [658] 658,44 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[27, 6], Operations: ['98-51=47', '47-41=6'] Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[47, 68], Operations: ['98-51=47', '27+41=68'] Exploring Operation: 68-47=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 47+68=115, Resulting Numbers: [115] 115,44 unequal: No Solution Exploring Operation: 47*68=3196, Resulting Numbers: [3196] 3196,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[51, 27, 57], Operations: ['98-41=57'] Exploring Operation: 57-51=6, Resulting Numbers: [27, 6] Generated Node #0,2,0: 44:[27, 6] Operation: 57-51=6 Exploring Operation: 51-27=24, Resulting Numbers: [57, 24] Generated Node #0,2,1: 44:[57, 24] Operation: 51-27=24 Exploring Operation: 57-27=30, Resulting Numbers: [51, 30] Generated Node #0,2,2: 44:[51, 30] Operation: 57-27=30 Exploring Operation: 51+27=78, Resulting Numbers: [57, 78] Generated Node #0,2,3: 44:[57, 78] Operation: 51+27=78 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[27, 6], Operations: ['98-41=57', '57-51=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,44 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[57, 24], Operations: ['98-41=57', '51-27=24'] Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,44 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 57*24=1368, Resulting Numbers: [1368] 1368,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[51, 30], Operations: ['98-41=57', '57-27=30'] Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,44 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,44 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[57, 78], Operations: ['98-41=57', '51+27=78'] Exploring Operation: 78-57=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 57+78=135, Resulting Numbers: [135] 135,44 unequal: No Solution Exploring Operation: 57*78=4446, Resulting Numbers: [4446] 4446,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[51, 41, 71], Operations: ['98-27=71'] Exploring Operation: 71-51=20, Resulting Numbers: [41, 20] Generated Node #0,0,0: 44:[41, 20] Operation: 71-51=20 Exploring Operation: 51+41=92, Resulting Numbers: [71, 92] Generated Node #0,0,1: 44:[71, 92] Operation: 51+41=92 Exploring Operation: 51-41=10, Resulting Numbers: [71, 10] Generated Node #0,0,2: 44:[71, 10] Operation: 51-41=10 Exploring Operation: 71-41=30, Resulting Numbers: [51, 30] Generated Node #0,0,3: 44:[51, 30] Operation: 71-41=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[41, 20], Operations: ['98-27=71', '71-51=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,44 unequal: No Solution Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 44:[51, 30], Operations: ['98-27=71', '71-41=30'] Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,44 unequal: No Solution Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[71, 10], Operations: ['98-27=71', '51-41=10'] Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,44 unequal: No Solution Exploring Operation: 71*10=710, Resulting Numbers: [710] 710,44 unequal: No Solution Exploring Operation: 71+10=81, Resulting Numbers: [81] 81,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[71, 92], Operations: ['98-27=71', '51+41=92'] Exploring Operation: 71+92=163, Resulting Numbers: [163] 163,44 unequal: No Solution Exploring Operation: 71*92=6532, Resulting Numbers: [6532] 6532,44 unequal: No Solution Exploring Operation: 92-71=21, Resulting Numbers: [21] 21,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[98, 41, 24], Operations: ['51-27=24'] Exploring Operation: 41+24=65, Resulting Numbers: [98, 65] Generated Node #0,1,0: 44:[98, 65] Operation: 41+24=65 Exploring Operation: 98-24=74, Resulting Numbers: [41, 74] Generated Node #0,1,1: 44:[41, 74] Operation: 98-24=74 Exploring Operation: 41-24=17, Resulting Numbers: [98, 17] Generated Node #0,1,2: 44:[98, 17] Operation: 41-24=17 Exploring Operation: 98-41=57, Resulting Numbers: [24, 57] Generated Node #0,1,3: 44:[24, 57] Operation: 98-41=57 Moving to Node #0,1,3 Current State: 44:[24, 57], Operations: ['51-27=24', '98-41=57'] Exploring Operation: 24*57=1368, Resulting Numbers: [1368] 1368,44 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 24+57=81, Resulting Numbers: [81] 81,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[41, 74], Operations: ['51-27=24', '98-24=74'] Exploring Operation: 41+74=115, Resulting Numbers: [115] 115,44 unequal: No Solution Exploring Operation: 41*74=3034, Resulting Numbers: [3034] 3034,44 unequal: No Solution Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[98, 17], Operations: ['51-27=24', '41-24=17'] Exploring Operation: 98+17=115, Resulting Numbers: [115] 115,44 unequal: No Solution Exploring Operation: 98*17=1666, Resulting Numbers: [1666] 1666,44 unequal: No Solution Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[98, 65], Operations: ['51-27=24', '41+24=65'] Exploring Operation: 98+65=163, Resulting Numbers: [163] 163,44 unequal: No Solution Exploring Operation: 98-65=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 98*65=6370, Resulting Numbers: [6370] 6370,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 15, 14, 16, 76 ]
10
[ "14+76=90", "90/15=6", "16-6=10" ]
Current State: 10:[15, 14, 16, 76], Operations: [] Exploring Operation: 14+76=90, Resulting Numbers: [15, 16, 90] Generated Node #2: [15, 16, 90] from Operation: 14+76=90 Current State: 10:[15, 16, 90], Operations: ['14+76=90'] Exploring Operation: 90/15=6, Resulting Numbers: [16, 6] Generated Node #3: [16, 6] from Operation: 90/15=6 Current State: 10:[16, 6], Operations: ['14+76=90', '90/15=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[15, 14, 16, 76], Operations: [] Exploring Operation: 16-15=1, Resulting Numbers: [14, 76, 1] Generated Node #0,0: 10:[14, 76, 1] Operation: 16-15=1 Exploring Operation: 76-16=60, Resulting Numbers: [15, 14, 60] Generated Node #0,1: 10:[15, 14, 60] Operation: 76-16=60 Exploring Operation: 76-15=61, Resulting Numbers: [14, 16, 61] Generated Node #0,2: 10:[14, 16, 61] Operation: 76-15=61 Exploring Operation: 16-14=2, Resulting Numbers: [15, 76, 2] Generated Node #0,3: 10:[15, 76, 2] Operation: 16-14=2 Exploring Operation: 76-14=62, Resulting Numbers: [15, 16, 62] Generated Node #0,4: 10:[15, 16, 62] Operation: 76-14=62 Moving to Node #0,1 Current State: 10:[15, 14, 60], Operations: ['76-16=60'] Exploring Operation: 15-14=1, Resulting Numbers: [60, 1] Generated Node #0,1,0: 10:[60, 1] Operation: 15-14=1 Exploring Operation: 60-15=45, Resulting Numbers: [14, 45] Generated Node #0,1,1: 10:[14, 45] Operation: 60-15=45 Exploring Operation: 60/15=4, Resulting Numbers: [14, 4] Generated Node #0,1,2: 10:[14, 4] Operation: 60/15=4 Exploring Operation: 15+14=29, Resulting Numbers: [60, 29] Generated Node #0,1,3: 10:[60, 29] Operation: 15+14=29 Exploring Operation: 60-14=46, Resulting Numbers: [15, 46] Generated Node #0,1,4: 10:[15, 46] Operation: 60-14=46 Moving to Node #0,2 Current State: 10:[14, 16, 61], Operations: ['76-15=61'] Exploring Operation: 14+61=75, Resulting Numbers: [16, 75] Generated Node #0,2,0: 10:[16, 75] Operation: 14+61=75 Exploring Operation: 16-14=2, Resulting Numbers: [61, 2] Generated Node #0,2,1: 10:[61, 2] Operation: 16-14=2 Exploring Operation: 14+16=30, Resulting Numbers: [61, 30] Generated Node #0,2,2: 10:[61, 30] Operation: 14+16=30 Exploring Operation: 61-16=45, Resulting Numbers: [14, 45] Generated Node #0,2,3: 10:[14, 45] Operation: 61-16=45 Exploring Operation: 61-14=47, Resulting Numbers: [16, 47] Generated Node #0,2,4: 10:[16, 47] Operation: 61-14=47 Moving to Node #0,4 Current State: 10:[15, 16, 62], Operations: ['76-14=62'] Exploring Operation: 62-16=46, Resulting Numbers: [15, 46] Generated Node #0,4,0: 10:[15, 46] Operation: 62-16=46 Exploring Operation: 15+16=31, Resulting Numbers: [62, 31] Generated Node #0,4,1: 10:[62, 31] Operation: 15+16=31 Exploring Operation: 16-15=1, Resulting Numbers: [62, 1] Generated Node #0,4,2: 10:[62, 1] Operation: 16-15=1 Exploring Operation: 62-15=47, Resulting Numbers: [16, 47] Generated Node #0,4,3: 10:[16, 47] Operation: 62-15=47 Exploring Operation: 15+62=77, Resulting Numbers: [16, 77] Generated Node #0,4,4: 10:[16, 77] Operation: 15+62=77 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 10:[15, 46], Operations: ['76-14=62', '62-16=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,10 unequal: No Solution Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 10:[16, 47], Operations: ['76-14=62', '62-15=47'] Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 10:[62, 1], Operations: ['76-14=62', '16-15=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,10 unequal: No Solution Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,10 unequal: No Solution Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 10:[62, 31], Operations: ['76-14=62', '15+16=31'] Exploring Operation: 62/31=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 62*31=1922, Resulting Numbers: [1922] 1922,10 unequal: No Solution Exploring Operation: 62+31=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 62-31=31, Resulting Numbers: [31] 31,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 10:[16, 77], Operations: ['76-14=62', '15+62=77'] Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,10 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,10 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: 10:[14, 76, 1], Operations: ['16-15=1'] Exploring Operation: 76-1=75, Resulting Numbers: [14, 75] Generated Node #0,0,0: 10:[14, 75] Operation: 76-1=75 Exploring Operation: 76-14=62, Resulting Numbers: [1, 62] Generated Node #0,0,1: 10:[1, 62] Operation: 76-14=62 Exploring Operation: 14-1=13, Resulting Numbers: [76, 13] Generated Node #0,0,2: 10:[76, 13] Operation: 14-1=13 Exploring Operation: 14/1=14, Resulting Numbers: [76, 14] Generated Node #0,0,3: 10:[76, 14] Operation: 14/1=14 Exploring Operation: 14*1=14, Resulting Numbers: [76, 14] Generated Node #0,0,4: 10:[76, 14] Operation: 14*1=14 Moving to Node #0,3 Current State: 10:[15, 76, 2], Operations: ['16-14=2'] Exploring Operation: 76-15=61, Resulting Numbers: [2, 61] Generated Node #0,3,0: 10:[2, 61] Operation: 76-15=61 Exploring Operation: 76-2=74, Resulting Numbers: [15, 74] Generated Node #0,3,1: 10:[15, 74] Operation: 76-2=74 Exploring Operation: 76/2=38, Resulting Numbers: [15, 38] Generated Node #0,3,2: 10:[15, 38] Operation: 76/2=38 Exploring Operation: 15+2=17, Resulting Numbers: [76, 17] Generated Node #0,3,3: 10:[76, 17] Operation: 15+2=17 Exploring Operation: 15-2=13, Resulting Numbers: [76, 13] Generated Node #0,3,4: 10:[76, 13] Operation: 15-2=13 Moving to Node #0,1,2 Current State: 10:[14, 4], Operations: ['76-16=60', '60/15=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,10 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[15, 14, 16, 76], Operations: [] Exploring Operation: 76-16=60, Resulting Numbers: [15, 14, 60] Generated Node #0,1: 10:[15, 14, 60] Operation: 76-16=60 Moving to Node #0,1 Current State: 10:[15, 14, 60], Operations: ['76-16=60'] Exploring Operation: 60/15=4, Resulting Numbers: [14, 4] Generated Node #0,1,2: 10:[14, 4] Operation: 60/15=4 Moving to Node #0,1,2 Current State: 10:[14, 4], Operations: ['76-16=60', '60/15=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.953125
hs_5
sum_heuristic
[ 54, 24, 48, 3 ]
60
[ "48/24=2", "3*2=6", "54+6=60" ]
Current State: 60:[54, 24, 48, 3], Operations: [] Exploring Operation: 48/24=2, Resulting Numbers: [54, 3, 2] Generated Node #2: [54, 3, 2] from Operation: 48/24=2 Current State: 60:[54, 3, 2], Operations: ['48/24=2'] Exploring Operation: 3*2=6, Resulting Numbers: [54, 6] Generated Node #3: [54, 6] from Operation: 3*2=6 Current State: 60:[54, 6], Operations: ['48/24=2', '3*2=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[54, 24, 48, 3], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [24, 3, 6] Generated Node #0,0: 60:[24, 3, 6] Operation: 54-48=6 Exploring Operation: 48/24=2, Resulting Numbers: [54, 3, 2] Generated Node #0,1: 60:[54, 3, 2] Operation: 48/24=2 Moving to Node #0,0 Current State: 60:[24, 3, 6], Operations: ['54-48=6'] Exploring Operation: 24/6=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 60:[3, 4] Operation: 24/6=4 Exploring Operation: 24+6=30, Resulting Numbers: [3, 30] Generated Node #0,0,1: 60:[3, 30] Operation: 24+6=30 Moving to Node #0,1 Current State: 60:[54, 3, 2], Operations: ['48/24=2'] Exploring Operation: 54/3=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 60:[2, 18] Operation: 54/3=18 Exploring Operation: 54+3=57, Resulting Numbers: [2, 57] Generated Node #0,1,1: 60:[2, 57] Operation: 54+3=57 Moving to Node #0,0,0 Current State: 60:[3, 4], Operations: ['54-48=6', '24/6=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[3, 30], Operations: ['54-48=6', '24+6=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,60 unequal: No Solution Moving to Node #0,1,0 Current State: 60:[2, 18], Operations: ['48/24=2', '54/3=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[2, 57], Operations: ['48/24=2', '54+3=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,60 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 61, 86, 88, 83 ]
82
[ "83-61=22", "88/22=4", "86-4=82" ]
Current State: 82:[61, 86, 88, 83], Operations: [] Exploring Operation: 83-61=22, Resulting Numbers: [86, 88, 22] Generated Node #2: [86, 88, 22] from Operation: 83-61=22 Current State: 82:[86, 88, 22], Operations: ['83-61=22'] Exploring Operation: 88/22=4, Resulting Numbers: [86, 4] Generated Node #3: [86, 4] from Operation: 88/22=4 Current State: 82:[86, 4], Operations: ['83-61=22', '88/22=4'] Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[61, 86, 88, 83], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [61, 83, 2] Generated Node #0,0: 82:[61, 83, 2] Operation: 88-86=2 Exploring Operation: 86-61=25, Resulting Numbers: [88, 83, 25] Generated Node #0,1: 82:[88, 83, 25] Operation: 86-61=25 Exploring Operation: 88-61=27, Resulting Numbers: [86, 83, 27] Generated Node #0,2: 82:[86, 83, 27] Operation: 88-61=27 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[86, 83, 27], Operations: ['88-61=27'] Exploring Operation: 86-27=59, Resulting Numbers: [83, 59] Generated Node #0,2,0: 82:[83, 59] Operation: 86-27=59 Exploring Operation: 83-27=56, Resulting Numbers: [86, 56] Generated Node #0,2,1: 82:[86, 56] Operation: 83-27=56 Exploring Operation: 86-83=3, Resulting Numbers: [27, 3] Generated Node #0,2,2: 82:[27, 3] Operation: 86-83=3 Moving to Node #0,2,2 Current State: 82:[27, 3], Operations: ['88-61=27', '86-83=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,82 unequal: No Solution Moving to Node #0,2,0 Current State: 82:[83, 59], Operations: ['88-61=27', '86-27=59'] Exploring Operation: 83+59=142, Resulting Numbers: [142] 142,82 unequal: No Solution Exploring Operation: 83-59=24, Resulting Numbers: [24] 24,82 unequal: No Solution Exploring Operation: 83*59=4897, Resulting Numbers: [4897] 4897,82 unequal: No Solution Moving to Node #0,2,1 Current State: 82:[86, 56], Operations: ['88-61=27', '83-27=56'] Exploring Operation: 86+56=142, Resulting Numbers: [142] 142,82 unequal: No Solution Exploring Operation: 86-56=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 86*56=4816, Resulting Numbers: [4816] 4816,82 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 Current State: 82:[61, 83, 2], Operations: ['88-86=2'] Exploring Operation: 61-2=59, Resulting Numbers: [83, 59] Generated Node #0,0,0: 82:[83, 59] Operation: 61-2=59 Exploring Operation: 61+2=63, Resulting Numbers: [83, 63] Generated Node #0,0,1: 82:[83, 63] Operation: 61+2=63 Exploring Operation: 83-61=22, Resulting Numbers: [2, 22] Generated Node #0,0,2: 82:[2, 22] Operation: 83-61=22 Moving to Node #0,0,0 Current State: 82:[83, 59], Operations: ['88-86=2', '61-2=59'] Exploring Operation: 83+59=142, Resulting Numbers: [142] 142,82 unequal: No Solution Exploring Operation: 83*59=4897, Resulting Numbers: [4897] 4897,82 unequal: No Solution Exploring Operation: 83-59=24, Resulting Numbers: [24] 24,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[2, 22], Operations: ['88-86=2', '83-61=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,82 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[83, 63], Operations: ['88-86=2', '61+2=63'] Exploring Operation: 83-63=20, Resulting Numbers: [20] 20,82 unequal: No Solution Exploring Operation: 83+63=146, Resulting Numbers: [146] 146,82 unequal: No Solution Exploring Operation: 83*63=5229, Resulting Numbers: [5229] 5229,82 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 #0,1 Current State: 82:[88, 83, 25], Operations: ['86-61=25'] Exploring Operation: 88-83=5, Resulting Numbers: [25, 5] Generated Node #0,1,0: 82:[25, 5] Operation: 88-83=5 Exploring Operation: 88-25=63, Resulting Numbers: [83, 63] Generated Node #0,1,1: 82:[83, 63] Operation: 88-25=63 Exploring Operation: 83-25=58, Resulting Numbers: [88, 58] Generated Node #0,1,2: 82:[88, 58] Operation: 83-25=58 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[25, 5], Operations: ['86-61=25', '88-83=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,82 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,82 unequal: No Solution No 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: 82:[83, 63], Operations: ['86-61=25', '88-25=63'] Exploring Operation: 83+63=146, Resulting Numbers: [146] 146,82 unequal: No Solution Exploring Operation: 83*63=5229, Resulting Numbers: [5229] 5229,82 unequal: No Solution Exploring Operation: 83-63=20, Resulting Numbers: [20] 20,82 unequal: No Solution No 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: 82:[88, 58], Operations: ['86-61=25', '83-25=58'] Exploring Operation: 88*58=5104, Resulting Numbers: [5104] 5104,82 unequal: No Solution Exploring Operation: 88-58=30, Resulting Numbers: [30] 30,82 unequal: No Solution Exploring Operation: 88+58=146, Resulting Numbers: [146] 146,82 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
[ 90, 5, 3, 18 ]
89
[ "90+5=95", "18/3=6", "95-6=89" ]
Current State: 89:[90, 5, 3, 18], Operations: [] Exploring Operation: 90+5=95, Resulting Numbers: [3, 18, 95] Generated Node #2: [3, 18, 95] from Operation: 90+5=95 Current State: 89:[3, 18, 95], Operations: ['90+5=95'] Exploring Operation: 18/3=6, Resulting Numbers: [95, 6] Generated Node #3: [95, 6] from Operation: 18/3=6 Current State: 89:[95, 6], Operations: ['90+5=95', '18/3=6'] Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[90, 5, 3, 18], Operations: [] Exploring Operation: 5*18=90, Resulting Numbers: [90, 3, 90] Generated Node #0,0: 89:[90, 3, 90] Operation: 5*18=90 Exploring Operation: 3*18=54, Resulting Numbers: [90, 5, 54] Generated Node #0,1: 89:[90, 5, 54] Operation: 3*18=54 Moving to Node #0,0 Current State: 89:[90, 3, 90], Operations: ['5*18=90'] Exploring Operation: 90-3=87, Resulting Numbers: [90, 87] Generated Node #0,0,0: 89:[90, 87] Operation: 90-3=87 Exploring Operation: 90-3=87, Resulting Numbers: [90, 87] Generated Node #0,0,1: 89:[90, 87] Operation: 90-3=87 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[90, 87], Operations: ['5*18=90', '90-3=87'] Exploring Operation: 90+87=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[90, 87], Operations: ['5*18=90', '90-3=87'] Exploring Operation: 90+87=177, Resulting Numbers: [177] 177,89 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[90, 5, 54], Operations: ['3*18=54'] Exploring Operation: 90-5=85, Resulting Numbers: [54, 85] Generated Node #0,1,0: 89:[54, 85] Operation: 90-5=85 Exploring Operation: 5+54=59, Resulting Numbers: [90, 59] Generated Node #0,1,1: 89:[90, 59] Operation: 5+54=59 Moving to Node #0,1,1 Current State: 89:[90, 59], Operations: ['3*18=54', '5+54=59'] Exploring Operation: 90-59=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 90+59=149, Resulting Numbers: [149] 149,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[54, 85], Operations: ['3*18=54', '90-5=85'] Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 54+85=139, Resulting Numbers: [139] 139,89 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 46, 97, 85, 18 ]
52
[ "97-46=51", "85+18=103", "103-51=52" ]
Current State: 52:[46, 97, 85, 18], Operations: [] Exploring Operation: 97-46=51, Resulting Numbers: [85, 18, 51] Generated Node #2: [85, 18, 51] from Operation: 97-46=51 Current State: 52:[85, 18, 51], Operations: ['97-46=51'] Exploring Operation: 85+18=103, Resulting Numbers: [51, 103] Generated Node #3: [51, 103] from Operation: 85+18=103 Current State: 52:[51, 103], Operations: ['97-46=51', '85+18=103'] Exploring Operation: 103-51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[46, 97, 85, 18], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [46, 18, 12] Generated Node #0,0: 52:[46, 18, 12] Operation: 97-85=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[46, 18, 12], Operations: ['97-85=12'] Exploring Operation: 46-18=28, Resulting Numbers: [12, 28] Generated Node #0,0,0: 52:[12, 28] Operation: 46-18=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[12, 28], Operations: ['97-85=12', '46-18=28'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,52 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
[ 85, 22, 97, 47 ]
57
[ "85+22=107", "97-47=50", "107-50=57" ]
Current State: 57:[85, 22, 97, 47], Operations: [] Exploring Operation: 85+22=107, Resulting Numbers: [97, 47, 107] Generated Node #2: [97, 47, 107] from Operation: 85+22=107 Current State: 57:[97, 47, 107], Operations: ['85+22=107'] Exploring Operation: 97-47=50, Resulting Numbers: [107, 50] Generated Node #3: [107, 50] from Operation: 97-47=50 Current State: 57:[107, 50], Operations: ['85+22=107', '97-47=50'] Exploring Operation: 107-50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[85, 22, 97, 47], Operations: [] Exploring Operation: 97-85=12, Resulting Numbers: [22, 47, 12] Generated Node #0,0: 57:[22, 47, 12] Operation: 97-85=12 Exploring Operation: 97-47=50, Resulting Numbers: [85, 22, 50] Generated Node #0,1: 57:[85, 22, 50] Operation: 97-47=50 Moving to Node #0,0 Current State: 57:[22, 47, 12], Operations: ['97-85=12'] Exploring Operation: 47-22=25, Resulting Numbers: [12, 25] Generated Node #0,0,0: 57:[12, 25] Operation: 47-22=25 Exploring Operation: 47+12=59, Resulting Numbers: [22, 59] Generated Node #0,0,1: 57:[22, 59] Operation: 47+12=59 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[22, 59], Operations: ['97-85=12', '47+12=59'] Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 22+59=81, Resulting Numbers: [81] 81,57 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:[12, 25], Operations: ['97-85=12', '47-22=25'] Exploring Operation: 12+25=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 57:[85, 22, 50], Operations: ['97-47=50'] Exploring Operation: 85-22=63, Resulting Numbers: [50, 63] Generated Node #0,1,0: 57:[50, 63] Operation: 85-22=63 Exploring Operation: 85-50=35, Resulting Numbers: [22, 35] Generated Node #0,1,1: 57:[22, 35] Operation: 85-50=35 Moving to Node #0,1,0 Current State: 57:[50, 63], Operations: ['97-47=50', '85-22=63'] Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 50+63=113, Resulting Numbers: [113] 113,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[22, 35], Operations: ['97-47=50', '85-50=35'] Exploring Operation: 22+35=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[85, 22, 97, 47], Operations: [] Exploring Operation: 97-47=50, Resulting Numbers: [85, 22, 50] Generated Node #0,1: 57:[85, 22, 50] Operation: 97-47=50 Moving to Node #0,1 Current State: 57:[85, 22, 50], Operations: ['97-47=50'] Exploring Operation: 85-50=35, Resulting Numbers: [22, 35] Generated Node #0,1,1: 57:[22, 35] Operation: 85-50=35 Moving to Node #0,1,1 Current State: 57:[22, 35], Operations: ['97-47=50', '85-50=35'] Exploring Operation: 22+35=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 7, 64, 2, 85 ]
16
[ "7+64=71", "2+85=87", "87-71=16" ]
Current State: 16:[7, 64, 2, 85], Operations: [] Exploring Operation: 7+64=71, Resulting Numbers: [2, 85, 71] Generated Node #2: [2, 85, 71] from Operation: 7+64=71 Current State: 16:[2, 85, 71], Operations: ['7+64=71'] Exploring Operation: 2+85=87, Resulting Numbers: [71, 87] Generated Node #3: [71, 87] from Operation: 2+85=87 Current State: 16:[71, 87], Operations: ['7+64=71', '2+85=87'] Exploring Operation: 87-71=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[7, 64, 2, 85], Operations: [] Exploring Operation: 85-64=21, Resulting Numbers: [7, 2, 21] Generated Node #0,0: 16:[7, 2, 21] Operation: 85-64=21 Moving to Node #0,0 Current State: 16:[7, 2, 21], Operations: ['85-64=21'] Exploring Operation: 21/7=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 16:[2, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[2, 3], Operations: ['85-64=21', '21/7=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 30, 43, 72, 38 ]
12
[ "43-38=5", "30/5=6", "72/6=12" ]
Current State: 12:[30, 43, 72, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [30, 72, 5] Generated Node #2: [30, 72, 5] from Operation: 43-38=5 Current State: 12:[30, 72, 5], Operations: ['43-38=5'] Exploring Operation: 30/5=6, Resulting Numbers: [72, 6] Generated Node #3: [72, 6] from Operation: 30/5=6 Current State: 12:[72, 6], Operations: ['43-38=5', '30/5=6'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[30, 43, 72, 38], Operations: [] Exploring Operation: 72-38=34, Resulting Numbers: [30, 43, 34] Generated Node #0,0: 12:[30, 43, 34] Operation: 72-38=34 Exploring Operation: 43-38=5, Resulting Numbers: [30, 72, 5] Generated Node #0,1: 12:[30, 72, 5] Operation: 43-38=5 Exploring Operation: 72-43=29, Resulting Numbers: [30, 38, 29] Generated Node #0,2: 12:[30, 38, 29] Operation: 72-43=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[30, 38, 29], Operations: ['72-43=29'] Exploring Operation: 30-29=1, Resulting Numbers: [38, 1] Generated Node #0,2,0: 12:[38, 1] Operation: 30-29=1 Exploring Operation: 38-30=8, Resulting Numbers: [29, 8] Generated Node #0,2,1: 12:[29, 8] Operation: 38-30=8 Exploring Operation: 38-29=9, Resulting Numbers: [30, 9] Generated Node #0,2,2: 12:[30, 9] Operation: 38-29=9 Moving to Node #0,2,1 Current State: 12:[29, 8], Operations: ['72-43=29', '38-30=8'] Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[30, 9], Operations: ['72-43=29', '38-29=9'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[38, 1], Operations: ['72-43=29', '30-29=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[30, 43, 34], Operations: ['72-38=34'] Exploring Operation: 34-30=4, Resulting Numbers: [43, 4] Generated Node #0,0,0: 12:[43, 4] Operation: 34-30=4 Exploring Operation: 43-30=13, Resulting Numbers: [34, 13] Generated Node #0,0,1: 12:[34, 13] Operation: 43-30=13 Exploring Operation: 43-34=9, Resulting Numbers: [30, 9] Generated Node #0,0,2: 12:[30, 9] Operation: 43-34=9 Moving to Node #0,0,2 Current State: 12:[30, 9], Operations: ['72-38=34', '43-34=9'] Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,12 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[34, 13], Operations: ['72-38=34', '43-30=13'] Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[43, 4], Operations: ['72-38=34', '34-30=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,12 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[30, 72, 5], Operations: ['43-38=5'] Exploring Operation: 30-5=25, Resulting Numbers: [72, 25] Generated Node #0,1,0: 12:[72, 25] Operation: 30-5=25 Exploring Operation: 30/5=6, Resulting Numbers: [72, 6] Generated Node #0,1,1: 12:[72, 6] Operation: 30/5=6 Exploring Operation: 72-30=42, Resulting Numbers: [5, 42] Generated Node #0,1,2: 12:[5, 42] Operation: 72-30=42 Moving to Node #0,1,2 Current State: 12:[5, 42], Operations: ['43-38=5', '72-30=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,12 unequal: No Solution Exploring Operation: 5*42=210, Resulting Numbers: [210] 210,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[72, 6], Operations: ['43-38=5', '30/5=6'] Exploring Operation: 72+6=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[30, 43, 72, 38], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [30, 72, 5] Generated Node #0,1: 12:[30, 72, 5] Operation: 43-38=5 Moving to Node #0,1 Current State: 12:[30, 72, 5], Operations: ['43-38=5'] Exploring Operation: 30/5=6, Resulting Numbers: [72, 6] Generated Node #0,1,1: 12:[72, 6] Operation: 30/5=6 Moving to Node #0,1,1 Current State: 12:[72, 6], Operations: ['43-38=5', '30/5=6'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_3
mult_heuristic
[ 22, 81, 84, 18 ]
28
[ "84-81=3", "18/3=6", "22+6=28" ]
Current State: 28:[22, 81, 84, 18], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [22, 18, 3] Generated Node #2: [22, 18, 3] from Operation: 84-81=3 Current State: 28:[22, 18, 3], Operations: ['84-81=3'] Exploring Operation: 18/3=6, Resulting Numbers: [22, 6] Generated Node #3: [22, 6] from Operation: 18/3=6 Current State: 28:[22, 6], Operations: ['84-81=3', '18/3=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[22, 81, 84, 18], Operations: [] Exploring Operation: 84-22=62, Resulting Numbers: [81, 18, 62] Generated Node #0,0: 28:[81, 18, 62] Operation: 84-22=62 Exploring Operation: 81-18=63, Resulting Numbers: [22, 84, 63] Generated Node #0,1: 28:[22, 84, 63] Operation: 81-18=63 Exploring Operation: 81-22=59, Resulting Numbers: [84, 18, 59] Generated Node #0,2: 28:[84, 18, 59] Operation: 81-22=59 Exploring Operation: 84-81=3, Resulting Numbers: [22, 18, 3] Generated Node #0,3: 28:[22, 18, 3] Operation: 84-81=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 28:[22, 18, 3], Operations: ['84-81=3'] Exploring Operation: 22-18=4, Resulting Numbers: [3, 4] Generated Node #0,3,0: 28:[3, 4] Operation: 22-18=4 Exploring Operation: 18-3=15, Resulting Numbers: [22, 15] Generated Node #0,3,1: 28:[22, 15] Operation: 18-3=15 Exploring Operation: 22+3=25, Resulting Numbers: [18, 25] Generated Node #0,3,2: 28:[18, 25] Operation: 22+3=25 Exploring Operation: 18/3=6, Resulting Numbers: [22, 6] Generated Node #0,3,3: 28:[22, 6] Operation: 18/3=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 28:[3, 4], Operations: ['84-81=3', '22-18=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 28:[22, 15], Operations: ['84-81=3', '18-3=15'] Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,28 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 28:[18, 25], Operations: ['84-81=3', '22+3=25'] Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,28 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,28 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 28:[22, 6], Operations: ['84-81=3', '18/3=6'] Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,28 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[22, 81, 84, 18], Operations: [] Exploring Operation: 84-81=3, Resulting Numbers: [22, 18, 3] Generated Node #0,3: 28:[22, 18, 3] Operation: 84-81=3 Moving to Node #0,3 Current State: 28:[22, 18, 3], Operations: ['84-81=3'] Exploring Operation: 18/3=6, Resulting Numbers: [22, 6] Generated Node #0,3,3: 28:[22, 6] Operation: 18/3=6 Moving to Node #0,3,3 Current State: 28:[22, 6], Operations: ['84-81=3', '18/3=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 34, 63, 5, 28 ]
63
[ "34-5=29", "29-28=1", "63*1=63" ]
Current State: 63:[34, 63, 5, 28], Operations: [] Exploring Operation: 34-5=29, Resulting Numbers: [63, 28, 29] Generated Node #2: [63, 28, 29] from Operation: 34-5=29 Current State: 63:[63, 28, 29], Operations: ['34-5=29'] Exploring Operation: 29-28=1, Resulting Numbers: [63, 1] Generated Node #3: [63, 1] from Operation: 29-28=1 Current State: 63:[63, 1], Operations: ['34-5=29', '29-28=1'] Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[34, 63, 5, 28], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [63, 5, 6] Generated Node #0,0: 63:[63, 5, 6] Operation: 34-28=6 Exploring Operation: 28-5=23, Resulting Numbers: [34, 63, 23] Generated Node #0,1: 63:[34, 63, 23] Operation: 28-5=23 Exploring Operation: 34-5=29, Resulting Numbers: [63, 28, 29] Generated Node #0,2: 63:[63, 28, 29] Operation: 34-5=29 Exploring Operation: 63-34=29, Resulting Numbers: [5, 28, 29] Generated Node #0,3: 63:[5, 28, 29] Operation: 63-34=29 Exploring Operation: 34+28=62, Resulting Numbers: [63, 5, 62] Generated Node #0,4: 63:[63, 5, 62] Operation: 34+28=62 Moving to Node #0,0 Current State: 63:[63, 5, 6], Operations: ['34-28=6'] Exploring Operation: 63-5=58, Resulting Numbers: [6, 58] Generated Node #0,0,0: 63:[6, 58] Operation: 63-5=58 Exploring Operation: 5+6=11, Resulting Numbers: [63, 11] Generated Node #0,0,1: 63:[63, 11] Operation: 5+6=11 Exploring Operation: 6-5=1, Resulting Numbers: [63, 1] Generated Node #0,0,2: 63:[63, 1] Operation: 6-5=1 Exploring Operation: 63+5=68, Resulting Numbers: [6, 68] Generated Node #0,0,3: 63:[6, 68] Operation: 63+5=68 Exploring Operation: 63+6=69, Resulting Numbers: [5, 69] Generated Node #0,0,4: 63:[5, 69] Operation: 63+6=69 Moving to Node #0,4 Current State: 63:[63, 5, 62], Operations: ['34+28=62'] Exploring Operation: 63+5=68, Resulting Numbers: [62, 68] Generated Node #0,4,0: 63:[62, 68] Operation: 63+5=68 Exploring Operation: 62-5=57, Resulting Numbers: [63, 57] Generated Node #0,4,1: 63:[63, 57] Operation: 62-5=57 Exploring Operation: 63-62=1, Resulting Numbers: [5, 1] Generated Node #0,4,2: 63:[5, 1] Operation: 63-62=1 Exploring Operation: 5+62=67, Resulting Numbers: [63, 67] Generated Node #0,4,3: 63:[63, 67] Operation: 5+62=67 Exploring Operation: 63-5=58, Resulting Numbers: [62, 58] Generated Node #0,4,4: 63:[62, 58] Operation: 63-5=58 Moving to Node #0,1 Current State: 63:[34, 63, 23], Operations: ['28-5=23'] Exploring Operation: 34-23=11, Resulting Numbers: [63, 11] Generated Node #0,1,0: 63:[63, 11] Operation: 34-23=11 Exploring Operation: 34+63=97, Resulting Numbers: [23, 97] Generated Node #0,1,1: 63:[23, 97] Operation: 34+63=97 Exploring Operation: 63-34=29, Resulting Numbers: [23, 29] Generated Node #0,1,2: 63:[23, 29] Operation: 63-34=29 Exploring Operation: 63-23=40, Resulting Numbers: [34, 40] Generated Node #0,1,3: 63:[34, 40] Operation: 63-23=40 Exploring Operation: 34+23=57, Resulting Numbers: [63, 57] Generated Node #0,1,4: 63:[63, 57] Operation: 34+23=57 Moving to Node #0,2 Current State: 63:[63, 28, 29], Operations: ['34-5=29'] Exploring Operation: 29-28=1, Resulting Numbers: [63, 1] Generated Node #0,2,0: 63:[63, 1] Operation: 29-28=1 Exploring Operation: 28+29=57, Resulting Numbers: [63, 57] Generated Node #0,2,1: 63:[63, 57] Operation: 28+29=57 Exploring Operation: 63-29=34, Resulting Numbers: [28, 34] Generated Node #0,2,2: 63:[28, 34] Operation: 63-29=34 Exploring Operation: 63+28=91, Resulting Numbers: [29, 91] Generated Node #0,2,3: 63:[29, 91] Operation: 63+28=91 Exploring Operation: 63-28=35, Resulting Numbers: [29, 35] Generated Node #0,2,4: 63:[29, 35] Operation: 63-28=35 Moving to Node #0,3 Current State: 63:[5, 28, 29], Operations: ['63-34=29'] Exploring Operation: 5+28=33, Resulting Numbers: [29, 33] Generated Node #0,3,0: 63:[29, 33] Operation: 5+28=33 Exploring Operation: 28-5=23, Resulting Numbers: [29, 23] Generated Node #0,3,1: 63:[29, 23] Operation: 28-5=23 Exploring Operation: 28+29=57, Resulting Numbers: [5, 57] Generated Node #0,3,2: 63:[5, 57] Operation: 28+29=57 Exploring Operation: 29-5=24, Resulting Numbers: [28, 24] Generated Node #0,3,3: 63:[28, 24] Operation: 29-5=24 Exploring Operation: 29-28=1, Resulting Numbers: [5, 1] Generated Node #0,3,4: 63:[5, 1] Operation: 29-28=1 Moving to Node #0,0,1 Current State: 63:[63, 11], Operations: ['34-28=6', '5+6=11'] Exploring Operation: 63*11=693, Resulting Numbers: [693] 693,63 unequal: No Solution Exploring Operation: 63+11=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[63, 1], Operations: ['34-28=6', '6-5=1'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[34, 63, 5, 28], Operations: [] Exploring Operation: 34-28=6, Resulting Numbers: [63, 5, 6] Generated Node #0,0: 63:[63, 5, 6] Operation: 34-28=6 Moving to Node #0,0 Current State: 63:[63, 5, 6], Operations: ['34-28=6'] Exploring Operation: 6-5=1, Resulting Numbers: [63, 1] Generated Node #0,0,2: 63:[63, 1] Operation: 6-5=1 Moving to Node #0,0,2 Current State: 63:[63, 1], Operations: ['34-28=6', '6-5=1'] Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.966146
hs_5
sum_heuristic
[ 4, 14, 23, 91 ]
58
[ "4*14=56", "23+91=114", "114-56=58" ]
Current State: 58:[4, 14, 23, 91], Operations: [] Exploring Operation: 4*14=56, Resulting Numbers: [23, 91, 56] Generated Node #2: [23, 91, 56] from Operation: 4*14=56 Current State: 58:[23, 91, 56], Operations: ['4*14=56'] Exploring Operation: 23+91=114, Resulting Numbers: [56, 114] Generated Node #3: [56, 114] from Operation: 23+91=114 Current State: 58:[56, 114], Operations: ['4*14=56', '23+91=114'] Exploring Operation: 114-56=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[4, 14, 23, 91], Operations: [] Exploring Operation: 23-14=9, Resulting Numbers: [4, 91, 9] Generated Node #0,0: 58:[4, 91, 9] Operation: 23-14=9 Exploring Operation: 91-14=77, Resulting Numbers: [4, 23, 77] Generated Node #0,1: 58:[4, 23, 77] Operation: 91-14=77 Exploring Operation: 4*14=56, Resulting Numbers: [23, 91, 56] Generated Node #0,2: 58:[23, 91, 56] Operation: 4*14=56 Exploring Operation: 91-23=68, Resulting Numbers: [4, 14, 68] Generated Node #0,3: 58:[4, 14, 68] Operation: 91-23=68 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[4, 14, 68], Operations: ['91-23=68'] Exploring Operation: 4*14=56, Resulting Numbers: [68, 56] Generated Node #0,3,0: 58:[68, 56] Operation: 4*14=56 Exploring Operation: 68-14=54, Resulting Numbers: [4, 54] Generated Node #0,3,1: 58:[4, 54] Operation: 68-14=54 Exploring Operation: 68-4=64, Resulting Numbers: [14, 64] Generated Node #0,3,2: 58:[14, 64] Operation: 68-4=64 Exploring Operation: 14-4=10, Resulting Numbers: [68, 10] Generated Node #0,3,3: 58:[68, 10] Operation: 14-4=10 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 58:[4, 54], Operations: ['91-23=68', '68-14=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[4, 14, 23, 91], Operations: [] Exploring Operation: 91-23=68, Resulting Numbers: [4, 14, 68] Generated Node #0,3: 58:[4, 14, 68] Operation: 91-23=68 Moving to Node #0,3 Current State: 58:[4, 14, 68], Operations: ['91-23=68'] Exploring Operation: 68-14=54, Resulting Numbers: [4, 54] Generated Node #0,3,1: 58:[4, 54] Operation: 68-14=54 Moving to Node #0,3,1 Current State: 58:[4, 54], Operations: ['91-23=68', '68-14=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 45, 89, 53, 16 ]
39
[ "53-45=8", "16*8=128", "128-89=39" ]
Current State: 39:[45, 89, 53, 16], Operations: [] Exploring Operation: 53-45=8, Resulting Numbers: [89, 16, 8] Generated Node #2: [89, 16, 8] from Operation: 53-45=8 Current State: 39:[89, 16, 8], Operations: ['53-45=8'] Exploring Operation: 16*8=128, Resulting Numbers: [89, 128] Generated Node #3: [89, 128] from Operation: 16*8=128 Current State: 39:[89, 128], Operations: ['53-45=8', '16*8=128'] Exploring Operation: 128-89=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[45, 89, 53, 16], Operations: [] Exploring Operation: 89-16=73, Resulting Numbers: [45, 53, 73] Generated Node #0,0: 39:[45, 53, 73] Operation: 89-16=73 Exploring Operation: 89-53=36, Resulting Numbers: [45, 16, 36] Generated Node #0,1: 39:[45, 16, 36] Operation: 89-53=36 Exploring Operation: 89-45=44, Resulting Numbers: [53, 16, 44] Generated Node #0,2: 39:[53, 16, 44] Operation: 89-45=44 Moving to Node #0,1 Current State: 39:[45, 16, 36], Operations: ['89-53=36'] Exploring Operation: 45-16=29, Resulting Numbers: [36, 29] Generated Node #0,1,0: 39:[36, 29] Operation: 45-16=29 Exploring Operation: 36-16=20, Resulting Numbers: [45, 20] Generated Node #0,1,1: 39:[45, 20] Operation: 36-16=20 Exploring Operation: 45-36=9, Resulting Numbers: [16, 9] Generated Node #0,1,2: 39:[16, 9] Operation: 45-36=9 Moving to Node #0,2 Current State: 39:[53, 16, 44], Operations: ['89-45=44'] Exploring Operation: 53-44=9, Resulting Numbers: [16, 9] Generated Node #0,2,0: 39:[16, 9] Operation: 53-44=9 Exploring Operation: 53-16=37, Resulting Numbers: [44, 37] Generated Node #0,2,1: 39:[44, 37] Operation: 53-16=37 Exploring Operation: 44-16=28, Resulting Numbers: [53, 28] Generated Node #0,2,2: 39:[53, 28] Operation: 44-16=28 Moving to Node #0,0 Current State: 39:[45, 53, 73], Operations: ['89-16=73'] Exploring Operation: 73-45=28, Resulting Numbers: [53, 28] Generated Node #0,0,0: 39:[53, 28] Operation: 73-45=28 Exploring Operation: 73-53=20, Resulting Numbers: [45, 20] Generated Node #0,0,1: 39:[45, 20] Operation: 73-53=20 Exploring Operation: 53-45=8, Resulting Numbers: [73, 8] Generated Node #0,0,2: 39:[73, 8] Operation: 53-45=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[45, 20], Operations: ['89-16=73', '73-53=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,39 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[53, 28], Operations: ['89-16=73', '73-45=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[73, 8], Operations: ['89-16=73', '53-45=8'] Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,39 unequal: No Solution Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 39:[16, 9], Operations: ['89-53=36', '45-36=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[16, 9], Operations: ['89-45=44', '53-44=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,39 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[44, 37], Operations: ['89-45=44', '53-16=37'] Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,39 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[45, 20], Operations: ['89-53=36', '36-16=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,39 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[36, 29], Operations: ['89-53=36', '45-16=29'] Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,39 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[53, 28], Operations: ['89-45=44', '44-16=28'] Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,39 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,39 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 45, 94, 98, 8 ]
69
[ "94+98=192", "192/8=24", "45+24=69" ]
Current State: 69:[45, 94, 98, 8], Operations: [] Exploring Operation: 94+98=192, Resulting Numbers: [45, 8, 192] Generated Node #2: [45, 8, 192] from Operation: 94+98=192 Current State: 69:[45, 8, 192], Operations: ['94+98=192'] Exploring Operation: 192/8=24, Resulting Numbers: [45, 24] Generated Node #3: [45, 24] from Operation: 192/8=24 Current State: 69:[45, 24], Operations: ['94+98=192', '192/8=24'] Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[45, 94, 98, 8], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [45, 8, 4] Generated Node #0,0: 69:[45, 8, 4] Operation: 98-94=4 Exploring Operation: 98-45=53, Resulting Numbers: [94, 8, 53] Generated Node #0,1: 69:[94, 8, 53] Operation: 98-45=53 Exploring Operation: 94-45=49, Resulting Numbers: [98, 8, 49] Generated Node #0,2: 69:[98, 8, 49] Operation: 94-45=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[45, 8, 4], Operations: ['98-94=4'] Exploring Operation: 45-4=41, Resulting Numbers: [8, 41] Generated Node #0,0,0: 69:[8, 41] Operation: 45-4=41 Exploring Operation: 45+8=53, Resulting Numbers: [4, 53] Generated Node #0,0,1: 69:[4, 53] Operation: 45+8=53 Exploring Operation: 45-8=37, Resulting Numbers: [4, 37] Generated Node #0,0,2: 69:[4, 37] Operation: 45-8=37 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[4, 37], Operations: ['98-94=4', '45-8=37'] Exploring Operation: 4*37=148, Resulting Numbers: [148] 148,69 unequal: No Solution Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,69 unequal: No Solution No 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: 69:[4, 53], Operations: ['98-94=4', '45+8=53'] Exploring Operation: 4+53=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 4*53=212, Resulting Numbers: [212] 212,69 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,69 unequal: No Solution No 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: 69:[8, 41], Operations: ['98-94=4', '45-4=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[94, 8, 53], Operations: ['98-45=53'] Exploring Operation: 94-53=41, Resulting Numbers: [8, 41] Generated Node #0,1,0: 69:[8, 41] Operation: 94-53=41 Exploring Operation: 8+53=61, Resulting Numbers: [94, 61] Generated Node #0,1,1: 69:[94, 61] Operation: 8+53=61 Exploring Operation: 94-8=86, Resulting Numbers: [53, 86] Generated Node #0,1,2: 69:[53, 86] Operation: 94-8=86 Moving to Node #0,1,0 Current State: 69:[8, 41], Operations: ['98-45=53', '94-53=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,69 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,69 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[94, 61], Operations: ['98-45=53', '8+53=61'] Exploring Operation: 94*61=5734, Resulting Numbers: [5734] 5734,69 unequal: No Solution Exploring Operation: 94+61=155, Resulting Numbers: [155] 155,69 unequal: No Solution Exploring Operation: 94-61=33, Resulting Numbers: [33] 33,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[53, 86], Operations: ['98-45=53', '94-8=86'] Exploring Operation: 86-53=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 53*86=4558, Resulting Numbers: [4558] 4558,69 unequal: No Solution Exploring Operation: 53+86=139, Resulting Numbers: [139] 139,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[98, 8, 49], Operations: ['94-45=49'] Exploring Operation: 98/49=2, Resulting Numbers: [8, 2] Generated Node #0,2,0: 69:[8, 2] Operation: 98/49=2 Exploring Operation: 98-8=90, Resulting Numbers: [49, 90] Generated Node #0,2,1: 69:[49, 90] Operation: 98-8=90 Exploring Operation: 98-49=49, Resulting Numbers: [8, 49] Generated Node #0,2,2: 69:[8, 49] Operation: 98-49=49 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 69:[8, 2], Operations: ['94-45=49', '98/49=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,69 unequal: No Solution No 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: 69:[8, 49], Operations: ['94-45=49', '98-49=49'] Exploring Operation: 8*49=392, Resulting Numbers: [392] 392,69 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,69 unequal: No Solution No 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: 69:[49, 90], Operations: ['94-45=49', '98-8=90'] Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 49+90=139, Resulting Numbers: [139] 139,69 unequal: No Solution Exploring Operation: 49*90=4410, Resulting Numbers: [4410] 4410,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 18, 18, 21, 4 ]
69
[ "21-18=3", "18*4=72", "72-3=69" ]
Current State: 69:[18, 18, 21, 4], Operations: [] Exploring Operation: 21-18=3, Resulting Numbers: [4, 3] Generated Node #2: [4, 3] from Operation: 21-18=3 Current State: 69:[4, 3], Operations: ['21-18=3'] Exploring Operation: 18*4=72, Resulting Numbers: [3, 72] Generated Node #3: [3, 72] from Operation: 18*4=72 Current State: 69:[3, 72], Operations: ['21-18=3', '18*4=72'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[18, 18, 21, 4], Operations: [] Exploring Operation: 18/18=1, Resulting Numbers: [21, 4, 1] Generated Node #0,0: 69:[21, 4, 1] Operation: 18/18=1 Exploring Operation: 18-18=0, Resulting Numbers: [21, 4, 0] Generated Node #0,1: 69:[21, 4, 0] Operation: 18-18=0 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[21, 4, 1], Operations: ['18/18=1'] Exploring Operation: 21+1=22, Resulting Numbers: [4, 22] Generated Node #0,0,0: 69:[4, 22] Operation: 21+1=22 Exploring Operation: 4-1=3, Resulting Numbers: [21, 3] Generated Node #0,0,1: 69:[21, 3] Operation: 4-1=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[4, 22], Operations: ['18/18=1', '21+1=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,69 unequal: No Solution No 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: 69:[21, 3], Operations: ['18/18=1', '4-1=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[21, 4, 0], Operations: ['18-18=0'] Exploring Operation: 21+0=21, Resulting Numbers: [4, 21] Generated Node #0,1,0: 69:[4, 21] Operation: 21+0=21 Exploring Operation: 21-0=21, Resulting Numbers: [4, 21] Generated Node #0,1,1: 69:[4, 21] Operation: 21-0=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[4, 21], Operations: ['18-18=0', '21+0=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,69 unequal: No Solution No 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: 69:[4, 21], Operations: ['18-18=0', '21-0=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 68, 74, 23, 44 ]
15
[ "74-68=6", "44-23=21", "21-6=15" ]
Current State: 15:[68, 74, 23, 44], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [23, 44, 6] Generated Node #2: [23, 44, 6] from Operation: 74-68=6 Current State: 15:[23, 44, 6], Operations: ['74-68=6'] Exploring Operation: 44-23=21, Resulting Numbers: [6, 21] Generated Node #3: [6, 21] from Operation: 44-23=21 Current State: 15:[6, 21], Operations: ['74-68=6', '44-23=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[68, 74, 23, 44], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [23, 44, 6] Generated Node #0,0: 15:[23, 44, 6] Operation: 74-68=6 Exploring Operation: 68-44=24, Resulting Numbers: [74, 23, 24] Generated Node #0,1: 15:[74, 23, 24] Operation: 68-44=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[23, 44, 6], Operations: ['74-68=6'] Exploring Operation: 44-23=21, Resulting Numbers: [6, 21] Generated Node #0,0,0: 15:[6, 21] Operation: 44-23=21 Exploring Operation: 23-6=17, Resulting Numbers: [44, 17] Generated Node #0,0,1: 15:[44, 17] Operation: 23-6=17 Moving to Node #0,0,0 Current State: 15:[6, 21], Operations: ['74-68=6', '44-23=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[68, 74, 23, 44], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [23, 44, 6] Generated Node #0,0: 15:[23, 44, 6] Operation: 74-68=6 Moving to Node #0,0 Current State: 15:[23, 44, 6], Operations: ['74-68=6'] Exploring Operation: 44-23=21, Resulting Numbers: [6, 21] Generated Node #0,0,0: 15:[6, 21] Operation: 44-23=21 Moving to Node #0,0,0 Current State: 15:[6, 21], Operations: ['74-68=6', '44-23=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 23, 95, 19, 27 ]
97
[ "19+27=46", "46/23=2", "95+2=97" ]
Current State: 97:[23, 95, 19, 27], Operations: [] Exploring Operation: 19+27=46, Resulting Numbers: [23, 95, 46] Generated Node #2: [23, 95, 46] from Operation: 19+27=46 Current State: 97:[23, 95, 46], Operations: ['19+27=46'] Exploring Operation: 46/23=2, Resulting Numbers: [95, 2] Generated Node #3: [95, 2] from Operation: 46/23=2 Current State: 97:[95, 2], Operations: ['19+27=46', '46/23=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[23, 95, 19, 27], Operations: [] Exploring Operation: 23+19=42, Resulting Numbers: [95, 27, 42] Generated Node #0,0: 97:[95, 27, 42] Operation: 23+19=42 Exploring Operation: 95+19=114, Resulting Numbers: [23, 27, 114] Generated Node #0,1: 97:[23, 27, 114] Operation: 95+19=114 Exploring Operation: 19+27=46, Resulting Numbers: [23, 95, 46] Generated Node #0,2: 97:[23, 95, 46] Operation: 19+27=46 Exploring Operation: 23+27=50, Resulting Numbers: [95, 19, 50] Generated Node #0,3: 97:[95, 19, 50] Operation: 23+27=50 Exploring Operation: 23-19=4, Resulting Numbers: [95, 27, 4] Generated Node #0,4: 97:[95, 27, 4] Operation: 23-19=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[95, 27, 42], Operations: ['23+19=42'] Exploring Operation: 27+42=69, Resulting Numbers: [95, 69] Generated Node #0,0,0: 97:[95, 69] Operation: 27+42=69 Exploring Operation: 42-27=15, Resulting Numbers: [95, 15] Generated Node #0,0,1: 97:[95, 15] Operation: 42-27=15 Exploring Operation: 95+27=122, Resulting Numbers: [42, 122] Generated Node #0,0,2: 97:[42, 122] Operation: 95+27=122 Exploring Operation: 95-27=68, Resulting Numbers: [42, 68] Generated Node #0,0,3: 97:[42, 68] Operation: 95-27=68 Exploring Operation: 95+42=137, Resulting Numbers: [27, 137] Generated Node #0,0,4: 97:[27, 137] Operation: 95+42=137 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[95, 69], Operations: ['23+19=42', '27+42=69'] Exploring Operation: 95*69=6555, Resulting Numbers: [6555] 6555,97 unequal: No Solution Exploring Operation: 95+69=164, Resulting Numbers: [164] 164,97 unequal: No Solution Exploring Operation: 95-69=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 #0,0,2 Current State: 97:[42, 122], Operations: ['23+19=42', '95+27=122'] Exploring Operation: 122-42=80, Resulting Numbers: [80] 80,97 unequal: No Solution Exploring Operation: 42+122=164, Resulting Numbers: [164] 164,97 unequal: No Solution Exploring Operation: 42*122=5124, Resulting Numbers: [5124] 5124,97 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 #0,0,1 Current State: 97:[95, 15], Operations: ['23+19=42', '42-27=15'] Exploring Operation: 95*15=1425, Resulting Numbers: [1425] 1425,97 unequal: No Solution Exploring Operation: 95+15=110, Resulting Numbers: [110] 110,97 unequal: No Solution Exploring Operation: 95-15=80, Resulting Numbers: [80] 80,97 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 #0,0,3 Current State: 97:[42, 68], Operations: ['23+19=42', '95-27=68'] Exploring Operation: 42+68=110, Resulting Numbers: [110] 110,97 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 42*68=2856, Resulting Numbers: [2856] 2856,97 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 #0,0,4 Current State: 97:[27, 137], Operations: ['23+19=42', '95+42=137'] Exploring Operation: 137-27=110, Resulting Numbers: [110] 110,97 unequal: No Solution Exploring Operation: 27*137=3699, Resulting Numbers: [3699] 3699,97 unequal: No Solution Exploring Operation: 27+137=164, Resulting Numbers: [164] 164,97 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 #0,2 Current State: 97:[23, 95, 46], Operations: ['19+27=46'] Exploring Operation: 46-23=23, Resulting Numbers: [95, 23] Generated Node #0,2,0: 97:[95, 23] Operation: 46-23=23 Exploring Operation: 46/23=2, Resulting Numbers: [95, 2] Generated Node #0,2,1: 97:[95, 2] Operation: 46/23=2 Exploring Operation: 23+95=118, Resulting Numbers: [46, 118] Generated Node #0,2,2: 97:[46, 118] Operation: 23+95=118 Exploring Operation: 23+46=69, Resulting Numbers: [95, 69] Generated Node #0,2,3: 97:[95, 69] Operation: 23+46=69 Exploring Operation: 95-23=72, Resulting Numbers: [46, 72] Generated Node #0,2,4: 97:[46, 72] Operation: 95-23=72 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 97:[95, 69], Operations: ['19+27=46', '23+46=69'] Exploring Operation: 95*69=6555, Resulting Numbers: [6555] 6555,97 unequal: No Solution Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 95+69=164, Resulting Numbers: [164] 164,97 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:[46, 118], Operations: ['19+27=46', '23+95=118'] Exploring Operation: 46*118=5428, Resulting Numbers: [5428] 5428,97 unequal: No Solution Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,97 unequal: No Solution Exploring Operation: 46+118=164, Resulting Numbers: [164] 164,97 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:[95, 23], Operations: ['19+27=46', '46-23=23'] Exploring Operation: 95+23=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,97 unequal: No Solution Exploring Operation: 95*23=2185, Resulting Numbers: [2185] 2185,97 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 #0,2,4 Current State: 97:[46, 72], Operations: ['19+27=46', '95-23=72'] Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 46+72=118, Resulting Numbers: [118] 118,97 unequal: No Solution Exploring Operation: 46*72=3312, Resulting Numbers: [3312] 3312,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[95, 2], Operations: ['19+27=46', '46/23=2'] Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[23, 95, 19, 27], Operations: [] Exploring Operation: 19+27=46, Resulting Numbers: [23, 95, 46] Generated Node #0,2: 97:[23, 95, 46] Operation: 19+27=46 Moving to Node #0,2 Current State: 97:[23, 95, 46], Operations: ['19+27=46'] Exploring Operation: 46/23=2, Resulting Numbers: [95, 2] Generated Node #0,2,1: 97:[95, 2] Operation: 46/23=2 Moving to Node #0,2,1 Current State: 97:[95, 2], Operations: ['19+27=46', '46/23=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.958333
hs_5
mult_heuristic
[ 5, 21, 22, 41 ]
42
[ "5*21=105", "22+41=63", "105-63=42" ]
Current State: 42:[5, 21, 22, 41], Operations: [] Exploring Operation: 5*21=105, Resulting Numbers: [22, 41, 105] Generated Node #2: [22, 41, 105] from Operation: 5*21=105 Current State: 42:[22, 41, 105], Operations: ['5*21=105'] Exploring Operation: 22+41=63, Resulting Numbers: [105, 63] Generated Node #3: [105, 63] from Operation: 22+41=63 Current State: 42:[105, 63], Operations: ['5*21=105', '22+41=63'] Exploring Operation: 105-63=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[5, 21, 22, 41], Operations: [] Exploring Operation: 21+22=43, Resulting Numbers: [5, 41, 43] Generated Node #0,0: 42:[5, 41, 43] Operation: 21+22=43 Moving to Node #0,0 Current State: 42:[5, 41, 43], Operations: ['21+22=43'] Exploring Operation: 43-41=2, Resulting Numbers: [5, 2] Generated Node #0,0,0: 42:[5, 2] Operation: 43-41=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[5, 2], Operations: ['21+22=43', '43-41=2'] Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 58, 12, 4, 95 ]
79
[ "58*12=696", "696/4=174", "174-95=79" ]
Current State: 79:[58, 12, 4, 95], Operations: [] Exploring Operation: 58*12=696, Resulting Numbers: [4, 95, 696] Generated Node #2: [4, 95, 696] from Operation: 58*12=696 Current State: 79:[4, 95, 696], Operations: ['58*12=696'] Exploring Operation: 696/4=174, Resulting Numbers: [95, 174] Generated Node #3: [95, 174] from Operation: 696/4=174 Current State: 79:[95, 174], Operations: ['58*12=696', '696/4=174'] Exploring Operation: 174-95=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[58, 12, 4, 95], Operations: [] Exploring Operation: 12+4=16, Resulting Numbers: [58, 95, 16] Generated Node #0,0: 79:[58, 95, 16] Operation: 12+4=16 Exploring Operation: 12*4=48, Resulting Numbers: [58, 95, 48] Generated Node #0,1: 79:[58, 95, 48] Operation: 12*4=48 Exploring Operation: 58+4=62, Resulting Numbers: [12, 95, 62] Generated Node #0,2: 79:[12, 95, 62] Operation: 58+4=62 Exploring Operation: 95-12=83, Resulting Numbers: [58, 4, 83] Generated Node #0,3: 79:[58, 4, 83] Operation: 95-12=83 Exploring Operation: 58+12=70, Resulting Numbers: [4, 95, 70] Generated Node #0,4: 79:[4, 95, 70] Operation: 58+12=70 Moving to Node #0,1 Current State: 79:[58, 95, 48], Operations: ['12*4=48'] Exploring Operation: 95-48=47, Resulting Numbers: [58, 47] Generated Node #0,1,0: 79:[58, 47] Operation: 95-48=47 Exploring Operation: 58-48=10, Resulting Numbers: [95, 10] Generated Node #0,1,1: 79:[95, 10] Operation: 58-48=10 Exploring Operation: 95-58=37, Resulting Numbers: [48, 37] Generated Node #0,1,2: 79:[48, 37] Operation: 95-58=37 Exploring Operation: 58+48=106, Resulting Numbers: [95, 106] Generated Node #0,1,3: 79:[95, 106] Operation: 58+48=106 Exploring Operation: 95+48=143, Resulting Numbers: [58, 143] Generated Node #0,1,4: 79:[58, 143] Operation: 95+48=143 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[95, 106], Operations: ['12*4=48', '58+48=106'] Exploring Operation: 95+106=201, Resulting Numbers: [201] 201,79 unequal: No Solution Exploring Operation: 106-95=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 95*106=10070, Resulting Numbers: [10070] 10070,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[58, 47], Operations: ['12*4=48', '95-48=47'] Exploring Operation: 58*47=2726, Resulting Numbers: [2726] 2726,79 unequal: No Solution Exploring Operation: 58-47=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 58+47=105, Resulting Numbers: [105] 105,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[48, 37], Operations: ['12*4=48', '95-58=37'] Exploring Operation: 48*37=1776, Resulting Numbers: [1776] 1776,79 unequal: No Solution Exploring Operation: 48-37=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 48+37=85, Resulting Numbers: [85] 85,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[95, 10], Operations: ['12*4=48', '58-48=10'] Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 95+10=105, Resulting Numbers: [105] 105,79 unequal: No Solution Exploring Operation: 95*10=950, Resulting Numbers: [950] 950,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 79:[58, 143], Operations: ['12*4=48', '95+48=143'] Exploring Operation: 143-58=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 58+143=201, Resulting Numbers: [201] 201,79 unequal: No Solution Exploring Operation: 58*143=8294, Resulting Numbers: [8294] 8294,79 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: 79:[12, 95, 62], Operations: ['58+4=62'] Exploring Operation: 95-62=33, Resulting Numbers: [12, 33] Generated Node #0,2,0: 79:[12, 33] Operation: 95-62=33 Exploring Operation: 12+62=74, Resulting Numbers: [95, 74] Generated Node #0,2,1: 79:[95, 74] Operation: 12+62=74 Exploring Operation: 62-12=50, Resulting Numbers: [95, 50] Generated Node #0,2,2: 79:[95, 50] Operation: 62-12=50 Exploring Operation: 95-12=83, Resulting Numbers: [62, 83] Generated Node #0,2,3: 79:[62, 83] Operation: 95-12=83 Exploring Operation: 12+95=107, Resulting Numbers: [62, 107] Generated Node #0,2,4: 79:[62, 107] Operation: 12+95=107 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[95, 74], Operations: ['58+4=62', '12+62=74'] Exploring Operation: 95+74=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 95*74=7030, Resulting Numbers: [7030] 7030,79 unequal: No Solution Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[62, 83], Operations: ['58+4=62', '95-12=83'] Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 62+83=145, Resulting Numbers: [145] 145,79 unequal: No Solution Exploring Operation: 62*83=5146, Resulting Numbers: [5146] 5146,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[95, 50], Operations: ['58+4=62', '62-12=50'] Exploring Operation: 95+50=145, Resulting Numbers: [145] 145,79 unequal: No Solution Exploring Operation: 95*50=4750, Resulting Numbers: [4750] 4750,79 unequal: No Solution Exploring Operation: 95-50=45, Resulting Numbers: [45] 45,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 79:[62, 107], Operations: ['58+4=62', '12+95=107'] Exploring Operation: 62+107=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 107-62=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 62*107=6634, Resulting Numbers: [6634] 6634,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[12, 33], Operations: ['58+4=62', '95-62=33'] Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,79 unequal: No Solution Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,79 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,79 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: 79:[4, 95, 70], Operations: ['58+12=70'] Exploring Operation: 4+95=99, Resulting Numbers: [70, 99] Generated Node #0,4,0: 79:[70, 99] Operation: 4+95=99 Exploring Operation: 70-4=66, Resulting Numbers: [95, 66] Generated Node #0,4,1: 79:[95, 66] Operation: 70-4=66 Exploring Operation: 4+70=74, Resulting Numbers: [95, 74] Generated Node #0,4,2: 79:[95, 74] Operation: 4+70=74 Exploring Operation: 95-4=91, Resulting Numbers: [70, 91] Generated Node #0,4,3: 79:[70, 91] Operation: 95-4=91 Exploring Operation: 95-70=25, Resulting Numbers: [4, 25] Generated Node #0,4,4: 79:[4, 25] Operation: 95-70=25 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 79:[95, 74], Operations: ['58+12=70', '4+70=74'] Exploring Operation: 95+74=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 95*74=7030, Resulting Numbers: [7030] 7030,79 unequal: No Solution Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 79:[70, 91], Operations: ['58+12=70', '95-4=91'] Exploring Operation: 70*91=6370, Resulting Numbers: [6370] 6370,79 unequal: No Solution Exploring Operation: 91-70=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 70+91=161, Resulting Numbers: [161] 161,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 79:[70, 99], Operations: ['58+12=70', '4+95=99'] Exploring Operation: 99-70=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 70*99=6930, Resulting Numbers: [6930] 6930,79 unequal: No Solution Exploring Operation: 70+99=169, Resulting Numbers: [169] 169,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 79:[95, 66], Operations: ['58+12=70', '70-4=66'] Exploring Operation: 95-66=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 95+66=161, Resulting Numbers: [161] 161,79 unequal: No Solution Exploring Operation: 95*66=6270, Resulting Numbers: [6270] 6270,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 79:[4, 25], Operations: ['58+12=70', '95-70=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 79:[58, 95, 16], Operations: ['12+4=16'] Exploring Operation: 95-16=79, Resulting Numbers: [58, 79] Generated Node #0,0,0: 79:[58, 79] Operation: 95-16=79 Exploring Operation: 58+16=74, Resulting Numbers: [95, 74] Generated Node #0,0,1: 79:[95, 74] Operation: 58+16=74 Exploring Operation: 95+16=111, Resulting Numbers: [58, 111] Generated Node #0,0,2: 79:[58, 111] Operation: 95+16=111 Exploring Operation: 58-16=42, Resulting Numbers: [95, 42] Generated Node #0,0,3: 79:[95, 42] Operation: 58-16=42 Exploring Operation: 95-58=37, Resulting Numbers: [16, 37] Generated Node #0,0,4: 79:[16, 37] Operation: 95-58=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[58, 79], Operations: ['12+4=16', '95-16=79'] Exploring Operation: 58+79=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 58*79=4582, Resulting Numbers: [4582] 4582,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[95, 74], Operations: ['12+4=16', '58+16=74'] Exploring Operation: 95-74=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 95+74=169, Resulting Numbers: [169] 169,79 unequal: No Solution Exploring Operation: 95*74=7030, Resulting Numbers: [7030] 7030,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[58, 111], Operations: ['12+4=16', '95+16=111'] Exploring Operation: 58*111=6438, Resulting Numbers: [6438] 6438,79 unequal: No Solution Exploring Operation: 111-58=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 58+111=169, Resulting Numbers: [169] 169,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[95, 42], Operations: ['12+4=16', '58-16=42'] Exploring Operation: 95-42=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 95*42=3990, Resulting Numbers: [3990] 3990,79 unequal: No Solution Exploring Operation: 95+42=137, Resulting Numbers: [137] 137,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 79:[16, 37], Operations: ['12+4=16', '95-58=37'] Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,79 unequal: No Solution Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,79 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: 79:[58, 4, 83], Operations: ['95-12=83'] Exploring Operation: 83-4=79, Resulting Numbers: [58, 79] Generated Node #0,3,0: 79:[58, 79] Operation: 83-4=79 Exploring Operation: 4+83=87, Resulting Numbers: [58, 87] Generated Node #0,3,1: 79:[58, 87] Operation: 4+83=87 Exploring Operation: 58-4=54, Resulting Numbers: [83, 54] Generated Node #0,3,2: 79:[83, 54] Operation: 58-4=54 Exploring Operation: 83-58=25, Resulting Numbers: [4, 25] Generated Node #0,3,3: 79:[4, 25] Operation: 83-58=25 Exploring Operation: 58+4=62, Resulting Numbers: [83, 62] Generated Node #0,3,4: 79:[83, 62] Operation: 58+4=62 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[58, 79], Operations: ['95-12=83', '83-4=79'] Exploring Operation: 58+79=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 58*79=4582, Resulting Numbers: [4582] 4582,79 unequal: No Solution Exploring Operation: 79-58=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 79:[83, 62], Operations: ['95-12=83', '58+4=62'] Exploring Operation: 83+62=145, Resulting Numbers: [145] 145,79 unequal: No Solution Exploring Operation: 83*62=5146, Resulting Numbers: [5146] 5146,79 unequal: No Solution Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[58, 87], Operations: ['95-12=83', '4+83=87'] Exploring Operation: 87-58=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 58+87=145, Resulting Numbers: [145] 145,79 unequal: No Solution Exploring Operation: 58*87=5046, Resulting Numbers: [5046] 5046,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[83, 54], Operations: ['95-12=83', '58-4=54'] Exploring Operation: 83+54=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 83*54=4482, Resulting Numbers: [4482] 4482,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[4, 25], Operations: ['95-12=83', '83-58=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,79 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
[ 39, 45, 88, 59 ]
63
[ "39+45=84", "88+59=147", "147-84=63" ]
Current State: 63:[39, 45, 88, 59], Operations: [] Exploring Operation: 39+45=84, Resulting Numbers: [88, 59, 84] Generated Node #2: [88, 59, 84] from Operation: 39+45=84 Current State: 63:[88, 59, 84], Operations: ['39+45=84'] Exploring Operation: 88+59=147, Resulting Numbers: [84, 147] Generated Node #3: [84, 147] from Operation: 88+59=147 Current State: 63:[84, 147], Operations: ['39+45=84', '88+59=147'] Exploring Operation: 147-84=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[39, 45, 88, 59], Operations: [] Exploring Operation: 88-45=43, Resulting Numbers: [39, 59, 43] Generated Node #0,0: 63:[39, 59, 43] Operation: 88-45=43 Exploring Operation: 45-39=6, Resulting Numbers: [88, 59, 6] Generated Node #0,1: 63:[88, 59, 6] Operation: 45-39=6 Exploring Operation: 88-39=49, Resulting Numbers: [45, 59, 49] Generated Node #0,2: 63:[45, 59, 49] Operation: 88-39=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[88, 59, 6], Operations: ['45-39=6'] Exploring Operation: 88-59=29, Resulting Numbers: [6, 29] Generated Node #0,1,0: 63:[6, 29] Operation: 88-59=29 Exploring Operation: 59+6=65, Resulting Numbers: [88, 65] Generated Node #0,1,1: 63:[88, 65] Operation: 59+6=65 Exploring Operation: 88-6=82, Resulting Numbers: [59, 82] Generated Node #0,1,2: 63:[59, 82] Operation: 88-6=82 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[6, 29], Operations: ['45-39=6', '88-59=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,63 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,63 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 #0,1,2 Current State: 63:[59, 82], Operations: ['45-39=6', '88-6=82'] Exploring Operation: 59*82=4838, Resulting Numbers: [4838] 4838,63 unequal: No Solution Exploring Operation: 59+82=141, Resulting Numbers: [141] 141,63 unequal: No Solution Exploring Operation: 82-59=23, Resulting Numbers: [23] 23,63 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 #0,1,1 Current State: 63:[88, 65], Operations: ['45-39=6', '59+6=65'] Exploring Operation: 88-65=23, Resulting Numbers: [23] 23,63 unequal: No Solution Exploring Operation: 88*65=5720, Resulting Numbers: [5720] 5720,63 unequal: No Solution Exploring Operation: 88+65=153, Resulting Numbers: [153] 153,63 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 #0,2 Current State: 63:[45, 59, 49], Operations: ['88-39=49'] Exploring Operation: 49-45=4, Resulting Numbers: [59, 4] Generated Node #0,2,0: 63:[59, 4] Operation: 49-45=4 Exploring Operation: 59-45=14, Resulting Numbers: [49, 14] Generated Node #0,2,1: 63:[49, 14] Operation: 59-45=14 Exploring Operation: 59-49=10, Resulting Numbers: [45, 10] Generated Node #0,2,2: 63:[45, 10] Operation: 59-49=10 Moving to Node #0,2,0 Current State: 63:[59, 4], Operations: ['88-39=49', '49-45=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[39, 45, 88, 59], Operations: [] Exploring Operation: 88-39=49, Resulting Numbers: [45, 59, 49] Generated Node #0,2: 63:[45, 59, 49] Operation: 88-39=49 Moving to Node #0,2 Current State: 63:[45, 59, 49], Operations: ['88-39=49'] Exploring Operation: 49-45=4, Resulting Numbers: [59, 4] Generated Node #0,2,0: 63:[59, 4] Operation: 49-45=4 Moving to Node #0,2,0 Current State: 63:[59, 4], Operations: ['88-39=49', '49-45=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 20, 10, 93, 46 ]
10
[ "20*46=920", "10*93=930", "930-920=10" ]
Current State: 10:[20, 10, 93, 46], Operations: [] Exploring Operation: 20*46=920, Resulting Numbers: [10, 93, 920] Generated Node #2: [10, 93, 920] from Operation: 20*46=920 Current State: 10:[10, 93, 920], Operations: ['20*46=920'] Exploring Operation: 10*93=930, Resulting Numbers: [920, 930] Generated Node #3: [920, 930] from Operation: 10*93=930 Current State: 10:[920, 930], Operations: ['20*46=920', '10*93=930'] Exploring Operation: 930-920=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[20, 10, 93, 46], Operations: [] Exploring Operation: 93-46=47, Resulting Numbers: [20, 10, 47] Generated Node #0,0: 10:[20, 10, 47] Operation: 93-46=47 Exploring Operation: 93-20=73, Resulting Numbers: [10, 46, 73] Generated Node #0,1: 10:[10, 46, 73] Operation: 93-20=73 Moving to Node #0,0 Current State: 10:[20, 10, 47], Operations: ['93-46=47'] Exploring Operation: 47-20=27, Resulting Numbers: [10, 27] Generated Node #0,0,0: 10:[10, 27] Operation: 47-20=27 Exploring Operation: 20-10=10, Resulting Numbers: [47, 10] Generated Node #0,0,1: 10:[47, 10] Operation: 20-10=10 Moving to Node #0,1 Current State: 10:[10, 46, 73], Operations: ['93-20=73'] Exploring Operation: 46-10=36, Resulting Numbers: [73, 36] Generated Node #0,1,0: 10:[73, 36] Operation: 46-10=36 Exploring Operation: 73-46=27, Resulting Numbers: [10, 27] Generated Node #0,1,1: 10:[10, 27] Operation: 73-46=27 Moving to Node #0,0,0 Current State: 10:[10, 27], Operations: ['93-46=47', '47-20=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[10, 27], Operations: ['93-20=73', '73-46=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[47, 10], Operations: ['93-46=47', '20-10=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[73, 36], Operations: ['93-20=73', '46-10=36'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 73+36=109, Resulting Numbers: [109] 109,10 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 85, 19, 52, 13 ]
26
[ "85+19=104", "52/13=4", "104/4=26" ]
Current State: 26:[85, 19, 52, 13], Operations: [] Exploring Operation: 85+19=104, Resulting Numbers: [52, 13, 104] Generated Node #2: [52, 13, 104] from Operation: 85+19=104 Current State: 26:[52, 13, 104], Operations: ['85+19=104'] Exploring Operation: 52/13=4, Resulting Numbers: [104, 4] Generated Node #3: [104, 4] from Operation: 52/13=4 Current State: 26:[104, 4], Operations: ['85+19=104', '52/13=4'] Exploring Operation: 104/4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[85, 19, 52, 13], Operations: [] Exploring Operation: 52-19=33, Resulting Numbers: [85, 13, 33] Generated Node #0,0: 26:[85, 13, 33] Operation: 52-19=33 Exploring Operation: 85-19=66, Resulting Numbers: [52, 13, 66] Generated Node #0,1: 26:[52, 13, 66] Operation: 85-19=66 Exploring Operation: 85-52=33, Resulting Numbers: [19, 13, 33] Generated Node #0,2: 26:[19, 13, 33] Operation: 85-52=33 Exploring Operation: 52/13=4, Resulting Numbers: [85, 19, 4] Generated Node #0,3: 26:[85, 19, 4] Operation: 52/13=4 Moving to Node #0,2 Current State: 26:[19, 13, 33], Operations: ['85-52=33'] Exploring Operation: 33-19=14, Resulting Numbers: [13, 14] Generated Node #0,2,0: 26:[13, 14] Operation: 33-19=14 Exploring Operation: 19-13=6, Resulting Numbers: [33, 6] Generated Node #0,2,1: 26:[33, 6] Operation: 19-13=6 Exploring Operation: 19+13=32, Resulting Numbers: [33, 32] Generated Node #0,2,2: 26:[33, 32] Operation: 19+13=32 Exploring Operation: 33-13=20, Resulting Numbers: [19, 20] Generated Node #0,2,3: 26:[19, 20] Operation: 33-13=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[13, 14], Operations: ['85-52=33', '33-19=14'] Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,26 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[33, 6], Operations: ['85-52=33', '19-13=6'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,26 unequal: No Solution Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 26:[19, 20], Operations: ['85-52=33', '33-13=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 26:[33, 32], Operations: ['85-52=33', '19+13=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 26:[52, 13, 66], Operations: ['85-19=66'] Exploring Operation: 66-13=53, Resulting Numbers: [52, 53] Generated Node #0,1,0: 26:[52, 53] Operation: 66-13=53 Exploring Operation: 66-52=14, Resulting Numbers: [13, 14] Generated Node #0,1,1: 26:[13, 14] Operation: 66-52=14 Exploring Operation: 52-13=39, Resulting Numbers: [66, 39] Generated Node #0,1,2: 26:[66, 39] Operation: 52-13=39 Exploring Operation: 52/13=4, Resulting Numbers: [66, 4] Generated Node #0,1,3: 26:[66, 4] Operation: 52/13=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[13, 14], Operations: ['85-19=66', '66-52=14'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,26 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 26:[66, 4], Operations: ['85-19=66', '52/13=4'] Exploring Operation: 66*4=264, Resulting Numbers: [264] 264,26 unequal: No Solution Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 66+4=70, Resulting Numbers: [70] 70,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[52, 53], Operations: ['85-19=66', '66-13=53'] Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,26 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[66, 39], Operations: ['85-19=66', '52-13=39'] Exploring Operation: 66+39=105, Resulting Numbers: [105] 105,26 unequal: No Solution Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 66*39=2574, Resulting Numbers: [2574] 2574,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 26:[85, 13, 33], Operations: ['52-19=33'] Exploring Operation: 33-13=20, Resulting Numbers: [85, 20] Generated Node #0,0,0: 26:[85, 20] Operation: 33-13=20 Exploring Operation: 85-13=72, Resulting Numbers: [33, 72] Generated Node #0,0,1: 26:[33, 72] Operation: 85-13=72 Exploring Operation: 85-33=52, Resulting Numbers: [13, 52] Generated Node #0,0,2: 26:[13, 52] Operation: 85-33=52 Exploring Operation: 85+13=98, Resulting Numbers: [33, 98] Generated Node #0,0,3: 26:[33, 98] Operation: 85+13=98 Moving to Node #0,3 Current State: 26:[85, 19, 4], Operations: ['52/13=4'] Exploring Operation: 85-4=81, Resulting Numbers: [19, 81] Generated Node #0,3,0: 26:[19, 81] Operation: 85-4=81 Exploring Operation: 19+4=23, Resulting Numbers: [85, 23] Generated Node #0,3,1: 26:[85, 23] Operation: 19+4=23 Exploring Operation: 85-19=66, Resulting Numbers: [4, 66] Generated Node #0,3,2: 26:[4, 66] Operation: 85-19=66 Exploring Operation: 19-4=15, Resulting Numbers: [85, 15] Generated Node #0,3,3: 26:[85, 15] Operation: 19-4=15 Moving to Node #0,0,2 Current State: 26:[13, 52], Operations: ['52-19=33', '85-33=52'] Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,26 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[4, 66], Operations: ['52/13=4', '85-19=66'] Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 4*66=264, Resulting Numbers: [264] 264,26 unequal: No Solution Exploring Operation: 4+66=70, Resulting Numbers: [70] 70,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[33, 72], Operations: ['52-19=33', '85-13=72'] Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,26 unequal: No Solution Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[19, 81], Operations: ['52/13=4', '85-4=81'] Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,26 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,26 unequal: No Solution Moving to Node #0,3,3 Current State: 26:[85, 15], Operations: ['52/13=4', '19-4=15'] Exploring Operation: 85-15=70, Resulting Numbers: [70] 70,26 unequal: No Solution Exploring Operation: 85+15=100, Resulting Numbers: [100] 100,26 unequal: No Solution Exploring Operation: 85*15=1275, Resulting Numbers: [1275] 1275,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[85, 23], Operations: ['52/13=4', '19+4=23'] Exploring Operation: 85+23=108, Resulting Numbers: [108] 108,26 unequal: No Solution Exploring Operation: 85-23=62, Resulting Numbers: [62] 62,26 unequal: No Solution Exploring Operation: 85*23=1955, Resulting Numbers: [1955] 1955,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[85, 20], Operations: ['52-19=33', '33-13=20'] Exploring Operation: 85*20=1700, Resulting Numbers: [1700] 1700,26 unequal: No Solution Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,26 unequal: No Solution Exploring Operation: 85+20=105, Resulting Numbers: [105] 105,26 unequal: No Solution Moving to Node #0,0,3 Current State: 26:[33, 98], Operations: ['52-19=33', '85+13=98'] Exploring Operation: 33*98=3234, Resulting Numbers: [3234] 3234,26 unequal: No Solution Exploring Operation: 33+98=131, Resulting Numbers: [131] 131,26 unequal: No Solution Exploring Operation: 98-33=65, Resulting Numbers: [65] 65,26 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 35, 46, 86, 54 ]
59
[ "35+46=81", "86+54=140", "140-81=59" ]
Current State: 59:[35, 46, 86, 54], Operations: [] Exploring Operation: 35+46=81, Resulting Numbers: [86, 54, 81] Generated Node #2: [86, 54, 81] from Operation: 35+46=81 Current State: 59:[86, 54, 81], Operations: ['35+46=81'] Exploring Operation: 86+54=140, Resulting Numbers: [81, 140] Generated Node #3: [81, 140] from Operation: 86+54=140 Current State: 59:[81, 140], Operations: ['35+46=81', '86+54=140'] Exploring Operation: 140-81=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[35, 46, 86, 54], Operations: [] Exploring Operation: 86-35=51, Resulting Numbers: [46, 54, 51] Generated Node #0,0: 59:[46, 54, 51] Operation: 86-35=51 Moving to Node #0,0 Current State: 59:[46, 54, 51], Operations: ['86-35=51'] Exploring Operation: 46+51=97, Resulting Numbers: [54, 97] Generated Node #0,0,0: 59:[54, 97] Operation: 46+51=97 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[54, 97], Operations: ['86-35=51', '46+51=97'] Exploring Operation: 97-54=43, Resulting Numbers: [43] 43,59 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
[ 76, 20, 6, 76 ]
14
[ "76+20=96", "6+76=82", "96-82=14" ]
Current State: 14:[76, 20, 6, 76], Operations: [] Exploring Operation: 76+20=96, Resulting Numbers: [6, 96] Generated Node #2: [6, 96] from Operation: 76+20=96 Current State: 14:[6, 96], Operations: ['76+20=96'] Exploring Operation: 6+76=82, Resulting Numbers: [96, 82] Generated Node #3: [96, 82] from Operation: 6+76=82 Current State: 14:[96, 82], Operations: ['76+20=96', '6+76=82'] Exploring Operation: 96-82=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[76, 20, 6, 76], Operations: [] Exploring Operation: 76/76=1, Resulting Numbers: [20, 6, 1] Generated Node #0,0: 14:[20, 6, 1] Operation: 76/76=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[20, 6, 1], Operations: ['76/76=1'] Exploring Operation: 20-6=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 14:[1, 14] Operation: 20-6=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[1, 14], Operations: ['76/76=1', '20-6=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[76, 20, 6, 76], Operations: [] Exploring Operation: 76/76=1, Resulting Numbers: [20, 6, 1] Generated Node #0,0: 14:[20, 6, 1] Operation: 76/76=1 Moving to Node #0,0 Current State: 14:[20, 6, 1], Operations: ['76/76=1'] Exploring Operation: 20-6=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 14:[1, 14] Operation: 20-6=14 Moving to Node #0,0,0 Current State: 14:[1, 14], Operations: ['76/76=1', '20-6=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 69, 87, 66, 6 ]
69
[ "87-69=18", "18/6=3", "66+3=69" ]
Current State: 69:[69, 87, 66, 6], Operations: [] Exploring Operation: 87-69=18, Resulting Numbers: [66, 6, 18] Generated Node #2: [66, 6, 18] from Operation: 87-69=18 Current State: 69:[66, 6, 18], Operations: ['87-69=18'] Exploring Operation: 18/6=3, Resulting Numbers: [66, 3] Generated Node #3: [66, 3] from Operation: 18/6=3 Current State: 69:[66, 3], Operations: ['87-69=18', '18/6=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[69, 87, 66, 6], Operations: [] Exploring Operation: 87-69=18, Resulting Numbers: [66, 6, 18] Generated Node #0,0: 69:[66, 6, 18] Operation: 87-69=18 Exploring Operation: 87-6=81, Resulting Numbers: [69, 66, 81] Generated Node #0,1: 69:[69, 66, 81] Operation: 87-6=81 Exploring Operation: 87-66=21, Resulting Numbers: [69, 6, 21] Generated Node #0,2: 69:[69, 6, 21] Operation: 87-66=21 Exploring Operation: 69-66=3, Resulting Numbers: [87, 6, 3] Generated Node #0,3: 69:[87, 6, 3] Operation: 69-66=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[69, 6, 21], Operations: ['87-66=21'] Exploring Operation: 21-6=15, Resulting Numbers: [69, 15] Generated Node #0,2,0: 69:[69, 15] Operation: 21-6=15 Exploring Operation: 69+6=75, Resulting Numbers: [21, 75] Generated Node #0,2,1: 69:[21, 75] Operation: 69+6=75 Exploring Operation: 69-6=63, Resulting Numbers: [21, 63] Generated Node #0,2,2: 69:[21, 63] Operation: 69-6=63 Exploring Operation: 6+21=27, Resulting Numbers: [69, 27] Generated Node #0,2,3: 69:[69, 27] Operation: 6+21=27 Moving to Node #0,2,3 Current State: 69:[69, 27], Operations: ['87-66=21', '6+21=27'] Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,69 unequal: No Solution Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,69 unequal: No Solution Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[21, 75], Operations: ['87-66=21', '69+6=75'] Exploring Operation: 21+75=96, Resulting Numbers: [96] 96,69 unequal: No Solution Exploring Operation: 21*75=1575, Resulting Numbers: [1575] 1575,69 unequal: No Solution Exploring Operation: 75-21=54, Resulting Numbers: [54] 54,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[69, 15], Operations: ['87-66=21', '21-6=15'] Exploring Operation: 69*15=1035, Resulting Numbers: [1035] 1035,69 unequal: No Solution Exploring Operation: 69+15=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[21, 63], Operations: ['87-66=21', '69-6=63'] Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 21*63=1323, Resulting Numbers: [1323] 1323,69 unequal: No Solution Exploring Operation: 21+63=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[66, 6, 18], Operations: ['87-69=18'] Exploring Operation: 66+6=72, Resulting Numbers: [18, 72] Generated Node #0,0,0: 69:[18, 72] Operation: 66+6=72 Exploring Operation: 18-6=12, Resulting Numbers: [66, 12] Generated Node #0,0,1: 69:[66, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [66, 3] Generated Node #0,0,2: 69:[66, 3] Operation: 18/6=3 Exploring Operation: 6+18=24, Resulting Numbers: [66, 24] Generated Node #0,0,3: 69:[66, 24] Operation: 6+18=24 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 69:[66, 3], Operations: ['87-69=18', '18/6=3'] Exploring Operation: 66*3=198, Resulting Numbers: [198] 198,69 unequal: No Solution Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[69, 87, 66, 6], Operations: [] Exploring Operation: 87-69=18, Resulting Numbers: [66, 6, 18] Generated Node #0,0: 69:[66, 6, 18] Operation: 87-69=18 Moving to Node #0,0 Current State: 69:[66, 6, 18], Operations: ['87-69=18'] Exploring Operation: 18/6=3, Resulting Numbers: [66, 3] Generated Node #0,0,2: 69:[66, 3] Operation: 18/6=3 Moving to Node #0,0,2 Current State: 69:[66, 3], Operations: ['87-69=18', '18/6=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 35, 33, 53, 25 ]
56
[ "35-33=2", "53-25=28", "2*28=56" ]
Current State: 56:[35, 33, 53, 25], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [53, 25, 2] Generated Node #2: [53, 25, 2] from Operation: 35-33=2 Current State: 56:[53, 25, 2], Operations: ['35-33=2'] Exploring Operation: 53-25=28, Resulting Numbers: [2, 28] Generated Node #3: [2, 28] from Operation: 53-25=28 Current State: 56:[2, 28], Operations: ['35-33=2', '53-25=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[35, 33, 53, 25], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [53, 25, 2] Generated Node #0,0: 56:[53, 25, 2] Operation: 35-33=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[53, 25, 2], Operations: ['35-33=2'] Exploring Operation: 53-25=28, Resulting Numbers: [2, 28] Generated Node #0,0,0: 56:[2, 28] Operation: 53-25=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[2, 28], Operations: ['35-33=2', '53-25=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[35, 33, 53, 25], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [53, 25, 2] Generated Node #0,0: 56:[53, 25, 2] Operation: 35-33=2 Moving to Node #0,0 Current State: 56:[53, 25, 2], Operations: ['35-33=2'] Exploring Operation: 53-25=28, Resulting Numbers: [2, 28] Generated Node #0,0,0: 56:[2, 28] Operation: 53-25=28 Moving to Node #0,0,0 Current State: 56:[2, 28], Operations: ['35-33=2', '53-25=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 13, 87, 21, 60 ]
51
[ "13*87=1131", "1131-60=1071", "1071/21=51" ]
Current State: 51:[13, 87, 21, 60], Operations: [] Exploring Operation: 13*87=1131, Resulting Numbers: [21, 60, 1131] Generated Node #2: [21, 60, 1131] from Operation: 13*87=1131 Current State: 51:[21, 60, 1131], Operations: ['13*87=1131'] Exploring Operation: 1131-60=1071, Resulting Numbers: [21, 1071] Generated Node #3: [21, 1071] from Operation: 1131-60=1071 Current State: 51:[21, 1071], Operations: ['13*87=1131', '1131-60=1071'] Exploring Operation: 1071/21=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[13, 87, 21, 60], Operations: [] Exploring Operation: 87-13=74, Resulting Numbers: [21, 60, 74] Generated Node #0,0: 51:[21, 60, 74] Operation: 87-13=74 Exploring Operation: 60-13=47, Resulting Numbers: [87, 21, 47] Generated Node #0,1: 51:[87, 21, 47] Operation: 60-13=47 Exploring Operation: 87-60=27, Resulting Numbers: [13, 21, 27] Generated Node #0,2: 51:[13, 21, 27] Operation: 87-60=27 Exploring Operation: 87-21=66, Resulting Numbers: [13, 60, 66] Generated Node #0,3: 51:[13, 60, 66] Operation: 87-21=66 Moving to Node #0,2 Current State: 51:[13, 21, 27], Operations: ['87-60=27'] Exploring Operation: 21-13=8, Resulting Numbers: [27, 8] Generated Node #0,2,0: 51:[27, 8] Operation: 21-13=8 Exploring Operation: 21+27=48, Resulting Numbers: [13, 48] Generated Node #0,2,1: 51:[13, 48] Operation: 21+27=48 Exploring Operation: 27-21=6, Resulting Numbers: [13, 6] Generated Node #0,2,2: 51:[13, 6] Operation: 27-21=6 Exploring Operation: 27-13=14, Resulting Numbers: [21, 14] Generated Node #0,2,3: 51:[21, 14] Operation: 27-13=14 Moving to Node #0,3 Current State: 51:[13, 60, 66], Operations: ['87-21=66'] Exploring Operation: 13+60=73, Resulting Numbers: [66, 73] Generated Node #0,3,0: 51:[66, 73] Operation: 13+60=73 Exploring Operation: 66-60=6, Resulting Numbers: [13, 6] Generated Node #0,3,1: 51:[13, 6] Operation: 66-60=6 Exploring Operation: 60-13=47, Resulting Numbers: [66, 47] Generated Node #0,3,2: 51:[66, 47] Operation: 60-13=47 Exploring Operation: 66-13=53, Resulting Numbers: [60, 53] Generated Node #0,3,3: 51:[60, 53] Operation: 66-13=53 Moving to Node #0,0 Current State: 51:[21, 60, 74], Operations: ['87-13=74'] Exploring Operation: 74-60=14, Resulting Numbers: [21, 14] Generated Node #0,0,0: 51:[21, 14] Operation: 74-60=14 Exploring Operation: 74-21=53, Resulting Numbers: [60, 53] Generated Node #0,0,1: 51:[60, 53] Operation: 74-21=53 Exploring Operation: 60-21=39, Resulting Numbers: [74, 39] Generated Node #0,0,2: 51:[74, 39] Operation: 60-21=39 Exploring Operation: 21+60=81, Resulting Numbers: [74, 81] Generated Node #0,0,3: 51:[74, 81] Operation: 21+60=81 Moving to Node #0,1 Current State: 51:[87, 21, 47], Operations: ['60-13=47'] Exploring Operation: 21+47=68, Resulting Numbers: [87, 68] Generated Node #0,1,0: 51:[87, 68] Operation: 21+47=68 Exploring Operation: 87-47=40, Resulting Numbers: [21, 40] Generated Node #0,1,1: 51:[21, 40] Operation: 87-47=40 Exploring Operation: 47-21=26, Resulting Numbers: [87, 26] Generated Node #0,1,2: 51:[87, 26] Operation: 47-21=26 Exploring Operation: 87-21=66, Resulting Numbers: [47, 66] Generated Node #0,1,3: 51:[47, 66] Operation: 87-21=66 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 51:[21, 40], Operations: ['60-13=47', '87-47=40'] Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,51 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,51 unequal: No Solution No 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: 51:[47, 66], Operations: ['60-13=47', '87-21=66'] Exploring Operation: 47*66=3102, Resulting Numbers: [3102] 3102,51 unequal: No Solution Exploring Operation: 47+66=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,51 unequal: No Solution No 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: 51:[87, 26], Operations: ['60-13=47', '47-21=26'] Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,51 unequal: No Solution Exploring Operation: 87*26=2262, Resulting Numbers: [2262] 2262,51 unequal: No Solution Exploring Operation: 87+26=113, Resulting Numbers: [113] 113,51 unequal: No Solution No 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: 51:[87, 68], Operations: ['60-13=47', '21+47=68'] Exploring Operation: 87+68=155, Resulting Numbers: [155] 155,51 unequal: No Solution Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 87*68=5916, Resulting Numbers: [5916] 5916,51 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: 51:[13, 48], Operations: ['87-60=27', '21+27=48'] Exploring Operation: 13*48=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[21, 14], Operations: ['87-60=27', '27-13=14'] Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[13, 6], Operations: ['87-60=27', '27-21=6'] Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,51 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,3,1 Current State: 51:[13, 6], Operations: ['87-21=66', '66-60=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,51 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[21, 14], Operations: ['87-13=74', '74-60=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,51 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,51 unequal: No Solution Moving to Node #0,3,3 Current State: 51:[60, 53], Operations: ['87-21=66', '66-13=53'] Exploring Operation: 60*53=3180, Resulting Numbers: [3180] 3180,51 unequal: No Solution Exploring Operation: 60+53=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[60, 53], Operations: ['87-13=74', '74-21=53'] Exploring Operation: 60*53=3180, Resulting Numbers: [3180] 3180,51 unequal: No Solution Exploring Operation: 60+53=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 60-53=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[27, 8], Operations: ['87-60=27', '21-13=8'] Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,51 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,3,2 Current State: 51:[66, 47], Operations: ['87-21=66', '60-13=47'] Exploring Operation: 66*47=3102, Resulting Numbers: [3102] 3102,51 unequal: No Solution Exploring Operation: 66+47=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[74, 39], Operations: ['87-13=74', '60-21=39'] Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,51 unequal: No Solution Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,51 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,51 unequal: No Solution Moving to Node #0,3,0 Current State: 51:[66, 73], Operations: ['87-21=66', '13+60=73'] Exploring Operation: 66+73=139, Resulting Numbers: [139] 139,51 unequal: No Solution Exploring Operation: 66*73=4818, Resulting Numbers: [4818] 4818,51 unequal: No Solution Exploring Operation: 73-66=7, Resulting Numbers: [7] 7,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[74, 81], Operations: ['87-13=74', '21+60=81'] Exploring Operation: 81-74=7, Resulting Numbers: [7] 7,51 unequal: No Solution Exploring Operation: 74+81=155, Resulting Numbers: [155] 155,51 unequal: No Solution Exploring Operation: 74*81=5994, Resulting Numbers: [5994] 5994,51 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 28, 20, 4, 46 ]
70
[ "4+46=50", "28*50=1400", "1400/20=70" ]
Current State: 70:[28, 20, 4, 46], Operations: [] Exploring Operation: 4+46=50, Resulting Numbers: [28, 20, 50] Generated Node #2: [28, 20, 50] from Operation: 4+46=50 Current State: 70:[28, 20, 50], Operations: ['4+46=50'] Exploring Operation: 28*50=1400, Resulting Numbers: [20, 1400] Generated Node #3: [20, 1400] from Operation: 28*50=1400 Current State: 70:[20, 1400], Operations: ['4+46=50', '28*50=1400'] Exploring Operation: 1400/20=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[28, 20, 4, 46], Operations: [] Exploring Operation: 28+46=74, Resulting Numbers: [20, 4, 74] Generated Node #0,0: 70:[20, 4, 74] Operation: 28+46=74 Exploring Operation: 46-28=18, Resulting Numbers: [20, 4, 18] Generated Node #0,1: 70:[20, 4, 18] Operation: 46-28=18 Exploring Operation: 20+46=66, Resulting Numbers: [28, 4, 66] Generated Node #0,2: 70:[28, 4, 66] Operation: 20+46=66 Moving to Node #0,0 Current State: 70:[20, 4, 74], Operations: ['28+46=74'] Exploring Operation: 20-4=16, Resulting Numbers: [74, 16] Generated Node #0,0,0: 70:[74, 16] Operation: 20-4=16 Exploring Operation: 74-4=70, Resulting Numbers: [20, 70] Generated Node #0,0,1: 70:[20, 70] Operation: 74-4=70 Exploring Operation: 20/4=5, Resulting Numbers: [74, 5] Generated Node #0,0,2: 70:[74, 5] Operation: 20/4=5 Moving to Node #0,1 Current State: 70:[20, 4, 18], Operations: ['46-28=18'] Exploring Operation: 20/4=5, Resulting Numbers: [18, 5] Generated Node #0,1,0: 70:[18, 5] Operation: 20/4=5 Exploring Operation: 20+18=38, Resulting Numbers: [4, 38] Generated Node #0,1,1: 70:[4, 38] Operation: 20+18=38 Exploring Operation: 20-18=2, Resulting Numbers: [4, 2] Generated Node #0,1,2: 70:[4, 2] Operation: 20-18=2 Moving to Node #0,2 Current State: 70:[28, 4, 66], Operations: ['20+46=66'] Exploring Operation: 66-28=38, Resulting Numbers: [4, 38] Generated Node #0,2,0: 70:[4, 38] Operation: 66-28=38 Exploring Operation: 28/4=7, Resulting Numbers: [66, 7] Generated Node #0,2,1: 70:[66, 7] Operation: 28/4=7 Exploring Operation: 28+4=32, Resulting Numbers: [66, 32] Generated Node #0,2,2: 70:[66, 32] Operation: 28+4=32 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 70:[4, 38], Operations: ['20+46=66', '66-28=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,70 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[66, 7], Operations: ['20+46=66', '28/4=7'] Exploring Operation: 66+7=73, Resulting Numbers: [73] 73,70 unequal: No Solution Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,70 unequal: No Solution Exploring Operation: 66*7=462, Resulting Numbers: [462] 462,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 70:[66, 32], Operations: ['20+46=66', '28+4=32'] Exploring Operation: 66*32=2112, Resulting Numbers: [2112] 2112,70 unequal: No Solution Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,70 unequal: No Solution Exploring Operation: 66+32=98, Resulting Numbers: [98] 98,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 70:[4, 2], Operations: ['46-28=18', '20-18=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[4, 38], Operations: ['46-28=18', '20+18=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,70 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[74, 5], Operations: ['28+46=74', '20/4=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,70 unequal: No Solution Exploring Operation: 74*5=370, Resulting Numbers: [370] 370,70 unequal: No Solution Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[18, 5], Operations: ['46-28=18', '20/4=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,70 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[74, 16], Operations: ['28+46=74', '20-4=16'] Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,70 unequal: No Solution Exploring Operation: 74+16=90, Resulting Numbers: [90] 90,70 unequal: No Solution Exploring Operation: 74*16=1184, Resulting Numbers: [1184] 1184,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[20, 70], Operations: ['28+46=74', '74-4=70'] Exploring Operation: 20*70=1400, Resulting Numbers: [1400] 1400,70 unequal: No Solution Exploring Operation: 70-20=50, Resulting Numbers: [50] 50,70 unequal: No Solution Exploring Operation: 20+70=90, Resulting Numbers: [90] 90,70 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 61, 78, 84, 57 ]
44
[ "78-61=17", "84-57=27", "17+27=44" ]
Current State: 44:[61, 78, 84, 57], Operations: [] Exploring Operation: 78-61=17, Resulting Numbers: [84, 57, 17] Generated Node #2: [84, 57, 17] from Operation: 78-61=17 Current State: 44:[84, 57, 17], Operations: ['78-61=17'] Exploring Operation: 84-57=27, Resulting Numbers: [17, 27] Generated Node #3: [17, 27] from Operation: 84-57=27 Current State: 44:[17, 27], Operations: ['78-61=17', '84-57=27'] Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[61, 78, 84, 57], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [78, 57, 23] Generated Node #0,0: 44:[78, 57, 23] Operation: 84-61=23 Exploring Operation: 84-78=6, Resulting Numbers: [61, 57, 6] Generated Node #0,1: 44:[61, 57, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[61, 57, 6], Operations: ['84-78=6'] Exploring Operation: 61-6=55, Resulting Numbers: [57, 55] Generated Node #0,1,0: 44:[57, 55] Operation: 61-6=55 Exploring Operation: 61-57=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 44:[6, 4] Operation: 61-57=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 44:[6, 4], Operations: ['84-78=6', '61-57=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 44:[57, 55], Operations: ['84-78=6', '61-6=55'] Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 57+55=112, Resulting Numbers: [112] 112,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[78, 57, 23], Operations: ['84-61=23'] Exploring Operation: 78-23=55, Resulting Numbers: [57, 55] Generated Node #0,0,0: 44:[57, 55] Operation: 78-23=55 Exploring Operation: 78-57=21, Resulting Numbers: [23, 21] Generated Node #0,0,1: 44:[23, 21] Operation: 78-57=21 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[23, 21], Operations: ['84-61=23', '78-57=21'] Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[61, 78, 84, 57], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [78, 57, 23] Generated Node #0,0: 44:[78, 57, 23] Operation: 84-61=23 Moving to Node #0,0 Current State: 44:[78, 57, 23], Operations: ['84-61=23'] Exploring Operation: 78-57=21, Resulting Numbers: [23, 21] Generated Node #0,0,1: 44:[23, 21] Operation: 78-57=21 Moving to Node #0,0,1 Current State: 44:[23, 21], Operations: ['84-61=23', '78-57=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 1, 92, 79, 4 ]
53
[ "92-79=13", "4*13=52", "1+52=53" ]
Current State: 53:[1, 92, 79, 4], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [1, 4, 13] Generated Node #2: [1, 4, 13] from Operation: 92-79=13 Current State: 53:[1, 4, 13], Operations: ['92-79=13'] Exploring Operation: 4*13=52, Resulting Numbers: [1, 52] Generated Node #3: [1, 52] from Operation: 4*13=52 Current State: 53:[1, 52], Operations: ['92-79=13', '4*13=52'] Exploring Operation: 1+52=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[1, 92, 79, 4], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [1, 79, 23] Generated Node #0,0: 53:[1, 79, 23] Operation: 92/4=23 Exploring Operation: 92-1=91, Resulting Numbers: [79, 4, 91] Generated Node #0,1: 53:[79, 4, 91] Operation: 92-1=91 Exploring Operation: 92-4=88, Resulting Numbers: [1, 79, 88] Generated Node #0,2: 53:[1, 79, 88] Operation: 92-4=88 Exploring Operation: 79-1=78, Resulting Numbers: [92, 4, 78] Generated Node #0,3: 53:[92, 4, 78] Operation: 79-1=78 Exploring Operation: 1+4=5, Resulting Numbers: [92, 79, 5] Generated Node #0,4: 53:[92, 79, 5] Operation: 1+4=5 Moving to Node #0,0 Current State: 53:[1, 79, 23], Operations: ['92/4=23'] Exploring Operation: 79-23=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 53:[1, 56] Operation: 79-23=56 Exploring Operation: 79-1=78, Resulting Numbers: [23, 78] Generated Node #0,0,1: 53:[23, 78] Operation: 79-1=78 Exploring Operation: 1*79=79, Resulting Numbers: [23, 79] Generated Node #0,0,2: 53:[23, 79] Operation: 1*79=79 Exploring Operation: 79/1=79, Resulting Numbers: [23, 79] Generated Node #0,0,3: 53:[23, 79] Operation: 79/1=79 Exploring Operation: 1+23=24, Resulting Numbers: [79, 24] Generated Node #0,0,4: 53:[79, 24] Operation: 1+23=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[1, 56], Operations: ['92/4=23', '79-23=56'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,53 unequal: No Solution Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,53 unequal: No Solution Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,53 unequal: No Solution Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,53 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 #0,0,1 Current State: 53:[23, 78], Operations: ['92/4=23', '79-1=78'] Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,53 unequal: No Solution Exploring Operation: 23+78=101, Resulting Numbers: [101] 101,53 unequal: No Solution Exploring Operation: 23*78=1794, Resulting Numbers: [1794] 1794,53 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 #0,0,4 Current State: 53:[79, 24], Operations: ['92/4=23', '1+23=24'] Exploring Operation: 79-24=55, Resulting Numbers: [55] 55,53 unequal: No Solution Exploring Operation: 79*24=1896, Resulting Numbers: [1896] 1896,53 unequal: No Solution Exploring Operation: 79+24=103, Resulting Numbers: [103] 103,53 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 #0,0,2 Current State: 53:[23, 79], Operations: ['92/4=23', '1*79=79'] Exploring Operation: 23+79=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,53 unequal: No Solution Exploring Operation: 23*79=1817, Resulting Numbers: [1817] 1817,53 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 #0,0,3 Current State: 53:[23, 79], Operations: ['92/4=23', '79/1=79'] Exploring Operation: 23*79=1817, Resulting Numbers: [1817] 1817,53 unequal: No Solution Exploring Operation: 23+79=102, Resulting Numbers: [102] 102,53 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,53 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: 53:[1, 79, 88], Operations: ['92-4=88'] Exploring Operation: 79/1=79, Resulting Numbers: [88, 79] Generated Node #0,2,0: 53:[88, 79] Operation: 79/1=79 Exploring Operation: 88-1=87, Resulting Numbers: [79, 87] Generated Node #0,2,1: 53:[79, 87] Operation: 88-1=87 Exploring Operation: 1*88=88, Resulting Numbers: [79, 88] Generated Node #0,2,2: 53:[79, 88] Operation: 1*88=88 Exploring Operation: 1*79=79, Resulting Numbers: [88, 79] Generated Node #0,2,3: 53:[88, 79] Operation: 1*79=79 Exploring Operation: 79-1=78, Resulting Numbers: [88, 78] Generated Node #0,2,4: 53:[88, 78] Operation: 79-1=78 Moving to Node #0,4 Current State: 53:[92, 79, 5], Operations: ['1+4=5'] Exploring Operation: 79+5=84, Resulting Numbers: [92, 84] Generated Node #0,4,0: 53:[92, 84] Operation: 79+5=84 Exploring Operation: 92+5=97, Resulting Numbers: [79, 97] Generated Node #0,4,1: 53:[79, 97] Operation: 92+5=97 Exploring Operation: 92-79=13, Resulting Numbers: [5, 13] Generated Node #0,4,2: 53:[5, 13] Operation: 92-79=13 Exploring Operation: 92-5=87, Resulting Numbers: [79, 87] Generated Node #0,4,3: 53:[79, 87] Operation: 92-5=87 Exploring Operation: 79-5=74, Resulting Numbers: [92, 74] Generated Node #0,4,4: 53:[92, 74] Operation: 79-5=74 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 53:[79, 87], Operations: ['1+4=5', '92-5=87'] Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,53 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 53:[92, 74], Operations: ['1+4=5', '79-5=74'] Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 92+74=166, Resulting Numbers: [166] 166,53 unequal: No Solution Exploring Operation: 92*74=6808, Resulting Numbers: [6808] 6808,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 53:[92, 84], Operations: ['1+4=5', '79+5=84'] Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 92*84=7728, Resulting Numbers: [7728] 7728,53 unequal: No Solution Exploring Operation: 92+84=176, Resulting Numbers: [176] 176,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 53:[79, 97], Operations: ['1+4=5', '92+5=97'] Exploring Operation: 79+97=176, Resulting Numbers: [176] 176,53 unequal: No Solution Exploring Operation: 97-79=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 79*97=7663, Resulting Numbers: [7663] 7663,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 53:[5, 13], Operations: ['1+4=5', '92-79=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[79, 4, 91], Operations: ['92-1=91'] Exploring Operation: 91-4=87, Resulting Numbers: [79, 87] Generated Node #0,1,0: 53:[79, 87] Operation: 91-4=87 Exploring Operation: 79-4=75, Resulting Numbers: [91, 75] Generated Node #0,1,1: 53:[91, 75] Operation: 79-4=75 Exploring Operation: 79+4=83, Resulting Numbers: [91, 83] Generated Node #0,1,2: 53:[91, 83] Operation: 79+4=83 Exploring Operation: 91-79=12, Resulting Numbers: [4, 12] Generated Node #0,1,3: 53:[4, 12] Operation: 91-79=12 Exploring Operation: 4+91=95, Resulting Numbers: [79, 95] Generated Node #0,1,4: 53:[79, 95] Operation: 4+91=95 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[79, 87], Operations: ['92-1=91', '91-4=87'] Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,53 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,53 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:[91, 75], Operations: ['92-1=91', '79-4=75'] Exploring Operation: 91-75=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 91*75=6825, Resulting Numbers: [6825] 6825,53 unequal: No Solution Exploring Operation: 91+75=166, Resulting Numbers: [166] 166,53 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 #0,1,2 Current State: 53:[91, 83], Operations: ['92-1=91', '79+4=83'] Exploring Operation: 91*83=7553, Resulting Numbers: [7553] 7553,53 unequal: No Solution Exploring Operation: 91+83=174, Resulting Numbers: [174] 174,53 unequal: No Solution Exploring Operation: 91-83=8, Resulting Numbers: [8] 8,53 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 #0,1,4 Current State: 53:[79, 95], Operations: ['92-1=91', '4+91=95'] Exploring Operation: 79*95=7505, Resulting Numbers: [7505] 7505,53 unequal: No Solution Exploring Operation: 79+95=174, Resulting Numbers: [174] 174,53 unequal: No Solution Exploring Operation: 95-79=16, Resulting Numbers: [16] 16,53 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 #0,1,3 Current State: 53:[4, 12], Operations: ['92-1=91', '91-79=12'] Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,53 unequal: No Solution Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 53:[92, 4, 78], Operations: ['79-1=78'] Exploring Operation: 92/4=23, Resulting Numbers: [78, 23] Generated Node #0,3,0: 53:[78, 23] Operation: 92/4=23 Exploring Operation: 92-4=88, Resulting Numbers: [78, 88] Generated Node #0,3,1: 53:[78, 88] Operation: 92-4=88 Exploring Operation: 78-4=74, Resulting Numbers: [92, 74] Generated Node #0,3,2: 53:[92, 74] Operation: 78-4=74 Exploring Operation: 92+4=96, Resulting Numbers: [78, 96] Generated Node #0,3,3: 53:[78, 96] Operation: 92+4=96 Exploring Operation: 4+78=82, Resulting Numbers: [92, 82] Generated Node #0,3,4: 53:[92, 82] Operation: 4+78=82 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[78, 23], Operations: ['79-1=78', '92/4=23'] Exploring Operation: 78+23=101, Resulting Numbers: [101] 101,53 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,53 unequal: No Solution Exploring Operation: 78*23=1794, Resulting Numbers: [1794] 1794,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[78, 88], Operations: ['79-1=78', '92-4=88'] Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 78*88=6864, Resulting Numbers: [6864] 6864,53 unequal: No Solution Exploring Operation: 78+88=166, Resulting Numbers: [166] 166,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[92, 74], Operations: ['79-1=78', '78-4=74'] Exploring Operation: 92+74=166, Resulting Numbers: [166] 166,53 unequal: No Solution Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 92*74=6808, Resulting Numbers: [6808] 6808,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 53:[78, 96], Operations: ['79-1=78', '92+4=96'] Exploring Operation: 96-78=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 78*96=7488, Resulting Numbers: [7488] 7488,53 unequal: No Solution Exploring Operation: 78+96=174, Resulting Numbers: [174] 174,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 53:[92, 82], Operations: ['79-1=78', '4+78=82'] Exploring Operation: 92-82=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 92+82=174, Resulting Numbers: [174] 174,53 unequal: No Solution Exploring Operation: 92*82=7544, Resulting Numbers: [7544] 7544,53 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: 53:[79, 87], Operations: ['92-4=88', '88-1=87'] Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,53 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[88, 78], Operations: ['92-4=88', '79-1=78'] Exploring Operation: 88+78=166, Resulting Numbers: [166] 166,53 unequal: No Solution Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,53 unequal: No Solution Exploring Operation: 88*78=6864, Resulting Numbers: [6864] 6864,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[88, 79], Operations: ['92-4=88', '79/1=79'] Exploring Operation: 88+79=167, Resulting Numbers: [167] 167,53 unequal: No Solution Exploring Operation: 88*79=6952, Resulting Numbers: [6952] 6952,53 unequal: No Solution Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[79, 88], Operations: ['92-4=88', '1*88=88'] Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 79+88=167, Resulting Numbers: [167] 167,53 unequal: No Solution Exploring Operation: 79*88=6952, Resulting Numbers: [6952] 6952,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[88, 79], Operations: ['92-4=88', '1*79=79'] Exploring Operation: 88+79=167, Resulting Numbers: [167] 167,53 unequal: No Solution Exploring Operation: 88*79=6952, Resulting Numbers: [6952] 6952,53 unequal: No Solution Exploring Operation: 88-79=9, Resulting Numbers: [9] 9,53 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 10, 33, 76, 86 ]
67
[ "86-76=10", "10*10=100", "100-33=67" ]
Current State: 67:[10, 33, 76, 86], Operations: [] Exploring Operation: 86-76=10, Resulting Numbers: [10, 33, 10] Generated Node #2: [10, 33, 10] from Operation: 86-76=10 Current State: 67:[10, 33, 10], Operations: ['86-76=10'] Exploring Operation: 10*10=100, Resulting Numbers: [33, 100] Generated Node #3: [33, 100] from Operation: 10*10=100 Current State: 67:[33, 100], Operations: ['86-76=10', '10*10=100'] Exploring Operation: 100-33=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[10, 33, 76, 86], Operations: [] Exploring Operation: 10+33=43, Resulting Numbers: [76, 86, 43] Generated Node #0,0: 67:[76, 86, 43] Operation: 10+33=43 Exploring Operation: 86-10=76, Resulting Numbers: [33, 76, 76] Generated Node #0,1: 67:[33, 76, 76] Operation: 86-10=76 Moving to Node #0,0 Current State: 67:[76, 86, 43], Operations: ['10+33=43'] Exploring Operation: 86-43=43, Resulting Numbers: [76, 43] Generated Node #0,0,0: 67:[76, 43] Operation: 86-43=43 Exploring Operation: 76-43=33, Resulting Numbers: [86, 33] Generated Node #0,0,1: 67:[86, 33] Operation: 76-43=33 Moving to Node #0,1 Current State: 67:[33, 76, 76], Operations: ['86-10=76'] Exploring Operation: 76-33=43, Resulting Numbers: [76, 43] Generated Node #0,1,0: 67:[76, 43] Operation: 76-33=43 Exploring Operation: 76-33=43, Resulting Numbers: [76, 43] Generated Node #0,1,1: 67:[76, 43] Operation: 76-33=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[76, 43], Operations: ['86-10=76', '76-33=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[76, 43], Operations: ['86-10=76', '76-33=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,67 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: 67:[76, 43], Operations: ['10+33=43', '86-43=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[86, 33], Operations: ['10+33=43', '76-43=33'] Exploring Operation: 86+33=119, Resulting Numbers: [119] 119,67 unequal: No Solution Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,67 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 66, 65, 14, 35 ]
92
[ "65*14=910", "910/35=26", "66+26=92" ]
Current State: 92:[66, 65, 14, 35], Operations: [] Exploring Operation: 65*14=910, Resulting Numbers: [66, 35, 910] Generated Node #2: [66, 35, 910] from Operation: 65*14=910 Current State: 92:[66, 35, 910], Operations: ['65*14=910'] Exploring Operation: 910/35=26, Resulting Numbers: [66, 26] Generated Node #3: [66, 26] from Operation: 910/35=26 Current State: 92:[66, 26], Operations: ['65*14=910', '910/35=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[66, 65, 14, 35], Operations: [] Exploring Operation: 66-14=52, Resulting Numbers: [65, 35, 52] Generated Node #0,0: 92:[65, 35, 52] Operation: 66-14=52 Exploring Operation: 66-65=1, Resulting Numbers: [14, 35, 1] Generated Node #0,1: 92:[14, 35, 1] Operation: 66-65=1 Moving to Node #0,1 Current State: 92:[14, 35, 1], Operations: ['66-65=1'] Exploring Operation: 14+35=49, Resulting Numbers: [1, 49] Generated Node #0,1,0: 92:[1, 49] Operation: 14+35=49 Exploring Operation: 35-14=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 92:[1, 21] Operation: 35-14=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[1, 21], Operations: ['66-65=1', '35-14=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[1, 49], Operations: ['66-65=1', '14+35=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 92:[65, 35, 52], Operations: ['66-14=52'] Exploring Operation: 65-35=30, Resulting Numbers: [52, 30] Generated Node #0,0,0: 92:[52, 30] Operation: 65-35=30 Exploring Operation: 65+35=100, Resulting Numbers: [52, 100] Generated Node #0,0,1: 92:[52, 100] Operation: 65+35=100 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[52, 30], Operations: ['66-14=52', '65-35=30'] Exploring Operation: 52+30=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 52-30=22, Resulting Numbers: [22] 22,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[52, 100], Operations: ['66-14=52', '65+35=100'] Exploring Operation: 52+100=152, Resulting Numbers: [152] 152,92 unequal: No Solution Exploring Operation: 100-52=48, Resulting Numbers: [48] 48,92 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
[ 23, 32, 37, 88 ]
96
[ "23+88=111", "32*111=3552", "3552/37=96" ]
Current State: 96:[23, 32, 37, 88], Operations: [] Exploring Operation: 23+88=111, Resulting Numbers: [32, 37, 111] Generated Node #2: [32, 37, 111] from Operation: 23+88=111 Current State: 96:[32, 37, 111], Operations: ['23+88=111'] Exploring Operation: 32*111=3552, Resulting Numbers: [37, 3552] Generated Node #3: [37, 3552] from Operation: 32*111=3552 Current State: 96:[37, 3552], Operations: ['23+88=111', '32*111=3552'] Exploring Operation: 3552/37=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[23, 32, 37, 88], Operations: [] Exploring Operation: 37-23=14, Resulting Numbers: [32, 88, 14] Generated Node #0,0: 96:[32, 88, 14] Operation: 37-23=14 Exploring Operation: 37-32=5, Resulting Numbers: [23, 88, 5] Generated Node #0,1: 96:[23, 88, 5] Operation: 37-32=5 Exploring Operation: 88-37=51, Resulting Numbers: [23, 32, 51] Generated Node #0,2: 96:[23, 32, 51] Operation: 88-37=51 Moving to Node #0,2 Current State: 96:[23, 32, 51], Operations: ['88-37=51'] Exploring Operation: 51-32=19, Resulting Numbers: [23, 19] Generated Node #0,2,0: 96:[23, 19] Operation: 51-32=19 Exploring Operation: 51-23=28, Resulting Numbers: [32, 28] Generated Node #0,2,1: 96:[32, 28] Operation: 51-23=28 Exploring Operation: 32-23=9, Resulting Numbers: [51, 9] Generated Node #0,2,2: 96:[51, 9] Operation: 32-23=9 Moving to Node #0,0 Current State: 96:[32, 88, 14], Operations: ['37-23=14'] Exploring Operation: 32+14=46, Resulting Numbers: [88, 46] Generated Node #0,0,0: 96:[88, 46] Operation: 32+14=46 Exploring Operation: 88-32=56, Resulting Numbers: [14, 56] Generated Node #0,0,1: 96:[14, 56] Operation: 88-32=56 Exploring Operation: 88+14=102, Resulting Numbers: [32, 102] Generated Node #0,0,2: 96:[32, 102] Operation: 88+14=102 Moving to Node #0,1 Current State: 96:[23, 88, 5], Operations: ['37-32=5'] Exploring Operation: 23-5=18, Resulting Numbers: [88, 18] Generated Node #0,1,0: 96:[88, 18] Operation: 23-5=18 Exploring Operation: 23+5=28, Resulting Numbers: [88, 28] Generated Node #0,1,1: 96:[88, 28] Operation: 23+5=28 Exploring Operation: 88+5=93, Resulting Numbers: [23, 93] Generated Node #0,1,2: 96:[23, 93] Operation: 88+5=93 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 96:[23, 93], Operations: ['37-32=5', '88+5=93'] Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 23+93=116, Resulting Numbers: [116] 116,96 unequal: No Solution Exploring Operation: 23*93=2139, Resulting Numbers: [2139] 2139,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[88, 18], Operations: ['37-32=5', '23-5=18'] Exploring Operation: 88-18=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 88+18=106, Resulting Numbers: [106] 106,96 unequal: No Solution Exploring Operation: 88*18=1584, Resulting Numbers: [1584] 1584,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[88, 28], Operations: ['37-32=5', '23+5=28'] Exploring Operation: 88+28=116, Resulting Numbers: [116] 116,96 unequal: No Solution Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 88*28=2464, Resulting Numbers: [2464] 2464,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 96:[23, 19], Operations: ['88-37=51', '51-32=19'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 23+19=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 23*19=437, Resulting Numbers: [437] 437,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[51, 9], Operations: ['88-37=51', '32-23=9'] Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[32, 28], Operations: ['88-37=51', '51-23=28'] Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,96 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[32, 102], Operations: ['37-23=14', '88+14=102'] Exploring Operation: 32+102=134, Resulting Numbers: [134] 134,96 unequal: No Solution Exploring Operation: 102-32=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 32*102=3264, Resulting Numbers: [3264] 3264,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[88, 46], Operations: ['37-23=14', '32+14=46'] Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 88*46=4048, Resulting Numbers: [4048] 4048,96 unequal: No Solution Exploring Operation: 88+46=134, Resulting Numbers: [134] 134,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[14, 56], Operations: ['37-23=14', '88-32=56'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,96 unequal: No Solution Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 12, 87, 24, 81 ]
22
[ "87-81=6", "12/6=2", "24-2=22" ]
Current State: 22:[12, 87, 24, 81], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [12, 24, 6] Generated Node #2: [12, 24, 6] from Operation: 87-81=6 Current State: 22:[12, 24, 6], Operations: ['87-81=6'] Exploring Operation: 12/6=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 12/6=2 Current State: 22:[24, 2], Operations: ['87-81=6', '12/6=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[12, 87, 24, 81], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [12, 24, 6] Generated Node #0,0: 22:[12, 24, 6] Operation: 87-81=6 Exploring Operation: 87-12=75, Resulting Numbers: [24, 81, 75] Generated Node #0,1: 22:[24, 81, 75] Operation: 87-12=75 Exploring Operation: 81-24=57, Resulting Numbers: [12, 87, 57] Generated Node #0,2: 22:[12, 87, 57] Operation: 81-24=57 Exploring Operation: 87-24=63, Resulting Numbers: [12, 81, 63] Generated Node #0,3: 22:[12, 81, 63] Operation: 87-24=63 Moving to Node #0,0 Current State: 22:[12, 24, 6], Operations: ['87-81=6'] Exploring Operation: 24/12=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 22:[6, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [6, 12] Generated Node #0,0,1: 22:[6, 12] Operation: 24-12=12 Exploring Operation: 12/6=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 22:[24, 2] Operation: 12/6=2 Exploring Operation: 24/6=4, Resulting Numbers: [12, 4] Generated Node #0,0,3: 22:[12, 4] Operation: 24/6=4 Moving to Node #0,3 Current State: 22:[12, 81, 63], Operations: ['87-24=63'] Exploring Operation: 81-12=69, Resulting Numbers: [63, 69] Generated Node #0,3,0: 22:[63, 69] Operation: 81-12=69 Exploring Operation: 12+81=93, Resulting Numbers: [63, 93] Generated Node #0,3,1: 22:[63, 93] Operation: 12+81=93 Exploring Operation: 81-63=18, Resulting Numbers: [12, 18] Generated Node #0,3,2: 22:[12, 18] Operation: 81-63=18 Exploring Operation: 63-12=51, Resulting Numbers: [81, 51] Generated Node #0,3,3: 22:[81, 51] Operation: 63-12=51 Moving to Node #0,2 Current State: 22:[12, 87, 57], Operations: ['81-24=57'] Exploring Operation: 12+87=99, Resulting Numbers: [57, 99] Generated Node #0,2,0: 22:[57, 99] Operation: 12+87=99 Exploring Operation: 87-12=75, Resulting Numbers: [57, 75] Generated Node #0,2,1: 22:[57, 75] Operation: 87-12=75 Exploring Operation: 57-12=45, Resulting Numbers: [87, 45] Generated Node #0,2,2: 22:[87, 45] Operation: 57-12=45 Exploring Operation: 87-57=30, Resulting Numbers: [12, 30] Generated Node #0,2,3: 22:[12, 30] Operation: 87-57=30 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 22:[12, 30], Operations: ['81-24=57', '87-57=30'] Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 12*30=360, Resulting Numbers: [360] 360,22 unequal: No Solution Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,22 unequal: No Solution No 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: 22:[57, 75], Operations: ['81-24=57', '87-12=75'] Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 57+75=132, Resulting Numbers: [132] 132,22 unequal: No Solution Exploring Operation: 57*75=4275, Resulting Numbers: [4275] 4275,22 unequal: No Solution No 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: 22:[87, 45], Operations: ['81-24=57', '57-12=45'] Exploring Operation: 87*45=3915, Resulting Numbers: [3915] 3915,22 unequal: No Solution Exploring Operation: 87+45=132, Resulting Numbers: [132] 132,22 unequal: No Solution Exploring Operation: 87-45=42, Resulting Numbers: [42] 42,22 unequal: No Solution No 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: 22:[57, 99], Operations: ['81-24=57', '12+87=99'] Exploring Operation: 99-57=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 57*99=5643, Resulting Numbers: [5643] 5643,22 unequal: No Solution Exploring Operation: 57+99=156, Resulting Numbers: [156] 156,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 22:[24, 81, 75], Operations: ['87-12=75'] Exploring Operation: 75-24=51, Resulting Numbers: [81, 51] Generated Node #0,1,0: 22:[81, 51] Operation: 75-24=51 Exploring Operation: 81-24=57, Resulting Numbers: [75, 57] Generated Node #0,1,1: 22:[75, 57] Operation: 81-24=57 Exploring Operation: 81-75=6, Resulting Numbers: [24, 6] Generated Node #0,1,2: 22:[24, 6] Operation: 81-75=6 Exploring Operation: 24+81=105, Resulting Numbers: [75, 105] Generated Node #0,1,3: 22:[75, 105] Operation: 24+81=105 Moving to Node #0,0,2 Current State: 22:[24, 2], Operations: ['87-81=6', '12/6=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[12, 87, 24, 81], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [12, 24, 6] Generated Node #0,0: 22:[12, 24, 6] Operation: 87-81=6 Moving to Node #0,0 Current State: 22:[12, 24, 6], Operations: ['87-81=6'] Exploring Operation: 12/6=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 22:[24, 2] Operation: 12/6=2 Moving to Node #0,0,2 Current State: 22:[24, 2], Operations: ['87-81=6', '12/6=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 55, 4, 62, 61 ]
51
[ "55-4=51", "62-61=1", "51*1=51" ]
Current State: 51:[55, 4, 62, 61], Operations: [] Exploring Operation: 55-4=51, Resulting Numbers: [62, 61, 51] Generated Node #2: [62, 61, 51] from Operation: 55-4=51 Current State: 51:[62, 61, 51], Operations: ['55-4=51'] Exploring Operation: 62-61=1, Resulting Numbers: [51, 1] Generated Node #3: [51, 1] from Operation: 62-61=1 Current State: 51:[51, 1], Operations: ['55-4=51', '62-61=1'] Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[55, 4, 62, 61], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [4, 61, 7] Generated Node #0,0: 51:[4, 61, 7] Operation: 62-55=7 Exploring Operation: 61-55=6, Resulting Numbers: [4, 62, 6] Generated Node #0,1: 51:[4, 62, 6] Operation: 61-55=6 Exploring Operation: 62-61=1, Resulting Numbers: [55, 4, 1] Generated Node #0,2: 51:[55, 4, 1] Operation: 62-61=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[55, 4, 1], Operations: ['62-61=1'] Exploring Operation: 4-1=3, Resulting Numbers: [55, 3] Generated Node #0,2,0: 51:[55, 3] Operation: 4-1=3 Exploring Operation: 55-4=51, Resulting Numbers: [1, 51] Generated Node #0,2,1: 51:[1, 51] Operation: 55-4=51 Exploring Operation: 55-1=54, Resulting Numbers: [4, 54] Generated Node #0,2,2: 51:[4, 54] Operation: 55-1=54 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 51:[1, 51], Operations: ['62-61=1', '55-4=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[55, 4, 62, 61], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [55, 4, 1] Generated Node #0,2: 51:[55, 4, 1] Operation: 62-61=1 Moving to Node #0,2 Current State: 51:[55, 4, 1], Operations: ['62-61=1'] Exploring Operation: 55-4=51, Resulting Numbers: [1, 51] Generated Node #0,2,1: 51:[1, 51] Operation: 55-4=51 Moving to Node #0,2,1 Current State: 51:[1, 51], Operations: ['62-61=1', '55-4=51'] Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 70, 9, 30, 43 ]
47
[ "43-30=13", "9*13=117", "117-70=47" ]
Current State: 47:[70, 9, 30, 43], Operations: [] Exploring Operation: 43-30=13, Resulting Numbers: [70, 9, 13] Generated Node #2: [70, 9, 13] from Operation: 43-30=13 Current State: 47:[70, 9, 13], Operations: ['43-30=13'] Exploring Operation: 9*13=117, Resulting Numbers: [70, 117] Generated Node #3: [70, 117] from Operation: 9*13=117 Current State: 47:[70, 117], Operations: ['43-30=13', '9*13=117'] Exploring Operation: 117-70=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[70, 9, 30, 43], Operations: [] Exploring Operation: 70-9=61, Resulting Numbers: [30, 43, 61] Generated Node #0,0: 47:[30, 43, 61] Operation: 70-9=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[30, 43, 61], Operations: ['70-9=61'] Exploring Operation: 61-30=31, Resulting Numbers: [43, 31] Generated Node #0,0,0: 47:[43, 31] Operation: 61-30=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[43, 31], Operations: ['70-9=61', '61-30=31'] Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,47 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 No solution found.
0
hs_1
mult_heuristic
[ 34, 7, 70, 57 ]
91
[ "57-34=23", "7*23=161", "161-70=91" ]
Current State: 91:[34, 7, 70, 57], Operations: [] Exploring Operation: 57-34=23, Resulting Numbers: [7, 70, 23] Generated Node #2: [7, 70, 23] from Operation: 57-34=23 Current State: 91:[7, 70, 23], Operations: ['57-34=23'] Exploring Operation: 7*23=161, Resulting Numbers: [70, 161] Generated Node #3: [70, 161] from Operation: 7*23=161 Current State: 91:[70, 161], Operations: ['57-34=23', '7*23=161'] Exploring Operation: 161-70=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[34, 7, 70, 57], Operations: [] Exploring Operation: 57-34=23, Resulting Numbers: [7, 70, 23] Generated Node #0,0: 91:[7, 70, 23] Operation: 57-34=23 Exploring Operation: 70-57=13, Resulting Numbers: [34, 7, 13] Generated Node #0,1: 91:[34, 7, 13] Operation: 70-57=13 Exploring Operation: 34+57=91, Resulting Numbers: [7, 70, 91] Generated Node #0,2: 91:[7, 70, 91] Operation: 34+57=91 Moving to Node #0,1 Current State: 91:[34, 7, 13], Operations: ['70-57=13'] Exploring Operation: 34-7=27, Resulting Numbers: [13, 27] Generated Node #0,1,0: 91:[13, 27] Operation: 34-7=27 Exploring Operation: 34-13=21, Resulting Numbers: [7, 21] Generated Node #0,1,1: 91:[7, 21] Operation: 34-13=21 Exploring Operation: 7*13=91, Resulting Numbers: [34, 91] Generated Node #0,1,2: 91:[34, 91] Operation: 7*13=91 Moving to Node #0,2 Current State: 91:[7, 70, 91], Operations: ['34+57=91'] Exploring Operation: 70/7=10, Resulting Numbers: [91, 10] Generated Node #0,2,0: 91:[91, 10] Operation: 70/7=10 Exploring Operation: 7+70=77, Resulting Numbers: [91, 77] Generated Node #0,2,1: 91:[91, 77] Operation: 7+70=77 Exploring Operation: 91-70=21, Resulting Numbers: [7, 21] Generated Node #0,2,2: 91:[7, 21] Operation: 91-70=21 Moving to Node #0,0 Current State: 91:[7, 70, 23], Operations: ['57-34=23'] Exploring Operation: 7+70=77, Resulting Numbers: [23, 77] Generated Node #0,0,0: 91:[23, 77] Operation: 7+70=77 Exploring Operation: 70+23=93, Resulting Numbers: [7, 93] Generated Node #0,0,1: 91:[7, 93] Operation: 70+23=93 Exploring Operation: 70/7=10, Resulting Numbers: [23, 10] Generated Node #0,0,2: 91:[23, 10] Operation: 70/7=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[7, 93], Operations: ['57-34=23', '70+23=93'] Exploring Operation: 7*93=651, Resulting Numbers: [651] 651,91 unequal: No Solution Exploring Operation: 93-7=86, Resulting Numbers: [86] 86,91 unequal: No Solution Exploring Operation: 7+93=100, Resulting Numbers: [100] 100,91 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 #0,0,2 Current State: 91:[23, 10], Operations: ['57-34=23', '70/7=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,91 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,91 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 #0,0,0 Current State: 91:[23, 77], Operations: ['57-34=23', '7+70=77'] Exploring Operation: 23+77=100, Resulting Numbers: [100] 100,91 unequal: No Solution Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 23*77=1771, Resulting Numbers: [1771] 1771,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 91:[91, 10], Operations: ['34+57=91', '70/7=10'] Exploring Operation: 91+10=101, Resulting Numbers: [101] 101,91 unequal: No Solution Exploring Operation: 91*10=910, Resulting Numbers: [910] 910,91 unequal: No Solution Exploring Operation: 91-10=81, Resulting Numbers: [81] 81,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[7, 21], Operations: ['70-57=13', '34-13=21'] Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,91 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[7, 21], Operations: ['34+57=91', '91-70=21'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,91 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[91, 77], Operations: ['34+57=91', '7+70=77'] Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,91 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[13, 27], Operations: ['70-57=13', '34-7=27'] Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,91 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[34, 91], Operations: ['70-57=13', '7*13=91'] Exploring Operation: 34*91=3094, Resulting Numbers: [3094] 3094,91 unequal: No Solution Exploring Operation: 91-34=57, Resulting Numbers: [57] 57,91 unequal: No Solution Exploring Operation: 34+91=125, Resulting Numbers: [125] 125,91 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 24, 53, 77, 34 ]
14
[ "53-24=29", "77-34=43", "43-29=14" ]
Current State: 14:[24, 53, 77, 34], Operations: [] Exploring Operation: 53-24=29, Resulting Numbers: [77, 34, 29] Generated Node #2: [77, 34, 29] from Operation: 53-24=29 Current State: 14:[77, 34, 29], Operations: ['53-24=29'] Exploring Operation: 77-34=43, Resulting Numbers: [29, 43] Generated Node #3: [29, 43] from Operation: 77-34=43 Current State: 14:[29, 43], Operations: ['53-24=29', '77-34=43'] Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[24, 53, 77, 34], Operations: [] Exploring Operation: 77-34=43, Resulting Numbers: [24, 53, 43] Generated Node #0,0: 14:[24, 53, 43] Operation: 77-34=43 Exploring Operation: 53-24=29, Resulting Numbers: [77, 34, 29] Generated Node #0,1: 14:[77, 34, 29] Operation: 53-24=29 Exploring Operation: 77-24=53, Resulting Numbers: [53, 34, 53] Generated Node #0,2: 14:[53, 34, 53] Operation: 77-24=53 Exploring Operation: 53-34=19, Resulting Numbers: [24, 77, 19] Generated Node #0,3: 14:[24, 77, 19] Operation: 53-34=19 Exploring Operation: 77-53=24, Resulting Numbers: [24, 34, 24] Generated Node #0,4: 14:[24, 34, 24] Operation: 77-53=24 Start Sub Search at level 1: Moving to Node #0,4 Current State: 14:[24, 34, 24], Operations: ['77-53=24'] Exploring Operation: 24-24=0, Resulting Numbers: [34, 0] Generated Node #0,4,0: 14:[34, 0] Operation: 24-24=0 Exploring Operation: 34-24=10, Resulting Numbers: [24, 10] Generated Node #0,4,1: 14:[24, 10] Operation: 34-24=10 Exploring Operation: 24/24=1, Resulting Numbers: [34, 1] Generated Node #0,4,2: 14:[34, 1] Operation: 24/24=1 Exploring Operation: 34-24=10, Resulting Numbers: [24, 10] Generated Node #0,4,3: 14:[24, 10] Operation: 34-24=10 Exploring Operation: 24+34=58, Resulting Numbers: [24, 58] Generated Node #0,4,4: 14:[24, 58] Operation: 24+34=58 Moving to Node #0,4,1 Current State: 14:[24, 10], Operations: ['77-53=24', '34-24=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[24, 53, 77, 34], Operations: [] Exploring Operation: 77-53=24, Resulting Numbers: [24, 34, 24] Generated Node #0,4: 14:[24, 34, 24] Operation: 77-53=24 Moving to Node #0,4 Current State: 14:[24, 34, 24], Operations: ['77-53=24'] Exploring Operation: 34-24=10, Resulting Numbers: [24, 10] Generated Node #0,4,1: 14:[24, 10] Operation: 34-24=10 Moving to Node #0,4,1 Current State: 14:[24, 10], Operations: ['77-53=24', '34-24=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 79, 99, 97, 82 ]
76
[ "99-97=2", "79*2=158", "158-82=76" ]
Current State: 76:[79, 99, 97, 82], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [79, 82, 2] Generated Node #2: [79, 82, 2] from Operation: 99-97=2 Current State: 76:[79, 82, 2], Operations: ['99-97=2'] Exploring Operation: 79*2=158, Resulting Numbers: [82, 158] Generated Node #3: [82, 158] from Operation: 79*2=158 Current State: 76:[82, 158], Operations: ['99-97=2', '79*2=158'] Exploring Operation: 158-82=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[79, 99, 97, 82], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [79, 82, 2] Generated Node #0,0: 76:[79, 82, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 76:[79, 82, 2], Operations: ['99-97=2'] Exploring Operation: 82-79=3, Resulting Numbers: [2, 3] Generated Node #0,0,0: 76:[2, 3] Operation: 82-79=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[2, 3], Operations: ['99-97=2', '82-79=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 76, 39, 3, 34 ]
61
[ "39-34=5", "3*5=15", "76-15=61" ]
Current State: 61:[76, 39, 3, 34], Operations: [] Exploring Operation: 39-34=5, Resulting Numbers: [76, 3, 5] Generated Node #2: [76, 3, 5] from Operation: 39-34=5 Current State: 61:[76, 3, 5], Operations: ['39-34=5'] Exploring Operation: 3*5=15, Resulting Numbers: [76, 15] Generated Node #3: [76, 15] from Operation: 3*5=15 Current State: 61:[76, 15], Operations: ['39-34=5', '3*5=15'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[76, 39, 3, 34], Operations: [] Exploring Operation: 76-3=73, Resulting Numbers: [39, 34, 73] Generated Node #0,0: 61:[39, 34, 73] Operation: 76-3=73 Exploring Operation: 39+3=42, Resulting Numbers: [76, 34, 42] Generated Node #0,1: 61:[76, 34, 42] Operation: 39+3=42 Exploring Operation: 3+34=37, Resulting Numbers: [76, 39, 37] Generated Node #0,2: 61:[76, 39, 37] Operation: 3+34=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[39, 34, 73], Operations: ['76-3=73'] Exploring Operation: 73-39=34, Resulting Numbers: [34, 34] Generated Node #0,0,0: 61:[34, 34] Operation: 73-39=34 Exploring Operation: 39+34=73, Resulting Numbers: [73, 73] Generated Node #0,0,1: 61:[73, 73] Operation: 39+34=73 Exploring Operation: 73-34=39, Resulting Numbers: [39, 39] Generated Node #0,0,2: 61:[39, 39] Operation: 73-34=39 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[73, 73], Operations: ['76-3=73', '39+34=73'] Exploring Operation: 73/73=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 73-73=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 73+73=146, Resulting Numbers: [146] 146,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[39, 39], Operations: ['76-3=73', '73-34=39'] Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,61 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[34, 34], Operations: ['76-3=73', '73-39=34'] Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,61 unequal: No Solution Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[76, 34, 42], Operations: ['39+3=42'] Exploring Operation: 34+42=76, Resulting Numbers: [76, 76] Generated Node #0,1,0: 61:[76, 76] Operation: 34+42=76 Exploring Operation: 76-42=34, Resulting Numbers: [34, 34] Generated Node #0,1,1: 61:[34, 34] Operation: 76-42=34 Exploring Operation: 76-34=42, Resulting Numbers: [42, 42] Generated Node #0,1,2: 61:[42, 42] Operation: 76-34=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[76, 76], Operations: ['39+3=42', '34+42=76'] Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[42, 42], Operations: ['39+3=42', '76-34=42'] Exploring Operation: 42-42=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 42/42=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[34, 34], Operations: ['39+3=42', '76-42=34'] Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[76, 39, 37], Operations: ['3+34=37'] Exploring Operation: 39+37=76, Resulting Numbers: [76, 76] Generated Node #0,2,0: 61:[76, 76] Operation: 39+37=76 Exploring Operation: 76-37=39, Resulting Numbers: [39, 39] Generated Node #0,2,1: 61:[39, 39] Operation: 76-37=39 Exploring Operation: 76-39=37, Resulting Numbers: [37, 37] Generated Node #0,2,2: 61:[37, 37] Operation: 76-39=37 Moving to Node #0,2,0 Current State: 61:[76, 76], Operations: ['3+34=37', '39+37=76'] Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[39, 39], Operations: ['3+34=37', '76-37=39'] Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[37, 37], Operations: ['3+34=37', '76-39=37'] Exploring Operation: 37+37=74, Resulting Numbers: [74] 74,61 unequal: No Solution Exploring Operation: 37-37=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 37/37=1, Resulting Numbers: [1] 1,61 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
[ 7, 9, 67, 87 ]
22
[ "9-7=2", "87-67=20", "2+20=22" ]
Current State: 22:[7, 9, 67, 87], Operations: [] Exploring Operation: 9-7=2, Resulting Numbers: [67, 87, 2] Generated Node #2: [67, 87, 2] from Operation: 9-7=2 Current State: 22:[67, 87, 2], Operations: ['9-7=2'] Exploring Operation: 87-67=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 87-67=20 Current State: 22:[2, 20], Operations: ['9-7=2', '87-67=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[7, 9, 67, 87], Operations: [] Exploring Operation: 87-7=80, Resulting Numbers: [9, 67, 80] Generated Node #0,0: 22:[9, 67, 80] Operation: 87-7=80 Exploring Operation: 87-67=20, Resulting Numbers: [7, 9, 20] Generated Node #0,1: 22:[7, 9, 20] Operation: 87-67=20 Exploring Operation: 67-7=60, Resulting Numbers: [9, 87, 60] Generated Node #0,2: 22:[9, 87, 60] Operation: 67-7=60 Exploring Operation: 67-9=58, Resulting Numbers: [7, 87, 58] Generated Node #0,3: 22:[7, 87, 58] Operation: 67-9=58 Exploring Operation: 87-9=78, Resulting Numbers: [7, 67, 78] Generated Node #0,4: 22:[7, 67, 78] Operation: 87-9=78 Moving to Node #0,1 Current State: 22:[7, 9, 20], Operations: ['87-67=20'] Exploring Operation: 9-7=2, Resulting Numbers: [20, 2] Generated Node #0,1,0: 22:[20, 2] Operation: 9-7=2 Exploring Operation: 20-9=11, Resulting Numbers: [7, 11] Generated Node #0,1,1: 22:[7, 11] Operation: 20-9=11 Exploring Operation: 7+9=16, Resulting Numbers: [20, 16] Generated Node #0,1,2: 22:[20, 16] Operation: 7+9=16 Exploring Operation: 7+20=27, Resulting Numbers: [9, 27] Generated Node #0,1,3: 22:[9, 27] Operation: 7+20=27 Exploring Operation: 20-7=13, Resulting Numbers: [9, 13] Generated Node #0,1,4: 22:[9, 13] Operation: 20-7=13 Moving to Node #0,2 Current State: 22:[9, 87, 60], Operations: ['67-7=60'] Exploring Operation: 87-9=78, Resulting Numbers: [60, 78] Generated Node #0,2,0: 22:[60, 78] Operation: 87-9=78 Exploring Operation: 87-60=27, Resulting Numbers: [9, 27] Generated Node #0,2,1: 22:[9, 27] Operation: 87-60=27 Exploring Operation: 9+87=96, Resulting Numbers: [60, 96] Generated Node #0,2,2: 22:[60, 96] Operation: 9+87=96 Exploring Operation: 9+60=69, Resulting Numbers: [87, 69] Generated Node #0,2,3: 22:[87, 69] Operation: 9+60=69 Exploring Operation: 60-9=51, Resulting Numbers: [87, 51] Generated Node #0,2,4: 22:[87, 51] Operation: 60-9=51 Moving to Node #0,4 Current State: 22:[7, 67, 78], Operations: ['87-9=78'] Exploring Operation: 7+67=74, Resulting Numbers: [78, 74] Generated Node #0,4,0: 22:[78, 74] Operation: 7+67=74 Exploring Operation: 67-7=60, Resulting Numbers: [78, 60] Generated Node #0,4,1: 22:[78, 60] Operation: 67-7=60 Exploring Operation: 7+78=85, Resulting Numbers: [67, 85] Generated Node #0,4,2: 22:[67, 85] Operation: 7+78=85 Exploring Operation: 78-7=71, Resulting Numbers: [67, 71] Generated Node #0,4,3: 22:[67, 71] Operation: 78-7=71 Exploring Operation: 78-67=11, Resulting Numbers: [7, 11] Generated Node #0,4,4: 22:[7, 11] Operation: 78-67=11 Moving to Node #0,0 Current State: 22:[9, 67, 80], Operations: ['87-7=80'] Exploring Operation: 80-67=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 22:[9, 13] Operation: 80-67=13 Exploring Operation: 80-9=71, Resulting Numbers: [67, 71] Generated Node #0,0,1: 22:[67, 71] Operation: 80-9=71 Exploring Operation: 67-9=58, Resulting Numbers: [80, 58] Generated Node #0,0,2: 22:[80, 58] Operation: 67-9=58 Exploring Operation: 9+80=89, Resulting Numbers: [67, 89] Generated Node #0,0,3: 22:[67, 89] Operation: 9+80=89 Exploring Operation: 9+67=76, Resulting Numbers: [80, 76] Generated Node #0,0,4: 22:[80, 76] Operation: 9+67=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[9, 13], Operations: ['87-7=80', '80-67=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,22 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[7, 9, 67, 87], Operations: [] Exploring Operation: 87-7=80, Resulting Numbers: [9, 67, 80] Generated Node #0,0: 22:[9, 67, 80] Operation: 87-7=80 Moving to Node #0,0 Current State: 22:[9, 67, 80], Operations: ['87-7=80'] Exploring Operation: 80-67=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 22:[9, 13] Operation: 80-67=13 Moving to Node #0,0,0 Current State: 22:[9, 13], Operations: ['87-7=80', '80-67=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_5
mult_heuristic
[ 21, 5, 27, 3 ]
72
[ "21*3=63", "5*27=135", "135-63=72" ]
Current State: 72:[21, 5, 27, 3], Operations: [] Exploring Operation: 21*3=63, Resulting Numbers: [5, 27, 63] Generated Node #2: [5, 27, 63] from Operation: 21*3=63 Current State: 72:[5, 27, 63], Operations: ['21*3=63'] Exploring Operation: 5*27=135, Resulting Numbers: [63, 135] Generated Node #3: [63, 135] from Operation: 5*27=135 Current State: 72:[63, 135], Operations: ['21*3=63', '5*27=135'] Exploring Operation: 135-63=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[21, 5, 27, 3], Operations: [] Exploring Operation: 21-3=18, Resulting Numbers: [5, 27, 18] Generated Node #0,0: 72:[5, 27, 18] Operation: 21-3=18 Exploring Operation: 27-21=6, Resulting Numbers: [5, 3, 6] Generated Node #0,1: 72:[5, 3, 6] Operation: 27-21=6 Exploring Operation: 21+3=24, Resulting Numbers: [5, 27, 24] Generated Node #0,2: 72:[5, 27, 24] Operation: 21+3=24 Moving to Node #0,1 Current State: 72:[5, 3, 6], Operations: ['27-21=6'] Exploring Operation: 5-3=2, Resulting Numbers: [6, 2] Generated Node #0,1,0: 72:[6, 2] Operation: 5-3=2 Exploring Operation: 5+3=8, Resulting Numbers: [6, 8] Generated Node #0,1,1: 72:[6, 8] Operation: 5+3=8 Exploring Operation: 5+6=11, Resulting Numbers: [3, 11] Generated Node #0,1,2: 72:[3, 11] Operation: 5+6=11 Moving to Node #0,0 Current State: 72:[5, 27, 18], Operations: ['21-3=18'] Exploring Operation: 5+27=32, Resulting Numbers: [18, 32] Generated Node #0,0,0: 72:[18, 32] Operation: 5+27=32 Exploring Operation: 27-18=9, Resulting Numbers: [5, 9] Generated Node #0,0,1: 72:[5, 9] Operation: 27-18=9 Exploring Operation: 27-5=22, Resulting Numbers: [18, 22] Generated Node #0,0,2: 72:[18, 22] Operation: 27-5=22 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[5, 9], Operations: ['21-3=18', '27-18=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,72 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,72 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 #0,0,2 Current State: 72:[18, 22], Operations: ['21-3=18', '27-5=22'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,72 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,72 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 #0,0,0 Current State: 72:[18, 32], Operations: ['21-3=18', '5+27=32'] Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,72 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 72:[5, 27, 24], Operations: ['21+3=24'] Exploring Operation: 27-24=3, Resulting Numbers: [5, 3] Generated Node #0,2,0: 72:[5, 3] Operation: 27-24=3 Exploring Operation: 27-5=22, Resulting Numbers: [24, 22] Generated Node #0,2,1: 72:[24, 22] Operation: 27-5=22 Exploring Operation: 5+27=32, Resulting Numbers: [24, 32] Generated Node #0,2,2: 72:[24, 32] Operation: 5+27=32 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[5, 3], Operations: ['21+3=24', '27-24=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[24, 22], Operations: ['21+3=24', '27-5=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,72 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[24, 32], Operations: ['21+3=24', '5+27=32'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 72:[6, 2], Operations: ['27-21=6', '5-3=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[6, 8], Operations: ['27-21=6', '5+3=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[3, 11], Operations: ['27-21=6', '5+6=11'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,72 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 34, 65, 38, 4 ]
64
[ "38-34=4", "4/4=1", "65-1=64" ]
Current State: 64:[34, 65, 38, 4], Operations: [] Exploring Operation: 38-34=4, Resulting Numbers: [65, 4, 4] Generated Node #2: [65, 4, 4] from Operation: 38-34=4 Current State: 64:[65, 4, 4], Operations: ['38-34=4'] Exploring Operation: 4/4=1, Resulting Numbers: [65, 1] Generated Node #3: [65, 1] from Operation: 4/4=1 Current State: 64:[65, 1], Operations: ['38-34=4', '4/4=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[34, 65, 38, 4], Operations: [] Exploring Operation: 65-34=31, Resulting Numbers: [38, 4, 31] Generated Node #0,0: 64:[38, 4, 31] Operation: 65-34=31 Exploring Operation: 38-34=4, Resulting Numbers: [65, 4, 4] Generated Node #0,1: 64:[65, 4, 4] Operation: 38-34=4 Exploring Operation: 38-4=34, Resulting Numbers: [34, 65, 34] Generated Node #0,2: 64:[34, 65, 34] Operation: 38-4=34 Moving to Node #0,1 Current State: 64:[65, 4, 4], Operations: ['38-34=4'] Exploring Operation: 4*4=16, Resulting Numbers: [65, 16] Generated Node #0,1,0: 64:[65, 16] Operation: 4*4=16 Exploring Operation: 4+4=8, Resulting Numbers: [65, 8] Generated Node #0,1,1: 64:[65, 8] Operation: 4+4=8 Exploring Operation: 4/4=1, Resulting Numbers: [65, 1] Generated Node #0,1,2: 64:[65, 1] Operation: 4/4=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 64:[65, 16], Operations: ['38-34=4', '4*4=16'] Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,64 unequal: No Solution Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,64 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,64 unequal: No Solution No 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: 64:[65, 8], Operations: ['38-34=4', '4+4=8'] Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,64 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,64 unequal: No Solution No 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: 64:[65, 1], Operations: ['38-34=4', '4/4=1'] Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,64 unequal: No Solution Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[34, 65, 38, 4], Operations: [] Exploring Operation: 38-34=4, Resulting Numbers: [65, 4, 4] Generated Node #0,1: 64:[65, 4, 4] Operation: 38-34=4 Moving to Node #0,1 Current State: 64:[65, 4, 4], Operations: ['38-34=4'] Exploring Operation: 4/4=1, Resulting Numbers: [65, 1] Generated Node #0,1,2: 64:[65, 1] Operation: 4/4=1 Moving to Node #0,1,2 Current State: 64:[65, 1], Operations: ['38-34=4', '4/4=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 90, 31, 73, 2 ]
96
[ "90+31=121", "121-73=48", "2*48=96" ]
Current State: 96:[90, 31, 73, 2], Operations: [] Exploring Operation: 90+31=121, Resulting Numbers: [73, 2, 121] Generated Node #2: [73, 2, 121] from Operation: 90+31=121 Current State: 96:[73, 2, 121], Operations: ['90+31=121'] Exploring Operation: 121-73=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 121-73=48 Current State: 96:[2, 48], Operations: ['90+31=121', '121-73=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[90, 31, 73, 2], Operations: [] Exploring Operation: 73-31=42, Resulting Numbers: [90, 2, 42] Generated Node #0,0: 96:[90, 2, 42] Operation: 73-31=42 Exploring Operation: 90/2=45, Resulting Numbers: [31, 73, 45] Generated Node #0,1: 96:[31, 73, 45] Operation: 90/2=45 Exploring Operation: 31+73=104, Resulting Numbers: [90, 2, 104] Generated Node #0,2: 96:[90, 2, 104] Operation: 31+73=104 Exploring Operation: 90-73=17, Resulting Numbers: [31, 2, 17] Generated Node #0,3: 96:[31, 2, 17] Operation: 90-73=17 Exploring Operation: 90+2=92, Resulting Numbers: [31, 73, 92] Generated Node #0,4: 96:[31, 73, 92] Operation: 90+2=92 Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[31, 2, 17], Operations: ['90-73=17'] Exploring Operation: 17-2=15, Resulting Numbers: [31, 15] Generated Node #0,3,0: 96:[31, 15] Operation: 17-2=15 Exploring Operation: 2*17=34, Resulting Numbers: [31, 34] Generated Node #0,3,1: 96:[31, 34] Operation: 2*17=34 Exploring Operation: 31+2=33, Resulting Numbers: [17, 33] Generated Node #0,3,2: 96:[17, 33] Operation: 31+2=33 Exploring Operation: 31+17=48, Resulting Numbers: [2, 48] Generated Node #0,3,3: 96:[2, 48] Operation: 31+17=48 Exploring Operation: 31-17=14, Resulting Numbers: [2, 14] Generated Node #0,3,4: 96:[2, 14] Operation: 31-17=14 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 96:[2, 48], Operations: ['90-73=17', '31+17=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[90, 31, 73, 2], Operations: [] Exploring Operation: 90-73=17, Resulting Numbers: [31, 2, 17] Generated Node #0,3: 96:[31, 2, 17] Operation: 90-73=17 Moving to Node #0,3 Current State: 96:[31, 2, 17], Operations: ['90-73=17'] Exploring Operation: 31+17=48, Resulting Numbers: [2, 48] Generated Node #0,3,3: 96:[2, 48] Operation: 31+17=48 Moving to Node #0,3,3 Current State: 96:[2, 48], Operations: ['90-73=17', '31+17=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic