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
[ 34, 58, 47, 44 ]
72
[ "58-34=24", "47-44=3", "24*3=72" ]
Current State: 72:[34, 58, 47, 44], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [47, 44, 24] Generated Node #2: [47, 44, 24] from Operation: 58-34=24 Current State: 72:[47, 44, 24], Operations: ['58-34=24'] Exploring Operation: 47-44=3, Resulting Numbers: [24, 3] Generated Node #3: [24, 3] from Operation: 47-44=3 Current State: 72:[24, 3], Operations: ['58-34=24', '47-44=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[34, 58, 47, 44], Operations: [] Exploring Operation: 58-44=14, Resulting Numbers: [34, 47, 14] Generated Node #0,0: 72:[34, 47, 14] Operation: 58-44=14 Exploring Operation: 47-44=3, Resulting Numbers: [34, 58, 3] Generated Node #0,1: 72:[34, 58, 3] Operation: 47-44=3 Exploring Operation: 58-47=11, Resulting Numbers: [34, 44, 11] Generated Node #0,2: 72:[34, 44, 11] Operation: 58-47=11 Moving to Node #0,2 Current State: 72:[34, 44, 11], Operations: ['58-47=11'] Exploring Operation: 44/11=4, Resulting Numbers: [34, 4] Generated Node #0,2,0: 72:[34, 4] Operation: 44/11=4 Exploring Operation: 44-34=10, Resulting Numbers: [11, 10] Generated Node #0,2,1: 72:[11, 10] Operation: 44-34=10 Exploring Operation: 44-11=33, Resulting Numbers: [34, 33] Generated Node #0,2,2: 72:[34, 33] Operation: 44-11=33 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[34, 4], Operations: ['58-47=11', '44/11=4'] Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 34*4=136, Resulting Numbers: [136] 136,72 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,72 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:[11, 10], Operations: ['58-47=11', '44-34=10'] Exploring Operation: 11*10=110, Resulting Numbers: [110] 110,72 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,72 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:[34, 33], Operations: ['58-47=11', '44-11=33'] Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,72 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,72 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: 72:[34, 47, 14], Operations: ['58-44=14'] Exploring Operation: 34+47=81, Resulting Numbers: [14, 81] Generated Node #0,0,0: 72:[14, 81] Operation: 34+47=81 Exploring Operation: 47-34=13, Resulting Numbers: [14, 13] Generated Node #0,0,1: 72:[14, 13] Operation: 47-34=13 Exploring Operation: 47-14=33, Resulting Numbers: [34, 33] Generated Node #0,0,2: 72:[34, 33] Operation: 47-14=33 Moving to Node #0,1 Current State: 72:[34, 58, 3], Operations: ['47-44=3'] Exploring Operation: 58-34=24, Resulting Numbers: [3, 24] Generated Node #0,1,0: 72:[3, 24] Operation: 58-34=24 Exploring Operation: 58+3=61, Resulting Numbers: [34, 61] Generated Node #0,1,1: 72:[34, 61] Operation: 58+3=61 Exploring Operation: 34+3=37, Resulting Numbers: [58, 37] Generated Node #0,1,2: 72:[58, 37] Operation: 34+3=37 Moving to Node #0,1,0 Current State: 72:[3, 24], Operations: ['47-44=3', '58-34=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[34, 58, 47, 44], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [34, 58, 3] Generated Node #0,1: 72:[34, 58, 3] Operation: 47-44=3 Moving to Node #0,1 Current State: 72:[34, 58, 3], Operations: ['47-44=3'] Exploring Operation: 58-34=24, Resulting Numbers: [3, 24] Generated Node #0,1,0: 72:[3, 24] Operation: 58-34=24 Moving to Node #0,1,0 Current State: 72:[3, 24], Operations: ['47-44=3', '58-34=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 5, 90, 25, 92 ]
10
[ "25-5=20", "92-90=2", "20/2=10" ]
Current State: 10:[5, 90, 25, 92], Operations: [] Exploring Operation: 25-5=20, Resulting Numbers: [90, 92, 20] Generated Node #2: [90, 92, 20] from Operation: 25-5=20 Current State: 10:[90, 92, 20], Operations: ['25-5=20'] Exploring Operation: 92-90=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 92-90=2 Current State: 10:[20, 2], Operations: ['25-5=20', '92-90=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[5, 90, 25, 92], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [5, 92, 65] Generated Node #0,0: 10:[5, 92, 65] Operation: 90-25=65 Exploring Operation: 90/5=18, Resulting Numbers: [25, 92, 18] Generated Node #0,1: 10:[25, 92, 18] Operation: 90/5=18 Exploring Operation: 92-90=2, Resulting Numbers: [5, 25, 2] Generated Node #0,2: 10:[5, 25, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[5, 25, 2], Operations: ['92-90=2'] Exploring Operation: 25/5=5, Resulting Numbers: [2, 5] Generated Node #0,2,0: 10:[2, 5] Operation: 25/5=5 Exploring Operation: 25-2=23, Resulting Numbers: [5, 23] Generated Node #0,2,1: 10:[5, 23] Operation: 25-2=23 Exploring Operation: 25-5=20, Resulting Numbers: [2, 20] Generated Node #0,2,2: 10:[2, 20] Operation: 25-5=20 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 10:[2, 5], Operations: ['92-90=2', '25/5=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[5, 90, 25, 92], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [5, 25, 2] Generated Node #0,2: 10:[5, 25, 2] Operation: 92-90=2 Moving to Node #0,2 Current State: 10:[5, 25, 2], Operations: ['92-90=2'] Exploring Operation: 25/5=5, Resulting Numbers: [2, 5] Generated Node #0,2,0: 10:[2, 5] Operation: 25/5=5 Moving to Node #0,2,0 Current State: 10:[2, 5], Operations: ['92-90=2', '25/5=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 97, 88, 47, 16 ]
79
[ "97+47=144", "144/16=9", "88-9=79" ]
Current State: 79:[97, 88, 47, 16], Operations: [] Exploring Operation: 97+47=144, Resulting Numbers: [88, 16, 144] Generated Node #2: [88, 16, 144] from Operation: 97+47=144 Current State: 79:[88, 16, 144], Operations: ['97+47=144'] Exploring Operation: 144/16=9, Resulting Numbers: [88, 9] Generated Node #3: [88, 9] from Operation: 144/16=9 Current State: 79:[88, 9], Operations: ['97+47=144', '144/16=9'] Exploring Operation: 88-9=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[97, 88, 47, 16], Operations: [] Exploring Operation: 97-16=81, Resulting Numbers: [88, 47, 81] Generated Node #0,0: 79:[88, 47, 81] Operation: 97-16=81 Moving to Node #0,0 Current State: 79:[88, 47, 81], Operations: ['97-16=81'] Exploring Operation: 88-47=41, Resulting Numbers: [81, 41] Generated Node #0,0,0: 79:[81, 41] Operation: 88-47=41 Moving to Node #0,0,0 Current State: 79:[81, 41], Operations: ['97-16=81', '88-47=41'] Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 10, 7, 82, 45 ]
87
[ "45-10=35", "35/7=5", "82+5=87" ]
Current State: 87:[10, 7, 82, 45], Operations: [] Exploring Operation: 45-10=35, Resulting Numbers: [7, 82, 35] Generated Node #2: [7, 82, 35] from Operation: 45-10=35 Current State: 87:[7, 82, 35], Operations: ['45-10=35'] Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 35/7=5 Current State: 87:[82, 5], Operations: ['45-10=35', '35/7=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[10, 7, 82, 45], Operations: [] Exploring Operation: 45-10=35, Resulting Numbers: [7, 82, 35] Generated Node #0,0: 87:[7, 82, 35] Operation: 45-10=35 Exploring Operation: 82-45=37, Resulting Numbers: [10, 7, 37] Generated Node #0,1: 87:[10, 7, 37] Operation: 82-45=37 Exploring Operation: 45-7=38, Resulting Numbers: [10, 82, 38] Generated Node #0,2: 87:[10, 82, 38] Operation: 45-7=38 Exploring Operation: 10-7=3, Resulting Numbers: [82, 45, 3] Generated Node #0,3: 87:[82, 45, 3] Operation: 10-7=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[7, 82, 35], Operations: ['45-10=35'] Exploring Operation: 82-7=75, Resulting Numbers: [35, 75] Generated Node #0,0,0: 87:[35, 75] Operation: 82-7=75 Exploring Operation: 7+82=89, Resulting Numbers: [35, 89] Generated Node #0,0,1: 87:[35, 89] Operation: 7+82=89 Exploring Operation: 35-7=28, Resulting Numbers: [82, 28] Generated Node #0,0,2: 87:[82, 28] Operation: 35-7=28 Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #0,0,3: 87:[82, 5] Operation: 35/7=5 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[82, 28], Operations: ['45-10=35', '35-7=28'] Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,87 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,87 unequal: No Solution No 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: 87:[82, 5], Operations: ['45-10=35', '35/7=5'] Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,87 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[10, 7, 82, 45], Operations: [] Exploring Operation: 45-10=35, Resulting Numbers: [7, 82, 35] Generated Node #0,0: 87:[7, 82, 35] Operation: 45-10=35 Moving to Node #0,0 Current State: 87:[7, 82, 35], Operations: ['45-10=35'] Exploring Operation: 35/7=5, Resulting Numbers: [82, 5] Generated Node #0,0,3: 87:[82, 5] Operation: 35/7=5 Moving to Node #0,0,3 Current State: 87:[82, 5], Operations: ['45-10=35', '35/7=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 14, 89, 15, 36 ]
31
[ "89-14=75", "75/15=5", "36-5=31" ]
Current State: 31:[14, 89, 15, 36], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [15, 36, 75] Generated Node #2: [15, 36, 75] from Operation: 89-14=75 Current State: 31:[15, 36, 75], Operations: ['89-14=75'] Exploring Operation: 75/15=5, Resulting Numbers: [36, 5] Generated Node #3: [36, 5] from Operation: 75/15=5 Current State: 31:[36, 5], Operations: ['89-14=75', '75/15=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[14, 89, 15, 36], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [15, 36, 75] Generated Node #0,0: 31:[15, 36, 75] Operation: 89-14=75 Exploring Operation: 89-36=53, Resulting Numbers: [14, 15, 53] Generated Node #0,1: 31:[14, 15, 53] Operation: 89-36=53 Moving to Node #0,1 Current State: 31:[14, 15, 53], Operations: ['89-36=53'] Exploring Operation: 53-14=39, Resulting Numbers: [15, 39] Generated Node #0,1,0: 31:[15, 39] Operation: 53-14=39 Exploring Operation: 14+15=29, Resulting Numbers: [53, 29] Generated Node #0,1,1: 31:[53, 29] Operation: 14+15=29 Moving to Node #0,0 Current State: 31:[15, 36, 75], Operations: ['89-14=75'] Exploring Operation: 75-36=39, Resulting Numbers: [15, 39] Generated Node #0,0,0: 31:[15, 39] Operation: 75-36=39 Exploring Operation: 75/15=5, Resulting Numbers: [36, 5] Generated Node #0,0,1: 31:[36, 5] Operation: 75/15=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[15, 39], Operations: ['89-14=75', '75-36=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[36, 5], Operations: ['89-14=75', '75/15=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[14, 89, 15, 36], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [15, 36, 75] Generated Node #0,0: 31:[15, 36, 75] Operation: 89-14=75 Moving to Node #0,0 Current State: 31:[15, 36, 75], Operations: ['89-14=75'] Exploring Operation: 75/15=5, Resulting Numbers: [36, 5] Generated Node #0,0,1: 31:[36, 5] Operation: 75/15=5 Moving to Node #0,0,1 Current State: 31:[36, 5], Operations: ['89-14=75', '75/15=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
mult_heuristic
[ 79, 8, 4, 35 ]
69
[ "79-8=71", "4*35=140", "140-71=69" ]
Current State: 69:[79, 8, 4, 35], Operations: [] Exploring Operation: 79-8=71, Resulting Numbers: [4, 35, 71] Generated Node #2: [4, 35, 71] from Operation: 79-8=71 Current State: 69:[4, 35, 71], Operations: ['79-8=71'] Exploring Operation: 4*35=140, Resulting Numbers: [71, 140] Generated Node #3: [71, 140] from Operation: 4*35=140 Current State: 69:[71, 140], Operations: ['79-8=71', '4*35=140'] Exploring Operation: 140-71=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[79, 8, 4, 35], Operations: [] Exploring Operation: 35-8=27, Resulting Numbers: [79, 4, 27] Generated Node #0,0: 69:[79, 4, 27] Operation: 35-8=27 Exploring Operation: 79-4=75, Resulting Numbers: [8, 35, 75] Generated Node #0,1: 69:[8, 35, 75] Operation: 79-4=75 Exploring Operation: 79-8=71, Resulting Numbers: [4, 35, 71] Generated Node #0,2: 69:[4, 35, 71] Operation: 79-8=71 Exploring Operation: 8/4=2, Resulting Numbers: [79, 35, 2] Generated Node #0,3: 69:[79, 35, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [79, 35, 4] Generated Node #0,4: 69:[79, 35, 4] Operation: 8-4=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[79, 4, 27], Operations: ['35-8=27'] Exploring Operation: 79-27=52, Resulting Numbers: [4, 52] Generated Node #0,0,0: 69:[4, 52] Operation: 79-27=52 Exploring Operation: 27-4=23, Resulting Numbers: [79, 23] Generated Node #0,0,1: 69:[79, 23] Operation: 27-4=23 Exploring Operation: 4+27=31, Resulting Numbers: [79, 31] Generated Node #0,0,2: 69:[79, 31] Operation: 4+27=31 Exploring Operation: 79-4=75, Resulting Numbers: [27, 75] Generated Node #0,0,3: 69:[27, 75] Operation: 79-4=75 Exploring Operation: 79+4=83, Resulting Numbers: [27, 83] Generated Node #0,0,4: 69:[27, 83] Operation: 79+4=83 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[79, 23], Operations: ['35-8=27', '27-4=23'] Exploring Operation: 79*23=1817, Resulting Numbers: [1817] 1817,69 unequal: No Solution Exploring Operation: 79+23=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,69 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 #0,0,3 Current State: 69:[27, 75], Operations: ['35-8=27', '79-4=75'] Exploring Operation: 27+75=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 27*75=2025, Resulting Numbers: [2025] 2025,69 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:[4, 52], Operations: ['35-8=27', '79-27=52'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,69 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 #0,0,2 Current State: 69:[79, 31], Operations: ['35-8=27', '4+27=31'] Exploring Operation: 79*31=2449, Resulting Numbers: [2449] 2449,69 unequal: No Solution Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 79+31=110, Resulting Numbers: [110] 110,69 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 #0,0,4 Current State: 69:[27, 83], Operations: ['35-8=27', '79+4=83'] Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 27*83=2241, Resulting Numbers: [2241] 2241,69 unequal: No Solution Exploring Operation: 27+83=110, Resulting Numbers: [110] 110,69 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 #0,2 Current State: 69:[4, 35, 71], Operations: ['79-8=71'] Exploring Operation: 4+35=39, Resulting Numbers: [71, 39] Generated Node #0,2,0: 69:[71, 39] Operation: 4+35=39 Exploring Operation: 4+71=75, Resulting Numbers: [35, 75] Generated Node #0,2,1: 69:[35, 75] Operation: 4+71=75 Exploring Operation: 71-35=36, Resulting Numbers: [4, 36] Generated Node #0,2,2: 69:[4, 36] Operation: 71-35=36 Exploring Operation: 35-4=31, Resulting Numbers: [71, 31] Generated Node #0,2,3: 69:[71, 31] Operation: 35-4=31 Exploring Operation: 71-4=67, Resulting Numbers: [35, 67] Generated Node #0,2,4: 69:[35, 67] Operation: 71-4=67 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 69:[71, 31], Operations: ['79-8=71', '35-4=31'] Exploring Operation: 71*31=2201, Resulting Numbers: [2201] 2201,69 unequal: No Solution Exploring Operation: 71-31=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 71+31=102, Resulting Numbers: [102] 102,69 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:[4, 36], Operations: ['79-8=71', '71-35=36'] Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,69 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,69 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 #0,2,4 Current State: 69:[35, 67], Operations: ['79-8=71', '71-4=67'] Exploring Operation: 35+67=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 35*67=2345, Resulting Numbers: [2345] 2345,69 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 #0,2,0 Current State: 69:[71, 39], Operations: ['79-8=71', '4+35=39'] Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 71*39=2769, Resulting Numbers: [2769] 2769,69 unequal: No Solution Exploring Operation: 71+39=110, Resulting Numbers: [110] 110,69 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:[35, 75], Operations: ['79-8=71', '4+71=75'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,69 unequal: No Solution Exploring Operation: 35*75=2625, Resulting Numbers: [2625] 2625,69 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:[8, 35, 75], Operations: ['79-4=75'] Exploring Operation: 35-8=27, Resulting Numbers: [75, 27] Generated Node #0,1,0: 69:[75, 27] Operation: 35-8=27 Exploring Operation: 75-8=67, Resulting Numbers: [35, 67] Generated Node #0,1,1: 69:[35, 67] Operation: 75-8=67 Exploring Operation: 8+75=83, Resulting Numbers: [35, 83] Generated Node #0,1,2: 69:[35, 83] Operation: 8+75=83 Exploring Operation: 8+35=43, Resulting Numbers: [75, 43] Generated Node #0,1,3: 69:[75, 43] Operation: 8+35=43 Exploring Operation: 75-35=40, Resulting Numbers: [8, 40] Generated Node #0,1,4: 69:[8, 40] Operation: 75-35=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[75, 27], Operations: ['79-4=75', '35-8=27'] Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,69 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,69 unequal: No Solution Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,69 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:[35, 67], Operations: ['79-4=75', '75-8=67'] Exploring Operation: 35*67=2345, Resulting Numbers: [2345] 2345,69 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 35+67=102, Resulting Numbers: [102] 102,69 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 #0,1,4 Current State: 69:[8, 40], Operations: ['79-4=75', '75-35=40'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,69 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,69 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 #0,1,2 Current State: 69:[35, 83], Operations: ['79-4=75', '8+75=83'] Exploring Operation: 35+83=118, Resulting Numbers: [118] 118,69 unequal: No Solution Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 35*83=2905, Resulting Numbers: [2905] 2905,69 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 #0,1,3 Current State: 69:[75, 43], Operations: ['79-4=75', '8+35=43'] Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,69 unequal: No Solution Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,69 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 #0,3 Current State: 69:[79, 35, 2], Operations: ['8/4=2'] Exploring Operation: 79-2=77, Resulting Numbers: [35, 77] Generated Node #0,3,0: 69:[35, 77] Operation: 79-2=77 Exploring Operation: 79-35=44, Resulting Numbers: [2, 44] Generated Node #0,3,1: 69:[2, 44] Operation: 79-35=44 Exploring Operation: 35-2=33, Resulting Numbers: [79, 33] Generated Node #0,3,2: 69:[79, 33] Operation: 35-2=33 Exploring Operation: 35*2=70, Resulting Numbers: [79, 70] Generated Node #0,3,3: 69:[79, 70] Operation: 35*2=70 Exploring Operation: 79+2=81, Resulting Numbers: [35, 81] Generated Node #0,3,4: 69:[35, 81] Operation: 79+2=81 Moving to Node #0,3,3 Current State: 69:[79, 70], Operations: ['8/4=2', '35*2=70'] Exploring Operation: 79+70=149, Resulting Numbers: [149] 149,69 unequal: No Solution Exploring Operation: 79*70=5530, Resulting Numbers: [5530] 5530,69 unequal: No Solution Exploring Operation: 79-70=9, Resulting Numbers: [9] 9,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[79, 33], Operations: ['8/4=2', '35-2=33'] Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,69 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[35, 77], Operations: ['8/4=2', '79-2=77'] Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 35*77=2695, Resulting Numbers: [2695] 2695,69 unequal: No Solution Exploring Operation: 35+77=112, Resulting Numbers: [112] 112,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[2, 44], Operations: ['8/4=2', '79-35=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,69 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[35, 81], Operations: ['8/4=2', '79+2=81'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,69 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 #0,4 Current State: 69:[79, 35, 4], Operations: ['8-4=4'] Exploring Operation: 79-4=75, Resulting Numbers: [35, 75] Generated Node #0,4,0: 69:[35, 75] Operation: 79-4=75 Exploring Operation: 35-4=31, Resulting Numbers: [79, 31] Generated Node #0,4,1: 69:[79, 31] Operation: 35-4=31 Exploring Operation: 79+4=83, Resulting Numbers: [35, 83] Generated Node #0,4,2: 69:[35, 83] Operation: 79+4=83 Exploring Operation: 79-35=44, Resulting Numbers: [4, 44] Generated Node #0,4,3: 69:[4, 44] Operation: 79-35=44 Exploring Operation: 35+4=39, Resulting Numbers: [79, 39] Generated Node #0,4,4: 69:[79, 39] Operation: 35+4=39 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 69:[35, 75], Operations: ['8-4=4', '79-4=75'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 35*75=2625, Resulting Numbers: [2625] 2625,69 unequal: No Solution Exploring Operation: 35+75=110, Resulting Numbers: [110] 110,69 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 #0,4,1 Current State: 69:[79, 31], Operations: ['8-4=4', '35-4=31'] Exploring Operation: 79-31=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 79+31=110, Resulting Numbers: [110] 110,69 unequal: No Solution Exploring Operation: 79*31=2449, Resulting Numbers: [2449] 2449,69 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 #0,4,3 Current State: 69:[4, 44], Operations: ['8-4=4', '79-35=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,69 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 #0,4,2 Current State: 69:[35, 83], Operations: ['8-4=4', '79+4=83'] Exploring Operation: 83-35=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 35+83=118, Resulting Numbers: [118] 118,69 unequal: No Solution Exploring Operation: 35*83=2905, Resulting Numbers: [2905] 2905,69 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 #0,4,4 Current State: 69:[79, 39], Operations: ['8-4=4', '35+4=39'] Exploring Operation: 79*39=3081, Resulting Numbers: [3081] 3081,69 unequal: No Solution Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 79+39=118, Resulting Numbers: [118] 118,69 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_5
sum_heuristic
[ 71, 41, 32, 40 ]
38
[ "71-41=30", "40-32=8", "30+8=38" ]
Current State: 38:[71, 41, 32, 40], Operations: [] Exploring Operation: 71-41=30, Resulting Numbers: [32, 40, 30] Generated Node #2: [32, 40, 30] from Operation: 71-41=30 Current State: 38:[32, 40, 30], Operations: ['71-41=30'] Exploring Operation: 40-32=8, Resulting Numbers: [30, 8] Generated Node #3: [30, 8] from Operation: 40-32=8 Current State: 38:[30, 8], Operations: ['71-41=30', '40-32=8'] Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[71, 41, 32, 40], Operations: [] Exploring Operation: 71-32=39, Resulting Numbers: [41, 40, 39] Generated Node #0,0: 38:[41, 40, 39] Operation: 71-32=39 Moving to Node #0,0 Current State: 38:[41, 40, 39], Operations: ['71-32=39'] Exploring Operation: 41-40=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 38:[39, 1] Operation: 41-40=1 Moving to Node #0,0,0 Current State: 38:[39, 1], Operations: ['71-32=39', '41-40=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[71, 41, 32, 40], Operations: [] Exploring Operation: 71-32=39, Resulting Numbers: [41, 40, 39] Generated Node #0,0: 38:[41, 40, 39] Operation: 71-32=39 Moving to Node #0,0 Current State: 38:[41, 40, 39], Operations: ['71-32=39'] Exploring Operation: 41-40=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 38:[39, 1] Operation: 41-40=1 Moving to Node #0,0,0 Current State: 38:[39, 1], Operations: ['71-32=39', '41-40=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 37, 35, 44, 53 ]
75
[ "37-35=2", "44/2=22", "53+22=75" ]
Current State: 75:[37, 35, 44, 53], Operations: [] Exploring Operation: 37-35=2, Resulting Numbers: [44, 53, 2] Generated Node #2: [44, 53, 2] from Operation: 37-35=2 Current State: 75:[44, 53, 2], Operations: ['37-35=2'] Exploring Operation: 44/2=22, Resulting Numbers: [53, 22] Generated Node #3: [53, 22] from Operation: 44/2=22 Current State: 75:[53, 22], Operations: ['37-35=2', '44/2=22'] Exploring Operation: 53+22=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 35, 44, 53], Operations: [] Exploring Operation: 53-37=16, Resulting Numbers: [35, 44, 16] Generated Node #0,0: 75:[35, 44, 16] Operation: 53-37=16 Exploring Operation: 44-37=7, Resulting Numbers: [35, 53, 7] Generated Node #0,1: 75:[35, 53, 7] Operation: 44-37=7 Exploring Operation: 53-44=9, Resulting Numbers: [37, 35, 9] Generated Node #0,2: 75:[37, 35, 9] Operation: 53-44=9 Exploring Operation: 53-35=18, Resulting Numbers: [37, 44, 18] Generated Node #0,3: 75:[37, 44, 18] Operation: 53-35=18 Moving to Node #0,2 Current State: 75:[37, 35, 9], Operations: ['53-44=9'] Exploring Operation: 35-9=26, Resulting Numbers: [37, 26] Generated Node #0,2,0: 75:[37, 26] Operation: 35-9=26 Exploring Operation: 37-9=28, Resulting Numbers: [35, 28] Generated Node #0,2,1: 75:[35, 28] Operation: 37-9=28 Exploring Operation: 37-35=2, Resulting Numbers: [9, 2] Generated Node #0,2,2: 75:[9, 2] Operation: 37-35=2 Exploring Operation: 37+35=72, Resulting Numbers: [9, 72] Generated Node #0,2,3: 75:[9, 72] Operation: 37+35=72 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[9, 2], Operations: ['53-44=9', '37-35=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,75 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 #0,2,3 Current State: 75:[9, 72], Operations: ['53-44=9', '37+35=72'] Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 9+72=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 9*72=648, Resulting Numbers: [648] 648,75 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 #0,2,0 Current State: 75:[37, 26], Operations: ['53-44=9', '35-9=26'] Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 37*26=962, Resulting Numbers: [962] 962,75 unequal: No Solution Exploring Operation: 37+26=63, Resulting Numbers: [63] 63,75 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 #0,2,1 Current State: 75:[35, 28], Operations: ['53-44=9', '37-9=28'] Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,75 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 75:[35, 44, 16], Operations: ['53-37=16'] Exploring Operation: 35+44=79, Resulting Numbers: [16, 79] Generated Node #0,0,0: 75:[16, 79] Operation: 35+44=79 Exploring Operation: 35-16=19, Resulting Numbers: [44, 19] Generated Node #0,0,1: 75:[44, 19] Operation: 35-16=19 Exploring Operation: 44-35=9, Resulting Numbers: [16, 9] Generated Node #0,0,2: 75:[16, 9] Operation: 44-35=9 Exploring Operation: 44-16=28, Resulting Numbers: [35, 28] Generated Node #0,0,3: 75:[35, 28] Operation: 44-16=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[16, 79], Operations: ['53-37=16', '35+44=79'] Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 16*79=1264, Resulting Numbers: [1264] 1264,75 unequal: No Solution Exploring Operation: 16+79=95, Resulting Numbers: [95] 95,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[16, 9], Operations: ['53-37=16', '44-35=9'] Exploring Operation: 16*9=144, Resulting Numbers: [144] 144,75 unequal: No Solution Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 75:[35, 28], Operations: ['53-37=16', '44-16=28'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[44, 19], Operations: ['53-37=16', '35-16=19'] Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,75 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 75:[37, 44, 18], Operations: ['53-35=18'] Exploring Operation: 44-37=7, Resulting Numbers: [18, 7] Generated Node #0,3,0: 75:[18, 7] Operation: 44-37=7 Exploring Operation: 37+44=81, Resulting Numbers: [18, 81] Generated Node #0,3,1: 75:[18, 81] Operation: 37+44=81 Exploring Operation: 37-18=19, Resulting Numbers: [44, 19] Generated Node #0,3,2: 75:[44, 19] Operation: 37-18=19 Exploring Operation: 44-18=26, Resulting Numbers: [37, 26] Generated Node #0,3,3: 75:[37, 26] Operation: 44-18=26 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 75:[18, 7], Operations: ['53-35=18', '44-37=7'] Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,75 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,75 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 #0,3,1 Current State: 75:[18, 81], Operations: ['53-35=18', '37+44=81'] Exploring Operation: 18*81=1458, Resulting Numbers: [1458] 1458,75 unequal: No Solution Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 18+81=99, Resulting Numbers: [99] 99,75 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 #0,3,3 Current State: 75:[37, 26], Operations: ['53-35=18', '44-18=26'] Exploring Operation: 37+26=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 37*26=962, Resulting Numbers: [962] 962,75 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 #0,3,2 Current State: 75:[44, 19], Operations: ['53-35=18', '37-18=19'] Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,75 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,75 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: 75:[35, 53, 7], Operations: ['44-37=7'] Exploring Operation: 35+53=88, Resulting Numbers: [7, 88] Generated Node #0,1,0: 75:[7, 88] Operation: 35+53=88 Exploring Operation: 35/7=5, Resulting Numbers: [53, 5] Generated Node #0,1,1: 75:[53, 5] Operation: 35/7=5 Exploring Operation: 53-35=18, Resulting Numbers: [7, 18] Generated Node #0,1,2: 75:[7, 18] Operation: 53-35=18 Exploring Operation: 35-7=28, Resulting Numbers: [53, 28] Generated Node #0,1,3: 75:[53, 28] Operation: 35-7=28 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 75:[7, 18], Operations: ['44-37=7', '53-35=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,75 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[7, 88], Operations: ['44-37=7', '35+53=88'] Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 7*88=616, Resulting Numbers: [616] 616,75 unequal: No Solution Exploring Operation: 7+88=95, Resulting Numbers: [95] 95,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[53, 5], Operations: ['44-37=7', '35/7=5'] Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,75 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,75 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 75:[53, 28], Operations: ['44-37=7', '35-7=28'] Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,75 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,75 unequal: No Solution Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,75 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
[ 10, 77, 90, 71 ]
48
[ "77-10=67", "90-71=19", "67-19=48" ]
Current State: 48:[10, 77, 90, 71], Operations: [] Exploring Operation: 77-10=67, Resulting Numbers: [90, 71, 67] Generated Node #2: [90, 71, 67] from Operation: 77-10=67 Current State: 48:[90, 71, 67], Operations: ['77-10=67'] Exploring Operation: 90-71=19, Resulting Numbers: [67, 19] Generated Node #3: [67, 19] from Operation: 90-71=19 Current State: 48:[67, 19], Operations: ['77-10=67', '90-71=19'] Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[10, 77, 90, 71], Operations: [] Exploring Operation: 90-77=13, Resulting Numbers: [10, 71, 13] Generated Node #0,0: 48:[10, 71, 13] Operation: 90-77=13 Exploring Operation: 90-71=19, Resulting Numbers: [10, 77, 19] Generated Node #0,1: 48:[10, 77, 19] Operation: 90-71=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[10, 71, 13], Operations: ['90-77=13'] Exploring Operation: 71-13=58, Resulting Numbers: [10, 58] Generated Node #0,0,0: 48:[10, 58] Operation: 71-13=58 Exploring Operation: 71-10=61, Resulting Numbers: [13, 61] Generated Node #0,0,1: 48:[13, 61] Operation: 71-10=61 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[10, 58], Operations: ['90-77=13', '71-13=58'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[10, 77, 90, 71], Operations: [] Exploring Operation: 90-77=13, Resulting Numbers: [10, 71, 13] Generated Node #0,0: 48:[10, 71, 13] Operation: 90-77=13 Moving to Node #0,0 Current State: 48:[10, 71, 13], Operations: ['90-77=13'] Exploring Operation: 71-13=58, Resulting Numbers: [10, 58] Generated Node #0,0,0: 48:[10, 58] Operation: 71-13=58 Moving to Node #0,0,0 Current State: 48:[10, 58], Operations: ['90-77=13', '71-13=58'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 22, 2, 75, 93 ]
58
[ "93-75=18", "2*18=36", "22+36=58" ]
Current State: 58:[22, 2, 75, 93], Operations: [] Exploring Operation: 93-75=18, Resulting Numbers: [22, 2, 18] Generated Node #2: [22, 2, 18] from Operation: 93-75=18 Current State: 58:[22, 2, 18], Operations: ['93-75=18'] Exploring Operation: 2*18=36, Resulting Numbers: [22, 36] Generated Node #3: [22, 36] from Operation: 2*18=36 Current State: 58:[22, 36], Operations: ['93-75=18', '2*18=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[22, 2, 75, 93], Operations: [] Exploring Operation: 93-75=18, Resulting Numbers: [22, 2, 18] Generated Node #0,0: 58:[22, 2, 18] Operation: 93-75=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[22, 2, 18], Operations: ['93-75=18'] Exploring Operation: 22-18=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 58:[2, 4] Operation: 22-18=4 Moving to Node #0,0,0 Current State: 58:[2, 4], Operations: ['93-75=18', '22-18=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,58 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
[ 63, 21, 8, 61 ]
58
[ "63-61=2", "21+8=29", "2*29=58" ]
Current State: 58:[63, 21, 8, 61], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [21, 8, 2] Generated Node #2: [21, 8, 2] from Operation: 63-61=2 Current State: 58:[21, 8, 2], Operations: ['63-61=2'] Exploring Operation: 21+8=29, Resulting Numbers: [2, 29] Generated Node #3: [2, 29] from Operation: 21+8=29 Current State: 58:[2, 29], Operations: ['63-61=2', '21+8=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[63, 21, 8, 61], Operations: [] Exploring Operation: 21+8=29, Resulting Numbers: [63, 61, 29] Generated Node #0,0: 58:[63, 61, 29] Operation: 21+8=29 Exploring Operation: 63/21=3, Resulting Numbers: [8, 61, 3] Generated Node #0,1: 58:[8, 61, 3] Operation: 63/21=3 Moving to Node #0,0 Current State: 58:[63, 61, 29], Operations: ['21+8=29'] Exploring Operation: 63-29=34, Resulting Numbers: [61, 34] Generated Node #0,0,0: 58:[61, 34] Operation: 63-29=34 Exploring Operation: 63-61=2, Resulting Numbers: [29, 2] Generated Node #0,0,1: 58:[29, 2] Operation: 63-61=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[29, 2], Operations: ['21+8=29', '63-61=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[63, 21, 8, 61], Operations: [] Exploring Operation: 21+8=29, Resulting Numbers: [63, 61, 29] Generated Node #0,0: 58:[63, 61, 29] Operation: 21+8=29 Moving to Node #0,0 Current State: 58:[63, 61, 29], Operations: ['21+8=29'] Exploring Operation: 63-61=2, Resulting Numbers: [29, 2] Generated Node #0,0,1: 58:[29, 2] Operation: 63-61=2 Moving to Node #0,0,1 Current State: 58:[29, 2], Operations: ['21+8=29', '63-61=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 57, 63, 2, 90 ]
60
[ "57+63=120", "2*90=180", "180-120=60" ]
Current State: 60:[57, 63, 2, 90], Operations: [] Exploring Operation: 57+63=120, Resulting Numbers: [2, 90, 120] Generated Node #2: [2, 90, 120] from Operation: 57+63=120 Current State: 60:[2, 90, 120], Operations: ['57+63=120'] Exploring Operation: 2*90=180, Resulting Numbers: [120, 180] Generated Node #3: [120, 180] from Operation: 2*90=180 Current State: 60:[120, 180], Operations: ['57+63=120', '2*90=180'] Exploring Operation: 180-120=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[57, 63, 2, 90], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [57, 63, 45] Generated Node #0,0: 60:[57, 63, 45] Operation: 90/2=45 Exploring Operation: 90-57=33, Resulting Numbers: [63, 2, 33] Generated Node #0,1: 60:[63, 2, 33] Operation: 90-57=33 Exploring Operation: 90-63=27, Resulting Numbers: [57, 2, 27] Generated Node #0,2: 60:[57, 2, 27] Operation: 90-63=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[63, 2, 33], Operations: ['90-57=33'] Exploring Operation: 63-2=61, Resulting Numbers: [33, 61] Generated Node #0,1,0: 60:[33, 61] Operation: 63-2=61 Exploring Operation: 63-33=30, Resulting Numbers: [2, 30] Generated Node #0,1,1: 60:[2, 30] Operation: 63-33=30 Exploring Operation: 33-2=31, Resulting Numbers: [63, 31] Generated Node #0,1,2: 60:[63, 31] Operation: 33-2=31 Moving to Node #0,1,1 Current State: 60:[2, 30], Operations: ['90-57=33', '63-33=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,60 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[57, 63, 2, 90], Operations: [] Exploring Operation: 90-57=33, Resulting Numbers: [63, 2, 33] Generated Node #0,1: 60:[63, 2, 33] Operation: 90-57=33 Moving to Node #0,1 Current State: 60:[63, 2, 33], Operations: ['90-57=33'] Exploring Operation: 63-33=30, Resulting Numbers: [2, 30] Generated Node #0,1,1: 60:[2, 30] Operation: 63-33=30 Moving to Node #0,1,1 Current State: 60:[2, 30], Operations: ['90-57=33', '63-33=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 11, 79, 15, 6 ]
89
[ "79-11=68", "15+6=21", "68+21=89" ]
Current State: 89:[11, 79, 15, 6], Operations: [] Exploring Operation: 79-11=68, Resulting Numbers: [15, 6, 68] Generated Node #2: [15, 6, 68] from Operation: 79-11=68 Current State: 89:[15, 6, 68], Operations: ['79-11=68'] Exploring Operation: 15+6=21, Resulting Numbers: [68, 21] Generated Node #3: [68, 21] from Operation: 15+6=21 Current State: 89:[68, 21], Operations: ['79-11=68', '15+6=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[11, 79, 15, 6], Operations: [] Exploring Operation: 15*6=90, Resulting Numbers: [11, 79, 90] Generated Node #0,0: 89:[11, 79, 90] Operation: 15*6=90 Exploring Operation: 11+15=26, Resulting Numbers: [79, 6, 26] Generated Node #0,1: 89:[79, 6, 26] Operation: 11+15=26 Exploring Operation: 11+6=17, Resulting Numbers: [79, 15, 17] Generated Node #0,2: 89:[79, 15, 17] Operation: 11+6=17 Exploring Operation: 11*6=66, Resulting Numbers: [79, 15, 66] Generated Node #0,3: 89:[79, 15, 66] Operation: 11*6=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[11, 79, 90], Operations: ['15*6=90'] Exploring Operation: 90-11=79, Resulting Numbers: [79, 79] Generated Node #0,0,0: 89:[79, 79] Operation: 90-11=79 Exploring Operation: 11+79=90, Resulting Numbers: [90, 90] Generated Node #0,0,1: 89:[90, 90] Operation: 11+79=90 Exploring Operation: 79-11=68, Resulting Numbers: [90, 68] Generated Node #0,0,2: 89:[90, 68] Operation: 79-11=68 Exploring Operation: 11+90=101, Resulting Numbers: [79, 101] Generated Node #0,0,3: 89:[79, 101] Operation: 11+90=101 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[90, 90], Operations: ['15*6=90', '11+79=90'] Exploring Operation: 90-90=0, Resulting Numbers: [0] 0,89 unequal: No Solution Exploring Operation: 90+90=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 90*90=8100, Resulting Numbers: [8100] 8100,89 unequal: No Solution Exploring Operation: 90/90=1, Resulting Numbers: [1] 1,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[79, 79], Operations: ['15*6=90', '90-11=79'] Exploring Operation: 79*79=6241, Resulting Numbers: [6241] 6241,89 unequal: No Solution Exploring Operation: 79/79=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 79-79=0, Resulting Numbers: [0] 0,89 unequal: No Solution Exploring Operation: 79+79=158, Resulting Numbers: [158] 158,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[90, 68], Operations: ['15*6=90', '79-11=68'] Exploring Operation: 90+68=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,89 unequal: No Solution Exploring Operation: 90*68=6120, Resulting Numbers: [6120] 6120,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[79, 101], Operations: ['15*6=90', '11+90=101'] Exploring Operation: 79*101=7979, Resulting Numbers: [7979] 7979,89 unequal: No Solution Exploring Operation: 79+101=180, Resulting Numbers: [180] 180,89 unequal: No Solution Exploring Operation: 101-79=22, Resulting Numbers: [22] 22,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[79, 15, 66], Operations: ['11*6=66'] Exploring Operation: 79-15=64, Resulting Numbers: [66, 64] Generated Node #0,3,0: 89:[66, 64] Operation: 79-15=64 Exploring Operation: 15+66=81, Resulting Numbers: [79, 81] Generated Node #0,3,1: 89:[79, 81] Operation: 15+66=81 Exploring Operation: 66-15=51, Resulting Numbers: [79, 51] Generated Node #0,3,2: 89:[79, 51] Operation: 66-15=51 Exploring Operation: 79+15=94, Resulting Numbers: [66, 94] Generated Node #0,3,3: 89:[66, 94] Operation: 79+15=94 Moving to Node #0,3,1 Current State: 89:[79, 81], Operations: ['11*6=66', '15+66=81'] Exploring Operation: 81-79=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 79*81=6399, Resulting Numbers: [6399] 6399,89 unequal: No Solution Exploring Operation: 79+81=160, Resulting Numbers: [160] 160,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[66, 94], Operations: ['11*6=66', '79+15=94'] Exploring Operation: 94-66=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 66*94=6204, Resulting Numbers: [6204] 6204,89 unequal: No Solution Exploring Operation: 66+94=160, Resulting Numbers: [160] 160,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[79, 51], Operations: ['11*6=66', '66-15=51'] Exploring Operation: 79+51=130, Resulting Numbers: [130] 130,89 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 79*51=4029, Resulting Numbers: [4029] 4029,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[66, 64], Operations: ['11*6=66', '79-15=64'] Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 66+64=130, Resulting Numbers: [130] 130,89 unequal: No Solution Exploring Operation: 66*64=4224, Resulting Numbers: [4224] 4224,89 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 #0,1 Current State: 89:[79, 6, 26], Operations: ['11+15=26'] Exploring Operation: 6*26=156, Resulting Numbers: [79, 156] Generated Node #0,1,0: 89:[79, 156] Operation: 6*26=156 Exploring Operation: 79-6=73, Resulting Numbers: [26, 73] Generated Node #0,1,1: 89:[26, 73] Operation: 79-6=73 Exploring Operation: 6+26=32, Resulting Numbers: [79, 32] Generated Node #0,1,2: 89:[79, 32] Operation: 6+26=32 Exploring Operation: 79+6=85, Resulting Numbers: [26, 85] Generated Node #0,1,3: 89:[26, 85] Operation: 79+6=85 Moving to Node #0,1,2 Current State: 89:[79, 32], Operations: ['11+15=26', '6+26=32'] Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,89 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[26, 85], Operations: ['11+15=26', '79+6=85'] Exploring Operation: 85-26=59, Resulting Numbers: [59] 59,89 unequal: No Solution Exploring Operation: 26+85=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 26*85=2210, Resulting Numbers: [2210] 2210,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[79, 156], Operations: ['11+15=26', '6*26=156'] Exploring Operation: 79*156=12324, Resulting Numbers: [12324] 12324,89 unequal: No Solution Exploring Operation: 79+156=235, Resulting Numbers: [235] 235,89 unequal: No Solution Exploring Operation: 156-79=77, Resulting Numbers: [77] 77,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[26, 73], Operations: ['11+15=26', '79-6=73'] Exploring Operation: 26*73=1898, Resulting Numbers: [1898] 1898,89 unequal: No Solution Exploring Operation: 26+73=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 73-26=47, Resulting Numbers: [47] 47,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[79, 15, 17], Operations: ['11+6=17'] Exploring Operation: 79+17=96, Resulting Numbers: [15, 96] Generated Node #0,2,0: 89:[15, 96] Operation: 79+17=96 Exploring Operation: 15+17=32, Resulting Numbers: [79, 32] Generated Node #0,2,1: 89:[79, 32] Operation: 15+17=32 Exploring Operation: 79+15=94, Resulting Numbers: [17, 94] Generated Node #0,2,2: 89:[17, 94] Operation: 79+15=94 Exploring Operation: 79-15=64, Resulting Numbers: [17, 64] Generated Node #0,2,3: 89:[17, 64] Operation: 79-15=64 Moving to Node #0,2,1 Current State: 89:[79, 32], Operations: ['11+6=17', '15+17=32'] Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[17, 94], Operations: ['11+6=17', '79+15=94'] Exploring Operation: 17*94=1598, Resulting Numbers: [1598] 1598,89 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 17+94=111, Resulting Numbers: [111] 111,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[15, 96], Operations: ['11+6=17', '79+17=96'] Exploring Operation: 15*96=1440, Resulting Numbers: [1440] 1440,89 unequal: No Solution Exploring Operation: 15+96=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 96-15=81, Resulting Numbers: [81] 81,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[17, 64], Operations: ['11+6=17', '79-15=64'] Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 11, 4, 44, 2 ]
62
[ "44-11=33", "2*33=66", "66-4=62" ]
Current State: 62:[11, 4, 44, 2], Operations: [] Exploring Operation: 44-11=33, Resulting Numbers: [4, 2, 33] Generated Node #2: [4, 2, 33] from Operation: 44-11=33 Current State: 62:[4, 2, 33], Operations: ['44-11=33'] Exploring Operation: 2*33=66, Resulting Numbers: [4, 66] Generated Node #3: [4, 66] from Operation: 2*33=66 Current State: 62:[4, 66], Operations: ['44-11=33', '2*33=66'] Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[11, 4, 44, 2], Operations: [] Exploring Operation: 11+44=55, Resulting Numbers: [4, 2, 55] Generated Node #0,0: 62:[4, 2, 55] Operation: 11+44=55 Exploring Operation: 44/11=4, Resulting Numbers: [4, 2, 4] Generated Node #0,1: 62:[4, 2, 4] Operation: 44/11=4 Exploring Operation: 11-4=7, Resulting Numbers: [44, 2, 7] Generated Node #0,2: 62:[44, 2, 7] Operation: 11-4=7 Exploring Operation: 44-11=33, Resulting Numbers: [4, 2, 33] Generated Node #0,3: 62:[4, 2, 33] Operation: 44-11=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[4, 2, 4], Operations: ['44/11=4'] Exploring Operation: 4/4=1, Resulting Numbers: [2, 1] Generated Node #0,1,0: 62:[2, 1] Operation: 4/4=1 Exploring Operation: 4-2=2, Resulting Numbers: [4, 2] Generated Node #0,1,1: 62:[4, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [4, 2] Generated Node #0,1,2: 62:[4, 2] Operation: 4/2=2 Exploring Operation: 4-4=0, Resulting Numbers: [2, 0] Generated Node #0,1,3: 62:[2, 0] Operation: 4-4=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[2, 1], Operations: ['44/11=4', '4/4=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,62 unequal: No Solution No 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: 62:[4, 2], Operations: ['44/11=4', '4-2=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,62 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,62 unequal: No Solution No 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: 62:[4, 2], Operations: ['44/11=4', '4/2=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,62 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,62 unequal: No Solution No 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: 62:[2, 0], Operations: ['44/11=4', '4-4=0'] Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,62 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,62 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: 62:[4, 2, 33], Operations: ['44-11=33'] Exploring Operation: 33-2=31, Resulting Numbers: [4, 31] Generated Node #0,3,0: 62:[4, 31] Operation: 33-2=31 Exploring Operation: 4/2=2, Resulting Numbers: [33, 2] Generated Node #0,3,1: 62:[33, 2] Operation: 4/2=2 Exploring Operation: 33-4=29, Resulting Numbers: [2, 29] Generated Node #0,3,2: 62:[2, 29] Operation: 33-4=29 Exploring Operation: 4-2=2, Resulting Numbers: [33, 2] Generated Node #0,3,3: 62:[33, 2] Operation: 4-2=2 Moving to Node #0,3,0 Current State: 62:[4, 31], Operations: ['44-11=33', '33-2=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,62 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[2, 29], Operations: ['44-11=33', '33-4=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,62 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,62 unequal: No Solution Moving to Node #0,3,1 Current State: 62:[33, 2], Operations: ['44-11=33', '4/2=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,62 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[33, 2], Operations: ['44-11=33', '4-2=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,62 unequal: No Solution Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[4, 2, 55], Operations: ['11+44=55'] Exploring Operation: 2+55=57, Resulting Numbers: [4, 57] Generated Node #0,0,0: 62:[4, 57] Operation: 2+55=57 Exploring Operation: 4/2=2, Resulting Numbers: [55, 2] Generated Node #0,0,1: 62:[55, 2] Operation: 4/2=2 Exploring Operation: 4+55=59, Resulting Numbers: [2, 59] Generated Node #0,0,2: 62:[2, 59] Operation: 4+55=59 Exploring Operation: 4-2=2, Resulting Numbers: [55, 2] Generated Node #0,0,3: 62:[55, 2] Operation: 4-2=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[2, 59], Operations: ['11+44=55', '4+55=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,62 unequal: No Solution No 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: 62:[4, 57], Operations: ['11+44=55', '2+55=57'] Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,62 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,62 unequal: No Solution No 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: 62:[55, 2], Operations: ['11+44=55', '4/2=2'] Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,62 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,62 unequal: No Solution No 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: 62:[55, 2], Operations: ['11+44=55', '4-2=2'] Exploring Operation: 55*2=110, Resulting Numbers: [110] 110,62 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,62 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: 62:[44, 2, 7], Operations: ['11-4=7'] Exploring Operation: 44/2=22, Resulting Numbers: [7, 22] Generated Node #0,2,0: 62:[7, 22] Operation: 44/2=22 Exploring Operation: 44-2=42, Resulting Numbers: [7, 42] Generated Node #0,2,1: 62:[7, 42] Operation: 44-2=42 Exploring Operation: 44-7=37, Resulting Numbers: [2, 37] Generated Node #0,2,2: 62:[2, 37] Operation: 44-7=37 Exploring Operation: 44+7=51, Resulting Numbers: [2, 51] Generated Node #0,2,3: 62:[2, 51] Operation: 44+7=51 Moving to Node #0,2,2 Current State: 62:[2, 37], Operations: ['11-4=7', '44-7=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,62 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,62 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[2, 51], Operations: ['11-4=7', '44+7=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,62 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,62 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[7, 22], Operations: ['11-4=7', '44/2=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[7, 42], Operations: ['11-4=7', '44-2=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,62 unequal: No Solution Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,62 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,62 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
[ 52, 91, 19, 19 ]
52
[ "19-19=0", "91*0=0", "52+0=52" ]
Current State: 52:[52, 91, 19, 19], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [52, 91, 0] Generated Node #2: [52, 91, 0] from Operation: 19-19=0 Current State: 52:[52, 91, 0], Operations: ['19-19=0'] Exploring Operation: 91*0=0, Resulting Numbers: [52, 0] Generated Node #3: [52, 0] from Operation: 91*0=0 Current State: 52:[52, 0], Operations: ['19-19=0', '91*0=0'] Exploring Operation: 52+0=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[52, 91, 19, 19], Operations: [] Exploring Operation: 91-52=39, Resulting Numbers: [19, 19, 39] Generated Node #0,0: 52:[19, 19, 39] Operation: 91-52=39 Exploring Operation: 19/19=1, Resulting Numbers: [52, 91, 1] Generated Node #0,1: 52:[52, 91, 1] Operation: 19/19=1 Exploring Operation: 91-19=72, Resulting Numbers: [52, 19, 72] Generated Node #0,2: 52:[52, 19, 72] Operation: 91-19=72 Exploring Operation: 19-19=0, Resulting Numbers: [52, 91, 0] Generated Node #0,3: 52:[52, 91, 0] Operation: 19-19=0 Exploring Operation: 91-19=72, Resulting Numbers: [52, 19, 72] Generated Node #0,4: 52:[52, 19, 72] Operation: 91-19=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[19, 19, 39], Operations: ['91-52=39'] Exploring Operation: 19+39=58, Resulting Numbers: [19, 58] Generated Node #0,0,0: 52:[19, 58] Operation: 19+39=58 Exploring Operation: 39-19=20, Resulting Numbers: [19, 20] Generated Node #0,0,1: 52:[19, 20] Operation: 39-19=20 Exploring Operation: 19+39=58, Resulting Numbers: [19, 58] Generated Node #0,0,2: 52:[19, 58] Operation: 19+39=58 Exploring Operation: 39-19=20, Resulting Numbers: [19, 20] Generated Node #0,0,3: 52:[19, 20] Operation: 39-19=20 Exploring Operation: 19/19=1, Resulting Numbers: [39, 1] Generated Node #0,0,4: 52:[39, 1] Operation: 19/19=1 Moving to Node #0,0,0 Current State: 52:[19, 58], Operations: ['91-52=39', '19+39=58'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 19*58=1102, Resulting Numbers: [1102] 1102,52 unequal: No Solution Exploring Operation: 19+58=77, Resulting Numbers: [77] 77,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[19, 58], Operations: ['91-52=39', '19+39=58'] Exploring Operation: 19+58=77, Resulting Numbers: [77] 77,52 unequal: No Solution Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 19*58=1102, Resulting Numbers: [1102] 1102,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[19, 20], Operations: ['91-52=39', '39-19=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,52 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[19, 20], Operations: ['91-52=39', '39-19=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[39, 1], Operations: ['91-52=39', '19/19=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,52 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 #0,2 Current State: 52:[52, 19, 72], Operations: ['91-19=72'] Exploring Operation: 52+19=71, Resulting Numbers: [72, 71] Generated Node #0,2,0: 52:[72, 71] Operation: 52+19=71 Exploring Operation: 72-52=20, Resulting Numbers: [19, 20] Generated Node #0,2,1: 52:[19, 20] Operation: 72-52=20 Exploring Operation: 52-19=33, Resulting Numbers: [72, 33] Generated Node #0,2,2: 52:[72, 33] Operation: 52-19=33 Exploring Operation: 72-19=53, Resulting Numbers: [52, 53] Generated Node #0,2,3: 52:[52, 53] Operation: 72-19=53 Exploring Operation: 19+72=91, Resulting Numbers: [52, 91] Generated Node #0,2,4: 52:[52, 91] Operation: 19+72=91 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[52, 53], Operations: ['91-19=72', '72-19=53'] Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,52 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,52 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 #0,2,1 Current State: 52:[19, 20], Operations: ['91-19=72', '72-52=20'] Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,52 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,52 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 #0,2,2 Current State: 52:[72, 33], Operations: ['91-19=72', '52-19=33'] Exploring Operation: 72*33=2376, Resulting Numbers: [2376] 2376,52 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 72+33=105, Resulting Numbers: [105] 105,52 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 #0,2,0 Current State: 52:[72, 71], Operations: ['91-19=72', '52+19=71'] Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,52 unequal: No Solution Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,52 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 #0,2,4 Current State: 52:[52, 91], Operations: ['91-19=72', '19+72=91'] Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,52 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 #0,4 Current State: 52:[52, 19, 72], Operations: ['91-19=72'] Exploring Operation: 19+72=91, Resulting Numbers: [52, 91] Generated Node #0,4,0: 52:[52, 91] Operation: 19+72=91 Exploring Operation: 72-19=53, Resulting Numbers: [52, 53] Generated Node #0,4,1: 52:[52, 53] Operation: 72-19=53 Exploring Operation: 52-19=33, Resulting Numbers: [72, 33] Generated Node #0,4,2: 52:[72, 33] Operation: 52-19=33 Exploring Operation: 72-52=20, Resulting Numbers: [19, 20] Generated Node #0,4,3: 52:[19, 20] Operation: 72-52=20 Exploring Operation: 52+19=71, Resulting Numbers: [72, 71] Generated Node #0,4,4: 52:[72, 71] Operation: 52+19=71 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 52:[52, 53], Operations: ['91-19=72', '72-19=53'] Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,52 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,52 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 #0,4,3 Current State: 52:[19, 20], Operations: ['91-19=72', '72-52=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,52 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,52 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 #0,4,2 Current State: 52:[72, 33], Operations: ['91-19=72', '52-19=33'] Exploring Operation: 72*33=2376, Resulting Numbers: [2376] 2376,52 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 72+33=105, Resulting Numbers: [105] 105,52 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 #0,4,0 Current State: 52:[52, 91], Operations: ['91-19=72', '19+72=91'] Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,52 unequal: No Solution Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,52 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 #0,4,4 Current State: 52:[72, 71], Operations: ['91-19=72', '52+19=71'] Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,52 unequal: No Solution Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,52 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 #0,1 Current State: 52:[52, 91, 1], Operations: ['19/19=1'] Exploring Operation: 52/1=52, Resulting Numbers: [91, 52] Generated Node #0,1,0: 52:[91, 52] Operation: 52/1=52 Exploring Operation: 91-52=39, Resulting Numbers: [1, 39] Generated Node #0,1,1: 52:[1, 39] Operation: 91-52=39 Exploring Operation: 52*1=52, Resulting Numbers: [91, 52] Generated Node #0,1,2: 52:[91, 52] Operation: 52*1=52 Exploring Operation: 91*1=91, Resulting Numbers: [52, 91] Generated Node #0,1,3: 52:[52, 91] Operation: 91*1=91 Exploring Operation: 91-1=90, Resulting Numbers: [52, 90] Generated Node #0,1,4: 52:[52, 90] Operation: 91-1=90 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[1, 39], Operations: ['19/19=1', '91-52=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,52 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:[52, 90], Operations: ['19/19=1', '91-1=90'] Exploring Operation: 52+90=142, Resulting Numbers: [142] 142,52 unequal: No Solution Exploring Operation: 52*90=4680, Resulting Numbers: [4680] 4680,52 unequal: No Solution Exploring Operation: 90-52=38, Resulting Numbers: [38] 38,52 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 #0,1,0 Current State: 52:[91, 52], Operations: ['19/19=1', '52/1=52'] Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,52 unequal: No Solution Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,52 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:[91, 52], Operations: ['19/19=1', '52*1=52'] Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,52 unequal: No Solution Exploring Operation: 91+52=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 91*52=4732, Resulting Numbers: [4732] 4732,52 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:[52, 91], Operations: ['19/19=1', '91*1=91'] Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,52 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,52 unequal: No Solution Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,52 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:[52, 91, 0], Operations: ['19-19=0'] Exploring Operation: 91-52=39, Resulting Numbers: [0, 39] Generated Node #0,3,0: 52:[0, 39] Operation: 91-52=39 Exploring Operation: 91*0=0, Resulting Numbers: [52, 0] Generated Node #0,3,1: 52:[52, 0] Operation: 91*0=0 Exploring Operation: 52+0=52, Resulting Numbers: [91, 52] Generated Node #0,3,2: 52:[91, 52] Operation: 52+0=52 Exploring Operation: 52-0=52, Resulting Numbers: [91, 52] Generated Node #0,3,3: 52:[91, 52] Operation: 52-0=52 Exploring Operation: 91+0=91, Resulting Numbers: [52, 91] Generated Node #0,3,4: 52:[52, 91] Operation: 91+0=91 Moving to Node #0,3,1 Current State: 52:[52, 0], Operations: ['19-19=0', '91*0=0'] Exploring Operation: 52+0=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[52, 91, 19, 19], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [52, 91, 0] Generated Node #0,3: 52:[52, 91, 0] Operation: 19-19=0 Moving to Node #0,3 Current State: 52:[52, 91, 0], Operations: ['19-19=0'] Exploring Operation: 91*0=0, Resulting Numbers: [52, 0] Generated Node #0,3,1: 52:[52, 0] Operation: 91*0=0 Moving to Node #0,3,1 Current State: 52:[52, 0], Operations: ['19-19=0', '91*0=0'] Exploring Operation: 52+0=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.915799
hs_5
mult_heuristic
[ 21, 42, 55, 6 ]
83
[ "21+55=76", "42/6=7", "76+7=83" ]
Current State: 83:[21, 42, 55, 6], Operations: [] Exploring Operation: 21+55=76, Resulting Numbers: [42, 6, 76] Generated Node #2: [42, 6, 76] from Operation: 21+55=76 Current State: 83:[42, 6, 76], Operations: ['21+55=76'] Exploring Operation: 42/6=7, Resulting Numbers: [76, 7] Generated Node #3: [76, 7] from Operation: 42/6=7 Current State: 83:[76, 7], Operations: ['21+55=76', '42/6=7'] Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[21, 42, 55, 6], Operations: [] Exploring Operation: 21+42=63, Resulting Numbers: [55, 6, 63] Generated Node #0,0: 83:[55, 6, 63] Operation: 21+42=63 Exploring Operation: 21*6=126, Resulting Numbers: [42, 55, 126] Generated Node #0,1: 83:[42, 55, 126] Operation: 21*6=126 Exploring Operation: 21+55=76, Resulting Numbers: [42, 6, 76] Generated Node #0,2: 83:[42, 6, 76] Operation: 21+55=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[42, 55, 126], Operations: ['21*6=126'] Exploring Operation: 126-55=71, Resulting Numbers: [42, 71] Generated Node #0,1,0: 83:[42, 71] Operation: 126-55=71 Exploring Operation: 42+55=97, Resulting Numbers: [126, 97] Generated Node #0,1,1: 83:[126, 97] Operation: 42+55=97 Exploring Operation: 126-42=84, Resulting Numbers: [55, 84] Generated Node #0,1,2: 83:[55, 84] Operation: 126-42=84 Moving to Node #0,1,2 Current State: 83:[55, 84], Operations: ['21*6=126', '126-42=84'] Exploring Operation: 55*84=4620, Resulting Numbers: [4620] 4620,83 unequal: No Solution Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 55+84=139, Resulting Numbers: [139] 139,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[42, 71], Operations: ['21*6=126', '126-55=71'] Exploring Operation: 42*71=2982, Resulting Numbers: [2982] 2982,83 unequal: No Solution Exploring Operation: 71-42=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 42+71=113, Resulting Numbers: [113] 113,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[126, 97], Operations: ['21*6=126', '42+55=97'] Exploring Operation: 126*97=12222, Resulting Numbers: [12222] 12222,83 unequal: No Solution Exploring Operation: 126-97=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 126+97=223, Resulting Numbers: [223] 223,83 unequal: No Solution No 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: 83:[55, 6, 63], Operations: ['21+42=63'] Exploring Operation: 55+6=61, Resulting Numbers: [63, 61] Generated Node #0,0,0: 83:[63, 61] Operation: 55+6=61 Exploring Operation: 6+63=69, Resulting Numbers: [55, 69] Generated Node #0,0,1: 83:[55, 69] Operation: 6+63=69 Exploring Operation: 55-6=49, Resulting Numbers: [63, 49] Generated Node #0,0,2: 83:[63, 49] Operation: 55-6=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[63, 61], Operations: ['21+42=63', '55+6=61'] Exploring Operation: 63+61=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 63*61=3843, Resulting Numbers: [3843] 3843,83 unequal: No Solution Exploring Operation: 63-61=2, Resulting Numbers: [2] 2,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[55, 69], Operations: ['21+42=63', '6+63=69'] Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 55*69=3795, Resulting Numbers: [3795] 3795,83 unequal: No Solution Exploring Operation: 55+69=124, Resulting Numbers: [124] 124,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[63, 49], Operations: ['21+42=63', '55-6=49'] Exploring Operation: 63+49=112, Resulting Numbers: [112] 112,83 unequal: No Solution Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 63*49=3087, Resulting Numbers: [3087] 3087,83 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: 83:[42, 6, 76], Operations: ['21+55=76'] Exploring Operation: 42-6=36, Resulting Numbers: [76, 36] Generated Node #0,2,0: 83:[76, 36] Operation: 42-6=36 Exploring Operation: 6+76=82, Resulting Numbers: [42, 82] Generated Node #0,2,1: 83:[42, 82] Operation: 6+76=82 Exploring Operation: 42+6=48, Resulting Numbers: [76, 48] Generated Node #0,2,2: 83:[76, 48] Operation: 42+6=48 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[42, 82], Operations: ['21+55=76', '6+76=82'] Exploring Operation: 42*82=3444, Resulting Numbers: [3444] 3444,83 unequal: No Solution Exploring Operation: 42+82=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[76, 48], Operations: ['21+55=76', '42+6=48'] Exploring Operation: 76+48=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 76*48=3648, Resulting Numbers: [3648] 3648,83 unequal: No Solution Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[76, 36], Operations: ['21+55=76', '42-6=36'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 76*36=2736, Resulting Numbers: [2736] 2736,83 unequal: No Solution Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,83 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
[ 18, 71, 62, 17 ]
91
[ "18*62=1116", "71*17=1207", "1207-1116=91" ]
Current State: 91:[18, 71, 62, 17], Operations: [] Exploring Operation: 18*62=1116, Resulting Numbers: [71, 17, 1116] Generated Node #2: [71, 17, 1116] from Operation: 18*62=1116 Current State: 91:[71, 17, 1116], Operations: ['18*62=1116'] Exploring Operation: 71*17=1207, Resulting Numbers: [1116, 1207] Generated Node #3: [1116, 1207] from Operation: 71*17=1207 Current State: 91:[1116, 1207], Operations: ['18*62=1116', '71*17=1207'] Exploring Operation: 1207-1116=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[18, 71, 62, 17], Operations: [] Exploring Operation: 18+71=89, Resulting Numbers: [62, 17, 89] Generated Node #0,0: 91:[62, 17, 89] Operation: 18+71=89 Exploring Operation: 62+17=79, Resulting Numbers: [18, 71, 79] Generated Node #0,1: 91:[18, 71, 79] Operation: 62+17=79 Exploring Operation: 71+17=88, Resulting Numbers: [18, 62, 88] Generated Node #0,2: 91:[18, 62, 88] Operation: 71+17=88 Exploring Operation: 71-62=9, Resulting Numbers: [18, 17, 9] Generated Node #0,3: 91:[18, 17, 9] Operation: 71-62=9 Exploring Operation: 18+62=80, Resulting Numbers: [71, 17, 80] Generated Node #0,4: 91:[71, 17, 80] Operation: 18+62=80 Moving to Node #0,3 Current State: 91:[18, 17, 9], Operations: ['71-62=9'] Exploring Operation: 18-17=1, Resulting Numbers: [9, 1] Generated Node #0,3,0: 91:[9, 1] Operation: 18-17=1 Exploring Operation: 18+9=27, Resulting Numbers: [17, 27] Generated Node #0,3,1: 91:[17, 27] Operation: 18+9=27 Exploring Operation: 18-9=9, Resulting Numbers: [17, 9] Generated Node #0,3,2: 91:[17, 9] Operation: 18-9=9 Exploring Operation: 18/9=2, Resulting Numbers: [17, 2] Generated Node #0,3,3: 91:[17, 2] Operation: 18/9=2 Exploring Operation: 17-9=8, Resulting Numbers: [18, 8] Generated Node #0,3,4: 91:[18, 8] Operation: 17-9=8 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 91:[17, 9], Operations: ['71-62=9', '18-9=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,91 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,91 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 #0,3,4 Current State: 91:[18, 8], Operations: ['71-62=9', '17-9=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,91 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,91 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 #0,3,0 Current State: 91:[9, 1], Operations: ['71-62=9', '18-17=1'] Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,91 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 #0,3,3 Current State: 91:[17, 2], Operations: ['71-62=9', '18/9=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,91 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,91 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,91 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 #0,3,1 Current State: 91:[17, 27], Operations: ['71-62=9', '18+9=27'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,91 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: 91:[71, 17, 80], Operations: ['18+62=80'] Exploring Operation: 80-17=63, Resulting Numbers: [71, 63] Generated Node #0,4,0: 91:[71, 63] Operation: 80-17=63 Exploring Operation: 71-17=54, Resulting Numbers: [80, 54] Generated Node #0,4,1: 91:[80, 54] Operation: 71-17=54 Exploring Operation: 80-71=9, Resulting Numbers: [17, 9] Generated Node #0,4,2: 91:[17, 9] Operation: 80-71=9 Exploring Operation: 71+17=88, Resulting Numbers: [80, 88] Generated Node #0,4,3: 91:[80, 88] Operation: 71+17=88 Exploring Operation: 17+80=97, Resulting Numbers: [71, 97] Generated Node #0,4,4: 91:[71, 97] Operation: 17+80=97 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 91:[17, 9], Operations: ['18+62=80', '80-71=9'] Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,91 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,91 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 #0,4,3 Current State: 91:[80, 88], Operations: ['18+62=80', '71+17=88'] Exploring Operation: 80+88=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 80*88=7040, Resulting Numbers: [7040] 7040,91 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 #0,4,4 Current State: 91:[71, 97], Operations: ['18+62=80', '17+80=97'] Exploring Operation: 97-71=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 71+97=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 71*97=6887, Resulting Numbers: [6887] 6887,91 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 #0,4,0 Current State: 91:[71, 63], Operations: ['18+62=80', '80-17=63'] Exploring Operation: 71-63=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 71*63=4473, Resulting Numbers: [4473] 4473,91 unequal: No Solution Exploring Operation: 71+63=134, Resulting Numbers: [134] 134,91 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 #0,4,1 Current State: 91:[80, 54], Operations: ['18+62=80', '71-17=54'] Exploring Operation: 80+54=134, Resulting Numbers: [134] 134,91 unequal: No Solution Exploring Operation: 80*54=4320, Resulting Numbers: [4320] 4320,91 unequal: No Solution Exploring Operation: 80-54=26, Resulting Numbers: [26] 26,91 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:[62, 17, 89], Operations: ['18+71=89'] Exploring Operation: 62-17=45, Resulting Numbers: [89, 45] Generated Node #0,0,0: 91:[89, 45] Operation: 62-17=45 Exploring Operation: 17+89=106, Resulting Numbers: [62, 106] Generated Node #0,0,1: 91:[62, 106] Operation: 17+89=106 Exploring Operation: 62+17=79, Resulting Numbers: [89, 79] Generated Node #0,0,2: 91:[89, 79] Operation: 62+17=79 Exploring Operation: 89-17=72, Resulting Numbers: [62, 72] Generated Node #0,0,3: 91:[62, 72] Operation: 89-17=72 Exploring Operation: 89-62=27, Resulting Numbers: [17, 27] Generated Node #0,0,4: 91:[17, 27] Operation: 89-62=27 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 91:[89, 79], Operations: ['18+71=89', '62+17=79'] Exploring Operation: 89*79=7031, Resulting Numbers: [7031] 7031,91 unequal: No Solution Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 89+79=168, Resulting Numbers: [168] 168,91 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 #0,0,4 Current State: 91:[17, 27], Operations: ['18+71=89', '89-62=27'] Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,91 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,91 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:[89, 45], Operations: ['18+71=89', '62-17=45'] Exploring Operation: 89-45=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 89*45=4005, Resulting Numbers: [4005] 4005,91 unequal: No Solution Exploring Operation: 89+45=134, Resulting Numbers: [134] 134,91 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 #0,0,1 Current State: 91:[62, 106], Operations: ['18+71=89', '17+89=106'] Exploring Operation: 62+106=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 106-62=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 62*106=6572, Resulting Numbers: [6572] 6572,91 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 #0,0,3 Current State: 91:[62, 72], Operations: ['18+71=89', '89-17=72'] Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 62+72=134, Resulting Numbers: [134] 134,91 unequal: No Solution Exploring Operation: 62*72=4464, Resulting Numbers: [4464] 4464,91 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: 91:[18, 71, 79], Operations: ['62+17=79'] Exploring Operation: 18+71=89, Resulting Numbers: [79, 89] Generated Node #0,1,0: 91:[79, 89] Operation: 18+71=89 Exploring Operation: 18+79=97, Resulting Numbers: [71, 97] Generated Node #0,1,1: 91:[71, 97] Operation: 18+79=97 Exploring Operation: 71-18=53, Resulting Numbers: [79, 53] Generated Node #0,1,2: 91:[79, 53] Operation: 71-18=53 Exploring Operation: 79-18=61, Resulting Numbers: [71, 61] Generated Node #0,1,3: 91:[71, 61] Operation: 79-18=61 Exploring Operation: 79-71=8, Resulting Numbers: [18, 8] Generated Node #0,1,4: 91:[18, 8] Operation: 79-71=8 Moving to Node #0,2 Current State: 91:[18, 62, 88], Operations: ['71+17=88'] Exploring Operation: 88-62=26, Resulting Numbers: [18, 26] Generated Node #0,2,0: 91:[18, 26] Operation: 88-62=26 Exploring Operation: 62-18=44, Resulting Numbers: [88, 44] Generated Node #0,2,1: 91:[88, 44] Operation: 62-18=44 Exploring Operation: 18+62=80, Resulting Numbers: [88, 80] Generated Node #0,2,2: 91:[88, 80] Operation: 18+62=80 Exploring Operation: 88-18=70, Resulting Numbers: [62, 70] Generated Node #0,2,3: 91:[62, 70] Operation: 88-18=70 Exploring Operation: 18+88=106, Resulting Numbers: [62, 106] Generated Node #0,2,4: 91:[62, 106] Operation: 18+88=106 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[88, 80], Operations: ['71+17=88', '18+62=80'] Exploring Operation: 88*80=7040, Resulting Numbers: [7040] 7040,91 unequal: No Solution Exploring Operation: 88+80=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,91 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 #0,2,0 Current State: 91:[18, 26], Operations: ['71+17=88', '88-62=26'] Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,91 unequal: No Solution Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,91 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 #0,2,1 Current State: 91:[88, 44], Operations: ['71+17=88', '62-18=44'] Exploring Operation: 88-44=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 88/44=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 88*44=3872, Resulting Numbers: [3872] 3872,91 unequal: No Solution Exploring Operation: 88+44=132, Resulting Numbers: [132] 132,91 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 #0,2,4 Current State: 91:[62, 106], Operations: ['71+17=88', '18+88=106'] Exploring Operation: 106-62=44, Resulting Numbers: [44] 44,91 unequal: No Solution Exploring Operation: 62*106=6572, Resulting Numbers: [6572] 6572,91 unequal: No Solution Exploring Operation: 62+106=168, Resulting Numbers: [168] 168,91 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 #0,2,3 Current State: 91:[62, 70], Operations: ['71+17=88', '88-18=70'] Exploring Operation: 62+70=132, Resulting Numbers: [132] 132,91 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,91 unequal: No Solution Exploring Operation: 62*70=4340, Resulting Numbers: [4340] 4340,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 91:[18, 8], Operations: ['62+17=79', '79-71=8'] Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,91 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[79, 89], Operations: ['62+17=79', '18+71=89'] Exploring Operation: 79*89=7031, Resulting Numbers: [7031] 7031,91 unequal: No Solution Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,91 unequal: No Solution Exploring Operation: 79+89=168, Resulting Numbers: [168] 168,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[71, 97], Operations: ['62+17=79', '18+79=97'] Exploring Operation: 71*97=6887, Resulting Numbers: [6887] 6887,91 unequal: No Solution Exploring Operation: 97-71=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 71+97=168, Resulting Numbers: [168] 168,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[79, 53], Operations: ['62+17=79', '71-18=53'] Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 79+53=132, Resulting Numbers: [132] 132,91 unequal: No Solution Exploring Operation: 79*53=4187, Resulting Numbers: [4187] 4187,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[71, 61], Operations: ['62+17=79', '79-18=61'] Exploring Operation: 71*61=4331, Resulting Numbers: [4331] 4331,91 unequal: No Solution Exploring Operation: 71+61=132, Resulting Numbers: [132] 132,91 unequal: No Solution Exploring Operation: 71-61=10, Resulting Numbers: [10] 10,91 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 64, 70, 64, 5 ]
76
[ "64/64=1", "70+5=75", "1+75=76" ]
Current State: 76:[64, 70, 64, 5], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [70, 5, 1] Generated Node #2: [70, 5, 1] from Operation: 64/64=1 Current State: 76:[70, 5, 1], Operations: ['64/64=1'] Exploring Operation: 70+5=75, Resulting Numbers: [1, 75] Generated Node #3: [1, 75] from Operation: 70+5=75 Current State: 76:[1, 75], Operations: ['64/64=1', '70+5=75'] Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[64, 70, 64, 5], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [70, 5, 1] Generated Node #0,0: 76:[70, 5, 1] Operation: 64/64=1 Exploring Operation: 64-64=0, Resulting Numbers: [70, 5, 0] Generated Node #0,1: 76:[70, 5, 0] Operation: 64-64=0 Moving to Node #0,0 Current State: 76:[70, 5, 1], Operations: ['64/64=1'] Exploring Operation: 70+5=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 76:[1, 75] Operation: 70+5=75 Exploring Operation: 70/5=14, Resulting Numbers: [1, 14] Generated Node #0,0,1: 76:[1, 14] Operation: 70/5=14 Moving to Node #0,1 Current State: 76:[70, 5, 0], Operations: ['64-64=0'] Exploring Operation: 70*0=0, Resulting Numbers: [5, 0] Generated Node #0,1,0: 76:[5, 0] Operation: 70*0=0 Exploring Operation: 70+5=75, Resulting Numbers: [0, 75] Generated Node #0,1,1: 76:[0, 75] Operation: 70+5=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[5, 0], Operations: ['64-64=0', '70*0=0'] Exploring Operation: 5+0=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 5-0=5, Resulting Numbers: [5] 5,76 unequal: No Solution No 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: 76:[0, 75], Operations: ['64-64=0', '70+5=75'] Exploring Operation: 75-0=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 0+75=75, Resulting Numbers: [75] 75,76 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: 76:[1, 75], Operations: ['64/64=1', '70+5=75'] Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[64, 70, 64, 5], Operations: [] Exploring Operation: 64/64=1, Resulting Numbers: [70, 5, 1] Generated Node #0,0: 76:[70, 5, 1] Operation: 64/64=1 Moving to Node #0,0 Current State: 76:[70, 5, 1], Operations: ['64/64=1'] Exploring Operation: 70+5=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 76:[1, 75] Operation: 70+5=75 Moving to Node #0,0,0 Current State: 76:[1, 75], Operations: ['64/64=1', '70+5=75'] Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 26, 91, 38, 13 ]
83
[ "26*38=988", "91+988=1079", "1079/13=83" ]
Current State: 83:[26, 91, 38, 13], Operations: [] Exploring Operation: 26*38=988, Resulting Numbers: [91, 13, 988] Generated Node #2: [91, 13, 988] from Operation: 26*38=988 Current State: 83:[91, 13, 988], Operations: ['26*38=988'] Exploring Operation: 91+988=1079, Resulting Numbers: [13, 1079] Generated Node #3: [13, 1079] from Operation: 91+988=1079 Current State: 83:[13, 1079], Operations: ['26*38=988', '91+988=1079'] Exploring Operation: 1079/13=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[26, 91, 38, 13], Operations: [] Exploring Operation: 26+13=39, Resulting Numbers: [91, 38, 39] Generated Node #0,0: 83:[91, 38, 39] Operation: 26+13=39 Exploring Operation: 26-13=13, Resulting Numbers: [91, 38, 13] Generated Node #0,1: 83:[91, 38, 13] Operation: 26-13=13 Exploring Operation: 26+38=64, Resulting Numbers: [91, 13, 64] Generated Node #0,2: 83:[91, 13, 64] Operation: 26+38=64 Exploring Operation: 38+13=51, Resulting Numbers: [26, 91, 51] Generated Node #0,3: 83:[26, 91, 51] Operation: 38+13=51 Exploring Operation: 91-13=78, Resulting Numbers: [26, 38, 78] Generated Node #0,4: 83:[26, 38, 78] Operation: 91-13=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[91, 38, 39], Operations: ['26+13=39'] Exploring Operation: 91+38=129, Resulting Numbers: [39, 129] Generated Node #0,0,0: 83:[39, 129] Operation: 91+38=129 Exploring Operation: 39-38=1, Resulting Numbers: [91, 1] Generated Node #0,0,1: 83:[91, 1] Operation: 39-38=1 Exploring Operation: 91-39=52, Resulting Numbers: [38, 52] Generated Node #0,0,2: 83:[38, 52] Operation: 91-39=52 Exploring Operation: 38+39=77, Resulting Numbers: [91, 77] Generated Node #0,0,3: 83:[91, 77] Operation: 38+39=77 Exploring Operation: 91-38=53, Resulting Numbers: [39, 53] Generated Node #0,0,4: 83:[39, 53] Operation: 91-38=53 Moving to Node #0,0,3 Current State: 83:[91, 77], Operations: ['26+13=39', '38+39=77'] Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,83 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[39, 53], Operations: ['26+13=39', '91-38=53'] Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,83 unequal: No Solution Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[38, 52], Operations: ['26+13=39', '91-39=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,83 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[39, 129], Operations: ['26+13=39', '91+38=129'] Exploring Operation: 39*129=5031, Resulting Numbers: [5031] 5031,83 unequal: No Solution Exploring Operation: 129-39=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 39+129=168, Resulting Numbers: [168] 168,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[91, 1], Operations: ['26+13=39', '39-38=1'] Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,83 unequal: No Solution Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,83 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,83 unequal: No Solution No 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: 83:[91, 13, 64], Operations: ['26+38=64'] Exploring Operation: 91-13=78, Resulting Numbers: [64, 78] Generated Node #0,2,0: 83:[64, 78] Operation: 91-13=78 Exploring Operation: 91/13=7, Resulting Numbers: [64, 7] Generated Node #0,2,1: 83:[64, 7] Operation: 91/13=7 Exploring Operation: 13+64=77, Resulting Numbers: [91, 77] Generated Node #0,2,2: 83:[91, 77] Operation: 13+64=77 Exploring Operation: 64-13=51, Resulting Numbers: [91, 51] Generated Node #0,2,3: 83:[91, 51] Operation: 64-13=51 Exploring Operation: 91+13=104, Resulting Numbers: [64, 104] Generated Node #0,2,4: 83:[64, 104] Operation: 91+13=104 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[91, 77], Operations: ['26+38=64', '13+64=77'] Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,83 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[64, 78], Operations: ['26+38=64', '91-13=78'] Exploring Operation: 64*78=4992, Resulting Numbers: [4992] 4992,83 unequal: No Solution Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 64+78=142, Resulting Numbers: [142] 142,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[91, 51], Operations: ['26+38=64', '64-13=51'] Exploring Operation: 91+51=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 91*51=4641, Resulting Numbers: [4641] 4641,83 unequal: No Solution Exploring Operation: 91-51=40, Resulting Numbers: [40] 40,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 83:[64, 104], Operations: ['26+38=64', '91+13=104'] Exploring Operation: 64*104=6656, Resulting Numbers: [6656] 6656,83 unequal: No Solution Exploring Operation: 64+104=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 104-64=40, Resulting Numbers: [40] 40,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[64, 7], Operations: ['26+38=64', '91/13=7'] Exploring Operation: 64+7=71, Resulting Numbers: [71] 71,83 unequal: No Solution Exploring Operation: 64*7=448, Resulting Numbers: [448] 448,83 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,83 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: 83:[26, 91, 51], Operations: ['38+13=51'] Exploring Operation: 91-51=40, Resulting Numbers: [26, 40] Generated Node #0,3,0: 83:[26, 40] Operation: 91-51=40 Exploring Operation: 91-26=65, Resulting Numbers: [51, 65] Generated Node #0,3,1: 83:[51, 65] Operation: 91-26=65 Exploring Operation: 51-26=25, Resulting Numbers: [91, 25] Generated Node #0,3,2: 83:[91, 25] Operation: 51-26=25 Exploring Operation: 26+51=77, Resulting Numbers: [91, 77] Generated Node #0,3,3: 83:[91, 77] Operation: 26+51=77 Exploring Operation: 26+91=117, Resulting Numbers: [51, 117] Generated Node #0,3,4: 83:[51, 117] Operation: 26+91=117 Moving to Node #0,3,3 Current State: 83:[91, 77], Operations: ['38+13=51', '26+51=77'] Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[51, 65], Operations: ['38+13=51', '91-26=65'] Exploring Operation: 65-51=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 51+65=116, Resulting Numbers: [116] 116,83 unequal: No Solution Exploring Operation: 51*65=3315, Resulting Numbers: [3315] 3315,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[91, 25], Operations: ['38+13=51', '51-26=25'] Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 91*25=2275, Resulting Numbers: [2275] 2275,83 unequal: No Solution Exploring Operation: 91+25=116, Resulting Numbers: [116] 116,83 unequal: No Solution Moving to Node #0,3,4 Current State: 83:[51, 117], Operations: ['38+13=51', '26+91=117'] Exploring Operation: 117-51=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 51+117=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 51*117=5967, Resulting Numbers: [5967] 5967,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[26, 40], Operations: ['38+13=51', '91-51=40'] Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,83 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,83 unequal: No Solution No 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: 83:[26, 38, 78], Operations: ['91-13=78'] Exploring Operation: 78-26=52, Resulting Numbers: [38, 52] Generated Node #0,4,0: 83:[38, 52] Operation: 78-26=52 Exploring Operation: 26+38=64, Resulting Numbers: [78, 64] Generated Node #0,4,1: 83:[78, 64] Operation: 26+38=64 Exploring Operation: 38+78=116, Resulting Numbers: [26, 116] Generated Node #0,4,2: 83:[26, 116] Operation: 38+78=116 Exploring Operation: 26+78=104, Resulting Numbers: [38, 104] Generated Node #0,4,3: 83:[38, 104] Operation: 26+78=104 Exploring Operation: 38-26=12, Resulting Numbers: [78, 12] Generated Node #0,4,4: 83:[78, 12] Operation: 38-26=12 Moving to Node #0,4,1 Current State: 83:[78, 64], Operations: ['91-13=78', '26+38=64'] Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 78*64=4992, Resulting Numbers: [4992] 4992,83 unequal: No Solution Exploring Operation: 78+64=142, Resulting Numbers: [142] 142,83 unequal: No Solution Moving to Node #0,4,3 Current State: 83:[38, 104], Operations: ['91-13=78', '26+78=104'] Exploring Operation: 38+104=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 38*104=3952, Resulting Numbers: [3952] 3952,83 unequal: No Solution Exploring Operation: 104-38=66, Resulting Numbers: [66] 66,83 unequal: No Solution Moving to Node #0,4,0 Current State: 83:[38, 52], Operations: ['91-13=78', '78-26=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,83 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[78, 12], Operations: ['91-13=78', '38-26=12'] Exploring Operation: 78*12=936, Resulting Numbers: [936] 936,83 unequal: No Solution Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 78+12=90, Resulting Numbers: [90] 90,83 unequal: No Solution Moving to Node #0,4,2 Current State: 83:[26, 116], Operations: ['91-13=78', '38+78=116'] Exploring Operation: 26+116=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 116-26=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 26*116=3016, Resulting Numbers: [3016] 3016,83 unequal: No Solution No 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: 83:[91, 38, 13], Operations: ['26-13=13'] Exploring Operation: 91-13=78, Resulting Numbers: [38, 78] Generated Node #0,1,0: 83:[38, 78] Operation: 91-13=78 Exploring Operation: 91+13=104, Resulting Numbers: [38, 104] Generated Node #0,1,1: 83:[38, 104] Operation: 91+13=104 Exploring Operation: 91-38=53, Resulting Numbers: [13, 53] Generated Node #0,1,2: 83:[13, 53] Operation: 91-38=53 Exploring Operation: 38-13=25, Resulting Numbers: [91, 25] Generated Node #0,1,3: 83:[91, 25] Operation: 38-13=25 Exploring Operation: 38+13=51, Resulting Numbers: [91, 51] Generated Node #0,1,4: 83:[91, 51] Operation: 38+13=51 Moving to Node #0,1,4 Current State: 83:[91, 51], Operations: ['26-13=13', '38+13=51'] Exploring Operation: 91-51=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 91+51=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 91*51=4641, Resulting Numbers: [4641] 4641,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[38, 78], Operations: ['26-13=13', '91-13=78'] Exploring Operation: 38*78=2964, Resulting Numbers: [2964] 2964,83 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 38+78=116, Resulting Numbers: [116] 116,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[38, 104], Operations: ['26-13=13', '91+13=104'] Exploring Operation: 38+104=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 38*104=3952, Resulting Numbers: [3952] 3952,83 unequal: No Solution Exploring Operation: 104-38=66, Resulting Numbers: [66] 66,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[91, 25], Operations: ['26-13=13', '38-13=25'] Exploring Operation: 91*25=2275, Resulting Numbers: [2275] 2275,83 unequal: No Solution Exploring Operation: 91-25=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 91+25=116, Resulting Numbers: [116] 116,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[13, 53], Operations: ['26-13=13', '91-38=53'] Exploring Operation: 13*53=689, Resulting Numbers: [689] 689,83 unequal: No Solution Exploring Operation: 53-13=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 13+53=66, Resulting Numbers: [66] 66,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 85, 36, 6, 53 ]
13
[ "85+53=138", "138/6=23", "36-23=13" ]
Current State: 13:[85, 36, 6, 53], Operations: [] Exploring Operation: 85+53=138, Resulting Numbers: [36, 6, 138] Generated Node #2: [36, 6, 138] from Operation: 85+53=138 Current State: 13:[36, 6, 138], Operations: ['85+53=138'] Exploring Operation: 138/6=23, Resulting Numbers: [36, 23] Generated Node #3: [36, 23] from Operation: 138/6=23 Current State: 13:[36, 23], Operations: ['85+53=138', '138/6=23'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[85, 36, 6, 53], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [36, 6, 32] Generated Node #0,0: 13:[36, 6, 32] Operation: 85-53=32 Exploring Operation: 85-36=49, Resulting Numbers: [6, 53, 49] Generated Node #0,1: 13:[6, 53, 49] Operation: 85-36=49 Exploring Operation: 53-36=17, Resulting Numbers: [85, 6, 17] Generated Node #0,2: 13:[85, 6, 17] Operation: 53-36=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[36, 6, 32], Operations: ['85-53=32'] Exploring Operation: 36/6=6, Resulting Numbers: [32, 6] Generated Node #0,0,0: 13:[32, 6] Operation: 36/6=6 Exploring Operation: 36-6=30, Resulting Numbers: [32, 30] Generated Node #0,0,1: 13:[32, 30] Operation: 36-6=30 Exploring Operation: 36-32=4, Resulting Numbers: [6, 4] Generated Node #0,0,2: 13:[6, 4] Operation: 36-32=4 Moving to Node #0,0,2 Current State: 13:[6, 4], Operations: ['85-53=32', '36-32=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[32, 6], Operations: ['85-53=32', '36/6=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,13 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[32, 30], Operations: ['85-53=32', '36-6=30'] Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 32+30=62, Resulting Numbers: [62] 62,13 unequal: No Solution Exploring Operation: 32*30=960, Resulting Numbers: [960] 960,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[6, 53, 49], Operations: ['85-36=49'] Exploring Operation: 49-6=43, Resulting Numbers: [53, 43] Generated Node #0,1,0: 13:[53, 43] Operation: 49-6=43 Exploring Operation: 53-49=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 13:[6, 4] Operation: 53-49=4 Exploring Operation: 53-6=47, Resulting Numbers: [49, 47] Generated Node #0,1,2: 13:[49, 47] Operation: 53-6=47 Moving to Node #0,1,1 Current State: 13:[6, 4], Operations: ['85-36=49', '53-49=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[53, 43], Operations: ['85-36=49', '49-6=43'] Exploring Operation: 53-43=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 53*43=2279, Resulting Numbers: [2279] 2279,13 unequal: No Solution Exploring Operation: 53+43=96, Resulting Numbers: [96] 96,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[49, 47], Operations: ['85-36=49', '53-6=47'] Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,13 unequal: No Solution Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[85, 6, 17], Operations: ['53-36=17'] Exploring Operation: 85-17=68, Resulting Numbers: [6, 68] Generated Node #0,2,0: 13:[6, 68] Operation: 85-17=68 Exploring Operation: 85-6=79, Resulting Numbers: [17, 79] Generated Node #0,2,1: 13:[17, 79] Operation: 85-6=79 Exploring Operation: 85/17=5, Resulting Numbers: [6, 5] Generated Node #0,2,2: 13:[6, 5] Operation: 85/17=5 Moving to Node #0,2,2 Current State: 13:[6, 5], Operations: ['53-36=17', '85/17=5'] Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,13 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[6, 68], Operations: ['53-36=17', '85-17=68'] Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,13 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,13 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[17, 79], Operations: ['53-36=17', '85-6=79'] Exploring Operation: 17+79=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 17*79=1343, Resulting Numbers: [1343] 1343,13 unequal: No Solution Exploring Operation: 79-17=62, Resulting Numbers: [62] 62,13 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
[ 48, 78, 76, 4 ]
34
[ "76-48=28", "4*28=112", "112-78=34" ]
Current State: 34:[48, 78, 76, 4], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [78, 4, 28] Generated Node #2: [78, 4, 28] from Operation: 76-48=28 Current State: 34:[78, 4, 28], Operations: ['76-48=28'] Exploring Operation: 4*28=112, Resulting Numbers: [78, 112] Generated Node #3: [78, 112] from Operation: 4*28=112 Current State: 34:[78, 112], Operations: ['76-48=28', '4*28=112'] Exploring Operation: 112-78=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[48, 78, 76, 4], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [48, 4, 2] Generated Node #0,0: 34:[48, 4, 2] Operation: 78-76=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[48, 4, 2], Operations: ['78-76=2'] Exploring Operation: 48/4=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 34:[2, 12] Operation: 48/4=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[2, 12], Operations: ['78-76=2', '48/4=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 74, 58, 52 ]
31
[ "74-37=37", "58-52=6", "37-6=31" ]
Current State: 31:[37, 74, 58, 52], Operations: [] Exploring Operation: 74-37=37, Resulting Numbers: [58, 52, 37] Generated Node #2: [58, 52, 37] from Operation: 74-37=37 Current State: 31:[58, 52, 37], Operations: ['74-37=37'] Exploring Operation: 58-52=6, Resulting Numbers: [37, 6] Generated Node #3: [37, 6] from Operation: 58-52=6 Current State: 31:[37, 6], Operations: ['74-37=37', '58-52=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[37, 74, 58, 52], Operations: [] Exploring Operation: 74-52=22, Resulting Numbers: [37, 58, 22] Generated Node #0,0: 31:[37, 58, 22] Operation: 74-52=22 Exploring Operation: 74-37=37, Resulting Numbers: [58, 52, 37] Generated Node #0,1: 31:[58, 52, 37] Operation: 74-37=37 Exploring Operation: 74-58=16, Resulting Numbers: [37, 52, 16] Generated Node #0,2: 31:[37, 52, 16] Operation: 74-58=16 Moving to Node #0,0 Current State: 31:[37, 58, 22], Operations: ['74-52=22'] Exploring Operation: 58-22=36, Resulting Numbers: [37, 36] Generated Node #0,0,0: 31:[37, 36] Operation: 58-22=36 Exploring Operation: 58-37=21, Resulting Numbers: [22, 21] Generated Node #0,0,1: 31:[22, 21] Operation: 58-37=21 Exploring Operation: 37-22=15, Resulting Numbers: [58, 15] Generated Node #0,0,2: 31:[58, 15] Operation: 37-22=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[37, 36], Operations: ['74-52=22', '58-22=36'] Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,31 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,31 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[22, 21], Operations: ['74-52=22', '58-37=21'] Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,31 unequal: No Solution Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,31 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[58, 15], Operations: ['74-52=22', '37-22=15'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,31 unequal: No Solution Exploring Operation: 58+15=73, Resulting Numbers: [73] 73,31 unequal: No Solution Exploring Operation: 58*15=870, Resulting Numbers: [870] 870,31 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: 31:[37, 52, 16], Operations: ['74-58=16'] Exploring Operation: 52-37=15, Resulting Numbers: [16, 15] Generated Node #0,2,0: 31:[16, 15] Operation: 52-37=15 Exploring Operation: 37-16=21, Resulting Numbers: [52, 21] Generated Node #0,2,1: 31:[52, 21] Operation: 37-16=21 Exploring Operation: 52-16=36, Resulting Numbers: [37, 36] Generated Node #0,2,2: 31:[37, 36] Operation: 52-16=36 Moving to Node #0,1 Current State: 31:[58, 52, 37], Operations: ['74-37=37'] Exploring Operation: 58-37=21, Resulting Numbers: [52, 21] Generated Node #0,1,0: 31:[52, 21] Operation: 58-37=21 Exploring Operation: 58-52=6, Resulting Numbers: [37, 6] Generated Node #0,1,1: 31:[37, 6] Operation: 58-52=6 Exploring Operation: 52-37=15, Resulting Numbers: [58, 15] Generated Node #0,1,2: 31:[58, 15] Operation: 52-37=15 Moving to Node #0,2,2 Current State: 31:[37, 36], Operations: ['74-58=16', '52-16=36'] Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,31 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[52, 21], Operations: ['74-58=16', '37-16=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,31 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[37, 74, 58, 52], Operations: [] Exploring Operation: 74-58=16, Resulting Numbers: [37, 52, 16] Generated Node #0,2: 31:[37, 52, 16] Operation: 74-58=16 Moving to Node #0,2 Current State: 31:[37, 52, 16], Operations: ['74-58=16'] Exploring Operation: 37-16=21, Resulting Numbers: [52, 21] Generated Node #0,2,1: 31:[52, 21] Operation: 37-16=21 Moving to Node #0,2,1 Current State: 31:[52, 21], Operations: ['74-58=16', '37-16=21'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.973958
hs_3
mult_heuristic
[ 39, 97, 39, 77 ]
20
[ "39+97=136", "39+77=116", "136-116=20" ]
Current State: 20:[39, 97, 39, 77], Operations: [] Exploring Operation: 39+97=136, Resulting Numbers: [77, 136] Generated Node #2: [77, 136] from Operation: 39+97=136 Current State: 20:[77, 136], Operations: ['39+97=136'] Exploring Operation: 39+77=116, Resulting Numbers: [136, 116] Generated Node #3: [136, 116] from Operation: 39+77=116 Current State: 20:[136, 116], Operations: ['39+97=136', '39+77=116'] Exploring Operation: 136-116=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[39, 97, 39, 77], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [39, 77, 58] Generated Node #0,0: 20:[39, 77, 58] Operation: 97-39=58 Exploring Operation: 97-77=20, Resulting Numbers: [39, 39, 20] Generated Node #0,1: 20:[39, 39, 20] Operation: 97-77=20 Exploring Operation: 97-39=58, Resulting Numbers: [39, 77, 58] Generated Node #0,2: 20:[39, 77, 58] Operation: 97-39=58 Exploring Operation: 77-39=38, Resulting Numbers: [97, 39, 38] Generated Node #0,3: 20:[97, 39, 38] Operation: 77-39=38 Moving to Node #0,1 Current State: 20:[39, 39, 20], Operations: ['97-77=20'] Exploring Operation: 39/39=1, Resulting Numbers: [20, 1] Generated Node #0,1,0: 20:[20, 1] Operation: 39/39=1 Exploring Operation: 39-20=19, Resulting Numbers: [39, 19] Generated Node #0,1,1: 20:[39, 19] Operation: 39-20=19 Exploring Operation: 39-20=19, Resulting Numbers: [39, 19] Generated Node #0,1,2: 20:[39, 19] Operation: 39-20=19 Exploring Operation: 39-39=0, Resulting Numbers: [20, 0] Generated Node #0,1,3: 20:[20, 0] Operation: 39-39=0 Moving to Node #0,2 Current State: 20:[39, 77, 58], Operations: ['97-39=58'] Exploring Operation: 58-39=19, Resulting Numbers: [77, 19] Generated Node #0,2,0: 20:[77, 19] Operation: 58-39=19 Exploring Operation: 39+77=116, Resulting Numbers: [58, 116] Generated Node #0,2,1: 20:[58, 116] Operation: 39+77=116 Exploring Operation: 77-39=38, Resulting Numbers: [58, 38] Generated Node #0,2,2: 20:[58, 38] Operation: 77-39=38 Exploring Operation: 77-58=19, Resulting Numbers: [39, 19] Generated Node #0,2,3: 20:[39, 19] Operation: 77-58=19 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 20:[39, 19], Operations: ['97-39=58', '77-58=19'] Exploring Operation: 39*19=741, Resulting Numbers: [741] 741,20 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,20 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[39, 97, 39, 77], Operations: [] Exploring Operation: 97-39=58, Resulting Numbers: [39, 77, 58] Generated Node #0,2: 20:[39, 77, 58] Operation: 97-39=58 Moving to Node #0,2 Current State: 20:[39, 77, 58], Operations: ['97-39=58'] Exploring Operation: 77-58=19, Resulting Numbers: [39, 19] Generated Node #0,2,3: 20:[39, 19] Operation: 77-58=19 Moving to Node #0,2,3 Current State: 20:[39, 19], Operations: ['97-39=58', '77-58=19'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 12, 15, 56, 14 ]
33
[ "12*56=672", "672/14=48", "48-15=33" ]
Current State: 33:[12, 15, 56, 14], Operations: [] Exploring Operation: 12*56=672, Resulting Numbers: [15, 14, 672] Generated Node #2: [15, 14, 672] from Operation: 12*56=672 Current State: 33:[15, 14, 672], Operations: ['12*56=672'] Exploring Operation: 672/14=48, Resulting Numbers: [15, 48] Generated Node #3: [15, 48] from Operation: 672/14=48 Current State: 33:[15, 48], Operations: ['12*56=672', '672/14=48'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[12, 15, 56, 14], Operations: [] Exploring Operation: 56-15=41, Resulting Numbers: [12, 14, 41] Generated Node #0,0: 33:[12, 14, 41] Operation: 56-15=41 Exploring Operation: 56/14=4, Resulting Numbers: [12, 15, 4] Generated Node #0,1: 33:[12, 15, 4] Operation: 56/14=4 Exploring Operation: 56-14=42, Resulting Numbers: [12, 15, 42] Generated Node #0,2: 33:[12, 15, 42] Operation: 56-14=42 Exploring Operation: 56-12=44, Resulting Numbers: [15, 14, 44] Generated Node #0,3: 33:[15, 14, 44] Operation: 56-12=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[12, 15, 4], Operations: ['56/14=4'] Exploring Operation: 12+15=27, Resulting Numbers: [4, 27] Generated Node #0,1,0: 33:[4, 27] Operation: 12+15=27 Exploring Operation: 15-12=3, Resulting Numbers: [4, 3] Generated Node #0,1,1: 33:[4, 3] Operation: 15-12=3 Exploring Operation: 15-4=11, Resulting Numbers: [12, 11] Generated Node #0,1,2: 33:[12, 11] Operation: 15-4=11 Exploring Operation: 12/4=3, Resulting Numbers: [15, 3] Generated Node #0,1,3: 33:[15, 3] Operation: 12/4=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 33:[4, 3], Operations: ['56/14=4', '15-12=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,33 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,33 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 33:[12, 11], Operations: ['56/14=4', '15-4=11'] Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,33 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 33:[15, 3], Operations: ['56/14=4', '12/4=3'] Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,33 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[4, 27], Operations: ['56/14=4', '12+15=27'] Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,33 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,33 unequal: No Solution Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[12, 14, 41], Operations: ['56-15=41'] Exploring Operation: 41-12=29, Resulting Numbers: [14, 29] Generated Node #0,0,0: 33:[14, 29] Operation: 41-12=29 Exploring Operation: 12+14=26, Resulting Numbers: [41, 26] Generated Node #0,0,1: 33:[41, 26] Operation: 12+14=26 Exploring Operation: 41-14=27, Resulting Numbers: [12, 27] Generated Node #0,0,2: 33:[12, 27] Operation: 41-14=27 Exploring Operation: 14-12=2, Resulting Numbers: [41, 2] Generated Node #0,0,3: 33:[41, 2] Operation: 14-12=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[14, 29], Operations: ['56-15=41', '41-12=29'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 14*29=406, Resulting Numbers: [406] 406,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 33:[12, 27], Operations: ['56-15=41', '41-14=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,33 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 33:[41, 2], Operations: ['56-15=41', '14-12=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,33 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[41, 26], Operations: ['56-15=41', '12+14=26'] Exploring Operation: 41*26=1066, Resulting Numbers: [1066] 1066,33 unequal: No Solution Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 41+26=67, Resulting Numbers: [67] 67,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[12, 15, 42], Operations: ['56-14=42'] Exploring Operation: 15-12=3, Resulting Numbers: [42, 3] Generated Node #0,2,0: 33:[42, 3] Operation: 15-12=3 Exploring Operation: 12+15=27, Resulting Numbers: [42, 27] Generated Node #0,2,1: 33:[42, 27] Operation: 12+15=27 Exploring Operation: 42-15=27, Resulting Numbers: [12, 27] Generated Node #0,2,2: 33:[12, 27] Operation: 42-15=27 Exploring Operation: 42-12=30, Resulting Numbers: [15, 30] Generated Node #0,2,3: 33:[15, 30] Operation: 42-12=30 Moving to Node #0,2,2 Current State: 33:[12, 27], Operations: ['56-14=42', '42-15=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,33 unequal: No Solution Moving to Node #0,2,3 Current State: 33:[15, 30], Operations: ['56-14=42', '42-12=30'] Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,33 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,2,0 Current State: 33:[42, 3], Operations: ['56-14=42', '15-12=3'] Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,33 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[42, 27], Operations: ['56-14=42', '12+15=27'] Exploring Operation: 42*27=1134, Resulting Numbers: [1134] 1134,33 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 42+27=69, Resulting Numbers: [69] 69,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 33:[15, 14, 44], Operations: ['56-12=44'] Exploring Operation: 15+14=29, Resulting Numbers: [44, 29] Generated Node #0,3,0: 33:[44, 29] Operation: 15+14=29 Exploring Operation: 44-15=29, Resulting Numbers: [14, 29] Generated Node #0,3,1: 33:[14, 29] Operation: 44-15=29 Exploring Operation: 44-14=30, Resulting Numbers: [15, 30] Generated Node #0,3,2: 33:[15, 30] Operation: 44-14=30 Exploring Operation: 15-14=1, Resulting Numbers: [44, 1] Generated Node #0,3,3: 33:[44, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 33:[14, 29], Operations: ['56-12=44', '44-15=29'] Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 14*29=406, Resulting Numbers: [406] 406,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 33:[15, 30], Operations: ['56-12=44', '44-14=30'] Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,33 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 33:[44, 1], Operations: ['56-12=44', '15-14=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,33 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,33 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 33:[44, 29], Operations: ['56-12=44', '15+14=29'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,33 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 9, 21, 40, 97 ]
69
[ "21-9=12", "97-40=57", "12+57=69" ]
Current State: 69:[9, 21, 40, 97], Operations: [] Exploring Operation: 21-9=12, Resulting Numbers: [40, 97, 12] Generated Node #2: [40, 97, 12] from Operation: 21-9=12 Current State: 69:[40, 97, 12], Operations: ['21-9=12'] Exploring Operation: 97-40=57, Resulting Numbers: [12, 57] Generated Node #3: [12, 57] from Operation: 97-40=57 Current State: 69:[12, 57], Operations: ['21-9=12', '97-40=57'] Exploring Operation: 12+57=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[9, 21, 40, 97], Operations: [] Exploring Operation: 97-21=76, Resulting Numbers: [9, 40, 76] Generated Node #0,0: 69:[9, 40, 76] Operation: 97-21=76 Exploring Operation: 97-9=88, Resulting Numbers: [21, 40, 88] Generated Node #0,1: 69:[21, 40, 88] Operation: 97-9=88 Exploring Operation: 40-9=31, Resulting Numbers: [21, 97, 31] Generated Node #0,2: 69:[21, 97, 31] Operation: 40-9=31 Exploring Operation: 97-40=57, Resulting Numbers: [9, 21, 57] Generated Node #0,3: 69:[9, 21, 57] Operation: 97-40=57 Exploring Operation: 40-21=19, Resulting Numbers: [9, 97, 19] Generated Node #0,4: 69:[9, 97, 19] Operation: 40-21=19 Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[9, 21, 57], Operations: ['97-40=57'] Exploring Operation: 21-9=12, Resulting Numbers: [57, 12] Generated Node #0,3,0: 69:[57, 12] Operation: 21-9=12 Exploring Operation: 57-21=36, Resulting Numbers: [9, 36] Generated Node #0,3,1: 69:[9, 36] Operation: 57-21=36 Exploring Operation: 21+57=78, Resulting Numbers: [9, 78] Generated Node #0,3,2: 69:[9, 78] Operation: 21+57=78 Exploring Operation: 9+57=66, Resulting Numbers: [21, 66] Generated Node #0,3,3: 69:[21, 66] Operation: 9+57=66 Exploring Operation: 9+21=30, Resulting Numbers: [57, 30] Generated Node #0,3,4: 69:[57, 30] Operation: 9+21=30 Moving to Node #0,3,3 Current State: 69:[21, 66], Operations: ['97-40=57', '9+57=66'] Exploring Operation: 21*66=1386, Resulting Numbers: [1386] 1386,69 unequal: No Solution Exploring Operation: 21+66=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[9, 78], Operations: ['97-40=57', '21+57=78'] Exploring Operation: 9+78=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[9, 21, 40, 97], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [9, 21, 57] Generated Node #0,3: 69:[9, 21, 57] Operation: 97-40=57 Moving to Node #0,3 Current State: 69:[9, 21, 57], Operations: ['97-40=57'] Exploring Operation: 21+57=78, Resulting Numbers: [9, 78] Generated Node #0,3,2: 69:[9, 78] Operation: 21+57=78 Moving to Node #0,3,2 Current State: 69:[9, 78], Operations: ['97-40=57', '21+57=78'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 1, 98, 2, 11 ]
38
[ "1*98=98", "98/2=49", "49-11=38" ]
Current State: 38:[1, 98, 2, 11], Operations: [] Exploring Operation: 1*98=98, Resulting Numbers: [2, 11, 98] Generated Node #2: [2, 11, 98] from Operation: 1*98=98 Current State: 38:[2, 11, 98], Operations: ['1*98=98'] Exploring Operation: 98/2=49, Resulting Numbers: [11, 49] Generated Node #3: [11, 49] from Operation: 98/2=49 Current State: 38:[11, 49], Operations: ['1*98=98', '98/2=49'] Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[1, 98, 2, 11], Operations: [] Exploring Operation: 98-1=97, Resulting Numbers: [2, 11, 97] Generated Node #0,0: 38:[2, 11, 97] Operation: 98-1=97 Exploring Operation: 2*11=22, Resulting Numbers: [1, 98, 22] Generated Node #0,1: 38:[1, 98, 22] Operation: 2*11=22 Exploring Operation: 98-11=87, Resulting Numbers: [1, 2, 87] Generated Node #0,2: 38:[1, 2, 87] Operation: 98-11=87 Exploring Operation: 98/2=49, Resulting Numbers: [1, 11, 49] Generated Node #0,3: 38:[1, 11, 49] Operation: 98/2=49 Moving to Node #0,3 Current State: 38:[1, 11, 49], Operations: ['98/2=49'] Exploring Operation: 49-11=38, Resulting Numbers: [1, 38] Generated Node #0,3,0: 38:[1, 38] Operation: 49-11=38 Exploring Operation: 1*11=11, Resulting Numbers: [49, 11] Generated Node #0,3,1: 38:[49, 11] Operation: 1*11=11 Exploring Operation: 49-1=48, Resulting Numbers: [11, 48] Generated Node #0,3,2: 38:[11, 48] Operation: 49-1=48 Exploring Operation: 1+11=12, Resulting Numbers: [49, 12] Generated Node #0,3,3: 38:[49, 12] Operation: 1+11=12 Moving to Node #0,2 Current State: 38:[1, 2, 87], Operations: ['98-11=87'] Exploring Operation: 87-1=86, Resulting Numbers: [2, 86] Generated Node #0,2,0: 38:[2, 86] Operation: 87-1=86 Exploring Operation: 1*2=2, Resulting Numbers: [87, 2] Generated Node #0,2,1: 38:[87, 2] Operation: 1*2=2 Exploring Operation: 2/1=2, Resulting Numbers: [87, 2] Generated Node #0,2,2: 38:[87, 2] Operation: 2/1=2 Exploring Operation: 87-2=85, Resulting Numbers: [1, 85] Generated Node #0,2,3: 38:[1, 85] Operation: 87-2=85 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 38:[2, 86], Operations: ['98-11=87', '87-1=86'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,38 unequal: No Solution Exploring Operation: 2*86=172, Resulting Numbers: [172] 172,38 unequal: No Solution Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,38 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,38 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 #0,2,3 Current State: 38:[1, 85], Operations: ['98-11=87', '87-2=85'] Exploring Operation: 1+85=86, Resulting Numbers: [86] 86,38 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,38 unequal: No Solution Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,38 unequal: No Solution Exploring Operation: 1*85=85, Resulting Numbers: [85] 85,38 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 #0,2,1 Current State: 38:[87, 2], Operations: ['98-11=87', '1*2=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,38 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,38 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,38 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 #0,2,2 Current State: 38:[87, 2], Operations: ['98-11=87', '2/1=2'] Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,38 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,38 unequal: No Solution Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,38 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:[1, 98, 22], Operations: ['2*11=22'] Exploring Operation: 98-22=76, Resulting Numbers: [1, 76] Generated Node #0,1,0: 38:[1, 76] Operation: 98-22=76 Exploring Operation: 98-1=97, Resulting Numbers: [22, 97] Generated Node #0,1,1: 38:[22, 97] Operation: 98-1=97 Exploring Operation: 22-1=21, Resulting Numbers: [98, 21] Generated Node #0,1,2: 38:[98, 21] Operation: 22-1=21 Exploring Operation: 1*98=98, Resulting Numbers: [22, 98] Generated Node #0,1,3: 38:[22, 98] Operation: 1*98=98 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[1, 76], Operations: ['2*11=22', '98-22=76'] Exploring Operation: 1*76=76, Resulting Numbers: [76] 76,38 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,38 unequal: No Solution Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,38 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:[22, 97], Operations: ['2*11=22', '98-1=97'] Exploring Operation: 22*97=2134, Resulting Numbers: [2134] 2134,38 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,38 unequal: No Solution Exploring Operation: 22+97=119, Resulting Numbers: [119] 119,38 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:[98, 21], Operations: ['2*11=22', '22-1=21'] Exploring Operation: 98+21=119, Resulting Numbers: [119] 119,38 unequal: No Solution Exploring Operation: 98-21=77, Resulting Numbers: [77] 77,38 unequal: No Solution Exploring Operation: 98*21=2058, Resulting Numbers: [2058] 2058,38 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:[22, 98], Operations: ['2*11=22', '1*98=98'] Exploring Operation: 22+98=120, Resulting Numbers: [120] 120,38 unequal: No Solution Exploring Operation: 98-22=76, Resulting Numbers: [76] 76,38 unequal: No Solution Exploring Operation: 22*98=2156, Resulting Numbers: [2156] 2156,38 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: 38:[2, 11, 97], Operations: ['98-1=97'] Exploring Operation: 2+11=13, Resulting Numbers: [97, 13] Generated Node #0,0,0: 38:[97, 13] Operation: 2+11=13 Exploring Operation: 2*11=22, Resulting Numbers: [97, 22] Generated Node #0,0,1: 38:[97, 22] Operation: 2*11=22 Exploring Operation: 97-2=95, Resulting Numbers: [11, 95] Generated Node #0,0,2: 38:[11, 95] Operation: 97-2=95 Exploring Operation: 97-11=86, Resulting Numbers: [2, 86] Generated Node #0,0,3: 38:[2, 86] Operation: 97-11=86 Moving to Node #0,3,0 Current State: 38:[1, 38], Operations: ['98/2=49', '49-11=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[1, 98, 2, 11], Operations: [] Exploring Operation: 98/2=49, Resulting Numbers: [1, 11, 49] Generated Node #0,3: 38:[1, 11, 49] Operation: 98/2=49 Moving to Node #0,3 Current State: 38:[1, 11, 49], Operations: ['98/2=49'] Exploring Operation: 49-11=38, Resulting Numbers: [1, 38] Generated Node #0,3,0: 38:[1, 38] Operation: 49-11=38 Moving to Node #0,3,0 Current State: 38:[1, 38], Operations: ['98/2=49', '49-11=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.954861
hs_4
sum_heuristic
[ 43, 43, 65, 79 ]
72
[ "43+43=86", "79-65=14", "86-14=72" ]
Current State: 72:[43, 43, 65, 79], Operations: [] Exploring Operation: 43+43=86, Resulting Numbers: [65, 79, 86] Generated Node #2: [65, 79, 86] from Operation: 43+43=86 Current State: 72:[65, 79, 86], Operations: ['43+43=86'] Exploring Operation: 79-65=14, Resulting Numbers: [86, 14] Generated Node #3: [86, 14] from Operation: 79-65=14 Current State: 72:[86, 14], Operations: ['43+43=86', '79-65=14'] Exploring Operation: 86-14=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[43, 43, 65, 79], Operations: [] Exploring Operation: 43/43=1, Resulting Numbers: [65, 79, 1] Generated Node #0,0: 72:[65, 79, 1] Operation: 43/43=1 Exploring Operation: 79-43=36, Resulting Numbers: [43, 65, 36] Generated Node #0,1: 72:[43, 65, 36] Operation: 79-43=36 Exploring Operation: 43-43=0, Resulting Numbers: [65, 79, 0] Generated Node #0,2: 72:[65, 79, 0] Operation: 43-43=0 Exploring Operation: 79-43=36, Resulting Numbers: [43, 65, 36] Generated Node #0,3: 72:[43, 65, 36] Operation: 79-43=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[43, 65, 36], Operations: ['79-43=36'] Exploring Operation: 65-43=22, Resulting Numbers: [36, 22] Generated Node #0,1,0: 72:[36, 22] Operation: 65-43=22 Exploring Operation: 43-36=7, Resulting Numbers: [65, 7] Generated Node #0,1,1: 72:[65, 7] Operation: 43-36=7 Exploring Operation: 43+36=79, Resulting Numbers: [65, 79] Generated Node #0,1,2: 72:[65, 79] Operation: 43+36=79 Exploring Operation: 65-36=29, Resulting Numbers: [43, 29] Generated Node #0,1,3: 72:[43, 29] Operation: 65-36=29 Moving to Node #0,1,0 Current State: 72:[36, 22], Operations: ['79-43=36', '65-43=22'] Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,72 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[65, 7], Operations: ['79-43=36', '43-36=7'] Exploring Operation: 65*7=455, Resulting Numbers: [455] 455,72 unequal: No Solution Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[43, 43, 65, 79], Operations: [] Exploring Operation: 79-43=36, Resulting Numbers: [43, 65, 36] Generated Node #0,1: 72:[43, 65, 36] Operation: 79-43=36 Moving to Node #0,1 Current State: 72:[43, 65, 36], Operations: ['79-43=36'] Exploring Operation: 43-36=7, Resulting Numbers: [65, 7] Generated Node #0,1,1: 72:[65, 7] Operation: 43-36=7 Moving to Node #0,1,1 Current State: 72:[65, 7], Operations: ['79-43=36', '43-36=7'] Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 59, 8, 17, 56 ]
16
[ "17*56=952", "952-8=944", "944/59=16" ]
Current State: 16:[59, 8, 17, 56], Operations: [] Exploring Operation: 17*56=952, Resulting Numbers: [59, 8, 952] Generated Node #2: [59, 8, 952] from Operation: 17*56=952 Current State: 16:[59, 8, 952], Operations: ['17*56=952'] Exploring Operation: 952-8=944, Resulting Numbers: [59, 944] Generated Node #3: [59, 944] from Operation: 952-8=944 Current State: 16:[59, 944], Operations: ['17*56=952', '952-8=944'] Exploring Operation: 944/59=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[59, 8, 17, 56], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [8, 17, 3] Generated Node #0,0: 16:[8, 17, 3] Operation: 59-56=3 Moving to Node #0,0 Current State: 16:[8, 17, 3], Operations: ['59-56=3'] Exploring Operation: 17-8=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 16:[3, 9] Operation: 17-8=9 Moving to Node #0,0,0 Current State: 16:[3, 9], Operations: ['59-56=3', '17-8=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,16 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 36, 20, 90, 27 ]
18
[ "36+90=126", "27-20=7", "126/7=18" ]
Current State: 18:[36, 20, 90, 27], Operations: [] Exploring Operation: 36+90=126, Resulting Numbers: [20, 27, 126] Generated Node #2: [20, 27, 126] from Operation: 36+90=126 Current State: 18:[20, 27, 126], Operations: ['36+90=126'] Exploring Operation: 27-20=7, Resulting Numbers: [126, 7] Generated Node #3: [126, 7] from Operation: 27-20=7 Current State: 18:[126, 7], Operations: ['36+90=126', '27-20=7'] Exploring Operation: 126/7=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[36, 20, 90, 27], Operations: [] Exploring Operation: 90-27=63, Resulting Numbers: [36, 20, 63] Generated Node #0,0: 18:[36, 20, 63] Operation: 90-27=63 Exploring Operation: 36-20=16, Resulting Numbers: [90, 27, 16] Generated Node #0,1: 18:[90, 27, 16] Operation: 36-20=16 Exploring Operation: 36-27=9, Resulting Numbers: [20, 90, 9] Generated Node #0,2: 18:[20, 90, 9] Operation: 36-27=9 Exploring Operation: 90-36=54, Resulting Numbers: [20, 27, 54] Generated Node #0,3: 18:[20, 27, 54] Operation: 90-36=54 Exploring Operation: 90-20=70, Resulting Numbers: [36, 27, 70] Generated Node #0,4: 18:[36, 27, 70] Operation: 90-20=70 Moving to Node #0,3 Current State: 18:[20, 27, 54], Operations: ['90-36=54'] Exploring Operation: 54-20=34, Resulting Numbers: [27, 34] Generated Node #0,3,0: 18:[27, 34] Operation: 54-20=34 Exploring Operation: 54-27=27, Resulting Numbers: [20, 27] Generated Node #0,3,1: 18:[20, 27] Operation: 54-27=27 Exploring Operation: 27-20=7, Resulting Numbers: [54, 7] Generated Node #0,3,2: 18:[54, 7] Operation: 27-20=7 Exploring Operation: 20+27=47, Resulting Numbers: [54, 47] Generated Node #0,3,3: 18:[54, 47] Operation: 20+27=47 Exploring Operation: 54/27=2, Resulting Numbers: [20, 2] Generated Node #0,3,4: 18:[20, 2] Operation: 54/27=2 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 18:[20, 2], Operations: ['90-36=54', '54/27=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[36, 20, 90, 27], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [20, 27, 54] Generated Node #0,3: 18:[20, 27, 54] Operation: 90-36=54 Moving to Node #0,3 Current State: 18:[20, 27, 54], Operations: ['90-36=54'] Exploring Operation: 54/27=2, Resulting Numbers: [20, 2] Generated Node #0,3,4: 18:[20, 2] Operation: 54/27=2 Moving to Node #0,3,4 Current State: 18:[20, 2], Operations: ['90-36=54', '54/27=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 92, 11, 45, 45 ]
11
[ "45-45=0", "92*0=0", "11+0=11" ]
Current State: 11:[92, 11, 45, 45], Operations: [] Exploring Operation: 45-45=0, Resulting Numbers: [92, 11, 0] Generated Node #2: [92, 11, 0] from Operation: 45-45=0 Current State: 11:[92, 11, 0], Operations: ['45-45=0'] Exploring Operation: 92*0=0, Resulting Numbers: [11, 0] Generated Node #3: [11, 0] from Operation: 92*0=0 Current State: 11:[11, 0], Operations: ['45-45=0', '92*0=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[92, 11, 45, 45], Operations: [] Exploring Operation: 92-45=47, Resulting Numbers: [11, 45, 47] Generated Node #0,0: 11:[11, 45, 47] Operation: 92-45=47 Exploring Operation: 92-45=47, Resulting Numbers: [11, 45, 47] Generated Node #0,1: 11:[11, 45, 47] Operation: 92-45=47 Exploring Operation: 45/45=1, Resulting Numbers: [92, 11, 1] Generated Node #0,2: 11:[92, 11, 1] Operation: 45/45=1 Moving to Node #0,0 Current State: 11:[11, 45, 47], Operations: ['92-45=47'] Exploring Operation: 45-11=34, Resulting Numbers: [47, 34] Generated Node #0,0,0: 11:[47, 34] Operation: 45-11=34 Exploring Operation: 47-11=36, Resulting Numbers: [45, 36] Generated Node #0,0,1: 11:[45, 36] Operation: 47-11=36 Exploring Operation: 47-45=2, Resulting Numbers: [11, 2] Generated Node #0,0,2: 11:[11, 2] Operation: 47-45=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[11, 2], Operations: ['92-45=47', '47-45=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[47, 34], Operations: ['92-45=47', '45-11=34'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[45, 36], Operations: ['92-45=47', '47-11=36'] Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 45*36=1620, Resulting Numbers: [1620] 1620,11 unequal: No Solution Exploring Operation: 45+36=81, Resulting Numbers: [81] 81,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 11:[11, 45, 47], Operations: ['92-45=47'] Exploring Operation: 47-11=36, Resulting Numbers: [45, 36] Generated Node #0,1,0: 11:[45, 36] Operation: 47-11=36 Exploring Operation: 47-45=2, Resulting Numbers: [11, 2] Generated Node #0,1,1: 11:[11, 2] Operation: 47-45=2 Exploring Operation: 45-11=34, Resulting Numbers: [47, 34] Generated Node #0,1,2: 11:[47, 34] Operation: 45-11=34 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[11, 2], Operations: ['92-45=47', '47-45=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[45, 36], Operations: ['92-45=47', '47-11=36'] Exploring Operation: 45+36=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 45*36=1620, Resulting Numbers: [1620] 1620,11 unequal: No Solution Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[47, 34], Operations: ['92-45=47', '45-11=34'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,11 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,11 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: 11:[92, 11, 1], Operations: ['45/45=1'] Exploring Operation: 92-1=91, Resulting Numbers: [11, 91] Generated Node #0,2,0: 11:[11, 91] Operation: 92-1=91 Exploring Operation: 92*1=92, Resulting Numbers: [11, 92] Generated Node #0,2,1: 11:[11, 92] Operation: 92*1=92 Exploring Operation: 92-11=81, Resulting Numbers: [1, 81] Generated Node #0,2,2: 11:[1, 81] Operation: 92-11=81 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[11, 91], Operations: ['45/45=1', '92-1=91'] Exploring Operation: 91-11=80, Resulting Numbers: [80] 80,11 unequal: No Solution Exploring Operation: 11*91=1001, Resulting Numbers: [1001] 1001,11 unequal: No Solution Exploring Operation: 11+91=102, Resulting Numbers: [102] 102,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[1, 81], Operations: ['45/45=1', '92-11=81'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,11 unequal: No Solution Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[11, 92], Operations: ['45/45=1', '92*1=92'] Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,11 unequal: No Solution Exploring Operation: 11*92=1012, Resulting Numbers: [1012] 1012,11 unequal: No Solution Exploring Operation: 11+92=103, Resulting Numbers: [103] 103,11 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
[ 36, 13, 30, 7 ]
26
[ "36+13=49", "30-7=23", "49-23=26" ]
Current State: 26:[36, 13, 30, 7], Operations: [] Exploring Operation: 36+13=49, Resulting Numbers: [30, 7, 49] Generated Node #2: [30, 7, 49] from Operation: 36+13=49 Current State: 26:[30, 7, 49], Operations: ['36+13=49'] Exploring Operation: 30-7=23, Resulting Numbers: [49, 23] Generated Node #3: [49, 23] from Operation: 30-7=23 Current State: 26:[49, 23], Operations: ['36+13=49', '30-7=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[36, 13, 30, 7], Operations: [] Exploring Operation: 36-13=23, Resulting Numbers: [30, 7, 23] Generated Node #0,0: 26:[30, 7, 23] Operation: 36-13=23 Exploring Operation: 36-30=6, Resulting Numbers: [13, 7, 6] Generated Node #0,1: 26:[13, 7, 6] Operation: 36-30=6 Exploring Operation: 36-7=29, Resulting Numbers: [13, 30, 29] Generated Node #0,2: 26:[13, 30, 29] Operation: 36-7=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[13, 30, 29], Operations: ['36-7=29'] Exploring Operation: 30-13=17, Resulting Numbers: [29, 17] Generated Node #0,2,0: 26:[29, 17] Operation: 30-13=17 Exploring Operation: 29-13=16, Resulting Numbers: [30, 16] Generated Node #0,2,1: 26:[30, 16] Operation: 29-13=16 Exploring Operation: 30-29=1, Resulting Numbers: [13, 1] Generated Node #0,2,2: 26:[13, 1] Operation: 30-29=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 26:[13, 1], Operations: ['36-7=29', '30-29=1'] Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,26 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,26 unequal: No Solution No 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: 26:[29, 17], Operations: ['36-7=29', '30-13=17'] Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,26 unequal: No Solution No 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: 26:[30, 16], Operations: ['36-7=29', '29-13=16'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,26 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: 26:[13, 7, 6], Operations: ['36-30=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13, 13] Generated Node #0,1,0: 26:[13, 13] Operation: 7+6=13 Exploring Operation: 13-7=6, Resulting Numbers: [6, 6] Generated Node #0,1,1: 26:[6, 6] Operation: 13-7=6 Exploring Operation: 7-6=1, Resulting Numbers: [13, 1] Generated Node #0,1,2: 26:[13, 1] Operation: 7-6=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 26:[13, 13], Operations: ['36-30=6', '7+6=13'] Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[36, 13, 30, 7], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [13, 7, 6] Generated Node #0,1: 26:[13, 7, 6] Operation: 36-30=6 Moving to Node #0,1 Current State: 26:[13, 7, 6], Operations: ['36-30=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13, 13] Generated Node #0,1,0: 26:[13, 13] Operation: 7+6=13 Moving to Node #0,1,0 Current State: 26:[13, 13], Operations: ['36-30=6', '7+6=13'] Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 92, 53, 6, 13 ]
46
[ "92-53=39", "13-6=7", "39+7=46" ]
Current State: 46:[92, 53, 6, 13], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [6, 13, 39] Generated Node #2: [6, 13, 39] from Operation: 92-53=39 Current State: 46:[6, 13, 39], Operations: ['92-53=39'] Exploring Operation: 13-6=7, Resulting Numbers: [39, 7] Generated Node #3: [39, 7] from Operation: 13-6=7 Current State: 46:[39, 7], Operations: ['92-53=39', '13-6=7'] Exploring Operation: 39+7=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[92, 53, 6, 13], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [6, 13, 39] Generated Node #0,0: 46:[6, 13, 39] Operation: 92-53=39 Moving to Node #0,0 Current State: 46:[6, 13, 39], Operations: ['92-53=39'] Exploring Operation: 39/13=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 46:[6, 3] Operation: 39/13=3 Moving to Node #0,0,0 Current State: 46:[6, 3], Operations: ['92-53=39', '39/13=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,46 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 5, 5, 51, 21 ]
47
[ "5*5=25", "51+21=72", "72-25=47" ]
Current State: 47:[5, 5, 51, 21], Operations: [] Exploring Operation: 5*5=25, Resulting Numbers: [51, 21, 25] Generated Node #2: [51, 21, 25] from Operation: 5*5=25 Current State: 47:[51, 21, 25], Operations: ['5*5=25'] Exploring Operation: 51+21=72, Resulting Numbers: [25, 72] Generated Node #3: [25, 72] from Operation: 51+21=72 Current State: 47:[25, 72], Operations: ['5*5=25', '51+21=72'] Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[5, 5, 51, 21], Operations: [] Exploring Operation: 51-5=46, Resulting Numbers: [5, 21, 46] Generated Node #0,0: 47:[5, 21, 46] Operation: 51-5=46 Exploring Operation: 5+21=26, Resulting Numbers: [5, 51, 26] Generated Node #0,1: 47:[5, 51, 26] Operation: 5+21=26 Exploring Operation: 5+5=10, Resulting Numbers: [51, 21, 10] Generated Node #0,2: 47:[51, 21, 10] Operation: 5+5=10 Exploring Operation: 5+21=26, Resulting Numbers: [5, 51, 26] Generated Node #0,3: 47:[5, 51, 26] Operation: 5+21=26 Exploring Operation: 5*5=25, Resulting Numbers: [51, 21, 25] Generated Node #0,4: 47:[51, 21, 25] Operation: 5*5=25 Moving to Node #0,4 Current State: 47:[51, 21, 25], Operations: ['5*5=25'] Exploring Operation: 51-25=26, Resulting Numbers: [21, 26] Generated Node #0,4,0: 47:[21, 26] Operation: 51-25=26 Exploring Operation: 51-21=30, Resulting Numbers: [25, 30] Generated Node #0,4,1: 47:[25, 30] Operation: 51-21=30 Exploring Operation: 51+21=72, Resulting Numbers: [25, 72] Generated Node #0,4,2: 47:[25, 72] Operation: 51+21=72 Exploring Operation: 25-21=4, Resulting Numbers: [51, 4] Generated Node #0,4,3: 47:[51, 4] Operation: 25-21=4 Exploring Operation: 21+25=46, Resulting Numbers: [51, 46] Generated Node #0,4,4: 47:[51, 46] Operation: 21+25=46 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 47:[51, 46], Operations: ['5*5=25', '21+25=46'] Exploring Operation: 51+46=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 51*46=2346, Resulting Numbers: [2346] 2346,47 unequal: No Solution Exploring Operation: 51-46=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 47:[25, 30], Operations: ['5*5=25', '51-21=30'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,47 unequal: No Solution Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 47:[21, 26], Operations: ['5*5=25', '51-25=26'] Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,47 unequal: No Solution Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[5, 5, 51, 21], Operations: [] Exploring Operation: 5*5=25, Resulting Numbers: [51, 21, 25] Generated Node #0,4: 47:[51, 21, 25] Operation: 5*5=25 Moving to Node #0,4 Current State: 47:[51, 21, 25], Operations: ['5*5=25'] Exploring Operation: 51-25=26, Resulting Numbers: [21, 26] Generated Node #0,4,0: 47:[21, 26] Operation: 51-25=26 Moving to Node #0,4,0 Current State: 47:[21, 26], Operations: ['5*5=25', '51-25=26'] Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 97, 71, 73, 18 ]
81
[ "97-71=26", "73-18=55", "26+55=81" ]
Current State: 81:[97, 71, 73, 18], Operations: [] Exploring Operation: 97-71=26, Resulting Numbers: [73, 18, 26] Generated Node #2: [73, 18, 26] from Operation: 97-71=26 Current State: 81:[73, 18, 26], Operations: ['97-71=26'] Exploring Operation: 73-18=55, Resulting Numbers: [26, 55] Generated Node #3: [26, 55] from Operation: 73-18=55 Current State: 81:[26, 55], Operations: ['97-71=26', '73-18=55'] Exploring Operation: 26+55=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[97, 71, 73, 18], Operations: [] Exploring Operation: 97-71=26, Resulting Numbers: [73, 18, 26] Generated Node #0,0: 81:[73, 18, 26] Operation: 97-71=26 Exploring Operation: 97-18=79, Resulting Numbers: [71, 73, 79] Generated Node #0,1: 81:[71, 73, 79] Operation: 97-18=79 Exploring Operation: 73-71=2, Resulting Numbers: [97, 18, 2] Generated Node #0,2: 81:[97, 18, 2] Operation: 73-71=2 Exploring Operation: 97-73=24, Resulting Numbers: [71, 18, 24] Generated Node #0,3: 81:[71, 18, 24] Operation: 97-73=24 Moving to Node #0,0 Current State: 81:[73, 18, 26], Operations: ['97-71=26'] Exploring Operation: 73-18=55, Resulting Numbers: [26, 55] Generated Node #0,0,0: 81:[26, 55] Operation: 73-18=55 Exploring Operation: 18+26=44, Resulting Numbers: [73, 44] Generated Node #0,0,1: 81:[73, 44] Operation: 18+26=44 Exploring Operation: 26-18=8, Resulting Numbers: [73, 8] Generated Node #0,0,2: 81:[73, 8] Operation: 26-18=8 Exploring Operation: 73+18=91, Resulting Numbers: [26, 91] Generated Node #0,0,3: 81:[26, 91] Operation: 73+18=91 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 81:[73, 8], Operations: ['97-71=26', '26-18=8'] Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[97, 71, 73, 18], Operations: [] Exploring Operation: 97-71=26, Resulting Numbers: [73, 18, 26] Generated Node #0,0: 81:[73, 18, 26] Operation: 97-71=26 Moving to Node #0,0 Current State: 81:[73, 18, 26], Operations: ['97-71=26'] Exploring Operation: 26-18=8, Resulting Numbers: [73, 8] Generated Node #0,0,2: 81:[73, 8] Operation: 26-18=8 Moving to Node #0,0,2 Current State: 81:[73, 8], Operations: ['97-71=26', '26-18=8'] Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 98, 2, 52, 46 ]
98
[ "98*2=196", "52+46=98", "196-98=98" ]
Current State: 98:[98, 2, 52, 46], Operations: [] Exploring Operation: 98*2=196, Resulting Numbers: [52, 46, 196] Generated Node #2: [52, 46, 196] from Operation: 98*2=196 Current State: 98:[52, 46, 196], Operations: ['98*2=196'] Exploring Operation: 52+46=98, Resulting Numbers: [196, 98] Generated Node #3: [196, 98] from Operation: 52+46=98 Current State: 98:[196, 98], Operations: ['98*2=196', '52+46=98'] Exploring Operation: 196-98=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[98, 2, 52, 46], Operations: [] Exploring Operation: 52-2=50, Resulting Numbers: [98, 46, 50] Generated Node #0,0: 98:[98, 46, 50] Operation: 52-2=50 Exploring Operation: 52-46=6, Resulting Numbers: [98, 2, 6] Generated Node #0,1: 98:[98, 2, 6] Operation: 52-46=6 Exploring Operation: 52+46=98, Resulting Numbers: [98, 2, 98] Generated Node #0,2: 98:[98, 2, 98] Operation: 52+46=98 Moving to Node #0,2 Current State: 98:[98, 2, 98], Operations: ['52+46=98'] Exploring Operation: 98/2=49, Resulting Numbers: [98, 49] Generated Node #0,2,0: 98:[98, 49] Operation: 98/2=49 Exploring Operation: 98/98=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 98:[2, 1] Operation: 98/98=1 Exploring Operation: 98/2=49, Resulting Numbers: [98, 49] Generated Node #0,2,2: 98:[98, 49] Operation: 98/2=49 Moving to Node #0,1 Current State: 98:[98, 2, 6], Operations: ['52-46=6'] Exploring Operation: 6/2=3, Resulting Numbers: [98, 3] Generated Node #0,1,0: 98:[98, 3] Operation: 6/2=3 Exploring Operation: 98/2=49, Resulting Numbers: [6, 49] Generated Node #0,1,1: 98:[6, 49] Operation: 98/2=49 Exploring Operation: 2+6=8, Resulting Numbers: [98, 8] Generated Node #0,1,2: 98:[98, 8] Operation: 2+6=8 Moving to Node #0,0 Current State: 98:[98, 46, 50], Operations: ['52-2=50'] Exploring Operation: 98-46=52, Resulting Numbers: [50, 52] Generated Node #0,0,0: 98:[50, 52] Operation: 98-46=52 Exploring Operation: 50-46=4, Resulting Numbers: [98, 4] Generated Node #0,0,1: 98:[98, 4] Operation: 50-46=4 Exploring Operation: 46+50=96, Resulting Numbers: [98, 96] Generated Node #0,0,2: 98:[98, 96] Operation: 46+50=96 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 98:[98, 4], Operations: ['52-2=50', '50-46=4'] Exploring Operation: 98-4=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 98+4=102, Resulting Numbers: [102] 102,98 unequal: No Solution Exploring Operation: 98*4=392, Resulting Numbers: [392] 392,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 98:[98, 96], Operations: ['52-2=50', '46+50=96'] Exploring Operation: 98*96=9408, Resulting Numbers: [9408] 9408,98 unequal: No Solution Exploring Operation: 98-96=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 98+96=194, Resulting Numbers: [194] 194,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[50, 52], Operations: ['52-2=50', '98-46=52'] Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,98 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,98 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: 98:[98, 49], Operations: ['52+46=98', '98/2=49'] Exploring Operation: 98/49=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 98+49=147, Resulting Numbers: [147] 147,98 unequal: No Solution Exploring Operation: 98-49=49, Resulting Numbers: [49] 49,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[98, 49], Operations: ['52+46=98', '98/2=49'] Exploring Operation: 98-49=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 98/49=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 98+49=147, Resulting Numbers: [147] 147,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[2, 1], Operations: ['52+46=98', '98/98=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,98 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[98, 8], Operations: ['52-46=6', '2+6=8'] Exploring Operation: 98*8=784, Resulting Numbers: [784] 784,98 unequal: No Solution Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,98 unequal: No Solution Exploring Operation: 98+8=106, Resulting Numbers: [106] 106,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[6, 49], Operations: ['52-46=6', '98/2=49'] Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,98 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[98, 3], Operations: ['52-46=6', '6/2=3'] Exploring Operation: 98+3=101, Resulting Numbers: [101] 101,98 unequal: No Solution Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,98 unequal: No Solution Exploring Operation: 98*3=294, Resulting Numbers: [294] 294,98 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 70, 75, 55, 35 ]
55
[ "70+75=145", "55+35=90", "145-90=55" ]
Current State: 55:[70, 75, 55, 35], Operations: [] Exploring Operation: 70+75=145, Resulting Numbers: [55, 35, 145] Generated Node #2: [55, 35, 145] from Operation: 70+75=145 Current State: 55:[55, 35, 145], Operations: ['70+75=145'] Exploring Operation: 55+35=90, Resulting Numbers: [145, 90] Generated Node #3: [145, 90] from Operation: 55+35=90 Current State: 55:[145, 90], Operations: ['70+75=145', '55+35=90'] Exploring Operation: 145-90=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[70, 75, 55, 35], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [55, 35, 5] Generated Node #0,0: 55:[55, 35, 5] Operation: 75-70=5 Exploring Operation: 70-35=35, Resulting Numbers: [75, 55, 35] Generated Node #0,1: 55:[75, 55, 35] Operation: 70-35=35 Exploring Operation: 70/35=2, Resulting Numbers: [75, 55, 2] Generated Node #0,2: 55:[75, 55, 2] Operation: 70/35=2 Exploring Operation: 75-35=40, Resulting Numbers: [70, 55, 40] Generated Node #0,3: 55:[70, 55, 40] Operation: 75-35=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[55, 35, 5], Operations: ['75-70=5'] Exploring Operation: 35+5=40, Resulting Numbers: [55, 40] Generated Node #0,0,0: 55:[55, 40] Operation: 35+5=40 Exploring Operation: 35/5=7, Resulting Numbers: [55, 7] Generated Node #0,0,1: 55:[55, 7] Operation: 35/5=7 Exploring Operation: 35-5=30, Resulting Numbers: [55, 30] Generated Node #0,0,2: 55:[55, 30] Operation: 35-5=30 Exploring Operation: 55-35=20, Resulting Numbers: [5, 20] Generated Node #0,0,3: 55:[5, 20] Operation: 55-35=20 Moving to Node #0,0,1 Current State: 55:[55, 7], Operations: ['75-70=5', '35/5=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,55 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,55 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,55 unequal: No Solution Moving to Node #0,0,3 Current State: 55:[5, 20], Operations: ['75-70=5', '55-35=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,55 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,55 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[55, 40], Operations: ['75-70=5', '35+5=40'] Exploring Operation: 55+40=95, Resulting Numbers: [95] 95,55 unequal: No Solution Exploring Operation: 55-40=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 55*40=2200, Resulting Numbers: [2200] 2200,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[55, 30], Operations: ['75-70=5', '35-5=30'] Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,55 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,55 unequal: No Solution Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[75, 55, 2], Operations: ['70/35=2'] Exploring Operation: 75+2=77, Resulting Numbers: [55, 77] Generated Node #0,2,0: 55:[55, 77] Operation: 75+2=77 Exploring Operation: 75-2=73, Resulting Numbers: [55, 73] Generated Node #0,2,1: 55:[55, 73] Operation: 75-2=73 Exploring Operation: 55+2=57, Resulting Numbers: [75, 57] Generated Node #0,2,2: 55:[75, 57] Operation: 55+2=57 Exploring Operation: 75-55=20, Resulting Numbers: [2, 20] Generated Node #0,2,3: 55:[2, 20] Operation: 75-55=20 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[2, 20], Operations: ['70/35=2', '75-55=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,55 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,55 unequal: No Solution No 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: 55:[55, 73], Operations: ['70/35=2', '75-2=73'] Exploring Operation: 55*73=4015, Resulting Numbers: [4015] 4015,55 unequal: No Solution Exploring Operation: 55+73=128, Resulting Numbers: [128] 128,55 unequal: No Solution Exploring Operation: 73-55=18, Resulting Numbers: [18] 18,55 unequal: No Solution No 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: 55:[55, 77], Operations: ['70/35=2', '75+2=77'] Exploring Operation: 77-55=22, Resulting Numbers: [22] 22,55 unequal: No Solution Exploring Operation: 55*77=4235, Resulting Numbers: [4235] 4235,55 unequal: No Solution Exploring Operation: 55+77=132, Resulting Numbers: [132] 132,55 unequal: No Solution No 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: 55:[75, 57], Operations: ['70/35=2', '55+2=57'] Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,55 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,55 unequal: No Solution Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,55 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: 55:[70, 55, 40], Operations: ['75-35=40'] Exploring Operation: 55-40=15, Resulting Numbers: [70, 15] Generated Node #0,3,0: 55:[70, 15] Operation: 55-40=15 Exploring Operation: 70-55=15, Resulting Numbers: [40, 15] Generated Node #0,3,1: 55:[40, 15] Operation: 70-55=15 Exploring Operation: 70+40=110, Resulting Numbers: [55, 110] Generated Node #0,3,2: 55:[55, 110] Operation: 70+40=110 Exploring Operation: 70-40=30, Resulting Numbers: [55, 30] Generated Node #0,3,3: 55:[55, 30] Operation: 70-40=30 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[70, 15], Operations: ['75-35=40', '55-40=15'] Exploring Operation: 70+15=85, Resulting Numbers: [85] 85,55 unequal: No Solution Exploring Operation: 70*15=1050, Resulting Numbers: [1050] 1050,55 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[70, 75, 55, 35], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [70, 55, 40] Generated Node #0,3: 55:[70, 55, 40] Operation: 75-35=40 Moving to Node #0,3 Current State: 55:[70, 55, 40], Operations: ['75-35=40'] Exploring Operation: 55-40=15, Resulting Numbers: [70, 15] Generated Node #0,3,0: 55:[70, 15] Operation: 55-40=15 Moving to Node #0,3,0 Current State: 55:[70, 15], Operations: ['75-35=40', '55-40=15'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 4, 76, 32, 61 ]
10
[ "76/4=19", "61-32=29", "29-19=10" ]
Current State: 10:[4, 76, 32, 61], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [32, 61, 19] Generated Node #2: [32, 61, 19] from Operation: 76/4=19 Current State: 10:[32, 61, 19], Operations: ['76/4=19'] Exploring Operation: 61-32=29, Resulting Numbers: [19, 29] Generated Node #3: [19, 29] from Operation: 61-32=29 Current State: 10:[19, 29], Operations: ['76/4=19', '61-32=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[4, 76, 32, 61], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [32, 61, 19] Generated Node #0,0: 10:[32, 61, 19] Operation: 76/4=19 Exploring Operation: 76-61=15, Resulting Numbers: [4, 32, 15] Generated Node #0,1: 10:[4, 32, 15] Operation: 76-61=15 Exploring Operation: 76-32=44, Resulting Numbers: [4, 61, 44] Generated Node #0,2: 10:[4, 61, 44] Operation: 76-32=44 Moving to Node #0,1 Current State: 10:[4, 32, 15], Operations: ['76-61=15'] Exploring Operation: 32/4=8, Resulting Numbers: [15, 8] Generated Node #0,1,0: 10:[15, 8] Operation: 32/4=8 Exploring Operation: 32-15=17, Resulting Numbers: [4, 17] Generated Node #0,1,1: 10:[4, 17] Operation: 32-15=17 Exploring Operation: 32-4=28, Resulting Numbers: [15, 28] Generated Node #0,1,2: 10:[15, 28] Operation: 32-4=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[15, 8], Operations: ['76-61=15', '32/4=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,10 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,10 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,10 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 #0,1,1 Current State: 10:[4, 17], Operations: ['76-61=15', '32-15=17'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,10 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,10 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 #0,1,2 Current State: 10:[15, 28], Operations: ['76-61=15', '32-4=28'] Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,10 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,10 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,10 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:[32, 61, 19], Operations: ['76/4=19'] Exploring Operation: 32-19=13, Resulting Numbers: [61, 13] Generated Node #0,0,0: 10:[61, 13] Operation: 32-19=13 Exploring Operation: 61-19=42, Resulting Numbers: [32, 42] Generated Node #0,0,1: 10:[32, 42] Operation: 61-19=42 Exploring Operation: 61-32=29, Resulting Numbers: [19, 29] Generated Node #0,0,2: 10:[19, 29] Operation: 61-32=29 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[19, 29], Operations: ['76/4=19', '61-32=29'] Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[4, 76, 32, 61], Operations: [] Exploring Operation: 76/4=19, Resulting Numbers: [32, 61, 19] Generated Node #0,0: 10:[32, 61, 19] Operation: 76/4=19 Moving to Node #0,0 Current State: 10:[32, 61, 19], Operations: ['76/4=19'] Exploring Operation: 61-32=29, Resulting Numbers: [19, 29] Generated Node #0,0,2: 10:[19, 29] Operation: 61-32=29 Moving to Node #0,0,2 Current State: 10:[19, 29], Operations: ['76/4=19', '61-32=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 88, 28, 12, 75 ]
80
[ "88-28=60", "60/12=5", "75+5=80" ]
Current State: 80:[88, 28, 12, 75], Operations: [] Exploring Operation: 88-28=60, Resulting Numbers: [12, 75, 60] Generated Node #2: [12, 75, 60] from Operation: 88-28=60 Current State: 80:[12, 75, 60], Operations: ['88-28=60'] Exploring Operation: 60/12=5, Resulting Numbers: [75, 5] Generated Node #3: [75, 5] from Operation: 60/12=5 Current State: 80:[75, 5], Operations: ['88-28=60', '60/12=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[88, 28, 12, 75], Operations: [] Exploring Operation: 88-75=13, Resulting Numbers: [28, 12, 13] Generated Node #0,0: 80:[28, 12, 13] Operation: 88-75=13 Exploring Operation: 28+12=40, Resulting Numbers: [88, 75, 40] Generated Node #0,1: 80:[88, 75, 40] Operation: 28+12=40 Moving to Node #0,0 Current State: 80:[28, 12, 13], Operations: ['88-75=13'] Exploring Operation: 28+12=40, Resulting Numbers: [13, 40] Generated Node #0,0,0: 80:[13, 40] Operation: 28+12=40 Exploring Operation: 28-12=16, Resulting Numbers: [13, 16] Generated Node #0,0,1: 80:[13, 16] Operation: 28-12=16 Moving to Node #0,1 Current State: 80:[88, 75, 40], Operations: ['28+12=40'] Exploring Operation: 88-40=48, Resulting Numbers: [75, 48] Generated Node #0,1,0: 80:[75, 48] Operation: 88-40=48 Exploring Operation: 88-75=13, Resulting Numbers: [40, 13] Generated Node #0,1,1: 80:[40, 13] Operation: 88-75=13 Moving to Node #0,0,0 Current State: 80:[13, 40], Operations: ['88-75=13', '28+12=40'] Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,80 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[40, 13], Operations: ['28+12=40', '88-75=13'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[13, 16], Operations: ['88-75=13', '28-12=16'] Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[75, 48], Operations: ['28+12=40', '88-40=48'] Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 75+48=123, Resulting Numbers: [123] 123,80 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 24, 25, 52, 86 ]
34
[ "25-24=1", "86-52=34", "1*34=34" ]
Current State: 34:[24, 25, 52, 86], Operations: [] Exploring Operation: 25-24=1, Resulting Numbers: [52, 86, 1] Generated Node #2: [52, 86, 1] from Operation: 25-24=1 Current State: 34:[52, 86, 1], Operations: ['25-24=1'] Exploring Operation: 86-52=34, Resulting Numbers: [1, 34] Generated Node #3: [1, 34] from Operation: 86-52=34 Current State: 34:[1, 34], Operations: ['25-24=1', '86-52=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[24, 25, 52, 86], Operations: [] Exploring Operation: 86-25=61, Resulting Numbers: [24, 52, 61] Generated Node #0,0: 34:[24, 52, 61] Operation: 86-25=61 Exploring Operation: 86-24=62, Resulting Numbers: [25, 52, 62] Generated Node #0,1: 34:[25, 52, 62] Operation: 86-24=62 Exploring Operation: 52-24=28, Resulting Numbers: [25, 86, 28] Generated Node #0,2: 34:[25, 86, 28] Operation: 52-24=28 Exploring Operation: 86-52=34, Resulting Numbers: [24, 25, 34] Generated Node #0,3: 34:[24, 25, 34] Operation: 86-52=34 Start Sub Search at level 1: Moving to Node #0,3 Current State: 34:[24, 25, 34], Operations: ['86-52=34'] Exploring Operation: 34-24=10, Resulting Numbers: [25, 10] Generated Node #0,3,0: 34:[25, 10] Operation: 34-24=10 Exploring Operation: 24+25=49, Resulting Numbers: [34, 49] Generated Node #0,3,1: 34:[34, 49] Operation: 24+25=49 Exploring Operation: 34-25=9, Resulting Numbers: [24, 9] Generated Node #0,3,2: 34:[24, 9] Operation: 34-25=9 Exploring Operation: 25-24=1, Resulting Numbers: [34, 1] Generated Node #0,3,3: 34:[34, 1] Operation: 25-24=1 Moving to Node #0,3,3 Current State: 34:[34, 1], Operations: ['86-52=34', '25-24=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[24, 25, 52, 86], Operations: [] Exploring Operation: 86-52=34, Resulting Numbers: [24, 25, 34] Generated Node #0,3: 34:[24, 25, 34] Operation: 86-52=34 Moving to Node #0,3 Current State: 34:[24, 25, 34], Operations: ['86-52=34'] Exploring Operation: 25-24=1, Resulting Numbers: [34, 1] Generated Node #0,3,3: 34:[34, 1] Operation: 25-24=1 Moving to Node #0,3,3 Current State: 34:[34, 1], Operations: ['86-52=34', '25-24=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 96, 58, 67, 55 ]
53
[ "96-67=29", "58/29=2", "55-2=53" ]
Current State: 53:[96, 58, 67, 55], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [58, 55, 29] Generated Node #2: [58, 55, 29] from Operation: 96-67=29 Current State: 53:[58, 55, 29], Operations: ['96-67=29'] Exploring Operation: 58/29=2, Resulting Numbers: [55, 2] Generated Node #3: [55, 2] from Operation: 58/29=2 Current State: 53:[55, 2], Operations: ['96-67=29', '58/29=2'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[96, 58, 67, 55], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [67, 55, 38] Generated Node #0,0: 53:[67, 55, 38] Operation: 96-58=38 Exploring Operation: 96-67=29, Resulting Numbers: [58, 55, 29] Generated Node #0,1: 53:[58, 55, 29] Operation: 96-67=29 Exploring Operation: 96-55=41, Resulting Numbers: [58, 67, 41] Generated Node #0,2: 53:[58, 67, 41] Operation: 96-55=41 Moving to Node #0,0 Current State: 53:[67, 55, 38], Operations: ['96-58=38'] Exploring Operation: 67-38=29, Resulting Numbers: [55, 29] Generated Node #0,0,0: 53:[55, 29] Operation: 67-38=29 Exploring Operation: 55-38=17, Resulting Numbers: [67, 17] Generated Node #0,0,1: 53:[67, 17] Operation: 55-38=17 Exploring Operation: 67+38=105, Resulting Numbers: [55, 105] Generated Node #0,0,2: 53:[55, 105] Operation: 67+38=105 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[55, 29], Operations: ['96-58=38', '67-38=29'] Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,53 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,53 unequal: No Solution Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,53 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:[67, 17], Operations: ['96-58=38', '55-38=17'] Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,53 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,53 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:[55, 105], Operations: ['96-58=38', '67+38=105'] Exploring Operation: 55+105=160, Resulting Numbers: [160] 160,53 unequal: No Solution Exploring Operation: 105-55=50, Resulting Numbers: [50] 50,53 unequal: No Solution Exploring Operation: 55*105=5775, Resulting Numbers: [5775] 5775,53 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:[58, 55, 29], Operations: ['96-67=29'] Exploring Operation: 58-29=29, Resulting Numbers: [55, 29] Generated Node #0,1,0: 53:[55, 29] Operation: 58-29=29 Exploring Operation: 58+29=87, Resulting Numbers: [55, 87] Generated Node #0,1,1: 53:[55, 87] Operation: 58+29=87 Exploring Operation: 55-29=26, Resulting Numbers: [58, 26] Generated Node #0,1,2: 53:[58, 26] Operation: 55-29=26 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[55, 29], Operations: ['96-67=29', '58-29=29'] Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,53 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,53 unequal: No Solution Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,53 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:[58, 26], Operations: ['96-67=29', '55-29=26'] Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,53 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,53 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:[55, 87], Operations: ['96-67=29', '58+29=87'] Exploring Operation: 87-55=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 55*87=4785, Resulting Numbers: [4785] 4785,53 unequal: No Solution Exploring Operation: 55+87=142, Resulting Numbers: [142] 142,53 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:[58, 67, 41], Operations: ['96-55=41'] Exploring Operation: 58-41=17, Resulting Numbers: [67, 17] Generated Node #0,2,0: 53:[67, 17] Operation: 58-41=17 Exploring Operation: 67-41=26, Resulting Numbers: [58, 26] Generated Node #0,2,1: 53:[58, 26] Operation: 67-41=26 Exploring Operation: 67-58=9, Resulting Numbers: [41, 9] Generated Node #0,2,2: 53:[41, 9] Operation: 67-58=9 Moving to Node #0,2,1 Current State: 53:[58, 26], Operations: ['96-55=41', '67-41=26'] Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[67, 17], Operations: ['96-55=41', '58-41=17'] Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,53 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,53 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[41, 9], Operations: ['96-55=41', '67-58=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,53 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,53 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,53 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 34, 6, 57, 61 ]
17
[ "6+57=63", "63-61=2", "34/2=17" ]
Current State: 17:[34, 6, 57, 61], Operations: [] Exploring Operation: 6+57=63, Resulting Numbers: [34, 61, 63] Generated Node #2: [34, 61, 63] from Operation: 6+57=63 Current State: 17:[34, 61, 63], Operations: ['6+57=63'] Exploring Operation: 63-61=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 63-61=2 Current State: 17:[34, 2], Operations: ['6+57=63', '63-61=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[34, 6, 57, 61], Operations: [] Exploring Operation: 61-34=27, Resulting Numbers: [6, 57, 27] Generated Node #0,0: 17:[6, 57, 27] Operation: 61-34=27 Exploring Operation: 57-34=23, Resulting Numbers: [6, 61, 23] Generated Node #0,1: 17:[6, 61, 23] Operation: 57-34=23 Exploring Operation: 61-57=4, Resulting Numbers: [34, 6, 4] Generated Node #0,2: 17:[34, 6, 4] Operation: 61-57=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[34, 6, 4], Operations: ['61-57=4'] Exploring Operation: 34-6=28, Resulting Numbers: [4, 28] Generated Node #0,2,0: 17:[4, 28] Operation: 34-6=28 Exploring Operation: 6+4=10, Resulting Numbers: [34, 10] Generated Node #0,2,1: 17:[34, 10] Operation: 6+4=10 Exploring Operation: 34-4=30, Resulting Numbers: [6, 30] Generated Node #0,2,2: 17:[6, 30] Operation: 34-4=30 Moving to Node #0,2,0 Current State: 17:[4, 28], Operations: ['61-57=4', '34-6=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[34, 10], Operations: ['61-57=4', '6+4=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[6, 30], Operations: ['61-57=4', '34-4=30'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,17 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,17 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 #0,0 Current State: 17:[6, 57, 27], Operations: ['61-34=27'] Exploring Operation: 57-27=30, Resulting Numbers: [6, 30] Generated Node #0,0,0: 17:[6, 30] Operation: 57-27=30 Exploring Operation: 27-6=21, Resulting Numbers: [57, 21] Generated Node #0,0,1: 17:[57, 21] Operation: 27-6=21 Exploring Operation: 57-6=51, Resulting Numbers: [27, 51] Generated Node #0,0,2: 17:[27, 51] Operation: 57-6=51 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[6, 30], Operations: ['61-34=27', '57-27=30'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,17 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,17 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 #0,0,1 Current State: 17:[57, 21], Operations: ['61-34=27', '27-6=21'] Exploring Operation: 57*21=1197, Resulting Numbers: [1197] 1197,17 unequal: No Solution Exploring Operation: 57+21=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,17 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 #0,0,2 Current State: 17:[27, 51], Operations: ['61-34=27', '57-6=51'] Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,17 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[6, 61, 23], Operations: ['57-34=23'] Exploring Operation: 61-23=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 17:[6, 38] Operation: 61-23=38 Exploring Operation: 23-6=17, Resulting Numbers: [61, 17] Generated Node #0,1,1: 17:[61, 17] Operation: 23-6=17 Exploring Operation: 61-6=55, Resulting Numbers: [23, 55] Generated Node #0,1,2: 17:[23, 55] Operation: 61-6=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[6, 38], Operations: ['57-34=23', '61-23=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,17 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:[61, 17], Operations: ['57-34=23', '23-6=17'] Exploring Operation: 61*17=1037, Resulting Numbers: [1037] 1037,17 unequal: No Solution Exploring Operation: 61+17=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,17 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 #0,1,2 Current State: 17:[23, 55], Operations: ['57-34=23', '61-6=55'] Exploring Operation: 23+55=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 23*55=1265, Resulting Numbers: [1265] 1265,17 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 8, 97, 29, 93 ]
84
[ "29-8=21", "97-93=4", "21*4=84" ]
Current State: 84:[8, 97, 29, 93], Operations: [] Exploring Operation: 29-8=21, Resulting Numbers: [97, 93, 21] Generated Node #2: [97, 93, 21] from Operation: 29-8=21 Current State: 84:[97, 93, 21], Operations: ['29-8=21'] Exploring Operation: 97-93=4, Resulting Numbers: [21, 4] Generated Node #3: [21, 4] from Operation: 97-93=4 Current State: 84:[21, 4], Operations: ['29-8=21', '97-93=4'] Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[8, 97, 29, 93], Operations: [] Exploring Operation: 97-8=89, Resulting Numbers: [29, 93, 89] Generated Node #0,0: 84:[29, 93, 89] Operation: 97-8=89 Exploring Operation: 97-93=4, Resulting Numbers: [8, 29, 4] Generated Node #0,1: 84:[8, 29, 4] Operation: 97-93=4 Exploring Operation: 93-8=85, Resulting Numbers: [97, 29, 85] Generated Node #0,2: 84:[97, 29, 85] Operation: 93-8=85 Moving to Node #0,1 Current State: 84:[8, 29, 4], Operations: ['97-93=4'] Exploring Operation: 8-4=4, Resulting Numbers: [29, 4] Generated Node #0,1,0: 84:[29, 4] Operation: 8-4=4 Exploring Operation: 8+4=12, Resulting Numbers: [29, 12] Generated Node #0,1,1: 84:[29, 12] Operation: 8+4=12 Exploring Operation: 29-8=21, Resulting Numbers: [4, 21] Generated Node #0,1,2: 84:[4, 21] Operation: 29-8=21 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[4, 21], Operations: ['97-93=4', '29-8=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[8, 97, 29, 93], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [8, 29, 4] Generated Node #0,1: 84:[8, 29, 4] Operation: 97-93=4 Moving to Node #0,1 Current State: 84:[8, 29, 4], Operations: ['97-93=4'] Exploring Operation: 29-8=21, Resulting Numbers: [4, 21] Generated Node #0,1,2: 84:[4, 21] Operation: 29-8=21 Moving to Node #0,1,2 Current State: 84:[4, 21], Operations: ['97-93=4', '29-8=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 5, 17, 60, 28 ]
23
[ "17-5=12", "60/12=5", "28-5=23" ]
Current State: 23:[5, 17, 60, 28], Operations: [] Exploring Operation: 17-5=12, Resulting Numbers: [60, 28, 12] Generated Node #2: [60, 28, 12] from Operation: 17-5=12 Current State: 23:[60, 28, 12], Operations: ['17-5=12'] Exploring Operation: 60/12=5, Resulting Numbers: [28, 5] Generated Node #3: [28, 5] from Operation: 60/12=5 Current State: 23:[28, 5], Operations: ['17-5=12', '60/12=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[5, 17, 60, 28], Operations: [] Exploring Operation: 60-5=55, Resulting Numbers: [17, 28, 55] Generated Node #0,0: 23:[17, 28, 55] Operation: 60-5=55 Exploring Operation: 5+17=22, Resulting Numbers: [60, 28, 22] Generated Node #0,1: 23:[60, 28, 22] Operation: 5+17=22 Exploring Operation: 60/5=12, Resulting Numbers: [17, 28, 12] Generated Node #0,2: 23:[17, 28, 12] Operation: 60/5=12 Exploring Operation: 60-28=32, Resulting Numbers: [5, 17, 32] Generated Node #0,3: 23:[5, 17, 32] Operation: 60-28=32 Moving to Node #0,2 Current State: 23:[17, 28, 12], Operations: ['60/5=12'] Exploring Operation: 28-12=16, Resulting Numbers: [17, 16] Generated Node #0,2,0: 23:[17, 16] Operation: 28-12=16 Exploring Operation: 17-12=5, Resulting Numbers: [28, 5] Generated Node #0,2,1: 23:[28, 5] Operation: 17-12=5 Exploring Operation: 28-17=11, Resulting Numbers: [12, 11] Generated Node #0,2,2: 23:[12, 11] Operation: 28-17=11 Exploring Operation: 17+12=29, Resulting Numbers: [28, 29] Generated Node #0,2,3: 23:[28, 29] Operation: 17+12=29 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[28, 29], Operations: ['60/5=12', '17+12=29'] Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[17, 16], Operations: ['60/5=12', '28-12=16'] Exploring Operation: 17*16=272, Resulting Numbers: [272] 272,23 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[28, 5], Operations: ['60/5=12', '17-12=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,23 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[5, 17, 60, 28], Operations: [] Exploring Operation: 60/5=12, Resulting Numbers: [17, 28, 12] Generated Node #0,2: 23:[17, 28, 12] Operation: 60/5=12 Moving to Node #0,2 Current State: 23:[17, 28, 12], Operations: ['60/5=12'] Exploring Operation: 17-12=5, Resulting Numbers: [28, 5] Generated Node #0,2,1: 23:[28, 5] Operation: 17-12=5 Moving to Node #0,2,1 Current State: 23:[28, 5], Operations: ['60/5=12', '17-12=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 51, 87, 65, 65 ]
87
[ "65-65=0", "51*0=0", "87+0=87" ]
Current State: 87:[51, 87, 65, 65], Operations: [] Exploring Operation: 65-65=0, Resulting Numbers: [51, 87, 0] Generated Node #2: [51, 87, 0] from Operation: 65-65=0 Current State: 87:[51, 87, 0], Operations: ['65-65=0'] Exploring Operation: 51*0=0, Resulting Numbers: [87, 0] Generated Node #3: [87, 0] from Operation: 51*0=0 Current State: 87:[87, 0], Operations: ['65-65=0', '51*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[51, 87, 65, 65], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [87, 65, 14] Generated Node #0,0: 87:[87, 65, 14] Operation: 65-51=14 Exploring Operation: 87-51=36, Resulting Numbers: [65, 65, 36] Generated Node #0,1: 87:[65, 65, 36] Operation: 87-51=36 Exploring Operation: 65-51=14, Resulting Numbers: [87, 65, 14] Generated Node #0,2: 87:[87, 65, 14] Operation: 65-51=14 Exploring Operation: 65-65=0, Resulting Numbers: [51, 87, 0] Generated Node #0,3: 87:[51, 87, 0] Operation: 65-65=0 Exploring Operation: 65/65=1, Resulting Numbers: [51, 87, 1] Generated Node #0,4: 87:[51, 87, 1] Operation: 65/65=1 Moving to Node #0,4 Current State: 87:[51, 87, 1], Operations: ['65/65=1'] Exploring Operation: 51-1=50, Resulting Numbers: [87, 50] Generated Node #0,4,0: 87:[87, 50] Operation: 51-1=50 Exploring Operation: 51/1=51, Resulting Numbers: [87, 51] Generated Node #0,4,1: 87:[87, 51] Operation: 51/1=51 Exploring Operation: 87*1=87, Resulting Numbers: [51, 87] Generated Node #0,4,2: 87:[51, 87] Operation: 87*1=87 Exploring Operation: 51*1=51, Resulting Numbers: [87, 51] Generated Node #0,4,3: 87:[87, 51] Operation: 51*1=51 Exploring Operation: 87-51=36, Resulting Numbers: [1, 36] Generated Node #0,4,4: 87:[1, 36] Operation: 87-51=36 Moving to Node #0,3 Current State: 87:[51, 87, 0], Operations: ['65-65=0'] Exploring Operation: 87+0=87, Resulting Numbers: [51, 87] Generated Node #0,3,0: 87:[51, 87] Operation: 87+0=87 Exploring Operation: 51*0=0, Resulting Numbers: [87, 0] Generated Node #0,3,1: 87:[87, 0] Operation: 51*0=0 Exploring Operation: 87-51=36, Resulting Numbers: [0, 36] Generated Node #0,3,2: 87:[0, 36] Operation: 87-51=36 Exploring Operation: 51+0=51, Resulting Numbers: [87, 51] Generated Node #0,3,3: 87:[87, 51] Operation: 51+0=51 Exploring Operation: 51-0=51, Resulting Numbers: [87, 51] Generated Node #0,3,4: 87:[87, 51] Operation: 51-0=51 Moving to Node #0,0 Current State: 87:[87, 65, 14], Operations: ['65-51=14'] Exploring Operation: 65+14=79, Resulting Numbers: [87, 79] Generated Node #0,0,0: 87:[87, 79] Operation: 65+14=79 Exploring Operation: 87+14=101, Resulting Numbers: [65, 101] Generated Node #0,0,1: 87:[65, 101] Operation: 87+14=101 Exploring Operation: 87-65=22, Resulting Numbers: [14, 22] Generated Node #0,0,2: 87:[14, 22] Operation: 87-65=22 Exploring Operation: 87-14=73, Resulting Numbers: [65, 73] Generated Node #0,0,3: 87:[65, 73] Operation: 87-14=73 Exploring Operation: 65-14=51, Resulting Numbers: [87, 51] Generated Node #0,0,4: 87:[87, 51] Operation: 65-14=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[87, 79], Operations: ['65-51=14', '65+14=79'] Exploring Operation: 87+79=166, Resulting Numbers: [166] 166,87 unequal: No Solution Exploring Operation: 87*79=6873, Resulting Numbers: [6873] 6873,87 unequal: No Solution Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[14, 22], Operations: ['65-51=14', '87-65=22'] Exploring Operation: 22-14=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 14+22=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 14*22=308, Resulting Numbers: [308] 308,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 87:[87, 51], Operations: ['65-51=14', '65-14=51'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 87*51=4437, Resulting Numbers: [4437] 4437,87 unequal: No Solution Exploring Operation: 87+51=138, Resulting Numbers: [138] 138,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[65, 101], Operations: ['65-51=14', '87+14=101'] Exploring Operation: 65*101=6565, Resulting Numbers: [6565] 6565,87 unequal: No Solution Exploring Operation: 65+101=166, Resulting Numbers: [166] 166,87 unequal: No Solution Exploring Operation: 101-65=36, Resulting Numbers: [36] 36,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 87:[65, 73], Operations: ['65-51=14', '87-14=73'] Exploring Operation: 65*73=4745, Resulting Numbers: [4745] 4745,87 unequal: No Solution Exploring Operation: 73-65=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 65+73=138, Resulting Numbers: [138] 138,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 87:[87, 65, 14], Operations: ['65-51=14'] Exploring Operation: 87+14=101, Resulting Numbers: [65, 101] Generated Node #0,2,0: 87:[65, 101] Operation: 87+14=101 Exploring Operation: 65-14=51, Resulting Numbers: [87, 51] Generated Node #0,2,1: 87:[87, 51] Operation: 65-14=51 Exploring Operation: 65+14=79, Resulting Numbers: [87, 79] Generated Node #0,2,2: 87:[87, 79] Operation: 65+14=79 Exploring Operation: 87-14=73, Resulting Numbers: [65, 73] Generated Node #0,2,3: 87:[65, 73] Operation: 87-14=73 Exploring Operation: 87-65=22, Resulting Numbers: [14, 22] Generated Node #0,2,4: 87:[14, 22] Operation: 87-65=22 Moving to Node #0,1 Current State: 87:[65, 65, 36], Operations: ['87-51=36'] Exploring Operation: 65-36=29, Resulting Numbers: [65, 29] Generated Node #0,1,0: 87:[65, 29] Operation: 65-36=29 Exploring Operation: 65+36=101, Resulting Numbers: [65, 101] Generated Node #0,1,1: 87:[65, 101] Operation: 65+36=101 Exploring Operation: 65-65=0, Resulting Numbers: [36, 0] Generated Node #0,1,2: 87:[36, 0] Operation: 65-65=0 Exploring Operation: 65/65=1, Resulting Numbers: [36, 1] Generated Node #0,1,3: 87:[36, 1] Operation: 65/65=1 Exploring Operation: 65-36=29, Resulting Numbers: [65, 29] Generated Node #0,1,4: 87:[65, 29] Operation: 65-36=29 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[36, 1], Operations: ['87-51=36', '65/65=1'] Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,87 unequal: No Solution Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[36, 0], Operations: ['87-51=36', '65-65=0'] Exploring Operation: 36+0=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 36-0=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 36*0=0, Resulting Numbers: [0] 0,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[65, 29], Operations: ['87-51=36', '65-36=29'] Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,87 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 87:[65, 29], Operations: ['87-51=36', '65-36=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,87 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 65*29=1885, Resulting Numbers: [1885] 1885,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[65, 101], Operations: ['87-51=36', '65+36=101'] Exploring Operation: 65*101=6565, Resulting Numbers: [6565] 6565,87 unequal: No Solution Exploring Operation: 65+101=166, Resulting Numbers: [166] 166,87 unequal: No Solution Exploring Operation: 101-65=36, Resulting Numbers: [36] 36,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 87:[87, 0], Operations: ['65-65=0', '51*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[51, 87, 65, 65], Operations: [] Exploring Operation: 65-65=0, Resulting Numbers: [51, 87, 0] Generated Node #0,3: 87:[51, 87, 0] Operation: 65-65=0 Moving to Node #0,3 Current State: 87:[51, 87, 0], Operations: ['65-65=0'] Exploring Operation: 51*0=0, Resulting Numbers: [87, 0] Generated Node #0,3,1: 87:[87, 0] Operation: 51*0=0 Moving to Node #0,3,1 Current State: 87:[87, 0], Operations: ['65-65=0', '51*0=0'] Exploring Operation: 87+0=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.942708
hs_5
sum_heuristic
[ 85, 12, 73, 24 ]
23
[ "85-12=73", "73/73=1", "24-1=23" ]
Current State: 23:[85, 12, 73, 24], Operations: [] Exploring Operation: 85-12=73, Resulting Numbers: [73, 24, 73] Generated Node #2: [73, 24, 73] from Operation: 85-12=73 Current State: 23:[73, 24, 73], Operations: ['85-12=73'] Exploring Operation: 73/73=1, Resulting Numbers: [24, 1] Generated Node #3: [24, 1] from Operation: 73/73=1 Current State: 23:[24, 1], Operations: ['85-12=73', '73/73=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[85, 12, 73, 24], Operations: [] Exploring Operation: 85-24=61, Resulting Numbers: [12, 73, 61] Generated Node #0,0: 23:[12, 73, 61] Operation: 85-24=61 Exploring Operation: 85-12=73, Resulting Numbers: [73, 24, 73] Generated Node #0,1: 23:[73, 24, 73] Operation: 85-12=73 Exploring Operation: 85-73=12, Resulting Numbers: [12, 24, 12] Generated Node #0,2: 23:[12, 24, 12] Operation: 85-73=12 Exploring Operation: 73-12=61, Resulting Numbers: [85, 24, 61] Generated Node #0,3: 23:[85, 24, 61] Operation: 73-12=61 Exploring Operation: 73-24=49, Resulting Numbers: [85, 12, 49] Generated Node #0,4: 23:[85, 12, 49] Operation: 73-24=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[12, 24, 12], Operations: ['85-73=12'] Exploring Operation: 12+24=36, Resulting Numbers: [12, 36] Generated Node #0,2,0: 23:[12, 36] Operation: 12+24=36 Exploring Operation: 24-12=12, Resulting Numbers: [12, 12] Generated Node #0,2,1: 23:[12, 12] Operation: 24-12=12 Exploring Operation: 12/12=1, Resulting Numbers: [24, 1] Generated Node #0,2,2: 23:[24, 1] Operation: 12/12=1 Exploring Operation: 24-12=12, Resulting Numbers: [12, 12] Generated Node #0,2,3: 23:[12, 12] Operation: 24-12=12 Exploring Operation: 12+12=24, Resulting Numbers: [24, 24] Generated Node #0,2,4: 23:[24, 24] Operation: 12+12=24 Moving to Node #0,2,4 Current State: 23:[24, 24], Operations: ['85-73=12', '12+12=24'] Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,23 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[12, 12], Operations: ['85-73=12', '24-12=12'] Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,23 unequal: No Solution Moving to Node #0,2,1 Current State: 23:[12, 12], Operations: ['85-73=12', '24-12=12'] Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,23 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[24, 1], Operations: ['85-73=12', '12/12=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,23 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[85, 12, 73, 24], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [12, 24, 12] Generated Node #0,2: 23:[12, 24, 12] Operation: 85-73=12 Moving to Node #0,2 Current State: 23:[12, 24, 12], Operations: ['85-73=12'] Exploring Operation: 12/12=1, Resulting Numbers: [24, 1] Generated Node #0,2,2: 23:[24, 1] Operation: 12/12=1 Moving to Node #0,2,2 Current State: 23:[24, 1], Operations: ['85-73=12', '12/12=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
mult_heuristic
[ 20, 71, 4, 9 ]
85
[ "20/4=5", "71+9=80", "5+80=85" ]
Current State: 85:[20, 71, 4, 9], Operations: [] Exploring Operation: 20/4=5, Resulting Numbers: [71, 9, 5] Generated Node #2: [71, 9, 5] from Operation: 20/4=5 Current State: 85:[71, 9, 5], Operations: ['20/4=5'] Exploring Operation: 71+9=80, Resulting Numbers: [5, 80] Generated Node #3: [5, 80] from Operation: 71+9=80 Current State: 85:[5, 80], Operations: ['20/4=5', '71+9=80'] Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[20, 71, 4, 9], Operations: [] Exploring Operation: 20+71=91, Resulting Numbers: [4, 9, 91] Generated Node #0,0: 85:[4, 9, 91] Operation: 20+71=91 Exploring Operation: 71+9=80, Resulting Numbers: [20, 4, 80] Generated Node #0,1: 85:[20, 4, 80] Operation: 71+9=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[20, 4, 80], Operations: ['71+9=80'] Exploring Operation: 80/20=4, Resulting Numbers: [4, 4] Generated Node #0,1,0: 85:[4, 4] Operation: 80/20=4 Exploring Operation: 4+80=84, Resulting Numbers: [20, 84] Generated Node #0,1,1: 85:[20, 84] Operation: 4+80=84 Moving to Node #0,1,0 Current State: 85:[4, 4], Operations: ['71+9=80', '80/20=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[20, 84], Operations: ['71+9=80', '4+80=84'] Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,85 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[4, 9, 91], Operations: ['20+71=91'] Exploring Operation: 91-9=82, Resulting Numbers: [4, 82] Generated Node #0,0,0: 85:[4, 82] Operation: 91-9=82 Exploring Operation: 9-4=5, Resulting Numbers: [91, 5] Generated Node #0,0,1: 85:[91, 5] Operation: 9-4=5 Moving to Node #0,0,0 Current State: 85:[4, 82], Operations: ['20+71=91', '91-9=82'] Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,85 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[91, 5], Operations: ['20+71=91', '9-4=5'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,85 unequal: No Solution Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 35, 24, 9, 12 ]
52
[ "35-9=26", "24/12=2", "26*2=52" ]
Current State: 52:[35, 24, 9, 12], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [24, 12, 26] Generated Node #2: [24, 12, 26] from Operation: 35-9=26 Current State: 52:[24, 12, 26], Operations: ['35-9=26'] Exploring Operation: 24/12=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 24/12=2 Current State: 52:[26, 2], Operations: ['35-9=26', '24/12=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[35, 24, 9, 12], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [24, 12, 26] Generated Node #0,0: 52:[24, 12, 26] Operation: 35-9=26 Exploring Operation: 35-24=11, Resulting Numbers: [9, 12, 11] Generated Node #0,1: 52:[9, 12, 11] Operation: 35-24=11 Exploring Operation: 35+12=47, Resulting Numbers: [24, 9, 47] Generated Node #0,2: 52:[24, 9, 47] Operation: 35+12=47 Exploring Operation: 35+9=44, Resulting Numbers: [24, 12, 44] Generated Node #0,3: 52:[24, 12, 44] Operation: 35+9=44 Exploring Operation: 35-12=23, Resulting Numbers: [24, 9, 23] Generated Node #0,4: 52:[24, 9, 23] Operation: 35-12=23 Moving to Node #0,0 Current State: 52:[24, 12, 26], Operations: ['35-9=26'] Exploring Operation: 24/12=2, Resulting Numbers: [26, 2] Generated Node #0,0,0: 52:[26, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [26, 12] Generated Node #0,0,1: 52:[26, 12] Operation: 24-12=12 Exploring Operation: 26-12=14, Resulting Numbers: [24, 14] Generated Node #0,0,2: 52:[24, 14] Operation: 26-12=14 Exploring Operation: 24+26=50, Resulting Numbers: [12, 50] Generated Node #0,0,3: 52:[12, 50] Operation: 24+26=50 Exploring Operation: 26-24=2, Resulting Numbers: [12, 2] Generated Node #0,0,4: 52:[12, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[26, 2], Operations: ['35-9=26', '24/12=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,52 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[35, 24, 9, 12], Operations: [] Exploring Operation: 35-9=26, Resulting Numbers: [24, 12, 26] Generated Node #0,0: 52:[24, 12, 26] Operation: 35-9=26 Moving to Node #0,0 Current State: 52:[24, 12, 26], Operations: ['35-9=26'] Exploring Operation: 24/12=2, Resulting Numbers: [26, 2] Generated Node #0,0,0: 52:[26, 2] Operation: 24/12=2 Moving to Node #0,0,0 Current State: 52:[26, 2], Operations: ['35-9=26', '24/12=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 57, 46, 71, 2 ]
53
[ "71-57=14", "14/2=7", "46+7=53" ]
Current State: 53:[57, 46, 71, 2], Operations: [] Exploring Operation: 71-57=14, Resulting Numbers: [46, 2, 14] Generated Node #2: [46, 2, 14] from Operation: 71-57=14 Current State: 53:[46, 2, 14], Operations: ['71-57=14'] Exploring Operation: 14/2=7, Resulting Numbers: [46, 7] Generated Node #3: [46, 7] from Operation: 14/2=7 Current State: 53:[46, 7], Operations: ['71-57=14', '14/2=7'] Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[57, 46, 71, 2], Operations: [] Exploring Operation: 71-2=69, Resulting Numbers: [57, 46, 69] Generated Node #0,0: 53:[57, 46, 69] Operation: 71-2=69 Exploring Operation: 57+2=59, Resulting Numbers: [46, 71, 59] Generated Node #0,1: 53:[46, 71, 59] Operation: 57+2=59 Exploring Operation: 57-2=55, Resulting Numbers: [46, 71, 55] Generated Node #0,2: 53:[46, 71, 55] Operation: 57-2=55 Exploring Operation: 46-2=44, Resulting Numbers: [57, 71, 44] Generated Node #0,3: 53:[57, 71, 44] Operation: 46-2=44 Exploring Operation: 46+2=48, Resulting Numbers: [57, 71, 48] Generated Node #0,4: 53:[57, 71, 48] Operation: 46+2=48 Moving to Node #0,0 Current State: 53:[57, 46, 69], Operations: ['71-2=69'] Exploring Operation: 57+46=103, Resulting Numbers: [69, 103] Generated Node #0,0,0: 53:[69, 103] Operation: 57+46=103 Exploring Operation: 69-46=23, Resulting Numbers: [57, 23] Generated Node #0,0,1: 53:[57, 23] Operation: 69-46=23 Exploring Operation: 46+69=115, Resulting Numbers: [57, 115] Generated Node #0,0,2: 53:[57, 115] Operation: 46+69=115 Exploring Operation: 57-46=11, Resulting Numbers: [69, 11] Generated Node #0,0,3: 53:[69, 11] Operation: 57-46=11 Exploring Operation: 69-57=12, Resulting Numbers: [46, 12] Generated Node #0,0,4: 53:[46, 12] Operation: 69-57=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[57, 23], Operations: ['71-2=69', '69-46=23'] Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,53 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,53 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:[46, 12], Operations: ['71-2=69', '69-57=12'] Exploring Operation: 46+12=58, Resulting Numbers: [58] 58,53 unequal: No Solution Exploring Operation: 46*12=552, Resulting Numbers: [552] 552,53 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,53 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:[69, 11], Operations: ['71-2=69', '57-46=11'] Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,53 unequal: No Solution Exploring Operation: 69*11=759, Resulting Numbers: [759] 759,53 unequal: No Solution Exploring Operation: 69+11=80, Resulting Numbers: [80] 80,53 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 #0,0,0 Current State: 53:[69, 103], Operations: ['71-2=69', '57+46=103'] Exploring Operation: 69*103=7107, Resulting Numbers: [7107] 7107,53 unequal: No Solution Exploring Operation: 103-69=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 69+103=172, Resulting Numbers: [172] 172,53 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:[57, 115], Operations: ['71-2=69', '46+69=115'] Exploring Operation: 57*115=6555, Resulting Numbers: [6555] 6555,53 unequal: No Solution Exploring Operation: 57+115=172, Resulting Numbers: [172] 172,53 unequal: No Solution Exploring Operation: 115-57=58, Resulting Numbers: [58] 58,53 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: 53:[57, 71, 48], Operations: ['46+2=48'] Exploring Operation: 57+48=105, Resulting Numbers: [71, 105] Generated Node #0,4,0: 53:[71, 105] Operation: 57+48=105 Exploring Operation: 57-48=9, Resulting Numbers: [71, 9] Generated Node #0,4,1: 53:[71, 9] Operation: 57-48=9 Exploring Operation: 71+48=119, Resulting Numbers: [57, 119] Generated Node #0,4,2: 53:[57, 119] Operation: 71+48=119 Exploring Operation: 71-48=23, Resulting Numbers: [57, 23] Generated Node #0,4,3: 53:[57, 23] Operation: 71-48=23 Exploring Operation: 71-57=14, Resulting Numbers: [48, 14] Generated Node #0,4,4: 53:[48, 14] Operation: 71-57=14 Moving to Node #0,2 Current State: 53:[46, 71, 55], Operations: ['57-2=55'] Exploring Operation: 46+55=101, Resulting Numbers: [71, 101] Generated Node #0,2,0: 53:[71, 101] Operation: 46+55=101 Exploring Operation: 71-46=25, Resulting Numbers: [55, 25] Generated Node #0,2,1: 53:[55, 25] Operation: 71-46=25 Exploring Operation: 55-46=9, Resulting Numbers: [71, 9] Generated Node #0,2,2: 53:[71, 9] Operation: 55-46=9 Exploring Operation: 46+71=117, Resulting Numbers: [55, 117] Generated Node #0,2,3: 53:[55, 117] Operation: 46+71=117 Exploring Operation: 71-55=16, Resulting Numbers: [46, 16] Generated Node #0,2,4: 53:[46, 16] Operation: 71-55=16 Moving to Node #0,1 Current State: 53:[46, 71, 59], Operations: ['57+2=59'] Exploring Operation: 59-46=13, Resulting Numbers: [71, 13] Generated Node #0,1,0: 53:[71, 13] Operation: 59-46=13 Exploring Operation: 71-46=25, Resulting Numbers: [59, 25] Generated Node #0,1,1: 53:[59, 25] Operation: 71-46=25 Exploring Operation: 46+71=117, Resulting Numbers: [59, 117] Generated Node #0,1,2: 53:[59, 117] Operation: 46+71=117 Exploring Operation: 71-59=12, Resulting Numbers: [46, 12] Generated Node #0,1,3: 53:[46, 12] Operation: 71-59=12 Exploring Operation: 46+59=105, Resulting Numbers: [71, 105] Generated Node #0,1,4: 53:[71, 105] Operation: 46+59=105 Moving to Node #0,3 Current State: 53:[57, 71, 44], Operations: ['46-2=44'] Exploring Operation: 57-44=13, Resulting Numbers: [71, 13] Generated Node #0,3,0: 53:[71, 13] Operation: 57-44=13 Exploring Operation: 71-57=14, Resulting Numbers: [44, 14] Generated Node #0,3,1: 53:[44, 14] Operation: 71-57=14 Exploring Operation: 71+44=115, Resulting Numbers: [57, 115] Generated Node #0,3,2: 53:[57, 115] Operation: 71+44=115 Exploring Operation: 57+44=101, Resulting Numbers: [71, 101] Generated Node #0,3,3: 53:[71, 101] Operation: 57+44=101 Exploring Operation: 71-44=27, Resulting Numbers: [57, 27] Generated Node #0,3,4: 53:[57, 27] Operation: 71-44=27 Moving to Node #0,2,1 Current State: 53:[55, 25], Operations: ['57-2=55', '71-46=25'] Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 55*25=1375, Resulting Numbers: [1375] 1375,53 unequal: No Solution Exploring Operation: 55+25=80, Resulting Numbers: [80] 80,53 unequal: No Solution Moving to Node #0,3,4 Current State: 53:[57, 27], Operations: ['46-2=44', '71-44=27'] Exploring Operation: 57*27=1539, Resulting Numbers: [1539] 1539,53 unequal: No Solution Exploring Operation: 57-27=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 57+27=84, Resulting Numbers: [84] 84,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[57, 23], Operations: ['46+2=48', '71-48=23'] Exploring Operation: 57*23=1311, Resulting Numbers: [1311] 1311,53 unequal: No Solution Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 57+23=80, Resulting Numbers: [80] 80,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[59, 25], Operations: ['57+2=59', '71-46=25'] Exploring Operation: 59+25=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 59-25=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 59*25=1475, Resulting Numbers: [1475] 1475,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[46, 16], Operations: ['57-2=55', '71-55=16'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,53 unequal: No Solution Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[48, 14], Operations: ['46+2=48', '71-57=14'] Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[46, 12], Operations: ['57+2=59', '71-59=12'] Exploring Operation: 46*12=552, Resulting Numbers: [552] 552,53 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 46+12=58, Resulting Numbers: [58] 58,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[44, 14], Operations: ['46-2=44', '71-57=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,53 unequal: No Solution Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[71, 13], Operations: ['57+2=59', '59-46=13'] Exploring Operation: 71+13=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 71*13=923, Resulting Numbers: [923] 923,53 unequal: No Solution Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[71, 13], Operations: ['46-2=44', '57-44=13'] Exploring Operation: 71+13=84, Resulting Numbers: [84] 84,53 unequal: No Solution Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,53 unequal: No Solution Exploring Operation: 71*13=923, Resulting Numbers: [923] 923,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[71, 9], Operations: ['46+2=48', '57-48=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[71, 9], Operations: ['57-2=55', '55-46=9'] Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,53 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,53 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[57, 115], Operations: ['46-2=44', '71+44=115'] Exploring Operation: 57+115=172, Resulting Numbers: [172] 172,53 unequal: No Solution Exploring Operation: 57*115=6555, Resulting Numbers: [6555] 6555,53 unequal: No Solution Exploring Operation: 115-57=58, Resulting Numbers: [58] 58,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[71, 101], Operations: ['57-2=55', '46+55=101'] Exploring Operation: 71+101=172, Resulting Numbers: [172] 172,53 unequal: No Solution Exploring Operation: 71*101=7171, Resulting Numbers: [7171] 7171,53 unequal: No Solution Exploring Operation: 101-71=30, Resulting Numbers: [30] 30,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[55, 117], Operations: ['57-2=55', '46+71=117'] Exploring Operation: 117-55=62, Resulting Numbers: [62] 62,53 unequal: No Solution Exploring Operation: 55*117=6435, Resulting Numbers: [6435] 6435,53 unequal: No Solution Exploring Operation: 55+117=172, Resulting Numbers: [172] 172,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[71, 101], Operations: ['46-2=44', '57+44=101'] Exploring Operation: 101-71=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 71+101=172, Resulting Numbers: [172] 172,53 unequal: No Solution Exploring Operation: 71*101=7171, Resulting Numbers: [7171] 7171,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[57, 119], Operations: ['46+2=48', '71+48=119'] Exploring Operation: 57*119=6783, Resulting Numbers: [6783] 6783,53 unequal: No Solution Exploring Operation: 57+119=176, Resulting Numbers: [176] 176,53 unequal: No Solution Exploring Operation: 119-57=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,1,4 Current State: 53:[71, 105], Operations: ['57+2=59', '46+59=105'] Exploring Operation: 71*105=7455, Resulting Numbers: [7455] 7455,53 unequal: No Solution Exploring Operation: 105-71=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 71+105=176, Resulting Numbers: [176] 176,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[59, 117], Operations: ['57+2=59', '46+71=117'] Exploring Operation: 59*117=6903, Resulting Numbers: [6903] 6903,53 unequal: No Solution Exploring Operation: 59+117=176, Resulting Numbers: [176] 176,53 unequal: No Solution Exploring Operation: 117-59=58, Resulting Numbers: [58] 58,53 unequal: No Solution Moving to Node #0,4,0 Current State: 53:[71, 105], Operations: ['46+2=48', '57+48=105'] Exploring Operation: 105-71=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 71*105=7455, Resulting Numbers: [7455] 7455,53 unequal: No Solution Exploring Operation: 71+105=176, Resulting Numbers: [176] 176,53 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 35, 20, 57, 63 ]
61
[ "35+20=55", "63-57=6", "55+6=61" ]
Current State: 61:[35, 20, 57, 63], Operations: [] Exploring Operation: 35+20=55, Resulting Numbers: [57, 63, 55] Generated Node #2: [57, 63, 55] from Operation: 35+20=55 Current State: 61:[57, 63, 55], Operations: ['35+20=55'] Exploring Operation: 63-57=6, Resulting Numbers: [55, 6] Generated Node #3: [55, 6] from Operation: 63-57=6 Current State: 61:[55, 6], Operations: ['35+20=55', '63-57=6'] Exploring Operation: 55+6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[35, 20, 57, 63], Operations: [] Exploring Operation: 35+20=55, Resulting Numbers: [57, 63, 55] Generated Node #0,0: 61:[57, 63, 55] Operation: 35+20=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[57, 63, 55], Operations: ['35+20=55'] Exploring Operation: 57+55=112, Resulting Numbers: [63, 112] Generated Node #0,0,0: 61:[63, 112] Operation: 57+55=112 Moving to Node #0,0,0 Current State: 61:[63, 112], Operations: ['35+20=55', '57+55=112'] Exploring Operation: 112-63=49, Resulting Numbers: [49] 49,61 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
[ 9, 48, 65, 3 ]
72
[ "65-9=56", "48/3=16", "56+16=72" ]
Current State: 72:[9, 48, 65, 3], Operations: [] Exploring Operation: 65-9=56, Resulting Numbers: [48, 3, 56] Generated Node #2: [48, 3, 56] from Operation: 65-9=56 Current State: 72:[48, 3, 56], Operations: ['65-9=56'] Exploring Operation: 48/3=16, Resulting Numbers: [56, 16] Generated Node #3: [56, 16] from Operation: 48/3=16 Current State: 72:[56, 16], Operations: ['65-9=56', '48/3=16'] Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[9, 48, 65, 3], Operations: [] Exploring Operation: 48-9=39, Resulting Numbers: [65, 3, 39] Generated Node #0,0: 72:[65, 3, 39] Operation: 48-9=39 Exploring Operation: 9+65=74, Resulting Numbers: [48, 3, 74] Generated Node #0,1: 72:[48, 3, 74] Operation: 9+65=74 Exploring Operation: 48-3=45, Resulting Numbers: [9, 65, 45] Generated Node #0,2: 72:[9, 65, 45] Operation: 48-3=45 Exploring Operation: 65-48=17, Resulting Numbers: [9, 3, 17] Generated Node #0,3: 72:[9, 3, 17] Operation: 65-48=17 Exploring Operation: 48/3=16, Resulting Numbers: [9, 65, 16] Generated Node #0,4: 72:[9, 65, 16] Operation: 48/3=16 Moving to Node #0,3 Current State: 72:[9, 3, 17], Operations: ['65-48=17'] Exploring Operation: 9+17=26, Resulting Numbers: [3, 26] Generated Node #0,3,0: 72:[3, 26] Operation: 9+17=26 Exploring Operation: 9/3=3, Resulting Numbers: [17, 3] Generated Node #0,3,1: 72:[17, 3] Operation: 9/3=3 Exploring Operation: 9+3=12, Resulting Numbers: [17, 12] Generated Node #0,3,2: 72:[17, 12] Operation: 9+3=12 Exploring Operation: 17-9=8, Resulting Numbers: [3, 8] Generated Node #0,3,3: 72:[3, 8] Operation: 17-9=8 Exploring Operation: 9-3=6, Resulting Numbers: [17, 6] Generated Node #0,3,4: 72:[17, 6] Operation: 9-3=6 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[3, 8], Operations: ['65-48=17', '17-9=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[17, 3], Operations: ['65-48=17', '9/3=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 72:[17, 12], Operations: ['65-48=17', '9+3=12'] Exploring Operation: 17*12=204, Resulting Numbers: [204] 204,72 unequal: No Solution Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 72:[17, 6], Operations: ['65-48=17', '9-3=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,72 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[3, 26], Operations: ['65-48=17', '9+17=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,72 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: 72:[9, 65, 16], Operations: ['48/3=16'] Exploring Operation: 16-9=7, Resulting Numbers: [65, 7] Generated Node #0,4,0: 72:[65, 7] Operation: 16-9=7 Exploring Operation: 9+16=25, Resulting Numbers: [65, 25] Generated Node #0,4,1: 72:[65, 25] Operation: 9+16=25 Exploring Operation: 9+65=74, Resulting Numbers: [16, 74] Generated Node #0,4,2: 72:[16, 74] Operation: 9+65=74 Exploring Operation: 65-16=49, Resulting Numbers: [9, 49] Generated Node #0,4,3: 72:[9, 49] Operation: 65-16=49 Exploring Operation: 65+16=81, Resulting Numbers: [9, 81] Generated Node #0,4,4: 72:[9, 81] Operation: 65+16=81 Moving to Node #0,0 Current State: 72:[65, 3, 39], Operations: ['48-9=39'] Exploring Operation: 65+3=68, Resulting Numbers: [39, 68] Generated Node #0,0,0: 72:[39, 68] Operation: 65+3=68 Exploring Operation: 39/3=13, Resulting Numbers: [65, 13] Generated Node #0,0,1: 72:[65, 13] Operation: 39/3=13 Exploring Operation: 39-3=36, Resulting Numbers: [65, 36] Generated Node #0,0,2: 72:[65, 36] Operation: 39-3=36 Exploring Operation: 65-39=26, Resulting Numbers: [3, 26] Generated Node #0,0,3: 72:[3, 26] Operation: 65-39=26 Exploring Operation: 65-3=62, Resulting Numbers: [39, 62] Generated Node #0,0,4: 72:[39, 62] Operation: 65-3=62 Moving to Node #0,1 Current State: 72:[48, 3, 74], Operations: ['9+65=74'] Exploring Operation: 74-3=71, Resulting Numbers: [48, 71] Generated Node #0,1,0: 72:[48, 71] Operation: 74-3=71 Exploring Operation: 48-3=45, Resulting Numbers: [74, 45] Generated Node #0,1,1: 72:[74, 45] Operation: 48-3=45 Exploring Operation: 48/3=16, Resulting Numbers: [74, 16] Generated Node #0,1,2: 72:[74, 16] Operation: 48/3=16 Exploring Operation: 74-48=26, Resulting Numbers: [3, 26] Generated Node #0,1,3: 72:[3, 26] Operation: 74-48=26 Exploring Operation: 48+3=51, Resulting Numbers: [74, 51] Generated Node #0,1,4: 72:[74, 51] Operation: 48+3=51 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 72:[3, 26], Operations: ['9+65=74', '74-48=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 72:[74, 16], Operations: ['9+65=74', '48/3=16'] Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 74*16=1184, Resulting Numbers: [1184] 1184,72 unequal: No Solution Exploring Operation: 74+16=90, Resulting Numbers: [90] 90,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[74, 45], Operations: ['9+65=74', '48-3=45'] Exploring Operation: 74+45=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 74*45=3330, Resulting Numbers: [3330] 3330,72 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[48, 71], Operations: ['9+65=74', '74-3=71'] Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,72 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 72:[74, 51], Operations: ['9+65=74', '48+3=51'] Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 74+51=125, Resulting Numbers: [125] 125,72 unequal: No Solution Exploring Operation: 74*51=3774, Resulting Numbers: [3774] 3774,72 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:[9, 65, 45], Operations: ['48-3=45'] Exploring Operation: 45-9=36, Resulting Numbers: [65, 36] Generated Node #0,2,0: 72:[65, 36] Operation: 45-9=36 Exploring Operation: 45/9=5, Resulting Numbers: [65, 5] Generated Node #0,2,1: 72:[65, 5] Operation: 45/9=5 Exploring Operation: 65-9=56, Resulting Numbers: [45, 56] Generated Node #0,2,2: 72:[45, 56] Operation: 65-9=56 Exploring Operation: 9+65=74, Resulting Numbers: [45, 74] Generated Node #0,2,3: 72:[45, 74] Operation: 9+65=74 Exploring Operation: 65-45=20, Resulting Numbers: [9, 20] Generated Node #0,2,4: 72:[9, 20] Operation: 65-45=20 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 72:[9, 20], Operations: ['48-3=45', '65-45=20'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 9+20=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,72 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 #0,2,0 Current State: 72:[65, 36], Operations: ['48-3=45', '45-9=36'] Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 65+36=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 65*36=2340, Resulting Numbers: [2340] 2340,72 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:[65, 5], Operations: ['48-3=45', '45/9=5'] Exploring Operation: 65+5=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 65*5=325, Resulting Numbers: [325] 325,72 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,72 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 #0,2,3 Current State: 72:[45, 74], Operations: ['48-3=45', '9+65=74'] Exploring Operation: 45*74=3330, Resulting Numbers: [3330] 3330,72 unequal: No Solution Exploring Operation: 45+74=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[45, 56], Operations: ['48-3=45', '65-9=56'] Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,72 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 72:[3, 26], Operations: ['48-9=39', '65-39=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[16, 74], Operations: ['48/3=16', '9+65=74'] Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,72 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,72 unequal: No Solution Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[39, 68], Operations: ['48-9=39', '65+3=68'] Exploring Operation: 68-39=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 39+68=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 39*68=2652, Resulting Numbers: [2652] 2652,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[65, 36], Operations: ['48-9=39', '39-3=36'] Exploring Operation: 65+36=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 65*36=2340, Resulting Numbers: [2340] 2340,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[65, 25], Operations: ['48/3=16', '9+16=25'] Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,72 unequal: No Solution Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,72 unequal: No Solution Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[65, 13], Operations: ['48-9=39', '39/3=13'] Exploring Operation: 65/13=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 65*13=845, Resulting Numbers: [845] 845,72 unequal: No Solution Exploring Operation: 65+13=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[65, 7], Operations: ['48/3=16', '16-9=7'] Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[9, 48, 65, 3], Operations: [] Exploring Operation: 48/3=16, Resulting Numbers: [9, 65, 16] Generated Node #0,4: 72:[9, 65, 16] Operation: 48/3=16 Moving to Node #0,4 Current State: 72:[9, 65, 16], Operations: ['48/3=16'] Exploring Operation: 16-9=7, Resulting Numbers: [65, 7] Generated Node #0,4,0: 72:[65, 7] Operation: 16-9=7 Moving to Node #0,4,0 Current State: 72:[65, 7], Operations: ['48/3=16', '16-9=7'] Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.913194
hs_5
mult_heuristic
[ 50, 80, 43, 11 ]
24
[ "80-50=30", "43+11=54", "54-30=24" ]
Current State: 24:[50, 80, 43, 11], Operations: [] Exploring Operation: 80-50=30, Resulting Numbers: [43, 11, 30] Generated Node #2: [43, 11, 30] from Operation: 80-50=30 Current State: 24:[43, 11, 30], Operations: ['80-50=30'] Exploring Operation: 43+11=54, Resulting Numbers: [30, 54] Generated Node #3: [30, 54] from Operation: 43+11=54 Current State: 24:[30, 54], Operations: ['80-50=30', '43+11=54'] Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[50, 80, 43, 11], Operations: [] Exploring Operation: 80-43=37, Resulting Numbers: [50, 11, 37] Generated Node #0,0: 24:[50, 11, 37] Operation: 80-43=37 Exploring Operation: 80-50=30, Resulting Numbers: [43, 11, 30] Generated Node #0,1: 24:[43, 11, 30] Operation: 80-50=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[43, 11, 30], Operations: ['80-50=30'] Exploring Operation: 43-30=13, Resulting Numbers: [11, 13] Generated Node #0,1,0: 24:[11, 13] Operation: 43-30=13 Exploring Operation: 43-11=32, Resulting Numbers: [30, 32] Generated Node #0,1,1: 24:[30, 32] Operation: 43-11=32 Moving to Node #0,1,0 Current State: 24:[11, 13], Operations: ['80-50=30', '43-30=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[50, 80, 43, 11], Operations: [] Exploring Operation: 80-50=30, Resulting Numbers: [43, 11, 30] Generated Node #0,1: 24:[43, 11, 30] Operation: 80-50=30 Moving to Node #0,1 Current State: 24:[43, 11, 30], Operations: ['80-50=30'] Exploring Operation: 43-30=13, Resulting Numbers: [11, 13] Generated Node #0,1,0: 24:[11, 13] Operation: 43-30=13 Moving to Node #0,1,0 Current State: 24:[11, 13], Operations: ['80-50=30', '43-30=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 70, 60, 99, 10 ]
21
[ "70+60=130", "99+10=109", "130-109=21" ]
Current State: 21:[70, 60, 99, 10], Operations: [] Exploring Operation: 70+60=130, Resulting Numbers: [99, 10, 130] Generated Node #2: [99, 10, 130] from Operation: 70+60=130 Current State: 21:[99, 10, 130], Operations: ['70+60=130'] Exploring Operation: 99+10=109, Resulting Numbers: [130, 109] Generated Node #3: [130, 109] from Operation: 99+10=109 Current State: 21:[130, 109], Operations: ['70+60=130', '99+10=109'] Exploring Operation: 130-109=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[70, 60, 99, 10], Operations: [] Exploring Operation: 99-70=29, Resulting Numbers: [60, 10, 29] Generated Node #0,0: 21:[60, 10, 29] Operation: 99-70=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[60, 10, 29], Operations: ['99-70=29'] Exploring Operation: 60/10=6, Resulting Numbers: [29, 6] Generated Node #0,0,0: 21:[29, 6] Operation: 60/10=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[29, 6], Operations: ['99-70=29', '60/10=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 31, 27, 14, 71 ]
27
[ "31+27=58", "14+71=85", "85-58=27" ]
Current State: 27:[31, 27, 14, 71], Operations: [] Exploring Operation: 31+27=58, Resulting Numbers: [14, 71, 58] Generated Node #2: [14, 71, 58] from Operation: 31+27=58 Current State: 27:[14, 71, 58], Operations: ['31+27=58'] Exploring Operation: 14+71=85, Resulting Numbers: [58, 85] Generated Node #3: [58, 85] from Operation: 14+71=85 Current State: 27:[58, 85], Operations: ['31+27=58', '14+71=85'] Exploring Operation: 85-58=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[31, 27, 14, 71], Operations: [] Exploring Operation: 71-31=40, Resulting Numbers: [27, 14, 40] Generated Node #0,0: 27:[27, 14, 40] Operation: 71-31=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[27, 14, 40], Operations: ['71-31=40'] Exploring Operation: 40-14=26, Resulting Numbers: [27, 26] Generated Node #0,0,0: 27:[27, 26] Operation: 40-14=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[27, 26], Operations: ['71-31=40', '40-14=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 39, 74, 83 ]
26
[ "28+83=111", "39*74=2886", "2886/111=26" ]
Current State: 26:[28, 39, 74, 83], Operations: [] Exploring Operation: 28+83=111, Resulting Numbers: [39, 74, 111] Generated Node #2: [39, 74, 111] from Operation: 28+83=111 Current State: 26:[39, 74, 111], Operations: ['28+83=111'] Exploring Operation: 39*74=2886, Resulting Numbers: [111, 2886] Generated Node #3: [111, 2886] from Operation: 39*74=2886 Current State: 26:[111, 2886], Operations: ['28+83=111', '39*74=2886'] Exploring Operation: 2886/111=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[28, 39, 74, 83], Operations: [] Exploring Operation: 83-74=9, Resulting Numbers: [28, 39, 9] Generated Node #0,0: 26:[28, 39, 9] Operation: 83-74=9 Exploring Operation: 74-39=35, Resulting Numbers: [28, 83, 35] Generated Node #0,1: 26:[28, 83, 35] Operation: 74-39=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[28, 39, 9], Operations: ['83-74=9'] Exploring Operation: 39-9=30, Resulting Numbers: [28, 30] Generated Node #0,0,0: 26:[28, 30] Operation: 39-9=30 Exploring Operation: 39-28=11, Resulting Numbers: [9, 11] Generated Node #0,0,1: 26:[9, 11] Operation: 39-28=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 26:[28, 30], Operations: ['83-74=9', '39-9=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,26 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,26 unequal: No Solution No 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: 26:[9, 11], Operations: ['83-74=9', '39-28=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,26 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: 26:[28, 83, 35], Operations: ['74-39=35'] Exploring Operation: 83-28=55, Resulting Numbers: [35, 55] Generated Node #0,1,0: 26:[35, 55] Operation: 83-28=55 Exploring Operation: 83-35=48, Resulting Numbers: [28, 48] Generated Node #0,1,1: 26:[28, 48] Operation: 83-35=48 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[28, 48], Operations: ['74-39=35', '83-35=48'] Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,26 unequal: No Solution Exploring Operation: 28+48=76, Resulting Numbers: [76] 76,26 unequal: No Solution No 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: 26:[35, 55], Operations: ['74-39=35', '83-28=55'] Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,26 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,26 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 93, 33, 44, 2 ]
41
[ "93+33=126", "126-44=82", "82/2=41" ]
Current State: 41:[93, 33, 44, 2], Operations: [] Exploring Operation: 93+33=126, Resulting Numbers: [44, 2, 126] Generated Node #2: [44, 2, 126] from Operation: 93+33=126 Current State: 41:[44, 2, 126], Operations: ['93+33=126'] Exploring Operation: 126-44=82, Resulting Numbers: [2, 82] Generated Node #3: [2, 82] from Operation: 126-44=82 Current State: 41:[2, 82], Operations: ['93+33=126', '126-44=82'] Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[93, 33, 44, 2], Operations: [] Exploring Operation: 93-44=49, Resulting Numbers: [33, 2, 49] Generated Node #0,0: 41:[33, 2, 49] Operation: 93-44=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[33, 2, 49], Operations: ['93-44=49'] Exploring Operation: 33+2=35, Resulting Numbers: [49, 35] Generated Node #0,0,0: 41:[49, 35] Operation: 33+2=35 Moving to Node #0,0,0 Current State: 41:[49, 35], Operations: ['93-44=49', '33+2=35'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,41 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
[ 9, 23, 3, 15 ]
11
[ "9*3=27", "23+15=38", "38-27=11" ]
Current State: 11:[9, 23, 3, 15], Operations: [] Exploring Operation: 9*3=27, Resulting Numbers: [23, 15, 27] Generated Node #2: [23, 15, 27] from Operation: 9*3=27 Current State: 11:[23, 15, 27], Operations: ['9*3=27'] Exploring Operation: 23+15=38, Resulting Numbers: [27, 38] Generated Node #3: [27, 38] from Operation: 23+15=38 Current State: 11:[27, 38], Operations: ['9*3=27', '23+15=38'] Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[9, 23, 3, 15], Operations: [] Exploring Operation: 23-9=14, Resulting Numbers: [3, 15, 14] Generated Node #0,0: 11:[3, 15, 14] Operation: 23-9=14 Exploring Operation: 15-3=12, Resulting Numbers: [9, 23, 12] Generated Node #0,1: 11:[9, 23, 12] Operation: 15-3=12 Exploring Operation: 23-15=8, Resulting Numbers: [9, 3, 8] Generated Node #0,2: 11:[9, 3, 8] Operation: 23-15=8 Exploring Operation: 23-3=20, Resulting Numbers: [9, 15, 20] Generated Node #0,3: 11:[9, 15, 20] Operation: 23-3=20 Moving to Node #0,2 Current State: 11:[9, 3, 8], Operations: ['23-15=8'] Exploring Operation: 9-3=6, Resulting Numbers: [8, 6] Generated Node #0,2,0: 11:[8, 6] Operation: 9-3=6 Exploring Operation: 8-3=5, Resulting Numbers: [9, 5] Generated Node #0,2,1: 11:[9, 5] Operation: 8-3=5 Exploring Operation: 3+8=11, Resulting Numbers: [9, 11] Generated Node #0,2,2: 11:[9, 11] Operation: 3+8=11 Exploring Operation: 9+3=12, Resulting Numbers: [8, 12] Generated Node #0,2,3: 11:[8, 12] Operation: 9+3=12 Moving to Node #0,1 Current State: 11:[9, 23, 12], Operations: ['15-3=12'] Exploring Operation: 23-12=11, Resulting Numbers: [9, 11] Generated Node #0,1,0: 11:[9, 11] Operation: 23-12=11 Exploring Operation: 12-9=3, Resulting Numbers: [23, 3] Generated Node #0,1,1: 11:[23, 3] Operation: 12-9=3 Exploring Operation: 9+23=32, Resulting Numbers: [12, 32] Generated Node #0,1,2: 11:[12, 32] Operation: 9+23=32 Exploring Operation: 23-9=14, Resulting Numbers: [12, 14] Generated Node #0,1,3: 11:[12, 14] Operation: 23-9=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[9, 11], Operations: ['15-3=12', '23-12=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 11:[12, 14], Operations: ['15-3=12', '23-9=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 12*14=168, Resulting Numbers: [168] 168,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[23, 3], Operations: ['15-3=12', '12-9=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,11 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[12, 32], Operations: ['15-3=12', '9+23=32'] Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,11 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,11 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: 11:[3, 15, 14], Operations: ['23-9=14'] Exploring Operation: 15/3=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 11:[14, 5] Operation: 15/3=5 Exploring Operation: 15-3=12, Resulting Numbers: [14, 12] Generated Node #0,0,1: 11:[14, 12] Operation: 15-3=12 Exploring Operation: 14-3=11, Resulting Numbers: [15, 11] Generated Node #0,0,2: 11:[15, 11] Operation: 14-3=11 Exploring Operation: 3+15=18, Resulting Numbers: [14, 18] Generated Node #0,0,3: 11:[14, 18] Operation: 3+15=18 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 11:[14, 12], Operations: ['23-9=14', '15-3=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[15, 11], Operations: ['23-9=14', '14-3=11'] Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,11 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[14, 5], Operations: ['23-9=14', '15/3=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,11 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,11 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[14, 18], Operations: ['23-9=14', '3+15=18'] Exploring Operation: 14*18=252, Resulting Numbers: [252] 252,11 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,11 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: 11:[9, 15, 20], Operations: ['23-3=20'] Exploring Operation: 9+15=24, Resulting Numbers: [20, 24] Generated Node #0,3,0: 11:[20, 24] Operation: 9+15=24 Exploring Operation: 20-15=5, Resulting Numbers: [9, 5] Generated Node #0,3,1: 11:[9, 5] Operation: 20-15=5 Exploring Operation: 15-9=6, Resulting Numbers: [20, 6] Generated Node #0,3,2: 11:[20, 6] Operation: 15-9=6 Exploring Operation: 20-9=11, Resulting Numbers: [15, 11] Generated Node #0,3,3: 11:[15, 11] Operation: 20-9=11 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[15, 11], Operations: ['23-3=20', '20-9=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 11:[9, 5], Operations: ['23-3=20', '20-15=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[20, 6], Operations: ['23-3=20', '15-9=6'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[20, 24], Operations: ['23-3=20', '9+15=24'] Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,11 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 11:[9, 11], Operations: ['23-15=8', '3+8=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,11 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[8, 12], Operations: ['23-15=8', '9+3=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,11 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[9, 5], Operations: ['23-15=8', '8-3=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[8, 6], Operations: ['23-15=8', '9-3=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,11 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,11 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 17, 25, 56, 75 ]
100
[ "17+25=42", "56*75=4200", "4200/42=100" ]
Current State: 100:[17, 25, 56, 75], Operations: [] Exploring Operation: 17+25=42, Resulting Numbers: [56, 75, 42] Generated Node #2: [56, 75, 42] from Operation: 17+25=42 Current State: 100:[56, 75, 42], Operations: ['17+25=42'] Exploring Operation: 56*75=4200, Resulting Numbers: [42, 4200] Generated Node #3: [42, 4200] from Operation: 56*75=4200 Current State: 100:[42, 4200], Operations: ['17+25=42', '56*75=4200'] Exploring Operation: 4200/42=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[17, 25, 56, 75], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [17, 25, 19] Generated Node #0,0: 100:[17, 25, 19] Operation: 75-56=19 Exploring Operation: 75-25=50, Resulting Numbers: [17, 56, 50] Generated Node #0,1: 100:[17, 56, 50] Operation: 75-25=50 Exploring Operation: 25+75=100, Resulting Numbers: [17, 56, 100] Generated Node #0,2: 100:[17, 56, 100] Operation: 25+75=100 Moving to Node #0,0 Current State: 100:[17, 25, 19], Operations: ['75-56=19'] Exploring Operation: 25-19=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 100:[17, 6] Operation: 25-19=6 Exploring Operation: 19-17=2, Resulting Numbers: [25, 2] Generated Node #0,0,1: 100:[25, 2] Operation: 19-17=2 Exploring Operation: 25-17=8, Resulting Numbers: [19, 8] Generated Node #0,0,2: 100:[19, 8] Operation: 25-17=8 Moving to Node #0,1 Current State: 100:[17, 56, 50], Operations: ['75-25=50'] Exploring Operation: 56-17=39, Resulting Numbers: [50, 39] Generated Node #0,1,0: 100:[50, 39] Operation: 56-17=39 Exploring Operation: 56+50=106, Resulting Numbers: [17, 106] Generated Node #0,1,1: 100:[17, 106] Operation: 56+50=106 Exploring Operation: 56-50=6, Resulting Numbers: [17, 6] Generated Node #0,1,2: 100:[17, 6] Operation: 56-50=6 Moving to Node #0,2 Current State: 100:[17, 56, 100], Operations: ['25+75=100'] Exploring Operation: 100-56=44, Resulting Numbers: [17, 44] Generated Node #0,2,0: 100:[17, 44] Operation: 100-56=44 Exploring Operation: 56-17=39, Resulting Numbers: [100, 39] Generated Node #0,2,1: 100:[100, 39] Operation: 56-17=39 Exploring Operation: 17+56=73, Resulting Numbers: [100, 73] Generated Node #0,2,2: 100:[100, 73] Operation: 17+56=73 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[17, 44], Operations: ['25+75=100', '100-56=44'] Exploring Operation: 44-17=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 17*44=748, Resulting Numbers: [748] 748,100 unequal: No Solution Exploring Operation: 17+44=61, Resulting Numbers: [61] 61,100 unequal: No Solution No 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: 100:[100, 39], Operations: ['25+75=100', '56-17=39'] Exploring Operation: 100-39=61, Resulting Numbers: [61] 61,100 unequal: No Solution Exploring Operation: 100+39=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 100*39=3900, Resulting Numbers: [3900] 3900,100 unequal: No Solution No 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: 100:[100, 73], Operations: ['25+75=100', '17+56=73'] Exploring Operation: 100-73=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 100+73=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 100*73=7300, Resulting Numbers: [7300] 7300,100 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: 100:[25, 2], Operations: ['75-56=19', '19-17=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[19, 8], Operations: ['75-56=19', '25-17=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,100 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[17, 6], Operations: ['75-56=19', '25-19=6'] Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,100 unequal: No Solution Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,100 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[17, 6], Operations: ['75-25=50', '56-50=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,100 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[17, 106], Operations: ['75-25=50', '56+50=106'] Exploring Operation: 106-17=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 17+106=123, Resulting Numbers: [123] 123,100 unequal: No Solution Exploring Operation: 17*106=1802, Resulting Numbers: [1802] 1802,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[50, 39], Operations: ['75-25=50', '56-17=39'] Exploring Operation: 50+39=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 50*39=1950, Resulting Numbers: [1950] 1950,100 unequal: No Solution Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,100 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 71, 96, 43, 7 ]
25
[ "96-71=25", "43+7=50", "50-25=25" ]
Current State: 25:[71, 96, 43, 7], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [43, 7, 25] Generated Node #2: [43, 7, 25] from Operation: 96-71=25 Current State: 25:[43, 7, 25], Operations: ['96-71=25'] Exploring Operation: 43+7=50, Resulting Numbers: [25, 50] Generated Node #3: [25, 50] from Operation: 43+7=50 Current State: 25:[25, 50], Operations: ['96-71=25', '43+7=50'] Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[71, 96, 43, 7], Operations: [] Exploring Operation: 71-43=28, Resulting Numbers: [96, 7, 28] Generated Node #0,0: 25:[96, 7, 28] Operation: 71-43=28 Exploring Operation: 96-71=25, Resulting Numbers: [43, 7, 25] Generated Node #0,1: 25:[43, 7, 25] Operation: 96-71=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[43, 7, 25], Operations: ['96-71=25'] Exploring Operation: 43-25=18, Resulting Numbers: [7, 18] Generated Node #0,1,0: 25:[7, 18] Operation: 43-25=18 Exploring Operation: 43-7=36, Resulting Numbers: [25, 36] Generated Node #0,1,1: 25:[25, 36] Operation: 43-7=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[7, 18], Operations: ['96-71=25', '43-25=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[71, 96, 43, 7], Operations: [] Exploring Operation: 96-71=25, Resulting Numbers: [43, 7, 25] Generated Node #0,1: 25:[43, 7, 25] Operation: 96-71=25 Moving to Node #0,1 Current State: 25:[43, 7, 25], Operations: ['96-71=25'] Exploring Operation: 43-25=18, Resulting Numbers: [7, 18] Generated Node #0,1,0: 25:[7, 18] Operation: 43-25=18 Moving to Node #0,1,0 Current State: 25:[7, 18], Operations: ['96-71=25', '43-25=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 79, 72, 10, 90 ]
63
[ "79-72=7", "90/10=9", "7*9=63" ]
Current State: 63:[79, 72, 10, 90], Operations: [] Exploring Operation: 79-72=7, Resulting Numbers: [10, 90, 7] Generated Node #2: [10, 90, 7] from Operation: 79-72=7 Current State: 63:[10, 90, 7], Operations: ['79-72=7'] Exploring Operation: 90/10=9, Resulting Numbers: [7, 9] Generated Node #3: [7, 9] from Operation: 90/10=9 Current State: 63:[7, 9], Operations: ['79-72=7', '90/10=9'] Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[79, 72, 10, 90], Operations: [] Exploring Operation: 90-79=11, Resulting Numbers: [72, 10, 11] Generated Node #0,0: 63:[72, 10, 11] Operation: 90-79=11 Moving to Node #0,0 Current State: 63:[72, 10, 11], Operations: ['90-79=11'] Exploring Operation: 72-10=62, Resulting Numbers: [11, 62] Generated Node #0,0,0: 63:[11, 62] Operation: 72-10=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[11, 62], Operations: ['90-79=11', '72-10=62'] Exploring Operation: 11+62=73, Resulting Numbers: [73] 73,63 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
[ 31, 29, 56, 21 ]
98
[ "31-29=2", "21*2=42", "56+42=98" ]
Current State: 98:[31, 29, 56, 21], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [56, 21, 2] Generated Node #2: [56, 21, 2] from Operation: 31-29=2 Current State: 98:[56, 21, 2], Operations: ['31-29=2'] Exploring Operation: 21*2=42, Resulting Numbers: [56, 42] Generated Node #3: [56, 42] from Operation: 21*2=42 Current State: 98:[56, 42], Operations: ['31-29=2', '21*2=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[31, 29, 56, 21], Operations: [] Exploring Operation: 31-21=10, Resulting Numbers: [29, 56, 10] Generated Node #0,0: 98:[29, 56, 10] Operation: 31-21=10 Exploring Operation: 31+21=52, Resulting Numbers: [29, 56, 52] Generated Node #0,1: 98:[29, 56, 52] Operation: 31+21=52 Exploring Operation: 31+29=60, Resulting Numbers: [56, 21, 60] Generated Node #0,2: 98:[56, 21, 60] Operation: 31+29=60 Exploring Operation: 31-29=2, Resulting Numbers: [56, 21, 2] Generated Node #0,3: 98:[56, 21, 2] Operation: 31-29=2 Exploring Operation: 29+21=50, Resulting Numbers: [31, 56, 50] Generated Node #0,4: 98:[31, 56, 50] Operation: 29+21=50 Moving to Node #0,3 Current State: 98:[56, 21, 2], Operations: ['31-29=2'] Exploring Operation: 56-21=35, Resulting Numbers: [2, 35] Generated Node #0,3,0: 98:[2, 35] Operation: 56-21=35 Exploring Operation: 56+2=58, Resulting Numbers: [21, 58] Generated Node #0,3,1: 98:[21, 58] Operation: 56+2=58 Exploring Operation: 21*2=42, Resulting Numbers: [56, 42] Generated Node #0,3,2: 98:[56, 42] Operation: 21*2=42 Exploring Operation: 21-2=19, Resulting Numbers: [56, 19] Generated Node #0,3,3: 98:[56, 19] Operation: 21-2=19 Exploring Operation: 56-2=54, Resulting Numbers: [21, 54] Generated Node #0,3,4: 98:[21, 54] Operation: 56-2=54 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[56, 19], Operations: ['31-29=2', '21-2=19'] Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 56*19=1064, Resulting Numbers: [1064] 1064,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 98:[21, 54], Operations: ['31-29=2', '56-2=54'] Exploring Operation: 21+54=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 21*54=1134, Resulting Numbers: [1134] 1134,98 unequal: No Solution Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 98:[2, 35], Operations: ['31-29=2', '56-21=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,98 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,98 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 98:[56, 42], Operations: ['31-29=2', '21*2=42'] Exploring Operation: 56*42=2352, Resulting Numbers: [2352] 2352,98 unequal: No Solution Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[31, 29, 56, 21], Operations: [] Exploring Operation: 31-29=2, Resulting Numbers: [56, 21, 2] Generated Node #0,3: 98:[56, 21, 2] Operation: 31-29=2 Moving to Node #0,3 Current State: 98:[56, 21, 2], Operations: ['31-29=2'] Exploring Operation: 21*2=42, Resulting Numbers: [56, 42] Generated Node #0,3,2: 98:[56, 42] Operation: 21*2=42 Moving to Node #0,3,2 Current State: 98:[56, 42], Operations: ['31-29=2', '21*2=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 27, 78, 24, 90 ]
63
[ "78-27=51", "24+90=114", "114-51=63" ]
Current State: 63:[27, 78, 24, 90], Operations: [] Exploring Operation: 78-27=51, Resulting Numbers: [24, 90, 51] Generated Node #2: [24, 90, 51] from Operation: 78-27=51 Current State: 63:[24, 90, 51], Operations: ['78-27=51'] Exploring Operation: 24+90=114, Resulting Numbers: [51, 114] Generated Node #3: [51, 114] from Operation: 24+90=114 Current State: 63:[51, 114], Operations: ['78-27=51', '24+90=114'] Exploring Operation: 114-51=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[27, 78, 24, 90], Operations: [] Exploring Operation: 78-27=51, Resulting Numbers: [24, 90, 51] Generated Node #0,0: 63:[24, 90, 51] Operation: 78-27=51 Exploring Operation: 90-24=66, Resulting Numbers: [27, 78, 66] Generated Node #0,1: 63:[27, 78, 66] Operation: 90-24=66 Exploring Operation: 90-27=63, Resulting Numbers: [78, 24, 63] Generated Node #0,2: 63:[78, 24, 63] Operation: 90-27=63 Exploring Operation: 90-78=12, Resulting Numbers: [27, 24, 12] Generated Node #0,3: 63:[27, 24, 12] Operation: 90-78=12 Exploring Operation: 27-24=3, Resulting Numbers: [78, 90, 3] Generated Node #0,4: 63:[78, 90, 3] Operation: 27-24=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 63:[27, 24, 12], Operations: ['90-78=12'] Exploring Operation: 24-12=12, Resulting Numbers: [27, 12] Generated Node #0,3,0: 63:[27, 12] Operation: 24-12=12 Exploring Operation: 27-12=15, Resulting Numbers: [24, 15] Generated Node #0,3,1: 63:[24, 15] Operation: 27-12=15 Exploring Operation: 24/12=2, Resulting Numbers: [27, 2] Generated Node #0,3,2: 63:[27, 2] Operation: 24/12=2 Exploring Operation: 27+24=51, Resulting Numbers: [12, 51] Generated Node #0,3,3: 63:[12, 51] Operation: 27+24=51 Exploring Operation: 27-24=3, Resulting Numbers: [12, 3] Generated Node #0,3,4: 63:[12, 3] Operation: 27-24=3 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 63:[12, 3], Operations: ['90-78=12', '27-24=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,63 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,63 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 #0,3,2 Current State: 63:[27, 2], Operations: ['90-78=12', '24/12=2'] Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,63 unequal: No Solution Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,63 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 #0,3,0 Current State: 63:[27, 12], Operations: ['90-78=12', '24-12=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,63 unequal: No Solution Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,63 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 63:[24, 15], Operations: ['90-78=12', '27-12=15'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,63 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,63 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 #0,3,3 Current State: 63:[12, 51], Operations: ['90-78=12', '27+24=51'] Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,63 unequal: No Solution Exploring Operation: 12+51=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[27, 78, 24, 90], Operations: [] Exploring Operation: 90-78=12, Resulting Numbers: [27, 24, 12] Generated Node #0,3: 63:[27, 24, 12] Operation: 90-78=12 Moving to Node #0,3 Current State: 63:[27, 24, 12], Operations: ['90-78=12'] Exploring Operation: 27+24=51, Resulting Numbers: [12, 51] Generated Node #0,3,3: 63:[12, 51] Operation: 27+24=51 Moving to Node #0,3,3 Current State: 63:[12, 51], Operations: ['90-78=12', '27+24=51'] Exploring Operation: 12+51=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_5
sum_heuristic
[ 31, 7, 68, 71 ]
78
[ "31*7=217", "68+71=139", "217-139=78" ]
Current State: 78:[31, 7, 68, 71], Operations: [] Exploring Operation: 31*7=217, Resulting Numbers: [68, 71, 217] Generated Node #2: [68, 71, 217] from Operation: 31*7=217 Current State: 78:[68, 71, 217], Operations: ['31*7=217'] Exploring Operation: 68+71=139, Resulting Numbers: [217, 139] Generated Node #3: [217, 139] from Operation: 68+71=139 Current State: 78:[217, 139], Operations: ['31*7=217', '68+71=139'] Exploring Operation: 217-139=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[31, 7, 68, 71], Operations: [] Exploring Operation: 68-31=37, Resulting Numbers: [7, 71, 37] Generated Node #0,0: 78:[7, 71, 37] Operation: 68-31=37 Exploring Operation: 71-68=3, Resulting Numbers: [31, 7, 3] Generated Node #0,1: 78:[31, 7, 3] Operation: 71-68=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[31, 7, 3], Operations: ['71-68=3'] Exploring Operation: 31-7=24, Resulting Numbers: [3, 24] Generated Node #0,1,0: 78:[3, 24] Operation: 31-7=24 Exploring Operation: 31+7=38, Resulting Numbers: [3, 38] Generated Node #0,1,1: 78:[3, 38] Operation: 31+7=38 Moving to Node #0,1,1 Current State: 78:[3, 38], Operations: ['71-68=3', '31+7=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,78 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[3, 24], Operations: ['71-68=3', '31-7=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,78 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[7, 71, 37], Operations: ['68-31=37'] Exploring Operation: 71-37=34, Resulting Numbers: [7, 34] Generated Node #0,0,0: 78:[7, 34] Operation: 71-37=34 Exploring Operation: 7+71=78, Resulting Numbers: [37, 78] Generated Node #0,0,1: 78:[37, 78] Operation: 7+71=78 Moving to Node #0,0,1 Current State: 78:[37, 78], Operations: ['68-31=37', '7+71=78'] Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,78 unequal: No Solution Exploring Operation: 37+78=115, Resulting Numbers: [115] 115,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[7, 34], Operations: ['68-31=37', '71-37=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,78 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 11, 54, 17, 75 ]
15
[ "54-11=43", "75-17=58", "58-43=15" ]
Current State: 15:[11, 54, 17, 75], Operations: [] Exploring Operation: 54-11=43, Resulting Numbers: [17, 75, 43] Generated Node #2: [17, 75, 43] from Operation: 54-11=43 Current State: 15:[17, 75, 43], Operations: ['54-11=43'] Exploring Operation: 75-17=58, Resulting Numbers: [43, 58] Generated Node #3: [43, 58] from Operation: 75-17=58 Current State: 15:[43, 58], Operations: ['54-11=43', '75-17=58'] Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[11, 54, 17, 75], Operations: [] Exploring Operation: 75-17=58, Resulting Numbers: [11, 54, 58] Generated Node #0,0: 15:[11, 54, 58] Operation: 75-17=58 Exploring Operation: 54-17=37, Resulting Numbers: [11, 75, 37] Generated Node #0,1: 15:[11, 75, 37] Operation: 54-17=37 Exploring Operation: 75-54=21, Resulting Numbers: [11, 17, 21] Generated Node #0,2: 15:[11, 17, 21] Operation: 75-54=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[11, 17, 21], Operations: ['75-54=21'] Exploring Operation: 21-11=10, Resulting Numbers: [17, 10] Generated Node #0,2,0: 15:[17, 10] Operation: 21-11=10 Exploring Operation: 17-11=6, Resulting Numbers: [21, 6] Generated Node #0,2,1: 15:[21, 6] Operation: 17-11=6 Exploring Operation: 21-17=4, Resulting Numbers: [11, 4] Generated Node #0,2,2: 15:[11, 4] Operation: 21-17=4 Moving to Node #0,2,2 Current State: 15:[11, 4], Operations: ['75-54=21', '21-17=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[11, 54, 17, 75], Operations: [] Exploring Operation: 75-54=21, Resulting Numbers: [11, 17, 21] Generated Node #0,2: 15:[11, 17, 21] Operation: 75-54=21 Moving to Node #0,2 Current State: 15:[11, 17, 21], Operations: ['75-54=21'] Exploring Operation: 21-17=4, Resulting Numbers: [11, 4] Generated Node #0,2,2: 15:[11, 4] Operation: 21-17=4 Moving to Node #0,2,2 Current State: 15:[11, 4], Operations: ['75-54=21', '21-17=4'] Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 24, 7, 43, 10 ]
16
[ "24-7=17", "43-10=33", "33-17=16" ]
Current State: 16:[24, 7, 43, 10], Operations: [] Exploring Operation: 24-7=17, Resulting Numbers: [43, 10, 17] Generated Node #2: [43, 10, 17] from Operation: 24-7=17 Current State: 16:[43, 10, 17], Operations: ['24-7=17'] Exploring Operation: 43-10=33, Resulting Numbers: [17, 33] Generated Node #3: [17, 33] from Operation: 43-10=33 Current State: 16:[17, 33], Operations: ['24-7=17', '43-10=33'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[24, 7, 43, 10], Operations: [] Exploring Operation: 43-10=33, Resulting Numbers: [24, 7, 33] Generated Node #0,0: 16:[24, 7, 33] Operation: 43-10=33 Exploring Operation: 43-24=19, Resulting Numbers: [7, 10, 19] Generated Node #0,1: 16:[7, 10, 19] Operation: 43-24=19 Exploring Operation: 24-7=17, Resulting Numbers: [43, 10, 17] Generated Node #0,2: 16:[43, 10, 17] Operation: 24-7=17 Exploring Operation: 43-7=36, Resulting Numbers: [24, 10, 36] Generated Node #0,3: 16:[24, 10, 36] Operation: 43-7=36 Exploring Operation: 24-10=14, Resulting Numbers: [7, 43, 14] Generated Node #0,4: 16:[7, 43, 14] Operation: 24-10=14 Moving to Node #0,1 Current State: 16:[7, 10, 19], Operations: ['43-24=19'] Exploring Operation: 19-10=9, Resulting Numbers: [7, 9] Generated Node #0,1,0: 16:[7, 9] Operation: 19-10=9 Exploring Operation: 10-7=3, Resulting Numbers: [19, 3] Generated Node #0,1,1: 16:[19, 3] Operation: 10-7=3 Exploring Operation: 7+19=26, Resulting Numbers: [10, 26] Generated Node #0,1,2: 16:[10, 26] Operation: 7+19=26 Exploring Operation: 19-7=12, Resulting Numbers: [10, 12] Generated Node #0,1,3: 16:[10, 12] Operation: 19-7=12 Exploring Operation: 7+10=17, Resulting Numbers: [19, 17] Generated Node #0,1,4: 16:[19, 17] Operation: 7+10=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[7, 9], Operations: ['43-24=19', '19-10=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,16 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[24, 7, 43, 10], Operations: [] Exploring Operation: 43-24=19, Resulting Numbers: [7, 10, 19] Generated Node #0,1: 16:[7, 10, 19] Operation: 43-24=19 Moving to Node #0,1 Current State: 16:[7, 10, 19], Operations: ['43-24=19'] Exploring Operation: 19-10=9, Resulting Numbers: [7, 9] Generated Node #0,1,0: 16:[7, 9] Operation: 19-10=9 Moving to Node #0,1,0 Current State: 16:[7, 9], Operations: ['43-24=19', '19-10=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 72, 19, 6, 36 ]
11
[ "72-19=53", "6+36=42", "53-42=11" ]
Current State: 11:[72, 19, 6, 36], Operations: [] Exploring Operation: 72-19=53, Resulting Numbers: [6, 36, 53] Generated Node #2: [6, 36, 53] from Operation: 72-19=53 Current State: 11:[6, 36, 53], Operations: ['72-19=53'] Exploring Operation: 6+36=42, Resulting Numbers: [53, 42] Generated Node #3: [53, 42] from Operation: 6+36=42 Current State: 11:[53, 42], Operations: ['72-19=53', '6+36=42'] Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[72, 19, 6, 36], Operations: [] Exploring Operation: 72/6=12, Resulting Numbers: [19, 36, 12] Generated Node #0,0: 11:[19, 36, 12] Operation: 72/6=12 Exploring Operation: 72-36=36, Resulting Numbers: [19, 6, 36] Generated Node #0,1: 11:[19, 6, 36] Operation: 72-36=36 Exploring Operation: 36-19=17, Resulting Numbers: [72, 6, 17] Generated Node #0,2: 11:[72, 6, 17] Operation: 36-19=17 Exploring Operation: 72-19=53, Resulting Numbers: [6, 36, 53] Generated Node #0,3: 11:[6, 36, 53] Operation: 72-19=53 Exploring Operation: 72/36=2, Resulting Numbers: [19, 6, 2] Generated Node #0,4: 11:[19, 6, 2] Operation: 72/36=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 11:[19, 6, 2], Operations: ['72/36=2'] Exploring Operation: 19-6=13, Resulting Numbers: [2, 13] Generated Node #0,4,0: 11:[2, 13] Operation: 19-6=13 Exploring Operation: 19-2=17, Resulting Numbers: [6, 17] Generated Node #0,4,1: 11:[6, 17] Operation: 19-2=17 Exploring Operation: 6+2=8, Resulting Numbers: [19, 8] Generated Node #0,4,2: 11:[19, 8] Operation: 6+2=8 Exploring Operation: 19+2=21, Resulting Numbers: [6, 21] Generated Node #0,4,3: 11:[6, 21] Operation: 19+2=21 Exploring Operation: 6*2=12, Resulting Numbers: [19, 12] Generated Node #0,4,4: 11:[19, 12] Operation: 6*2=12 Moving to Node #0,4,4 Current State: 11:[19, 12], Operations: ['72/36=2', '6*2=12'] Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,11 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[6, 17], Operations: ['72/36=2', '19-2=17'] Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,11 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[72, 19, 6, 36], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [19, 6, 2] Generated Node #0,4: 11:[19, 6, 2] Operation: 72/36=2 Moving to Node #0,4 Current State: 11:[19, 6, 2], Operations: ['72/36=2'] Exploring Operation: 19-2=17, Resulting Numbers: [6, 17] Generated Node #0,4,1: 11:[6, 17] Operation: 19-2=17 Moving to Node #0,4,1 Current State: 11:[6, 17], Operations: ['72/36=2', '19-2=17'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 32, 45, 90, 82 ]
100
[ "82-32=50", "90/45=2", "50*2=100" ]
Current State: 100:[32, 45, 90, 82], Operations: [] Exploring Operation: 82-32=50, Resulting Numbers: [45, 90, 50] Generated Node #2: [45, 90, 50] from Operation: 82-32=50 Current State: 100:[45, 90, 50], Operations: ['82-32=50'] Exploring Operation: 90/45=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 90/45=2 Current State: 100:[50, 2], Operations: ['82-32=50', '90/45=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[32, 45, 90, 82], Operations: [] Exploring Operation: 82-32=50, Resulting Numbers: [45, 90, 50] Generated Node #0,0: 100:[45, 90, 50] Operation: 82-32=50 Exploring Operation: 90-82=8, Resulting Numbers: [32, 45, 8] Generated Node #0,1: 100:[32, 45, 8] Operation: 90-82=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[32, 45, 8], Operations: ['90-82=8'] Exploring Operation: 32/8=4, Resulting Numbers: [45, 4] Generated Node #0,1,0: 100:[45, 4] Operation: 32/8=4 Exploring Operation: 45-32=13, Resulting Numbers: [8, 13] Generated Node #0,1,1: 100:[8, 13] Operation: 45-32=13 Moving to Node #0,1,0 Current State: 100:[45, 4], Operations: ['90-82=8', '32/8=4'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[8, 13], Operations: ['90-82=8', '45-32=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,100 unequal: No Solution No 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: 100:[45, 90, 50], Operations: ['82-32=50'] Exploring Operation: 90-45=45, Resulting Numbers: [50, 45] Generated Node #0,0,0: 100:[50, 45] Operation: 90-45=45 Exploring Operation: 90/45=2, Resulting Numbers: [50, 2] Generated Node #0,0,1: 100:[50, 2] Operation: 90/45=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[50, 2], Operations: ['82-32=50', '90/45=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[32, 45, 90, 82], Operations: [] Exploring Operation: 82-32=50, Resulting Numbers: [45, 90, 50] Generated Node #0,0: 100:[45, 90, 50] Operation: 82-32=50 Moving to Node #0,0 Current State: 100:[45, 90, 50], Operations: ['82-32=50'] Exploring Operation: 90/45=2, Resulting Numbers: [50, 2] Generated Node #0,0,1: 100:[50, 2] Operation: 90/45=2 Moving to Node #0,0,1 Current State: 100:[50, 2], Operations: ['82-32=50', '90/45=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 16, 34, 49, 72 ]
41
[ "34-16=18", "72-49=23", "18+23=41" ]
Current State: 41:[16, 34, 49, 72], Operations: [] Exploring Operation: 34-16=18, Resulting Numbers: [49, 72, 18] Generated Node #2: [49, 72, 18] from Operation: 34-16=18 Current State: 41:[49, 72, 18], Operations: ['34-16=18'] Exploring Operation: 72-49=23, Resulting Numbers: [18, 23] Generated Node #3: [18, 23] from Operation: 72-49=23 Current State: 41:[18, 23], Operations: ['34-16=18', '72-49=23'] Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[16, 34, 49, 72], Operations: [] Exploring Operation: 72-16=56, Resulting Numbers: [34, 49, 56] Generated Node #0,0: 41:[34, 49, 56] Operation: 72-16=56 Exploring Operation: 72-34=38, Resulting Numbers: [16, 49, 38] Generated Node #0,1: 41:[16, 49, 38] Operation: 72-34=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[34, 49, 56], Operations: ['72-16=56'] Exploring Operation: 56-34=22, Resulting Numbers: [49, 22] Generated Node #0,0,0: 41:[49, 22] Operation: 56-34=22 Exploring Operation: 49-34=15, Resulting Numbers: [56, 15] Generated Node #0,0,1: 41:[56, 15] Operation: 49-34=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[49, 22], Operations: ['72-16=56', '56-34=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,41 unequal: No Solution Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[56, 15], Operations: ['72-16=56', '49-34=15'] Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[16, 34, 49, 72], Operations: [] Exploring Operation: 72-16=56, Resulting Numbers: [34, 49, 56] Generated Node #0,0: 41:[34, 49, 56] Operation: 72-16=56 Moving to Node #0,0 Current State: 41:[34, 49, 56], Operations: ['72-16=56'] Exploring Operation: 49-34=15, Resulting Numbers: [56, 15] Generated Node #0,0,1: 41:[56, 15] Operation: 49-34=15 Moving to Node #0,0,1 Current State: 41:[56, 15], Operations: ['72-16=56', '49-34=15'] Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 7, 5, 30, 18 ]
36
[ "7+5=12", "30+18=48", "48-12=36" ]
Current State: 36:[7, 5, 30, 18], Operations: [] Exploring Operation: 7+5=12, Resulting Numbers: [30, 18, 12] Generated Node #2: [30, 18, 12] from Operation: 7+5=12 Current State: 36:[30, 18, 12], Operations: ['7+5=12'] Exploring Operation: 30+18=48, Resulting Numbers: [12, 48] Generated Node #3: [12, 48] from Operation: 30+18=48 Current State: 36:[12, 48], Operations: ['7+5=12', '30+18=48'] Exploring Operation: 48-12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[7, 5, 30, 18], Operations: [] Exploring Operation: 30/5=6, Resulting Numbers: [7, 18, 6] Generated Node #0,0: 36:[7, 18, 6] Operation: 30/5=6 Moving to Node #0,0 Current State: 36:[7, 18, 6], Operations: ['30/5=6'] Exploring Operation: 18-7=11, Resulting Numbers: [6, 11] Generated Node #0,0,0: 36:[6, 11] Operation: 18-7=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[6, 11], Operations: ['30/5=6', '18-7=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,36 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
[ 87, 94, 89, 1 ]
91
[ "87+94=181", "89+1=90", "181-90=91" ]
Current State: 91:[87, 94, 89, 1], Operations: [] Exploring Operation: 87+94=181, Resulting Numbers: [89, 1, 181] Generated Node #2: [89, 1, 181] from Operation: 87+94=181 Current State: 91:[89, 1, 181], Operations: ['87+94=181'] Exploring Operation: 89+1=90, Resulting Numbers: [181, 90] Generated Node #3: [181, 90] from Operation: 89+1=90 Current State: 91:[181, 90], Operations: ['87+94=181', '89+1=90'] Exploring Operation: 181-90=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[87, 94, 89, 1], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [89, 1, 7] Generated Node #0,0: 91:[89, 1, 7] Operation: 94-87=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[89, 1, 7], Operations: ['94-87=7'] Exploring Operation: 89+1=90, Resulting Numbers: [7, 90] Generated Node #0,0,0: 91:[7, 90] Operation: 89+1=90 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[7, 90], Operations: ['94-87=7', '89+1=90'] Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 12, 14, 19, 42 ]
15
[ "12*14=168", "168/42=4", "19-4=15" ]
Current State: 15:[12, 14, 19, 42], Operations: [] Exploring Operation: 12*14=168, Resulting Numbers: [19, 42, 168] Generated Node #2: [19, 42, 168] from Operation: 12*14=168 Current State: 15:[19, 42, 168], Operations: ['12*14=168'] Exploring Operation: 168/42=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 168/42=4 Current State: 15:[19, 4], Operations: ['12*14=168', '168/42=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[12, 14, 19, 42], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [12, 19, 3] Generated Node #0,0: 15:[12, 19, 3] Operation: 42/14=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[12, 19, 3], Operations: ['42/14=3'] Exploring Operation: 19-12=7, Resulting Numbers: [3, 7] Generated Node #0,0,0: 15:[3, 7] Operation: 19-12=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[3, 7], Operations: ['42/14=3', '19-12=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 78, 83, 34, 68 ]
88
[ "83*68=5644", "5644/34=166", "166-78=88" ]
Current State: 88:[78, 83, 34, 68], Operations: [] Exploring Operation: 83*68=5644, Resulting Numbers: [78, 34, 5644] Generated Node #2: [78, 34, 5644] from Operation: 83*68=5644 Current State: 88:[78, 34, 5644], Operations: ['83*68=5644'] Exploring Operation: 5644/34=166, Resulting Numbers: [78, 166] Generated Node #3: [78, 166] from Operation: 5644/34=166 Current State: 88:[78, 166], Operations: ['83*68=5644', '5644/34=166'] Exploring Operation: 166-78=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[78, 83, 34, 68], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [78, 83, 2] Generated Node #0,0: 88:[78, 83, 2] Operation: 68/34=2 Exploring Operation: 78-68=10, Resulting Numbers: [83, 34, 10] Generated Node #0,1: 88:[83, 34, 10] Operation: 78-68=10 Moving to Node #0,0 Current State: 88:[78, 83, 2], Operations: ['68/34=2'] Exploring Operation: 78/2=39, Resulting Numbers: [83, 39] Generated Node #0,0,0: 88:[83, 39] Operation: 78/2=39 Exploring Operation: 83-78=5, Resulting Numbers: [2, 5] Generated Node #0,0,1: 88:[2, 5] Operation: 83-78=5 Moving to Node #0,1 Current State: 88:[83, 34, 10], Operations: ['78-68=10'] Exploring Operation: 83-34=49, Resulting Numbers: [10, 49] Generated Node #0,1,0: 88:[10, 49] Operation: 83-34=49 Exploring Operation: 34+10=44, Resulting Numbers: [83, 44] Generated Node #0,1,1: 88:[83, 44] Operation: 34+10=44 Moving to Node #0,0,1 Current State: 88:[2, 5], Operations: ['68/34=2', '83-78=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[83, 44], Operations: ['78-68=10', '34+10=44'] Exploring Operation: 83+44=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[10, 49], Operations: ['78-68=10', '83-34=49'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[83, 39], Operations: ['68/34=2', '78/2=39'] Exploring Operation: 83+39=122, Resulting Numbers: [122] 122,88 unequal: No Solution Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,88 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 3, 36, 70, 76 ]
38
[ "3*36=108", "70+76=146", "146-108=38" ]
Current State: 38:[3, 36, 70, 76], Operations: [] Exploring Operation: 3*36=108, Resulting Numbers: [70, 76, 108] Generated Node #2: [70, 76, 108] from Operation: 3*36=108 Current State: 38:[70, 76, 108], Operations: ['3*36=108'] Exploring Operation: 70+76=146, Resulting Numbers: [108, 146] Generated Node #3: [108, 146] from Operation: 70+76=146 Current State: 38:[108, 146], Operations: ['3*36=108', '70+76=146'] Exploring Operation: 146-108=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 36, 70, 76], Operations: [] Exploring Operation: 70-36=34, Resulting Numbers: [3, 76, 34] Generated Node #0,0: 38:[3, 76, 34] Operation: 70-36=34 Exploring Operation: 76-36=40, Resulting Numbers: [3, 70, 40] Generated Node #0,1: 38:[3, 70, 40] Operation: 76-36=40 Exploring Operation: 76-70=6, Resulting Numbers: [3, 36, 6] Generated Node #0,2: 38:[3, 36, 6] Operation: 76-70=6 Exploring Operation: 70-3=67, Resulting Numbers: [36, 76, 67] Generated Node #0,3: 38:[36, 76, 67] Operation: 70-3=67 Exploring Operation: 76-3=73, Resulting Numbers: [36, 70, 73] Generated Node #0,4: 38:[36, 70, 73] Operation: 76-3=73 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[3, 36, 6], Operations: ['76-70=6'] Exploring Operation: 3+36=39, Resulting Numbers: [6, 39] Generated Node #0,2,0: 38:[6, 39] Operation: 3+36=39 Exploring Operation: 6/3=2, Resulting Numbers: [36, 2] Generated Node #0,2,1: 38:[36, 2] Operation: 6/3=2 Exploring Operation: 3*6=18, Resulting Numbers: [36, 18] Generated Node #0,2,2: 38:[36, 18] Operation: 3*6=18 Exploring Operation: 6-3=3, Resulting Numbers: [36, 3] Generated Node #0,2,3: 38:[36, 3] Operation: 6-3=3 Exploring Operation: 36+6=42, Resulting Numbers: [3, 42] Generated Node #0,2,4: 38:[3, 42] Operation: 36+6=42 Moving to Node #0,2,1 Current State: 38:[36, 2], Operations: ['76-70=6', '6/3=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,38 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[3, 36, 70, 76], Operations: [] Exploring Operation: 76-70=6, Resulting Numbers: [3, 36, 6] Generated Node #0,2: 38:[3, 36, 6] Operation: 76-70=6 Moving to Node #0,2 Current State: 38:[3, 36, 6], Operations: ['76-70=6'] Exploring Operation: 6/3=2, Resulting Numbers: [36, 2] Generated Node #0,2,1: 38:[36, 2] Operation: 6/3=2 Moving to Node #0,2,1 Current State: 38:[36, 2], Operations: ['76-70=6', '6/3=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 85, 14, 21, 93 ]
12
[ "93-85=8", "21*8=168", "168/14=12" ]
Current State: 12:[85, 14, 21, 93], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [14, 21, 8] Generated Node #2: [14, 21, 8] from Operation: 93-85=8 Current State: 12:[14, 21, 8], Operations: ['93-85=8'] Exploring Operation: 21*8=168, Resulting Numbers: [14, 168] Generated Node #3: [14, 168] from Operation: 21*8=168 Current State: 12:[14, 168], Operations: ['93-85=8', '21*8=168'] Exploring Operation: 168/14=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[85, 14, 21, 93], Operations: [] Exploring Operation: 93-85=8, Resulting Numbers: [14, 21, 8] Generated Node #0,0: 12:[14, 21, 8] Operation: 93-85=8 Moving to Node #0,0 Current State: 12:[14, 21, 8], Operations: ['93-85=8'] Exploring Operation: 21-14=7, Resulting Numbers: [8, 7] Generated Node #0,0,0: 12:[8, 7] Operation: 21-14=7 Moving to Node #0,0,0 Current State: 12:[8, 7], Operations: ['93-85=8', '21-14=7'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,12 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 19, 65, 28, 49 ]
46
[ "19+65=84", "84/28=3", "49-3=46" ]
Current State: 46:[19, 65, 28, 49], Operations: [] Exploring Operation: 19+65=84, Resulting Numbers: [28, 49, 84] Generated Node #2: [28, 49, 84] from Operation: 19+65=84 Current State: 46:[28, 49, 84], Operations: ['19+65=84'] Exploring Operation: 84/28=3, Resulting Numbers: [49, 3] Generated Node #3: [49, 3] from Operation: 84/28=3 Current State: 46:[49, 3], Operations: ['19+65=84', '84/28=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[19, 65, 28, 49], Operations: [] Exploring Operation: 65-19=46, Resulting Numbers: [28, 49, 46] Generated Node #0,0: 46:[28, 49, 46] Operation: 65-19=46 Exploring Operation: 65-49=16, Resulting Numbers: [19, 28, 16] Generated Node #0,1: 46:[19, 28, 16] Operation: 65-49=16 Exploring Operation: 65-28=37, Resulting Numbers: [19, 49, 37] Generated Node #0,2: 46:[19, 49, 37] Operation: 65-28=37 Moving to Node #0,0 Current State: 46:[28, 49, 46], Operations: ['65-19=46'] Exploring Operation: 49-46=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 46:[28, 3] Operation: 49-46=3 Exploring Operation: 49-28=21, Resulting Numbers: [46, 21] Generated Node #0,0,1: 46:[46, 21] Operation: 49-28=21 Exploring Operation: 46-28=18, Resulting Numbers: [49, 18] Generated Node #0,0,2: 46:[49, 18] Operation: 46-28=18 Moving to Node #0,1 Current State: 46:[19, 28, 16], Operations: ['65-49=16'] Exploring Operation: 28+16=44, Resulting Numbers: [19, 44] Generated Node #0,1,0: 46:[19, 44] Operation: 28+16=44 Exploring Operation: 19-16=3, Resulting Numbers: [28, 3] Generated Node #0,1,1: 46:[28, 3] Operation: 19-16=3 Exploring Operation: 19+28=47, Resulting Numbers: [16, 47] Generated Node #0,1,2: 46:[16, 47] Operation: 19+28=47 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[19, 44], Operations: ['65-49=16', '28+16=44'] Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,46 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,46 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:[28, 3], Operations: ['65-49=16', '19-16=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,46 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,46 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:[16, 47], Operations: ['65-49=16', '19+28=47'] Exploring Operation: 16+47=63, Resulting Numbers: [63] 63,46 unequal: No Solution Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 16*47=752, Resulting Numbers: [752] 752,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 46:[19, 49, 37], Operations: ['65-28=37'] Exploring Operation: 19+37=56, Resulting Numbers: [49, 56] Generated Node #0,2,0: 46:[49, 56] Operation: 19+37=56 Exploring Operation: 37-19=18, Resulting Numbers: [49, 18] Generated Node #0,2,1: 46:[49, 18] Operation: 37-19=18 Exploring Operation: 49-37=12, Resulting Numbers: [19, 12] Generated Node #0,2,2: 46:[19, 12] Operation: 49-37=12 Moving to Node #0,0,1 Current State: 46:[46, 21], Operations: ['65-19=46', '49-28=21'] Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[28, 3], Operations: ['65-19=46', '49-46=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,46 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[49, 18], Operations: ['65-19=46', '46-28=18'] Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,46 unequal: No Solution Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[49, 18], Operations: ['65-28=37', '37-19=18'] Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,46 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[49, 56], Operations: ['65-28=37', '19+37=56'] Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,46 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[19, 12], Operations: ['65-28=37', '49-37=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,46 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 7, 89, 34, 94 ]
68
[ "7+89=96", "96-94=2", "34*2=68" ]
Current State: 68:[7, 89, 34, 94], Operations: [] Exploring Operation: 7+89=96, Resulting Numbers: [34, 94, 96] Generated Node #2: [34, 94, 96] from Operation: 7+89=96 Current State: 68:[34, 94, 96], Operations: ['7+89=96'] Exploring Operation: 96-94=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 96-94=2 Current State: 68:[34, 2], Operations: ['7+89=96', '96-94=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[7, 89, 34, 94], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [7, 34, 5] Generated Node #0,0: 68:[7, 34, 5] Operation: 94-89=5 Exploring Operation: 94-34=60, Resulting Numbers: [7, 89, 60] Generated Node #0,1: 68:[7, 89, 60] Operation: 94-34=60 Moving to Node #0,0 Current State: 68:[7, 34, 5], Operations: ['94-89=5'] Exploring Operation: 7*5=35, Resulting Numbers: [34, 35] Generated Node #0,0,0: 68:[34, 35] Operation: 7*5=35 Exploring Operation: 7-5=2, Resulting Numbers: [34, 2] Generated Node #0,0,1: 68:[34, 2] Operation: 7-5=2 Moving to Node #0,1 Current State: 68:[7, 89, 60], Operations: ['94-34=60'] Exploring Operation: 89-60=29, Resulting Numbers: [7, 29] Generated Node #0,1,0: 68:[7, 29] Operation: 89-60=29 Exploring Operation: 89-7=82, Resulting Numbers: [60, 82] Generated Node #0,1,1: 68:[60, 82] Operation: 89-7=82 Moving to Node #0,0,1 Current State: 68:[34, 2], Operations: ['94-89=5', '7-5=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[7, 89, 34, 94], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [7, 34, 5] Generated Node #0,0: 68:[7, 34, 5] Operation: 94-89=5 Moving to Node #0,0 Current State: 68:[7, 34, 5], Operations: ['94-89=5'] Exploring Operation: 7-5=2, Resulting Numbers: [34, 2] Generated Node #0,0,1: 68:[34, 2] Operation: 7-5=2 Moving to Node #0,0,1 Current State: 68:[34, 2], Operations: ['94-89=5', '7-5=2'] Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 3, 34, 24, 27 ]
71
[ "3*27=81", "34-24=10", "81-10=71" ]
Current State: 71:[3, 34, 24, 27], Operations: [] Exploring Operation: 3*27=81, Resulting Numbers: [34, 24, 81] Generated Node #2: [34, 24, 81] from Operation: 3*27=81 Current State: 71:[34, 24, 81], Operations: ['3*27=81'] Exploring Operation: 34-24=10, Resulting Numbers: [81, 10] Generated Node #3: [81, 10] from Operation: 34-24=10 Current State: 71:[81, 10], Operations: ['3*27=81', '34-24=10'] Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[3, 34, 24, 27], Operations: [] Exploring Operation: 3*27=81, Resulting Numbers: [34, 24, 81] Generated Node #0,0: 71:[34, 24, 81] Operation: 3*27=81 Exploring Operation: 3*34=102, Resulting Numbers: [24, 27, 102] Generated Node #0,1: 71:[24, 27, 102] Operation: 3*34=102 Exploring Operation: 3*24=72, Resulting Numbers: [34, 27, 72] Generated Node #0,2: 71:[34, 27, 72] Operation: 3*24=72 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[34, 27, 72], Operations: ['3*24=72'] Exploring Operation: 34+27=61, Resulting Numbers: [72, 61] Generated Node #0,2,0: 71:[72, 61] Operation: 34+27=61 Exploring Operation: 72-27=45, Resulting Numbers: [34, 45] Generated Node #0,2,1: 71:[34, 45] Operation: 72-27=45 Exploring Operation: 34-27=7, Resulting Numbers: [72, 7] Generated Node #0,2,2: 71:[72, 7] Operation: 34-27=7 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 71:[72, 61], Operations: ['3*24=72', '34+27=61'] Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,71 unequal: No Solution Exploring Operation: 72+61=133, Resulting Numbers: [133] 133,71 unequal: No Solution Exploring Operation: 72*61=4392, Resulting Numbers: [4392] 4392,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[34, 45], Operations: ['3*24=72', '72-27=45'] Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,71 unequal: No Solution Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,71 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 71:[72, 7], Operations: ['3*24=72', '34-27=7'] Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,71 unequal: No Solution Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,71 unequal: No Solution Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[34, 24, 81], Operations: ['3*27=81'] Exploring Operation: 34+24=58, Resulting Numbers: [81, 58] Generated Node #0,0,0: 71:[81, 58] Operation: 34+24=58 Exploring Operation: 34-24=10, Resulting Numbers: [81, 10] Generated Node #0,0,1: 71:[81, 10] Operation: 34-24=10 Exploring Operation: 81-24=57, Resulting Numbers: [34, 57] Generated Node #0,0,2: 71:[34, 57] Operation: 81-24=57 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[81, 58], Operations: ['3*27=81', '34+24=58'] Exploring Operation: 81+58=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 81*58=4698, Resulting Numbers: [4698] 4698,71 unequal: No Solution Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 71:[34, 57], Operations: ['3*27=81', '81-24=57'] Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[81, 10], Operations: ['3*27=81', '34-24=10'] Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[3, 34, 24, 27], Operations: [] Exploring Operation: 3*27=81, Resulting Numbers: [34, 24, 81] Generated Node #0,0: 71:[34, 24, 81] Operation: 3*27=81 Moving to Node #0,0 Current State: 71:[34, 24, 81], Operations: ['3*27=81'] Exploring Operation: 34-24=10, Resulting Numbers: [81, 10] Generated Node #0,0,1: 71:[81, 10] Operation: 34-24=10 Moving to Node #0,0,1 Current State: 71:[81, 10], Operations: ['3*27=81', '34-24=10'] Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_3
mult_heuristic
[ 73, 12, 6, 97 ]
16
[ "97-73=24", "24/6=4", "12+4=16" ]
Current State: 16:[73, 12, 6, 97], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [12, 6, 24] Generated Node #2: [12, 6, 24] from Operation: 97-73=24 Current State: 16:[12, 6, 24], Operations: ['97-73=24'] Exploring Operation: 24/6=4, Resulting Numbers: [12, 4] Generated Node #3: [12, 4] from Operation: 24/6=4 Current State: 16:[12, 4], Operations: ['97-73=24', '24/6=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[73, 12, 6, 97], Operations: [] Exploring Operation: 73-12=61, Resulting Numbers: [6, 97, 61] Generated Node #0,0: 16:[6, 97, 61] Operation: 73-12=61 Exploring Operation: 97-73=24, Resulting Numbers: [12, 6, 24] Generated Node #0,1: 16:[12, 6, 24] Operation: 97-73=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[12, 6, 24], Operations: ['97-73=24'] Exploring Operation: 24/12=2, Resulting Numbers: [6, 2] Generated Node #0,1,0: 16:[6, 2] Operation: 24/12=2 Exploring Operation: 24/6=4, Resulting Numbers: [12, 4] Generated Node #0,1,1: 16:[12, 4] Operation: 24/6=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[6, 2], Operations: ['97-73=24', '24/12=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[12, 4], Operations: ['97-73=24', '24/6=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[73, 12, 6, 97], Operations: [] Exploring Operation: 97-73=24, Resulting Numbers: [12, 6, 24] Generated Node #0,1: 16:[12, 6, 24] Operation: 97-73=24 Moving to Node #0,1 Current State: 16:[12, 6, 24], Operations: ['97-73=24'] Exploring Operation: 24/6=4, Resulting Numbers: [12, 4] Generated Node #0,1,1: 16:[12, 4] Operation: 24/6=4 Moving to Node #0,1,1 Current State: 16:[12, 4], Operations: ['97-73=24', '24/6=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 41, 2, 82, 28 ]
32
[ "82/41=2", "2+28=30", "2+30=32" ]
Current State: 32:[41, 2, 82, 28], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [2, 28, 2] Generated Node #2: [2, 28, 2] from Operation: 82/41=2 Current State: 32:[2, 28, 2], Operations: ['82/41=2'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,32 equal: Goal Reached Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[41, 2, 82, 28], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [41, 28, 41] Generated Node #0,0: 32:[41, 28, 41] Operation: 82/2=41 Exploring Operation: 82-41=41, Resulting Numbers: [2, 28, 41] Generated Node #0,1: 32:[2, 28, 41] Operation: 82-41=41 Exploring Operation: 82/41=2, Resulting Numbers: [2, 28, 2] Generated Node #0,2: 32:[2, 28, 2] Operation: 82/41=2 Exploring Operation: 82-28=54, Resulting Numbers: [41, 2, 54] Generated Node #0,3: 32:[41, 2, 54] Operation: 82-28=54 Moving to Node #0,2 Current State: 32:[2, 28, 2], Operations: ['82/41=2'] Exploring Operation: 28/2=14, Resulting Numbers: [2, 14] Generated Node #0,2,0: 32:[2, 14] Operation: 28/2=14 Exploring Operation: 28/2=14, Resulting Numbers: [2, 14] Generated Node #0,2,1: 32:[2, 14] Operation: 28/2=14 Exploring Operation: 28+2=30, Resulting Numbers: [2, 30] Generated Node #0,2,2: 32:[2, 30] Operation: 28+2=30 Exploring Operation: 2+28=30, Resulting Numbers: [2, 30] Generated Node #0,2,3: 32:[2, 30] Operation: 2+28=30 Moving to Node #0,1 Current State: 32:[2, 28, 41], Operations: ['82-41=41'] Exploring Operation: 28/2=14, Resulting Numbers: [41, 14] Generated Node #0,1,0: 32:[41, 14] Operation: 28/2=14 Exploring Operation: 41-2=39, Resulting Numbers: [28, 39] Generated Node #0,1,1: 32:[28, 39] Operation: 41-2=39 Exploring Operation: 2+28=30, Resulting Numbers: [41, 30] Generated Node #0,1,2: 32:[41, 30] Operation: 2+28=30 Exploring Operation: 41-28=13, Resulting Numbers: [2, 13] Generated Node #0,1,3: 32:[2, 13] Operation: 41-28=13 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[2, 13], Operations: ['82-41=41', '41-28=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[41, 14], Operations: ['82-41=41', '28/2=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,32 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,32 unequal: No Solution Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[28, 39], Operations: ['82-41=41', '41-2=39'] Exploring Operation: 28*39=1092, Resulting Numbers: [1092] 1092,32 unequal: No Solution Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 28+39=67, Resulting Numbers: [67] 67,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[41, 30], Operations: ['82-41=41', '2+28=30'] Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,32 unequal: No Solution Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 32:[41, 28, 41], Operations: ['82/2=41'] Exploring Operation: 41-28=13, Resulting Numbers: [41, 13] Generated Node #0,0,0: 32:[41, 13] Operation: 41-28=13 Exploring Operation: 41-41=0, Resulting Numbers: [28, 0] Generated Node #0,0,1: 32:[28, 0] Operation: 41-41=0 Exploring Operation: 41-28=13, Resulting Numbers: [41, 13] Generated Node #0,0,2: 32:[41, 13] Operation: 41-28=13 Exploring Operation: 41/41=1, Resulting Numbers: [28, 1] Generated Node #0,0,3: 32:[28, 1] Operation: 41/41=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[28, 1], Operations: ['82/2=41', '41/41=1'] Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,32 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,32 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[28, 0], Operations: ['82/2=41', '41-41=0'] Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 28*0=0, Resulting Numbers: [0] 0,32 unequal: No Solution Exploring Operation: 28-0=28, Resulting Numbers: [28] 28,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[41, 13], Operations: ['82/2=41', '41-28=13'] Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,32 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[41, 13], Operations: ['82/2=41', '41-28=13'] Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,32 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,32 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: 32:[41, 2, 54], Operations: ['82-28=54'] Exploring Operation: 54-41=13, Resulting Numbers: [2, 13] Generated Node #0,3,0: 32:[2, 13] Operation: 54-41=13 Exploring Operation: 54/2=27, Resulting Numbers: [41, 27] Generated Node #0,3,1: 32:[41, 27] Operation: 54/2=27 Exploring Operation: 41-2=39, Resulting Numbers: [54, 39] Generated Node #0,3,2: 32:[54, 39] Operation: 41-2=39 Exploring Operation: 54-2=52, Resulting Numbers: [41, 52] Generated Node #0,3,3: 32:[41, 52] Operation: 54-2=52 Moving to Node #0,2,0 Current State: 32:[2, 14], Operations: ['82/41=2', '28/2=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,32 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,32 unequal: No Solution Moving to Node #0,2,2 Current State: 32:[2, 30], Operations: ['82/41=2', '28+2=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,32 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[41, 2, 82, 28], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [2, 28, 2] Generated Node #0,2: 32:[2, 28, 2] Operation: 82/41=2 Moving to Node #0,2 Current State: 32:[2, 28, 2], Operations: ['82/41=2'] Exploring Operation: 28+2=30, Resulting Numbers: [2, 30] Generated Node #0,2,2: 32:[2, 30] Operation: 28+2=30 Moving to Node #0,2,2 Current State: 32:[2, 30], Operations: ['82/41=2', '28+2=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.951389
hs_4
sum_heuristic
[ 57, 42, 2, 60 ]
78
[ "57+42=99", "99-60=39", "2*39=78" ]
Current State: 78:[57, 42, 2, 60], Operations: [] Exploring Operation: 57+42=99, Resulting Numbers: [2, 60, 99] Generated Node #2: [2, 60, 99] from Operation: 57+42=99 Current State: 78:[2, 60, 99], Operations: ['57+42=99'] Exploring Operation: 99-60=39, Resulting Numbers: [2, 39] Generated Node #3: [2, 39] from Operation: 99-60=39 Current State: 78:[2, 39], Operations: ['57+42=99', '99-60=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[57, 42, 2, 60], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [2, 60, 15] Generated Node #0,0: 78:[2, 60, 15] Operation: 57-42=15 Exploring Operation: 60-42=18, Resulting Numbers: [57, 2, 18] Generated Node #0,1: 78:[57, 2, 18] Operation: 60-42=18 Exploring Operation: 60/2=30, Resulting Numbers: [57, 42, 30] Generated Node #0,2: 78:[57, 42, 30] Operation: 60/2=30 Exploring Operation: 60-57=3, Resulting Numbers: [42, 2, 3] Generated Node #0,3: 78:[42, 2, 3] Operation: 60-57=3 Moving to Node #0,3 Current State: 78:[42, 2, 3], Operations: ['60-57=3'] Exploring Operation: 2*3=6, Resulting Numbers: [42, 6] Generated Node #0,3,0: 78:[42, 6] Operation: 2*3=6 Exploring Operation: 42/3=14, Resulting Numbers: [2, 14] Generated Node #0,3,1: 78:[2, 14] Operation: 42/3=14 Exploring Operation: 42-3=39, Resulting Numbers: [2, 39] Generated Node #0,3,2: 78:[2, 39] Operation: 42-3=39 Exploring Operation: 42-2=40, Resulting Numbers: [3, 40] Generated Node #0,3,3: 78:[3, 40] Operation: 42-2=40 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[2, 39], Operations: ['60-57=3', '42-3=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[57, 42, 2, 60], Operations: [] Exploring Operation: 60-57=3, Resulting Numbers: [42, 2, 3] Generated Node #0,3: 78:[42, 2, 3] Operation: 60-57=3 Moving to Node #0,3 Current State: 78:[42, 2, 3], Operations: ['60-57=3'] Exploring Operation: 42-3=39, Resulting Numbers: [2, 39] Generated Node #0,3,2: 78:[2, 39] Operation: 42-3=39 Moving to Node #0,3,2 Current State: 78:[2, 39], Operations: ['60-57=3', '42-3=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 21, 7, 29, 98 ]
83
[ "21-7=14", "98-29=69", "14+69=83" ]
Current State: 83:[21, 7, 29, 98], Operations: [] Exploring Operation: 21-7=14, Resulting Numbers: [29, 98, 14] Generated Node #2: [29, 98, 14] from Operation: 21-7=14 Current State: 83:[29, 98, 14], Operations: ['21-7=14'] Exploring Operation: 98-29=69, Resulting Numbers: [14, 69] Generated Node #3: [14, 69] from Operation: 98-29=69 Current State: 83:[14, 69], Operations: ['21-7=14', '98-29=69'] Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[21, 7, 29, 98], Operations: [] Exploring Operation: 21*7=147, Resulting Numbers: [29, 98, 147] Generated Node #0,0: 83:[29, 98, 147] Operation: 21*7=147 Exploring Operation: 7+29=36, Resulting Numbers: [21, 98, 36] Generated Node #0,1: 83:[21, 98, 36] Operation: 7+29=36 Exploring Operation: 21+7=28, Resulting Numbers: [29, 98, 28] Generated Node #0,2: 83:[29, 98, 28] Operation: 21+7=28 Exploring Operation: 98-7=91, Resulting Numbers: [21, 29, 91] Generated Node #0,3: 83:[21, 29, 91] Operation: 98-7=91 Exploring Operation: 21+29=50, Resulting Numbers: [7, 98, 50] Generated Node #0,4: 83:[7, 98, 50] Operation: 21+29=50 Moving to Node #0,1 Current State: 83:[21, 98, 36], Operations: ['7+29=36'] Exploring Operation: 21+98=119, Resulting Numbers: [36, 119] Generated Node #0,1,0: 83:[36, 119] Operation: 21+98=119 Exploring Operation: 98-36=62, Resulting Numbers: [21, 62] Generated Node #0,1,1: 83:[21, 62] Operation: 98-36=62 Exploring Operation: 98-21=77, Resulting Numbers: [36, 77] Generated Node #0,1,2: 83:[36, 77] Operation: 98-21=77 Exploring Operation: 36-21=15, Resulting Numbers: [98, 15] Generated Node #0,1,3: 83:[98, 15] Operation: 36-21=15 Exploring Operation: 21+36=57, Resulting Numbers: [98, 57] Generated Node #0,1,4: 83:[98, 57] Operation: 21+36=57 Moving to Node #0,3 Current State: 83:[21, 29, 91], Operations: ['98-7=91'] Exploring Operation: 91-21=70, Resulting Numbers: [29, 70] Generated Node #0,3,0: 83:[29, 70] Operation: 91-21=70 Exploring Operation: 21+29=50, Resulting Numbers: [91, 50] Generated Node #0,3,1: 83:[91, 50] Operation: 21+29=50 Exploring Operation: 21+91=112, Resulting Numbers: [29, 112] Generated Node #0,3,2: 83:[29, 112] Operation: 21+91=112 Exploring Operation: 91-29=62, Resulting Numbers: [21, 62] Generated Node #0,3,3: 83:[21, 62] Operation: 91-29=62 Exploring Operation: 29-21=8, Resulting Numbers: [91, 8] Generated Node #0,3,4: 83:[91, 8] Operation: 29-21=8 Moving to Node #0,2 Current State: 83:[29, 98, 28], Operations: ['21+7=28'] Exploring Operation: 98-28=70, Resulting Numbers: [29, 70] Generated Node #0,2,0: 83:[29, 70] Operation: 98-28=70 Exploring Operation: 29-28=1, Resulting Numbers: [98, 1] Generated Node #0,2,1: 83:[98, 1] Operation: 29-28=1 Exploring Operation: 98-29=69, Resulting Numbers: [28, 69] Generated Node #0,2,2: 83:[28, 69] Operation: 98-29=69 Exploring Operation: 98+28=126, Resulting Numbers: [29, 126] Generated Node #0,2,3: 83:[29, 126] Operation: 98+28=126 Exploring Operation: 29+28=57, Resulting Numbers: [98, 57] Generated Node #0,2,4: 83:[98, 57] Operation: 29+28=57 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 83:[98, 57], Operations: ['21+7=28', '29+28=57'] Exploring Operation: 98-57=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 98+57=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 98*57=5586, Resulting Numbers: [5586] 5586,83 unequal: No Solution No 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: 83:[29, 70], Operations: ['21+7=28', '98-28=70'] Exploring Operation: 29*70=2030, Resulting Numbers: [2030] 2030,83 unequal: No Solution Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,83 unequal: No Solution No 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: 83:[28, 69], Operations: ['21+7=28', '98-29=69'] Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 28*69=1932, Resulting Numbers: [1932] 1932,83 unequal: No Solution No 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: 83:[98, 1], Operations: ['21+7=28', '29-28=1'] Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 98*1=98, Resulting Numbers: [98] 98,83 unequal: No Solution Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,83 unequal: No Solution Exploring Operation: 98+1=99, Resulting Numbers: [99] 99,83 unequal: No Solution No 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: 83:[29, 126], Operations: ['21+7=28', '98+28=126'] Exploring Operation: 29*126=3654, Resulting Numbers: [3654] 3654,83 unequal: No Solution Exploring Operation: 29+126=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 126-29=97, Resulting Numbers: [97] 97,83 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: 83:[7, 98, 50], Operations: ['21+29=50'] Exploring Operation: 98/7=14, Resulting Numbers: [50, 14] Generated Node #0,4,0: 83:[50, 14] Operation: 98/7=14 Exploring Operation: 98-7=91, Resulting Numbers: [50, 91] Generated Node #0,4,1: 83:[50, 91] Operation: 98-7=91 Exploring Operation: 50-7=43, Resulting Numbers: [98, 43] Generated Node #0,4,2: 83:[98, 43] Operation: 50-7=43 Exploring Operation: 7+50=57, Resulting Numbers: [98, 57] Generated Node #0,4,3: 83:[98, 57] Operation: 7+50=57 Exploring Operation: 7+98=105, Resulting Numbers: [50, 105] Generated Node #0,4,4: 83:[50, 105] Operation: 7+98=105 Moving to Node #0,0 Current State: 83:[29, 98, 147], Operations: ['21*7=147'] Exploring Operation: 29+147=176, Resulting Numbers: [98, 176] Generated Node #0,0,0: 83:[98, 176] Operation: 29+147=176 Exploring Operation: 147-98=49, Resulting Numbers: [29, 49] Generated Node #0,0,1: 83:[29, 49] Operation: 147-98=49 Exploring Operation: 98-29=69, Resulting Numbers: [147, 69] Generated Node #0,0,2: 83:[147, 69] Operation: 98-29=69 Exploring Operation: 29+98=127, Resulting Numbers: [147, 127] Generated Node #0,0,3: 83:[147, 127] Operation: 29+98=127 Exploring Operation: 147-29=118, Resulting Numbers: [98, 118] Generated Node #0,0,4: 83:[98, 118] Operation: 147-29=118 Moving to Node #0,1,4 Current State: 83:[98, 57], Operations: ['7+29=36', '21+36=57'] Exploring Operation: 98-57=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 98+57=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 98*57=5586, Resulting Numbers: [5586] 5586,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[91, 50], Operations: ['98-7=91', '21+29=50'] Exploring Operation: 91+50=141, Resulting Numbers: [141] 141,83 unequal: No Solution Exploring Operation: 91*50=4550, Resulting Numbers: [4550] 4550,83 unequal: No Solution Exploring Operation: 91-50=41, Resulting Numbers: [41] 41,83 unequal: No Solution Moving to Node #0,4,3 Current State: 83:[98, 57], Operations: ['21+29=50', '7+50=57'] Exploring Operation: 98+57=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 98*57=5586, Resulting Numbers: [5586] 5586,83 unequal: No Solution Exploring Operation: 98-57=41, Resulting Numbers: [41] 41,83 unequal: No Solution Moving to Node #0,4,1 Current State: 83:[50, 91], Operations: ['21+29=50', '98-7=91'] Exploring Operation: 91-50=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 50*91=4550, Resulting Numbers: [4550] 4550,83 unequal: No Solution Exploring Operation: 50+91=141, Resulting Numbers: [141] 141,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[98, 118], Operations: ['21*7=147', '147-29=118'] Exploring Operation: 98+118=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 98*118=11564, Resulting Numbers: [11564] 11564,83 unequal: No Solution Exploring Operation: 118-98=20, Resulting Numbers: [20] 20,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[36, 77], Operations: ['7+29=36', '98-21=77'] Exploring Operation: 36+77=113, Resulting Numbers: [113] 113,83 unequal: No Solution Exploring Operation: 36*77=2772, Resulting Numbers: [2772] 2772,83 unequal: No Solution Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[50, 105], Operations: ['21+29=50', '7+98=105'] Exploring Operation: 50+105=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 50*105=5250, Resulting Numbers: [5250] 5250,83 unequal: No Solution Exploring Operation: 105-50=55, Resulting Numbers: [55] 55,83 unequal: No Solution Moving to Node #0,4,2 Current State: 83:[98, 43], Operations: ['21+29=50', '50-7=43'] Exploring Operation: 98*43=4214, Resulting Numbers: [4214] 4214,83 unequal: No Solution Exploring Operation: 98+43=141, Resulting Numbers: [141] 141,83 unequal: No Solution Exploring Operation: 98-43=55, Resulting Numbers: [55] 55,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[29, 70], Operations: ['98-7=91', '91-21=70'] Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 29*70=2030, Resulting Numbers: [2030] 2030,83 unequal: No Solution Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[147, 69], Operations: ['21*7=147', '98-29=69'] Exploring Operation: 147-69=78, Resulting Numbers: [78] 78,83 unequal: No Solution Exploring Operation: 147*69=10143, Resulting Numbers: [10143] 10143,83 unequal: No Solution Exploring Operation: 147+69=216, Resulting Numbers: [216] 216,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[36, 119], Operations: ['7+29=36', '21+98=119'] Exploring Operation: 36+119=155, Resulting Numbers: [155] 155,83 unequal: No Solution Exploring Operation: 36*119=4284, Resulting Numbers: [4284] 4284,83 unequal: No Solution Exploring Operation: 119-36=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[21, 7, 29, 98], Operations: [] Exploring Operation: 7+29=36, Resulting Numbers: [21, 98, 36] Generated Node #0,1: 83:[21, 98, 36] Operation: 7+29=36 Moving to Node #0,1 Current State: 83:[21, 98, 36], Operations: ['7+29=36'] Exploring Operation: 21+98=119, Resulting Numbers: [36, 119] Generated Node #0,1,0: 83:[36, 119] Operation: 21+98=119 Moving to Node #0,1,0 Current State: 83:[36, 119], Operations: ['7+29=36', '21+98=119'] Exploring Operation: 119-36=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
0.927951
hs_5
sum_heuristic
[ 41, 59, 51, 30 ]
85
[ "59-41=18", "51*30=1530", "1530/18=85" ]
Current State: 85:[41, 59, 51, 30], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [51, 30, 18] Generated Node #2: [51, 30, 18] from Operation: 59-41=18 Current State: 85:[51, 30, 18], Operations: ['59-41=18'] Exploring Operation: 51*30=1530, Resulting Numbers: [18, 1530] Generated Node #3: [18, 1530] from Operation: 51*30=1530 Current State: 85:[18, 1530], Operations: ['59-41=18', '51*30=1530'] Exploring Operation: 1530/18=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[41, 59, 51, 30], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [41, 30, 8] Generated Node #0,0: 85:[41, 30, 8] Operation: 59-51=8 Moving to Node #0,0 Current State: 85:[41, 30, 8], Operations: ['59-51=8'] Exploring Operation: 41-30=11, Resulting Numbers: [8, 11] Generated Node #0,0,0: 85:[8, 11] Operation: 41-30=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[8, 11], Operations: ['59-51=8', '41-30=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,85 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
[ 13, 37, 78, 29 ]
73
[ "37-13=24", "78-29=49", "24+49=73" ]
Current State: 73:[13, 37, 78, 29], Operations: [] Exploring Operation: 37-13=24, Resulting Numbers: [78, 29, 24] Generated Node #2: [78, 29, 24] from Operation: 37-13=24 Current State: 73:[78, 29, 24], Operations: ['37-13=24'] Exploring Operation: 78-29=49, Resulting Numbers: [24, 49] Generated Node #3: [24, 49] from Operation: 78-29=49 Current State: 73:[24, 49], Operations: ['37-13=24', '78-29=49'] Exploring Operation: 24+49=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[13, 37, 78, 29], Operations: [] Exploring Operation: 13+37=50, Resulting Numbers: [78, 29, 50] Generated Node #0,0: 73:[78, 29, 50] Operation: 13+37=50 Exploring Operation: 37+29=66, Resulting Numbers: [13, 78, 66] Generated Node #0,1: 73:[13, 78, 66] Operation: 37+29=66 Exploring Operation: 13+29=42, Resulting Numbers: [37, 78, 42] Generated Node #0,2: 73:[37, 78, 42] Operation: 13+29=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[78, 29, 50], Operations: ['13+37=50'] Exploring Operation: 78-29=49, Resulting Numbers: [50, 49] Generated Node #0,0,0: 73:[50, 49] Operation: 78-29=49 Exploring Operation: 78+29=107, Resulting Numbers: [50, 107] Generated Node #0,0,1: 73:[50, 107] Operation: 78+29=107 Exploring Operation: 29+50=79, Resulting Numbers: [78, 79] Generated Node #0,0,2: 73:[78, 79] Operation: 29+50=79 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[78, 79], Operations: ['13+37=50', '29+50=79'] Exploring Operation: 78+79=157, Resulting Numbers: [157] 157,73 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 78*79=6162, Resulting Numbers: [6162] 6162,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[50, 49], Operations: ['13+37=50', '78-29=49'] Exploring Operation: 50*49=2450, Resulting Numbers: [2450] 2450,73 unequal: No Solution Exploring Operation: 50+49=99, Resulting Numbers: [99] 99,73 unequal: No Solution Exploring Operation: 50-49=1, Resulting Numbers: [1] 1,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[50, 107], Operations: ['13+37=50', '78+29=107'] Exploring Operation: 50+107=157, Resulting Numbers: [157] 157,73 unequal: No Solution Exploring Operation: 107-50=57, Resulting Numbers: [57] 57,73 unequal: No Solution Exploring Operation: 50*107=5350, Resulting Numbers: [5350] 5350,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[13, 78, 66], Operations: ['37+29=66'] Exploring Operation: 13+78=91, Resulting Numbers: [66, 91] Generated Node #0,1,0: 73:[66, 91] Operation: 13+78=91 Exploring Operation: 78-13=65, Resulting Numbers: [66, 65] Generated Node #0,1,1: 73:[66, 65] Operation: 78-13=65 Exploring Operation: 13+66=79, Resulting Numbers: [78, 79] Generated Node #0,1,2: 73:[78, 79] Operation: 13+66=79 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[78, 79], Operations: ['37+29=66', '13+66=79'] Exploring Operation: 78*79=6162, Resulting Numbers: [6162] 6162,73 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 78+79=157, Resulting Numbers: [157] 157,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[66, 65], Operations: ['37+29=66', '78-13=65'] Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 66+65=131, Resulting Numbers: [131] 131,73 unequal: No Solution Exploring Operation: 66*65=4290, Resulting Numbers: [4290] 4290,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[66, 91], Operations: ['37+29=66', '13+78=91'] Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,73 unequal: No Solution Exploring Operation: 66+91=157, Resulting Numbers: [157] 157,73 unequal: No Solution Exploring Operation: 66*91=6006, Resulting Numbers: [6006] 6006,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[37, 78, 42], Operations: ['13+29=42'] Exploring Operation: 78-37=41, Resulting Numbers: [42, 41] Generated Node #0,2,0: 73:[42, 41] Operation: 78-37=41 Exploring Operation: 37+42=79, Resulting Numbers: [78, 79] Generated Node #0,2,1: 73:[78, 79] Operation: 37+42=79 Exploring Operation: 37+78=115, Resulting Numbers: [42, 115] Generated Node #0,2,2: 73:[42, 115] Operation: 37+78=115 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[78, 79], Operations: ['13+29=42', '37+42=79'] Exploring Operation: 78*79=6162, Resulting Numbers: [6162] 6162,73 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 78+79=157, Resulting Numbers: [157] 157,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[42, 41], Operations: ['13+29=42', '78-37=41'] Exploring Operation: 42-41=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 42*41=1722, Resulting Numbers: [1722] 1722,73 unequal: No Solution Exploring Operation: 42+41=83, Resulting Numbers: [83] 83,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 73:[42, 115], Operations: ['13+29=42', '37+78=115'] Exploring Operation: 115-42=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[13, 37, 78, 29], Operations: [] Exploring Operation: 13+29=42, Resulting Numbers: [37, 78, 42] Generated Node #0,2: 73:[37, 78, 42] Operation: 13+29=42 Moving to Node #0,2 Current State: 73:[37, 78, 42], Operations: ['13+29=42'] Exploring Operation: 37+78=115, Resulting Numbers: [42, 115] Generated Node #0,2,2: 73:[42, 115] Operation: 37+78=115 Moving to Node #0,2,2 Current State: 73:[42, 115], Operations: ['13+29=42', '37+78=115'] Exploring Operation: 115-42=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_3
sum_heuristic
[ 2, 45, 89, 15 ]
74
[ "2*15=30", "89-45=44", "30+44=74" ]
Current State: 74:[2, 45, 89, 15], Operations: [] Exploring Operation: 2*15=30, Resulting Numbers: [45, 89, 30] Generated Node #2: [45, 89, 30] from Operation: 2*15=30 Current State: 74:[45, 89, 30], Operations: ['2*15=30'] Exploring Operation: 89-45=44, Resulting Numbers: [30, 44] Generated Node #3: [30, 44] from Operation: 89-45=44 Current State: 74:[30, 44], Operations: ['2*15=30', '89-45=44'] Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[2, 45, 89, 15], Operations: [] Exploring Operation: 89-15=74, Resulting Numbers: [2, 45, 74] Generated Node #0,0: 74:[2, 45, 74] Operation: 89-15=74 Exploring Operation: 89-45=44, Resulting Numbers: [2, 15, 44] Generated Node #0,1: 74:[2, 15, 44] Operation: 89-45=44 Exploring Operation: 45/15=3, Resulting Numbers: [2, 89, 3] Generated Node #0,2: 74:[2, 89, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[2, 45, 74], Operations: ['89-15=74'] Exploring Operation: 74/2=37, Resulting Numbers: [45, 37] Generated Node #0,0,0: 74:[45, 37] Operation: 74/2=37 Exploring Operation: 45-2=43, Resulting Numbers: [74, 43] Generated Node #0,0,1: 74:[74, 43] Operation: 45-2=43 Exploring Operation: 74-45=29, Resulting Numbers: [2, 29] Generated Node #0,0,2: 74:[2, 29] Operation: 74-45=29 Moving to Node #0,0,1 Current State: 74:[74, 43], Operations: ['89-15=74', '45-2=43'] Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,74 unequal: No Solution Exploring Operation: 74*43=3182, Resulting Numbers: [3182] 3182,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[45, 37], Operations: ['89-15=74', '74/2=37'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 45+37=82, Resulting Numbers: [82] 82,74 unequal: No Solution Exploring Operation: 45*37=1665, Resulting Numbers: [1665] 1665,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[2, 29], Operations: ['89-15=74', '74-45=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,74 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[2, 89, 3], Operations: ['45/15=3'] Exploring Operation: 3-2=1, Resulting Numbers: [89, 1] Generated Node #0,2,0: 74:[89, 1] Operation: 3-2=1 Exploring Operation: 89-3=86, Resulting Numbers: [2, 86] Generated Node #0,2,1: 74:[2, 86] Operation: 89-3=86 Exploring Operation: 89-2=87, Resulting Numbers: [3, 87] Generated Node #0,2,2: 74:[3, 87] Operation: 89-2=87 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[2, 86], Operations: ['45/15=3', '89-3=86'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,74 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 2+86=88, Resulting Numbers: [88] 88,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[3, 87], Operations: ['45/15=3', '89-2=87'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,74 unequal: No Solution Exploring Operation: 3+87=90, Resulting Numbers: [90] 90,74 unequal: No Solution Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[89, 1], Operations: ['45/15=3', '3-2=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,74 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,74 unequal: No Solution Exploring Operation: 89/1=89, Resulting Numbers: [89] 89,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[2, 15, 44], Operations: ['89-45=44'] Exploring Operation: 2*15=30, Resulting Numbers: [44, 30] Generated Node #0,1,0: 74:[44, 30] Operation: 2*15=30 Exploring Operation: 44-15=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 74:[2, 29] Operation: 44-15=29 Exploring Operation: 15+44=59, Resulting Numbers: [2, 59] Generated Node #0,1,2: 74:[2, 59] Operation: 15+44=59 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[2, 29], Operations: ['89-45=44', '44-15=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,74 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,74 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[44, 30], Operations: ['89-45=44', '2*15=30'] Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[2, 45, 89, 15], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [2, 15, 44] Generated Node #0,1: 74:[2, 15, 44] Operation: 89-45=44 Moving to Node #0,1 Current State: 74:[2, 15, 44], Operations: ['89-45=44'] Exploring Operation: 2*15=30, Resulting Numbers: [44, 30] Generated Node #0,1,0: 74:[44, 30] Operation: 2*15=30 Moving to Node #0,1,0 Current State: 74:[44, 30], Operations: ['89-45=44', '2*15=30'] Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
mult_heuristic
[ 15, 83, 71, 36 ]
12
[ "83-15=68", "71-68=3", "36/3=12" ]
Current State: 12:[15, 83, 71, 36], Operations: [] Exploring Operation: 83-15=68, Resulting Numbers: [71, 36, 68] Generated Node #2: [71, 36, 68] from Operation: 83-15=68 Current State: 12:[71, 36, 68], Operations: ['83-15=68'] Exploring Operation: 71-68=3, Resulting Numbers: [36, 3] Generated Node #3: [36, 3] from Operation: 71-68=3 Current State: 12:[36, 3], Operations: ['83-15=68', '71-68=3'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[15, 83, 71, 36], Operations: [] Exploring Operation: 83-36=47, Resulting Numbers: [15, 71, 47] Generated Node #0,0: 12:[15, 71, 47] Operation: 83-36=47 Exploring Operation: 71-36=35, Resulting Numbers: [15, 83, 35] Generated Node #0,1: 12:[15, 83, 35] Operation: 71-36=35 Exploring Operation: 83-71=12, Resulting Numbers: [15, 36, 12] Generated Node #0,2: 12:[15, 36, 12] Operation: 83-71=12 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[15, 36, 12], Operations: ['83-71=12'] Exploring Operation: 36-12=24, Resulting Numbers: [15, 24] Generated Node #0,2,0: 12:[15, 24] Operation: 36-12=24 Exploring Operation: 36-15=21, Resulting Numbers: [12, 21] Generated Node #0,2,1: 12:[12, 21] Operation: 36-15=21 Exploring Operation: 36/12=3, Resulting Numbers: [15, 3] Generated Node #0,2,2: 12:[15, 3] Operation: 36/12=3 Moving to Node #0,2,2 Current State: 12:[15, 3], Operations: ['83-71=12', '36/12=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,12 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[15, 83, 71, 36], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [15, 36, 12] Generated Node #0,2: 12:[15, 36, 12] Operation: 83-71=12 Moving to Node #0,2 Current State: 12:[15, 36, 12], Operations: ['83-71=12'] Exploring Operation: 36/12=3, Resulting Numbers: [15, 3] Generated Node #0,2,2: 12:[15, 3] Operation: 36/12=3 Moving to Node #0,2,2 Current State: 12:[15, 3], Operations: ['83-71=12', '36/12=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 57, 42, 2, 62 ]
49
[ "57-42=15", "2+62=64", "64-15=49" ]
Current State: 49:[57, 42, 2, 62], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [2, 62, 15] Generated Node #2: [2, 62, 15] from Operation: 57-42=15 Current State: 49:[2, 62, 15], Operations: ['57-42=15'] Exploring Operation: 2+62=64, Resulting Numbers: [15, 64] Generated Node #3: [15, 64] from Operation: 2+62=64 Current State: 49:[15, 64], Operations: ['57-42=15', '2+62=64'] Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[57, 42, 2, 62], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [42, 2, 5] Generated Node #0,0: 49:[42, 2, 5] Operation: 62-57=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[42, 2, 5], Operations: ['62-57=5'] Exploring Operation: 42+2=44, Resulting Numbers: [5, 44] Generated Node #0,0,0: 49:[5, 44] Operation: 42+2=44 Moving to Node #0,0,0 Current State: 49:[5, 44], Operations: ['62-57=5', '42+2=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[57, 42, 2, 62], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [42, 2, 5] Generated Node #0,0: 49:[42, 2, 5] Operation: 62-57=5 Moving to Node #0,0 Current State: 49:[42, 2, 5], Operations: ['62-57=5'] Exploring Operation: 42+2=44, Resulting Numbers: [5, 44] Generated Node #0,0,0: 49:[5, 44] Operation: 42+2=44 Moving to Node #0,0,0 Current State: 49:[5, 44], Operations: ['62-57=5', '42+2=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 31, 57, 50, 62 ]
95
[ "50-31=19", "62-57=5", "19*5=95" ]
Current State: 95:[31, 57, 50, 62], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [57, 62, 19] Generated Node #2: [57, 62, 19] from Operation: 50-31=19 Current State: 95:[57, 62, 19], Operations: ['50-31=19'] Exploring Operation: 62-57=5, Resulting Numbers: [19, 5] Generated Node #3: [19, 5] from Operation: 62-57=5 Current State: 95:[19, 5], Operations: ['50-31=19', '62-57=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[31, 57, 50, 62], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [31, 62, 7] Generated Node #0,0: 95:[31, 62, 7] Operation: 57-50=7 Exploring Operation: 62-57=5, Resulting Numbers: [31, 50, 5] Generated Node #0,1: 95:[31, 50, 5] Operation: 62-57=5 Moving to Node #0,1 Current State: 95:[31, 50, 5], Operations: ['62-57=5'] Exploring Operation: 50-31=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 95:[5, 19] Operation: 50-31=19 Exploring Operation: 31+50=81, Resulting Numbers: [5, 81] Generated Node #0,1,1: 95:[5, 81] Operation: 31+50=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[5, 19], Operations: ['62-57=5', '50-31=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[31, 57, 50, 62], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [31, 50, 5] Generated Node #0,1: 95:[31, 50, 5] Operation: 62-57=5 Moving to Node #0,1 Current State: 95:[31, 50, 5], Operations: ['62-57=5'] Exploring Operation: 50-31=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 95:[5, 19] Operation: 50-31=19 Moving to Node #0,1,0 Current State: 95:[5, 19], Operations: ['62-57=5', '50-31=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 7, 66, 92, 46 ]
48
[ "66-46=20", "7*20=140", "140-92=48" ]
Current State: 48:[7, 66, 92, 46], Operations: [] Exploring Operation: 66-46=20, Resulting Numbers: [7, 92, 20] Generated Node #2: [7, 92, 20] from Operation: 66-46=20 Current State: 48:[7, 92, 20], Operations: ['66-46=20'] Exploring Operation: 7*20=140, Resulting Numbers: [92, 140] Generated Node #3: [92, 140] from Operation: 7*20=140 Current State: 48:[92, 140], Operations: ['66-46=20', '7*20=140'] Exploring Operation: 140-92=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[7, 66, 92, 46], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [7, 66, 46] Generated Node #0,0: 48:[7, 66, 46] Operation: 92-46=46 Exploring Operation: 92/46=2, Resulting Numbers: [7, 66, 2] Generated Node #0,1: 48:[7, 66, 2] Operation: 92/46=2 Exploring Operation: 92-66=26, Resulting Numbers: [7, 46, 26] Generated Node #0,2: 48:[7, 46, 26] Operation: 92-66=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[7, 46, 26], Operations: ['92-66=26'] Exploring Operation: 26-7=19, Resulting Numbers: [46, 19] Generated Node #0,2,0: 48:[46, 19] Operation: 26-7=19 Exploring Operation: 7+46=53, Resulting Numbers: [26, 53] Generated Node #0,2,1: 48:[26, 53] Operation: 7+46=53 Exploring Operation: 46-26=20, Resulting Numbers: [7, 20] Generated Node #0,2,2: 48:[7, 20] Operation: 46-26=20 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[46, 19], Operations: ['92-66=26', '26-7=19'] Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,48 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 48:[7, 20], Operations: ['92-66=26', '46-26=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,48 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[26, 53], Operations: ['92-66=26', '7+46=53'] Exploring Operation: 26+53=79, Resulting Numbers: [79] 79,48 unequal: No Solution Exploring Operation: 53-26=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 26*53=1378, Resulting Numbers: [1378] 1378,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[7, 66, 2], Operations: ['92/46=2'] Exploring Operation: 66-2=64, Resulting Numbers: [7, 64] Generated Node #0,1,0: 48:[7, 64] Operation: 66-2=64 Exploring Operation: 66/2=33, Resulting Numbers: [7, 33] Generated Node #0,1,1: 48:[7, 33] Operation: 66/2=33 Exploring Operation: 66-7=59, Resulting Numbers: [2, 59] Generated Node #0,1,2: 48:[2, 59] Operation: 66-7=59 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 48:[7, 33], Operations: ['92/46=2', '66/2=33'] Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,48 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 48:[2, 59], Operations: ['92/46=2', '66-7=59'] Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,48 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,48 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[7, 64], Operations: ['92/46=2', '66-2=64'] Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,48 unequal: No Solution Exploring Operation: 7+64=71, Resulting Numbers: [71] 71,48 unequal: No Solution Exploring Operation: 7*64=448, Resulting Numbers: [448] 448,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[7, 66, 46], Operations: ['92-46=46'] Exploring Operation: 7+46=53, Resulting Numbers: [66, 53] Generated Node #0,0,0: 48:[66, 53] Operation: 7+46=53 Exploring Operation: 66-46=20, Resulting Numbers: [7, 20] Generated Node #0,0,1: 48:[7, 20] Operation: 66-46=20 Exploring Operation: 66-7=59, Resulting Numbers: [46, 59] Generated Node #0,0,2: 48:[46, 59] Operation: 66-7=59 Moving to Node #0,0,1 Current State: 48:[7, 20], Operations: ['92-46=46', '66-46=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,48 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,48 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[46, 59], Operations: ['92-46=46', '66-7=59'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,48 unequal: No Solution Exploring Operation: 46+59=105, Resulting Numbers: [105] 105,48 unequal: No Solution Exploring Operation: 46*59=2714, Resulting Numbers: [2714] 2714,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[66, 53], Operations: ['92-46=46', '7+46=53'] Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,48 unequal: No Solution Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,48 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,48 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
[ 57, 96, 24, 99 ]
93
[ "57-24=33", "99/33=3", "96-3=93" ]
Current State: 93:[57, 96, 24, 99], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [96, 99, 33] Generated Node #2: [96, 99, 33] from Operation: 57-24=33 Current State: 93:[96, 99, 33], Operations: ['57-24=33'] Exploring Operation: 99/33=3, Resulting Numbers: [96, 3] Generated Node #3: [96, 3] from Operation: 99/33=3 Current State: 93:[96, 3], Operations: ['57-24=33', '99/33=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[57, 96, 24, 99], Operations: [] Exploring Operation: 96-57=39, Resulting Numbers: [24, 99, 39] Generated Node #0,0: 93:[24, 99, 39] Operation: 96-57=39 Exploring Operation: 57-24=33, Resulting Numbers: [96, 99, 33] Generated Node #0,1: 93:[96, 99, 33] Operation: 57-24=33 Exploring Operation: 57+24=81, Resulting Numbers: [96, 99, 81] Generated Node #0,2: 93:[96, 99, 81] Operation: 57+24=81 Moving to Node #0,1 Current State: 93:[96, 99, 33], Operations: ['57-24=33'] Exploring Operation: 99-33=66, Resulting Numbers: [96, 66] Generated Node #0,1,0: 93:[96, 66] Operation: 99-33=66 Exploring Operation: 99-96=3, Resulting Numbers: [33, 3] Generated Node #0,1,1: 93:[33, 3] Operation: 99-96=3 Exploring Operation: 99/33=3, Resulting Numbers: [96, 3] Generated Node #0,1,2: 93:[96, 3] Operation: 99/33=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[33, 3], Operations: ['57-24=33', '99-96=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,93 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 93:[96, 3], Operations: ['57-24=33', '99/33=3'] Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,93 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[57, 96, 24, 99], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [96, 99, 33] Generated Node #0,1: 93:[96, 99, 33] Operation: 57-24=33 Moving to Node #0,1 Current State: 93:[96, 99, 33], Operations: ['57-24=33'] Exploring Operation: 99/33=3, Resulting Numbers: [96, 3] Generated Node #0,1,2: 93:[96, 3] Operation: 99/33=3 Moving to Node #0,1,2 Current State: 93:[96, 3], Operations: ['57-24=33', '99/33=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 99, 5, 55, 93 ]
91
[ "93-55=38", "5*38=190", "190-99=91" ]
Current State: 91:[99, 5, 55, 93], Operations: [] Exploring Operation: 93-55=38, Resulting Numbers: [99, 5, 38] Generated Node #2: [99, 5, 38] from Operation: 93-55=38 Current State: 91:[99, 5, 38], Operations: ['93-55=38'] Exploring Operation: 5*38=190, Resulting Numbers: [99, 190] Generated Node #3: [99, 190] from Operation: 5*38=190 Current State: 91:[99, 190], Operations: ['93-55=38', '5*38=190'] Exploring Operation: 190-99=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[99, 5, 55, 93], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [5, 93, 44] Generated Node #0,0: 91:[5, 93, 44] Operation: 99-55=44 Exploring Operation: 55/5=11, Resulting Numbers: [99, 93, 11] Generated Node #0,1: 91:[99, 93, 11] Operation: 55/5=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[99, 93, 11], Operations: ['55/5=11'] Exploring Operation: 99-93=6, Resulting Numbers: [11, 6] Generated Node #0,1,0: 91:[11, 6] Operation: 99-93=6 Exploring Operation: 99/11=9, Resulting Numbers: [93, 9] Generated Node #0,1,1: 91:[93, 9] Operation: 99/11=9 Moving to Node #0,1,0 Current State: 91:[11, 6], Operations: ['55/5=11', '99-93=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,91 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[93, 9], Operations: ['55/5=11', '99/11=9'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,91 unequal: No Solution Exploring Operation: 93+9=102, Resulting Numbers: [102] 102,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[5, 93, 44], Operations: ['99-55=44'] Exploring Operation: 44-5=39, Resulting Numbers: [93, 39] Generated Node #0,0,0: 91:[93, 39] Operation: 44-5=39 Exploring Operation: 93-5=88, Resulting Numbers: [44, 88] Generated Node #0,0,1: 91:[44, 88] Operation: 93-5=88 Moving to Node #0,0,0 Current State: 91:[93, 39], Operations: ['99-55=44', '44-5=39'] Exploring Operation: 93+39=132, Resulting Numbers: [132] 132,91 unequal: No Solution Exploring Operation: 93-39=54, Resulting Numbers: [54] 54,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[44, 88], Operations: ['99-55=44', '93-5=88'] Exploring Operation: 88/44=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 88-44=44, Resulting Numbers: [44] 44,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 86, 81, 58, 46 ]
84
[ "81-58=23", "46/23=2", "86-2=84" ]
Current State: 84:[86, 81, 58, 46], Operations: [] Exploring Operation: 81-58=23, Resulting Numbers: [86, 46, 23] Generated Node #2: [86, 46, 23] from Operation: 81-58=23 Current State: 84:[86, 46, 23], Operations: ['81-58=23'] Exploring Operation: 46/23=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 46/23=2 Current State: 84:[86, 2], Operations: ['81-58=23', '46/23=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[86, 81, 58, 46], Operations: [] Exploring Operation: 58-46=12, Resulting Numbers: [86, 81, 12] Generated Node #0,0: 84:[86, 81, 12] Operation: 58-46=12 Exploring Operation: 86-58=28, Resulting Numbers: [81, 46, 28] Generated Node #0,1: 84:[81, 46, 28] Operation: 86-58=28 Moving to Node #0,0 Current State: 84:[86, 81, 12], Operations: ['58-46=12'] Exploring Operation: 81+12=93, Resulting Numbers: [86, 93] Generated Node #0,0,0: 84:[86, 93] Operation: 81+12=93 Exploring Operation: 86-81=5, Resulting Numbers: [12, 5] Generated Node #0,0,1: 84:[12, 5] Operation: 86-81=5 Moving to Node #0,1 Current State: 84:[81, 46, 28], Operations: ['86-58=28'] Exploring Operation: 81-46=35, Resulting Numbers: [28, 35] Generated Node #0,1,0: 84:[28, 35] Operation: 81-46=35 Exploring Operation: 46-28=18, Resulting Numbers: [81, 18] Generated Node #0,1,1: 84:[81, 18] Operation: 46-28=18 Moving to Node #0,0,1 Current State: 84:[12, 5], Operations: ['58-46=12', '86-81=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[81, 18], Operations: ['86-58=28', '46-28=18'] Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,84 unequal: No Solution Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[28, 35], Operations: ['86-58=28', '81-46=35'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[86, 93], Operations: ['58-46=12', '81+12=93'] Exploring Operation: 93-86=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 86+93=179, Resulting Numbers: [179] 179,84 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 25, 51, 42, 28 ]
99
[ "25*51=1275", "42*28=1176", "1275-1176=99" ]
Current State: 99:[25, 51, 42, 28], Operations: [] Exploring Operation: 25*51=1275, Resulting Numbers: [42, 28, 1275] Generated Node #2: [42, 28, 1275] from Operation: 25*51=1275 Current State: 99:[42, 28, 1275], Operations: ['25*51=1275'] Exploring Operation: 42*28=1176, Resulting Numbers: [1275, 1176] Generated Node #3: [1275, 1176] from Operation: 42*28=1176 Current State: 99:[1275, 1176], Operations: ['25*51=1275', '42*28=1176'] Exploring Operation: 1275-1176=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[25, 51, 42, 28], Operations: [] Exploring Operation: 51-42=9, Resulting Numbers: [25, 28, 9] Generated Node #0,0: 99:[25, 28, 9] Operation: 51-42=9 Exploring Operation: 28-25=3, Resulting Numbers: [51, 42, 3] Generated Node #0,1: 99:[51, 42, 3] Operation: 28-25=3 Exploring Operation: 51+42=93, Resulting Numbers: [25, 28, 93] Generated Node #0,2: 99:[25, 28, 93] Operation: 51+42=93 Exploring Operation: 51-25=26, Resulting Numbers: [42, 28, 26] Generated Node #0,3: 99:[42, 28, 26] Operation: 51-25=26 Exploring Operation: 51-28=23, Resulting Numbers: [25, 42, 23] Generated Node #0,4: 99:[25, 42, 23] Operation: 51-28=23 Moving to Node #0,0 Current State: 99:[25, 28, 9], Operations: ['51-42=9'] Exploring Operation: 25+9=34, Resulting Numbers: [28, 34] Generated Node #0,0,0: 99:[28, 34] Operation: 25+9=34 Exploring Operation: 28-25=3, Resulting Numbers: [9, 3] Generated Node #0,0,1: 99:[9, 3] Operation: 28-25=3 Exploring Operation: 28+9=37, Resulting Numbers: [25, 37] Generated Node #0,0,2: 99:[25, 37] Operation: 28+9=37 Exploring Operation: 25-9=16, Resulting Numbers: [28, 16] Generated Node #0,0,3: 99:[28, 16] Operation: 25-9=16 Exploring Operation: 28-9=19, Resulting Numbers: [25, 19] Generated Node #0,0,4: 99:[25, 19] Operation: 28-9=19 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[9, 3], Operations: ['51-42=9', '28-25=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,99 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[28, 34], Operations: ['51-42=9', '25+9=34'] Exploring Operation: 34-28=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 28+34=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 28*34=952, Resulting Numbers: [952] 952,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 99:[28, 16], Operations: ['51-42=9', '25-9=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,99 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[25, 37], Operations: ['51-42=9', '28+9=37'] Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,99 unequal: No Solution Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,99 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 99:[25, 19], Operations: ['51-42=9', '28-9=19'] Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,99 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,99 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: 99:[25, 28, 93], Operations: ['51+42=93'] Exploring Operation: 25+93=118, Resulting Numbers: [28, 118] Generated Node #0,2,0: 99:[28, 118] Operation: 25+93=118 Exploring Operation: 93-25=68, Resulting Numbers: [28, 68] Generated Node #0,2,1: 99:[28, 68] Operation: 93-25=68 Exploring Operation: 25+28=53, Resulting Numbers: [93, 53] Generated Node #0,2,2: 99:[93, 53] Operation: 25+28=53 Exploring Operation: 28-25=3, Resulting Numbers: [93, 3] Generated Node #0,2,3: 99:[93, 3] Operation: 28-25=3 Exploring Operation: 28+93=121, Resulting Numbers: [25, 121] Generated Node #0,2,4: 99:[25, 121] Operation: 28+93=121 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 99:[93, 3], Operations: ['51+42=93', '28-25=3'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 93*3=279, Resulting Numbers: [279] 279,99 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[28, 118], Operations: ['51+42=93', '25+93=118'] Exploring Operation: 118-28=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 28+118=146, Resulting Numbers: [146] 146,99 unequal: No Solution Exploring Operation: 28*118=3304, Resulting Numbers: [3304] 3304,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[93, 53], Operations: ['51+42=93', '25+28=53'] Exploring Operation: 93-53=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 93*53=4929, Resulting Numbers: [4929] 4929,99 unequal: No Solution Exploring Operation: 93+53=146, Resulting Numbers: [146] 146,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 99:[25, 121], Operations: ['51+42=93', '28+93=121'] Exploring Operation: 25*121=3025, Resulting Numbers: [3025] 3025,99 unequal: No Solution Exploring Operation: 25+121=146, Resulting Numbers: [146] 146,99 unequal: No Solution Exploring Operation: 121-25=96, Resulting Numbers: [96] 96,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 99:[28, 68], Operations: ['51+42=93', '93-25=68'] Exploring Operation: 28+68=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 28*68=1904, Resulting Numbers: [1904] 1904,99 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: 99:[42, 28, 26], Operations: ['51-25=26'] Exploring Operation: 28+26=54, Resulting Numbers: [42, 54] Generated Node #0,3,0: 99:[42, 54] Operation: 28+26=54 Exploring Operation: 42-28=14, Resulting Numbers: [26, 14] Generated Node #0,3,1: 99:[26, 14] Operation: 42-28=14 Exploring Operation: 42+28=70, Resulting Numbers: [26, 70] Generated Node #0,3,2: 99:[26, 70] Operation: 42+28=70 Exploring Operation: 28-26=2, Resulting Numbers: [42, 2] Generated Node #0,3,3: 99:[42, 2] Operation: 28-26=2 Exploring Operation: 42-26=16, Resulting Numbers: [28, 16] Generated Node #0,3,4: 99:[28, 16] Operation: 42-26=16 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 99:[26, 14], Operations: ['51-25=26', '42-28=14'] Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,99 unequal: No Solution Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 26*14=364, Resulting Numbers: [364] 364,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 99:[42, 2], Operations: ['51-25=26', '28-26=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,99 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 99:[28, 16], Operations: ['51-25=26', '42-26=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,99 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 99:[42, 54], Operations: ['51-25=26', '28+26=54'] Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 42*54=2268, Resulting Numbers: [2268] 2268,99 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[26, 70], Operations: ['51-25=26', '42+28=70'] Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,99 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: 99:[51, 42, 3], Operations: ['28-25=3'] Exploring Operation: 51-42=9, Resulting Numbers: [3, 9] Generated Node #0,1,0: 99:[3, 9] Operation: 51-42=9 Exploring Operation: 51+42=93, Resulting Numbers: [3, 93] Generated Node #0,1,1: 99:[3, 93] Operation: 51+42=93 Exploring Operation: 51/3=17, Resulting Numbers: [42, 17] Generated Node #0,1,2: 99:[42, 17] Operation: 51/3=17 Exploring Operation: 51-3=48, Resulting Numbers: [42, 48] Generated Node #0,1,3: 99:[42, 48] Operation: 51-3=48 Exploring Operation: 42/3=14, Resulting Numbers: [51, 14] Generated Node #0,1,4: 99:[51, 14] Operation: 42/3=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[3, 9], Operations: ['28-25=3', '51-42=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,99 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[3, 93], Operations: ['28-25=3', '51+42=93'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,99 unequal: No Solution Exploring Operation: 3*93=279, Resulting Numbers: [279] 279,99 unequal: No Solution Exploring Operation: 3+93=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[42, 17], Operations: ['28-25=3', '51/3=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,99 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 99:[51, 14], Operations: ['28-25=3', '42/3=14'] Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,99 unequal: No Solution Exploring Operation: 51*14=714, Resulting Numbers: [714] 714,99 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[42, 48], Operations: ['28-25=3', '51-3=48'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,99 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: 99:[25, 42, 23], Operations: ['51-28=23'] Exploring Operation: 25-23=2, Resulting Numbers: [42, 2] Generated Node #0,4,0: 99:[42, 2] Operation: 25-23=2 Exploring Operation: 25+23=48, Resulting Numbers: [42, 48] Generated Node #0,4,1: 99:[42, 48] Operation: 25+23=48 Exploring Operation: 42-23=19, Resulting Numbers: [25, 19] Generated Node #0,4,2: 99:[25, 19] Operation: 42-23=19 Exploring Operation: 42+23=65, Resulting Numbers: [25, 65] Generated Node #0,4,3: 99:[25, 65] Operation: 42+23=65 Exploring Operation: 42-25=17, Resulting Numbers: [23, 17] Generated Node #0,4,4: 99:[23, 17] Operation: 42-25=17 Moving to Node #0,4,0 Current State: 99:[42, 2], Operations: ['51-28=23', '25-23=2'] Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,99 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,99 unequal: No Solution Moving to Node #0,4,4 Current State: 99:[23, 17], Operations: ['51-28=23', '42-25=17'] Exploring Operation: 23+17=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 23*17=391, Resulting Numbers: [391] 391,99 unequal: No Solution Moving to Node #0,4,2 Current State: 99:[25, 19], Operations: ['51-28=23', '42-23=19'] Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 25*19=475, Resulting Numbers: [475] 475,99 unequal: No Solution Moving to Node #0,4,1 Current State: 99:[42, 48], Operations: ['51-28=23', '25+23=48'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,99 unequal: No Solution Moving to Node #0,4,3 Current State: 99:[25, 65], Operations: ['51-28=23', '42+23=65'] Exploring Operation: 25*65=1625, Resulting Numbers: [1625] 1625,99 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,99 unequal: No Solution Exploring Operation: 25+65=90, Resulting Numbers: [90] 90,99 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 29, 32, 68, 67 ]
74
[ "29+32=61", "68+67=135", "135-61=74" ]
Current State: 74:[29, 32, 68, 67], Operations: [] Exploring Operation: 29+32=61, Resulting Numbers: [68, 67, 61] Generated Node #2: [68, 67, 61] from Operation: 29+32=61 Current State: 74:[68, 67, 61], Operations: ['29+32=61'] Exploring Operation: 68+67=135, Resulting Numbers: [61, 135] Generated Node #3: [61, 135] from Operation: 68+67=135 Current State: 74:[61, 135], Operations: ['29+32=61', '68+67=135'] Exploring Operation: 135-61=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[29, 32, 68, 67], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [29, 32, 1] Generated Node #0,0: 74:[29, 32, 1] Operation: 68-67=1 Exploring Operation: 68-29=39, Resulting Numbers: [32, 67, 39] Generated Node #0,1: 74:[32, 67, 39] Operation: 68-29=39 Exploring Operation: 32-29=3, Resulting Numbers: [68, 67, 3] Generated Node #0,2: 74:[68, 67, 3] Operation: 32-29=3 Exploring Operation: 67-29=38, Resulting Numbers: [32, 68, 38] Generated Node #0,3: 74:[32, 68, 38] Operation: 67-29=38 Exploring Operation: 68-32=36, Resulting Numbers: [29, 67, 36] Generated Node #0,4: 74:[29, 67, 36] Operation: 68-32=36 Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[32, 68, 38], Operations: ['67-29=38'] Exploring Operation: 32+38=70, Resulting Numbers: [68, 70] Generated Node #0,3,0: 74:[68, 70] Operation: 32+38=70 Exploring Operation: 68-32=36, Resulting Numbers: [38, 36] Generated Node #0,3,1: 74:[38, 36] Operation: 68-32=36 Exploring Operation: 32+68=100, Resulting Numbers: [38, 100] Generated Node #0,3,2: 74:[38, 100] Operation: 32+68=100 Exploring Operation: 38-32=6, Resulting Numbers: [68, 6] Generated Node #0,3,3: 74:[68, 6] Operation: 38-32=6 Exploring Operation: 68-38=30, Resulting Numbers: [32, 30] Generated Node #0,3,4: 74:[32, 30] Operation: 68-38=30 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 74:[38, 36], Operations: ['67-29=38', '68-32=36'] Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,74 unequal: No Solution Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[29, 32, 68, 67], Operations: [] Exploring Operation: 67-29=38, Resulting Numbers: [32, 68, 38] Generated Node #0,3: 74:[32, 68, 38] Operation: 67-29=38 Moving to Node #0,3 Current State: 74:[32, 68, 38], Operations: ['67-29=38'] Exploring Operation: 68-32=36, Resulting Numbers: [38, 36] Generated Node #0,3,1: 74:[38, 36] Operation: 68-32=36 Moving to Node #0,3,1 Current State: 74:[38, 36], Operations: ['67-29=38', '68-32=36'] Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 79, 80, 7, 94 ]
100
[ "80-79=1", "7+94=101", "101-1=100" ]
Current State: 100:[79, 80, 7, 94], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [7, 94, 1] Generated Node #2: [7, 94, 1] from Operation: 80-79=1 Current State: 100:[7, 94, 1], Operations: ['80-79=1'] Exploring Operation: 7+94=101, Resulting Numbers: [1, 101] Generated Node #3: [1, 101] from Operation: 7+94=101 Current State: 100:[1, 101], Operations: ['80-79=1', '7+94=101'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[79, 80, 7, 94], Operations: [] Exploring Operation: 94-79=15, Resulting Numbers: [80, 7, 15] Generated Node #0,0: 100:[80, 7, 15] Operation: 94-79=15 Exploring Operation: 80-79=1, Resulting Numbers: [7, 94, 1] Generated Node #0,1: 100:[7, 94, 1] Operation: 80-79=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[7, 94, 1], Operations: ['80-79=1'] Exploring Operation: 7+94=101, Resulting Numbers: [1, 101] Generated Node #0,1,0: 100:[1, 101] Operation: 7+94=101 Exploring Operation: 7-1=6, Resulting Numbers: [94, 6] Generated Node #0,1,1: 100:[94, 6] Operation: 7-1=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[1, 101], Operations: ['80-79=1', '7+94=101'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[79, 80, 7, 94], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [7, 94, 1] Generated Node #0,1: 100:[7, 94, 1] Operation: 80-79=1 Moving to Node #0,1 Current State: 100:[7, 94, 1], Operations: ['80-79=1'] Exploring Operation: 7+94=101, Resulting Numbers: [1, 101] Generated Node #0,1,0: 100:[1, 101] Operation: 7+94=101 Moving to Node #0,1,0 Current State: 100:[1, 101], Operations: ['80-79=1', '7+94=101'] Exploring Operation: 101-1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 40, 24, 9, 86 ]
71
[ "40*9=360", "360/24=15", "86-15=71" ]
Current State: 71:[40, 24, 9, 86], Operations: [] Exploring Operation: 40*9=360, Resulting Numbers: [24, 86, 360] Generated Node #2: [24, 86, 360] from Operation: 40*9=360 Current State: 71:[24, 86, 360], Operations: ['40*9=360'] Exploring Operation: 360/24=15, Resulting Numbers: [86, 15] Generated Node #3: [86, 15] from Operation: 360/24=15 Current State: 71:[86, 15], Operations: ['40*9=360', '360/24=15'] Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[40, 24, 9, 86], Operations: [] Exploring Operation: 40+24=64, Resulting Numbers: [9, 86, 64] Generated Node #0,0: 71:[9, 86, 64] Operation: 40+24=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[9, 86, 64], Operations: ['40+24=64'] Exploring Operation: 86-9=77, Resulting Numbers: [64, 77] Generated Node #0,0,0: 71:[64, 77] Operation: 86-9=77 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[64, 77], Operations: ['40+24=64', '86-9=77'] Exploring Operation: 77-64=13, Resulting Numbers: [13] 13,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 5, 15, 51 ]
16
[ "44-15=29", "51+29=80", "80/5=16" ]
Current State: 16:[44, 5, 15, 51], Operations: [] Exploring Operation: 44-15=29, Resulting Numbers: [5, 51, 29] Generated Node #2: [5, 51, 29] from Operation: 44-15=29 Current State: 16:[5, 51, 29], Operations: ['44-15=29'] Exploring Operation: 51+29=80, Resulting Numbers: [5, 80] Generated Node #3: [5, 80] from Operation: 51+29=80 Current State: 16:[5, 80], Operations: ['44-15=29', '51+29=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[44, 5, 15, 51], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [5, 15, 7] Generated Node #0,0: 16:[5, 15, 7] Operation: 51-44=7 Moving to Node #0,0 Current State: 16:[5, 15, 7], Operations: ['51-44=7'] Exploring Operation: 7-5=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 16:[15, 2] Operation: 7-5=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[15, 2], Operations: ['51-44=7', '7-5=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,16 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
[ 48, 51, 12, 84 ]
80
[ "51-48=3", "12/3=4", "84-4=80" ]
Current State: 80:[48, 51, 12, 84], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [12, 84, 3] Generated Node #2: [12, 84, 3] from Operation: 51-48=3 Current State: 80:[12, 84, 3], Operations: ['51-48=3'] Exploring Operation: 12/3=4, Resulting Numbers: [84, 4] Generated Node #3: [84, 4] from Operation: 12/3=4 Current State: 80:[84, 4], Operations: ['51-48=3', '12/3=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[48, 51, 12, 84], Operations: [] Exploring Operation: 84-48=36, Resulting Numbers: [51, 12, 36] Generated Node #0,0: 80:[51, 12, 36] Operation: 84-48=36 Exploring Operation: 51-12=39, Resulting Numbers: [48, 84, 39] Generated Node #0,1: 80:[48, 84, 39] Operation: 51-12=39 Exploring Operation: 48/12=4, Resulting Numbers: [51, 84, 4] Generated Node #0,2: 80:[51, 84, 4] Operation: 48/12=4 Exploring Operation: 51-48=3, Resulting Numbers: [12, 84, 3] Generated Node #0,3: 80:[12, 84, 3] Operation: 51-48=3 Moving to Node #0,3 Current State: 80:[12, 84, 3], Operations: ['51-48=3'] Exploring Operation: 84-3=81, Resulting Numbers: [12, 81] Generated Node #0,3,0: 80:[12, 81] Operation: 84-3=81 Exploring Operation: 12/3=4, Resulting Numbers: [84, 4] Generated Node #0,3,1: 80:[84, 4] Operation: 12/3=4 Exploring Operation: 12+3=15, Resulting Numbers: [84, 15] Generated Node #0,3,2: 80:[84, 15] Operation: 12+3=15 Exploring Operation: 84/12=7, Resulting Numbers: [3, 7] Generated Node #0,3,3: 80:[3, 7] Operation: 84/12=7 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 80:[3, 7], Operations: ['51-48=3', '84/12=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,80 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 #0,3,0 Current State: 80:[12, 81], Operations: ['51-48=3', '84-3=81'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 12*81=972, Resulting Numbers: [972] 972,80 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:[84, 4], Operations: ['51-48=3', '12/3=4'] Exploring Operation: 84*4=336, Resulting Numbers: [336] 336,80 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[48, 51, 12, 84], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [12, 84, 3] Generated Node #0,3: 80:[12, 84, 3] Operation: 51-48=3 Moving to Node #0,3 Current State: 80:[12, 84, 3], Operations: ['51-48=3'] Exploring Operation: 12/3=4, Resulting Numbers: [84, 4] Generated Node #0,3,1: 80:[84, 4] Operation: 12/3=4 Moving to Node #0,3,1 Current State: 80:[84, 4], Operations: ['51-48=3', '12/3=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 31, 28, 67, 19 ]
27
[ "31+28=59", "67+19=86", "86-59=27" ]
Current State: 27:[31, 28, 67, 19], Operations: [] Exploring Operation: 31+28=59, Resulting Numbers: [67, 19, 59] Generated Node #2: [67, 19, 59] from Operation: 31+28=59 Current State: 27:[67, 19, 59], Operations: ['31+28=59'] Exploring Operation: 67+19=86, Resulting Numbers: [59, 86] Generated Node #3: [59, 86] from Operation: 67+19=86 Current State: 27:[59, 86], Operations: ['31+28=59', '67+19=86'] Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[31, 28, 67, 19], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [28, 19, 36] Generated Node #0,0: 27:[28, 19, 36] Operation: 67-31=36 Exploring Operation: 67-28=39, Resulting Numbers: [31, 19, 39] Generated Node #0,1: 27:[31, 19, 39] Operation: 67-28=39 Exploring Operation: 28-19=9, Resulting Numbers: [31, 67, 9] Generated Node #0,2: 27:[31, 67, 9] Operation: 28-19=9 Exploring Operation: 31-19=12, Resulting Numbers: [28, 67, 12] Generated Node #0,3: 27:[28, 67, 12] Operation: 31-19=12 Exploring Operation: 67-19=48, Resulting Numbers: [31, 28, 48] Generated Node #0,4: 27:[31, 28, 48] Operation: 67-19=48 Moving to Node #0,0 Current State: 27:[28, 19, 36], Operations: ['67-31=36'] Exploring Operation: 19+36=55, Resulting Numbers: [28, 55] Generated Node #0,0,0: 27:[28, 55] Operation: 19+36=55 Exploring Operation: 36-19=17, Resulting Numbers: [28, 17] Generated Node #0,0,1: 27:[28, 17] Operation: 36-19=17 Exploring Operation: 36-28=8, Resulting Numbers: [19, 8] Generated Node #0,0,2: 27:[19, 8] Operation: 36-28=8 Exploring Operation: 28+19=47, Resulting Numbers: [36, 47] Generated Node #0,0,3: 27:[36, 47] Operation: 28+19=47 Exploring Operation: 28-19=9, Resulting Numbers: [36, 9] Generated Node #0,0,4: 27:[36, 9] Operation: 28-19=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[28, 17], Operations: ['67-31=36', '36-19=17'] Exploring Operation: 28+17=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,27 unequal: No Solution Exploring Operation: 28*17=476, Resulting Numbers: [476] 476,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 27:[19, 8], Operations: ['67-31=36', '36-28=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,27 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,27 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[31, 28, 67, 19], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [28, 19, 36] Generated Node #0,0: 27:[28, 19, 36] Operation: 67-31=36 Moving to Node #0,0 Current State: 27:[28, 19, 36], Operations: ['67-31=36'] Exploring Operation: 36-28=8, Resulting Numbers: [19, 8] Generated Node #0,0,2: 27:[19, 8] Operation: 36-28=8 Moving to Node #0,0,2 Current State: 27:[19, 8], Operations: ['67-31=36', '36-28=8'] Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 47, 70, 57, 88 ]
86
[ "47+70=117", "88-57=31", "117-31=86" ]
Current State: 86:[47, 70, 57, 88], Operations: [] Exploring Operation: 47+70=117, Resulting Numbers: [57, 88, 117] Generated Node #2: [57, 88, 117] from Operation: 47+70=117 Current State: 86:[57, 88, 117], Operations: ['47+70=117'] Exploring Operation: 88-57=31, Resulting Numbers: [117, 31] Generated Node #3: [117, 31] from Operation: 88-57=31 Current State: 86:[117, 31], Operations: ['47+70=117', '88-57=31'] Exploring Operation: 117-31=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[47, 70, 57, 88], Operations: [] Exploring Operation: 57-47=10, Resulting Numbers: [70, 88, 10] Generated Node #0,0: 86:[70, 88, 10] Operation: 57-47=10 Exploring Operation: 88-47=41, Resulting Numbers: [70, 57, 41] Generated Node #0,1: 86:[70, 57, 41] Operation: 88-47=41 Exploring Operation: 70-57=13, Resulting Numbers: [47, 88, 13] Generated Node #0,2: 86:[47, 88, 13] Operation: 70-57=13 Exploring Operation: 88-70=18, Resulting Numbers: [47, 57, 18] Generated Node #0,3: 86:[47, 57, 18] Operation: 88-70=18 Exploring Operation: 88-57=31, Resulting Numbers: [47, 70, 31] Generated Node #0,4: 86:[47, 70, 31] Operation: 88-57=31 Moving to Node #0,2 Current State: 86:[47, 88, 13], Operations: ['70-57=13'] Exploring Operation: 47-13=34, Resulting Numbers: [88, 34] Generated Node #0,2,0: 86:[88, 34] Operation: 47-13=34 Exploring Operation: 47+13=60, Resulting Numbers: [88, 60] Generated Node #0,2,1: 86:[88, 60] Operation: 47+13=60 Exploring Operation: 88+13=101, Resulting Numbers: [47, 101] Generated Node #0,2,2: 86:[47, 101] Operation: 88+13=101 Exploring Operation: 88-47=41, Resulting Numbers: [13, 41] Generated Node #0,2,3: 86:[13, 41] Operation: 88-47=41 Exploring Operation: 88-13=75, Resulting Numbers: [47, 75] Generated Node #0,2,4: 86:[47, 75] Operation: 88-13=75 Moving to Node #0,0 Current State: 86:[70, 88, 10], Operations: ['57-47=10'] Exploring Operation: 70/10=7, Resulting Numbers: [88, 7] Generated Node #0,0,0: 86:[88, 7] Operation: 70/10=7 Exploring Operation: 88-10=78, Resulting Numbers: [70, 78] Generated Node #0,0,1: 86:[70, 78] Operation: 88-10=78 Exploring Operation: 70-10=60, Resulting Numbers: [88, 60] Generated Node #0,0,2: 86:[88, 60] Operation: 70-10=60 Exploring Operation: 88-70=18, Resulting Numbers: [10, 18] Generated Node #0,0,3: 86:[10, 18] Operation: 88-70=18 Exploring Operation: 70+10=80, Resulting Numbers: [88, 80] Generated Node #0,0,4: 86:[88, 80] Operation: 70+10=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[88, 7], Operations: ['57-47=10', '70/10=7'] Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,86 unequal: No Solution Exploring Operation: 88*7=616, Resulting Numbers: [616] 616,86 unequal: No Solution Exploring Operation: 88+7=95, Resulting Numbers: [95] 95,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 86:[88, 80], Operations: ['57-47=10', '70+10=80'] Exploring Operation: 88+80=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 88*80=7040, Resulting Numbers: [7040] 7040,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[88, 60], Operations: ['57-47=10', '70-10=60'] Exploring Operation: 88+60=148, Resulting Numbers: [148] 148,86 unequal: No Solution Exploring Operation: 88*60=5280, Resulting Numbers: [5280] 5280,86 unequal: No Solution Exploring Operation: 88-60=28, Resulting Numbers: [28] 28,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[70, 78], Operations: ['57-47=10', '88-10=78'] Exploring Operation: 78-70=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 70+78=148, Resulting Numbers: [148] 148,86 unequal: No Solution Exploring Operation: 70*78=5460, Resulting Numbers: [5460] 5460,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 86:[10, 18], Operations: ['57-47=10', '88-70=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,86 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,86 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: 86:[70, 57, 41], Operations: ['88-47=41'] Exploring Operation: 57-41=16, Resulting Numbers: [70, 16] Generated Node #0,1,0: 86:[70, 16] Operation: 57-41=16 Exploring Operation: 70-57=13, Resulting Numbers: [41, 13] Generated Node #0,1,1: 86:[41, 13] Operation: 70-57=13 Exploring Operation: 70+41=111, Resulting Numbers: [57, 111] Generated Node #0,1,2: 86:[57, 111] Operation: 70+41=111 Exploring Operation: 57+41=98, Resulting Numbers: [70, 98] Generated Node #0,1,3: 86:[70, 98] Operation: 57+41=98 Exploring Operation: 70-41=29, Resulting Numbers: [57, 29] Generated Node #0,1,4: 86:[57, 29] Operation: 70-41=29 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[41, 13], Operations: ['88-47=41', '70-57=13'] Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,86 unequal: No Solution Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[70, 98], Operations: ['88-47=41', '57+41=98'] Exploring Operation: 70+98=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 70*98=6860, Resulting Numbers: [6860] 6860,86 unequal: No Solution Exploring Operation: 98-70=28, Resulting Numbers: [28] 28,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 86:[57, 29], Operations: ['88-47=41', '70-41=29'] Exploring Operation: 57-29=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 57+29=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[47, 70, 57, 88], Operations: [] Exploring Operation: 88-47=41, Resulting Numbers: [70, 57, 41] Generated Node #0,1: 86:[70, 57, 41] Operation: 88-47=41 Moving to Node #0,1 Current State: 86:[70, 57, 41], Operations: ['88-47=41'] Exploring Operation: 70-41=29, Resulting Numbers: [57, 29] Generated Node #0,1,4: 86:[57, 29] Operation: 70-41=29 Moving to Node #0,1,4 Current State: 86:[57, 29], Operations: ['88-47=41', '70-41=29'] Exploring Operation: 57+29=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 33, 15, 51, 23 ]
69
[ "33+15=48", "51-48=3", "23*3=69" ]
Current State: 69:[33, 15, 51, 23], Operations: [] Exploring Operation: 33+15=48, Resulting Numbers: [51, 23, 48] Generated Node #2: [51, 23, 48] from Operation: 33+15=48 Current State: 69:[51, 23, 48], Operations: ['33+15=48'] Exploring Operation: 51-48=3, Resulting Numbers: [23, 3] Generated Node #3: [23, 3] from Operation: 51-48=3 Current State: 69:[23, 3], Operations: ['33+15=48', '51-48=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[33, 15, 51, 23], Operations: [] Exploring Operation: 33-15=18, Resulting Numbers: [51, 23, 18] Generated Node #0,0: 69:[51, 23, 18] Operation: 33-15=18 Exploring Operation: 15+51=66, Resulting Numbers: [33, 23, 66] Generated Node #0,1: 69:[33, 23, 66] Operation: 15+51=66 Exploring Operation: 51-33=18, Resulting Numbers: [15, 23, 18] Generated Node #0,2: 69:[15, 23, 18] Operation: 51-33=18 Moving to Node #0,1 Current State: 69:[33, 23, 66], Operations: ['15+51=66'] Exploring Operation: 66/33=2, Resulting Numbers: [23, 2] Generated Node #0,1,0: 69:[23, 2] Operation: 66/33=2 Exploring Operation: 66-33=33, Resulting Numbers: [23, 33] Generated Node #0,1,1: 69:[23, 33] Operation: 66-33=33 Exploring Operation: 33-23=10, Resulting Numbers: [66, 10] Generated Node #0,1,2: 69:[66, 10] Operation: 33-23=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[23, 2], Operations: ['15+51=66', '66/33=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,69 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 #0,1,1 Current State: 69:[23, 33], Operations: ['15+51=66', '66-33=33'] Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,69 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 #0,1,2 Current State: 69:[66, 10], Operations: ['15+51=66', '33-23=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 66*10=660, Resulting Numbers: [660] 660,69 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[15, 23, 18], Operations: ['51-33=18'] Exploring Operation: 15+18=33, Resulting Numbers: [23, 33] Generated Node #0,2,0: 69:[23, 33] Operation: 15+18=33 Exploring Operation: 18-15=3, Resulting Numbers: [23, 3] Generated Node #0,2,1: 69:[23, 3] Operation: 18-15=3 Exploring Operation: 23-15=8, Resulting Numbers: [18, 8] Generated Node #0,2,2: 69:[18, 8] Operation: 23-15=8 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[23, 3], Operations: ['51-33=18', '18-15=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[33, 15, 51, 23], Operations: [] Exploring Operation: 51-33=18, Resulting Numbers: [15, 23, 18] Generated Node #0,2: 69:[15, 23, 18] Operation: 51-33=18 Moving to Node #0,2 Current State: 69:[15, 23, 18], Operations: ['51-33=18'] Exploring Operation: 18-15=3, Resulting Numbers: [23, 3] Generated Node #0,2,1: 69:[23, 3] Operation: 18-15=3 Moving to Node #0,2,1 Current State: 69:[23, 3], Operations: ['51-33=18', '18-15=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 41, 33, 3, 92 ]
28
[ "41-33=8", "92-8=84", "84/3=28" ]
Current State: 28:[41, 33, 3, 92], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [3, 92, 8] Generated Node #2: [3, 92, 8] from Operation: 41-33=8 Current State: 28:[3, 92, 8], Operations: ['41-33=8'] Exploring Operation: 92-8=84, Resulting Numbers: [3, 84] Generated Node #3: [3, 84] from Operation: 92-8=84 Current State: 28:[3, 84], Operations: ['41-33=8', '92-8=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[41, 33, 3, 92], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [3, 92, 8] Generated Node #0,0: 28:[3, 92, 8] Operation: 41-33=8 Exploring Operation: 92-41=51, Resulting Numbers: [33, 3, 51] Generated Node #0,1: 28:[33, 3, 51] Operation: 92-41=51 Exploring Operation: 33-3=30, Resulting Numbers: [41, 92, 30] Generated Node #0,2: 28:[41, 92, 30] Operation: 33-3=30 Exploring Operation: 92-33=59, Resulting Numbers: [41, 3, 59] Generated Node #0,3: 28:[41, 3, 59] Operation: 92-33=59 Exploring Operation: 41-3=38, Resulting Numbers: [33, 92, 38] Generated Node #0,4: 28:[33, 92, 38] Operation: 41-3=38 Moving to Node #0,1 Current State: 28:[33, 3, 51], Operations: ['92-41=51'] Exploring Operation: 51-33=18, Resulting Numbers: [3, 18] Generated Node #0,1,0: 28:[3, 18] Operation: 51-33=18 Exploring Operation: 33/3=11, Resulting Numbers: [51, 11] Generated Node #0,1,1: 28:[51, 11] Operation: 33/3=11 Exploring Operation: 51-3=48, Resulting Numbers: [33, 48] Generated Node #0,1,2: 28:[33, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [33, 17] Generated Node #0,1,3: 28:[33, 17] Operation: 51/3=17 Exploring Operation: 33-3=30, Resulting Numbers: [51, 30] Generated Node #0,1,4: 28:[51, 30] Operation: 33-3=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[3, 18], Operations: ['92-41=51', '51-33=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,28 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,28 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,28 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 #0,1,3 Current State: 28:[33, 17], Operations: ['92-41=51', '51/3=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,28 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,28 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,28 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 #0,1,2 Current State: 28:[33, 48], Operations: ['92-41=51', '51-3=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,28 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,28 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 #0,1,4 Current State: 28:[51, 30], Operations: ['92-41=51', '33-3=30'] Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,28 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,28 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,28 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 #0,1,1 Current State: 28:[51, 11], Operations: ['92-41=51', '33/3=11'] Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,28 unequal: No Solution Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,28 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: 28:[41, 3, 59], Operations: ['92-33=59'] Exploring Operation: 41-3=38, Resulting Numbers: [59, 38] Generated Node #0,3,0: 28:[59, 38] Operation: 41-3=38 Exploring Operation: 41+3=44, Resulting Numbers: [59, 44] Generated Node #0,3,1: 28:[59, 44] Operation: 41+3=44 Exploring Operation: 59-3=56, Resulting Numbers: [41, 56] Generated Node #0,3,2: 28:[41, 56] Operation: 59-3=56 Exploring Operation: 3+59=62, Resulting Numbers: [41, 62] Generated Node #0,3,3: 28:[41, 62] Operation: 3+59=62 Exploring Operation: 59-41=18, Resulting Numbers: [3, 18] Generated Node #0,3,4: 28:[3, 18] Operation: 59-41=18 Moving to Node #0,0 Current State: 28:[3, 92, 8], Operations: ['41-33=8'] Exploring Operation: 92-3=89, Resulting Numbers: [8, 89] Generated Node #0,0,0: 28:[8, 89] Operation: 92-3=89 Exploring Operation: 3+8=11, Resulting Numbers: [92, 11] Generated Node #0,0,1: 28:[92, 11] Operation: 3+8=11 Exploring Operation: 8-3=5, Resulting Numbers: [92, 5] Generated Node #0,0,2: 28:[92, 5] Operation: 8-3=5 Exploring Operation: 92-8=84, Resulting Numbers: [3, 84] Generated Node #0,0,3: 28:[3, 84] Operation: 92-8=84 Exploring Operation: 3+92=95, Resulting Numbers: [8, 95] Generated Node #0,0,4: 28:[8, 95] Operation: 3+92=95 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 28:[3, 84], Operations: ['41-33=8', '92-8=84'] Exploring Operation: 3*84=252, Resulting Numbers: [252] 252,28 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,28 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[41, 33, 3, 92], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [3, 92, 8] Generated Node #0,0: 28:[3, 92, 8] Operation: 41-33=8 Moving to Node #0,0 Current State: 28:[3, 92, 8], Operations: ['41-33=8'] Exploring Operation: 92-8=84, Resulting Numbers: [3, 84] Generated Node #0,0,3: 28:[3, 84] Operation: 92-8=84 Moving to Node #0,0,3 Current State: 28:[3, 84], Operations: ['41-33=8', '92-8=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic