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
[ 90, 36, 67, 82 ]
95
[ "90-36=54", "67+82=149", "149-54=95" ]
Current State: 95:[90, 36, 67, 82], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [67, 82, 54] Generated Node #2: [67, 82, 54] from Operation: 90-36=54 Current State: 95:[67, 82, 54], Operations: ['90-36=54'] Exploring Operation: 67+82=149, Resulting Numbers: [54, 149] Generated Node #3: [54, 149] from Operation: 67+82=149 Current State: 95:[54, 149], Operations: ['90-36=54', '67+82=149'] Exploring Operation: 149-54=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[90, 36, 67, 82], Operations: [] Exploring Operation: 67-36=31, Resulting Numbers: [90, 82, 31] Generated Node #0,0: 95:[90, 82, 31] Operation: 67-36=31 Exploring Operation: 90-67=23, Resulting Numbers: [36, 82, 23] Generated Node #0,1: 95:[36, 82, 23] Operation: 90-67=23 Exploring Operation: 90-82=8, Resulting Numbers: [36, 67, 8] Generated Node #0,2: 95:[36, 67, 8] Operation: 90-82=8 Exploring Operation: 36+67=103, Resulting Numbers: [90, 82, 103] Generated Node #0,3: 95:[90, 82, 103] Operation: 36+67=103 Exploring Operation: 82-67=15, Resulting Numbers: [90, 36, 15] Generated Node #0,4: 95:[90, 36, 15] Operation: 82-67=15 Start Sub Search at level 1: Moving to Node #0,3 Current State: 95:[90, 82, 103], Operations: ['36+67=103'] Exploring Operation: 82+103=185, Resulting Numbers: [90, 185] Generated Node #0,3,0: 95:[90, 185] Operation: 82+103=185 Exploring Operation: 103-90=13, Resulting Numbers: [82, 13] Generated Node #0,3,1: 95:[82, 13] Operation: 103-90=13 Exploring Operation: 90-82=8, Resulting Numbers: [103, 8] Generated Node #0,3,2: 95:[103, 8] Operation: 90-82=8 Exploring Operation: 90+82=172, Resulting Numbers: [103, 172] Generated Node #0,3,3: 95:[103, 172] Operation: 90+82=172 Exploring Operation: 103-82=21, Resulting Numbers: [90, 21] Generated Node #0,3,4: 95:[90, 21] Operation: 103-82=21 Moving to Node #0,3,4 Current State: 95:[90, 21], Operations: ['36+67=103', '103-82=21'] Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,95 unequal: No Solution Exploring Operation: 90+21=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 90*21=1890, Resulting Numbers: [1890] 1890,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[103, 8], Operations: ['36+67=103', '90-82=8'] Exploring Operation: 103+8=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 103*8=824, Resulting Numbers: [824] 824,95 unequal: No Solution Exploring Operation: 103-8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[90, 36, 67, 82], Operations: [] Exploring Operation: 36+67=103, Resulting Numbers: [90, 82, 103] Generated Node #0,3: 95:[90, 82, 103] Operation: 36+67=103 Moving to Node #0,3 Current State: 95:[90, 82, 103], Operations: ['36+67=103'] Exploring Operation: 90-82=8, Resulting Numbers: [103, 8] Generated Node #0,3,2: 95:[103, 8] Operation: 90-82=8 Moving to Node #0,3,2 Current State: 95:[103, 8], Operations: ['36+67=103', '90-82=8'] Exploring Operation: 103-8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 20, 80, 83, 97 ]
39
[ "20+97=117", "83-80=3", "117/3=39" ]
Current State: 39:[20, 80, 83, 97], Operations: [] Exploring Operation: 20+97=117, Resulting Numbers: [80, 83, 117] Generated Node #2: [80, 83, 117] from Operation: 20+97=117 Current State: 39:[80, 83, 117], Operations: ['20+97=117'] Exploring Operation: 83-80=3, Resulting Numbers: [117, 3] Generated Node #3: [117, 3] from Operation: 83-80=3 Current State: 39:[117, 3], Operations: ['20+97=117', '83-80=3'] Exploring Operation: 117/3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[20, 80, 83, 97], Operations: [] Exploring Operation: 97-83=14, Resulting Numbers: [20, 80, 14] Generated Node #0,0: 39:[20, 80, 14] Operation: 97-83=14 Exploring Operation: 80/20=4, Resulting Numbers: [83, 97, 4] Generated Node #0,1: 39:[83, 97, 4] Operation: 80/20=4 Exploring Operation: 83-80=3, Resulting Numbers: [20, 97, 3] Generated Node #0,2: 39:[20, 97, 3] Operation: 83-80=3 Exploring Operation: 97-80=17, Resulting Numbers: [20, 83, 17] Generated Node #0,3: 39:[20, 83, 17] Operation: 97-80=17 Moving to Node #0,0 Current State: 39:[20, 80, 14], Operations: ['97-83=14'] Exploring Operation: 20-14=6, Resulting Numbers: [80, 6] Generated Node #0,0,0: 39:[80, 6] Operation: 20-14=6 Exploring Operation: 80/20=4, Resulting Numbers: [14, 4] Generated Node #0,0,1: 39:[14, 4] Operation: 80/20=4 Exploring Operation: 80-14=66, Resulting Numbers: [20, 66] Generated Node #0,0,2: 39:[20, 66] Operation: 80-14=66 Exploring Operation: 80-20=60, Resulting Numbers: [14, 60] Generated Node #0,0,3: 39:[14, 60] Operation: 80-20=60 Moving to Node #0,3 Current State: 39:[20, 83, 17], Operations: ['97-80=17'] Exploring Operation: 20-17=3, Resulting Numbers: [83, 3] Generated Node #0,3,0: 39:[83, 3] Operation: 20-17=3 Exploring Operation: 83-20=63, Resulting Numbers: [17, 63] Generated Node #0,3,1: 39:[17, 63] Operation: 83-20=63 Exploring Operation: 20+17=37, Resulting Numbers: [83, 37] Generated Node #0,3,2: 39:[83, 37] Operation: 20+17=37 Exploring Operation: 83-17=66, Resulting Numbers: [20, 66] Generated Node #0,3,3: 39:[20, 66] Operation: 83-17=66 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[17, 63], Operations: ['97-80=17', '83-20=63'] Exploring Operation: 17+63=80, Resulting Numbers: [80] 80,39 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 17*63=1071, Resulting Numbers: [1071] 1071,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[20, 66], Operations: ['97-80=17', '83-17=66'] Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,39 unequal: No Solution Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 39:[83, 3], Operations: ['97-80=17', '20-17=3'] Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,39 unequal: No Solution Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,39 unequal: No Solution Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[83, 37], Operations: ['97-80=17', '20+17=37'] Exploring Operation: 83*37=3071, Resulting Numbers: [3071] 3071,39 unequal: No Solution Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 83+37=120, Resulting Numbers: [120] 120,39 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: 39:[20, 97, 3], Operations: ['83-80=3'] Exploring Operation: 20+3=23, Resulting Numbers: [97, 23] Generated Node #0,2,0: 39:[97, 23] Operation: 20+3=23 Exploring Operation: 97-20=77, Resulting Numbers: [3, 77] Generated Node #0,2,1: 39:[3, 77] Operation: 97-20=77 Exploring Operation: 20-3=17, Resulting Numbers: [97, 17] Generated Node #0,2,2: 39:[97, 17] Operation: 20-3=17 Exploring Operation: 97-3=94, Resulting Numbers: [20, 94] Generated Node #0,2,3: 39:[20, 94] Operation: 97-3=94 Moving to Node #0,1 Current State: 39:[83, 97, 4], Operations: ['80/20=4'] Exploring Operation: 83+4=87, Resulting Numbers: [97, 87] Generated Node #0,1,0: 39:[97, 87] Operation: 83+4=87 Exploring Operation: 97-4=93, Resulting Numbers: [83, 93] Generated Node #0,1,1: 39:[83, 93] Operation: 97-4=93 Exploring Operation: 97-83=14, Resulting Numbers: [4, 14] Generated Node #0,1,2: 39:[4, 14] Operation: 97-83=14 Exploring Operation: 83-4=79, Resulting Numbers: [97, 79] Generated Node #0,1,3: 39:[97, 79] Operation: 83-4=79 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[4, 14], Operations: ['80/20=4', '97-83=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,39 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[83, 93], Operations: ['80/20=4', '97-4=93'] Exploring Operation: 83+93=176, Resulting Numbers: [176] 176,39 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 83*93=7719, Resulting Numbers: [7719] 7719,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 39:[97, 79], Operations: ['80/20=4', '83-4=79'] Exploring Operation: 97*79=7663, Resulting Numbers: [7663] 7663,39 unequal: No Solution Exploring Operation: 97-79=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 97+79=176, Resulting Numbers: [176] 176,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[97, 87], Operations: ['80/20=4', '83+4=87'] Exploring Operation: 97-87=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 97*87=8439, Resulting Numbers: [8439] 8439,39 unequal: No Solution Exploring Operation: 97+87=184, Resulting Numbers: [184] 184,39 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: 39:[14, 4], Operations: ['97-83=14', '80/20=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,39 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[14, 60], Operations: ['97-83=14', '80-20=60'] Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 14*60=840, Resulting Numbers: [840] 840,39 unequal: No Solution Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[20, 66], Operations: ['97-83=14', '80-14=66'] Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,39 unequal: No Solution Exploring Operation: 20*66=1320, Resulting Numbers: [1320] 1320,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[3, 77], Operations: ['83-80=3', '97-20=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,39 unequal: No Solution Exploring Operation: 3*77=231, Resulting Numbers: [231] 231,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[80, 6], Operations: ['97-83=14', '20-14=6'] Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,39 unequal: No Solution Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,39 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[97, 17], Operations: ['83-80=3', '20-3=17'] Exploring Operation: 97+17=114, Resulting Numbers: [114] 114,39 unequal: No Solution Exploring Operation: 97*17=1649, Resulting Numbers: [1649] 1649,39 unequal: No Solution Exploring Operation: 97-17=80, Resulting Numbers: [80] 80,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[20, 94], Operations: ['83-80=3', '97-3=94'] Exploring Operation: 20*94=1880, Resulting Numbers: [1880] 1880,39 unequal: No Solution Exploring Operation: 94-20=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 20+94=114, Resulting Numbers: [114] 114,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[97, 23], Operations: ['83-80=3', '20+3=23'] Exploring Operation: 97-23=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 97+23=120, Resulting Numbers: [120] 120,39 unequal: No Solution Exploring Operation: 97*23=2231, Resulting Numbers: [2231] 2231,39 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 35, 61, 1, 5 ]
24
[ "35+61=96", "5-1=4", "96/4=24" ]
Current State: 24:[35, 61, 1, 5], Operations: [] Exploring Operation: 35+61=96, Resulting Numbers: [1, 5, 96] Generated Node #2: [1, 5, 96] from Operation: 35+61=96 Current State: 24:[1, 5, 96], Operations: ['35+61=96'] Exploring Operation: 5-1=4, Resulting Numbers: [96, 4] Generated Node #3: [96, 4] from Operation: 5-1=4 Current State: 24:[96, 4], Operations: ['35+61=96', '5-1=4'] Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[35, 61, 1, 5], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [1, 5, 26] Generated Node #0,0: 24:[1, 5, 26] Operation: 61-35=26 Exploring Operation: 35/5=7, Resulting Numbers: [61, 1, 7] Generated Node #0,1: 24:[61, 1, 7] Operation: 35/5=7 Exploring Operation: 35-5=30, Resulting Numbers: [61, 1, 30] Generated Node #0,2: 24:[61, 1, 30] Operation: 35-5=30 Exploring Operation: 61-5=56, Resulting Numbers: [35, 1, 56] Generated Node #0,3: 24:[35, 1, 56] Operation: 61-5=56 Moving to Node #0,0 Current State: 24:[1, 5, 26], Operations: ['61-35=26'] Exploring Operation: 1+5=6, Resulting Numbers: [26, 6] Generated Node #0,0,0: 24:[26, 6] Operation: 1+5=6 Exploring Operation: 1*5=5, Resulting Numbers: [26, 5] Generated Node #0,0,1: 24:[26, 5] Operation: 1*5=5 Exploring Operation: 26-1=25, Resulting Numbers: [5, 25] Generated Node #0,0,2: 24:[5, 25] Operation: 26-1=25 Exploring Operation: 5-1=4, Resulting Numbers: [26, 4] Generated Node #0,0,3: 24:[26, 4] Operation: 5-1=4 Moving to Node #0,1 Current State: 24:[61, 1, 7], Operations: ['35/5=7'] Exploring Operation: 7-1=6, Resulting Numbers: [61, 6] Generated Node #0,1,0: 24:[61, 6] Operation: 7-1=6 Exploring Operation: 1+7=8, Resulting Numbers: [61, 8] Generated Node #0,1,1: 24:[61, 8] Operation: 1+7=8 Exploring Operation: 61-1=60, Resulting Numbers: [7, 60] Generated Node #0,1,2: 24:[7, 60] Operation: 61-1=60 Exploring Operation: 61-7=54, Resulting Numbers: [1, 54] Generated Node #0,1,3: 24:[1, 54] Operation: 61-7=54 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 24:[1, 54], Operations: ['35/5=7', '61-7=54'] Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,24 unequal: No Solution Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,24 unequal: No Solution Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[61, 6], Operations: ['35/5=7', '7-1=6'] Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,24 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,24 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 24:[61, 8], Operations: ['35/5=7', '1+7=8'] Exploring Operation: 61+8=69, Resulting Numbers: [69] 69,24 unequal: No Solution Exploring Operation: 61*8=488, Resulting Numbers: [488] 488,24 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[7, 60], Operations: ['35/5=7', '61-1=60'] Exploring Operation: 7*60=420, Resulting Numbers: [420] 420,24 unequal: No Solution Exploring Operation: 7+60=67, Resulting Numbers: [67] 67,24 unequal: No Solution Exploring Operation: 60-7=53, Resulting Numbers: [53] 53,24 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: 24:[35, 1, 56], Operations: ['61-5=56'] Exploring Operation: 56-1=55, Resulting Numbers: [35, 55] Generated Node #0,3,0: 24:[35, 55] Operation: 56-1=55 Exploring Operation: 35-1=34, Resulting Numbers: [56, 34] Generated Node #0,3,1: 24:[56, 34] Operation: 35-1=34 Exploring Operation: 35*1=35, Resulting Numbers: [56, 35] Generated Node #0,3,2: 24:[56, 35] Operation: 35*1=35 Exploring Operation: 56-35=21, Resulting Numbers: [1, 21] Generated Node #0,3,3: 24:[1, 21] Operation: 56-35=21 Moving to Node #0,2 Current State: 24:[61, 1, 30], Operations: ['35-5=30'] Exploring Operation: 30-1=29, Resulting Numbers: [61, 29] Generated Node #0,2,0: 24:[61, 29] Operation: 30-1=29 Exploring Operation: 61*1=61, Resulting Numbers: [30, 61] Generated Node #0,2,1: 24:[30, 61] Operation: 61*1=61 Exploring Operation: 61-1=60, Resulting Numbers: [30, 60] Generated Node #0,2,2: 24:[30, 60] Operation: 61-1=60 Exploring Operation: 61-30=31, Resulting Numbers: [1, 31] Generated Node #0,2,3: 24:[1, 31] Operation: 61-30=31 Moving to Node #0,0,0 Current State: 24:[26, 6], Operations: ['61-35=26', '1+5=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[26, 4], Operations: ['61-35=26', '5-1=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[5, 25], Operations: ['61-35=26', '26-1=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,24 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[26, 5], Operations: ['61-35=26', '1*5=5'] Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,24 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,24 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[1, 21], Operations: ['61-5=56', '56-35=21'] Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[1, 31], Operations: ['35-5=30', '61-30=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,24 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 1+31=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[56, 34], Operations: ['61-5=56', '35-1=34'] Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,24 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 56*34=1904, Resulting Numbers: [1904] 1904,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[35, 55], Operations: ['61-5=56', '56-1=55'] Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,24 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,24 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[61, 29], Operations: ['35-5=30', '30-1=29'] Exploring Operation: 61*29=1769, Resulting Numbers: [1769] 1769,24 unequal: No Solution Exploring Operation: 61+29=90, Resulting Numbers: [90] 90,24 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[30, 60], Operations: ['35-5=30', '61-1=60'] Exploring Operation: 60-30=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 30+60=90, Resulting Numbers: [90] 90,24 unequal: No Solution Exploring Operation: 30*60=1800, Resulting Numbers: [1800] 1800,24 unequal: No Solution Exploring Operation: 60/30=2, Resulting Numbers: [2] 2,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[56, 35], Operations: ['61-5=56', '35*1=35'] Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,24 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[30, 61], Operations: ['35-5=30', '61*1=61'] Exploring Operation: 30*61=1830, Resulting Numbers: [1830] 1830,24 unequal: No Solution Exploring Operation: 30+61=91, Resulting Numbers: [91] 91,24 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,24 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 84, 49, 9, 5 ]
49
[ "84-49=35", "9+5=14", "35+14=49" ]
Current State: 49:[84, 49, 9, 5], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [9, 5, 35] Generated Node #2: [9, 5, 35] from Operation: 84-49=35 Current State: 49:[9, 5, 35], Operations: ['84-49=35'] Exploring Operation: 9+5=14, Resulting Numbers: [35, 14] Generated Node #3: [35, 14] from Operation: 9+5=14 Current State: 49:[35, 14], Operations: ['84-49=35', '9+5=14'] Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[84, 49, 9, 5], Operations: [] Exploring Operation: 84-9=75, Resulting Numbers: [49, 5, 75] Generated Node #0,0: 49:[49, 5, 75] Operation: 84-9=75 Exploring Operation: 9-5=4, Resulting Numbers: [84, 49, 4] Generated Node #0,1: 49:[84, 49, 4] Operation: 9-5=4 Exploring Operation: 84-49=35, Resulting Numbers: [9, 5, 35] Generated Node #0,2: 49:[9, 5, 35] Operation: 84-49=35 Exploring Operation: 84-5=79, Resulting Numbers: [49, 9, 79] Generated Node #0,3: 49:[49, 9, 79] Operation: 84-5=79 Moving to Node #0,2 Current State: 49:[9, 5, 35], Operations: ['84-49=35'] Exploring Operation: 9+35=44, Resulting Numbers: [5, 44] Generated Node #0,2,0: 49:[5, 44] Operation: 9+35=44 Exploring Operation: 9-5=4, Resulting Numbers: [35, 4] Generated Node #0,2,1: 49:[35, 4] Operation: 9-5=4 Exploring Operation: 5+35=40, Resulting Numbers: [9, 40] Generated Node #0,2,2: 49:[9, 40] Operation: 5+35=40 Exploring Operation: 35/5=7, Resulting Numbers: [9, 7] Generated Node #0,2,3: 49:[9, 7] Operation: 35/5=7 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 49:[9, 7], Operations: ['84-49=35', '35/5=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 49:[5, 44], Operations: ['84-49=35', '9+35=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,49 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[84, 49, 9, 5], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [9, 5, 35] Generated Node #0,2: 49:[9, 5, 35] Operation: 84-49=35 Moving to Node #0,2 Current State: 49:[9, 5, 35], Operations: ['84-49=35'] Exploring Operation: 9+35=44, Resulting Numbers: [5, 44] Generated Node #0,2,0: 49:[5, 44] Operation: 9+35=44 Moving to Node #0,2,0 Current State: 49:[5, 44], Operations: ['84-49=35', '9+35=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 55, 15, 99, 52 ]
28
[ "55-52=3", "99-15=84", "84/3=28" ]
Current State: 28:[55, 15, 99, 52], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [15, 99, 3] Generated Node #2: [15, 99, 3] from Operation: 55-52=3 Current State: 28:[15, 99, 3], Operations: ['55-52=3'] Exploring Operation: 99-15=84, Resulting Numbers: [3, 84] Generated Node #3: [3, 84] from Operation: 99-15=84 Current State: 28:[3, 84], Operations: ['55-52=3', '99-15=84'] Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[55, 15, 99, 52], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [15, 52, 44] Generated Node #0,0: 28:[15, 52, 44] Operation: 99-55=44 Moving to Node #0,0 Current State: 28:[15, 52, 44], Operations: ['99-55=44'] Exploring Operation: 52-44=8, Resulting Numbers: [15, 8] Generated Node #0,0,0: 28:[15, 8] Operation: 52-44=8 Moving to Node #0,0,0 Current State: 28:[15, 8], Operations: ['99-55=44', '52-44=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,28 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 22, 31, 5 ]
76
[ "31-22=9", "5*9=45", "31+45=76" ]
Current State: 76:[31, 22, 31, 5], Operations: [] Exploring Operation: 31-22=9, Resulting Numbers: [5, 9] Generated Node #2: [5, 9] from Operation: 31-22=9 Current State: 76:[5, 9], Operations: ['31-22=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,76 equal: Goal Reached Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[31, 22, 31, 5], Operations: [] Exploring Operation: 31/31=1, Resulting Numbers: [22, 5, 1] Generated Node #0,0: 76:[22, 5, 1] Operation: 31/31=1 Moving to Node #0,0 Current State: 76:[22, 5, 1], Operations: ['31/31=1'] Exploring Operation: 22-5=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 76:[1, 17] Operation: 22-5=17 Moving to Node #0,0,0 Current State: 76:[1, 17], Operations: ['31/31=1', '22-5=17'] Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,76 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 45, 57, 64, 76 ]
38
[ "45+57=102", "64+76=140", "140-102=38" ]
Current State: 38:[45, 57, 64, 76], Operations: [] Exploring Operation: 45+57=102, Resulting Numbers: [64, 76, 102] Generated Node #2: [64, 76, 102] from Operation: 45+57=102 Current State: 38:[64, 76, 102], Operations: ['45+57=102'] Exploring Operation: 64+76=140, Resulting Numbers: [102, 140] Generated Node #3: [102, 140] from Operation: 64+76=140 Current State: 38:[102, 140], Operations: ['45+57=102', '64+76=140'] Exploring Operation: 140-102=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[45, 57, 64, 76], Operations: [] Exploring Operation: 76-57=19, Resulting Numbers: [45, 64, 19] Generated Node #0,0: 38:[45, 64, 19] Operation: 76-57=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[45, 64, 19], Operations: ['76-57=19'] Exploring Operation: 64-45=19, Resulting Numbers: [19, 19] Generated Node #0,0,0: 38:[19, 19] Operation: 64-45=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[19, 19], Operations: ['76-57=19', '64-45=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[45, 57, 64, 76], Operations: [] Exploring Operation: 76-57=19, Resulting Numbers: [45, 64, 19] Generated Node #0,0: 38:[45, 64, 19] Operation: 76-57=19 Moving to Node #0,0 Current State: 38:[45, 64, 19], Operations: ['76-57=19'] Exploring Operation: 64-45=19, Resulting Numbers: [19, 19] Generated Node #0,0,0: 38:[19, 19] Operation: 64-45=19 Moving to Node #0,0,0 Current State: 38:[19, 19], Operations: ['76-57=19', '64-45=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 3, 37, 49, 81 ]
72
[ "3+37=40", "81-49=32", "40+32=72" ]
Current State: 72:[3, 37, 49, 81], Operations: [] Exploring Operation: 3+37=40, Resulting Numbers: [49, 81, 40] Generated Node #2: [49, 81, 40] from Operation: 3+37=40 Current State: 72:[49, 81, 40], Operations: ['3+37=40'] Exploring Operation: 81-49=32, Resulting Numbers: [40, 32] Generated Node #3: [40, 32] from Operation: 81-49=32 Current State: 72:[40, 32], Operations: ['3+37=40', '81-49=32'] Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[3, 37, 49, 81], Operations: [] Exploring Operation: 49-3=46, Resulting Numbers: [37, 81, 46] Generated Node #0,0: 72:[37, 81, 46] Operation: 49-3=46 Exploring Operation: 49-37=12, Resulting Numbers: [3, 81, 12] Generated Node #0,1: 72:[3, 81, 12] Operation: 49-37=12 Exploring Operation: 81/3=27, Resulting Numbers: [37, 49, 27] Generated Node #0,2: 72:[37, 49, 27] Operation: 81/3=27 Exploring Operation: 81-3=78, Resulting Numbers: [37, 49, 78] Generated Node #0,3: 72:[37, 49, 78] Operation: 81-3=78 Exploring Operation: 81-49=32, Resulting Numbers: [3, 37, 32] Generated Node #0,4: 72:[3, 37, 32] Operation: 81-49=32 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[3, 37, 32], Operations: ['81-49=32'] Exploring Operation: 3+32=35, Resulting Numbers: [37, 35] Generated Node #0,4,0: 72:[37, 35] Operation: 3+32=35 Exploring Operation: 37+32=69, Resulting Numbers: [3, 69] Generated Node #0,4,1: 72:[3, 69] Operation: 37+32=69 Exploring Operation: 32-3=29, Resulting Numbers: [37, 29] Generated Node #0,4,2: 72:[37, 29] Operation: 32-3=29 Exploring Operation: 37-3=34, Resulting Numbers: [32, 34] Generated Node #0,4,3: 72:[32, 34] Operation: 37-3=34 Exploring Operation: 37-32=5, Resulting Numbers: [3, 5] Generated Node #0,4,4: 72:[3, 5] Operation: 37-32=5 Moving to Node #0,4,4 Current State: 72:[3, 5], Operations: ['81-49=32', '37-32=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[37, 35], Operations: ['81-49=32', '3+32=35'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 37*35=1295, Resulting Numbers: [1295] 1295,72 unequal: No Solution Exploring Operation: 37+35=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[3, 37, 49, 81], Operations: [] Exploring Operation: 81-49=32, Resulting Numbers: [3, 37, 32] Generated Node #0,4: 72:[3, 37, 32] Operation: 81-49=32 Moving to Node #0,4 Current State: 72:[3, 37, 32], Operations: ['81-49=32'] Exploring Operation: 3+32=35, Resulting Numbers: [37, 35] Generated Node #0,4,0: 72:[37, 35] Operation: 3+32=35 Moving to Node #0,4,0 Current State: 72:[37, 35], Operations: ['81-49=32', '3+32=35'] Exploring Operation: 37+35=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 45, 1, 72, 35 ]
57
[ "72*35=2520", "2520/45=56", "1+56=57" ]
Current State: 57:[45, 1, 72, 35], Operations: [] Exploring Operation: 72*35=2520, Resulting Numbers: [45, 1, 2520] Generated Node #2: [45, 1, 2520] from Operation: 72*35=2520 Current State: 57:[45, 1, 2520], Operations: ['72*35=2520'] Exploring Operation: 2520/45=56, Resulting Numbers: [1, 56] Generated Node #3: [1, 56] from Operation: 2520/45=56 Current State: 57:[1, 56], Operations: ['72*35=2520', '2520/45=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[45, 1, 72, 35], Operations: [] Exploring Operation: 72-45=27, Resulting Numbers: [1, 35, 27] Generated Node #0,0: 57:[1, 35, 27] Operation: 72-45=27 Exploring Operation: 45-35=10, Resulting Numbers: [1, 72, 10] Generated Node #0,1: 57:[1, 72, 10] Operation: 45-35=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[1, 72, 10], Operations: ['45-35=10'] Exploring Operation: 72-10=62, Resulting Numbers: [1, 62] Generated Node #0,1,0: 57:[1, 62] Operation: 72-10=62 Exploring Operation: 72-1=71, Resulting Numbers: [10, 71] Generated Node #0,1,1: 57:[10, 71] Operation: 72-1=71 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[1, 62], Operations: ['45-35=10', '72-10=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[10, 71], Operations: ['45-35=10', '72-1=71'] Exploring Operation: 10+71=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[1, 35, 27], Operations: ['72-45=27'] Exploring Operation: 35-27=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 57:[1, 8] Operation: 35-27=8 Exploring Operation: 35+27=62, Resulting Numbers: [1, 62] Generated Node #0,0,1: 57:[1, 62] Operation: 35+27=62 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[1, 8], Operations: ['72-45=27', '35-27=8'] Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,57 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[1, 62], Operations: ['72-45=27', '35+27=62'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 11, 81, 71, 81 ]
82
[ "11+81=92", "81-71=10", "92-10=82" ]
Current State: 82:[11, 81, 71, 81], Operations: [] Exploring Operation: 11+81=92, Resulting Numbers: [71, 92] Generated Node #2: [71, 92] from Operation: 11+81=92 Current State: 82:[71, 92], Operations: ['11+81=92'] Exploring Operation: 81-71=10, Resulting Numbers: [92, 10] Generated Node #3: [92, 10] from Operation: 81-71=10 Current State: 82:[92, 10], Operations: ['11+81=92', '81-71=10'] Exploring Operation: 92-10=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[11, 81, 71, 81], Operations: [] Exploring Operation: 81-71=10, Resulting Numbers: [11, 81, 10] Generated Node #0,0: 82:[11, 81, 10] Operation: 81-71=10 Exploring Operation: 11+71=82, Resulting Numbers: [81, 81, 82] Generated Node #0,1: 82:[81, 81, 82] Operation: 11+71=82 Exploring Operation: 81-71=10, Resulting Numbers: [11, 81, 10] Generated Node #0,2: 82:[11, 81, 10] Operation: 81-71=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[81, 81, 82], Operations: ['11+71=82'] Exploring Operation: 82-81=1, Resulting Numbers: [81, 1] Generated Node #0,1,0: 82:[81, 1] Operation: 82-81=1 Exploring Operation: 81-81=0, Resulting Numbers: [82, 0] Generated Node #0,1,1: 82:[82, 0] Operation: 81-81=0 Exploring Operation: 81/81=1, Resulting Numbers: [82, 1] Generated Node #0,1,2: 82:[82, 1] Operation: 81/81=1 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[82, 1], Operations: ['11+71=82', '81/81=1'] Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[11, 81, 71, 81], Operations: [] Exploring Operation: 11+71=82, Resulting Numbers: [81, 81, 82] Generated Node #0,1: 82:[81, 81, 82] Operation: 11+71=82 Moving to Node #0,1 Current State: 82:[81, 81, 82], Operations: ['11+71=82'] Exploring Operation: 81/81=1, Resulting Numbers: [82, 1] Generated Node #0,1,2: 82:[82, 1] Operation: 81/81=1 Moving to Node #0,1,2 Current State: 82:[82, 1], Operations: ['11+71=82', '81/81=1'] Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 41, 96, 3, 70 ]
61
[ "70-41=29", "96/3=32", "29+32=61" ]
Current State: 61:[41, 96, 3, 70], Operations: [] Exploring Operation: 70-41=29, Resulting Numbers: [96, 3, 29] Generated Node #2: [96, 3, 29] from Operation: 70-41=29 Current State: 61:[96, 3, 29], Operations: ['70-41=29'] Exploring Operation: 96/3=32, Resulting Numbers: [29, 32] Generated Node #3: [29, 32] from Operation: 96/3=32 Current State: 61:[29, 32], Operations: ['70-41=29', '96/3=32'] Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[41, 96, 3, 70], Operations: [] Exploring Operation: 41+3=44, Resulting Numbers: [96, 70, 44] Generated Node #0,0: 61:[96, 70, 44] Operation: 41+3=44 Exploring Operation: 96/3=32, Resulting Numbers: [41, 70, 32] Generated Node #0,1: 61:[41, 70, 32] Operation: 96/3=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[41, 70, 32], Operations: ['96/3=32'] Exploring Operation: 41+32=73, Resulting Numbers: [70, 73] Generated Node #0,1,0: 61:[70, 73] Operation: 41+32=73 Exploring Operation: 70-32=38, Resulting Numbers: [41, 38] Generated Node #0,1,1: 61:[41, 38] Operation: 70-32=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[70, 73], Operations: ['96/3=32', '41+32=73'] Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,61 unequal: No Solution Exploring Operation: 70+73=143, Resulting Numbers: [143] 143,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[41, 38], Operations: ['96/3=32', '70-32=38'] Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,61 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[96, 70, 44], Operations: ['41+3=44'] Exploring Operation: 96-70=26, Resulting Numbers: [44, 26] Generated Node #0,0,0: 61:[44, 26] Operation: 96-70=26 Exploring Operation: 96-44=52, Resulting Numbers: [70, 52] Generated Node #0,0,1: 61:[70, 52] Operation: 96-44=52 Moving to Node #0,0,1 Current State: 61:[70, 52], Operations: ['41+3=44', '96-44=52'] Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[44, 26], Operations: ['41+3=44', '96-70=26'] Exploring Operation: 44+26=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,61 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
[ 36, 67, 41, 27 ]
68
[ "41-36=5", "27*5=135", "135-67=68" ]
Current State: 68:[36, 67, 41, 27], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [67, 27, 5] Generated Node #2: [67, 27, 5] from Operation: 41-36=5 Current State: 68:[67, 27, 5], Operations: ['41-36=5'] Exploring Operation: 27*5=135, Resulting Numbers: [67, 135] Generated Node #3: [67, 135] from Operation: 27*5=135 Current State: 68:[67, 135], Operations: ['41-36=5', '27*5=135'] Exploring Operation: 135-67=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[36, 67, 41, 27], Operations: [] Exploring Operation: 36-27=9, Resulting Numbers: [67, 41, 9] Generated Node #0,0: 68:[67, 41, 9] Operation: 36-27=9 Exploring Operation: 41-27=14, Resulting Numbers: [36, 67, 14] Generated Node #0,1: 68:[36, 67, 14] Operation: 41-27=14 Exploring Operation: 41+27=68, Resulting Numbers: [36, 67, 68] Generated Node #0,2: 68:[36, 67, 68] Operation: 41+27=68 Exploring Operation: 41-36=5, Resulting Numbers: [67, 27, 5] Generated Node #0,3: 68:[67, 27, 5] Operation: 41-36=5 Exploring Operation: 36+27=63, Resulting Numbers: [67, 41, 63] Generated Node #0,4: 68:[67, 41, 63] Operation: 36+27=63 Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[36, 67, 68], Operations: ['41+27=68'] Exploring Operation: 36+67=103, Resulting Numbers: [68, 103] Generated Node #0,2,0: 68:[68, 103] Operation: 36+67=103 Exploring Operation: 36+68=104, Resulting Numbers: [67, 104] Generated Node #0,2,1: 68:[67, 104] Operation: 36+68=104 Exploring Operation: 67-36=31, Resulting Numbers: [68, 31] Generated Node #0,2,2: 68:[68, 31] Operation: 67-36=31 Exploring Operation: 68-36=32, Resulting Numbers: [67, 32] Generated Node #0,2,3: 68:[67, 32] Operation: 68-36=32 Exploring Operation: 68-67=1, Resulting Numbers: [36, 1] Generated Node #0,2,4: 68:[36, 1] Operation: 68-67=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[68, 31], Operations: ['41+27=68', '67-36=31'] Exploring Operation: 68+31=99, Resulting Numbers: [99] 99,68 unequal: No Solution Exploring Operation: 68*31=2108, Resulting Numbers: [2108] 2108,68 unequal: No Solution Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,68 unequal: No Solution No 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: 68:[67, 32], Operations: ['41+27=68', '68-36=32'] Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 67*32=2144, Resulting Numbers: [2144] 2144,68 unequal: No Solution Exploring Operation: 67+32=99, Resulting Numbers: [99] 99,68 unequal: No Solution No 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: 68:[36, 1], Operations: ['41+27=68', '68-67=1'] Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,68 unequal: No Solution No 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: 68:[68, 103], Operations: ['41+27=68', '36+67=103'] Exploring Operation: 68+103=171, Resulting Numbers: [171] 171,68 unequal: No Solution Exploring Operation: 103-68=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 68*103=7004, Resulting Numbers: [7004] 7004,68 unequal: No Solution No 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: 68:[67, 104], Operations: ['41+27=68', '36+68=104'] Exploring Operation: 67+104=171, Resulting Numbers: [171] 171,68 unequal: No Solution Exploring Operation: 104-67=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 67*104=6968, Resulting Numbers: [6968] 6968,68 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: 68:[36, 67, 14], Operations: ['41-27=14'] Exploring Operation: 67+14=81, Resulting Numbers: [36, 81] Generated Node #0,1,0: 68:[36, 81] Operation: 67+14=81 Exploring Operation: 36-14=22, Resulting Numbers: [67, 22] Generated Node #0,1,1: 68:[67, 22] Operation: 36-14=22 Exploring Operation: 67-36=31, Resulting Numbers: [14, 31] Generated Node #0,1,2: 68:[14, 31] Operation: 67-36=31 Exploring Operation: 67-14=53, Resulting Numbers: [36, 53] Generated Node #0,1,3: 68:[36, 53] Operation: 67-14=53 Exploring Operation: 36+14=50, Resulting Numbers: [67, 50] Generated Node #0,1,4: 68:[67, 50] Operation: 36+14=50 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[67, 22], Operations: ['41-27=14', '36-14=22'] Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,68 unequal: No Solution No 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: 68:[14, 31], Operations: ['41-27=14', '67-36=31'] Exploring Operation: 14*31=434, Resulting Numbers: [434] 434,68 unequal: No Solution Exploring Operation: 14+31=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,68 unequal: No Solution No 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: 68:[36, 81], Operations: ['41-27=14', '67+14=81'] Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 36*81=2916, Resulting Numbers: [2916] 2916,68 unequal: No Solution Exploring Operation: 36+81=117, Resulting Numbers: [117] 117,68 unequal: No Solution No 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: 68:[36, 53], Operations: ['41-27=14', '67-14=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 36*53=1908, Resulting Numbers: [1908] 1908,68 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,68 unequal: No Solution No 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: 68:[67, 50], Operations: ['41-27=14', '36+14=50'] Exploring Operation: 67+50=117, Resulting Numbers: [117] 117,68 unequal: No Solution Exploring Operation: 67*50=3350, Resulting Numbers: [3350] 3350,68 unequal: No Solution Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,68 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: 68:[67, 27, 5], Operations: ['41-36=5'] Exploring Operation: 27+5=32, Resulting Numbers: [67, 32] Generated Node #0,3,0: 68:[67, 32] Operation: 27+5=32 Exploring Operation: 67-5=62, Resulting Numbers: [27, 62] Generated Node #0,3,1: 68:[27, 62] Operation: 67-5=62 Exploring Operation: 67+5=72, Resulting Numbers: [27, 72] Generated Node #0,3,2: 68:[27, 72] Operation: 67+5=72 Exploring Operation: 27-5=22, Resulting Numbers: [67, 22] Generated Node #0,3,3: 68:[67, 22] Operation: 27-5=22 Exploring Operation: 67-27=40, Resulting Numbers: [5, 40] Generated Node #0,3,4: 68:[5, 40] Operation: 67-27=40 Moving to Node #0,3,0 Current State: 68:[67, 32], Operations: ['41-36=5', '27+5=32'] Exploring Operation: 67+32=99, Resulting Numbers: [99] 99,68 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 67*32=2144, Resulting Numbers: [2144] 2144,68 unequal: No Solution Moving to Node #0,3,3 Current State: 68:[67, 22], Operations: ['41-36=5', '27-5=22'] Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,68 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,68 unequal: No Solution Moving to Node #0,3,4 Current State: 68:[5, 40], Operations: ['41-36=5', '67-27=40'] Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,68 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,68 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[27, 72], Operations: ['41-36=5', '67+5=72'] Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 27*72=1944, Resulting Numbers: [1944] 1944,68 unequal: No Solution Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[27, 62], Operations: ['41-36=5', '67-5=62'] Exploring Operation: 27+62=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 62-27=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 27*62=1674, Resulting Numbers: [1674] 1674,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[67, 41, 9], Operations: ['36-27=9'] Exploring Operation: 67-9=58, Resulting Numbers: [41, 58] Generated Node #0,0,0: 68:[41, 58] Operation: 67-9=58 Exploring Operation: 41+9=50, Resulting Numbers: [67, 50] Generated Node #0,0,1: 68:[67, 50] Operation: 41+9=50 Exploring Operation: 67-41=26, Resulting Numbers: [9, 26] Generated Node #0,0,2: 68:[9, 26] Operation: 67-41=26 Exploring Operation: 67+9=76, Resulting Numbers: [41, 76] Generated Node #0,0,3: 68:[41, 76] Operation: 67+9=76 Exploring Operation: 41-9=32, Resulting Numbers: [67, 32] Generated Node #0,0,4: 68:[67, 32] Operation: 41-9=32 Moving to Node #0,0,4 Current State: 68:[67, 32], Operations: ['36-27=9', '41-9=32'] Exploring Operation: 67*32=2144, Resulting Numbers: [2144] 2144,68 unequal: No Solution Exploring Operation: 67+32=99, Resulting Numbers: [99] 99,68 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[9, 26], Operations: ['36-27=9', '67-41=26'] Exploring Operation: 9+26=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 9*26=234, Resulting Numbers: [234] 234,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[41, 76], Operations: ['36-27=9', '67+9=76'] Exploring Operation: 41*76=3116, Resulting Numbers: [3116] 3116,68 unequal: No Solution Exploring Operation: 41+76=117, Resulting Numbers: [117] 117,68 unequal: No Solution Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[41, 58], Operations: ['36-27=9', '67-9=58'] Exploring Operation: 41+58=99, Resulting Numbers: [99] 99,68 unequal: No Solution Exploring Operation: 58-41=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 41*58=2378, Resulting Numbers: [2378] 2378,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[67, 50], Operations: ['36-27=9', '41+9=50'] Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,68 unequal: No Solution Exploring Operation: 67+50=117, Resulting Numbers: [117] 117,68 unequal: No Solution Exploring Operation: 67*50=3350, Resulting Numbers: [3350] 3350,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 68:[67, 41, 63], Operations: ['36+27=63'] Exploring Operation: 67-41=26, Resulting Numbers: [63, 26] Generated Node #0,4,0: 68:[63, 26] Operation: 67-41=26 Exploring Operation: 67+41=108, Resulting Numbers: [63, 108] Generated Node #0,4,1: 68:[63, 108] Operation: 67+41=108 Exploring Operation: 63-41=22, Resulting Numbers: [67, 22] Generated Node #0,4,2: 68:[67, 22] Operation: 63-41=22 Exploring Operation: 67-63=4, Resulting Numbers: [41, 4] Generated Node #0,4,3: 68:[41, 4] Operation: 67-63=4 Exploring Operation: 41+63=104, Resulting Numbers: [67, 104] Generated Node #0,4,4: 68:[67, 104] Operation: 41+63=104 Moving to Node #0,4,2 Current State: 68:[67, 22], Operations: ['36+27=63', '63-41=22'] Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,68 unequal: No Solution Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,68 unequal: No Solution Moving to Node #0,4,3 Current State: 68:[41, 4], Operations: ['36+27=63', '67-63=4'] Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,68 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 41*4=164, Resulting Numbers: [164] 164,68 unequal: No Solution Moving to Node #0,4,0 Current State: 68:[63, 26], Operations: ['36+27=63', '67-41=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,68 unequal: No Solution Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,68 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,68 unequal: No Solution Moving to Node #0,4,4 Current State: 68:[67, 104], Operations: ['36+27=63', '41+63=104'] Exploring Operation: 104-67=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 67*104=6968, Resulting Numbers: [6968] 6968,68 unequal: No Solution Exploring Operation: 67+104=171, Resulting Numbers: [171] 171,68 unequal: No Solution Moving to Node #0,4,1 Current State: 68:[63, 108], Operations: ['36+27=63', '67+41=108'] Exploring Operation: 63*108=6804, Resulting Numbers: [6804] 6804,68 unequal: No Solution Exploring Operation: 63+108=171, Resulting Numbers: [171] 171,68 unequal: No Solution Exploring Operation: 108-63=45, Resulting Numbers: [45] 45,68 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
[ 6, 8, 59, 19 ]
64
[ "6+8=14", "59+19=78", "78-14=64" ]
Current State: 64:[6, 8, 59, 19], Operations: [] Exploring Operation: 6+8=14, Resulting Numbers: [59, 19, 14] Generated Node #2: [59, 19, 14] from Operation: 6+8=14 Current State: 64:[59, 19, 14], Operations: ['6+8=14'] Exploring Operation: 59+19=78, Resulting Numbers: [14, 78] Generated Node #3: [14, 78] from Operation: 59+19=78 Current State: 64:[14, 78], Operations: ['6+8=14', '59+19=78'] Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[6, 8, 59, 19], Operations: [] Exploring Operation: 6+59=65, Resulting Numbers: [8, 19, 65] Generated Node #0,0: 64:[8, 19, 65] Operation: 6+59=65 Moving to Node #0,0 Current State: 64:[8, 19, 65], Operations: ['6+59=65'] Exploring Operation: 19-8=11, Resulting Numbers: [65, 11] Generated Node #0,0,0: 64:[65, 11] Operation: 19-8=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[65, 11], Operations: ['6+59=65', '19-8=11'] Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,64 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
[ 52, 92, 20, 73 ]
51
[ "52+92=144", "20+73=93", "144-93=51" ]
Current State: 51:[52, 92, 20, 73], Operations: [] Exploring Operation: 52+92=144, Resulting Numbers: [20, 73, 144] Generated Node #2: [20, 73, 144] from Operation: 52+92=144 Current State: 51:[20, 73, 144], Operations: ['52+92=144'] Exploring Operation: 20+73=93, Resulting Numbers: [144, 93] Generated Node #3: [144, 93] from Operation: 20+73=93 Current State: 51:[144, 93], Operations: ['52+92=144', '20+73=93'] Exploring Operation: 144-93=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[52, 92, 20, 73], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [52, 20, 19] Generated Node #0,0: 51:[52, 20, 19] Operation: 92-73=19 Exploring Operation: 92-52=40, Resulting Numbers: [20, 73, 40] Generated Node #0,1: 51:[20, 73, 40] Operation: 92-52=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[52, 20, 19], Operations: ['92-73=19'] Exploring Operation: 20+19=39, Resulting Numbers: [52, 39] Generated Node #0,0,0: 51:[52, 39] Operation: 20+19=39 Exploring Operation: 20-19=1, Resulting Numbers: [52, 1] Generated Node #0,0,1: 51:[52, 1] Operation: 20-19=1 Moving to Node #0,0,1 Current State: 51:[52, 1], Operations: ['92-73=19', '20-19=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[52, 92, 20, 73], Operations: [] Exploring Operation: 92-73=19, Resulting Numbers: [52, 20, 19] Generated Node #0,0: 51:[52, 20, 19] Operation: 92-73=19 Moving to Node #0,0 Current State: 51:[52, 20, 19], Operations: ['92-73=19'] Exploring Operation: 20-19=1, Resulting Numbers: [52, 1] Generated Node #0,0,1: 51:[52, 1] Operation: 20-19=1 Moving to Node #0,0,1 Current State: 51:[52, 1], Operations: ['92-73=19', '20-19=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 50, 2, 36, 27 ]
88
[ "50/2=25", "36+27=63", "25+63=88" ]
Current State: 88:[50, 2, 36, 27], Operations: [] Exploring Operation: 50/2=25, Resulting Numbers: [36, 27, 25] Generated Node #2: [36, 27, 25] from Operation: 50/2=25 Current State: 88:[36, 27, 25], Operations: ['50/2=25'] Exploring Operation: 36+27=63, Resulting Numbers: [25, 63] Generated Node #3: [25, 63] from Operation: 36+27=63 Current State: 88:[25, 63], Operations: ['50/2=25', '36+27=63'] Exploring Operation: 25+63=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[50, 2, 36, 27], Operations: [] Exploring Operation: 50-27=23, Resulting Numbers: [2, 36, 23] Generated Node #0,0: 88:[2, 36, 23] Operation: 50-27=23 Exploring Operation: 50-36=14, Resulting Numbers: [2, 27, 14] Generated Node #0,1: 88:[2, 27, 14] Operation: 50-36=14 Exploring Operation: 50+36=86, Resulting Numbers: [2, 27, 86] Generated Node #0,2: 88:[2, 27, 86] Operation: 50+36=86 Exploring Operation: 36-27=9, Resulting Numbers: [50, 2, 9] Generated Node #0,3: 88:[50, 2, 9] Operation: 36-27=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[2, 27, 86], Operations: ['50+36=86'] Exploring Operation: 86/2=43, Resulting Numbers: [27, 43] Generated Node #0,2,0: 88:[27, 43] Operation: 86/2=43 Exploring Operation: 27-2=25, Resulting Numbers: [86, 25] Generated Node #0,2,1: 88:[86, 25] Operation: 27-2=25 Exploring Operation: 2+86=88, Resulting Numbers: [27, 88] Generated Node #0,2,2: 88:[27, 88] Operation: 2+86=88 Exploring Operation: 2+27=29, Resulting Numbers: [86, 29] Generated Node #0,2,3: 88:[86, 29] Operation: 2+27=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[86, 25], Operations: ['50+36=86', '27-2=25'] Exploring Operation: 86+25=111, Resulting Numbers: [111] 111,88 unequal: No Solution Exploring Operation: 86*25=2150, Resulting Numbers: [2150] 2150,88 unequal: No Solution Exploring Operation: 86-25=61, Resulting Numbers: [61] 61,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 88:[27, 88], Operations: ['50+36=86', '2+86=88'] Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 27+88=115, Resulting Numbers: [115] 115,88 unequal: No Solution Exploring Operation: 27*88=2376, Resulting Numbers: [2376] 2376,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[27, 43], Operations: ['50+36=86', '86/2=43'] Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 27+43=70, Resulting Numbers: [70] 70,88 unequal: No Solution Exploring Operation: 27*43=1161, Resulting Numbers: [1161] 1161,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 88:[86, 29], Operations: ['50+36=86', '2+27=29'] Exploring Operation: 86-29=57, Resulting Numbers: [57] 57,88 unequal: No Solution Exploring Operation: 86+29=115, Resulting Numbers: [115] 115,88 unequal: No Solution Exploring Operation: 86*29=2494, Resulting Numbers: [2494] 2494,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[50, 2, 9], Operations: ['36-27=9'] Exploring Operation: 50/2=25, Resulting Numbers: [9, 25] Generated Node #0,3,0: 88:[9, 25] Operation: 50/2=25 Exploring Operation: 50-9=41, Resulting Numbers: [2, 41] Generated Node #0,3,1: 88:[2, 41] Operation: 50-9=41 Exploring Operation: 2+9=11, Resulting Numbers: [50, 11] Generated Node #0,3,2: 88:[50, 11] Operation: 2+9=11 Exploring Operation: 50-2=48, Resulting Numbers: [9, 48] Generated Node #0,3,3: 88:[9, 48] Operation: 50-2=48 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[2, 41], Operations: ['36-27=9', '50-9=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,88 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[9, 25], Operations: ['36-27=9', '50/2=25'] Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,88 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[9, 48], Operations: ['36-27=9', '50-2=48'] Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,88 unequal: No Solution Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,88 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[50, 11], Operations: ['36-27=9', '2+9=11'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 50*11=550, Resulting Numbers: [550] 550,88 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[2, 27, 14], Operations: ['50-36=14'] Exploring Operation: 27+14=41, Resulting Numbers: [2, 41] Generated Node #0,1,0: 88:[2, 41] Operation: 27+14=41 Exploring Operation: 27-14=13, Resulting Numbers: [2, 13] Generated Node #0,1,1: 88:[2, 13] Operation: 27-14=13 Exploring Operation: 14-2=12, Resulting Numbers: [27, 12] Generated Node #0,1,2: 88:[27, 12] Operation: 14-2=12 Exploring Operation: 27-2=25, Resulting Numbers: [14, 25] Generated Node #0,1,3: 88:[14, 25] Operation: 27-2=25 Moving to Node #0,1,1 Current State: 88:[2, 13], Operations: ['50-36=14', '27-14=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[2, 41], Operations: ['50-36=14', '27+14=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[14, 25], Operations: ['50-36=14', '27-2=25'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,88 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[27, 12], Operations: ['50-36=14', '14-2=12'] Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,88 unequal: No Solution Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,88 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[2, 36, 23], Operations: ['50-27=23'] Exploring Operation: 36/2=18, Resulting Numbers: [23, 18] Generated Node #0,0,0: 88:[23, 18] Operation: 36/2=18 Exploring Operation: 23-2=21, Resulting Numbers: [36, 21] Generated Node #0,0,1: 88:[36, 21] Operation: 23-2=21 Exploring Operation: 36-23=13, Resulting Numbers: [2, 13] Generated Node #0,0,2: 88:[2, 13] Operation: 36-23=13 Exploring Operation: 2+36=38, Resulting Numbers: [23, 38] Generated Node #0,0,3: 88:[23, 38] Operation: 2+36=38 Moving to Node #0,0,2 Current State: 88:[2, 13], Operations: ['50-27=23', '36-23=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[23, 18], Operations: ['50-27=23', '36/2=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,88 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[23, 38], Operations: ['50-27=23', '2+36=38'] Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,88 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[36, 21], Operations: ['50-27=23', '23-2=21'] Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 36*21=756, Resulting Numbers: [756] 756,88 unequal: No Solution Exploring Operation: 36+21=57, Resulting Numbers: [57] 57,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 67, 66, 99, 69 ]
35
[ "67+66=133", "99+69=168", "168-133=35" ]
Current State: 35:[67, 66, 99, 69], Operations: [] Exploring Operation: 67+66=133, Resulting Numbers: [99, 69, 133] Generated Node #2: [99, 69, 133] from Operation: 67+66=133 Current State: 35:[99, 69, 133], Operations: ['67+66=133'] Exploring Operation: 99+69=168, Resulting Numbers: [133, 168] Generated Node #3: [133, 168] from Operation: 99+69=168 Current State: 35:[133, 168], Operations: ['67+66=133', '99+69=168'] Exploring Operation: 168-133=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[67, 66, 99, 69], Operations: [] Exploring Operation: 99-67=32, Resulting Numbers: [66, 69, 32] Generated Node #0,0: 35:[66, 69, 32] Operation: 99-67=32 Exploring Operation: 99-69=30, Resulting Numbers: [67, 66, 30] Generated Node #0,1: 35:[67, 66, 30] Operation: 99-69=30 Exploring Operation: 99-66=33, Resulting Numbers: [67, 69, 33] Generated Node #0,2: 35:[67, 69, 33] Operation: 99-66=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[66, 69, 32], Operations: ['99-67=32'] Exploring Operation: 66-32=34, Resulting Numbers: [69, 34] Generated Node #0,0,0: 35:[69, 34] Operation: 66-32=34 Exploring Operation: 69-32=37, Resulting Numbers: [66, 37] Generated Node #0,0,1: 35:[66, 37] Operation: 69-32=37 Exploring Operation: 69-66=3, Resulting Numbers: [32, 3] Generated Node #0,0,2: 35:[32, 3] Operation: 69-66=3 Moving to Node #0,0,2 Current State: 35:[32, 3], Operations: ['99-67=32', '69-66=3'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,35 unequal: No Solution Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,35 unequal: No Solution Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[67, 66, 99, 69], Operations: [] Exploring Operation: 99-67=32, Resulting Numbers: [66, 69, 32] Generated Node #0,0: 35:[66, 69, 32] Operation: 99-67=32 Moving to Node #0,0 Current State: 35:[66, 69, 32], Operations: ['99-67=32'] Exploring Operation: 69-66=3, Resulting Numbers: [32, 3] Generated Node #0,0,2: 35:[32, 3] Operation: 69-66=3 Moving to Node #0,0,2 Current State: 35:[32, 3], Operations: ['99-67=32', '69-66=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 39, 20, 11, 41 ]
42
[ "41-39=2", "11*2=22", "20+22=42" ]
Current State: 42:[39, 20, 11, 41], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [20, 11, 2] Generated Node #2: [20, 11, 2] from Operation: 41-39=2 Current State: 42:[20, 11, 2], Operations: ['41-39=2'] Exploring Operation: 11*2=22, Resulting Numbers: [20, 22] Generated Node #3: [20, 22] from Operation: 11*2=22 Current State: 42:[20, 22], Operations: ['41-39=2', '11*2=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[39, 20, 11, 41], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [20, 11, 2] Generated Node #0,0: 42:[20, 11, 2] Operation: 41-39=2 Exploring Operation: 39-20=19, Resulting Numbers: [11, 41, 19] Generated Node #0,1: 42:[11, 41, 19] Operation: 39-20=19 Exploring Operation: 20-11=9, Resulting Numbers: [39, 41, 9] Generated Node #0,2: 42:[39, 41, 9] Operation: 20-11=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[20, 11, 2], Operations: ['41-39=2'] Exploring Operation: 11+2=13, Resulting Numbers: [20, 13] Generated Node #0,0,0: 42:[20, 13] Operation: 11+2=13 Exploring Operation: 11*2=22, Resulting Numbers: [20, 22] Generated Node #0,0,1: 42:[20, 22] Operation: 11*2=22 Exploring Operation: 20-11=9, Resulting Numbers: [2, 9] Generated Node #0,0,2: 42:[2, 9] Operation: 20-11=9 Moving to Node #0,0,0 Current State: 42:[20, 13], Operations: ['41-39=2', '11+2=13'] Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,42 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,42 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[20, 22], Operations: ['41-39=2', '11*2=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[39, 20, 11, 41], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [20, 11, 2] Generated Node #0,0: 42:[20, 11, 2] Operation: 41-39=2 Moving to Node #0,0 Current State: 42:[20, 11, 2], Operations: ['41-39=2'] Exploring Operation: 11*2=22, Resulting Numbers: [20, 22] Generated Node #0,0,1: 42:[20, 22] Operation: 11*2=22 Moving to Node #0,0,1 Current State: 42:[20, 22], Operations: ['41-39=2', '11*2=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 16, 57, 81, 57 ]
17
[ "57-16=41", "81-57=24", "41-24=17" ]
Current State: 17:[16, 57, 81, 57], Operations: [] Exploring Operation: 57-16=41, Resulting Numbers: [81, 41] Generated Node #2: [81, 41] from Operation: 57-16=41 Current State: 17:[81, 41], Operations: ['57-16=41'] Exploring Operation: 81-57=24, Resulting Numbers: [41, 24] Generated Node #3: [41, 24] from Operation: 81-57=24 Current State: 17:[41, 24], Operations: ['57-16=41', '81-57=24'] Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[16, 57, 81, 57], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [16, 57, 24] Generated Node #0,0: 17:[16, 57, 24] Operation: 81-57=24 Moving to Node #0,0 Current State: 17:[16, 57, 24], Operations: ['81-57=24'] Exploring Operation: 57-24=33, Resulting Numbers: [16, 33] Generated Node #0,0,0: 17:[16, 33] Operation: 57-24=33 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[16, 33], Operations: ['81-57=24', '57-24=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[16, 57, 81, 57], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [16, 57, 24] Generated Node #0,0: 17:[16, 57, 24] Operation: 81-57=24 Moving to Node #0,0 Current State: 17:[16, 57, 24], Operations: ['81-57=24'] Exploring Operation: 57-24=33, Resulting Numbers: [16, 33] Generated Node #0,0,0: 17:[16, 33] Operation: 57-24=33 Moving to Node #0,0,0 Current State: 17:[16, 33], Operations: ['81-57=24', '57-24=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 48, 2, 16, 27 ]
59
[ "48+16=64", "64/2=32", "27+32=59" ]
Current State: 59:[48, 2, 16, 27], Operations: [] Exploring Operation: 48+16=64, Resulting Numbers: [2, 27, 64] Generated Node #2: [2, 27, 64] from Operation: 48+16=64 Current State: 59:[2, 27, 64], Operations: ['48+16=64'] Exploring Operation: 64/2=32, Resulting Numbers: [27, 32] Generated Node #3: [27, 32] from Operation: 64/2=32 Current State: 59:[27, 32], Operations: ['48+16=64', '64/2=32'] Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[48, 2, 16, 27], Operations: [] Exploring Operation: 2+16=18, Resulting Numbers: [48, 27, 18] Generated Node #0,0: 59:[48, 27, 18] Operation: 2+16=18 Exploring Operation: 2+27=29, Resulting Numbers: [48, 16, 29] Generated Node #0,1: 59:[48, 16, 29] Operation: 2+27=29 Exploring Operation: 2*27=54, Resulting Numbers: [48, 16, 54] Generated Node #0,2: 59:[48, 16, 54] Operation: 2*27=54 Exploring Operation: 48+2=50, Resulting Numbers: [16, 27, 50] Generated Node #0,3: 59:[16, 27, 50] Operation: 48+2=50 Exploring Operation: 2*16=32, Resulting Numbers: [48, 27, 32] Generated Node #0,4: 59:[48, 27, 32] Operation: 2*16=32 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[48, 16, 54], Operations: ['2*27=54'] Exploring Operation: 54-16=38, Resulting Numbers: [48, 38] Generated Node #0,2,0: 59:[48, 38] Operation: 54-16=38 Exploring Operation: 48+16=64, Resulting Numbers: [54, 64] Generated Node #0,2,1: 59:[54, 64] Operation: 48+16=64 Exploring Operation: 48/16=3, Resulting Numbers: [54, 3] Generated Node #0,2,2: 59:[54, 3] Operation: 48/16=3 Exploring Operation: 16+54=70, Resulting Numbers: [48, 70] Generated Node #0,2,3: 59:[48, 70] Operation: 16+54=70 Exploring Operation: 48-16=32, Resulting Numbers: [54, 32] Generated Node #0,2,4: 59:[54, 32] Operation: 48-16=32 Moving to Node #0,2,1 Current State: 59:[54, 64], Operations: ['2*27=54', '48+16=64'] Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,59 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[48, 70], Operations: ['2*27=54', '16+54=70'] Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 48*70=3360, Resulting Numbers: [3360] 3360,59 unequal: No Solution Exploring Operation: 48+70=118, Resulting Numbers: [118] 118,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[48, 38], Operations: ['2*27=54', '54-16=38'] Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,59 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,2,4 Current State: 59:[54, 32], Operations: ['2*27=54', '48-16=32'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 54*32=1728, Resulting Numbers: [1728] 1728,59 unequal: No Solution Exploring Operation: 54+32=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[54, 3], Operations: ['2*27=54', '48/16=3'] Exploring Operation: 54*3=162, Resulting Numbers: [162] 162,59 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 59:[48, 27, 32], Operations: ['2*16=32'] Exploring Operation: 48+32=80, Resulting Numbers: [27, 80] Generated Node #0,4,0: 59:[27, 80] Operation: 48+32=80 Exploring Operation: 48+27=75, Resulting Numbers: [32, 75] Generated Node #0,4,1: 59:[32, 75] Operation: 48+27=75 Exploring Operation: 27+32=59, Resulting Numbers: [48, 59] Generated Node #0,4,2: 59:[48, 59] Operation: 27+32=59 Exploring Operation: 48-27=21, Resulting Numbers: [32, 21] Generated Node #0,4,3: 59:[32, 21] Operation: 48-27=21 Exploring Operation: 32-27=5, Resulting Numbers: [48, 5] Generated Node #0,4,4: 59:[48, 5] Operation: 32-27=5 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 59:[48, 59], Operations: ['2*16=32', '27+32=59'] Exploring Operation: 48+59=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 48*59=2832, Resulting Numbers: [2832] 2832,59 unequal: No Solution Exploring Operation: 59-48=11, Resulting Numbers: [11] 11,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 59:[32, 75], Operations: ['2*16=32', '48+27=75'] Exploring Operation: 32*75=2400, Resulting Numbers: [2400] 2400,59 unequal: No Solution Exploring Operation: 32+75=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 75-32=43, Resulting Numbers: [43] 43,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 59:[27, 80], Operations: ['2*16=32', '48+32=80'] Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 27*80=2160, Resulting Numbers: [2160] 2160,59 unequal: No Solution Exploring Operation: 27+80=107, Resulting Numbers: [107] 107,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 59:[32, 21], Operations: ['2*16=32', '48-27=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 59:[48, 5], Operations: ['2*16=32', '32-27=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[48, 27, 18], Operations: ['2+16=18'] Exploring Operation: 48-18=30, Resulting Numbers: [27, 30] Generated Node #0,0,0: 59:[27, 30] Operation: 48-18=30 Exploring Operation: 27-18=9, Resulting Numbers: [48, 9] Generated Node #0,0,1: 59:[48, 9] Operation: 27-18=9 Exploring Operation: 27+18=45, Resulting Numbers: [48, 45] Generated Node #0,0,2: 59:[48, 45] Operation: 27+18=45 Exploring Operation: 48+18=66, Resulting Numbers: [27, 66] Generated Node #0,0,3: 59:[27, 66] Operation: 48+18=66 Exploring Operation: 48+27=75, Resulting Numbers: [18, 75] Generated Node #0,0,4: 59:[18, 75] Operation: 48+27=75 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[48, 45], Operations: ['2+16=18', '27+18=45'] Exploring Operation: 48+45=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 48*45=2160, Resulting Numbers: [2160] 2160,59 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 59:[27, 66], Operations: ['2+16=18', '48+18=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,59 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 59:[18, 75], Operations: ['2+16=18', '48+27=75'] Exploring Operation: 18*75=1350, Resulting Numbers: [1350] 1350,59 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 18+75=93, Resulting Numbers: [93] 93,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[27, 30], Operations: ['2+16=18', '48-18=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,59 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[48, 9], Operations: ['2+16=18', '27-18=9'] Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,59 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[48, 16, 29], Operations: ['2+27=29'] Exploring Operation: 48-16=32, Resulting Numbers: [29, 32] Generated Node #0,1,0: 59:[29, 32] Operation: 48-16=32 Exploring Operation: 48+16=64, Resulting Numbers: [29, 64] Generated Node #0,1,1: 59:[29, 64] Operation: 48+16=64 Exploring Operation: 48+29=77, Resulting Numbers: [16, 77] Generated Node #0,1,2: 59:[16, 77] Operation: 48+29=77 Exploring Operation: 16+29=45, Resulting Numbers: [48, 45] Generated Node #0,1,3: 59:[48, 45] Operation: 16+29=45 Exploring Operation: 29-16=13, Resulting Numbers: [48, 13] Generated Node #0,1,4: 59:[48, 13] Operation: 29-16=13 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 59:[48, 45], Operations: ['2+27=29', '16+29=45'] Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 48+45=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 48*45=2160, Resulting Numbers: [2160] 2160,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[29, 64], Operations: ['2+27=29', '48+16=64'] Exploring Operation: 29*64=1856, Resulting Numbers: [1856] 1856,59 unequal: No Solution Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,59 unequal: No Solution Exploring Operation: 29+64=93, Resulting Numbers: [93] 93,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[29, 32], Operations: ['2+27=29', '48-16=32'] Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 29*32=928, Resulting Numbers: [928] 928,59 unequal: No Solution Exploring Operation: 32-29=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 59:[48, 13], Operations: ['2+27=29', '29-16=13'] Exploring Operation: 48+13=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,59 unequal: No Solution Exploring Operation: 48*13=624, Resulting Numbers: [624] 624,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[16, 77], Operations: ['2+27=29', '48+29=77'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[16, 27, 50], Operations: ['48+2=50'] Exploring Operation: 16+27=43, Resulting Numbers: [50, 43] Generated Node #0,3,0: 59:[50, 43] Operation: 16+27=43 Exploring Operation: 27+50=77, Resulting Numbers: [16, 77] Generated Node #0,3,1: 59:[16, 77] Operation: 27+50=77 Exploring Operation: 50-16=34, Resulting Numbers: [27, 34] Generated Node #0,3,2: 59:[27, 34] Operation: 50-16=34 Exploring Operation: 27-16=11, Resulting Numbers: [50, 11] Generated Node #0,3,3: 59:[50, 11] Operation: 27-16=11 Exploring Operation: 16+50=66, Resulting Numbers: [27, 66] Generated Node #0,3,4: 59:[27, 66] Operation: 16+50=66 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 59:[50, 43], Operations: ['48+2=50', '16+27=43'] Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 50+43=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 50*43=2150, Resulting Numbers: [2150] 2150,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 59:[27, 66], Operations: ['48+2=50', '16+50=66'] Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,59 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 59:[27, 34], Operations: ['48+2=50', '50-16=34'] Exploring Operation: 34-27=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 27*34=918, Resulting Numbers: [918] 918,59 unequal: No Solution Exploring Operation: 27+34=61, Resulting Numbers: [61] 61,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 59:[50, 11], Operations: ['48+2=50', '27-16=11'] Exploring Operation: 50*11=550, Resulting Numbers: [550] 550,59 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 59:[16, 77], Operations: ['48+2=50', '27+50=77'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,59 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,59 unequal: No Solution Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 2, 11, 1, 25 ]
11
[ "2+11=13", "25-1=24", "24-13=11" ]
Current State: 11:[2, 11, 1, 25], Operations: [] Exploring Operation: 2+11=13, Resulting Numbers: [1, 25, 13] Generated Node #2: [1, 25, 13] from Operation: 2+11=13 Current State: 11:[1, 25, 13], Operations: ['2+11=13'] Exploring Operation: 25-1=24, Resulting Numbers: [13, 24] Generated Node #3: [13, 24] from Operation: 25-1=24 Current State: 11:[13, 24], Operations: ['2+11=13', '25-1=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[2, 11, 1, 25], Operations: [] Exploring Operation: 25-11=14, Resulting Numbers: [2, 1, 14] Generated Node #0,0: 11:[2, 1, 14] Operation: 25-11=14 Exploring Operation: 2+1=3, Resulting Numbers: [11, 25, 3] Generated Node #0,1: 11:[11, 25, 3] Operation: 2+1=3 Exploring Operation: 25-2=23, Resulting Numbers: [11, 1, 23] Generated Node #0,2: 11:[11, 1, 23] Operation: 25-2=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[2, 1, 14], Operations: ['25-11=14'] Exploring Operation: 14-2=12, Resulting Numbers: [1, 12] Generated Node #0,0,0: 11:[1, 12] Operation: 14-2=12 Exploring Operation: 2+1=3, Resulting Numbers: [14, 3] Generated Node #0,0,1: 11:[14, 3] Operation: 2+1=3 Exploring Operation: 14-1=13, Resulting Numbers: [2, 13] Generated Node #0,0,2: 11:[2, 13] Operation: 14-1=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[1, 12], Operations: ['25-11=14', '14-2=12'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,11 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[2, 11, 1, 25], Operations: [] Exploring Operation: 25-11=14, Resulting Numbers: [2, 1, 14] Generated Node #0,0: 11:[2, 1, 14] Operation: 25-11=14 Moving to Node #0,0 Current State: 11:[2, 1, 14], Operations: ['25-11=14'] Exploring Operation: 14-2=12, Resulting Numbers: [1, 12] Generated Node #0,0,0: 11:[1, 12] Operation: 14-2=12 Moving to Node #0,0,0 Current State: 11:[1, 12], Operations: ['25-11=14', '14-2=12'] Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 27, 73, 12, 16 ]
74
[ "73-27=46", "12+16=28", "46+28=74" ]
Current State: 74:[27, 73, 12, 16], Operations: [] Exploring Operation: 73-27=46, Resulting Numbers: [12, 16, 46] Generated Node #2: [12, 16, 46] from Operation: 73-27=46 Current State: 74:[12, 16, 46], Operations: ['73-27=46'] Exploring Operation: 12+16=28, Resulting Numbers: [46, 28] Generated Node #3: [46, 28] from Operation: 12+16=28 Current State: 74:[46, 28], Operations: ['73-27=46', '12+16=28'] Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[27, 73, 12, 16], Operations: [] Exploring Operation: 27+16=43, Resulting Numbers: [73, 12, 43] Generated Node #0,0: 74:[73, 12, 43] Operation: 27+16=43 Exploring Operation: 27+12=39, Resulting Numbers: [73, 16, 39] Generated Node #0,1: 74:[73, 16, 39] Operation: 27+12=39 Exploring Operation: 16-12=4, Resulting Numbers: [27, 73, 4] Generated Node #0,2: 74:[27, 73, 4] Operation: 16-12=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[27, 73, 4], Operations: ['16-12=4'] Exploring Operation: 73-27=46, Resulting Numbers: [4, 46] Generated Node #0,2,0: 74:[4, 46] Operation: 73-27=46 Exploring Operation: 73+4=77, Resulting Numbers: [27, 77] Generated Node #0,2,1: 74:[27, 77] Operation: 73+4=77 Exploring Operation: 27+4=31, Resulting Numbers: [73, 31] Generated Node #0,2,2: 74:[73, 31] Operation: 27+4=31 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[73, 31], Operations: ['16-12=4', '27+4=31'] Exploring Operation: 73*31=2263, Resulting Numbers: [2263] 2263,74 unequal: No Solution Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 73+31=104, Resulting Numbers: [104] 104,74 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:[4, 46], Operations: ['16-12=4', '73-27=46'] Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,74 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,74 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 #0,2,1 Current State: 74:[27, 77], Operations: ['16-12=4', '73+4=77'] Exploring Operation: 27*77=2079, Resulting Numbers: [2079] 2079,74 unequal: No Solution Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 27+77=104, Resulting Numbers: [104] 104,74 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 #0,0 Current State: 74:[73, 12, 43], Operations: ['27+16=43'] Exploring Operation: 43-12=31, Resulting Numbers: [73, 31] Generated Node #0,0,0: 74:[73, 31] Operation: 43-12=31 Exploring Operation: 73+12=85, Resulting Numbers: [43, 85] Generated Node #0,0,1: 74:[43, 85] Operation: 73+12=85 Exploring Operation: 73-43=30, Resulting Numbers: [12, 30] Generated Node #0,0,2: 74:[12, 30] Operation: 73-43=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[73, 31], Operations: ['27+16=43', '43-12=31'] Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 73+31=104, Resulting Numbers: [104] 104,74 unequal: No Solution Exploring Operation: 73*31=2263, Resulting Numbers: [2263] 2263,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[43, 85], Operations: ['27+16=43', '73+12=85'] Exploring Operation: 43*85=3655, Resulting Numbers: [3655] 3655,74 unequal: No Solution Exploring Operation: 85-43=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 43+85=128, Resulting Numbers: [128] 128,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 74:[12, 30], Operations: ['27+16=43', '73-43=30'] Exploring Operation: 12*30=360, Resulting Numbers: [360] 360,74 unequal: No Solution Exploring Operation: 12+30=42, Resulting Numbers: [42] 42,74 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,74 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:[73, 16, 39], Operations: ['27+12=39'] Exploring Operation: 39-16=23, Resulting Numbers: [73, 23] Generated Node #0,1,0: 74:[73, 23] Operation: 39-16=23 Exploring Operation: 73-39=34, Resulting Numbers: [16, 34] Generated Node #0,1,1: 74:[16, 34] Operation: 73-39=34 Exploring Operation: 73+16=89, Resulting Numbers: [39, 89] Generated Node #0,1,2: 74:[39, 89] Operation: 73+16=89 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[73, 23], Operations: ['27+12=39', '39-16=23'] Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,74 unequal: No Solution Exploring Operation: 73*23=1679, Resulting Numbers: [1679] 1679,74 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 #0,1,1 Current State: 74:[16, 34], Operations: ['27+12=39', '73-39=34'] Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,74 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 #0,1,2 Current State: 74:[39, 89], Operations: ['27+12=39', '73+16=89'] Exploring Operation: 39+89=128, Resulting Numbers: [128] 128,74 unequal: No Solution Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 39*89=3471, Resulting Numbers: [3471] 3471,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 37, 9, 59, 23 ]
67
[ "37-23=14", "9*14=126", "126-59=67" ]
Current State: 67:[37, 9, 59, 23], Operations: [] Exploring Operation: 37-23=14, Resulting Numbers: [9, 59, 14] Generated Node #2: [9, 59, 14] from Operation: 37-23=14 Current State: 67:[9, 59, 14], Operations: ['37-23=14'] Exploring Operation: 9*14=126, Resulting Numbers: [59, 126] Generated Node #3: [59, 126] from Operation: 9*14=126 Current State: 67:[59, 126], Operations: ['37-23=14', '9*14=126'] Exploring Operation: 126-59=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[37, 9, 59, 23], Operations: [] Exploring Operation: 37-9=28, Resulting Numbers: [59, 23, 28] Generated Node #0,0: 67:[59, 23, 28] Operation: 37-9=28 Exploring Operation: 9+23=32, Resulting Numbers: [37, 59, 32] Generated Node #0,1: 67:[37, 59, 32] Operation: 9+23=32 Exploring Operation: 37+23=60, Resulting Numbers: [9, 59, 60] Generated Node #0,2: 67:[9, 59, 60] Operation: 37+23=60 Exploring Operation: 37+9=46, Resulting Numbers: [59, 23, 46] Generated Node #0,3: 67:[59, 23, 46] Operation: 37+9=46 Exploring Operation: 9+59=68, Resulting Numbers: [37, 23, 68] Generated Node #0,4: 67:[37, 23, 68] Operation: 9+59=68 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[37, 59, 32], Operations: ['9+23=32'] Exploring Operation: 37-32=5, Resulting Numbers: [59, 5] Generated Node #0,1,0: 67:[59, 5] Operation: 37-32=5 Exploring Operation: 59-32=27, Resulting Numbers: [37, 27] Generated Node #0,1,1: 67:[37, 27] Operation: 59-32=27 Exploring Operation: 59+32=91, Resulting Numbers: [37, 91] Generated Node #0,1,2: 67:[37, 91] Operation: 59+32=91 Exploring Operation: 37+32=69, Resulting Numbers: [59, 69] Generated Node #0,1,3: 67:[59, 69] Operation: 37+32=69 Exploring Operation: 37+59=96, Resulting Numbers: [32, 96] Generated Node #0,1,4: 67:[32, 96] Operation: 37+59=96 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 67:[59, 69], Operations: ['9+23=32', '37+32=69'] Exploring Operation: 59+69=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 59*69=4071, Resulting Numbers: [4071] 4071,67 unequal: No Solution No 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: 67:[37, 91], Operations: ['9+23=32', '59+32=91'] Exploring Operation: 37+91=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 37*91=3367, Resulting Numbers: [3367] 3367,67 unequal: No Solution No 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: 67:[32, 96], Operations: ['9+23=32', '37+59=96'] Exploring Operation: 32+96=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 96-32=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 96/32=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 32*96=3072, Resulting Numbers: [3072] 3072,67 unequal: No Solution No 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: 67:[59, 5], Operations: ['9+23=32', '37-32=5'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 59+5=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 59*5=295, Resulting Numbers: [295] 295,67 unequal: No Solution No 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: 67:[37, 27], Operations: ['9+23=32', '59-32=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,67 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,67 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: 67:[9, 59, 60], Operations: ['37+23=60'] Exploring Operation: 60-9=51, Resulting Numbers: [59, 51] Generated Node #0,2,0: 67:[59, 51] Operation: 60-9=51 Exploring Operation: 9+59=68, Resulting Numbers: [60, 68] Generated Node #0,2,1: 67:[60, 68] Operation: 9+59=68 Exploring Operation: 59-9=50, Resulting Numbers: [60, 50] Generated Node #0,2,2: 67:[60, 50] Operation: 59-9=50 Exploring Operation: 9+60=69, Resulting Numbers: [59, 69] Generated Node #0,2,3: 67:[59, 69] Operation: 9+60=69 Exploring Operation: 59+60=119, Resulting Numbers: [9, 119] Generated Node #0,2,4: 67:[9, 119] Operation: 59+60=119 Moving to Node #0,2,1 Current State: 67:[60, 68], Operations: ['37+23=60', '9+59=68'] Exploring Operation: 60+68=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 60*68=4080, Resulting Numbers: [4080] 4080,67 unequal: No Solution Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[59, 69], Operations: ['37+23=60', '9+60=69'] Exploring Operation: 59*69=4071, Resulting Numbers: [4071] 4071,67 unequal: No Solution Exploring Operation: 59+69=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[59, 51], Operations: ['37+23=60', '60-9=51'] Exploring Operation: 59+51=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 59*51=3009, Resulting Numbers: [3009] 3009,67 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[60, 50], Operations: ['37+23=60', '59-9=50'] Exploring Operation: 60+50=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 60*50=3000, Resulting Numbers: [3000] 3000,67 unequal: No Solution Moving to Node #0,2,4 Current State: 67:[9, 119], Operations: ['37+23=60', '59+60=119'] Exploring Operation: 9*119=1071, Resulting Numbers: [1071] 1071,67 unequal: No Solution Exploring Operation: 119-9=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 9+119=128, Resulting Numbers: [128] 128,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[59, 23, 46], Operations: ['37+9=46'] Exploring Operation: 46/23=2, Resulting Numbers: [59, 2] Generated Node #0,3,0: 67:[59, 2] Operation: 46/23=2 Exploring Operation: 59+23=82, Resulting Numbers: [46, 82] Generated Node #0,3,1: 67:[46, 82] Operation: 59+23=82 Exploring Operation: 46-23=23, Resulting Numbers: [59, 23] Generated Node #0,3,2: 67:[59, 23] Operation: 46-23=23 Exploring Operation: 59-23=36, Resulting Numbers: [46, 36] Generated Node #0,3,3: 67:[46, 36] Operation: 59-23=36 Exploring Operation: 23+46=69, Resulting Numbers: [59, 69] Generated Node #0,3,4: 67:[59, 69] Operation: 23+46=69 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 67:[59, 69], Operations: ['37+9=46', '23+46=69'] Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,67 unequal: No Solution Exploring Operation: 59+69=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 59*69=4071, Resulting Numbers: [4071] 4071,67 unequal: No Solution No 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: 67:[46, 82], Operations: ['37+9=46', '59+23=82'] Exploring Operation: 46+82=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,67 unequal: No Solution Exploring Operation: 46*82=3772, Resulting Numbers: [3772] 3772,67 unequal: No Solution No 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: 67:[59, 23], Operations: ['37+9=46', '46-23=23'] Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,67 unequal: No Solution Exploring Operation: 59+23=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 59*23=1357, Resulting Numbers: [1357] 1357,67 unequal: No Solution No 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: 67:[46, 36], Operations: ['37+9=46', '59-23=36'] Exploring Operation: 46+36=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 46*36=1656, Resulting Numbers: [1656] 1656,67 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,67 unequal: No Solution No 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: 67:[59, 2], Operations: ['37+9=46', '46/23=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 59*2=118, Resulting Numbers: [118] 118,67 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,67 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: 67:[37, 23, 68], Operations: ['9+59=68'] Exploring Operation: 68-37=31, Resulting Numbers: [23, 31] Generated Node #0,4,0: 67:[23, 31] Operation: 68-37=31 Exploring Operation: 23+68=91, Resulting Numbers: [37, 91] Generated Node #0,4,1: 67:[37, 91] Operation: 23+68=91 Exploring Operation: 37+23=60, Resulting Numbers: [68, 60] Generated Node #0,4,2: 67:[68, 60] Operation: 37+23=60 Exploring Operation: 68-23=45, Resulting Numbers: [37, 45] Generated Node #0,4,3: 67:[37, 45] Operation: 68-23=45 Exploring Operation: 37-23=14, Resulting Numbers: [68, 14] Generated Node #0,4,4: 67:[68, 14] Operation: 37-23=14 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 67:[68, 60], Operations: ['9+59=68', '37+23=60'] Exploring Operation: 68+60=128, Resulting Numbers: [128] 128,67 unequal: No Solution Exploring Operation: 68*60=4080, Resulting Numbers: [4080] 4080,67 unequal: No Solution Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,67 unequal: No Solution No 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: 67:[37, 45], Operations: ['9+59=68', '68-23=45'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,67 unequal: No Solution Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 37*45=1665, Resulting Numbers: [1665] 1665,67 unequal: No Solution No 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: 67:[37, 91], Operations: ['9+59=68', '23+68=91'] Exploring Operation: 37*91=3367, Resulting Numbers: [3367] 3367,67 unequal: No Solution Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 37+91=128, Resulting Numbers: [128] 128,67 unequal: No Solution No 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: 67:[68, 14], Operations: ['9+59=68', '37-23=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 68+14=82, Resulting Numbers: [82] 82,67 unequal: No Solution Exploring Operation: 68*14=952, Resulting Numbers: [952] 952,67 unequal: No Solution No 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: 67:[23, 31], Operations: ['9+59=68', '68-37=31'] Exploring Operation: 23*31=713, Resulting Numbers: [713] 713,67 unequal: No Solution Exploring Operation: 23+31=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,67 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: 67:[59, 23, 28], Operations: ['37-9=28'] Exploring Operation: 28-23=5, Resulting Numbers: [59, 5] Generated Node #0,0,0: 67:[59, 5] Operation: 28-23=5 Exploring Operation: 59+23=82, Resulting Numbers: [28, 82] Generated Node #0,0,1: 67:[28, 82] Operation: 59+23=82 Exploring Operation: 59-23=36, Resulting Numbers: [28, 36] Generated Node #0,0,2: 67:[28, 36] Operation: 59-23=36 Exploring Operation: 59+28=87, Resulting Numbers: [23, 87] Generated Node #0,0,3: 67:[23, 87] Operation: 59+28=87 Exploring Operation: 23+28=51, Resulting Numbers: [59, 51] Generated Node #0,0,4: 67:[59, 51] Operation: 23+28=51 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 67:[59, 51], Operations: ['37-9=28', '23+28=51'] Exploring Operation: 59+51=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 59*51=3009, Resulting Numbers: [3009] 3009,67 unequal: No Solution Exploring Operation: 59-51=8, Resulting Numbers: [8] 8,67 unequal: No Solution No 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: 67:[28, 82], Operations: ['37-9=28', '59+23=82'] Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,67 unequal: No Solution No 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: 67:[23, 87], Operations: ['37-9=28', '59+28=87'] Exploring Operation: 23+87=110, Resulting Numbers: [110] 110,67 unequal: No Solution Exploring Operation: 23*87=2001, Resulting Numbers: [2001] 2001,67 unequal: No Solution Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,67 unequal: No Solution No 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: 67:[59, 5], Operations: ['37-9=28', '28-23=5'] Exploring Operation: 59+5=64, Resulting Numbers: [64] 64,67 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 59*5=295, Resulting Numbers: [295] 295,67 unequal: No Solution No 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: 67:[28, 36], Operations: ['37-9=28', '59-23=36'] Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,67 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,67 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 14, 64, 5, 73 ]
83
[ "64-14=50", "50/5=10", "73+10=83" ]
Current State: 83:[14, 64, 5, 73], Operations: [] Exploring Operation: 64-14=50, Resulting Numbers: [5, 73, 50] Generated Node #2: [5, 73, 50] from Operation: 64-14=50 Current State: 83:[5, 73, 50], Operations: ['64-14=50'] Exploring Operation: 50/5=10, Resulting Numbers: [73, 10] Generated Node #3: [73, 10] from Operation: 50/5=10 Current State: 83:[73, 10], Operations: ['64-14=50', '50/5=10'] Exploring Operation: 73+10=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[14, 64, 5, 73], Operations: [] Exploring Operation: 14+64=78, Resulting Numbers: [5, 73, 78] Generated Node #0,0: 83:[5, 73, 78] Operation: 14+64=78 Exploring Operation: 14*5=70, Resulting Numbers: [64, 73, 70] Generated Node #0,1: 83:[64, 73, 70] Operation: 14*5=70 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[64, 73, 70], Operations: ['14*5=70'] Exploring Operation: 64+73=137, Resulting Numbers: [70, 137] Generated Node #0,1,0: 83:[70, 137] Operation: 64+73=137 Exploring Operation: 64+70=134, Resulting Numbers: [73, 134] Generated Node #0,1,1: 83:[73, 134] Operation: 64+70=134 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[73, 134], Operations: ['14*5=70', '64+70=134'] Exploring Operation: 134-73=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 73+134=207, Resulting Numbers: [207] 207,83 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 #0,1,0 Current State: 83:[70, 137], Operations: ['14*5=70', '64+73=137'] Exploring Operation: 70+137=207, Resulting Numbers: [207] 207,83 unequal: No Solution Exploring Operation: 137-70=67, Resulting Numbers: [67] 67,83 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 #0,0 Current State: 83:[5, 73, 78], Operations: ['14+64=78'] Exploring Operation: 5+78=83, Resulting Numbers: [73, 83] Generated Node #0,0,0: 83:[73, 83] Operation: 5+78=83 Exploring Operation: 5+73=78, Resulting Numbers: [78, 78] Generated Node #0,0,1: 83:[78, 78] Operation: 5+73=78 Moving to Node #0,0,0 Current State: 83:[73, 83], Operations: ['14+64=78', '5+78=83'] Exploring Operation: 83-73=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 73+83=156, Resulting Numbers: [156] 156,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[78, 78], Operations: ['14+64=78', '5+73=78'] Exploring Operation: 78+78=156, Resulting Numbers: [156] 156,83 unequal: No Solution Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,83 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
[ 14, 78, 58, 56 ]
32
[ "78-14=64", "58-56=2", "64/2=32" ]
Current State: 32:[14, 78, 58, 56], Operations: [] Exploring Operation: 78-14=64, Resulting Numbers: [58, 56, 64] Generated Node #2: [58, 56, 64] from Operation: 78-14=64 Current State: 32:[58, 56, 64], Operations: ['78-14=64'] Exploring Operation: 58-56=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 58-56=2 Current State: 32:[64, 2], Operations: ['78-14=64', '58-56=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[14, 78, 58, 56], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [14, 78, 2] Generated Node #0,0: 32:[14, 78, 2] Operation: 58-56=2 Exploring Operation: 78-56=22, Resulting Numbers: [14, 58, 22] Generated Node #0,1: 32:[14, 58, 22] Operation: 78-56=22 Exploring Operation: 56/14=4, Resulting Numbers: [78, 58, 4] Generated Node #0,2: 32:[78, 58, 4] Operation: 56/14=4 Exploring Operation: 78-58=20, Resulting Numbers: [14, 56, 20] Generated Node #0,3: 32:[14, 56, 20] Operation: 78-58=20 Moving to Node #0,3 Current State: 32:[14, 56, 20], Operations: ['78-58=20'] Exploring Operation: 14+20=34, Resulting Numbers: [56, 34] Generated Node #0,3,0: 32:[56, 34] Operation: 14+20=34 Exploring Operation: 56-20=36, Resulting Numbers: [14, 36] Generated Node #0,3,1: 32:[14, 36] Operation: 56-20=36 Exploring Operation: 56/14=4, Resulting Numbers: [20, 4] Generated Node #0,3,2: 32:[20, 4] Operation: 56/14=4 Exploring Operation: 56-14=42, Resulting Numbers: [20, 42] Generated Node #0,3,3: 32:[20, 42] Operation: 56-14=42 Moving to Node #0,1 Current State: 32:[14, 58, 22], Operations: ['78-56=22'] Exploring Operation: 22-14=8, Resulting Numbers: [58, 8] Generated Node #0,1,0: 32:[58, 8] Operation: 22-14=8 Exploring Operation: 58-22=36, Resulting Numbers: [14, 36] Generated Node #0,1,1: 32:[14, 36] Operation: 58-22=36 Exploring Operation: 58-14=44, Resulting Numbers: [22, 44] Generated Node #0,1,2: 32:[22, 44] Operation: 58-14=44 Exploring Operation: 14+22=36, Resulting Numbers: [58, 36] Generated Node #0,1,3: 32:[58, 36] Operation: 14+22=36 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[14, 36], Operations: ['78-56=22', '58-22=36'] Exploring Operation: 14*36=504, Resulting Numbers: [504] 504,32 unequal: No Solution Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[22, 44], Operations: ['78-56=22', '58-14=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,32 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,32 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,32 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:[58, 8], Operations: ['78-56=22', '22-14=8'] Exploring Operation: 58*8=464, Resulting Numbers: [464] 464,32 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,32 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,32 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 #0,1,3 Current State: 32:[58, 36], Operations: ['78-56=22', '14+22=36'] Exploring Operation: 58+36=94, Resulting Numbers: [94] 94,32 unequal: No Solution Exploring Operation: 58-36=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 58*36=2088, Resulting Numbers: [2088] 2088,32 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:[14, 78, 2], Operations: ['58-56=2'] Exploring Operation: 14+2=16, Resulting Numbers: [78, 16] Generated Node #0,0,0: 32:[78, 16] Operation: 14+2=16 Exploring Operation: 78/2=39, Resulting Numbers: [14, 39] Generated Node #0,0,1: 32:[14, 39] Operation: 78/2=39 Exploring Operation: 78-2=76, Resulting Numbers: [14, 76] Generated Node #0,0,2: 32:[14, 76] Operation: 78-2=76 Exploring Operation: 78-14=64, Resulting Numbers: [2, 64] Generated Node #0,0,3: 32:[2, 64] Operation: 78-14=64 Moving to Node #0,2 Current State: 32:[78, 58, 4], Operations: ['56/14=4'] Exploring Operation: 78-58=20, Resulting Numbers: [4, 20] Generated Node #0,2,0: 32:[4, 20] Operation: 78-58=20 Exploring Operation: 58-4=54, Resulting Numbers: [78, 54] Generated Node #0,2,1: 32:[78, 54] Operation: 58-4=54 Exploring Operation: 78+4=82, Resulting Numbers: [58, 82] Generated Node #0,2,2: 32:[58, 82] Operation: 78+4=82 Exploring Operation: 78-4=74, Resulting Numbers: [58, 74] Generated Node #0,2,3: 32:[58, 74] Operation: 78-4=74 Moving to Node #0,3,2 Current State: 32:[20, 4], Operations: ['78-58=20', '56/14=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,32 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[4, 20], Operations: ['56/14=4', '78-58=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[14, 36], Operations: ['78-58=20', '56-20=36'] Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,32 unequal: No Solution Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 14*36=504, Resulting Numbers: [504] 504,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[14, 39], Operations: ['58-56=2', '78/2=39'] Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,32 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,32 unequal: No Solution Moving to Node #0,3,3 Current State: 32:[20, 42], Operations: ['78-58=20', '56-14=42'] Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 20*42=840, Resulting Numbers: [840] 840,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[56, 34], Operations: ['78-58=20', '14+20=34'] Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,32 unequal: No Solution Exploring Operation: 56*34=1904, Resulting Numbers: [1904] 1904,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[2, 64], Operations: ['58-56=2', '78-14=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,32 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[14, 78, 58, 56], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [14, 78, 2] Generated Node #0,0: 32:[14, 78, 2] Operation: 58-56=2 Moving to Node #0,0 Current State: 32:[14, 78, 2], Operations: ['58-56=2'] Exploring Operation: 78-14=64, Resulting Numbers: [2, 64] Generated Node #0,0,3: 32:[2, 64] Operation: 78-14=64 Moving to Node #0,0,3 Current State: 32:[2, 64], Operations: ['58-56=2', '78-14=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.947917
hs_4
mult_heuristic
[ 75, 33, 98, 97 ]
87
[ "75+33=108", "98+97=195", "195-108=87" ]
Current State: 87:[75, 33, 98, 97], Operations: [] Exploring Operation: 75+33=108, Resulting Numbers: [98, 97, 108] Generated Node #2: [98, 97, 108] from Operation: 75+33=108 Current State: 87:[98, 97, 108], Operations: ['75+33=108'] Exploring Operation: 98+97=195, Resulting Numbers: [108, 195] Generated Node #3: [108, 195] from Operation: 98+97=195 Current State: 87:[108, 195], Operations: ['75+33=108', '98+97=195'] Exploring Operation: 195-108=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[75, 33, 98, 97], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [75, 33, 1] Generated Node #0,0: 87:[75, 33, 1] Operation: 98-97=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[75, 33, 1], Operations: ['98-97=1'] Exploring Operation: 75-33=42, Resulting Numbers: [1, 42] Generated Node #0,0,0: 87:[1, 42] Operation: 75-33=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[1, 42], Operations: ['98-97=1', '75-33=42'] Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,87 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
[ 21, 26, 6, 10 ]
31
[ "21+26=47", "6+10=16", "47-16=31" ]
Current State: 31:[21, 26, 6, 10], Operations: [] Exploring Operation: 21+26=47, Resulting Numbers: [6, 10, 47] Generated Node #2: [6, 10, 47] from Operation: 21+26=47 Current State: 31:[6, 10, 47], Operations: ['21+26=47'] Exploring Operation: 6+10=16, Resulting Numbers: [47, 16] Generated Node #3: [47, 16] from Operation: 6+10=16 Current State: 31:[47, 16], Operations: ['21+26=47', '6+10=16'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[21, 26, 6, 10], Operations: [] Exploring Operation: 6+10=16, Resulting Numbers: [21, 26, 16] Generated Node #0,0: 31:[21, 26, 16] Operation: 6+10=16 Exploring Operation: 21+6=27, Resulting Numbers: [26, 10, 27] Generated Node #0,1: 31:[26, 10, 27] Operation: 21+6=27 Exploring Operation: 21+10=31, Resulting Numbers: [26, 6, 31] Generated Node #0,2: 31:[26, 6, 31] Operation: 21+10=31 Moving to Node #0,0 Current State: 31:[21, 26, 16], Operations: ['6+10=16'] Exploring Operation: 21+26=47, Resulting Numbers: [16, 47] Generated Node #0,0,0: 31:[16, 47] Operation: 21+26=47 Exploring Operation: 26+16=42, Resulting Numbers: [21, 42] Generated Node #0,0,1: 31:[21, 42] Operation: 26+16=42 Exploring Operation: 21+16=37, Resulting Numbers: [26, 37] Generated Node #0,0,2: 31:[26, 37] Operation: 21+16=37 Moving to Node #0,1 Current State: 31:[26, 10, 27], Operations: ['21+6=27'] Exploring Operation: 26-10=16, Resulting Numbers: [27, 16] Generated Node #0,1,0: 31:[27, 16] Operation: 26-10=16 Exploring Operation: 10+27=37, Resulting Numbers: [26, 37] Generated Node #0,1,1: 31:[26, 37] Operation: 10+27=37 Exploring Operation: 26+10=36, Resulting Numbers: [27, 36] Generated Node #0,1,2: 31:[27, 36] Operation: 26+10=36 Moving to Node #0,2 Current State: 31:[26, 6, 31], Operations: ['21+10=31'] Exploring Operation: 26+6=32, Resulting Numbers: [31, 32] Generated Node #0,2,0: 31:[31, 32] Operation: 26+6=32 Exploring Operation: 26-6=20, Resulting Numbers: [31, 20] Generated Node #0,2,1: 31:[31, 20] Operation: 26-6=20 Exploring Operation: 6+31=37, Resulting Numbers: [26, 37] Generated Node #0,2,2: 31:[26, 37] Operation: 6+31=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[31, 32], Operations: ['21+10=31', '26+6=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[31, 20], Operations: ['21+10=31', '26-6=20'] Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,31 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[26, 37], Operations: ['21+10=31', '6+31=37'] Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 31:[27, 36], Operations: ['21+6=27', '26+10=36'] Exploring Operation: 27+36=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 27*36=972, Resulting Numbers: [972] 972,31 unequal: No Solution Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[26, 37], Operations: ['6+10=16', '21+16=37'] Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,31 unequal: No Solution Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[26, 37], Operations: ['21+6=27', '10+27=37'] Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 26*37=962, Resulting Numbers: [962] 962,31 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[27, 16], Operations: ['21+6=27', '26-10=16'] Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,31 unequal: No Solution Exploring Operation: 27*16=432, Resulting Numbers: [432] 432,31 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[21, 42], Operations: ['6+10=16', '26+16=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[16, 47], Operations: ['6+10=16', '21+26=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[21, 26, 6, 10], Operations: [] Exploring Operation: 6+10=16, Resulting Numbers: [21, 26, 16] Generated Node #0,0: 31:[21, 26, 16] Operation: 6+10=16 Moving to Node #0,0 Current State: 31:[21, 26, 16], Operations: ['6+10=16'] Exploring Operation: 21+26=47, Resulting Numbers: [16, 47] Generated Node #0,0,0: 31:[16, 47] Operation: 21+26=47 Moving to Node #0,0,0 Current State: 31:[16, 47], Operations: ['6+10=16', '21+26=47'] Exploring Operation: 47-16=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.96441
hs_3
sum_heuristic
[ 94, 9, 9, 18 ]
87
[ "94-9=85", "18/9=2", "85+2=87" ]
Current State: 87:[94, 9, 9, 18], Operations: [] Exploring Operation: 94-9=85, Resulting Numbers: [18, 85] Generated Node #2: [18, 85] from Operation: 94-9=85 Current State: 87:[18, 85], Operations: ['94-9=85'] Exploring Operation: 18/9=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 18/9=2 Current State: 87:[85, 2], Operations: ['94-9=85', '18/9=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[94, 9, 9, 18], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [94, 9, 2] Generated Node #0,0: 87:[94, 9, 2] Operation: 18/9=2 Exploring Operation: 18/9=2, Resulting Numbers: [94, 9, 2] Generated Node #0,1: 87:[94, 9, 2] Operation: 18/9=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[94, 9, 2], Operations: ['18/9=2'] Exploring Operation: 94-2=92, Resulting Numbers: [9, 92] Generated Node #0,0,0: 87:[9, 92] Operation: 94-2=92 Exploring Operation: 94-9=85, Resulting Numbers: [2, 85] Generated Node #0,0,1: 87:[2, 85] Operation: 94-9=85 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[2, 85], Operations: ['18/9=2', '94-9=85'] Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[94, 9, 9, 18], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [94, 9, 2] Generated Node #0,0: 87:[94, 9, 2] Operation: 18/9=2 Moving to Node #0,0 Current State: 87:[94, 9, 2], Operations: ['18/9=2'] Exploring Operation: 94-9=85, Resulting Numbers: [2, 85] Generated Node #0,0,1: 87:[2, 85] Operation: 94-9=85 Moving to Node #0,0,1 Current State: 87:[2, 85], Operations: ['18/9=2', '94-9=85'] Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 21, 64, 10, 35 ]
95
[ "21*35=735", "64*10=640", "735-640=95" ]
Current State: 95:[21, 64, 10, 35], Operations: [] Exploring Operation: 21*35=735, Resulting Numbers: [64, 10, 735] Generated Node #2: [64, 10, 735] from Operation: 21*35=735 Current State: 95:[64, 10, 735], Operations: ['21*35=735'] Exploring Operation: 64*10=640, Resulting Numbers: [735, 640] Generated Node #3: [735, 640] from Operation: 64*10=640 Current State: 95:[735, 640], Operations: ['21*35=735', '64*10=640'] Exploring Operation: 735-640=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[21, 64, 10, 35], Operations: [] Exploring Operation: 64+35=99, Resulting Numbers: [21, 10, 99] Generated Node #0,0: 95:[21, 10, 99] Operation: 64+35=99 Moving to Node #0,0 Current State: 95:[21, 10, 99], Operations: ['64+35=99'] Exploring Operation: 99-10=89, Resulting Numbers: [21, 89] Generated Node #0,0,0: 95:[21, 89] Operation: 99-10=89 Moving to Node #0,0,0 Current State: 95:[21, 89], Operations: ['64+35=99', '99-10=89'] Exploring Operation: 21+89=110, Resulting Numbers: [110] 110,95 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 92, 45, 28, 85 ]
66
[ "92-45=47", "28+85=113", "113-47=66" ]
Current State: 66:[92, 45, 28, 85], Operations: [] Exploring Operation: 92-45=47, Resulting Numbers: [28, 85, 47] Generated Node #2: [28, 85, 47] from Operation: 92-45=47 Current State: 66:[28, 85, 47], Operations: ['92-45=47'] Exploring Operation: 28+85=113, Resulting Numbers: [47, 113] Generated Node #3: [47, 113] from Operation: 28+85=113 Current State: 66:[47, 113], Operations: ['92-45=47', '28+85=113'] Exploring Operation: 113-47=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[92, 45, 28, 85], Operations: [] Exploring Operation: 92-85=7, Resulting Numbers: [45, 28, 7] Generated Node #0,0: 66:[45, 28, 7] Operation: 92-85=7 Exploring Operation: 85-45=40, Resulting Numbers: [92, 28, 40] Generated Node #0,1: 66:[92, 28, 40] Operation: 85-45=40 Exploring Operation: 85-28=57, Resulting Numbers: [92, 45, 57] Generated Node #0,2: 66:[92, 45, 57] Operation: 85-28=57 Exploring Operation: 92-45=47, Resulting Numbers: [28, 85, 47] Generated Node #0,3: 66:[28, 85, 47] Operation: 92-45=47 Exploring Operation: 92-28=64, Resulting Numbers: [45, 85, 64] Generated Node #0,4: 66:[45, 85, 64] Operation: 92-28=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[45, 28, 7], Operations: ['92-85=7'] Exploring Operation: 45-28=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 66:[7, 17] Operation: 45-28=17 Exploring Operation: 28/7=4, Resulting Numbers: [45, 4] Generated Node #0,0,1: 66:[45, 4] Operation: 28/7=4 Exploring Operation: 45-7=38, Resulting Numbers: [28, 38] Generated Node #0,0,2: 66:[28, 38] Operation: 45-7=38 Exploring Operation: 45+28=73, Resulting Numbers: [7, 73] Generated Node #0,0,3: 66:[7, 73] Operation: 45+28=73 Exploring Operation: 28-7=21, Resulting Numbers: [45, 21] Generated Node #0,0,4: 66:[45, 21] Operation: 28-7=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[7, 17], Operations: ['92-85=7', '45-28=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,66 unequal: No Solution No 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: 66:[7, 73], Operations: ['92-85=7', '45+28=73'] Exploring Operation: 7+73=80, Resulting Numbers: [80] 80,66 unequal: No Solution Exploring Operation: 7*73=511, Resulting Numbers: [511] 511,66 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[92, 45, 28, 85], Operations: [] Exploring Operation: 92-85=7, Resulting Numbers: [45, 28, 7] Generated Node #0,0: 66:[45, 28, 7] Operation: 92-85=7 Moving to Node #0,0 Current State: 66:[45, 28, 7], Operations: ['92-85=7'] Exploring Operation: 45+28=73, Resulting Numbers: [7, 73] Generated Node #0,0,3: 66:[7, 73] Operation: 45+28=73 Moving to Node #0,0,3 Current State: 66:[7, 73], Operations: ['92-85=7', '45+28=73'] Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 52, 18, 35, 54 ]
36
[ "35*54=1890", "1890-18=1872", "1872/52=36" ]
Current State: 36:[52, 18, 35, 54], Operations: [] Exploring Operation: 35*54=1890, Resulting Numbers: [52, 18, 1890] Generated Node #2: [52, 18, 1890] from Operation: 35*54=1890 Current State: 36:[52, 18, 1890], Operations: ['35*54=1890'] Exploring Operation: 1890-18=1872, Resulting Numbers: [52, 1872] Generated Node #3: [52, 1872] from Operation: 1890-18=1872 Current State: 36:[52, 1872], Operations: ['35*54=1890', '1890-18=1872'] Exploring Operation: 1872/52=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[52, 18, 35, 54], Operations: [] Exploring Operation: 54-18=36, Resulting Numbers: [52, 35, 36] Generated Node #0,0: 36:[52, 35, 36] Operation: 54-18=36 Exploring Operation: 54-52=2, Resulting Numbers: [18, 35, 2] Generated Node #0,1: 36:[18, 35, 2] Operation: 54-52=2 Exploring Operation: 54/18=3, Resulting Numbers: [52, 35, 3] Generated Node #0,2: 36:[52, 35, 3] Operation: 54/18=3 Exploring Operation: 54-35=19, Resulting Numbers: [52, 18, 19] Generated Node #0,3: 36:[52, 18, 19] Operation: 54-35=19 Moving to Node #0,1 Current State: 36:[18, 35, 2], Operations: ['54-52=2'] Exploring Operation: 18*2=36, Resulting Numbers: [35, 36] Generated Node #0,1,0: 36:[35, 36] Operation: 18*2=36 Exploring Operation: 18/2=9, Resulting Numbers: [35, 9] Generated Node #0,1,1: 36:[35, 9] Operation: 18/2=9 Exploring Operation: 35-18=17, Resulting Numbers: [2, 17] Generated Node #0,1,2: 36:[2, 17] Operation: 35-18=17 Exploring Operation: 35+2=37, Resulting Numbers: [18, 37] Generated Node #0,1,3: 36:[18, 37] Operation: 35+2=37 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[35, 36], Operations: ['54-52=2', '18*2=36'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,36 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[35, 9], Operations: ['54-52=2', '18/2=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,36 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,36 unequal: No Solution Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 36:[2, 17], Operations: ['54-52=2', '35-18=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,36 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 36:[18, 37], Operations: ['54-52=2', '35+2=37'] Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,36 unequal: No Solution Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,36 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: 36:[52, 35, 3], Operations: ['54/18=3'] Exploring Operation: 52-35=17, Resulting Numbers: [3, 17] Generated Node #0,2,0: 36:[3, 17] Operation: 52-35=17 Exploring Operation: 52+3=55, Resulting Numbers: [35, 55] Generated Node #0,2,1: 36:[35, 55] Operation: 52+3=55 Exploring Operation: 52-3=49, Resulting Numbers: [35, 49] Generated Node #0,2,2: 36:[35, 49] Operation: 52-3=49 Exploring Operation: 35+3=38, Resulting Numbers: [52, 38] Generated Node #0,2,3: 36:[52, 38] Operation: 35+3=38 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 36:[3, 17], Operations: ['54/18=3', '52-35=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[35, 49], Operations: ['54/18=3', '52-3=49'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 35*49=1715, Resulting Numbers: [1715] 1715,36 unequal: No Solution Exploring Operation: 35+49=84, Resulting Numbers: [84] 84,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 36:[52, 38], Operations: ['54/18=3', '35+3=38'] Exploring Operation: 52+38=90, Resulting Numbers: [90] 90,36 unequal: No Solution Exploring Operation: 52*38=1976, Resulting Numbers: [1976] 1976,36 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 36:[35, 55], Operations: ['54/18=3', '52+3=55'] Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,36 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,36 unequal: No Solution Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,36 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: 36:[52, 35, 36], Operations: ['54-18=36'] Exploring Operation: 52-36=16, Resulting Numbers: [35, 16] Generated Node #0,0,0: 36:[35, 16] Operation: 52-36=16 Exploring Operation: 52-35=17, Resulting Numbers: [36, 17] Generated Node #0,0,1: 36:[36, 17] Operation: 52-35=17 Exploring Operation: 36-35=1, Resulting Numbers: [52, 1] Generated Node #0,0,2: 36:[52, 1] Operation: 36-35=1 Exploring Operation: 52+35=87, Resulting Numbers: [36, 87] Generated Node #0,0,3: 36:[36, 87] Operation: 52+35=87 Moving to Node #0,3 Current State: 36:[52, 18, 19], Operations: ['54-35=19'] Exploring Operation: 19-18=1, Resulting Numbers: [52, 1] Generated Node #0,3,0: 36:[52, 1] Operation: 19-18=1 Exploring Operation: 52-19=33, Resulting Numbers: [18, 33] Generated Node #0,3,1: 36:[18, 33] Operation: 52-19=33 Exploring Operation: 18+19=37, Resulting Numbers: [52, 37] Generated Node #0,3,2: 36:[52, 37] Operation: 18+19=37 Exploring Operation: 52-18=34, Resulting Numbers: [19, 34] Generated Node #0,3,3: 36:[19, 34] Operation: 52-18=34 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 36:[18, 33], Operations: ['54-35=19', '52-19=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,36 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 36:[19, 34], Operations: ['54-35=19', '52-18=34'] Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 19*34=646, Resulting Numbers: [646] 646,36 unequal: No Solution Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 36:[52, 1], Operations: ['54-35=19', '19-18=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,36 unequal: No Solution Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,36 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[52, 37], Operations: ['54-35=19', '18+19=37'] Exploring Operation: 52*37=1924, Resulting Numbers: [1924] 1924,36 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,36 unequal: No Solution Exploring Operation: 52+37=89, Resulting Numbers: [89] 89,36 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: 36:[36, 17], Operations: ['54-18=36', '52-35=17'] Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,36 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[35, 16], Operations: ['54-18=36', '52-36=16'] Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,36 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,36 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,36 unequal: No Solution Moving to Node #0,0,2 Current State: 36:[52, 1], Operations: ['54-18=36', '36-35=1'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,36 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,36 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,36 unequal: No Solution Moving to Node #0,0,3 Current State: 36:[36, 87], Operations: ['54-18=36', '52+35=87'] Exploring Operation: 87-36=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 36+87=123, Resulting Numbers: [123] 123,36 unequal: No Solution Exploring Operation: 36*87=3132, Resulting Numbers: [3132] 3132,36 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 78, 73, 91, 34 ]
25
[ "78-73=5", "91+34=125", "125/5=25" ]
Current State: 25:[78, 73, 91, 34], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [91, 34, 5] Generated Node #2: [91, 34, 5] from Operation: 78-73=5 Current State: 25:[91, 34, 5], Operations: ['78-73=5'] Exploring Operation: 91+34=125, Resulting Numbers: [5, 125] Generated Node #3: [5, 125] from Operation: 91+34=125 Current State: 25:[5, 125], Operations: ['78-73=5', '91+34=125'] Exploring Operation: 125/5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[78, 73, 91, 34], Operations: [] Exploring Operation: 91-78=13, Resulting Numbers: [73, 34, 13] Generated Node #0,0: 25:[73, 34, 13] Operation: 91-78=13 Exploring Operation: 91-73=18, Resulting Numbers: [78, 34, 18] Generated Node #0,1: 25:[78, 34, 18] Operation: 91-73=18 Exploring Operation: 78-73=5, Resulting Numbers: [91, 34, 5] Generated Node #0,2: 25:[91, 34, 5] Operation: 78-73=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[73, 34, 13], Operations: ['91-78=13'] Exploring Operation: 73-34=39, Resulting Numbers: [13, 39] Generated Node #0,0,0: 25:[13, 39] Operation: 73-34=39 Exploring Operation: 34-13=21, Resulting Numbers: [73, 21] Generated Node #0,0,1: 25:[73, 21] Operation: 34-13=21 Exploring Operation: 73-13=60, Resulting Numbers: [34, 60] Generated Node #0,0,2: 25:[34, 60] Operation: 73-13=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[13, 39], Operations: ['91-78=13', '73-34=39'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,25 unequal: No Solution Exploring Operation: 13+39=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[34, 60], Operations: ['91-78=13', '73-13=60'] Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,25 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,25 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[73, 21], Operations: ['91-78=13', '34-13=21'] Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,25 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[78, 34, 18], Operations: ['91-73=18'] Exploring Operation: 78-34=44, Resulting Numbers: [18, 44] Generated Node #0,1,0: 25:[18, 44] Operation: 78-34=44 Exploring Operation: 34-18=16, Resulting Numbers: [78, 16] Generated Node #0,1,1: 25:[78, 16] Operation: 34-18=16 Exploring Operation: 78-18=60, Resulting Numbers: [34, 60] Generated Node #0,1,2: 25:[34, 60] Operation: 78-18=60 Moving to Node #0,1,0 Current State: 25:[18, 44], Operations: ['91-73=18', '78-34=44'] Exploring Operation: 18*44=792, Resulting Numbers: [792] 792,25 unequal: No Solution Exploring Operation: 18+44=62, Resulting Numbers: [62] 62,25 unequal: No Solution Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[34, 60], Operations: ['91-73=18', '78-18=60'] Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,25 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,25 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[78, 16], Operations: ['91-73=18', '34-18=16'] Exploring Operation: 78*16=1248, Resulting Numbers: [1248] 1248,25 unequal: No Solution Exploring Operation: 78-16=62, Resulting Numbers: [62] 62,25 unequal: No Solution Exploring Operation: 78+16=94, Resulting Numbers: [94] 94,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[91, 34, 5], Operations: ['78-73=5'] Exploring Operation: 91-5=86, Resulting Numbers: [34, 86] Generated Node #0,2,0: 25:[34, 86] Operation: 91-5=86 Exploring Operation: 91-34=57, Resulting Numbers: [5, 57] Generated Node #0,2,1: 25:[5, 57] Operation: 91-34=57 Exploring Operation: 34-5=29, Resulting Numbers: [91, 29] Generated Node #0,2,2: 25:[91, 29] Operation: 34-5=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[5, 57], Operations: ['78-73=5', '91-34=57'] Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,25 unequal: No Solution Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[34, 86], Operations: ['78-73=5', '91-5=86'] Exploring Operation: 34*86=2924, Resulting Numbers: [2924] 2924,25 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 34+86=120, Resulting Numbers: [120] 120,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[91, 29], Operations: ['78-73=5', '34-5=29'] Exploring Operation: 91*29=2639, Resulting Numbers: [2639] 2639,25 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,25 unequal: No Solution Exploring Operation: 91+29=120, Resulting Numbers: [120] 120,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 25, 3, 50, 2 ]
100
[ "25*3=75", "50/2=25", "75+25=100" ]
Current State: 100:[25, 3, 50, 2], Operations: [] Exploring Operation: 25*3=75, Resulting Numbers: [50, 2, 75] Generated Node #2: [50, 2, 75] from Operation: 25*3=75 Current State: 100:[50, 2, 75], Operations: ['25*3=75'] Exploring Operation: 50/2=25, Resulting Numbers: [75, 25] Generated Node #3: [75, 25] from Operation: 50/2=25 Current State: 100:[75, 25], Operations: ['25*3=75', '50/2=25'] Exploring Operation: 75+25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[25, 3, 50, 2], Operations: [] Exploring Operation: 25*2=50, Resulting Numbers: [3, 50, 50] Generated Node #0,0: 100:[3, 50, 50] Operation: 25*2=50 Exploring Operation: 3*2=6, Resulting Numbers: [25, 50, 6] Generated Node #0,1: 100:[25, 50, 6] Operation: 3*2=6 Exploring Operation: 50-25=25, Resulting Numbers: [3, 2, 25] Generated Node #0,2: 100:[3, 2, 25] Operation: 50-25=25 Exploring Operation: 3+2=5, Resulting Numbers: [25, 50, 5] Generated Node #0,3: 100:[25, 50, 5] Operation: 3+2=5 Exploring Operation: 50/25=2, Resulting Numbers: [3, 2, 2] Generated Node #0,4: 100:[3, 2, 2] Operation: 50/25=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[25, 50, 5], Operations: ['3+2=5'] Exploring Operation: 25/5=5, Resulting Numbers: [50, 5] Generated Node #0,3,0: 100:[50, 5] Operation: 25/5=5 Exploring Operation: 50-25=25, Resulting Numbers: [5, 25] Generated Node #0,3,1: 100:[5, 25] Operation: 50-25=25 Exploring Operation: 50/25=2, Resulting Numbers: [5, 2] Generated Node #0,3,2: 100:[5, 2] Operation: 50/25=2 Exploring Operation: 25-5=20, Resulting Numbers: [50, 20] Generated Node #0,3,3: 100:[50, 20] Operation: 25-5=20 Exploring Operation: 50/5=10, Resulting Numbers: [25, 10] Generated Node #0,3,4: 100:[25, 10] Operation: 50/5=10 Moving to Node #0,3,0 Current State: 100:[50, 5], Operations: ['3+2=5', '25/5=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,100 unequal: No Solution Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,100 unequal: No Solution Moving to Node #0,3,2 Current State: 100:[5, 2], Operations: ['3+2=5', '50/25=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,100 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,100 unequal: No Solution Moving to Node #0,3,4 Current State: 100:[25, 10], Operations: ['3+2=5', '50/5=10'] Exploring Operation: 25*10=250, Resulting Numbers: [250] 250,100 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,100 unequal: No Solution Moving to Node #0,3,1 Current State: 100:[5, 25], Operations: ['3+2=5', '50-25=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,100 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,100 unequal: No Solution Moving to Node #0,3,3 Current State: 100:[50, 20], Operations: ['3+2=5', '25-5=20'] Exploring Operation: 50*20=1000, Resulting Numbers: [1000] 1000,100 unequal: No Solution Exploring Operation: 50+20=70, Resulting Numbers: [70] 70,100 unequal: No Solution Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,100 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:[3, 50, 50], Operations: ['25*2=50'] Exploring Operation: 50+50=100, Resulting Numbers: [3, 100] Generated Node #0,0,0: 100:[3, 100] Operation: 50+50=100 Exploring Operation: 50/50=1, Resulting Numbers: [3, 1] Generated Node #0,0,1: 100:[3, 1] Operation: 50/50=1 Exploring Operation: 50-3=47, Resulting Numbers: [50, 47] Generated Node #0,0,2: 100:[50, 47] Operation: 50-3=47 Exploring Operation: 3+50=53, Resulting Numbers: [50, 53] Generated Node #0,0,3: 100:[50, 53] Operation: 3+50=53 Exploring Operation: 3+50=53, Resulting Numbers: [50, 53] Generated Node #0,0,4: 100:[50, 53] Operation: 3+50=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[3, 100], Operations: ['25*2=50', '50+50=100'] Exploring Operation: 3*100=300, Resulting Numbers: [300] 300,100 unequal: No Solution Exploring Operation: 100-3=97, Resulting Numbers: [97] 97,100 unequal: No Solution Exploring Operation: 3+100=103, Resulting Numbers: [103] 103,100 unequal: No Solution No 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: 100:[3, 1], Operations: ['25*2=50', '50/50=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,100 unequal: No Solution No 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: 100:[50, 47], Operations: ['25*2=50', '50-3=47'] Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,100 unequal: No Solution Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,100 unequal: No Solution Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,100 unequal: No Solution No 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: 100:[50, 53], Operations: ['25*2=50', '3+50=53'] Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,100 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,100 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,100 unequal: No Solution No 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: 100:[50, 53], Operations: ['25*2=50', '3+50=53'] Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,100 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,100 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: 100:[25, 50, 6], Operations: ['3*2=6'] Exploring Operation: 25-6=19, Resulting Numbers: [50, 19] Generated Node #0,1,0: 100:[50, 19] Operation: 25-6=19 Exploring Operation: 50+6=56, Resulting Numbers: [25, 56] Generated Node #0,1,1: 100:[25, 56] Operation: 50+6=56 Exploring Operation: 50-25=25, Resulting Numbers: [6, 25] Generated Node #0,1,2: 100:[6, 25] Operation: 50-25=25 Exploring Operation: 25+6=31, Resulting Numbers: [50, 31] Generated Node #0,1,3: 100:[50, 31] Operation: 25+6=31 Exploring Operation: 50/25=2, Resulting Numbers: [6, 2] Generated Node #0,1,4: 100:[6, 2] Operation: 50/25=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[50, 19], Operations: ['3*2=6', '25-6=19'] Exploring Operation: 50+19=69, Resulting Numbers: [69] 69,100 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 50*19=950, Resulting Numbers: [950] 950,100 unequal: No Solution No 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: 100:[6, 25], Operations: ['3*2=6', '50-25=25'] Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,100 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,100 unequal: No Solution No 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: 100:[6, 2], Operations: ['3*2=6', '50/25=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,100 unequal: No Solution No 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: 100:[25, 56], Operations: ['3*2=6', '50+6=56'] Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,100 unequal: No Solution No 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: 100:[50, 31], Operations: ['3*2=6', '25+6=31'] Exploring Operation: 50-31=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 50+31=81, Resulting Numbers: [81] 81,100 unequal: No Solution Exploring Operation: 50*31=1550, Resulting Numbers: [1550] 1550,100 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: 100:[3, 2, 25], Operations: ['50-25=25'] Exploring Operation: 3*2=6, Resulting Numbers: [25, 6] Generated Node #0,2,0: 100:[25, 6] Operation: 3*2=6 Exploring Operation: 2*25=50, Resulting Numbers: [3, 50] Generated Node #0,2,1: 100:[3, 50] Operation: 2*25=50 Exploring Operation: 25-3=22, Resulting Numbers: [2, 22] Generated Node #0,2,2: 100:[2, 22] Operation: 25-3=22 Exploring Operation: 3+2=5, Resulting Numbers: [25, 5] Generated Node #0,2,3: 100:[25, 5] Operation: 3+2=5 Exploring Operation: 3-2=1, Resulting Numbers: [25, 1] Generated Node #0,2,4: 100:[25, 1] Operation: 3-2=1 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 100:[25, 5], Operations: ['50-25=25', '3+2=5'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,100 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,100 unequal: No Solution No 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: 100:[25, 6], Operations: ['50-25=25', '3*2=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,100 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,100 unequal: No Solution No 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: 100:[3, 50], Operations: ['50-25=25', '2*25=50'] Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,100 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,100 unequal: No Solution Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,100 unequal: No Solution No 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: 100:[25, 1], Operations: ['50-25=25', '3-2=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,100 unequal: No Solution No 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: 100:[2, 22], Operations: ['50-25=25', '25-3=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,100 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,100 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: 100:[3, 2, 2], Operations: ['50/25=2'] Exploring Operation: 3+2=5, Resulting Numbers: [2, 5] Generated Node #0,4,0: 100:[2, 5] Operation: 3+2=5 Exploring Operation: 3+2=5, Resulting Numbers: [2, 5] Generated Node #0,4,1: 100:[2, 5] Operation: 3+2=5 Exploring Operation: 3-2=1, Resulting Numbers: [2, 1] Generated Node #0,4,2: 100:[2, 1] Operation: 3-2=1 Exploring Operation: 3*2=6, Resulting Numbers: [2, 6] Generated Node #0,4,3: 100:[2, 6] Operation: 3*2=6 Exploring Operation: 3*2=6, Resulting Numbers: [2, 6] Generated Node #0,4,4: 100:[2, 6] Operation: 3*2=6 Moving to Node #0,4,0 Current State: 100:[2, 5], Operations: ['50/25=2', '3+2=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,100 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,100 unequal: No Solution Moving to Node #0,4,1 Current State: 100:[2, 5], Operations: ['50/25=2', '3+2=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,100 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,100 unequal: No Solution Moving to Node #0,4,2 Current State: 100:[2, 1], Operations: ['50/25=2', '3-2=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Moving to Node #0,4,3 Current State: 100:[2, 6], Operations: ['50/25=2', '3*2=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Moving to Node #0,4,4 Current State: 100:[2, 6], Operations: ['50/25=2', '3*2=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,100 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
[ 90, 34, 21, 65 ]
100
[ "90-34=56", "65-21=44", "56+44=100" ]
Current State: 100:[90, 34, 21, 65], Operations: [] Exploring Operation: 90-34=56, Resulting Numbers: [21, 65, 56] Generated Node #2: [21, 65, 56] from Operation: 90-34=56 Current State: 100:[21, 65, 56], Operations: ['90-34=56'] Exploring Operation: 65-21=44, Resulting Numbers: [56, 44] Generated Node #3: [56, 44] from Operation: 65-21=44 Current State: 100:[56, 44], Operations: ['90-34=56', '65-21=44'] Exploring Operation: 56+44=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[90, 34, 21, 65], Operations: [] Exploring Operation: 90-65=25, Resulting Numbers: [34, 21, 25] Generated Node #0,0: 100:[34, 21, 25] Operation: 90-65=25 Moving to Node #0,0 Current State: 100:[34, 21, 25], Operations: ['90-65=25'] Exploring Operation: 34-25=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 100:[21, 9] Operation: 34-25=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[21, 9], Operations: ['90-65=25', '34-25=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 2, 86, 1, 96 ]
18
[ "86+1=87", "96-87=9", "2*9=18" ]
Current State: 18:[2, 86, 1, 96], Operations: [] Exploring Operation: 86+1=87, Resulting Numbers: [2, 96, 87] Generated Node #2: [2, 96, 87] from Operation: 86+1=87 Current State: 18:[2, 96, 87], Operations: ['86+1=87'] Exploring Operation: 96-87=9, Resulting Numbers: [2, 9] Generated Node #3: [2, 9] from Operation: 96-87=9 Current State: 18:[2, 9], Operations: ['86+1=87', '96-87=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[2, 86, 1, 96], Operations: [] Exploring Operation: 96/2=48, Resulting Numbers: [86, 1, 48] Generated Node #0,0: 18:[86, 1, 48] Operation: 96/2=48 Exploring Operation: 86-2=84, Resulting Numbers: [1, 96, 84] Generated Node #0,1: 18:[1, 96, 84] Operation: 86-2=84 Exploring Operation: 96-86=10, Resulting Numbers: [2, 1, 10] Generated Node #0,2: 18:[2, 1, 10] Operation: 96-86=10 Exploring Operation: 86/2=43, Resulting Numbers: [1, 96, 43] Generated Node #0,3: 18:[1, 96, 43] Operation: 86/2=43 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[2, 1, 10], Operations: ['96-86=10'] Exploring Operation: 2/1=2, Resulting Numbers: [10, 2] Generated Node #0,2,0: 18:[10, 2] Operation: 2/1=2 Exploring Operation: 10-1=9, Resulting Numbers: [2, 9] Generated Node #0,2,1: 18:[2, 9] Operation: 10-1=9 Exploring Operation: 2*1=2, Resulting Numbers: [10, 2] Generated Node #0,2,2: 18:[10, 2] Operation: 2*1=2 Exploring Operation: 2+1=3, Resulting Numbers: [10, 3] Generated Node #0,2,3: 18:[10, 3] Operation: 2+1=3 Moving to Node #0,2,1 Current State: 18:[2, 9], Operations: ['96-86=10', '10-1=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[2, 86, 1, 96], Operations: [] Exploring Operation: 96-86=10, Resulting Numbers: [2, 1, 10] Generated Node #0,2: 18:[2, 1, 10] Operation: 96-86=10 Moving to Node #0,2 Current State: 18:[2, 1, 10], Operations: ['96-86=10'] Exploring Operation: 10-1=9, Resulting Numbers: [2, 9] Generated Node #0,2,1: 18:[2, 9] Operation: 10-1=9 Moving to Node #0,2,1 Current State: 18:[2, 9], Operations: ['96-86=10', '10-1=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 9, 70, 72, 36 ]
90
[ "9+36=45", "72-70=2", "45*2=90" ]
Current State: 90:[9, 70, 72, 36], Operations: [] Exploring Operation: 9+36=45, Resulting Numbers: [70, 72, 45] Generated Node #2: [70, 72, 45] from Operation: 9+36=45 Current State: 90:[70, 72, 45], Operations: ['9+36=45'] Exploring Operation: 72-70=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 72-70=2 Current State: 90:[45, 2], Operations: ['9+36=45', '72-70=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[9, 70, 72, 36], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [9, 70, 2] Generated Node #0,0: 90:[9, 70, 2] Operation: 72/36=2 Exploring Operation: 72-70=2, Resulting Numbers: [9, 36, 2] Generated Node #0,1: 90:[9, 36, 2] Operation: 72-70=2 Exploring Operation: 70-36=34, Resulting Numbers: [9, 72, 34] Generated Node #0,2: 90:[9, 72, 34] Operation: 70-36=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[9, 36, 2], Operations: ['72-70=2'] Exploring Operation: 9+36=45, Resulting Numbers: [2, 45] Generated Node #0,1,0: 90:[2, 45] Operation: 9+36=45 Exploring Operation: 36/2=18, Resulting Numbers: [9, 18] Generated Node #0,1,1: 90:[9, 18] Operation: 36/2=18 Exploring Operation: 36/9=4, Resulting Numbers: [2, 4] Generated Node #0,1,2: 90:[2, 4] Operation: 36/9=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[2, 45], Operations: ['72-70=2', '9+36=45'] Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[9, 70, 72, 36], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [9, 36, 2] Generated Node #0,1: 90:[9, 36, 2] Operation: 72-70=2 Moving to Node #0,1 Current State: 90:[9, 36, 2], Operations: ['72-70=2'] Exploring Operation: 9+36=45, Resulting Numbers: [2, 45] Generated Node #0,1,0: 90:[2, 45] Operation: 9+36=45 Moving to Node #0,1,0 Current State: 90:[2, 45], Operations: ['72-70=2', '9+36=45'] Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 3, 99, 78, 6 ]
95
[ "3+99=102", "102/6=17", "78+17=95" ]
Current State: 95:[3, 99, 78, 6], Operations: [] Exploring Operation: 3+99=102, Resulting Numbers: [78, 6, 102] Generated Node #2: [78, 6, 102] from Operation: 3+99=102 Current State: 95:[78, 6, 102], Operations: ['3+99=102'] Exploring Operation: 102/6=17, Resulting Numbers: [78, 17] Generated Node #3: [78, 17] from Operation: 102/6=17 Current State: 95:[78, 17], Operations: ['3+99=102', '102/6=17'] Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[3, 99, 78, 6], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [3, 6, 21] Generated Node #0,0: 95:[3, 6, 21] Operation: 99-78=21 Moving to Node #0,0 Current State: 95:[3, 6, 21], Operations: ['99-78=21'] Exploring Operation: 21-3=18, Resulting Numbers: [6, 18] Generated Node #0,0,0: 95:[6, 18] Operation: 21-3=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[6, 18], Operations: ['99-78=21', '21-3=18'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 46, 78, 96, 37 ]
27
[ "78-46=32", "96-37=59", "59-32=27" ]
Current State: 27:[46, 78, 96, 37], Operations: [] Exploring Operation: 78-46=32, Resulting Numbers: [96, 37, 32] Generated Node #2: [96, 37, 32] from Operation: 78-46=32 Current State: 27:[96, 37, 32], Operations: ['78-46=32'] Exploring Operation: 96-37=59, Resulting Numbers: [32, 59] Generated Node #3: [32, 59] from Operation: 96-37=59 Current State: 27:[32, 59], Operations: ['78-46=32', '96-37=59'] Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[46, 78, 96, 37], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [46, 37, 18] Generated Node #0,0: 27:[46, 37, 18] Operation: 96-78=18 Exploring Operation: 78-46=32, Resulting Numbers: [96, 37, 32] Generated Node #0,1: 27:[96, 37, 32] Operation: 78-46=32 Exploring Operation: 96-46=50, Resulting Numbers: [78, 37, 50] Generated Node #0,2: 27:[78, 37, 50] Operation: 96-46=50 Moving to Node #0,0 Current State: 27:[46, 37, 18], Operations: ['96-78=18'] Exploring Operation: 46-37=9, Resulting Numbers: [18, 9] Generated Node #0,0,0: 27:[18, 9] Operation: 46-37=9 Exploring Operation: 46-18=28, Resulting Numbers: [37, 28] Generated Node #0,0,1: 27:[37, 28] Operation: 46-18=28 Exploring Operation: 37-18=19, Resulting Numbers: [46, 19] Generated Node #0,0,2: 27:[46, 19] Operation: 37-18=19 Moving to Node #0,1 Current State: 27:[96, 37, 32], Operations: ['78-46=32'] Exploring Operation: 96-37=59, Resulting Numbers: [32, 59] Generated Node #0,1,0: 27:[32, 59] Operation: 96-37=59 Exploring Operation: 96/32=3, Resulting Numbers: [37, 3] Generated Node #0,1,1: 27:[37, 3] Operation: 96/32=3 Exploring Operation: 96-32=64, Resulting Numbers: [37, 64] Generated Node #0,1,2: 27:[37, 64] Operation: 96-32=64 Moving to Node #0,2 Current State: 27:[78, 37, 50], Operations: ['96-46=50'] Exploring Operation: 78-50=28, Resulting Numbers: [37, 28] Generated Node #0,2,0: 27:[37, 28] Operation: 78-50=28 Exploring Operation: 50-37=13, Resulting Numbers: [78, 13] Generated Node #0,2,1: 27:[78, 13] Operation: 50-37=13 Exploring Operation: 78-37=41, Resulting Numbers: [50, 41] Generated Node #0,2,2: 27:[50, 41] Operation: 78-37=41 Moving to Node #0,0,0 Current State: 27:[18, 9], Operations: ['96-78=18', '46-37=9'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[46, 78, 96, 37], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [46, 37, 18] Generated Node #0,0: 27:[46, 37, 18] Operation: 96-78=18 Moving to Node #0,0 Current State: 27:[46, 37, 18], Operations: ['96-78=18'] Exploring Operation: 46-37=9, Resulting Numbers: [18, 9] Generated Node #0,0,0: 27:[18, 9] Operation: 46-37=9 Moving to Node #0,0,0 Current State: 27:[18, 9], Operations: ['96-78=18', '46-37=9'] Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 91, 56, 94, 69 ]
10
[ "91-56=35", "94-69=25", "35-25=10" ]
Current State: 10:[91, 56, 94, 69], Operations: [] Exploring Operation: 91-56=35, Resulting Numbers: [94, 69, 35] Generated Node #2: [94, 69, 35] from Operation: 91-56=35 Current State: 10:[94, 69, 35], Operations: ['91-56=35'] Exploring Operation: 94-69=25, Resulting Numbers: [35, 25] Generated Node #3: [35, 25] from Operation: 94-69=25 Current State: 10:[35, 25], Operations: ['91-56=35', '94-69=25'] Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[91, 56, 94, 69], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [56, 69, 3] Generated Node #0,0: 10:[56, 69, 3] Operation: 94-91=3 Moving to Node #0,0 Current State: 10:[56, 69, 3], Operations: ['94-91=3'] Exploring Operation: 69-56=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 10:[3, 13] Operation: 69-56=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[3, 13], Operations: ['94-91=3', '69-56=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[91, 56, 94, 69], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [56, 69, 3] Generated Node #0,0: 10:[56, 69, 3] Operation: 94-91=3 Moving to Node #0,0 Current State: 10:[56, 69, 3], Operations: ['94-91=3'] Exploring Operation: 69-56=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 10:[3, 13] Operation: 69-56=13 Moving to Node #0,0,0 Current State: 10:[3, 13], Operations: ['94-91=3', '69-56=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 3, 39, 21, 87 ]
21
[ "39+87=126", "126/3=42", "42-21=21" ]
Current State: 21:[3, 39, 21, 87], Operations: [] Exploring Operation: 39+87=126, Resulting Numbers: [3, 21, 126] Generated Node #2: [3, 21, 126] from Operation: 39+87=126 Current State: 21:[3, 21, 126], Operations: ['39+87=126'] Exploring Operation: 126/3=42, Resulting Numbers: [21, 42] Generated Node #3: [21, 42] from Operation: 126/3=42 Current State: 21:[21, 42], Operations: ['39+87=126', '126/3=42'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[3, 39, 21, 87], Operations: [] Exploring Operation: 87/3=29, Resulting Numbers: [39, 21, 29] Generated Node #0,0: 21:[39, 21, 29] Operation: 87/3=29 Moving to Node #0,0 Current State: 21:[39, 21, 29], Operations: ['87/3=29'] Exploring Operation: 39-29=10, Resulting Numbers: [21, 10] Generated Node #0,0,0: 21:[21, 10] Operation: 39-29=10 Moving to Node #0,0,0 Current State: 21:[21, 10], Operations: ['87/3=29', '39-29=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,21 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 39, 32, 63, 12 ]
44
[ "39-32=7", "63-12=51", "51-7=44" ]
Current State: 44:[39, 32, 63, 12], Operations: [] Exploring Operation: 39-32=7, Resulting Numbers: [63, 12, 7] Generated Node #2: [63, 12, 7] from Operation: 39-32=7 Current State: 44:[63, 12, 7], Operations: ['39-32=7'] Exploring Operation: 63-12=51, Resulting Numbers: [7, 51] Generated Node #3: [7, 51] from Operation: 63-12=51 Current State: 44:[7, 51], Operations: ['39-32=7', '63-12=51'] Exploring Operation: 51-7=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[39, 32, 63, 12], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [32, 12, 24] Generated Node #0,0: 44:[32, 12, 24] Operation: 63-39=24 Exploring Operation: 63-32=31, Resulting Numbers: [39, 12, 31] Generated Node #0,1: 44:[39, 12, 31] Operation: 63-32=31 Moving to Node #0,0 Current State: 44:[32, 12, 24], Operations: ['63-39=24'] Exploring Operation: 32+12=44, Resulting Numbers: [24, 44] Generated Node #0,0,0: 44:[24, 44] Operation: 32+12=44 Exploring Operation: 32-12=20, Resulting Numbers: [24, 20] Generated Node #0,0,1: 44:[24, 20] Operation: 32-12=20 Moving to Node #0,1 Current State: 44:[39, 12, 31], Operations: ['63-32=31'] Exploring Operation: 12+31=43, Resulting Numbers: [39, 43] Generated Node #0,1,0: 44:[39, 43] Operation: 12+31=43 Exploring Operation: 39-31=8, Resulting Numbers: [12, 8] Generated Node #0,1,1: 44:[12, 8] Operation: 39-31=8 Moving to Node #0,0,0 Current State: 44:[24, 44], Operations: ['63-39=24', '32+12=44'] Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[12, 8], Operations: ['63-32=31', '39-31=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[24, 20], Operations: ['63-39=24', '32-12=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[39, 32, 63, 12], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [32, 12, 24] Generated Node #0,0: 44:[32, 12, 24] Operation: 63-39=24 Moving to Node #0,0 Current State: 44:[32, 12, 24], Operations: ['63-39=24'] Exploring Operation: 32-12=20, Resulting Numbers: [24, 20] Generated Node #0,0,1: 44:[24, 20] Operation: 32-12=20 Moving to Node #0,0,1 Current State: 44:[24, 20], Operations: ['63-39=24', '32-12=20'] Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 24, 50, 19, 21 ]
66
[ "50-24=26", "19+21=40", "26+40=66" ]
Current State: 66:[24, 50, 19, 21], Operations: [] Exploring Operation: 50-24=26, Resulting Numbers: [19, 21, 26] Generated Node #2: [19, 21, 26] from Operation: 50-24=26 Current State: 66:[19, 21, 26], Operations: ['50-24=26'] Exploring Operation: 19+21=40, Resulting Numbers: [26, 40] Generated Node #3: [26, 40] from Operation: 19+21=40 Current State: 66:[26, 40], Operations: ['50-24=26', '19+21=40'] Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[24, 50, 19, 21], Operations: [] Exploring Operation: 50-24=26, Resulting Numbers: [19, 21, 26] Generated Node #0,0: 66:[19, 21, 26] Operation: 50-24=26 Exploring Operation: 50-19=31, Resulting Numbers: [24, 21, 31] Generated Node #0,1: 66:[24, 21, 31] Operation: 50-19=31 Exploring Operation: 50+19=69, Resulting Numbers: [24, 21, 69] Generated Node #0,2: 66:[24, 21, 69] Operation: 50+19=69 Moving to Node #0,1 Current State: 66:[24, 21, 31], Operations: ['50-19=31'] Exploring Operation: 31-24=7, Resulting Numbers: [21, 7] Generated Node #0,1,0: 66:[21, 7] Operation: 31-24=7 Exploring Operation: 31-21=10, Resulting Numbers: [24, 10] Generated Node #0,1,1: 66:[24, 10] Operation: 31-21=10 Exploring Operation: 24-21=3, Resulting Numbers: [31, 3] Generated Node #0,1,2: 66:[31, 3] Operation: 24-21=3 Moving to Node #0,2 Current State: 66:[24, 21, 69], Operations: ['50+19=69'] Exploring Operation: 24+21=45, Resulting Numbers: [69, 45] Generated Node #0,2,0: 66:[69, 45] Operation: 24+21=45 Exploring Operation: 69-24=45, Resulting Numbers: [21, 45] Generated Node #0,2,1: 66:[21, 45] Operation: 69-24=45 Exploring Operation: 24-21=3, Resulting Numbers: [69, 3] Generated Node #0,2,2: 66:[69, 3] Operation: 24-21=3 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[69, 3], Operations: ['50+19=69', '24-21=3'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[24, 50, 19, 21], Operations: [] Exploring Operation: 50+19=69, Resulting Numbers: [24, 21, 69] Generated Node #0,2: 66:[24, 21, 69] Operation: 50+19=69 Moving to Node #0,2 Current State: 66:[24, 21, 69], Operations: ['50+19=69'] Exploring Operation: 24-21=3, Resulting Numbers: [69, 3] Generated Node #0,2,2: 66:[69, 3] Operation: 24-21=3 Moving to Node #0,2,2 Current State: 66:[69, 3], Operations: ['50+19=69', '24-21=3'] Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 20, 42, 20, 92 ]
51
[ "20/20=1", "92-42=50", "1+50=51" ]
Current State: 51:[20, 42, 20, 92], Operations: [] Exploring Operation: 20/20=1, Resulting Numbers: [42, 92, 1] Generated Node #2: [42, 92, 1] from Operation: 20/20=1 Current State: 51:[42, 92, 1], Operations: ['20/20=1'] Exploring Operation: 92-42=50, Resulting Numbers: [1, 50] Generated Node #3: [1, 50] from Operation: 92-42=50 Current State: 51:[1, 50], Operations: ['20/20=1', '92-42=50'] Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[20, 42, 20, 92], Operations: [] Exploring Operation: 42-20=22, Resulting Numbers: [20, 92, 22] Generated Node #0,0: 51:[20, 92, 22] Operation: 42-20=22 Exploring Operation: 92-20=72, Resulting Numbers: [20, 42, 72] Generated Node #0,1: 51:[20, 42, 72] Operation: 92-20=72 Exploring Operation: 92-42=50, Resulting Numbers: [20, 20, 50] Generated Node #0,2: 51:[20, 20, 50] Operation: 92-42=50 Exploring Operation: 92-20=72, Resulting Numbers: [42, 20, 72] Generated Node #0,3: 51:[42, 20, 72] Operation: 92-20=72 Moving to Node #0,2 Current State: 51:[20, 20, 50], Operations: ['92-42=50'] Exploring Operation: 50-20=30, Resulting Numbers: [20, 30] Generated Node #0,2,0: 51:[20, 30] Operation: 50-20=30 Exploring Operation: 20-20=0, Resulting Numbers: [50, 0] Generated Node #0,2,1: 51:[50, 0] Operation: 20-20=0 Exploring Operation: 20/20=1, Resulting Numbers: [50, 1] Generated Node #0,2,2: 51:[50, 1] Operation: 20/20=1 Exploring Operation: 20+20=40, Resulting Numbers: [50, 40] Generated Node #0,2,3: 51:[50, 40] Operation: 20+20=40 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 51:[50, 1], Operations: ['92-42=50', '20/20=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[20, 42, 20, 92], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [20, 20, 50] Generated Node #0,2: 51:[20, 20, 50] Operation: 92-42=50 Moving to Node #0,2 Current State: 51:[20, 20, 50], Operations: ['92-42=50'] Exploring Operation: 20/20=1, Resulting Numbers: [50, 1] Generated Node #0,2,2: 51:[50, 1] Operation: 20/20=1 Moving to Node #0,2,2 Current State: 51:[50, 1], Operations: ['92-42=50', '20/20=1'] Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 42, 56, 12, 76 ]
74
[ "56-42=14", "12+76=88", "88-14=74" ]
Current State: 74:[42, 56, 12, 76], Operations: [] Exploring Operation: 56-42=14, Resulting Numbers: [12, 76, 14] Generated Node #2: [12, 76, 14] from Operation: 56-42=14 Current State: 74:[12, 76, 14], Operations: ['56-42=14'] Exploring Operation: 12+76=88, Resulting Numbers: [14, 88] Generated Node #3: [14, 88] from Operation: 12+76=88 Current State: 74:[14, 88], Operations: ['56-42=14', '12+76=88'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[42, 56, 12, 76], Operations: [] Exploring Operation: 56-42=14, Resulting Numbers: [12, 76, 14] Generated Node #0,0: 74:[12, 76, 14] Operation: 56-42=14 Exploring Operation: 56-12=44, Resulting Numbers: [42, 76, 44] Generated Node #0,1: 74:[42, 76, 44] Operation: 56-12=44 Exploring Operation: 56+12=68, Resulting Numbers: [42, 76, 68] Generated Node #0,2: 74:[42, 76, 68] Operation: 56+12=68 Moving to Node #0,2 Current State: 74:[42, 76, 68], Operations: ['56+12=68'] Exploring Operation: 68-42=26, Resulting Numbers: [76, 26] Generated Node #0,2,0: 74:[76, 26] Operation: 68-42=26 Exploring Operation: 76-42=34, Resulting Numbers: [68, 34] Generated Node #0,2,1: 74:[68, 34] Operation: 76-42=34 Exploring Operation: 76-68=8, Resulting Numbers: [42, 8] Generated Node #0,2,2: 74:[42, 8] Operation: 76-68=8 Moving to Node #0,1 Current State: 74:[42, 76, 44], Operations: ['56-12=44'] Exploring Operation: 76-42=34, Resulting Numbers: [44, 34] Generated Node #0,1,0: 74:[44, 34] Operation: 76-42=34 Exploring Operation: 76-44=32, Resulting Numbers: [42, 32] Generated Node #0,1,1: 74:[42, 32] Operation: 76-44=32 Exploring Operation: 44-42=2, Resulting Numbers: [76, 2] Generated Node #0,1,2: 74:[76, 2] Operation: 44-42=2 Moving to Node #0,0 Current State: 74:[12, 76, 14], Operations: ['56-42=14'] Exploring Operation: 14-12=2, Resulting Numbers: [76, 2] Generated Node #0,0,0: 74:[76, 2] Operation: 14-12=2 Exploring Operation: 12+14=26, Resulting Numbers: [76, 26] Generated Node #0,0,1: 74:[76, 26] Operation: 12+14=26 Exploring Operation: 76-12=64, Resulting Numbers: [14, 64] Generated Node #0,0,2: 74:[14, 64] Operation: 76-12=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[76, 2], Operations: ['56-42=14', '14-12=2'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,74 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[42, 56, 12, 76], Operations: [] Exploring Operation: 56-42=14, Resulting Numbers: [12, 76, 14] Generated Node #0,0: 74:[12, 76, 14] Operation: 56-42=14 Moving to Node #0,0 Current State: 74:[12, 76, 14], Operations: ['56-42=14'] Exploring Operation: 14-12=2, Resulting Numbers: [76, 2] Generated Node #0,0,0: 74:[76, 2] Operation: 14-12=2 Moving to Node #0,0,0 Current State: 74:[76, 2], Operations: ['56-42=14', '14-12=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 19, 66, 37, 59 ]
63
[ "19+66=85", "59-37=22", "85-22=63" ]
Current State: 63:[19, 66, 37, 59], Operations: [] Exploring Operation: 19+66=85, Resulting Numbers: [37, 59, 85] Generated Node #2: [37, 59, 85] from Operation: 19+66=85 Current State: 63:[37, 59, 85], Operations: ['19+66=85'] Exploring Operation: 59-37=22, Resulting Numbers: [85, 22] Generated Node #3: [85, 22] from Operation: 59-37=22 Current State: 63:[85, 22], Operations: ['19+66=85', '59-37=22'] Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[19, 66, 37, 59], Operations: [] Exploring Operation: 66-37=29, Resulting Numbers: [19, 59, 29] Generated Node #0,0: 63:[19, 59, 29] Operation: 66-37=29 Exploring Operation: 59-37=22, Resulting Numbers: [19, 66, 22] Generated Node #0,1: 63:[19, 66, 22] Operation: 59-37=22 Exploring Operation: 37-19=18, Resulting Numbers: [66, 59, 18] Generated Node #0,2: 63:[66, 59, 18] Operation: 37-19=18 Exploring Operation: 19+37=56, Resulting Numbers: [66, 59, 56] Generated Node #0,3: 63:[66, 59, 56] Operation: 19+37=56 Exploring Operation: 66-59=7, Resulting Numbers: [19, 37, 7] Generated Node #0,4: 63:[19, 37, 7] Operation: 66-59=7 Moving to Node #0,1 Current State: 63:[19, 66, 22], Operations: ['59-37=22'] Exploring Operation: 19+66=85, Resulting Numbers: [22, 85] Generated Node #0,1,0: 63:[22, 85] Operation: 19+66=85 Exploring Operation: 22-19=3, Resulting Numbers: [66, 3] Generated Node #0,1,1: 63:[66, 3] Operation: 22-19=3 Exploring Operation: 66-19=47, Resulting Numbers: [22, 47] Generated Node #0,1,2: 63:[22, 47] Operation: 66-19=47 Exploring Operation: 66/22=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 63:[19, 3] Operation: 66/22=3 Exploring Operation: 66-22=44, Resulting Numbers: [19, 44] Generated Node #0,1,4: 63:[19, 44] Operation: 66-22=44 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 63:[19, 3], Operations: ['59-37=22', '66/22=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,63 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,63 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,63 unequal: No Solution No 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: 63:[66, 3], Operations: ['59-37=22', '22-19=3'] Exploring Operation: 66+3=69, Resulting Numbers: [69] 69,63 unequal: No Solution Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[19, 66, 37, 59], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [19, 66, 22] Generated Node #0,1: 63:[19, 66, 22] Operation: 59-37=22 Moving to Node #0,1 Current State: 63:[19, 66, 22], Operations: ['59-37=22'] Exploring Operation: 22-19=3, Resulting Numbers: [66, 3] Generated Node #0,1,1: 63:[66, 3] Operation: 22-19=3 Moving to Node #0,1,1 Current State: 63:[66, 3], Operations: ['59-37=22', '22-19=3'] Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 26, 10, 57, 6 ]
67
[ "26-10=16", "57-6=51", "16+51=67" ]
Current State: 67:[26, 10, 57, 6], Operations: [] Exploring Operation: 26-10=16, Resulting Numbers: [57, 6, 16] Generated Node #2: [57, 6, 16] from Operation: 26-10=16 Current State: 67:[57, 6, 16], Operations: ['26-10=16'] Exploring Operation: 57-6=51, Resulting Numbers: [16, 51] Generated Node #3: [16, 51] from Operation: 57-6=51 Current State: 67:[16, 51], Operations: ['26-10=16', '57-6=51'] Exploring Operation: 16+51=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[26, 10, 57, 6], Operations: [] Exploring Operation: 10*6=60, Resulting Numbers: [26, 57, 60] Generated Node #0,0: 67:[26, 57, 60] Operation: 10*6=60 Exploring Operation: 26+6=32, Resulting Numbers: [10, 57, 32] Generated Node #0,1: 67:[10, 57, 32] Operation: 26+6=32 Exploring Operation: 10+6=16, Resulting Numbers: [26, 57, 16] Generated Node #0,2: 67:[26, 57, 16] Operation: 10+6=16 Exploring Operation: 26+10=36, Resulting Numbers: [57, 6, 36] Generated Node #0,3: 67:[57, 6, 36] Operation: 26+10=36 Exploring Operation: 10+57=67, Resulting Numbers: [26, 6, 67] Generated Node #0,4: 67:[26, 6, 67] Operation: 10+57=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[26, 57, 60], Operations: ['10*6=60'] Exploring Operation: 57+60=117, Resulting Numbers: [26, 117] Generated Node #0,0,0: 67:[26, 117] Operation: 57+60=117 Exploring Operation: 57-26=31, Resulting Numbers: [60, 31] Generated Node #0,0,1: 67:[60, 31] Operation: 57-26=31 Exploring Operation: 26+60=86, Resulting Numbers: [57, 86] Generated Node #0,0,2: 67:[57, 86] Operation: 26+60=86 Exploring Operation: 60-26=34, Resulting Numbers: [57, 34] Generated Node #0,0,3: 67:[57, 34] Operation: 60-26=34 Exploring Operation: 26+57=83, Resulting Numbers: [60, 83] Generated Node #0,0,4: 67:[60, 83] Operation: 26+57=83 Moving to Node #0,0,4 Current State: 67:[60, 83], Operations: ['10*6=60', '26+57=83'] Exploring Operation: 60+83=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 60*83=4980, Resulting Numbers: [4980] 4980,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[57, 86], Operations: ['10*6=60', '26+60=86'] Exploring Operation: 57*86=4902, Resulting Numbers: [4902] 4902,67 unequal: No Solution Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 57+86=143, Resulting Numbers: [143] 143,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[60, 31], Operations: ['10*6=60', '57-26=31'] Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 60+31=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 60*31=1860, Resulting Numbers: [1860] 1860,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[57, 34], Operations: ['10*6=60', '60-26=34'] Exploring Operation: 57+34=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 57*34=1938, Resulting Numbers: [1938] 1938,67 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[26, 117], Operations: ['10*6=60', '57+60=117'] Exploring Operation: 26+117=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 117-26=91, Resulting Numbers: [91] 91,67 unequal: No Solution Exploring Operation: 26*117=3042, Resulting Numbers: [3042] 3042,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[10, 57, 32], Operations: ['26+6=32'] Exploring Operation: 57-10=47, Resulting Numbers: [32, 47] Generated Node #0,1,0: 67:[32, 47] Operation: 57-10=47 Exploring Operation: 57+32=89, Resulting Numbers: [10, 89] Generated Node #0,1,1: 67:[10, 89] Operation: 57+32=89 Exploring Operation: 10+32=42, Resulting Numbers: [57, 42] Generated Node #0,1,2: 67:[57, 42] Operation: 10+32=42 Exploring Operation: 10+57=67, Resulting Numbers: [32, 67] Generated Node #0,1,3: 67:[32, 67] Operation: 10+57=67 Exploring Operation: 32-10=22, Resulting Numbers: [57, 22] Generated Node #0,1,4: 67:[57, 22] Operation: 32-10=22 Moving to Node #0,1,2 Current State: 67:[57, 42], Operations: ['26+6=32', '10+32=42'] Exploring Operation: 57*42=2394, Resulting Numbers: [2394] 2394,67 unequal: No Solution Exploring Operation: 57+42=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[32, 67], Operations: ['26+6=32', '10+57=67'] Exploring Operation: 32+67=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 32*67=2144, Resulting Numbers: [2144] 2144,67 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[32, 47], Operations: ['26+6=32', '57-10=47'] Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,67 unequal: No Solution Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,67 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[57, 22], Operations: ['26+6=32', '32-10=22'] Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 57+22=79, Resulting Numbers: [79] 79,67 unequal: No Solution Exploring Operation: 57*22=1254, Resulting Numbers: [1254] 1254,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[10, 89], Operations: ['26+6=32', '57+32=89'] Exploring Operation: 10*89=890, Resulting Numbers: [890] 890,67 unequal: No Solution Exploring Operation: 10+89=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 67:[26, 57, 16], Operations: ['10+6=16'] Exploring Operation: 26+57=83, Resulting Numbers: [16, 83] Generated Node #0,2,0: 67:[16, 83] Operation: 26+57=83 Exploring Operation: 26+16=42, Resulting Numbers: [57, 42] Generated Node #0,2,1: 67:[57, 42] Operation: 26+16=42 Exploring Operation: 57+16=73, Resulting Numbers: [26, 73] Generated Node #0,2,2: 67:[26, 73] Operation: 57+16=73 Exploring Operation: 26-16=10, Resulting Numbers: [57, 10] Generated Node #0,2,3: 67:[57, 10] Operation: 26-16=10 Exploring Operation: 57-16=41, Resulting Numbers: [26, 41] Generated Node #0,2,4: 67:[26, 41] Operation: 57-16=41 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 67:[57, 42], Operations: ['10+6=16', '26+16=42'] Exploring Operation: 57*42=2394, Resulting Numbers: [2394] 2394,67 unequal: No Solution Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,67 unequal: No Solution Exploring Operation: 57+42=99, Resulting Numbers: [99] 99,67 unequal: No Solution No 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: 67:[26, 73], Operations: ['10+6=16', '57+16=73'] Exploring Operation: 26*73=1898, Resulting Numbers: [1898] 1898,67 unequal: No Solution Exploring Operation: 26+73=99, Resulting Numbers: [99] 99,67 unequal: No Solution Exploring Operation: 73-26=47, Resulting Numbers: [47] 47,67 unequal: No Solution No 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: 67:[16, 83], Operations: ['10+6=16', '26+57=83'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[26, 10, 57, 6], Operations: [] Exploring Operation: 10+6=16, Resulting Numbers: [26, 57, 16] Generated Node #0,2: 67:[26, 57, 16] Operation: 10+6=16 Moving to Node #0,2 Current State: 67:[26, 57, 16], Operations: ['10+6=16'] Exploring Operation: 26+57=83, Resulting Numbers: [16, 83] Generated Node #0,2,0: 67:[16, 83] Operation: 26+57=83 Moving to Node #0,2,0 Current State: 67:[16, 83], Operations: ['10+6=16', '26+57=83'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947049
hs_5
sum_heuristic
[ 17, 67, 7, 31 ]
21
[ "17*7=119", "67+31=98", "119-98=21" ]
Current State: 21:[17, 67, 7, 31], Operations: [] Exploring Operation: 17*7=119, Resulting Numbers: [67, 31, 119] Generated Node #2: [67, 31, 119] from Operation: 17*7=119 Current State: 21:[67, 31, 119], Operations: ['17*7=119'] Exploring Operation: 67+31=98, Resulting Numbers: [119, 98] Generated Node #3: [119, 98] from Operation: 67+31=98 Current State: 21:[119, 98], Operations: ['17*7=119', '67+31=98'] Exploring Operation: 119-98=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[17, 67, 7, 31], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [17, 7, 36] Generated Node #0,0: 21:[17, 7, 36] Operation: 67-31=36 Moving to Node #0,0 Current State: 21:[17, 7, 36], Operations: ['67-31=36'] Exploring Operation: 36-17=19, Resulting Numbers: [7, 19] Generated Node #0,0,0: 21:[7, 19] Operation: 36-17=19 Moving to Node #0,0,0 Current State: 21:[7, 19], Operations: ['67-31=36', '36-17=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,21 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 92, 74, 36, 34 ]
17
[ "92-74=18", "36/18=2", "34/2=17" ]
Current State: 17:[92, 74, 36, 34], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [36, 34, 18] Generated Node #2: [36, 34, 18] from Operation: 92-74=18 Current State: 17:[36, 34, 18], Operations: ['92-74=18'] Exploring Operation: 36/18=2, Resulting Numbers: [34, 2] Generated Node #3: [34, 2] from Operation: 36/18=2 Current State: 17:[34, 2], Operations: ['92-74=18', '36/18=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[92, 74, 36, 34], Operations: [] Exploring Operation: 92-34=58, Resulting Numbers: [74, 36, 58] Generated Node #0,0: 17:[74, 36, 58] Operation: 92-34=58 Exploring Operation: 92-36=56, Resulting Numbers: [74, 34, 56] Generated Node #0,1: 17:[74, 34, 56] Operation: 92-36=56 Exploring Operation: 92-74=18, Resulting Numbers: [36, 34, 18] Generated Node #0,2: 17:[36, 34, 18] Operation: 92-74=18 Exploring Operation: 74-36=38, Resulting Numbers: [92, 34, 38] Generated Node #0,3: 17:[92, 34, 38] Operation: 74-36=38 Exploring Operation: 74-34=40, Resulting Numbers: [92, 36, 40] Generated Node #0,4: 17:[92, 36, 40] Operation: 74-34=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[36, 34, 18], Operations: ['92-74=18'] Exploring Operation: 36/18=2, Resulting Numbers: [34, 2] Generated Node #0,2,0: 17:[34, 2] Operation: 36/18=2 Exploring Operation: 36-18=18, Resulting Numbers: [34, 18] Generated Node #0,2,1: 17:[34, 18] Operation: 36-18=18 Exploring Operation: 36-34=2, Resulting Numbers: [18, 2] Generated Node #0,2,2: 17:[18, 2] Operation: 36-34=2 Exploring Operation: 34-18=16, Resulting Numbers: [36, 16] Generated Node #0,2,3: 17:[36, 16] Operation: 34-18=16 Exploring Operation: 36+34=70, Resulting Numbers: [18, 70] Generated Node #0,2,4: 17:[18, 70] Operation: 36+34=70 Moving to Node #0,2,2 Current State: 17:[18, 2], Operations: ['92-74=18', '36-34=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[34, 18], Operations: ['92-74=18', '36-18=18'] Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 34*18=612, Resulting Numbers: [612] 612,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[36, 16], Operations: ['92-74=18', '34-18=16'] Exploring Operation: 36+16=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 36*16=576, Resulting Numbers: [576] 576,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[34, 2], Operations: ['92-74=18', '36/18=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 34*2=68, Resulting Numbers: [68] 68,17 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[92, 74, 36, 34], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [36, 34, 18] Generated Node #0,2: 17:[36, 34, 18] Operation: 92-74=18 Moving to Node #0,2 Current State: 17:[36, 34, 18], Operations: ['92-74=18'] Exploring Operation: 36/18=2, Resulting Numbers: [34, 2] Generated Node #0,2,0: 17:[34, 2] Operation: 36/18=2 Moving to Node #0,2,0 Current State: 17:[34, 2], Operations: ['92-74=18', '36/18=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
mult_heuristic
[ 93, 95, 82, 16 ]
90
[ "93+95=188", "82+16=98", "188-98=90" ]
Current State: 90:[93, 95, 82, 16], Operations: [] Exploring Operation: 93+95=188, Resulting Numbers: [82, 16, 188] Generated Node #2: [82, 16, 188] from Operation: 93+95=188 Current State: 90:[82, 16, 188], Operations: ['93+95=188'] Exploring Operation: 82+16=98, Resulting Numbers: [188, 98] Generated Node #3: [188, 98] from Operation: 82+16=98 Current State: 90:[188, 98], Operations: ['93+95=188', '82+16=98'] Exploring Operation: 188-98=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[93, 95, 82, 16], Operations: [] Exploring Operation: 95-82=13, Resulting Numbers: [93, 16, 13] Generated Node #0,0: 90:[93, 16, 13] Operation: 95-82=13 Exploring Operation: 95-93=2, Resulting Numbers: [82, 16, 2] Generated Node #0,1: 90:[82, 16, 2] Operation: 95-93=2 Exploring Operation: 93-82=11, Resulting Numbers: [95, 16, 11] Generated Node #0,2: 90:[95, 16, 11] Operation: 93-82=11 Moving to Node #0,0 Current State: 90:[93, 16, 13], Operations: ['95-82=13'] Exploring Operation: 16+13=29, Resulting Numbers: [93, 29] Generated Node #0,0,0: 90:[93, 29] Operation: 16+13=29 Exploring Operation: 93-13=80, Resulting Numbers: [16, 80] Generated Node #0,0,1: 90:[16, 80] Operation: 93-13=80 Exploring Operation: 16-13=3, Resulting Numbers: [93, 3] Generated Node #0,0,2: 90:[93, 3] Operation: 16-13=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[93, 3], Operations: ['95-82=13', '16-13=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[93, 95, 82, 16], Operations: [] Exploring Operation: 95-82=13, Resulting Numbers: [93, 16, 13] Generated Node #0,0: 90:[93, 16, 13] Operation: 95-82=13 Moving to Node #0,0 Current State: 90:[93, 16, 13], Operations: ['95-82=13'] Exploring Operation: 16-13=3, Resulting Numbers: [93, 3] Generated Node #0,0,2: 90:[93, 3] Operation: 16-13=3 Moving to Node #0,0,2 Current State: 90:[93, 3], Operations: ['95-82=13', '16-13=3'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 65, 65, 51, 14 ]
38
[ "65/65=1", "51-14=37", "1+37=38" ]
Current State: 38:[65, 65, 51, 14], Operations: [] Exploring Operation: 65/65=1, Resulting Numbers: [51, 14, 1] Generated Node #2: [51, 14, 1] from Operation: 65/65=1 Current State: 38:[51, 14, 1], Operations: ['65/65=1'] Exploring Operation: 51-14=37, Resulting Numbers: [1, 37] Generated Node #3: [1, 37] from Operation: 51-14=37 Current State: 38:[1, 37], Operations: ['65/65=1', '51-14=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[65, 65, 51, 14], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [65, 14, 14] Generated Node #0,0: 38:[65, 14, 14] Operation: 65-51=14 Exploring Operation: 65/65=1, Resulting Numbers: [51, 14, 1] Generated Node #0,1: 38:[51, 14, 1] Operation: 65/65=1 Exploring Operation: 65-65=0, Resulting Numbers: [51, 14, 0] Generated Node #0,2: 38:[51, 14, 0] Operation: 65-65=0 Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[51, 14, 1], Operations: ['65/65=1'] Exploring Operation: 51-14=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 38:[1, 37] Operation: 51-14=37 Exploring Operation: 14+1=15, Resulting Numbers: [51, 15] Generated Node #0,1,1: 38:[51, 15] Operation: 14+1=15 Exploring Operation: 51-1=50, Resulting Numbers: [14, 50] Generated Node #0,1,2: 38:[14, 50] Operation: 51-1=50 Moving to Node #0,1,0 Current State: 38:[1, 37], Operations: ['65/65=1', '51-14=37'] Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,38 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,38 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[65, 65, 51, 14], Operations: [] Exploring Operation: 65/65=1, Resulting Numbers: [51, 14, 1] Generated Node #0,1: 38:[51, 14, 1] Operation: 65/65=1 Moving to Node #0,1 Current State: 38:[51, 14, 1], Operations: ['65/65=1'] Exploring Operation: 51-14=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 38:[1, 37] Operation: 51-14=37 Moving to Node #0,1,0 Current State: 38:[1, 37], Operations: ['65/65=1', '51-14=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 40, 10, 31, 58 ]
58
[ "40-10=30", "31-30=1", "58*1=58" ]
Current State: 58:[40, 10, 31, 58], Operations: [] Exploring Operation: 40-10=30, Resulting Numbers: [31, 58, 30] Generated Node #2: [31, 58, 30] from Operation: 40-10=30 Current State: 58:[31, 58, 30], Operations: ['40-10=30'] Exploring Operation: 31-30=1, Resulting Numbers: [58, 1] Generated Node #3: [58, 1] from Operation: 31-30=1 Current State: 58:[58, 1], Operations: ['40-10=30', '31-30=1'] Exploring Operation: 58*1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[40, 10, 31, 58], Operations: [] Exploring Operation: 40-10=30, Resulting Numbers: [31, 58, 30] Generated Node #0,0: 58:[31, 58, 30] Operation: 40-10=30 Exploring Operation: 40+10=50, Resulting Numbers: [31, 58, 50] Generated Node #0,1: 58:[31, 58, 50] Operation: 40+10=50 Exploring Operation: 40/10=4, Resulting Numbers: [31, 58, 4] Generated Node #0,2: 58:[31, 58, 4] Operation: 40/10=4 Exploring Operation: 40-31=9, Resulting Numbers: [10, 58, 9] Generated Node #0,3: 58:[10, 58, 9] Operation: 40-31=9 Exploring Operation: 31-10=21, Resulting Numbers: [40, 58, 21] Generated Node #0,4: 58:[40, 58, 21] Operation: 31-10=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[31, 58, 30], Operations: ['40-10=30'] Exploring Operation: 31+30=61, Resulting Numbers: [58, 61] Generated Node #0,0,0: 58:[58, 61] Operation: 31+30=61 Exploring Operation: 58-30=28, Resulting Numbers: [31, 28] Generated Node #0,0,1: 58:[31, 28] Operation: 58-30=28 Exploring Operation: 31+58=89, Resulting Numbers: [30, 89] Generated Node #0,0,2: 58:[30, 89] Operation: 31+58=89 Exploring Operation: 58-31=27, Resulting Numbers: [30, 27] Generated Node #0,0,3: 58:[30, 27] Operation: 58-31=27 Exploring Operation: 31-30=1, Resulting Numbers: [58, 1] Generated Node #0,0,4: 58:[58, 1] Operation: 31-30=1 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 58:[58, 1], Operations: ['40-10=30', '31-30=1'] Exploring Operation: 58+1=59, Resulting Numbers: [59] 59,58 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[40, 10, 31, 58], Operations: [] Exploring Operation: 40-10=30, Resulting Numbers: [31, 58, 30] Generated Node #0,0: 58:[31, 58, 30] Operation: 40-10=30 Moving to Node #0,0 Current State: 58:[31, 58, 30], Operations: ['40-10=30'] Exploring Operation: 31-30=1, Resulting Numbers: [58, 1] Generated Node #0,0,4: 58:[58, 1] Operation: 31-30=1 Moving to Node #0,0,4 Current State: 58:[58, 1], Operations: ['40-10=30', '31-30=1'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 32, 1, 72, 15 ]
26
[ "32-1=31", "72-15=57", "57-31=26" ]
Current State: 26:[32, 1, 72, 15], Operations: [] Exploring Operation: 32-1=31, Resulting Numbers: [72, 15, 31] Generated Node #2: [72, 15, 31] from Operation: 32-1=31 Current State: 26:[72, 15, 31], Operations: ['32-1=31'] Exploring Operation: 72-15=57, Resulting Numbers: [31, 57] Generated Node #3: [31, 57] from Operation: 72-15=57 Current State: 26:[31, 57], Operations: ['32-1=31', '72-15=57'] Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[32, 1, 72, 15], Operations: [] Exploring Operation: 32-15=17, Resulting Numbers: [1, 72, 17] Generated Node #0,0: 26:[1, 72, 17] Operation: 32-15=17 Exploring Operation: 72-32=40, Resulting Numbers: [1, 15, 40] Generated Node #0,1: 26:[1, 15, 40] Operation: 72-32=40 Exploring Operation: 32-1=31, Resulting Numbers: [72, 15, 31] Generated Node #0,2: 26:[72, 15, 31] Operation: 32-1=31 Exploring Operation: 72-1=71, Resulting Numbers: [32, 15, 71] Generated Node #0,3: 26:[32, 15, 71] Operation: 72-1=71 Exploring Operation: 72-15=57, Resulting Numbers: [32, 1, 57] Generated Node #0,4: 26:[32, 1, 57] Operation: 72-15=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[1, 15, 40], Operations: ['72-32=40'] Exploring Operation: 40-15=25, Resulting Numbers: [1, 25] Generated Node #0,1,0: 26:[1, 25] Operation: 40-15=25 Exploring Operation: 40-1=39, Resulting Numbers: [15, 39] Generated Node #0,1,1: 26:[15, 39] Operation: 40-1=39 Exploring Operation: 1*15=15, Resulting Numbers: [40, 15] Generated Node #0,1,2: 26:[40, 15] Operation: 1*15=15 Exploring Operation: 15-1=14, Resulting Numbers: [40, 14] Generated Node #0,1,3: 26:[40, 14] Operation: 15-1=14 Exploring Operation: 15/1=15, Resulting Numbers: [40, 15] Generated Node #0,1,4: 26:[40, 15] Operation: 15/1=15 Moving to Node #0,1,0 Current State: 26:[1, 25], Operations: ['72-32=40', '40-15=25'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[32, 1, 72, 15], Operations: [] Exploring Operation: 72-32=40, Resulting Numbers: [1, 15, 40] Generated Node #0,1: 26:[1, 15, 40] Operation: 72-32=40 Moving to Node #0,1 Current State: 26:[1, 15, 40], Operations: ['72-32=40'] Exploring Operation: 40-15=25, Resulting Numbers: [1, 25] Generated Node #0,1,0: 26:[1, 25] Operation: 40-15=25 Moving to Node #0,1,0 Current State: 26:[1, 25], Operations: ['72-32=40', '40-15=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 9, 81, 92, 64 ]
35
[ "92-81=11", "9*11=99", "99-64=35" ]
Current State: 35:[9, 81, 92, 64], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [9, 64, 11] Generated Node #2: [9, 64, 11] from Operation: 92-81=11 Current State: 35:[9, 64, 11], Operations: ['92-81=11'] Exploring Operation: 9*11=99, Resulting Numbers: [64, 99] Generated Node #3: [64, 99] from Operation: 9*11=99 Current State: 35:[64, 99], Operations: ['92-81=11', '9*11=99'] Exploring Operation: 99-64=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[9, 81, 92, 64], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [9, 64, 11] Generated Node #0,0: 35:[9, 64, 11] Operation: 92-81=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[9, 64, 11], Operations: ['92-81=11'] Exploring Operation: 64-11=53, Resulting Numbers: [9, 53] Generated Node #0,0,0: 35:[9, 53] Operation: 64-11=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[9, 53], Operations: ['92-81=11', '64-11=53'] Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 7, 6, 28, 80 ]
81
[ "7+80=87", "6*28=168", "168-87=81" ]
Current State: 81:[7, 6, 28, 80], Operations: [] Exploring Operation: 7+80=87, Resulting Numbers: [6, 28, 87] Generated Node #2: [6, 28, 87] from Operation: 7+80=87 Current State: 81:[6, 28, 87], Operations: ['7+80=87'] Exploring Operation: 6*28=168, Resulting Numbers: [87, 168] Generated Node #3: [87, 168] from Operation: 6*28=168 Current State: 81:[87, 168], Operations: ['7+80=87', '6*28=168'] Exploring Operation: 168-87=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[7, 6, 28, 80], Operations: [] Exploring Operation: 7+6=13, Resulting Numbers: [28, 80, 13] Generated Node #0,0: 81:[28, 80, 13] Operation: 7+6=13 Exploring Operation: 6+80=86, Resulting Numbers: [7, 28, 86] Generated Node #0,1: 81:[7, 28, 86] Operation: 6+80=86 Exploring Operation: 28/7=4, Resulting Numbers: [6, 80, 4] Generated Node #0,2: 81:[6, 80, 4] Operation: 28/7=4 Exploring Operation: 7-6=1, Resulting Numbers: [28, 80, 1] Generated Node #0,3: 81:[28, 80, 1] Operation: 7-6=1 Exploring Operation: 28-6=22, Resulting Numbers: [7, 80, 22] Generated Node #0,4: 81:[7, 80, 22] Operation: 28-6=22 Moving to Node #0,3 Current State: 81:[28, 80, 1], Operations: ['7-6=1'] Exploring Operation: 28-1=27, Resulting Numbers: [80, 27] Generated Node #0,3,0: 81:[80, 27] Operation: 28-1=27 Exploring Operation: 80*1=80, Resulting Numbers: [28, 80] Generated Node #0,3,1: 81:[28, 80] Operation: 80*1=80 Exploring Operation: 28/1=28, Resulting Numbers: [80, 28] Generated Node #0,3,2: 81:[80, 28] Operation: 28/1=28 Exploring Operation: 28*1=28, Resulting Numbers: [80, 28] Generated Node #0,3,3: 81:[80, 28] Operation: 28*1=28 Exploring Operation: 80+1=81, Resulting Numbers: [28, 81] Generated Node #0,3,4: 81:[28, 81] Operation: 80+1=81 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 81:[80, 27], Operations: ['7-6=1', '28-1=27'] Exploring Operation: 80*27=2160, Resulting Numbers: [2160] 2160,81 unequal: No Solution Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 81:[28, 81], Operations: ['7-6=1', '80+1=81'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 28+81=109, Resulting Numbers: [109] 109,81 unequal: No Solution Exploring Operation: 28*81=2268, Resulting Numbers: [2268] 2268,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[28, 80], Operations: ['7-6=1', '80*1=80'] Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,81 unequal: No Solution Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,81 unequal: No Solution Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 81:[80, 28], Operations: ['7-6=1', '28/1=28'] Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,81 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,81 unequal: No Solution Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 81:[80, 28], Operations: ['7-6=1', '28*1=28'] Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,81 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,81 unequal: No Solution Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 81:[6, 80, 4], Operations: ['28/7=4'] Exploring Operation: 6*4=24, Resulting Numbers: [80, 24] Generated Node #0,2,0: 81:[80, 24] Operation: 6*4=24 Exploring Operation: 6+4=10, Resulting Numbers: [80, 10] Generated Node #0,2,1: 81:[80, 10] Operation: 6+4=10 Exploring Operation: 6-4=2, Resulting Numbers: [80, 2] Generated Node #0,2,2: 81:[80, 2] Operation: 6-4=2 Exploring Operation: 80+4=84, Resulting Numbers: [6, 84] Generated Node #0,2,3: 81:[6, 84] Operation: 80+4=84 Exploring Operation: 6+80=86, Resulting Numbers: [4, 86] Generated Node #0,2,4: 81:[4, 86] Operation: 6+80=86 Moving to Node #0,0 Current State: 81:[28, 80, 13], Operations: ['7+6=13'] Exploring Operation: 80+13=93, Resulting Numbers: [28, 93] Generated Node #0,0,0: 81:[28, 93] Operation: 80+13=93 Exploring Operation: 28+13=41, Resulting Numbers: [80, 41] Generated Node #0,0,1: 81:[80, 41] Operation: 28+13=41 Exploring Operation: 28-13=15, Resulting Numbers: [80, 15] Generated Node #0,0,2: 81:[80, 15] Operation: 28-13=15 Exploring Operation: 80-28=52, Resulting Numbers: [13, 52] Generated Node #0,0,3: 81:[13, 52] Operation: 80-28=52 Exploring Operation: 80-13=67, Resulting Numbers: [28, 67] Generated Node #0,0,4: 81:[28, 67] Operation: 80-13=67 Moving to Node #0,1 Current State: 81:[7, 28, 86], Operations: ['6+80=86'] Exploring Operation: 86-7=79, Resulting Numbers: [28, 79] Generated Node #0,1,0: 81:[28, 79] Operation: 86-7=79 Exploring Operation: 28/7=4, Resulting Numbers: [86, 4] Generated Node #0,1,1: 81:[86, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [86, 21] Generated Node #0,1,2: 81:[86, 21] Operation: 28-7=21 Exploring Operation: 7+86=93, Resulting Numbers: [28, 93] Generated Node #0,1,3: 81:[28, 93] Operation: 7+86=93 Exploring Operation: 7+28=35, Resulting Numbers: [86, 35] Generated Node #0,1,4: 81:[86, 35] Operation: 7+28=35 Moving to Node #0,4 Current State: 81:[7, 80, 22], Operations: ['28-6=22'] Exploring Operation: 7+80=87, Resulting Numbers: [22, 87] Generated Node #0,4,0: 81:[22, 87] Operation: 7+80=87 Exploring Operation: 80-7=73, Resulting Numbers: [22, 73] Generated Node #0,4,1: 81:[22, 73] Operation: 80-7=73 Exploring Operation: 22-7=15, Resulting Numbers: [80, 15] Generated Node #0,4,2: 81:[80, 15] Operation: 22-7=15 Exploring Operation: 80+22=102, Resulting Numbers: [7, 102] Generated Node #0,4,3: 81:[7, 102] Operation: 80+22=102 Exploring Operation: 7+22=29, Resulting Numbers: [80, 29] Generated Node #0,4,4: 81:[80, 29] Operation: 7+22=29 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 81:[80, 29], Operations: ['28-6=22', '7+22=29'] Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,81 unequal: No Solution Exploring Operation: 80*29=2320, Resulting Numbers: [2320] 2320,81 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 81:[80, 15], Operations: ['28-6=22', '22-7=15'] Exploring Operation: 80*15=1200, Resulting Numbers: [1200] 1200,81 unequal: No Solution Exploring Operation: 80+15=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 81:[22, 87], Operations: ['28-6=22', '7+80=87'] Exploring Operation: 22+87=109, Resulting Numbers: [109] 109,81 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 22*87=1914, Resulting Numbers: [1914] 1914,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 81:[22, 73], Operations: ['28-6=22', '80-7=73'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,81 unequal: No Solution Exploring Operation: 22*73=1606, Resulting Numbers: [1606] 1606,81 unequal: No Solution Exploring Operation: 22+73=95, Resulting Numbers: [95] 95,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 81:[7, 102], Operations: ['28-6=22', '80+22=102'] Exploring Operation: 102-7=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 7*102=714, Resulting Numbers: [714] 714,81 unequal: No Solution Exploring Operation: 7+102=109, Resulting Numbers: [109] 109,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 81:[80, 10], Operations: ['28/7=4', '6+4=10'] Exploring Operation: 80*10=800, Resulting Numbers: [800] 800,81 unequal: No Solution Exploring Operation: 80+10=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,81 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[80, 2], Operations: ['28/7=4', '6-4=2'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,81 unequal: No Solution Exploring Operation: 80*2=160, Resulting Numbers: [160] 160,81 unequal: No Solution Exploring Operation: 80+2=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[28, 79], Operations: ['6+80=86', '86-7=79'] Exploring Operation: 28+79=107, Resulting Numbers: [107] 107,81 unequal: No Solution Exploring Operation: 79-28=51, Resulting Numbers: [51] 51,81 unequal: No Solution Exploring Operation: 28*79=2212, Resulting Numbers: [2212] 2212,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[80, 24], Operations: ['28/7=4', '6*4=24'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,81 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[86, 4], Operations: ['6+80=86', '28/7=4'] Exploring Operation: 86*4=344, Resulting Numbers: [344] 344,81 unequal: No Solution Exploring Operation: 86+4=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,81 unequal: No Solution Moving to Node #0,2,4 Current State: 81:[4, 86], Operations: ['28/7=4', '6+80=86'] Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 4+86=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 4*86=344, Resulting Numbers: [344] 344,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[6, 84], Operations: ['28/7=4', '80+4=84'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 6+84=90, Resulting Numbers: [90] 90,81 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,81 unequal: No Solution Exploring Operation: 6*84=504, Resulting Numbers: [504] 504,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[80, 15], Operations: ['7+6=13', '28-13=15'] Exploring Operation: 80*15=1200, Resulting Numbers: [1200] 1200,81 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 80+15=95, Resulting Numbers: [95] 95,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[86, 21], Operations: ['6+80=86', '28-7=21'] Exploring Operation: 86+21=107, Resulting Numbers: [107] 107,81 unequal: No Solution Exploring Operation: 86*21=1806, Resulting Numbers: [1806] 1806,81 unequal: No Solution Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[28, 93], Operations: ['7+6=13', '80+13=93'] Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,81 unequal: No Solution Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,81 unequal: No Solution Moving to Node #0,1,4 Current State: 81:[86, 35], Operations: ['6+80=86', '7+28=35'] Exploring Operation: 86*35=3010, Resulting Numbers: [3010] 3010,81 unequal: No Solution Exploring Operation: 86-35=51, Resulting Numbers: [51] 51,81 unequal: No Solution Exploring Operation: 86+35=121, Resulting Numbers: [121] 121,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[28, 93], Operations: ['6+80=86', '7+86=93'] Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,81 unequal: No Solution Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,81 unequal: No Solution Moving to Node #0,0,4 Current State: 81:[28, 67], Operations: ['7+6=13', '80-13=67'] Exploring Operation: 28*67=1876, Resulting Numbers: [1876] 1876,81 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 28+67=95, Resulting Numbers: [95] 95,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[80, 41], Operations: ['7+6=13', '28+13=41'] Exploring Operation: 80+41=121, Resulting Numbers: [121] 121,81 unequal: No Solution Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 80*41=3280, Resulting Numbers: [3280] 3280,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[13, 52], Operations: ['7+6=13', '80-28=52'] Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,81 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,81 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 25, 90, 75, 72 ]
68
[ "90-25=65", "75-72=3", "65+3=68" ]
Current State: 68:[25, 90, 75, 72], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [75, 72, 65] Generated Node #2: [75, 72, 65] from Operation: 90-25=65 Current State: 68:[75, 72, 65], Operations: ['90-25=65'] Exploring Operation: 75-72=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 75-72=3 Current State: 68:[65, 3], Operations: ['90-25=65', '75-72=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[25, 90, 75, 72], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [75, 72, 65] Generated Node #0,0: 68:[75, 72, 65] Operation: 90-25=65 Exploring Operation: 90-75=15, Resulting Numbers: [25, 72, 15] Generated Node #0,1: 68:[25, 72, 15] Operation: 90-75=15 Exploring Operation: 90-72=18, Resulting Numbers: [25, 75, 18] Generated Node #0,2: 68:[25, 75, 18] Operation: 90-72=18 Moving to Node #0,0 Current State: 68:[75, 72, 65], Operations: ['90-25=65'] Exploring Operation: 72-65=7, Resulting Numbers: [75, 7] Generated Node #0,0,0: 68:[75, 7] Operation: 72-65=7 Exploring Operation: 75-65=10, Resulting Numbers: [72, 10] Generated Node #0,0,1: 68:[72, 10] Operation: 75-65=10 Exploring Operation: 75-72=3, Resulting Numbers: [65, 3] Generated Node #0,0,2: 68:[65, 3] Operation: 75-72=3 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 68:[65, 3], Operations: ['90-25=65', '75-72=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,68 unequal: No Solution Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,68 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[25, 90, 75, 72], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [75, 72, 65] Generated Node #0,0: 68:[75, 72, 65] Operation: 90-25=65 Moving to Node #0,0 Current State: 68:[75, 72, 65], Operations: ['90-25=65'] Exploring Operation: 75-72=3, Resulting Numbers: [65, 3] Generated Node #0,0,2: 68:[65, 3] Operation: 75-72=3 Moving to Node #0,0,2 Current State: 68:[65, 3], Operations: ['90-25=65', '75-72=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 48, 68, 9, 47 ]
60
[ "48+68=116", "9+47=56", "116-56=60" ]
Current State: 60:[48, 68, 9, 47], Operations: [] Exploring Operation: 48+68=116, Resulting Numbers: [9, 47, 116] Generated Node #2: [9, 47, 116] from Operation: 48+68=116 Current State: 60:[9, 47, 116], Operations: ['48+68=116'] Exploring Operation: 9+47=56, Resulting Numbers: [116, 56] Generated Node #3: [116, 56] from Operation: 9+47=56 Current State: 60:[116, 56], Operations: ['48+68=116', '9+47=56'] Exploring Operation: 116-56=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[48, 68, 9, 47], Operations: [] Exploring Operation: 68-47=21, Resulting Numbers: [48, 9, 21] Generated Node #0,0: 60:[48, 9, 21] Operation: 68-47=21 Exploring Operation: 48-47=1, Resulting Numbers: [68, 9, 1] Generated Node #0,1: 60:[68, 9, 1] Operation: 48-47=1 Exploring Operation: 68-48=20, Resulting Numbers: [9, 47, 20] Generated Node #0,2: 60:[9, 47, 20] Operation: 68-48=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[68, 9, 1], Operations: ['48-47=1'] Exploring Operation: 9+1=10, Resulting Numbers: [68, 10] Generated Node #0,1,0: 60:[68, 10] Operation: 9+1=10 Exploring Operation: 68-9=59, Resulting Numbers: [1, 59] Generated Node #0,1,1: 60:[1, 59] Operation: 68-9=59 Exploring Operation: 68-1=67, Resulting Numbers: [9, 67] Generated Node #0,1,2: 60:[9, 67] Operation: 68-1=67 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 60:[1, 59], Operations: ['48-47=1', '68-9=59'] Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 1*59=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[48, 68, 9, 47], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [68, 9, 1] Generated Node #0,1: 60:[68, 9, 1] Operation: 48-47=1 Moving to Node #0,1 Current State: 60:[68, 9, 1], Operations: ['48-47=1'] Exploring Operation: 68-9=59, Resulting Numbers: [1, 59] Generated Node #0,1,1: 60:[1, 59] Operation: 68-9=59 Moving to Node #0,1,1 Current State: 60:[1, 59], Operations: ['48-47=1', '68-9=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 93, 63, 60, 60 ]
31
[ "93-63=30", "60/60=1", "30+1=31" ]
Current State: 31:[93, 63, 60, 60], Operations: [] Exploring Operation: 93-63=30, Resulting Numbers: [60, 60, 30] Generated Node #2: [60, 60, 30] from Operation: 93-63=30 Current State: 31:[60, 60, 30], Operations: ['93-63=30'] Exploring Operation: 60/60=1, Resulting Numbers: [30, 1] Generated Node #3: [30, 1] from Operation: 60/60=1 Current State: 31:[30, 1], Operations: ['93-63=30', '60/60=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[93, 63, 60, 60], Operations: [] Exploring Operation: 93-63=30, Resulting Numbers: [60, 60, 30] Generated Node #0,0: 31:[60, 60, 30] Operation: 93-63=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[60, 60, 30], Operations: ['93-63=30'] Exploring Operation: 60-30=30, Resulting Numbers: [60, 30] Generated Node #0,0,0: 31:[60, 30] Operation: 60-30=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[60, 30], Operations: ['93-63=30', '60-30=30'] Exploring Operation: 60-30=30, Resulting Numbers: [30] 30,31 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
[ 1, 86, 8, 97 ]
80
[ "1+86=87", "97-87=10", "8*10=80" ]
Current State: 80:[1, 86, 8, 97], Operations: [] Exploring Operation: 1+86=87, Resulting Numbers: [8, 97, 87] Generated Node #2: [8, 97, 87] from Operation: 1+86=87 Current State: 80:[8, 97, 87], Operations: ['1+86=87'] Exploring Operation: 97-87=10, Resulting Numbers: [8, 10] Generated Node #3: [8, 10] from Operation: 97-87=10 Current State: 80:[8, 10], Operations: ['1+86=87', '97-87=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[1, 86, 8, 97], Operations: [] Exploring Operation: 86-1=85, Resulting Numbers: [8, 97, 85] Generated Node #0,0: 80:[8, 97, 85] Operation: 86-1=85 Exploring Operation: 86-8=78, Resulting Numbers: [1, 97, 78] Generated Node #0,1: 80:[1, 97, 78] Operation: 86-8=78 Exploring Operation: 97-8=89, Resulting Numbers: [1, 86, 89] Generated Node #0,2: 80:[1, 86, 89] Operation: 97-8=89 Exploring Operation: 97-86=11, Resulting Numbers: [1, 8, 11] Generated Node #0,3: 80:[1, 8, 11] Operation: 97-86=11 Moving to Node #0,3 Current State: 80:[1, 8, 11], Operations: ['97-86=11'] Exploring Operation: 1*11=11, Resulting Numbers: [8, 11] Generated Node #0,3,0: 80:[8, 11] Operation: 1*11=11 Exploring Operation: 1*8=8, Resulting Numbers: [11, 8] Generated Node #0,3,1: 80:[11, 8] Operation: 1*8=8 Exploring Operation: 11-1=10, Resulting Numbers: [8, 10] Generated Node #0,3,2: 80:[8, 10] Operation: 11-1=10 Exploring Operation: 8/1=8, Resulting Numbers: [11, 8] Generated Node #0,3,3: 80:[11, 8] Operation: 8/1=8 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 80:[8, 10], Operations: ['97-86=11', '11-1=10'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[1, 86, 8, 97], Operations: [] Exploring Operation: 97-86=11, Resulting Numbers: [1, 8, 11] Generated Node #0,3: 80:[1, 8, 11] Operation: 97-86=11 Moving to Node #0,3 Current State: 80:[1, 8, 11], Operations: ['97-86=11'] Exploring Operation: 11-1=10, Resulting Numbers: [8, 10] Generated Node #0,3,2: 80:[8, 10] Operation: 11-1=10 Moving to Node #0,3,2 Current State: 80:[8, 10], Operations: ['97-86=11', '11-1=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 32, 37, 68, 32 ]
31
[ "32+37=69", "68+32=100", "100-69=31" ]
Current State: 31:[32, 37, 68, 32], Operations: [] Exploring Operation: 32+37=69, Resulting Numbers: [68, 69] Generated Node #2: [68, 69] from Operation: 32+37=69 Current State: 31:[68, 69], Operations: ['32+37=69'] Exploring Operation: 68+32=100, Resulting Numbers: [69, 100] Generated Node #3: [69, 100] from Operation: 68+32=100 Current State: 31:[69, 100], Operations: ['32+37=69', '68+32=100'] Exploring Operation: 100-69=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[32, 37, 68, 32], Operations: [] Exploring Operation: 68-37=31, Resulting Numbers: [32, 32, 31] Generated Node #0,0: 31:[32, 32, 31] Operation: 68-37=31 Moving to Node #0,0 Current State: 31:[32, 32, 31], Operations: ['68-37=31'] Exploring Operation: 32/32=1, Resulting Numbers: [31, 1] Generated Node #0,0,0: 31:[31, 1] Operation: 32/32=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[31, 1], Operations: ['68-37=31', '32/32=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[32, 37, 68, 32], Operations: [] Exploring Operation: 68-37=31, Resulting Numbers: [32, 32, 31] Generated Node #0,0: 31:[32, 32, 31] Operation: 68-37=31 Moving to Node #0,0 Current State: 31:[32, 32, 31], Operations: ['68-37=31'] Exploring Operation: 32/32=1, Resulting Numbers: [31, 1] Generated Node #0,0,0: 31:[31, 1] Operation: 32/32=1 Moving to Node #0,0,0 Current State: 31:[31, 1], Operations: ['68-37=31', '32/32=1'] Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 85, 29, 13, 7 ]
62
[ "85-29=56", "13-7=6", "56+6=62" ]
Current State: 62:[85, 29, 13, 7], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [13, 7, 56] Generated Node #2: [13, 7, 56] from Operation: 85-29=56 Current State: 62:[13, 7, 56], Operations: ['85-29=56'] Exploring Operation: 13-7=6, Resulting Numbers: [56, 6] Generated Node #3: [56, 6] from Operation: 13-7=6 Current State: 62:[56, 6], Operations: ['85-29=56', '13-7=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[85, 29, 13, 7], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [13, 7, 56] Generated Node #0,0: 62:[13, 7, 56] Operation: 85-29=56 Exploring Operation: 85-7=78, Resulting Numbers: [29, 13, 78] Generated Node #0,1: 62:[29, 13, 78] Operation: 85-7=78 Exploring Operation: 85-13=72, Resulting Numbers: [29, 7, 72] Generated Node #0,2: 62:[29, 7, 72] Operation: 85-13=72 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[29, 7, 72], Operations: ['85-13=72'] Exploring Operation: 29+7=36, Resulting Numbers: [72, 36] Generated Node #0,2,0: 62:[72, 36] Operation: 29+7=36 Exploring Operation: 72-7=65, Resulting Numbers: [29, 65] Generated Node #0,2,1: 62:[29, 65] Operation: 72-7=65 Exploring Operation: 72-29=43, Resulting Numbers: [7, 43] Generated Node #0,2,2: 62:[7, 43] Operation: 72-29=43 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[29, 65], Operations: ['85-13=72', '72-7=65'] Exploring Operation: 29+65=94, Resulting Numbers: [94] 94,62 unequal: No Solution Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 29*65=1885, Resulting Numbers: [1885] 1885,62 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 #0,2,0 Current State: 62:[72, 36], Operations: ['85-13=72', '29+7=36'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,62 unequal: No Solution Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,62 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 #0,2,2 Current State: 62:[7, 43], Operations: ['85-13=72', '72-29=43'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 7*43=301, Resulting Numbers: [301] 301,62 unequal: No Solution Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,62 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 #0,0 Current State: 62:[13, 7, 56], Operations: ['85-29=56'] Exploring Operation: 13-7=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 62:[56, 6] Operation: 13-7=6 Exploring Operation: 13+56=69, Resulting Numbers: [7, 69] Generated Node #0,0,1: 62:[7, 69] Operation: 13+56=69 Exploring Operation: 7+56=63, Resulting Numbers: [13, 63] Generated Node #0,0,2: 62:[13, 63] Operation: 7+56=63 Moving to Node #0,0,0 Current State: 62:[56, 6], Operations: ['85-29=56', '13-7=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,62 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,62 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[85, 29, 13, 7], Operations: [] Exploring Operation: 85-29=56, Resulting Numbers: [13, 7, 56] Generated Node #0,0: 62:[13, 7, 56] Operation: 85-29=56 Moving to Node #0,0 Current State: 62:[13, 7, 56], Operations: ['85-29=56'] Exploring Operation: 13-7=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 62:[56, 6] Operation: 13-7=6 Moving to Node #0,0,0 Current State: 62:[56, 6], Operations: ['85-29=56', '13-7=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 83, 88, 2, 20 ]
59
[ "83+20=103", "88/2=44", "103-44=59" ]
Current State: 59:[83, 88, 2, 20], Operations: [] Exploring Operation: 83+20=103, Resulting Numbers: [88, 2, 103] Generated Node #2: [88, 2, 103] from Operation: 83+20=103 Current State: 59:[88, 2, 103], Operations: ['83+20=103'] Exploring Operation: 88/2=44, Resulting Numbers: [103, 44] Generated Node #3: [103, 44] from Operation: 88/2=44 Current State: 59:[103, 44], Operations: ['83+20=103', '88/2=44'] Exploring Operation: 103-44=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[83, 88, 2, 20], Operations: [] Exploring Operation: 2*20=40, Resulting Numbers: [83, 88, 40] Generated Node #0,0: 59:[83, 88, 40] Operation: 2*20=40 Exploring Operation: 88/2=44, Resulting Numbers: [83, 20, 44] Generated Node #0,1: 59:[83, 20, 44] Operation: 88/2=44 Exploring Operation: 83-20=63, Resulting Numbers: [88, 2, 63] Generated Node #0,2: 59:[88, 2, 63] Operation: 83-20=63 Exploring Operation: 83-2=81, Resulting Numbers: [88, 20, 81] Generated Node #0,3: 59:[88, 20, 81] Operation: 83-2=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[83, 88, 40], Operations: ['2*20=40'] Exploring Operation: 83-40=43, Resulting Numbers: [88, 43] Generated Node #0,0,0: 59:[88, 43] Operation: 83-40=43 Exploring Operation: 83+40=123, Resulting Numbers: [88, 123] Generated Node #0,0,1: 59:[88, 123] Operation: 83+40=123 Exploring Operation: 88-40=48, Resulting Numbers: [83, 48] Generated Node #0,0,2: 59:[83, 48] Operation: 88-40=48 Exploring Operation: 88-83=5, Resulting Numbers: [40, 5] Generated Node #0,0,3: 59:[40, 5] Operation: 88-83=5 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 59:[83, 48], Operations: ['2*20=40', '88-40=48'] Exploring Operation: 83*48=3984, Resulting Numbers: [3984] 3984,59 unequal: No Solution Exploring Operation: 83+48=131, Resulting Numbers: [131] 131,59 unequal: No Solution Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[88, 43], Operations: ['2*20=40', '83-40=43'] Exploring Operation: 88+43=131, Resulting Numbers: [131] 131,59 unequal: No Solution Exploring Operation: 88-43=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 88*43=3784, Resulting Numbers: [3784] 3784,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 59:[40, 5], Operations: ['2*20=40', '88-83=5'] Exploring Operation: 40+5=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 40*5=200, Resulting Numbers: [200] 200,59 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,59 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[88, 123], Operations: ['2*20=40', '83+40=123'] Exploring Operation: 88*123=10824, Resulting Numbers: [10824] 10824,59 unequal: No Solution Exploring Operation: 88+123=211, Resulting Numbers: [211] 211,59 unequal: No Solution Exploring Operation: 123-88=35, Resulting Numbers: [35] 35,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[83, 20, 44], Operations: ['88/2=44'] Exploring Operation: 83-20=63, Resulting Numbers: [44, 63] Generated Node #0,1,0: 59:[44, 63] Operation: 83-20=63 Exploring Operation: 20+44=64, Resulting Numbers: [83, 64] Generated Node #0,1,1: 59:[83, 64] Operation: 20+44=64 Exploring Operation: 83-44=39, Resulting Numbers: [20, 39] Generated Node #0,1,2: 59:[20, 39] Operation: 83-44=39 Exploring Operation: 83+20=103, Resulting Numbers: [44, 103] Generated Node #0,1,3: 59:[44, 103] Operation: 83+20=103 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[44, 63], Operations: ['88/2=44', '83-20=63'] Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,59 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[83, 64], Operations: ['88/2=44', '20+44=64'] Exploring Operation: 83+64=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 83-64=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 83*64=5312, Resulting Numbers: [5312] 5312,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 59:[20, 39], Operations: ['88/2=44', '83-44=39'] Exploring Operation: 20*39=780, Resulting Numbers: [780] 780,59 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[83, 88, 2, 20], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [83, 20, 44] Generated Node #0,1: 59:[83, 20, 44] Operation: 88/2=44 Moving to Node #0,1 Current State: 59:[83, 20, 44], Operations: ['88/2=44'] Exploring Operation: 83-44=39, Resulting Numbers: [20, 39] Generated Node #0,1,2: 59:[20, 39] Operation: 83-44=39 Moving to Node #0,1,2 Current State: 59:[20, 39], Operations: ['88/2=44', '83-44=39'] Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 83, 45, 91, 13 ]
66
[ "83-45=38", "91+13=104", "104-38=66" ]
Current State: 66:[83, 45, 91, 13], Operations: [] Exploring Operation: 83-45=38, Resulting Numbers: [91, 13, 38] Generated Node #2: [91, 13, 38] from Operation: 83-45=38 Current State: 66:[91, 13, 38], Operations: ['83-45=38'] Exploring Operation: 91+13=104, Resulting Numbers: [38, 104] Generated Node #3: [38, 104] from Operation: 91+13=104 Current State: 66:[38, 104], Operations: ['83-45=38', '91+13=104'] Exploring Operation: 104-38=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[83, 45, 91, 13], Operations: [] Exploring Operation: 91-83=8, Resulting Numbers: [45, 13, 8] Generated Node #0,0: 66:[45, 13, 8] Operation: 91-83=8 Moving to Node #0,0 Current State: 66:[45, 13, 8], Operations: ['91-83=8'] Exploring Operation: 45-13=32, Resulting Numbers: [8, 32] Generated Node #0,0,0: 66:[8, 32] Operation: 45-13=32 Moving to Node #0,0,0 Current State: 66:[8, 32], Operations: ['91-83=8', '45-13=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,66 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 30, 45, 47, 28 ]
26
[ "47-45=2", "28*2=56", "56-30=26" ]
Current State: 26:[30, 45, 47, 28], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [30, 28, 2] Generated Node #2: [30, 28, 2] from Operation: 47-45=2 Current State: 26:[30, 28, 2], Operations: ['47-45=2'] Exploring Operation: 28*2=56, Resulting Numbers: [30, 56] Generated Node #3: [30, 56] from Operation: 28*2=56 Current State: 26:[30, 56], Operations: ['47-45=2', '28*2=56'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[30, 45, 47, 28], Operations: [] Exploring Operation: 45-30=15, Resulting Numbers: [47, 28, 15] Generated Node #0,0: 26:[47, 28, 15] Operation: 45-30=15 Exploring Operation: 47-30=17, Resulting Numbers: [45, 28, 17] Generated Node #0,1: 26:[45, 28, 17] Operation: 47-30=17 Exploring Operation: 47-45=2, Resulting Numbers: [30, 28, 2] Generated Node #0,2: 26:[30, 28, 2] Operation: 47-45=2 Moving to Node #0,2 Current State: 26:[30, 28, 2], Operations: ['47-45=2'] Exploring Operation: 30/2=15, Resulting Numbers: [28, 15] Generated Node #0,2,0: 26:[28, 15] Operation: 30/2=15 Exploring Operation: 30-2=28, Resulting Numbers: [28, 28] Generated Node #0,2,1: 26:[28, 28] Operation: 30-2=28 Exploring Operation: 30-28=2, Resulting Numbers: [2, 2] Generated Node #0,2,2: 26:[2, 2] Operation: 30-28=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 26:[2, 2], Operations: ['47-45=2', '30-28=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[28, 15], Operations: ['47-45=2', '30/2=15'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,26 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[28, 28], Operations: ['47-45=2', '30-2=28'] Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 26:[47, 28, 15], Operations: ['45-30=15'] Exploring Operation: 28-15=13, Resulting Numbers: [47, 13] Generated Node #0,0,0: 26:[47, 13] Operation: 28-15=13 Exploring Operation: 47-28=19, Resulting Numbers: [15, 19] Generated Node #0,0,1: 26:[15, 19] Operation: 47-28=19 Exploring Operation: 47-15=32, Resulting Numbers: [28, 32] Generated Node #0,0,2: 26:[28, 32] Operation: 47-15=32 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[15, 19], Operations: ['45-30=15', '47-28=19'] Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,26 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[28, 32], Operations: ['45-30=15', '47-15=32'] Exploring Operation: 28+32=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 28*32=896, Resulting Numbers: [896] 896,26 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[47, 13], Operations: ['45-30=15', '28-15=13'] Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,26 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 26:[45, 28, 17], Operations: ['47-30=17'] Exploring Operation: 45-28=17, Resulting Numbers: [17, 17] Generated Node #0,1,0: 26:[17, 17] Operation: 45-28=17 Exploring Operation: 45-17=28, Resulting Numbers: [28, 28] Generated Node #0,1,1: 26:[28, 28] Operation: 45-17=28 Exploring Operation: 28-17=11, Resulting Numbers: [45, 11] Generated Node #0,1,2: 26:[45, 11] Operation: 28-17=11 Moving to Node #0,1,1 Current State: 26:[28, 28], Operations: ['47-30=17', '45-17=28'] Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[17, 17], Operations: ['47-30=17', '45-28=17'] Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[45, 11], Operations: ['47-30=17', '28-17=11'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,26 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 13, 98, 14, 31 ]
51
[ "13+31=44", "98/14=7", "44+7=51" ]
Current State: 51:[13, 98, 14, 31], Operations: [] Exploring Operation: 13+31=44, Resulting Numbers: [98, 14, 44] Generated Node #2: [98, 14, 44] from Operation: 13+31=44 Current State: 51:[98, 14, 44], Operations: ['13+31=44'] Exploring Operation: 98/14=7, Resulting Numbers: [44, 7] Generated Node #3: [44, 7] from Operation: 98/14=7 Current State: 51:[44, 7], Operations: ['13+31=44', '98/14=7'] Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[13, 98, 14, 31], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [13, 31, 7] Generated Node #0,0: 51:[13, 31, 7] Operation: 98/14=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[13, 31, 7], Operations: ['98/14=7'] Exploring Operation: 31-13=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 51:[7, 18] Operation: 31-13=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[7, 18], Operations: ['98/14=7', '31-13=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,51 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
[ 7, 23, 27, 21 ]
13
[ "23-21=2", "7*2=14", "27-14=13" ]
Current State: 13:[7, 23, 27, 21], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [7, 27, 2] Generated Node #2: [7, 27, 2] from Operation: 23-21=2 Current State: 13:[7, 27, 2], Operations: ['23-21=2'] Exploring Operation: 7*2=14, Resulting Numbers: [27, 14] Generated Node #3: [27, 14] from Operation: 7*2=14 Current State: 13:[27, 14], Operations: ['23-21=2', '7*2=14'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[7, 23, 27, 21], Operations: [] Exploring Operation: 27-7=20, Resulting Numbers: [23, 21, 20] Generated Node #0,0: 13:[23, 21, 20] Operation: 27-7=20 Exploring Operation: 27-23=4, Resulting Numbers: [7, 21, 4] Generated Node #0,1: 13:[7, 21, 4] Operation: 27-23=4 Exploring Operation: 21-7=14, Resulting Numbers: [23, 27, 14] Generated Node #0,2: 13:[23, 27, 14] Operation: 21-7=14 Exploring Operation: 23-7=16, Resulting Numbers: [27, 21, 16] Generated Node #0,3: 13:[27, 21, 16] Operation: 23-7=16 Exploring Operation: 27-21=6, Resulting Numbers: [7, 23, 6] Generated Node #0,4: 13:[7, 23, 6] Operation: 27-21=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[7, 21, 4], Operations: ['27-23=4'] Exploring Operation: 21-7=14, Resulting Numbers: [4, 14] Generated Node #0,1,0: 13:[4, 14] Operation: 21-7=14 Exploring Operation: 21-4=17, Resulting Numbers: [7, 17] Generated Node #0,1,1: 13:[7, 17] Operation: 21-4=17 Exploring Operation: 7-4=3, Resulting Numbers: [21, 3] Generated Node #0,1,2: 13:[21, 3] Operation: 7-4=3 Exploring Operation: 7+4=11, Resulting Numbers: [21, 11] Generated Node #0,1,3: 13:[21, 11] Operation: 7+4=11 Exploring Operation: 21+4=25, Resulting Numbers: [7, 25] Generated Node #0,1,4: 13:[7, 25] Operation: 21+4=25 Moving to Node #0,1,0 Current State: 13:[4, 14], Operations: ['27-23=4', '21-7=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[21, 11], Operations: ['27-23=4', '7+4=11'] Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,13 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[7, 17], Operations: ['27-23=4', '21-4=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[21, 3], Operations: ['27-23=4', '7-4=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,13 unequal: No Solution Moving to Node #0,1,4 Current State: 13:[7, 25], Operations: ['27-23=4', '21+4=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,13 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,13 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 #0,4 Current State: 13:[7, 23, 6], Operations: ['27-21=6'] Exploring Operation: 7-6=1, Resulting Numbers: [23, 1] Generated Node #0,4,0: 13:[23, 1] Operation: 7-6=1 Exploring Operation: 23-7=16, Resulting Numbers: [6, 16] Generated Node #0,4,1: 13:[6, 16] Operation: 23-7=16 Exploring Operation: 23-6=17, Resulting Numbers: [7, 17] Generated Node #0,4,2: 13:[7, 17] Operation: 23-6=17 Exploring Operation: 7+6=13, Resulting Numbers: [23, 13] Generated Node #0,4,3: 13:[23, 13] Operation: 7+6=13 Exploring Operation: 23+6=29, Resulting Numbers: [7, 29] Generated Node #0,4,4: 13:[7, 29] Operation: 23+6=29 Moving to Node #0,4,1 Current State: 13:[6, 16], Operations: ['27-21=6', '23-7=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,13 unequal: No Solution Moving to Node #0,4,3 Current State: 13:[23, 13], Operations: ['27-21=6', '7+6=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,13 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,13 unequal: No Solution Moving to Node #0,4,2 Current State: 13:[7, 17], Operations: ['27-21=6', '23-6=17'] Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,13 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,4,0 Current State: 13:[23, 1], Operations: ['27-21=6', '7-6=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,13 unequal: No Solution Moving to Node #0,4,4 Current State: 13:[7, 29], Operations: ['27-21=6', '23+6=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,13 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[23, 21, 20], Operations: ['27-7=20'] Exploring Operation: 23-20=3, Resulting Numbers: [21, 3] Generated Node #0,0,0: 13:[21, 3] Operation: 23-20=3 Exploring Operation: 23-21=2, Resulting Numbers: [20, 2] Generated Node #0,0,1: 13:[20, 2] Operation: 23-21=2 Exploring Operation: 23+20=43, Resulting Numbers: [21, 43] Generated Node #0,0,2: 13:[21, 43] Operation: 23+20=43 Exploring Operation: 21-20=1, Resulting Numbers: [23, 1] Generated Node #0,0,3: 13:[23, 1] Operation: 21-20=1 Exploring Operation: 23+21=44, Resulting Numbers: [20, 44] Generated Node #0,0,4: 13:[20, 44] Operation: 23+21=44 Moving to Node #0,0,0 Current State: 13:[21, 3], Operations: ['27-7=20', '23-20=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,13 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[20, 2], Operations: ['27-7=20', '23-21=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[23, 1], Operations: ['27-7=20', '21-20=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,13 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[21, 43], Operations: ['27-7=20', '23+20=43'] Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,13 unequal: No Solution Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,13 unequal: No Solution Moving to Node #0,0,4 Current State: 13:[20, 44], Operations: ['27-7=20', '23+21=44'] Exploring Operation: 20+44=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 20*44=880, Resulting Numbers: [880] 880,13 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,13 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:[23, 27, 14], Operations: ['21-7=14'] Exploring Operation: 23+14=37, Resulting Numbers: [27, 37] Generated Node #0,2,0: 13:[27, 37] Operation: 23+14=37 Exploring Operation: 27-23=4, Resulting Numbers: [14, 4] Generated Node #0,2,1: 13:[14, 4] Operation: 27-23=4 Exploring Operation: 23-14=9, Resulting Numbers: [27, 9] Generated Node #0,2,2: 13:[27, 9] Operation: 23-14=9 Exploring Operation: 27-14=13, Resulting Numbers: [23, 13] Generated Node #0,2,3: 13:[23, 13] Operation: 27-14=13 Exploring Operation: 23+27=50, Resulting Numbers: [14, 50] Generated Node #0,2,4: 13:[14, 50] Operation: 23+27=50 Moving to Node #0,2,1 Current State: 13:[14, 4], Operations: ['21-7=14', '27-23=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,13 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,13 unequal: No Solution Moving to Node #0,2,3 Current State: 13:[23, 13], Operations: ['21-7=14', '27-14=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,13 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[27, 9], Operations: ['21-7=14', '23-14=9'] Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,13 unequal: No Solution Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,13 unequal: No Solution Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[27, 37], Operations: ['21-7=14', '23+14=37'] Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,13 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,13 unequal: No Solution Moving to Node #0,2,4 Current State: 13:[14, 50], Operations: ['21-7=14', '23+27=50'] Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,13 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 #0,3 Current State: 13:[27, 21, 16], Operations: ['23-7=16'] Exploring Operation: 27-21=6, Resulting Numbers: [16, 6] Generated Node #0,3,0: 13:[16, 6] Operation: 27-21=6 Exploring Operation: 27+21=48, Resulting Numbers: [16, 48] Generated Node #0,3,1: 13:[16, 48] Operation: 27+21=48 Exploring Operation: 27-16=11, Resulting Numbers: [21, 11] Generated Node #0,3,2: 13:[21, 11] Operation: 27-16=11 Exploring Operation: 21-16=5, Resulting Numbers: [27, 5] Generated Node #0,3,3: 13:[27, 5] Operation: 21-16=5 Exploring Operation: 27+16=43, Resulting Numbers: [21, 43] Generated Node #0,3,4: 13:[21, 43] Operation: 27+16=43 Moving to Node #0,3,0 Current State: 13:[16, 6], Operations: ['23-7=16', '27-21=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,13 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[21, 11], Operations: ['23-7=16', '27-16=11'] Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,13 unequal: No Solution Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,3,3 Current State: 13:[27, 5], Operations: ['23-7=16', '21-16=5'] Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,13 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[16, 48], Operations: ['23-7=16', '27+21=48'] Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 16*48=768, Resulting Numbers: [768] 768,13 unequal: No Solution Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,13 unequal: No Solution Moving to Node #0,3,4 Current State: 13:[21, 43], Operations: ['23-7=16', '27+16=43'] Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,13 unequal: No Solution Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,13 unequal: No Solution Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,13 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
[ 45, 15, 8, 39 ]
17
[ "45-15=30", "8+39=47", "47-30=17" ]
Current State: 17:[45, 15, 8, 39], Operations: [] Exploring Operation: 45-15=30, Resulting Numbers: [8, 39, 30] Generated Node #2: [8, 39, 30] from Operation: 45-15=30 Current State: 17:[8, 39, 30], Operations: ['45-15=30'] Exploring Operation: 8+39=47, Resulting Numbers: [30, 47] Generated Node #3: [30, 47] from Operation: 8+39=47 Current State: 17:[30, 47], Operations: ['45-15=30', '8+39=47'] Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[45, 15, 8, 39], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [15, 8, 6] Generated Node #0,0: 17:[15, 8, 6] Operation: 45-39=6 Moving to Node #0,0 Current State: 17:[15, 8, 6], Operations: ['45-39=6'] Exploring Operation: 8+6=14, Resulting Numbers: [15, 14] Generated Node #0,0,0: 17:[15, 14] Operation: 8+6=14 Moving to Node #0,0,0 Current State: 17:[15, 14], Operations: ['45-39=6', '8+6=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,17 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 1, 81, 56, 82 ]
56
[ "1+81=82", "56+82=138", "138-82=56" ]
Current State: 56:[1, 81, 56, 82], Operations: [] Exploring Operation: 1+81=82, Resulting Numbers: [56, 82, 82] Generated Node #2: [56, 82, 82] from Operation: 1+81=82 Current State: 56:[56, 82, 82], Operations: ['1+81=82'] Exploring Operation: 56+82=138, Resulting Numbers: [138] 138,56 equal: Goal Reached Exploring Operation: 138-82=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[1, 81, 56, 82], Operations: [] Exploring Operation: 81-1=80, Resulting Numbers: [56, 82, 80] Generated Node #0,0: 56:[56, 82, 80] Operation: 81-1=80 Exploring Operation: 81-56=25, Resulting Numbers: [1, 82, 25] Generated Node #0,1: 56:[1, 82, 25] Operation: 81-56=25 Exploring Operation: 82-56=26, Resulting Numbers: [1, 81, 26] Generated Node #0,2: 56:[1, 81, 26] Operation: 82-56=26 Exploring Operation: 82-81=1, Resulting Numbers: [1, 56, 1] Generated Node #0,3: 56:[1, 56, 1] Operation: 82-81=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[1, 56, 1], Operations: ['82-81=1'] Exploring Operation: 1*56=56, Resulting Numbers: [1, 56] Generated Node #0,3,0: 56:[1, 56] Operation: 1*56=56 Exploring Operation: 1+1=2, Resulting Numbers: [56, 2] Generated Node #0,3,1: 56:[56, 2] Operation: 1+1=2 Exploring Operation: 1*1=1, Resulting Numbers: [56, 1] Generated Node #0,3,2: 56:[56, 1] Operation: 1*1=1 Exploring Operation: 56/1=56, Resulting Numbers: [1, 56] Generated Node #0,3,3: 56:[1, 56] Operation: 56/1=56 Moving to Node #0,3,1 Current State: 56:[56, 2], Operations: ['82-81=1', '1+1=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,56 unequal: No Solution Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 56*2=112, Resulting Numbers: [112] 112,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[56, 1], Operations: ['82-81=1', '1*1=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[1, 81, 56, 82], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [1, 56, 1] Generated Node #0,3: 56:[1, 56, 1] Operation: 82-81=1 Moving to Node #0,3 Current State: 56:[1, 56, 1], Operations: ['82-81=1'] Exploring Operation: 1*1=1, Resulting Numbers: [56, 1] Generated Node #0,3,2: 56:[56, 1] Operation: 1*1=1 Moving to Node #0,3,2 Current State: 56:[56, 1], Operations: ['82-81=1', '1*1=1'] Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 42, 91, 52, 28 ]
58
[ "52*28=1456", "1456/91=16", "42+16=58" ]
Current State: 58:[42, 91, 52, 28], Operations: [] Exploring Operation: 52*28=1456, Resulting Numbers: [42, 91, 1456] Generated Node #2: [42, 91, 1456] from Operation: 52*28=1456 Current State: 58:[42, 91, 1456], Operations: ['52*28=1456'] Exploring Operation: 1456/91=16, Resulting Numbers: [42, 16] Generated Node #3: [42, 16] from Operation: 1456/91=16 Current State: 58:[42, 16], Operations: ['52*28=1456', '1456/91=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[42, 91, 52, 28], Operations: [] Exploring Operation: 91-42=49, Resulting Numbers: [52, 28, 49] Generated Node #0,0: 58:[52, 28, 49] Operation: 91-42=49 Exploring Operation: 91-52=39, Resulting Numbers: [42, 28, 39] Generated Node #0,1: 58:[42, 28, 39] Operation: 91-52=39 Exploring Operation: 91-28=63, Resulting Numbers: [42, 52, 63] Generated Node #0,2: 58:[42, 52, 63] Operation: 91-28=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[52, 28, 49], Operations: ['91-42=49'] Exploring Operation: 49-28=21, Resulting Numbers: [52, 21] Generated Node #0,0,0: 58:[52, 21] Operation: 49-28=21 Exploring Operation: 52-28=24, Resulting Numbers: [49, 24] Generated Node #0,0,1: 58:[49, 24] Operation: 52-28=24 Exploring Operation: 52-49=3, Resulting Numbers: [28, 3] Generated Node #0,0,2: 58:[28, 3] Operation: 52-49=3 Moving to Node #0,0,2 Current State: 58:[28, 3], Operations: ['91-42=49', '52-49=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,58 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[52, 21], Operations: ['91-42=49', '49-28=21'] Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,58 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[49, 24], Operations: ['91-42=49', '52-28=24'] Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,58 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,58 unequal: No Solution No 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: 58:[42, 28, 39], Operations: ['91-52=39'] Exploring Operation: 42+28=70, Resulting Numbers: [39, 70] Generated Node #0,1,0: 58:[39, 70] Operation: 42+28=70 Exploring Operation: 42-39=3, Resulting Numbers: [28, 3] Generated Node #0,1,1: 58:[28, 3] Operation: 42-39=3 Exploring Operation: 42-28=14, Resulting Numbers: [39, 14] Generated Node #0,1,2: 58:[39, 14] Operation: 42-28=14 Moving to Node #0,1,1 Current State: 58:[28, 3], Operations: ['91-52=39', '42-39=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[39, 70], Operations: ['91-52=39', '42+28=70'] Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,58 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[39, 14], Operations: ['91-52=39', '42-28=14'] Exploring Operation: 39+14=53, Resulting Numbers: [53] 53,58 unequal: No Solution Exploring Operation: 39*14=546, Resulting Numbers: [546] 546,58 unequal: No Solution Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,58 unequal: No Solution No 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: 58:[42, 52, 63], Operations: ['91-28=63'] Exploring Operation: 63-52=11, Resulting Numbers: [42, 11] Generated Node #0,2,0: 58:[42, 11] Operation: 63-52=11 Exploring Operation: 52-42=10, Resulting Numbers: [63, 10] Generated Node #0,2,1: 58:[63, 10] Operation: 52-42=10 Exploring Operation: 63-42=21, Resulting Numbers: [52, 21] Generated Node #0,2,2: 58:[52, 21] Operation: 63-42=21 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 58:[63, 10], Operations: ['91-28=63', '52-42=10'] Exploring Operation: 63*10=630, Resulting Numbers: [630] 630,58 unequal: No Solution Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,58 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,58 unequal: No Solution No 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: 58:[52, 21], Operations: ['91-28=63', '63-42=21'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,58 unequal: No Solution No 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: 58:[42, 11], Operations: ['91-28=63', '63-52=11'] Exploring Operation: 42*11=462, Resulting Numbers: [462] 462,58 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 42+11=53, Resulting Numbers: [53] 53,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 42, 11, 40, 2 ]
16
[ "40-11=29", "2*29=58", "58-42=16" ]
Current State: 16:[42, 11, 40, 2], Operations: [] Exploring Operation: 40-11=29, Resulting Numbers: [42, 2, 29] Generated Node #2: [42, 2, 29] from Operation: 40-11=29 Current State: 16:[42, 2, 29], Operations: ['40-11=29'] Exploring Operation: 2*29=58, Resulting Numbers: [42, 58] Generated Node #3: [42, 58] from Operation: 2*29=58 Current State: 16:[42, 58], Operations: ['40-11=29', '2*29=58'] Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[42, 11, 40, 2], Operations: [] Exploring Operation: 42-11=31, Resulting Numbers: [40, 2, 31] Generated Node #0,0: 16:[40, 2, 31] Operation: 42-11=31 Exploring Operation: 42/2=21, Resulting Numbers: [11, 40, 21] Generated Node #0,1: 16:[11, 40, 21] Operation: 42/2=21 Exploring Operation: 40/2=20, Resulting Numbers: [42, 11, 20] Generated Node #0,2: 16:[42, 11, 20] Operation: 40/2=20 Exploring Operation: 42-40=2, Resulting Numbers: [11, 2, 2] Generated Node #0,3: 16:[11, 2, 2] Operation: 42-40=2 Moving to Node #0,3 Current State: 16:[11, 2, 2], Operations: ['42-40=2'] Exploring Operation: 11-2=9, Resulting Numbers: [2, 9] Generated Node #0,3,0: 16:[2, 9] Operation: 11-2=9 Exploring Operation: 11+2=13, Resulting Numbers: [2, 13] Generated Node #0,3,1: 16:[2, 13] Operation: 11+2=13 Exploring Operation: 11-2=9, Resulting Numbers: [2, 9] Generated Node #0,3,2: 16:[2, 9] Operation: 11-2=9 Exploring Operation: 11+2=13, Resulting Numbers: [2, 13] Generated Node #0,3,3: 16:[2, 13] Operation: 11+2=13 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 16:[2, 9], Operations: ['42-40=2', '11-2=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,16 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 16:[2, 9], Operations: ['42-40=2', '11-2=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 16:[2, 13], Operations: ['42-40=2', '11+2=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 16:[2, 13], Operations: ['42-40=2', '11+2=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,16 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,16 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: 16:[11, 40, 21], Operations: ['42/2=21'] Exploring Operation: 40-11=29, Resulting Numbers: [21, 29] Generated Node #0,1,0: 16:[21, 29] Operation: 40-11=29 Exploring Operation: 40-21=19, Resulting Numbers: [11, 19] Generated Node #0,1,1: 16:[11, 19] Operation: 40-21=19 Exploring Operation: 21-11=10, Resulting Numbers: [40, 10] Generated Node #0,1,2: 16:[40, 10] Operation: 21-11=10 Exploring Operation: 11+40=51, Resulting Numbers: [21, 51] Generated Node #0,1,3: 16:[21, 51] Operation: 11+40=51 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[11, 19], Operations: ['42/2=21', '40-21=19'] Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,16 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[21, 29], Operations: ['42/2=21', '40-11=29'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,16 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 16:[40, 10], Operations: ['42/2=21', '21-11=10'] Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,16 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 16:[21, 51], Operations: ['42/2=21', '11+40=51'] Exploring Operation: 21*51=1071, Resulting Numbers: [1071] 1071,16 unequal: No Solution Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,16 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,16 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: 16:[42, 11, 20], Operations: ['40/2=20'] Exploring Operation: 42-20=22, Resulting Numbers: [11, 22] Generated Node #0,2,0: 16:[11, 22] Operation: 42-20=22 Exploring Operation: 20-11=9, Resulting Numbers: [42, 9] Generated Node #0,2,1: 16:[42, 9] Operation: 20-11=9 Exploring Operation: 42-11=31, Resulting Numbers: [20, 31] Generated Node #0,2,2: 16:[20, 31] Operation: 42-11=31 Exploring Operation: 42+11=53, Resulting Numbers: [20, 53] Generated Node #0,2,3: 16:[20, 53] Operation: 42+11=53 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[11, 22], Operations: ['40/2=20', '42-20=22'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[20, 31], Operations: ['40/2=20', '42-11=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[42, 9], Operations: ['40/2=20', '20-11=9'] Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,16 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[20, 53], Operations: ['40/2=20', '42+11=53'] Exploring Operation: 53-20=33, Resulting Numbers: [33] 33,16 unequal: No Solution Exploring Operation: 20+53=73, Resulting Numbers: [73] 73,16 unequal: No Solution Exploring Operation: 20*53=1060, Resulting Numbers: [1060] 1060,16 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: 16:[40, 2, 31], Operations: ['42-11=31'] Exploring Operation: 40-31=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 16:[2, 9] Operation: 40-31=9 Exploring Operation: 40/2=20, Resulting Numbers: [31, 20] Generated Node #0,0,1: 16:[31, 20] Operation: 40/2=20 Exploring Operation: 40-2=38, Resulting Numbers: [31, 38] Generated Node #0,0,2: 16:[31, 38] Operation: 40-2=38 Exploring Operation: 31-2=29, Resulting Numbers: [40, 29] Generated Node #0,0,3: 16:[40, 29] Operation: 31-2=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[2, 9], Operations: ['42-11=31', '40-31=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[31, 20], Operations: ['42-11=31', '40/2=20'] Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,16 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[31, 38], Operations: ['42-11=31', '40-2=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[40, 29], Operations: ['42-11=31', '31-2=29'] Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 40*29=1160, Resulting Numbers: [1160] 1160,16 unequal: No Solution Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,16 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
[ 7, 2, 71, 51 ]
25
[ "7-2=5", "71-51=20", "5+20=25" ]
Current State: 25:[7, 2, 71, 51], Operations: [] Exploring Operation: 7-2=5, Resulting Numbers: [71, 51, 5] Generated Node #2: [71, 51, 5] from Operation: 7-2=5 Current State: 25:[71, 51, 5], Operations: ['7-2=5'] Exploring Operation: 71-51=20, Resulting Numbers: [5, 20] Generated Node #3: [5, 20] from Operation: 71-51=20 Current State: 25:[5, 20], Operations: ['7-2=5', '71-51=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[7, 2, 71, 51], Operations: [] Exploring Operation: 71-7=64, Resulting Numbers: [2, 51, 64] Generated Node #0,0: 25:[2, 51, 64] Operation: 71-7=64 Exploring Operation: 7-2=5, Resulting Numbers: [71, 51, 5] Generated Node #0,1: 25:[71, 51, 5] Operation: 7-2=5 Exploring Operation: 71-51=20, Resulting Numbers: [7, 2, 20] Generated Node #0,2: 25:[7, 2, 20] Operation: 71-51=20 Exploring Operation: 51-7=44, Resulting Numbers: [2, 71, 44] Generated Node #0,3: 25:[2, 71, 44] Operation: 51-7=44 Moving to Node #0,2 Current State: 25:[7, 2, 20], Operations: ['71-51=20'] Exploring Operation: 7-2=5, Resulting Numbers: [20, 5] Generated Node #0,2,0: 25:[20, 5] Operation: 7-2=5 Exploring Operation: 7+20=27, Resulting Numbers: [2, 27] Generated Node #0,2,1: 25:[2, 27] Operation: 7+20=27 Exploring Operation: 2+20=22, Resulting Numbers: [7, 22] Generated Node #0,2,2: 25:[7, 22] Operation: 2+20=22 Exploring Operation: 20/2=10, Resulting Numbers: [7, 10] Generated Node #0,2,3: 25:[7, 10] Operation: 20/2=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[20, 5], Operations: ['71-51=20', '7-2=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,25 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[7, 2, 71, 51], Operations: [] Exploring Operation: 71-51=20, Resulting Numbers: [7, 2, 20] Generated Node #0,2: 25:[7, 2, 20] Operation: 71-51=20 Moving to Node #0,2 Current State: 25:[7, 2, 20], Operations: ['71-51=20'] Exploring Operation: 7-2=5, Resulting Numbers: [20, 5] Generated Node #0,2,0: 25:[20, 5] Operation: 7-2=5 Moving to Node #0,2,0 Current State: 25:[20, 5], Operations: ['71-51=20', '7-2=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 19, 44, 81, 91 ]
73
[ "19+44=63", "91-81=10", "63+10=73" ]
Current State: 73:[19, 44, 81, 91], Operations: [] Exploring Operation: 19+44=63, Resulting Numbers: [81, 91, 63] Generated Node #2: [81, 91, 63] from Operation: 19+44=63 Current State: 73:[81, 91, 63], Operations: ['19+44=63'] Exploring Operation: 91-81=10, Resulting Numbers: [63, 10] Generated Node #3: [63, 10] from Operation: 91-81=10 Current State: 73:[63, 10], Operations: ['19+44=63', '91-81=10'] Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[19, 44, 81, 91], Operations: [] Exploring Operation: 91-19=72, Resulting Numbers: [44, 81, 72] Generated Node #0,0: 73:[44, 81, 72] Operation: 91-19=72 Exploring Operation: 19+44=63, Resulting Numbers: [81, 91, 63] Generated Node #0,1: 73:[81, 91, 63] Operation: 19+44=63 Moving to Node #0,1 Current State: 73:[81, 91, 63], Operations: ['19+44=63'] Exploring Operation: 91-63=28, Resulting Numbers: [81, 28] Generated Node #0,1,0: 73:[81, 28] Operation: 91-63=28 Exploring Operation: 91-81=10, Resulting Numbers: [63, 10] Generated Node #0,1,1: 73:[63, 10] Operation: 91-81=10 Moving to Node #0,0 Current State: 73:[44, 81, 72], Operations: ['91-19=72'] Exploring Operation: 81-44=37, Resulting Numbers: [72, 37] Generated Node #0,0,0: 73:[72, 37] Operation: 81-44=37 Exploring Operation: 44+72=116, Resulting Numbers: [81, 116] Generated Node #0,0,1: 73:[81, 116] Operation: 44+72=116 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[72, 37], Operations: ['91-19=72', '81-44=37'] Exploring Operation: 72-37=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 72+37=109, Resulting Numbers: [109] 109,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[81, 116], Operations: ['91-19=72', '44+72=116'] Exploring Operation: 116-81=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 81+116=197, Resulting Numbers: [197] 197,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 73:[81, 28], Operations: ['19+44=63', '91-63=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[63, 10], Operations: ['19+44=63', '91-81=10'] Exploring Operation: 63-10=53, Resulting Numbers: [53] 53,73 unequal: No Solution Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[19, 44, 81, 91], Operations: [] Exploring Operation: 19+44=63, Resulting Numbers: [81, 91, 63] Generated Node #0,1: 73:[81, 91, 63] Operation: 19+44=63 Moving to Node #0,1 Current State: 73:[81, 91, 63], Operations: ['19+44=63'] Exploring Operation: 91-81=10, Resulting Numbers: [63, 10] Generated Node #0,1,1: 73:[63, 10] Operation: 91-81=10 Moving to Node #0,1,1 Current State: 73:[63, 10], Operations: ['19+44=63', '91-81=10'] Exploring Operation: 63+10=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
0.984375
hs_2
mult_heuristic
[ 74, 76, 87, 68 ]
38
[ "76-74=2", "87-68=19", "2*19=38" ]
Current State: 38:[74, 76, 87, 68], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [87, 68, 2] Generated Node #2: [87, 68, 2] from Operation: 76-74=2 Current State: 38:[87, 68, 2], Operations: ['76-74=2'] Exploring Operation: 87-68=19, Resulting Numbers: [2, 19] Generated Node #3: [2, 19] from Operation: 87-68=19 Current State: 38:[2, 19], Operations: ['76-74=2', '87-68=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[74, 76, 87, 68], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [74, 68, 11] Generated Node #0,0: 38:[74, 68, 11] Operation: 87-76=11 Exploring Operation: 87-74=13, Resulting Numbers: [76, 68, 13] Generated Node #0,1: 38:[76, 68, 13] Operation: 87-74=13 Moving to Node #0,0 Current State: 38:[74, 68, 11], Operations: ['87-76=11'] Exploring Operation: 74-68=6, Resulting Numbers: [11, 6] Generated Node #0,0,0: 38:[11, 6] Operation: 74-68=6 Exploring Operation: 74-11=63, Resulting Numbers: [68, 63] Generated Node #0,0,1: 38:[68, 63] Operation: 74-11=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[11, 6], Operations: ['87-76=11', '74-68=6'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[68, 63], Operations: ['87-76=11', '74-11=63'] Exploring Operation: 68+63=131, Resulting Numbers: [131] 131,38 unequal: No Solution Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,38 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:[76, 68, 13], Operations: ['87-74=13'] Exploring Operation: 76-68=8, Resulting Numbers: [13, 8] Generated Node #0,1,0: 38:[13, 8] Operation: 76-68=8 Exploring Operation: 76-13=63, Resulting Numbers: [68, 63] Generated Node #0,1,1: 38:[68, 63] Operation: 76-13=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[13, 8], Operations: ['87-74=13', '76-68=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,38 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:[68, 63], Operations: ['87-74=13', '76-13=63'] Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 68+63=131, Resulting Numbers: [131] 131,38 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
[ 87, 2, 44, 95 ]
69
[ "87-44=43", "95+43=138", "138/2=69" ]
Current State: 69:[87, 2, 44, 95], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [2, 95, 43] Generated Node #2: [2, 95, 43] from Operation: 87-44=43 Current State: 69:[2, 95, 43], Operations: ['87-44=43'] Exploring Operation: 95+43=138, Resulting Numbers: [2, 138] Generated Node #3: [2, 138] from Operation: 95+43=138 Current State: 69:[2, 138], Operations: ['87-44=43', '95+43=138'] Exploring Operation: 138/2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[87, 2, 44, 95], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [2, 44, 8] Generated Node #0,0: 69:[2, 44, 8] Operation: 95-87=8 Moving to Node #0,0 Current State: 69:[2, 44, 8], Operations: ['95-87=8'] Exploring Operation: 44/2=22, Resulting Numbers: [8, 22] Generated Node #0,0,0: 69:[8, 22] Operation: 44/2=22 Moving to Node #0,0,0 Current State: 69:[8, 22], Operations: ['95-87=8', '44/2=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 25, 10, 70, 83 ]
75
[ "10+70=80", "83-80=3", "25*3=75" ]
Current State: 75:[25, 10, 70, 83], Operations: [] Exploring Operation: 10+70=80, Resulting Numbers: [25, 83, 80] Generated Node #2: [25, 83, 80] from Operation: 10+70=80 Current State: 75:[25, 83, 80], Operations: ['10+70=80'] Exploring Operation: 83-80=3, Resulting Numbers: [25, 3] Generated Node #3: [25, 3] from Operation: 83-80=3 Current State: 75:[25, 3], Operations: ['10+70=80', '83-80=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[25, 10, 70, 83], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [25, 83, 7] Generated Node #0,0: 75:[25, 83, 7] Operation: 70/10=7 Exploring Operation: 83-70=13, Resulting Numbers: [25, 10, 13] Generated Node #0,1: 75:[25, 10, 13] Operation: 83-70=13 Exploring Operation: 83-10=73, Resulting Numbers: [25, 70, 73] Generated Node #0,2: 75:[25, 70, 73] Operation: 83-10=73 Moving to Node #0,1 Current State: 75:[25, 10, 13], Operations: ['83-70=13'] Exploring Operation: 13-10=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 75:[25, 3] Operation: 13-10=3 Exploring Operation: 10+13=23, Resulting Numbers: [25, 23] Generated Node #0,1,1: 75:[25, 23] Operation: 10+13=23 Exploring Operation: 25-10=15, Resulting Numbers: [13, 15] Generated Node #0,1,2: 75:[13, 15] Operation: 25-10=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[25, 3], Operations: ['83-70=13', '13-10=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[25, 10, 70, 83], Operations: [] Exploring Operation: 83-70=13, Resulting Numbers: [25, 10, 13] Generated Node #0,1: 75:[25, 10, 13] Operation: 83-70=13 Moving to Node #0,1 Current State: 75:[25, 10, 13], Operations: ['83-70=13'] Exploring Operation: 13-10=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 75:[25, 3] Operation: 13-10=3 Moving to Node #0,1,0 Current State: 75:[25, 3], Operations: ['83-70=13', '13-10=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 7, 59, 5, 68 ]
26
[ "7*5=35", "68-59=9", "35-9=26" ]
Current State: 26:[7, 59, 5, 68], Operations: [] Exploring Operation: 7*5=35, Resulting Numbers: [59, 68, 35] Generated Node #2: [59, 68, 35] from Operation: 7*5=35 Current State: 26:[59, 68, 35], Operations: ['7*5=35'] Exploring Operation: 68-59=9, Resulting Numbers: [35, 9] Generated Node #3: [35, 9] from Operation: 68-59=9 Current State: 26:[35, 9], Operations: ['7*5=35', '68-59=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[7, 59, 5, 68], Operations: [] Exploring Operation: 59-7=52, Resulting Numbers: [5, 68, 52] Generated Node #0,0: 26:[5, 68, 52] Operation: 59-7=52 Exploring Operation: 68-59=9, Resulting Numbers: [7, 5, 9] Generated Node #0,1: 26:[7, 5, 9] Operation: 68-59=9 Moving to Node #0,1 Current State: 26:[7, 5, 9], Operations: ['68-59=9'] Exploring Operation: 9-7=2, Resulting Numbers: [5, 2] Generated Node #0,1,0: 26:[5, 2] Operation: 9-7=2 Exploring Operation: 7-5=2, Resulting Numbers: [9, 2] Generated Node #0,1,1: 26:[9, 2] Operation: 7-5=2 Moving to Node #0,0 Current State: 26:[5, 68, 52], Operations: ['59-7=52'] Exploring Operation: 68-5=63, Resulting Numbers: [52, 63] Generated Node #0,0,0: 26:[52, 63] Operation: 68-5=63 Exploring Operation: 68-52=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 26:[5, 16] Operation: 68-52=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[5, 16], Operations: ['59-7=52', '68-52=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,26 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[52, 63], Operations: ['59-7=52', '68-5=63'] Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,26 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 26:[5, 2], Operations: ['68-59=9', '9-7=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,26 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[9, 2], Operations: ['68-59=9', '7-5=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,26 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 11, 4, 56, 66 ]
84
[ "11*4=44", "56*66=3696", "3696/44=84" ]
Current State: 84:[11, 4, 56, 66], Operations: [] Exploring Operation: 11*4=44, Resulting Numbers: [56, 66, 44] Generated Node #2: [56, 66, 44] from Operation: 11*4=44 Current State: 84:[56, 66, 44], Operations: ['11*4=44'] Exploring Operation: 56*66=3696, Resulting Numbers: [44, 3696] Generated Node #3: [44, 3696] from Operation: 56*66=3696 Current State: 84:[44, 3696], Operations: ['11*4=44', '56*66=3696'] Exploring Operation: 3696/44=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[11, 4, 56, 66], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [11, 4, 10] Generated Node #0,0: 84:[11, 4, 10] Operation: 66-56=10 Exploring Operation: 66/11=6, Resulting Numbers: [4, 56, 6] Generated Node #0,1: 84:[4, 56, 6] Operation: 66/11=6 Exploring Operation: 56-11=45, Resulting Numbers: [4, 66, 45] Generated Node #0,2: 84:[4, 66, 45] Operation: 56-11=45 Exploring Operation: 56/4=14, Resulting Numbers: [11, 66, 14] Generated Node #0,3: 84:[11, 66, 14] Operation: 56/4=14 Exploring Operation: 11+66=77, Resulting Numbers: [4, 56, 77] Generated Node #0,4: 84:[4, 56, 77] Operation: 11+66=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[11, 4, 10], Operations: ['66-56=10'] Exploring Operation: 11+10=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 84:[4, 21] Operation: 11+10=21 Exploring Operation: 11-4=7, Resulting Numbers: [10, 7] Generated Node #0,0,1: 84:[10, 7] Operation: 11-4=7 Exploring Operation: 11-10=1, Resulting Numbers: [4, 1] Generated Node #0,0,2: 84:[4, 1] Operation: 11-10=1 Exploring Operation: 4+10=14, Resulting Numbers: [11, 14] Generated Node #0,0,3: 84:[11, 14] Operation: 4+10=14 Exploring Operation: 10-4=6, Resulting Numbers: [11, 6] Generated Node #0,0,4: 84:[11, 6] Operation: 10-4=6 Moving to Node #0,0,0 Current State: 84:[4, 21], Operations: ['66-56=10', '11+10=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[11, 4, 56, 66], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [11, 4, 10] Generated Node #0,0: 84:[11, 4, 10] Operation: 66-56=10 Moving to Node #0,0 Current State: 84:[11, 4, 10], Operations: ['66-56=10'] Exploring Operation: 11+10=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 84:[4, 21] Operation: 11+10=21 Moving to Node #0,0,0 Current State: 84:[4, 21], Operations: ['66-56=10', '11+10=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 45, 63, 54, 15 ]
40
[ "63-15=48", "45*48=2160", "2160/54=40" ]
Current State: 40:[45, 63, 54, 15], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [45, 54, 48] Generated Node #2: [45, 54, 48] from Operation: 63-15=48 Current State: 40:[45, 54, 48], Operations: ['63-15=48'] Exploring Operation: 45*48=2160, Resulting Numbers: [54, 2160] Generated Node #3: [54, 2160] from Operation: 45*48=2160 Current State: 40:[54, 2160], Operations: ['63-15=48', '45*48=2160'] Exploring Operation: 2160/54=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[45, 63, 54, 15], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [45, 15, 9] Generated Node #0,0: 40:[45, 15, 9] Operation: 63-54=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[45, 15, 9], Operations: ['63-54=9'] Exploring Operation: 45/15=3, Resulting Numbers: [9, 3] Generated Node #0,0,0: 40:[9, 3] Operation: 45/15=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[9, 3], Operations: ['63-54=9', '45/15=3'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 10, 90, 97, 12 ]
94
[ "90/10=9", "97-12=85", "9+85=94" ]
Current State: 94:[10, 90, 97, 12], Operations: [] Exploring Operation: 90/10=9, Resulting Numbers: [97, 12, 9] Generated Node #2: [97, 12, 9] from Operation: 90/10=9 Current State: 94:[97, 12, 9], Operations: ['90/10=9'] Exploring Operation: 97-12=85, Resulting Numbers: [9, 85] Generated Node #3: [9, 85] from Operation: 97-12=85 Current State: 94:[9, 85], Operations: ['90/10=9', '97-12=85'] Exploring Operation: 9+85=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[10, 90, 97, 12], Operations: [] Exploring Operation: 10+90=100, Resulting Numbers: [97, 12, 100] Generated Node #0,0: 94:[97, 12, 100] Operation: 10+90=100 Exploring Operation: 12-10=2, Resulting Numbers: [90, 97, 2] Generated Node #0,1: 94:[90, 97, 2] Operation: 12-10=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[90, 97, 2], Operations: ['12-10=2'] Exploring Operation: 97-90=7, Resulting Numbers: [2, 7] Generated Node #0,1,0: 94:[2, 7] Operation: 97-90=7 Exploring Operation: 90+2=92, Resulting Numbers: [97, 92] Generated Node #0,1,1: 94:[97, 92] Operation: 90+2=92 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[2, 7], Operations: ['12-10=2', '97-90=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[97, 92], Operations: ['12-10=2', '90+2=92'] Exploring Operation: 97-92=5, Resulting Numbers: [5] 5,94 unequal: No Solution Exploring Operation: 97+92=189, Resulting Numbers: [189] 189,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[97, 12, 100], Operations: ['10+90=100'] Exploring Operation: 100-97=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 94:[12, 3] Operation: 100-97=3 Exploring Operation: 100-12=88, Resulting Numbers: [97, 88] Generated Node #0,0,1: 94:[97, 88] Operation: 100-12=88 Moving to Node #0,0,1 Current State: 94:[97, 88], Operations: ['10+90=100', '100-12=88'] Exploring Operation: 97-88=9, Resulting Numbers: [9] 9,94 unequal: No Solution Exploring Operation: 97+88=185, Resulting Numbers: [185] 185,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[12, 3], Operations: ['10+90=100', '100-97=3'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 9, 77, 32, 47 ]
52
[ "77-32=45", "45/9=5", "47+5=52" ]
Current State: 52:[9, 77, 32, 47], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [9, 47, 45] Generated Node #2: [9, 47, 45] from Operation: 77-32=45 Current State: 52:[9, 47, 45], Operations: ['77-32=45'] Exploring Operation: 45/9=5, Resulting Numbers: [47, 5] Generated Node #3: [47, 5] from Operation: 45/9=5 Current State: 52:[47, 5], Operations: ['77-32=45', '45/9=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[9, 77, 32, 47], Operations: [] Exploring Operation: 47-32=15, Resulting Numbers: [9, 77, 15] Generated Node #0,0: 52:[9, 77, 15] Operation: 47-32=15 Exploring Operation: 77-47=30, Resulting Numbers: [9, 32, 30] Generated Node #0,1: 52:[9, 32, 30] Operation: 77-47=30 Exploring Operation: 77-32=45, Resulting Numbers: [9, 47, 45] Generated Node #0,2: 52:[9, 47, 45] Operation: 77-32=45 Exploring Operation: 77-9=68, Resulting Numbers: [32, 47, 68] Generated Node #0,3: 52:[32, 47, 68] Operation: 77-9=68 Moving to Node #0,1 Current State: 52:[9, 32, 30], Operations: ['77-47=30'] Exploring Operation: 30-9=21, Resulting Numbers: [32, 21] Generated Node #0,1,0: 52:[32, 21] Operation: 30-9=21 Exploring Operation: 32+30=62, Resulting Numbers: [9, 62] Generated Node #0,1,1: 52:[9, 62] Operation: 32+30=62 Exploring Operation: 32-9=23, Resulting Numbers: [30, 23] Generated Node #0,1,2: 52:[30, 23] Operation: 32-9=23 Exploring Operation: 32-30=2, Resulting Numbers: [9, 2] Generated Node #0,1,3: 52:[9, 2] Operation: 32-30=2 Moving to Node #0,2 Current State: 52:[9, 47, 45], Operations: ['77-32=45'] Exploring Operation: 9+45=54, Resulting Numbers: [47, 54] Generated Node #0,2,0: 52:[47, 54] Operation: 9+45=54 Exploring Operation: 9+47=56, Resulting Numbers: [45, 56] Generated Node #0,2,1: 52:[45, 56] Operation: 9+47=56 Exploring Operation: 45/9=5, Resulting Numbers: [47, 5] Generated Node #0,2,2: 52:[47, 5] Operation: 45/9=5 Exploring Operation: 47-45=2, Resulting Numbers: [9, 2] Generated Node #0,2,3: 52:[9, 2] Operation: 47-45=2 Moving to Node #0,3 Current State: 52:[32, 47, 68], Operations: ['77-9=68'] Exploring Operation: 32+47=79, Resulting Numbers: [68, 79] Generated Node #0,3,0: 52:[68, 79] Operation: 32+47=79 Exploring Operation: 68-32=36, Resulting Numbers: [47, 36] Generated Node #0,3,1: 52:[47, 36] Operation: 68-32=36 Exploring Operation: 68-47=21, Resulting Numbers: [32, 21] Generated Node #0,3,2: 52:[32, 21] Operation: 68-47=21 Exploring Operation: 47-32=15, Resulting Numbers: [68, 15] Generated Node #0,3,3: 52:[68, 15] Operation: 47-32=15 Moving to Node #0,0 Current State: 52:[9, 77, 15], Operations: ['47-32=15'] Exploring Operation: 77-15=62, Resulting Numbers: [9, 62] Generated Node #0,0,0: 52:[9, 62] Operation: 77-15=62 Exploring Operation: 15-9=6, Resulting Numbers: [77, 6] Generated Node #0,0,1: 52:[77, 6] Operation: 15-9=6 Exploring Operation: 77-9=68, Resulting Numbers: [15, 68] Generated Node #0,0,2: 52:[15, 68] Operation: 77-9=68 Exploring Operation: 9+15=24, Resulting Numbers: [77, 24] Generated Node #0,0,3: 52:[77, 24] Operation: 9+15=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[9, 62], Operations: ['47-32=15', '77-15=62'] Exploring Operation: 62-9=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 9+62=71, Resulting Numbers: [71] 71,52 unequal: No Solution Exploring Operation: 9*62=558, Resulting Numbers: [558] 558,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 52:[15, 68], Operations: ['47-32=15', '77-9=68'] Exploring Operation: 15+68=83, Resulting Numbers: [83] 83,52 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 15*68=1020, Resulting Numbers: [1020] 1020,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[77, 6], Operations: ['47-32=15', '15-9=6'] Exploring Operation: 77*6=462, Resulting Numbers: [462] 462,52 unequal: No Solution Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,52 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 52:[77, 24], Operations: ['47-32=15', '9+15=24'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 77*24=1848, Resulting Numbers: [1848] 1848,52 unequal: No Solution Exploring Operation: 77+24=101, Resulting Numbers: [101] 101,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 52:[9, 2], Operations: ['77-47=30', '32-30=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[9, 2], Operations: ['77-32=45', '47-45=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,52 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[47, 5], Operations: ['77-32=45', '45/9=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[9, 77, 32, 47], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [9, 47, 45] Generated Node #0,2: 52:[9, 47, 45] Operation: 77-32=45 Moving to Node #0,2 Current State: 52:[9, 47, 45], Operations: ['77-32=45'] Exploring Operation: 45/9=5, Resulting Numbers: [47, 5] Generated Node #0,2,2: 52:[47, 5] Operation: 45/9=5 Moving to Node #0,2,2 Current State: 52:[47, 5], Operations: ['77-32=45', '45/9=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.962674
hs_4
mult_heuristic
[ 43, 70, 58, 98 ]
67
[ "70-43=27", "98-58=40", "27+40=67" ]
Current State: 67:[43, 70, 58, 98], Operations: [] Exploring Operation: 70-43=27, Resulting Numbers: [58, 98, 27] Generated Node #2: [58, 98, 27] from Operation: 70-43=27 Current State: 67:[58, 98, 27], Operations: ['70-43=27'] Exploring Operation: 98-58=40, Resulting Numbers: [27, 40] Generated Node #3: [27, 40] from Operation: 98-58=40 Current State: 67:[27, 40], Operations: ['70-43=27', '98-58=40'] Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[43, 70, 58, 98], Operations: [] Exploring Operation: 98-43=55, Resulting Numbers: [70, 58, 55] Generated Node #0,0: 67:[70, 58, 55] Operation: 98-43=55 Moving to Node #0,0 Current State: 67:[70, 58, 55], Operations: ['98-43=55'] Exploring Operation: 58+55=113, Resulting Numbers: [70, 113] Generated Node #0,0,0: 67:[70, 113] Operation: 58+55=113 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[70, 113], Operations: ['98-43=55', '58+55=113'] Exploring Operation: 113-70=43, Resulting Numbers: [43] 43,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 42, 91, 70, 76 ]
97
[ "91-42=49", "70+76=146", "146-49=97" ]
Current State: 97:[42, 91, 70, 76], Operations: [] Exploring Operation: 91-42=49, Resulting Numbers: [70, 76, 49] Generated Node #2: [70, 76, 49] from Operation: 91-42=49 Current State: 97:[70, 76, 49], Operations: ['91-42=49'] Exploring Operation: 70+76=146, Resulting Numbers: [49, 146] Generated Node #3: [49, 146] from Operation: 70+76=146 Current State: 97:[49, 146], Operations: ['91-42=49', '70+76=146'] Exploring Operation: 146-49=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[42, 91, 70, 76], Operations: [] Exploring Operation: 91-42=49, Resulting Numbers: [70, 76, 49] Generated Node #0,0: 97:[70, 76, 49] Operation: 91-42=49 Exploring Operation: 70-42=28, Resulting Numbers: [91, 76, 28] Generated Node #0,1: 97:[91, 76, 28] Operation: 70-42=28 Exploring Operation: 42+70=112, Resulting Numbers: [91, 76, 112] Generated Node #0,2: 97:[91, 76, 112] Operation: 42+70=112 Exploring Operation: 42+91=133, Resulting Numbers: [70, 76, 133] Generated Node #0,3: 97:[70, 76, 133] Operation: 42+91=133 Exploring Operation: 42+76=118, Resulting Numbers: [91, 70, 118] Generated Node #0,4: 97:[91, 70, 118] Operation: 42+76=118 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[91, 76, 112], Operations: ['42+70=112'] Exploring Operation: 91+76=167, Resulting Numbers: [112, 167] Generated Node #0,2,0: 97:[112, 167] Operation: 91+76=167 Exploring Operation: 76+112=188, Resulting Numbers: [91, 188] Generated Node #0,2,1: 97:[91, 188] Operation: 76+112=188 Exploring Operation: 112-76=36, Resulting Numbers: [91, 36] Generated Node #0,2,2: 97:[91, 36] Operation: 112-76=36 Exploring Operation: 112-91=21, Resulting Numbers: [76, 21] Generated Node #0,2,3: 97:[76, 21] Operation: 112-91=21 Exploring Operation: 91-76=15, Resulting Numbers: [112, 15] Generated Node #0,2,4: 97:[112, 15] Operation: 91-76=15 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[91, 36], Operations: ['42+70=112', '112-76=36'] Exploring Operation: 91-36=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 91*36=3276, Resulting Numbers: [3276] 3276,97 unequal: No Solution Exploring Operation: 91+36=127, Resulting Numbers: [127] 127,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[112, 167], Operations: ['42+70=112', '91+76=167'] Exploring Operation: 167-112=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 112*167=18704, Resulting Numbers: [18704] 18704,97 unequal: No Solution Exploring Operation: 112+167=279, Resulting Numbers: [279] 279,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[91, 188], Operations: ['42+70=112', '76+112=188'] Exploring Operation: 188-91=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[42, 91, 70, 76], Operations: [] Exploring Operation: 42+70=112, Resulting Numbers: [91, 76, 112] Generated Node #0,2: 97:[91, 76, 112] Operation: 42+70=112 Moving to Node #0,2 Current State: 97:[91, 76, 112], Operations: ['42+70=112'] Exploring Operation: 76+112=188, Resulting Numbers: [91, 188] Generated Node #0,2,1: 97:[91, 188] Operation: 76+112=188 Moving to Node #0,2,1 Current State: 97:[91, 188], Operations: ['42+70=112', '76+112=188'] Exploring Operation: 188-91=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 48, 49, 43, 62 ]
78
[ "48+49=97", "62-43=19", "97-19=78" ]
Current State: 78:[48, 49, 43, 62], Operations: [] Exploring Operation: 48+49=97, Resulting Numbers: [43, 62, 97] Generated Node #2: [43, 62, 97] from Operation: 48+49=97 Current State: 78:[43, 62, 97], Operations: ['48+49=97'] Exploring Operation: 62-43=19, Resulting Numbers: [97, 19] Generated Node #3: [97, 19] from Operation: 62-43=19 Current State: 78:[97, 19], Operations: ['48+49=97', '62-43=19'] Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[48, 49, 43, 62], Operations: [] Exploring Operation: 62-49=13, Resulting Numbers: [48, 43, 13] Generated Node #0,0: 78:[48, 43, 13] Operation: 62-49=13 Exploring Operation: 49-43=6, Resulting Numbers: [48, 62, 6] Generated Node #0,1: 78:[48, 62, 6] Operation: 49-43=6 Exploring Operation: 62-48=14, Resulting Numbers: [49, 43, 14] Generated Node #0,2: 78:[49, 43, 14] Operation: 62-48=14 Exploring Operation: 49-48=1, Resulting Numbers: [43, 62, 1] Generated Node #0,3: 78:[43, 62, 1] Operation: 49-48=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[48, 43, 13], Operations: ['62-49=13'] Exploring Operation: 48-13=35, Resulting Numbers: [43, 35] Generated Node #0,0,0: 78:[43, 35] Operation: 48-13=35 Exploring Operation: 43-13=30, Resulting Numbers: [48, 30] Generated Node #0,0,1: 78:[48, 30] Operation: 43-13=30 Exploring Operation: 48-43=5, Resulting Numbers: [13, 5] Generated Node #0,0,2: 78:[13, 5] Operation: 48-43=5 Exploring Operation: 48+43=91, Resulting Numbers: [13, 91] Generated Node #0,0,3: 78:[13, 91] Operation: 48+43=91 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 78:[13, 5], Operations: ['62-49=13', '48-43=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,78 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,78 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,78 unequal: No Solution No 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: 78:[43, 35], Operations: ['62-49=13', '48-13=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,78 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[48, 49, 43, 62], Operations: [] Exploring Operation: 62-49=13, Resulting Numbers: [48, 43, 13] Generated Node #0,0: 78:[48, 43, 13] Operation: 62-49=13 Moving to Node #0,0 Current State: 78:[48, 43, 13], Operations: ['62-49=13'] Exploring Operation: 48-13=35, Resulting Numbers: [43, 35] Generated Node #0,0,0: 78:[43, 35] Operation: 48-13=35 Moving to Node #0,0,0 Current State: 78:[43, 35], Operations: ['62-49=13', '48-13=35'] Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 24, 47, 42, 77 ]
36
[ "24+47=71", "77-42=35", "71-35=36" ]
Current State: 36:[24, 47, 42, 77], Operations: [] Exploring Operation: 24+47=71, Resulting Numbers: [42, 77, 71] Generated Node #2: [42, 77, 71] from Operation: 24+47=71 Current State: 36:[42, 77, 71], Operations: ['24+47=71'] Exploring Operation: 77-42=35, Resulting Numbers: [71, 35] Generated Node #3: [71, 35] from Operation: 77-42=35 Current State: 36:[71, 35], Operations: ['24+47=71', '77-42=35'] Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[24, 47, 42, 77], Operations: [] Exploring Operation: 77-42=35, Resulting Numbers: [24, 47, 35] Generated Node #0,0: 36:[24, 47, 35] Operation: 77-42=35 Exploring Operation: 77-47=30, Resulting Numbers: [24, 42, 30] Generated Node #0,1: 36:[24, 42, 30] Operation: 77-47=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[24, 47, 35], Operations: ['77-42=35'] Exploring Operation: 47-35=12, Resulting Numbers: [24, 12] Generated Node #0,0,0: 36:[24, 12] Operation: 47-35=12 Exploring Operation: 47-24=23, Resulting Numbers: [35, 23] Generated Node #0,0,1: 36:[35, 23] Operation: 47-24=23 Moving to Node #0,0,0 Current State: 36:[24, 12], Operations: ['77-42=35', '47-35=12'] Exploring Operation: 24-12=12, Resulting Numbers: [12] 12,36 unequal: No Solution Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[24, 47, 42, 77], Operations: [] Exploring Operation: 77-42=35, Resulting Numbers: [24, 47, 35] Generated Node #0,0: 36:[24, 47, 35] Operation: 77-42=35 Moving to Node #0,0 Current State: 36:[24, 47, 35], Operations: ['77-42=35'] Exploring Operation: 47-35=12, Resulting Numbers: [24, 12] Generated Node #0,0,0: 36:[24, 12] Operation: 47-35=12 Moving to Node #0,0,0 Current State: 36:[24, 12], Operations: ['77-42=35', '47-35=12'] Exploring Operation: 24+12=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 30, 7, 84, 52 ]
55
[ "30-7=23", "84-52=32", "23+32=55" ]
Current State: 55:[30, 7, 84, 52], Operations: [] Exploring Operation: 30-7=23, Resulting Numbers: [84, 52, 23] Generated Node #2: [84, 52, 23] from Operation: 30-7=23 Current State: 55:[84, 52, 23], Operations: ['30-7=23'] Exploring Operation: 84-52=32, Resulting Numbers: [23, 32] Generated Node #3: [23, 32] from Operation: 84-52=32 Current State: 55:[23, 32], Operations: ['30-7=23', '84-52=32'] Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[30, 7, 84, 52], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [30, 52, 12] Generated Node #0,0: 55:[30, 52, 12] Operation: 84/7=12 Exploring Operation: 84-30=54, Resulting Numbers: [7, 52, 54] Generated Node #0,1: 55:[7, 52, 54] Operation: 84-30=54 Moving to Node #0,1 Current State: 55:[7, 52, 54], Operations: ['84-30=54'] Exploring Operation: 7+52=59, Resulting Numbers: [54, 59] Generated Node #0,1,0: 55:[54, 59] Operation: 7+52=59 Exploring Operation: 54-52=2, Resulting Numbers: [7, 2] Generated Node #0,1,1: 55:[7, 2] Operation: 54-52=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[54, 59], Operations: ['84-30=54', '7+52=59'] Exploring Operation: 54+59=113, Resulting Numbers: [113] 113,55 unequal: No Solution Exploring Operation: 59-54=5, Resulting Numbers: [5] 5,55 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 #0,1,1 Current State: 55:[7, 2], Operations: ['84-30=54', '54-52=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,55 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: 55:[30, 52, 12], Operations: ['84/7=12'] Exploring Operation: 52-30=22, Resulting Numbers: [12, 22] Generated Node #0,0,0: 55:[12, 22] Operation: 52-30=22 Exploring Operation: 30-12=18, Resulting Numbers: [52, 18] Generated Node #0,0,1: 55:[52, 18] Operation: 30-12=18 Moving to Node #0,0,1 Current State: 55:[52, 18], Operations: ['84/7=12', '30-12=18'] Exploring Operation: 52+18=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[12, 22], Operations: ['84/7=12', '52-30=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,55 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,55 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 72, 68, 70, 34 ]
89
[ "70-68=2", "34/2=17", "72+17=89" ]
Current State: 89:[72, 68, 70, 34], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [72, 34, 2] Generated Node #2: [72, 34, 2] from Operation: 70-68=2 Current State: 89:[72, 34, 2], Operations: ['70-68=2'] Exploring Operation: 34/2=17, Resulting Numbers: [72, 17] Generated Node #3: [72, 17] from Operation: 34/2=17 Current State: 89:[72, 17], Operations: ['70-68=2', '34/2=17'] Exploring Operation: 72+17=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[72, 68, 70, 34], Operations: [] Exploring Operation: 70+34=104, Resulting Numbers: [72, 68, 104] Generated Node #0,0: 89:[72, 68, 104] Operation: 70+34=104 Exploring Operation: 72-34=38, Resulting Numbers: [68, 70, 38] Generated Node #0,1: 89:[68, 70, 38] Operation: 72-34=38 Exploring Operation: 72+34=106, Resulting Numbers: [68, 70, 106] Generated Node #0,2: 89:[68, 70, 106] Operation: 72+34=106 Exploring Operation: 68+34=102, Resulting Numbers: [72, 70, 102] Generated Node #0,3: 89:[72, 70, 102] Operation: 68+34=102 Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[72, 70, 102], Operations: ['68+34=102'] Exploring Operation: 72-70=2, Resulting Numbers: [102, 2] Generated Node #0,3,0: 89:[102, 2] Operation: 72-70=2 Exploring Operation: 102-70=32, Resulting Numbers: [72, 32] Generated Node #0,3,1: 89:[72, 32] Operation: 102-70=32 Exploring Operation: 72+70=142, Resulting Numbers: [102, 142] Generated Node #0,3,2: 89:[102, 142] Operation: 72+70=142 Exploring Operation: 102-72=30, Resulting Numbers: [70, 30] Generated Node #0,3,3: 89:[70, 30] Operation: 102-72=30 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 89:[102, 142], Operations: ['68+34=102', '72+70=142'] Exploring Operation: 102*142=14484, Resulting Numbers: [14484] 14484,89 unequal: No Solution Exploring Operation: 142-102=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 102+142=244, Resulting Numbers: [244] 244,89 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 #0,3,1 Current State: 89:[72, 32], Operations: ['68+34=102', '102-70=32'] Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 72*32=2304, Resulting Numbers: [2304] 2304,89 unequal: No Solution Exploring Operation: 72+32=104, Resulting Numbers: [104] 104,89 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 #0,3,3 Current State: 89:[70, 30], Operations: ['68+34=102', '102-72=30'] Exploring Operation: 70-30=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 70+30=100, Resulting Numbers: [100] 100,89 unequal: No Solution Exploring Operation: 70*30=2100, Resulting Numbers: [2100] 2100,89 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 #0,3,0 Current State: 89:[102, 2], Operations: ['68+34=102', '72-70=2'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,89 unequal: No Solution Exploring Operation: 102*2=204, Resulting Numbers: [204] 204,89 unequal: No Solution Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,89 unequal: No Solution Exploring Operation: 102+2=104, Resulting Numbers: [104] 104,89 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 #0,0 Current State: 89:[72, 68, 104], Operations: ['70+34=104'] Exploring Operation: 104-72=32, Resulting Numbers: [68, 32] Generated Node #0,0,0: 89:[68, 32] Operation: 104-72=32 Exploring Operation: 72+68=140, Resulting Numbers: [104, 140] Generated Node #0,0,1: 89:[104, 140] Operation: 72+68=140 Exploring Operation: 72-68=4, Resulting Numbers: [104, 4] Generated Node #0,0,2: 89:[104, 4] Operation: 72-68=4 Exploring Operation: 104-68=36, Resulting Numbers: [72, 36] Generated Node #0,0,3: 89:[72, 36] Operation: 104-68=36 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[104, 140], Operations: ['70+34=104', '72+68=140'] Exploring Operation: 104+140=244, Resulting Numbers: [244] 244,89 unequal: No Solution Exploring Operation: 140-104=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 104*140=14560, Resulting Numbers: [14560] 14560,89 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:[72, 36], Operations: ['70+34=104', '104-68=36'] Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,89 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 72*36=2592, Resulting Numbers: [2592] 2592,89 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:[68, 32], Operations: ['70+34=104', '104-72=32'] Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,89 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,89 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:[104, 4], Operations: ['70+34=104', '72-68=4'] Exploring Operation: 104+4=108, Resulting Numbers: [108] 108,89 unequal: No Solution Exploring Operation: 104-4=100, Resulting Numbers: [100] 100,89 unequal: No Solution Exploring Operation: 104*4=416, Resulting Numbers: [416] 416,89 unequal: No Solution Exploring Operation: 104/4=26, Resulting Numbers: [26] 26,89 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 #0,2 Current State: 89:[68, 70, 106], Operations: ['72+34=106'] Exploring Operation: 70-68=2, Resulting Numbers: [106, 2] Generated Node #0,2,0: 89:[106, 2] Operation: 70-68=2 Exploring Operation: 106-70=36, Resulting Numbers: [68, 36] Generated Node #0,2,1: 89:[68, 36] Operation: 106-70=36 Exploring Operation: 68+70=138, Resulting Numbers: [106, 138] Generated Node #0,2,2: 89:[106, 138] Operation: 68+70=138 Exploring Operation: 106-68=38, Resulting Numbers: [70, 38] Generated Node #0,2,3: 89:[70, 38] Operation: 106-68=38 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[106, 138], Operations: ['72+34=106', '68+70=138'] Exploring Operation: 106*138=14628, Resulting Numbers: [14628] 14628,89 unequal: No Solution Exploring Operation: 138-106=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 106+138=244, Resulting Numbers: [244] 244,89 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 #0,2,3 Current State: 89:[70, 38], Operations: ['72+34=106', '106-68=38'] Exploring Operation: 70-38=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 70*38=2660, Resulting Numbers: [2660] 2660,89 unequal: No Solution Exploring Operation: 70+38=108, Resulting Numbers: [108] 108,89 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 #0,2,1 Current State: 89:[68, 36], Operations: ['72+34=106', '106-70=36'] Exploring Operation: 68+36=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 68-36=32, Resulting Numbers: [32] 32,89 unequal: No Solution Exploring Operation: 68*36=2448, Resulting Numbers: [2448] 2448,89 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 #0,2,0 Current State: 89:[106, 2], Operations: ['72+34=106', '70-68=2'] Exploring Operation: 106/2=53, Resulting Numbers: [53] 53,89 unequal: No Solution Exploring Operation: 106*2=212, Resulting Numbers: [212] 212,89 unequal: No Solution Exploring Operation: 106-2=104, Resulting Numbers: [104] 104,89 unequal: No Solution Exploring Operation: 106+2=108, Resulting Numbers: [108] 108,89 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 #0,1 Current State: 89:[68, 70, 38], Operations: ['72-34=38'] Exploring Operation: 70+38=108, Resulting Numbers: [68, 108] Generated Node #0,1,0: 89:[68, 108] Operation: 70+38=108 Exploring Operation: 68-38=30, Resulting Numbers: [70, 30] Generated Node #0,1,1: 89:[70, 30] Operation: 68-38=30 Exploring Operation: 68+38=106, Resulting Numbers: [70, 106] Generated Node #0,1,2: 89:[70, 106] Operation: 68+38=106 Exploring Operation: 70-38=32, Resulting Numbers: [68, 32] Generated Node #0,1,3: 89:[68, 32] Operation: 70-38=32 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[70, 106], Operations: ['72-34=38', '68+38=106'] Exploring Operation: 70*106=7420, Resulting Numbers: [7420] 7420,89 unequal: No Solution Exploring Operation: 70+106=176, Resulting Numbers: [176] 176,89 unequal: No Solution Exploring Operation: 106-70=36, Resulting Numbers: [36] 36,89 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 #0,1,0 Current State: 89:[68, 108], Operations: ['72-34=38', '70+38=108'] Exploring Operation: 68+108=176, Resulting Numbers: [176] 176,89 unequal: No Solution Exploring Operation: 68*108=7344, Resulting Numbers: [7344] 7344,89 unequal: No Solution Exploring Operation: 108-68=40, Resulting Numbers: [40] 40,89 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 #0,1,1 Current State: 89:[70, 30], Operations: ['72-34=38', '68-38=30'] Exploring Operation: 70*30=2100, Resulting Numbers: [2100] 2100,89 unequal: No Solution Exploring Operation: 70-30=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 70+30=100, Resulting Numbers: [100] 100,89 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 #0,1,3 Current State: 89:[68, 32], Operations: ['72-34=38', '70-38=32'] Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,89 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,89 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,89 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 No solution found.
0
hs_4
sum_heuristic
[ 62, 72, 44, 79 ]
45
[ "72-62=10", "79-44=35", "10+35=45" ]
Current State: 45:[62, 72, 44, 79], Operations: [] Exploring Operation: 72-62=10, Resulting Numbers: [44, 79, 10] Generated Node #2: [44, 79, 10] from Operation: 72-62=10 Current State: 45:[44, 79, 10], Operations: ['72-62=10'] Exploring Operation: 79-44=35, Resulting Numbers: [10, 35] Generated Node #3: [10, 35] from Operation: 79-44=35 Current State: 45:[10, 35], Operations: ['72-62=10', '79-44=35'] Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[62, 72, 44, 79], Operations: [] Exploring Operation: 79-62=17, Resulting Numbers: [72, 44, 17] Generated Node #0,0: 45:[72, 44, 17] Operation: 79-62=17 Exploring Operation: 72-62=10, Resulting Numbers: [44, 79, 10] Generated Node #0,1: 45:[44, 79, 10] Operation: 72-62=10 Exploring Operation: 79-72=7, Resulting Numbers: [62, 44, 7] Generated Node #0,2: 45:[62, 44, 7] Operation: 79-72=7 Exploring Operation: 79-44=35, Resulting Numbers: [62, 72, 35] Generated Node #0,3: 45:[62, 72, 35] Operation: 79-44=35 Moving to Node #0,2 Current State: 45:[62, 44, 7], Operations: ['79-72=7'] Exploring Operation: 62-44=18, Resulting Numbers: [7, 18] Generated Node #0,2,0: 45:[7, 18] Operation: 62-44=18 Exploring Operation: 62+7=69, Resulting Numbers: [44, 69] Generated Node #0,2,1: 45:[44, 69] Operation: 62+7=69 Exploring Operation: 62-7=55, Resulting Numbers: [44, 55] Generated Node #0,2,2: 45:[44, 55] Operation: 62-7=55 Exploring Operation: 44+7=51, Resulting Numbers: [62, 51] Generated Node #0,2,3: 45:[62, 51] Operation: 44+7=51 Moving to Node #0,0 Current State: 45:[72, 44, 17], Operations: ['79-62=17'] Exploring Operation: 44+17=61, Resulting Numbers: [72, 61] Generated Node #0,0,0: 45:[72, 61] Operation: 44+17=61 Exploring Operation: 44-17=27, Resulting Numbers: [72, 27] Generated Node #0,0,1: 45:[72, 27] Operation: 44-17=27 Exploring Operation: 72-44=28, Resulting Numbers: [17, 28] Generated Node #0,0,2: 45:[17, 28] Operation: 72-44=28 Exploring Operation: 72-17=55, Resulting Numbers: [44, 55] Generated Node #0,0,3: 45:[44, 55] Operation: 72-17=55 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[44, 55], Operations: ['79-62=17', '72-17=55'] Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,45 unequal: No Solution Exploring Operation: 44*55=2420, Resulting Numbers: [2420] 2420,45 unequal: No Solution Exploring Operation: 44+55=99, Resulting Numbers: [99] 99,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[17, 28], Operations: ['79-62=17', '72-44=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[62, 72, 44, 79], Operations: [] Exploring Operation: 79-62=17, Resulting Numbers: [72, 44, 17] Generated Node #0,0: 45:[72, 44, 17] Operation: 79-62=17 Moving to Node #0,0 Current State: 45:[72, 44, 17], Operations: ['79-62=17'] Exploring Operation: 72-44=28, Resulting Numbers: [17, 28] Generated Node #0,0,2: 45:[17, 28] Operation: 72-44=28 Moving to Node #0,0,2 Current State: 45:[17, 28], Operations: ['79-62=17', '72-44=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 18, 40, 47, 25 ]
44
[ "40-18=22", "47-25=22", "22+22=44" ]
Current State: 44:[18, 40, 47, 25], Operations: [] Exploring Operation: 40-18=22, Resulting Numbers: [47, 25, 22] Generated Node #2: [47, 25, 22] from Operation: 40-18=22 Current State: 44:[47, 25, 22], Operations: ['40-18=22'] Exploring Operation: 47-25=22, Resulting Numbers: [22, 22] Generated Node #3: [22, 22] from Operation: 47-25=22 Current State: 44:[22, 22], Operations: ['40-18=22', '47-25=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[18, 40, 47, 25], Operations: [] Exploring Operation: 47-25=22, Resulting Numbers: [18, 40, 22] Generated Node #0,0: 44:[18, 40, 22] Operation: 47-25=22 Exploring Operation: 40-18=22, Resulting Numbers: [47, 25, 22] Generated Node #0,1: 44:[47, 25, 22] Operation: 40-18=22 Exploring Operation: 18+25=43, Resulting Numbers: [40, 47, 43] Generated Node #0,2: 44:[40, 47, 43] Operation: 18+25=43 Moving to Node #0,1 Current State: 44:[47, 25, 22], Operations: ['40-18=22'] Exploring Operation: 47-25=22, Resulting Numbers: [22, 22] Generated Node #0,1,0: 44:[22, 22] Operation: 47-25=22 Exploring Operation: 47-22=25, Resulting Numbers: [25, 25] Generated Node #0,1,1: 44:[25, 25] Operation: 47-22=25 Exploring Operation: 25-22=3, Resulting Numbers: [47, 3] Generated Node #0,1,2: 44:[47, 3] Operation: 25-22=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[22, 22], Operations: ['40-18=22', '47-25=22'] Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,44 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[18, 40, 47, 25], Operations: [] Exploring Operation: 40-18=22, Resulting Numbers: [47, 25, 22] Generated Node #0,1: 44:[47, 25, 22] Operation: 40-18=22 Moving to Node #0,1 Current State: 44:[47, 25, 22], Operations: ['40-18=22'] Exploring Operation: 47-25=22, Resulting Numbers: [22, 22] Generated Node #0,1,0: 44:[22, 22] Operation: 47-25=22 Moving to Node #0,1,0 Current State: 44:[22, 22], Operations: ['40-18=22', '47-25=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 89, 39, 72, 3 ]
53
[ "89+39=128", "72+3=75", "128-75=53" ]
Current State: 53:[89, 39, 72, 3], Operations: [] Exploring Operation: 89+39=128, Resulting Numbers: [72, 3, 128] Generated Node #2: [72, 3, 128] from Operation: 89+39=128 Current State: 53:[72, 3, 128], Operations: ['89+39=128'] Exploring Operation: 72+3=75, Resulting Numbers: [128, 75] Generated Node #3: [128, 75] from Operation: 72+3=75 Current State: 53:[128, 75], Operations: ['89+39=128', '72+3=75'] Exploring Operation: 128-75=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[89, 39, 72, 3], Operations: [] Exploring Operation: 39+3=42, Resulting Numbers: [89, 72, 42] Generated Node #0,0: 53:[89, 72, 42] Operation: 39+3=42 Exploring Operation: 89-3=86, Resulting Numbers: [39, 72, 86] Generated Node #0,1: 53:[39, 72, 86] Operation: 89-3=86 Exploring Operation: 89-39=50, Resulting Numbers: [72, 3, 50] Generated Node #0,2: 53:[72, 3, 50] Operation: 89-39=50 Exploring Operation: 72-3=69, Resulting Numbers: [89, 39, 69] Generated Node #0,3: 53:[89, 39, 69] Operation: 72-3=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[89, 72, 42], Operations: ['39+3=42'] Exploring Operation: 72-42=30, Resulting Numbers: [89, 30] Generated Node #0,0,0: 53:[89, 30] Operation: 72-42=30 Exploring Operation: 89-42=47, Resulting Numbers: [72, 47] Generated Node #0,0,1: 53:[72, 47] Operation: 89-42=47 Exploring Operation: 89+42=131, Resulting Numbers: [72, 131] Generated Node #0,0,2: 53:[72, 131] Operation: 89+42=131 Exploring Operation: 89-72=17, Resulting Numbers: [42, 17] Generated Node #0,0,3: 53:[42, 17] Operation: 89-72=17 Moving to Node #0,0,1 Current State: 53:[72, 47], Operations: ['39+3=42', '89-42=47'] Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,53 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[42, 17], Operations: ['39+3=42', '89-72=17'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,53 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,53 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[89, 30], Operations: ['39+3=42', '72-42=30'] Exploring Operation: 89*30=2670, Resulting Numbers: [2670] 2670,53 unequal: No Solution Exploring Operation: 89+30=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[72, 131], Operations: ['39+3=42', '89+42=131'] Exploring Operation: 131-72=59, Resulting Numbers: [59] 59,53 unequal: No Solution Exploring Operation: 72+131=203, Resulting Numbers: [203] 203,53 unequal: No Solution Exploring Operation: 72*131=9432, Resulting Numbers: [9432] 9432,53 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 Current State: 53:[39, 72, 86], Operations: ['89-3=86'] Exploring Operation: 39+72=111, Resulting Numbers: [86, 111] Generated Node #0,1,0: 53:[86, 111] Operation: 39+72=111 Exploring Operation: 72-39=33, Resulting Numbers: [86, 33] Generated Node #0,1,1: 53:[86, 33] Operation: 72-39=33 Exploring Operation: 86-39=47, Resulting Numbers: [72, 47] Generated Node #0,1,2: 53:[72, 47] Operation: 86-39=47 Exploring Operation: 86-72=14, Resulting Numbers: [39, 14] Generated Node #0,1,3: 53:[39, 14] Operation: 86-72=14 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[72, 47], Operations: ['89-3=86', '86-39=47'] Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,53 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[86, 33], Operations: ['89-3=86', '72-39=33'] Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[89, 39, 72, 3], Operations: [] Exploring Operation: 89-3=86, Resulting Numbers: [39, 72, 86] Generated Node #0,1: 53:[39, 72, 86] Operation: 89-3=86 Moving to Node #0,1 Current State: 53:[39, 72, 86], Operations: ['89-3=86'] Exploring Operation: 72-39=33, Resulting Numbers: [86, 33] Generated Node #0,1,1: 53:[86, 33] Operation: 72-39=33 Moving to Node #0,1,1 Current State: 53:[86, 33], Operations: ['89-3=86', '72-39=33'] Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 36, 10, 25, 85 ]
47
[ "25+85=110", "110/10=11", "36+11=47" ]
Current State: 47:[36, 10, 25, 85], Operations: [] Exploring Operation: 25+85=110, Resulting Numbers: [36, 10, 110] Generated Node #2: [36, 10, 110] from Operation: 25+85=110 Current State: 47:[36, 10, 110], Operations: ['25+85=110'] Exploring Operation: 110/10=11, Resulting Numbers: [36, 11] Generated Node #3: [36, 11] from Operation: 110/10=11 Current State: 47:[36, 11], Operations: ['25+85=110', '110/10=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[36, 10, 25, 85], Operations: [] Exploring Operation: 85-10=75, Resulting Numbers: [36, 25, 75] Generated Node #0,0: 47:[36, 25, 75] Operation: 85-10=75 Exploring Operation: 85-36=49, Resulting Numbers: [10, 25, 49] Generated Node #0,1: 47:[10, 25, 49] Operation: 85-36=49 Exploring Operation: 36+10=46, Resulting Numbers: [25, 85, 46] Generated Node #0,2: 47:[25, 85, 46] Operation: 36+10=46 Exploring Operation: 10+25=35, Resulting Numbers: [36, 85, 35] Generated Node #0,3: 47:[36, 85, 35] Operation: 10+25=35 Moving to Node #0,0 Current State: 47:[36, 25, 75], Operations: ['85-10=75'] Exploring Operation: 36+25=61, Resulting Numbers: [75, 61] Generated Node #0,0,0: 47:[75, 61] Operation: 36+25=61 Exploring Operation: 75/25=3, Resulting Numbers: [36, 3] Generated Node #0,0,1: 47:[36, 3] Operation: 75/25=3 Exploring Operation: 75-25=50, Resulting Numbers: [36, 50] Generated Node #0,0,2: 47:[36, 50] Operation: 75-25=50 Exploring Operation: 75-36=39, Resulting Numbers: [25, 39] Generated Node #0,0,3: 47:[25, 39] Operation: 75-36=39 Moving to Node #0,2 Current State: 47:[25, 85, 46], Operations: ['36+10=46'] Exploring Operation: 25+46=71, Resulting Numbers: [85, 71] Generated Node #0,2,0: 47:[85, 71] Operation: 25+46=71 Exploring Operation: 85-46=39, Resulting Numbers: [25, 39] Generated Node #0,2,1: 47:[25, 39] Operation: 85-46=39 Exploring Operation: 85-25=60, Resulting Numbers: [46, 60] Generated Node #0,2,2: 47:[46, 60] Operation: 85-25=60 Exploring Operation: 25+85=110, Resulting Numbers: [46, 110] Generated Node #0,2,3: 47:[46, 110] Operation: 25+85=110 Moving to Node #0,1 Current State: 47:[10, 25, 49], Operations: ['85-36=49'] Exploring Operation: 49-10=39, Resulting Numbers: [25, 39] Generated Node #0,1,0: 47:[25, 39] Operation: 49-10=39 Exploring Operation: 10+49=59, Resulting Numbers: [25, 59] Generated Node #0,1,1: 47:[25, 59] Operation: 10+49=59 Exploring Operation: 25-10=15, Resulting Numbers: [49, 15] Generated Node #0,1,2: 47:[49, 15] Operation: 25-10=15 Exploring Operation: 10+25=35, Resulting Numbers: [49, 35] Generated Node #0,1,3: 47:[49, 35] Operation: 10+25=35 Moving to Node #0,3 Current State: 47:[36, 85, 35], Operations: ['10+25=35'] Exploring Operation: 85-35=50, Resulting Numbers: [36, 50] Generated Node #0,3,0: 47:[36, 50] Operation: 85-35=50 Exploring Operation: 36-35=1, Resulting Numbers: [85, 1] Generated Node #0,3,1: 47:[85, 1] Operation: 36-35=1 Exploring Operation: 36+35=71, Resulting Numbers: [85, 71] Generated Node #0,3,2: 47:[85, 71] Operation: 36+35=71 Exploring Operation: 85-36=49, Resulting Numbers: [35, 49] Generated Node #0,3,3: 47:[35, 49] Operation: 85-36=49 Moving to Node #0,0,2 Current State: 47:[36, 50], Operations: ['85-10=75', '75-25=50'] Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[36, 50], Operations: ['10+25=35', '85-35=50'] Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[35, 49], Operations: ['10+25=35', '85-36=49'] Exploring Operation: 35+49=84, Resulting Numbers: [84] 84,47 unequal: No Solution Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 35*49=1715, Resulting Numbers: [1715] 1715,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[46, 60], Operations: ['36+10=46', '85-25=60'] Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,47 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[49, 35], Operations: ['85-36=49', '10+25=35'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 49*35=1715, Resulting Numbers: [1715] 1715,47 unequal: No Solution Exploring Operation: 49+35=84, Resulting Numbers: [84] 84,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[25, 39], Operations: ['36+10=46', '85-46=39'] Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[25, 39], Operations: ['85-10=75', '75-36=39'] Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,47 unequal: No Solution Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[25, 39], Operations: ['85-36=49', '49-10=39'] Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,47 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[49, 15], Operations: ['85-36=49', '25-10=15'] Exploring Operation: 49+15=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 49*15=735, Resulting Numbers: [735] 735,47 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[25, 59], Operations: ['85-36=49', '10+49=59'] Exploring Operation: 25*59=1475, Resulting Numbers: [1475] 1475,47 unequal: No Solution Exploring Operation: 59-25=34, Resulting Numbers: [34] 34,47 unequal: No Solution Exploring Operation: 25+59=84, Resulting Numbers: [84] 84,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[75, 61], Operations: ['85-10=75', '36+25=61'] Exploring Operation: 75-61=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 75*61=4575, Resulting Numbers: [4575] 4575,47 unequal: No Solution Exploring Operation: 75+61=136, Resulting Numbers: [136] 136,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[36, 3], Operations: ['85-10=75', '75/25=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,47 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[85, 71], Operations: ['36+10=46', '25+46=71'] Exploring Operation: 85*71=6035, Resulting Numbers: [6035] 6035,47 unequal: No Solution Exploring Operation: 85-71=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 85+71=156, Resulting Numbers: [156] 156,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[85, 71], Operations: ['10+25=35', '36+35=71'] Exploring Operation: 85*71=6035, Resulting Numbers: [6035] 6035,47 unequal: No Solution Exploring Operation: 85-71=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 85+71=156, Resulting Numbers: [156] 156,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[46, 110], Operations: ['36+10=46', '25+85=110'] Exploring Operation: 110-46=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 46*110=5060, Resulting Numbers: [5060] 5060,47 unequal: No Solution Exploring Operation: 46+110=156, Resulting Numbers: [156] 156,47 unequal: No Solution Moving to Node #0,3,1 Current State: 47:[85, 1], Operations: ['10+25=35', '36-35=1'] Exploring Operation: 85+1=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,47 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,47 unequal: No Solution Exploring Operation: 85*1=85, Resulting Numbers: [85] 85,47 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 97, 39, 44, 44 ]
48
[ "97+39=136", "44+44=88", "136-88=48" ]
Current State: 48:[97, 39, 44, 44], Operations: [] Exploring Operation: 97+39=136, Resulting Numbers: [44, 44, 136] Generated Node #2: [44, 44, 136] from Operation: 97+39=136 Current State: 48:[44, 44, 136], Operations: ['97+39=136'] Exploring Operation: 44+44=88, Resulting Numbers: [136, 88] Generated Node #3: [136, 88] from Operation: 44+44=88 Current State: 48:[136, 88], Operations: ['97+39=136', '44+44=88'] Exploring Operation: 136-88=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[97, 39, 44, 44], Operations: [] Exploring Operation: 97-44=53, Resulting Numbers: [39, 44, 53] Generated Node #0,0: 48:[39, 44, 53] Operation: 97-44=53 Exploring Operation: 97-39=58, Resulting Numbers: [44, 44, 58] Generated Node #0,1: 48:[44, 44, 58] Operation: 97-39=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[39, 44, 53], Operations: ['97-44=53'] Exploring Operation: 44-39=5, Resulting Numbers: [53, 5] Generated Node #0,0,0: 48:[53, 5] Operation: 44-39=5 Exploring Operation: 53-39=14, Resulting Numbers: [44, 14] Generated Node #0,0,1: 48:[44, 14] Operation: 53-39=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[53, 5], Operations: ['97-44=53', '44-39=5'] Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,48 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[97, 39, 44, 44], Operations: [] Exploring Operation: 97-44=53, Resulting Numbers: [39, 44, 53] Generated Node #0,0: 48:[39, 44, 53] Operation: 97-44=53 Moving to Node #0,0 Current State: 48:[39, 44, 53], Operations: ['97-44=53'] Exploring Operation: 44-39=5, Resulting Numbers: [53, 5] Generated Node #0,0,0: 48:[53, 5] Operation: 44-39=5 Moving to Node #0,0,0 Current State: 48:[53, 5], Operations: ['97-44=53', '44-39=5'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 30, 42, 57, 97 ]
82
[ "30+42=72", "57+97=154", "154-72=82" ]
Current State: 82:[30, 42, 57, 97], Operations: [] Exploring Operation: 30+42=72, Resulting Numbers: [57, 97, 72] Generated Node #2: [57, 97, 72] from Operation: 30+42=72 Current State: 82:[57, 97, 72], Operations: ['30+42=72'] Exploring Operation: 57+97=154, Resulting Numbers: [72, 154] Generated Node #3: [72, 154] from Operation: 57+97=154 Current State: 82:[72, 154], Operations: ['30+42=72', '57+97=154'] Exploring Operation: 154-72=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[30, 42, 57, 97], Operations: [] Exploring Operation: 57-30=27, Resulting Numbers: [42, 97, 27] Generated Node #0,0: 82:[42, 97, 27] Operation: 57-30=27 Exploring Operation: 97-57=40, Resulting Numbers: [30, 42, 40] Generated Node #0,1: 82:[30, 42, 40] Operation: 97-57=40 Exploring Operation: 30+57=87, Resulting Numbers: [42, 97, 87] Generated Node #0,2: 82:[42, 97, 87] Operation: 30+57=87 Moving to Node #0,1 Current State: 82:[30, 42, 40], Operations: ['97-57=40'] Exploring Operation: 30+42=72, Resulting Numbers: [40, 72] Generated Node #0,1,0: 82:[40, 72] Operation: 30+42=72 Exploring Operation: 40-30=10, Resulting Numbers: [42, 10] Generated Node #0,1,1: 82:[42, 10] Operation: 40-30=10 Exploring Operation: 42-30=12, Resulting Numbers: [40, 12] Generated Node #0,1,2: 82:[40, 12] Operation: 42-30=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[42, 10], Operations: ['97-57=40', '40-30=10'] Exploring Operation: 42*10=420, Resulting Numbers: [420] 420,82 unequal: No Solution Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[40, 72], Operations: ['97-57=40', '30+42=72'] Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 40+72=112, Resulting Numbers: [112] 112,82 unequal: No Solution Exploring Operation: 40*72=2880, Resulting Numbers: [2880] 2880,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 82:[40, 12], Operations: ['97-57=40', '42-30=12'] Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,82 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 82:[42, 97, 87], Operations: ['30+57=87'] Exploring Operation: 97-42=55, Resulting Numbers: [87, 55] Generated Node #0,2,0: 82:[87, 55] Operation: 97-42=55 Exploring Operation: 87-42=45, Resulting Numbers: [97, 45] Generated Node #0,2,1: 82:[97, 45] Operation: 87-42=45 Exploring Operation: 97-87=10, Resulting Numbers: [42, 10] Generated Node #0,2,2: 82:[42, 10] Operation: 97-87=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[42, 10], Operations: ['30+57=87', '97-87=10'] Exploring Operation: 42+10=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 42*10=420, Resulting Numbers: [420] 420,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 82:[87, 55], Operations: ['30+57=87', '97-42=55'] Exploring Operation: 87+55=142, Resulting Numbers: [142] 142,82 unequal: No Solution Exploring Operation: 87*55=4785, Resulting Numbers: [4785] 4785,82 unequal: No Solution Exploring Operation: 87-55=32, Resulting Numbers: [32] 32,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[97, 45], Operations: ['30+57=87', '87-42=45'] Exploring Operation: 97+45=142, Resulting Numbers: [142] 142,82 unequal: No Solution Exploring Operation: 97-45=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 97*45=4365, Resulting Numbers: [4365] 4365,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 82:[42, 97, 27], Operations: ['57-30=27'] Exploring Operation: 42+27=69, Resulting Numbers: [97, 69] Generated Node #0,0,0: 82:[97, 69] Operation: 42+27=69 Exploring Operation: 97-27=70, Resulting Numbers: [42, 70] Generated Node #0,0,1: 82:[42, 70] Operation: 97-27=70 Exploring Operation: 97-42=55, Resulting Numbers: [27, 55] Generated Node #0,0,2: 82:[27, 55] Operation: 97-42=55 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[42, 70], Operations: ['57-30=27', '97-27=70'] Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,82 unequal: No Solution Exploring Operation: 42*70=2940, Resulting Numbers: [2940] 2940,82 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 82:[97, 69], Operations: ['57-30=27', '42+27=69'] Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,82 unequal: No Solution Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 82:[27, 55], Operations: ['57-30=27', '97-42=55'] Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 27*55=1485, Resulting Numbers: [1485] 1485,82 unequal: No Solution Exploring Operation: 27+55=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[30, 42, 57, 97], Operations: [] Exploring Operation: 57-30=27, Resulting Numbers: [42, 97, 27] Generated Node #0,0: 82:[42, 97, 27] Operation: 57-30=27 Moving to Node #0,0 Current State: 82:[42, 97, 27], Operations: ['57-30=27'] Exploring Operation: 97-42=55, Resulting Numbers: [27, 55] Generated Node #0,0,2: 82:[27, 55] Operation: 97-42=55 Moving to Node #0,0,2 Current State: 82:[27, 55], Operations: ['57-30=27', '97-42=55'] Exploring Operation: 27+55=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_3
mult_heuristic
[ 63, 34, 28, 79 ]
79
[ "63-34=29", "29-28=1", "79*1=79" ]
Current State: 79:[63, 34, 28, 79], Operations: [] Exploring Operation: 63-34=29, Resulting Numbers: [28, 79, 29] Generated Node #2: [28, 79, 29] from Operation: 63-34=29 Current State: 79:[28, 79, 29], Operations: ['63-34=29'] Exploring Operation: 29-28=1, Resulting Numbers: [79, 1] Generated Node #3: [79, 1] from Operation: 29-28=1 Current State: 79:[79, 1], Operations: ['63-34=29', '29-28=1'] Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[63, 34, 28, 79], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [34, 79, 35] Generated Node #0,0: 79:[34, 79, 35] Operation: 63-28=35 Exploring Operation: 63+28=91, Resulting Numbers: [34, 79, 91] Generated Node #0,1: 79:[34, 79, 91] Operation: 63+28=91 Exploring Operation: 34+28=62, Resulting Numbers: [63, 79, 62] Generated Node #0,2: 79:[63, 79, 62] Operation: 34+28=62 Exploring Operation: 63+34=97, Resulting Numbers: [28, 79, 97] Generated Node #0,3: 79:[28, 79, 97] Operation: 63+34=97 Moving to Node #0,2 Current State: 79:[63, 79, 62], Operations: ['34+28=62'] Exploring Operation: 79-62=17, Resulting Numbers: [63, 17] Generated Node #0,2,0: 79:[63, 17] Operation: 79-62=17 Exploring Operation: 63-62=1, Resulting Numbers: [79, 1] Generated Node #0,2,1: 79:[79, 1] Operation: 63-62=1 Exploring Operation: 79+62=141, Resulting Numbers: [63, 141] Generated Node #0,2,2: 79:[63, 141] Operation: 79+62=141 Exploring Operation: 63+62=125, Resulting Numbers: [79, 125] Generated Node #0,2,3: 79:[79, 125] Operation: 63+62=125 Moving to Node #0,1 Current State: 79:[34, 79, 91], Operations: ['63+28=91'] Exploring Operation: 91-34=57, Resulting Numbers: [79, 57] Generated Node #0,1,0: 79:[79, 57] Operation: 91-34=57 Exploring Operation: 79-34=45, Resulting Numbers: [91, 45] Generated Node #0,1,1: 79:[91, 45] Operation: 79-34=45 Exploring Operation: 34+79=113, Resulting Numbers: [91, 113] Generated Node #0,1,2: 79:[91, 113] Operation: 34+79=113 Exploring Operation: 34+91=125, Resulting Numbers: [79, 125] Generated Node #0,1,3: 79:[79, 125] Operation: 34+91=125 Moving to Node #0,3 Current State: 79:[28, 79, 97], Operations: ['63+34=97'] Exploring Operation: 97-28=69, Resulting Numbers: [79, 69] Generated Node #0,3,0: 79:[79, 69] Operation: 97-28=69 Exploring Operation: 28+79=107, Resulting Numbers: [97, 107] Generated Node #0,3,1: 79:[97, 107] Operation: 28+79=107 Exploring Operation: 28+97=125, Resulting Numbers: [79, 125] Generated Node #0,3,2: 79:[79, 125] Operation: 28+97=125 Exploring Operation: 79-28=51, Resulting Numbers: [97, 51] Generated Node #0,3,3: 79:[97, 51] Operation: 79-28=51 Moving to Node #0,0 Current State: 79:[34, 79, 35], Operations: ['63-28=35'] Exploring Operation: 34+35=69, Resulting Numbers: [79, 69] Generated Node #0,0,0: 79:[79, 69] Operation: 34+35=69 Exploring Operation: 79-34=45, Resulting Numbers: [35, 45] Generated Node #0,0,1: 79:[35, 45] Operation: 79-34=45 Exploring Operation: 34+79=113, Resulting Numbers: [35, 113] Generated Node #0,0,2: 79:[35, 113] Operation: 34+79=113 Exploring Operation: 35-34=1, Resulting Numbers: [79, 1] Generated Node #0,0,3: 79:[79, 1] Operation: 35-34=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[79, 69], Operations: ['63-28=35', '34+35=69'] Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,79 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,79 unequal: No Solution Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[35, 45], Operations: ['63-28=35', '79-34=45'] Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,79 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[35, 113], Operations: ['63-28=35', '34+79=113'] Exploring Operation: 35*113=3955, Resulting Numbers: [3955] 3955,79 unequal: No Solution Exploring Operation: 35+113=148, Resulting Numbers: [148] 148,79 unequal: No Solution Exploring Operation: 113-35=78, Resulting Numbers: [78] 78,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[79, 1], Operations: ['63-28=35', '35-34=1'] Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 79/1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[63, 34, 28, 79], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [34, 79, 35] Generated Node #0,0: 79:[34, 79, 35] Operation: 63-28=35 Moving to Node #0,0 Current State: 79:[34, 79, 35], Operations: ['63-28=35'] Exploring Operation: 35-34=1, Resulting Numbers: [79, 1] Generated Node #0,0,3: 79:[79, 1] Operation: 35-34=1 Moving to Node #0,0,3 Current State: 79:[79, 1], Operations: ['63-28=35', '35-34=1'] Exploring Operation: 79/1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 50, 24, 56, 4 ]
40
[ "50-24=26", "56/4=14", "26+14=40" ]
Current State: 40:[50, 24, 56, 4], Operations: [] Exploring Operation: 50-24=26, Resulting Numbers: [56, 4, 26] Generated Node #2: [56, 4, 26] from Operation: 50-24=26 Current State: 40:[56, 4, 26], Operations: ['50-24=26'] Exploring Operation: 56/4=14, Resulting Numbers: [26, 14] Generated Node #3: [26, 14] from Operation: 56/4=14 Current State: 40:[26, 14], Operations: ['50-24=26', '56/4=14'] Exploring Operation: 26+14=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[50, 24, 56, 4], Operations: [] Exploring Operation: 56-24=32, Resulting Numbers: [50, 4, 32] Generated Node #0,0: 40:[50, 4, 32] Operation: 56-24=32 Exploring Operation: 56/4=14, Resulting Numbers: [50, 24, 14] Generated Node #0,1: 40:[50, 24, 14] Operation: 56/4=14 Exploring Operation: 56-50=6, Resulting Numbers: [24, 4, 6] Generated Node #0,2: 40:[24, 4, 6] Operation: 56-50=6 Moving to Node #0,2 Current State: 40:[24, 4, 6], Operations: ['56-50=6'] Exploring Operation: 24-4=20, Resulting Numbers: [6, 20] Generated Node #0,2,0: 40:[6, 20] Operation: 24-4=20 Exploring Operation: 24/4=6, Resulting Numbers: [6, 6] Generated Node #0,2,1: 40:[6, 6] Operation: 24/4=6 Exploring Operation: 24/6=4, Resulting Numbers: [4, 4] Generated Node #0,2,2: 40:[4, 4] Operation: 24/6=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[4, 4], Operations: ['56-50=6', '24/6=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[6, 20], Operations: ['56-50=6', '24-4=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,40 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[6, 6], Operations: ['56-50=6', '24/4=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,40 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 40:[50, 4, 32], Operations: ['56-24=32'] Exploring Operation: 32/4=8, Resulting Numbers: [50, 8] Generated Node #0,0,0: 40:[50, 8] Operation: 32/4=8 Exploring Operation: 50-32=18, Resulting Numbers: [4, 18] Generated Node #0,0,1: 40:[4, 18] Operation: 50-32=18 Exploring Operation: 50-4=46, Resulting Numbers: [32, 46] Generated Node #0,0,2: 40:[32, 46] Operation: 50-4=46 Moving to Node #0,1 Current State: 40:[50, 24, 14], Operations: ['56/4=14'] Exploring Operation: 24-14=10, Resulting Numbers: [50, 10] Generated Node #0,1,0: 40:[50, 10] Operation: 24-14=10 Exploring Operation: 50-14=36, Resulting Numbers: [24, 36] Generated Node #0,1,1: 40:[24, 36] Operation: 50-14=36 Exploring Operation: 50-24=26, Resulting Numbers: [14, 26] Generated Node #0,1,2: 40:[14, 26] Operation: 50-24=26 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[24, 36], Operations: ['56/4=14', '50-14=36'] Exploring Operation: 24+36=60, Resulting Numbers: [60] 60,40 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,40 unequal: No Solution Exploring Operation: 24*36=864, Resulting Numbers: [864] 864,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[50, 10], Operations: ['56/4=14', '24-14=10'] Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,40 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[50, 24, 56, 4], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [50, 24, 14] Generated Node #0,1: 40:[50, 24, 14] Operation: 56/4=14 Moving to Node #0,1 Current State: 40:[50, 24, 14], Operations: ['56/4=14'] Exploring Operation: 24-14=10, Resulting Numbers: [50, 10] Generated Node #0,1,0: 40:[50, 10] Operation: 24-14=10 Moving to Node #0,1,0 Current State: 40:[50, 10], Operations: ['56/4=14', '24-14=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_3
mult_heuristic
[ 70, 80, 81, 3 ]
72
[ "70+80=150", "81-3=78", "150-78=72" ]
Current State: 72:[70, 80, 81, 3], Operations: [] Exploring Operation: 70+80=150, Resulting Numbers: [81, 3, 150] Generated Node #2: [81, 3, 150] from Operation: 70+80=150 Current State: 72:[81, 3, 150], Operations: ['70+80=150'] Exploring Operation: 81-3=78, Resulting Numbers: [150, 78] Generated Node #3: [150, 78] from Operation: 81-3=78 Current State: 72:[150, 78], Operations: ['70+80=150', '81-3=78'] Exploring Operation: 150-78=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[70, 80, 81, 3], Operations: [] Exploring Operation: 80-3=77, Resulting Numbers: [70, 81, 77] Generated Node #0,0: 72:[70, 81, 77] Operation: 80-3=77 Exploring Operation: 81-80=1, Resulting Numbers: [70, 3, 1] Generated Node #0,1: 72:[70, 3, 1] Operation: 81-80=1 Exploring Operation: 80-70=10, Resulting Numbers: [81, 3, 10] Generated Node #0,2: 72:[81, 3, 10] Operation: 80-70=10 Exploring Operation: 81-70=11, Resulting Numbers: [80, 3, 11] Generated Node #0,3: 72:[80, 3, 11] Operation: 81-70=11 Exploring Operation: 81/3=27, Resulting Numbers: [70, 80, 27] Generated Node #0,4: 72:[70, 80, 27] Operation: 81/3=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[70, 3, 1], Operations: ['81-80=1'] Exploring Operation: 70*1=70, Resulting Numbers: [3, 70] Generated Node #0,1,0: 72:[3, 70] Operation: 70*1=70 Exploring Operation: 70/1=70, Resulting Numbers: [3, 70] Generated Node #0,1,1: 72:[3, 70] Operation: 70/1=70 Exploring Operation: 70+3=73, Resulting Numbers: [1, 73] Generated Node #0,1,2: 72:[1, 73] Operation: 70+3=73 Exploring Operation: 3+1=4, Resulting Numbers: [70, 4] Generated Node #0,1,3: 72:[70, 4] Operation: 3+1=4 Exploring Operation: 70+1=71, Resulting Numbers: [3, 71] Generated Node #0,1,4: 72:[3, 71] Operation: 70+1=71 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 72:[3, 71], Operations: ['81-80=1', '70+1=71'] Exploring Operation: 3+71=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 3*71=213, Resulting Numbers: [213] 213,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[3, 70], Operations: ['81-80=1', '70*1=70'] Exploring Operation: 3+70=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 3*70=210, Resulting Numbers: [210] 210,72 unequal: No Solution Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[3, 70], Operations: ['81-80=1', '70/1=70'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,72 unequal: No Solution Exploring Operation: 3*70=210, Resulting Numbers: [210] 210,72 unequal: No Solution Exploring Operation: 3+70=73, Resulting Numbers: [73] 73,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[1, 73], Operations: ['81-80=1', '70+3=73'] Exploring Operation: 1*73=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[70, 80, 81, 3], Operations: [] Exploring Operation: 81-80=1, Resulting Numbers: [70, 3, 1] Generated Node #0,1: 72:[70, 3, 1] Operation: 81-80=1 Moving to Node #0,1 Current State: 72:[70, 3, 1], Operations: ['81-80=1'] Exploring Operation: 70+3=73, Resulting Numbers: [1, 73] Generated Node #0,1,2: 72:[1, 73] Operation: 70+3=73 Moving to Node #0,1,2 Current State: 72:[1, 73], Operations: ['81-80=1', '70+3=73'] Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_5
sum_heuristic
[ 17, 83, 46, 86 ]
97
[ "86-83=3", "17*3=51", "46+51=97" ]
Current State: 97:[17, 83, 46, 86], Operations: [] Exploring Operation: 86-83=3, Resulting Numbers: [17, 46, 3] Generated Node #2: [17, 46, 3] from Operation: 86-83=3 Current State: 97:[17, 46, 3], Operations: ['86-83=3'] Exploring Operation: 17*3=51, Resulting Numbers: [46, 51] Generated Node #3: [46, 51] from Operation: 17*3=51 Current State: 97:[46, 51], Operations: ['86-83=3', '17*3=51'] Exploring Operation: 46+51=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[17, 83, 46, 86], Operations: [] Exploring Operation: 17+46=63, Resulting Numbers: [83, 86, 63] Generated Node #0,0: 97:[83, 86, 63] Operation: 17+46=63 Exploring Operation: 17+83=100, Resulting Numbers: [46, 86, 100] Generated Node #0,1: 97:[46, 86, 100] Operation: 17+83=100 Exploring Operation: 17+86=103, Resulting Numbers: [83, 46, 103] Generated Node #0,2: 97:[83, 46, 103] Operation: 17+86=103 Moving to Node #0,0 Current State: 97:[83, 86, 63], Operations: ['17+46=63'] Exploring Operation: 86+63=149, Resulting Numbers: [83, 149] Generated Node #0,0,0: 97:[83, 149] Operation: 86+63=149 Exploring Operation: 83-63=20, Resulting Numbers: [86, 20] Generated Node #0,0,1: 97:[86, 20] Operation: 83-63=20 Exploring Operation: 83+63=146, Resulting Numbers: [86, 146] Generated Node #0,0,2: 97:[86, 146] Operation: 83+63=146 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[86, 146], Operations: ['17+46=63', '83+63=146'] Exploring Operation: 86+146=232, Resulting Numbers: [232] 232,97 unequal: No Solution Exploring Operation: 86*146=12556, Resulting Numbers: [12556] 12556,97 unequal: No Solution Exploring Operation: 146-86=60, Resulting Numbers: [60] 60,97 unequal: No Solution No 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: 97:[83, 149], Operations: ['17+46=63', '86+63=149'] Exploring Operation: 149-83=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 83+149=232, Resulting Numbers: [232] 232,97 unequal: No Solution Exploring Operation: 83*149=12367, Resulting Numbers: [12367] 12367,97 unequal: No Solution No 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: 97:[86, 20], Operations: ['17+46=63', '83-63=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,97 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: 97:[46, 86, 100], Operations: ['17+83=100'] Exploring Operation: 100-46=54, Resulting Numbers: [86, 54] Generated Node #0,1,0: 97:[86, 54] Operation: 100-46=54 Exploring Operation: 86-46=40, Resulting Numbers: [100, 40] Generated Node #0,1,1: 97:[100, 40] Operation: 86-46=40 Exploring Operation: 46+86=132, Resulting Numbers: [100, 132] Generated Node #0,1,2: 97:[100, 132] Operation: 46+86=132 Moving to Node #0,2 Current State: 97:[83, 46, 103], Operations: ['17+86=103'] Exploring Operation: 83-46=37, Resulting Numbers: [103, 37] Generated Node #0,2,0: 97:[103, 37] Operation: 83-46=37 Exploring Operation: 83+46=129, Resulting Numbers: [103, 129] Generated Node #0,2,1: 97:[103, 129] Operation: 83+46=129 Exploring Operation: 103-46=57, Resulting Numbers: [83, 57] Generated Node #0,2,2: 97:[83, 57] Operation: 103-46=57 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[103, 129], Operations: ['17+86=103', '83+46=129'] Exploring Operation: 103+129=232, Resulting Numbers: [232] 232,97 unequal: No Solution Exploring Operation: 103*129=13287, Resulting Numbers: [13287] 13287,97 unequal: No Solution Exploring Operation: 129-103=26, Resulting Numbers: [26] 26,97 unequal: No Solution No 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: 97:[83, 57], Operations: ['17+86=103', '103-46=57'] Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,97 unequal: No Solution Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,97 unequal: No Solution No 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: 97:[103, 37], Operations: ['17+86=103', '83-46=37'] Exploring Operation: 103+37=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 103-37=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 103*37=3811, Resulting Numbers: [3811] 3811,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 97:[100, 132], Operations: ['17+83=100', '46+86=132'] Exploring Operation: 132-100=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 100*132=13200, Resulting Numbers: [13200] 13200,97 unequal: No Solution Exploring Operation: 100+132=232, Resulting Numbers: [232] 232,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[86, 54], Operations: ['17+83=100', '100-46=54'] Exploring Operation: 86-54=32, Resulting Numbers: [32] 32,97 unequal: No Solution Exploring Operation: 86+54=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 86*54=4644, Resulting Numbers: [4644] 4644,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[100, 40], Operations: ['17+83=100', '86-46=40'] Exploring Operation: 100*40=4000, Resulting Numbers: [4000] 4000,97 unequal: No Solution Exploring Operation: 100-40=60, Resulting Numbers: [60] 60,97 unequal: No Solution Exploring Operation: 100+40=140, Resulting Numbers: [140] 140,97 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 90, 53, 86, 34 ]
22
[ "53*34=1802", "90+1802=1892", "1892/86=22" ]
Current State: 22:[90, 53, 86, 34], Operations: [] Exploring Operation: 53*34=1802, Resulting Numbers: [90, 86, 1802] Generated Node #2: [90, 86, 1802] from Operation: 53*34=1802 Current State: 22:[90, 86, 1802], Operations: ['53*34=1802'] Exploring Operation: 90+1802=1892, Resulting Numbers: [86, 1892] Generated Node #3: [86, 1892] from Operation: 90+1802=1892 Current State: 22:[86, 1892], Operations: ['53*34=1802', '90+1802=1892'] Exploring Operation: 1892/86=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[90, 53, 86, 34], Operations: [] Exploring Operation: 86-53=33, Resulting Numbers: [90, 34, 33] Generated Node #0,0: 22:[90, 34, 33] Operation: 86-53=33 Exploring Operation: 86-34=52, Resulting Numbers: [90, 53, 52] Generated Node #0,1: 22:[90, 53, 52] Operation: 86-34=52 Exploring Operation: 90-86=4, Resulting Numbers: [53, 34, 4] Generated Node #0,2: 22:[53, 34, 4] Operation: 90-86=4 Exploring Operation: 90-53=37, Resulting Numbers: [86, 34, 37] Generated Node #0,3: 22:[86, 34, 37] Operation: 90-53=37 Exploring Operation: 90-34=56, Resulting Numbers: [53, 86, 56] Generated Node #0,4: 22:[53, 86, 56] Operation: 90-34=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[53, 34, 4], Operations: ['90-86=4'] Exploring Operation: 34-4=30, Resulting Numbers: [53, 30] Generated Node #0,2,0: 22:[53, 30] Operation: 34-4=30 Exploring Operation: 34+4=38, Resulting Numbers: [53, 38] Generated Node #0,2,1: 22:[53, 38] Operation: 34+4=38 Exploring Operation: 53-4=49, Resulting Numbers: [34, 49] Generated Node #0,2,2: 22:[34, 49] Operation: 53-4=49 Exploring Operation: 53+4=57, Resulting Numbers: [34, 57] Generated Node #0,2,3: 22:[34, 57] Operation: 53+4=57 Exploring Operation: 53-34=19, Resulting Numbers: [4, 19] Generated Node #0,2,4: 22:[4, 19] Operation: 53-34=19 Moving to Node #0,2,4 Current State: 22:[4, 19], Operations: ['90-86=4', '53-34=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,22 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[34, 49], Operations: ['90-86=4', '53-4=49'] Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,22 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[53, 30], Operations: ['90-86=4', '34-4=30'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,22 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[53, 38], Operations: ['90-86=4', '34+4=38'] Exploring Operation: 53*38=2014, Resulting Numbers: [2014] 2014,22 unequal: No Solution Exploring Operation: 53+38=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[34, 57], Operations: ['90-86=4', '53+4=57'] Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[90, 34, 33], Operations: ['86-53=33'] Exploring Operation: 90-33=57, Resulting Numbers: [34, 57] Generated Node #0,0,0: 22:[34, 57] Operation: 90-33=57 Exploring Operation: 90-34=56, Resulting Numbers: [33, 56] Generated Node #0,0,1: 22:[33, 56] Operation: 90-34=56 Exploring Operation: 90+34=124, Resulting Numbers: [33, 124] Generated Node #0,0,2: 22:[33, 124] Operation: 90+34=124 Exploring Operation: 34-33=1, Resulting Numbers: [90, 1] Generated Node #0,0,3: 22:[90, 1] Operation: 34-33=1 Exploring Operation: 90+33=123, Resulting Numbers: [34, 123] Generated Node #0,0,4: 22:[34, 123] Operation: 90+33=123 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[33, 56], Operations: ['86-53=33', '90-34=56'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,22 unequal: No Solution Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,22 unequal: No Solution No 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: 22:[34, 57], Operations: ['86-53=33', '90-33=57'] Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,22 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,22 unequal: No Solution No 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: 22:[90, 1], Operations: ['86-53=33', '34-33=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,22 unequal: No Solution Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,22 unequal: No Solution Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,22 unequal: No Solution No 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: 22:[33, 124], Operations: ['86-53=33', '90+34=124'] Exploring Operation: 124-33=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 33+124=157, Resulting Numbers: [157] 157,22 unequal: No Solution Exploring Operation: 33*124=4092, Resulting Numbers: [4092] 4092,22 unequal: No Solution No 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: 22:[34, 123], Operations: ['86-53=33', '90+33=123'] Exploring Operation: 123-34=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 34+123=157, Resulting Numbers: [157] 157,22 unequal: No Solution Exploring Operation: 34*123=4182, Resulting Numbers: [4182] 4182,22 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: 22:[86, 34, 37], Operations: ['90-53=37'] Exploring Operation: 37-34=3, Resulting Numbers: [86, 3] Generated Node #0,3,0: 22:[86, 3] Operation: 37-34=3 Exploring Operation: 86-34=52, Resulting Numbers: [37, 52] Generated Node #0,3,1: 22:[37, 52] Operation: 86-34=52 Exploring Operation: 86+37=123, Resulting Numbers: [34, 123] Generated Node #0,3,2: 22:[34, 123] Operation: 86+37=123 Exploring Operation: 86-37=49, Resulting Numbers: [34, 49] Generated Node #0,3,3: 22:[34, 49] Operation: 86-37=49 Exploring Operation: 86+34=120, Resulting Numbers: [37, 120] Generated Node #0,3,4: 22:[37, 120] Operation: 86+34=120 Moving to Node #0,3,3 Current State: 22:[34, 49], Operations: ['90-53=37', '86-37=49'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,22 unequal: No Solution Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[37, 52], Operations: ['90-53=37', '86-34=52'] Exploring Operation: 37*52=1924, Resulting Numbers: [1924] 1924,22 unequal: No Solution Exploring Operation: 37+52=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[86, 3], Operations: ['90-53=37', '37-34=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,22 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[34, 123], Operations: ['90-53=37', '86+37=123'] Exploring Operation: 34+123=157, Resulting Numbers: [157] 157,22 unequal: No Solution Exploring Operation: 34*123=4182, Resulting Numbers: [4182] 4182,22 unequal: No Solution Exploring Operation: 123-34=89, Resulting Numbers: [89] 89,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[37, 120], Operations: ['90-53=37', '86+34=120'] Exploring Operation: 120-37=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 37+120=157, Resulting Numbers: [157] 157,22 unequal: No Solution Exploring Operation: 37*120=4440, Resulting Numbers: [4440] 4440,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[90, 53, 52], Operations: ['86-34=52'] Exploring Operation: 90+53=143, Resulting Numbers: [52, 143] Generated Node #0,1,0: 22:[52, 143] Operation: 90+53=143 Exploring Operation: 90-53=37, Resulting Numbers: [52, 37] Generated Node #0,1,1: 22:[52, 37] Operation: 90-53=37 Exploring Operation: 90-52=38, Resulting Numbers: [53, 38] Generated Node #0,1,2: 22:[53, 38] Operation: 90-52=38 Exploring Operation: 90+52=142, Resulting Numbers: [53, 142] Generated Node #0,1,3: 22:[53, 142] Operation: 90+52=142 Exploring Operation: 53-52=1, Resulting Numbers: [90, 1] Generated Node #0,1,4: 22:[90, 1] Operation: 53-52=1 Moving to Node #0,1,1 Current State: 22:[52, 37], Operations: ['86-34=52', '90-53=37'] Exploring Operation: 52+37=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 52*37=1924, Resulting Numbers: [1924] 1924,22 unequal: No Solution Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[53, 38], Operations: ['86-34=52', '90-52=38'] Exploring Operation: 53+38=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 53*38=2014, Resulting Numbers: [2014] 2014,22 unequal: No Solution Moving to Node #0,1,4 Current State: 22:[90, 1], Operations: ['86-34=52', '53-52=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,22 unequal: No Solution Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 90+1=91, Resulting Numbers: [91] 91,22 unequal: No Solution Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[52, 143], Operations: ['86-34=52', '90+53=143'] Exploring Operation: 52+143=195, Resulting Numbers: [195] 195,22 unequal: No Solution Exploring Operation: 52*143=7436, Resulting Numbers: [7436] 7436,22 unequal: No Solution Exploring Operation: 143-52=91, Resulting Numbers: [91] 91,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[53, 142], Operations: ['86-34=52', '90+52=142'] Exploring Operation: 53*142=7526, Resulting Numbers: [7526] 7526,22 unequal: No Solution Exploring Operation: 53+142=195, Resulting Numbers: [195] 195,22 unequal: No Solution Exploring Operation: 142-53=89, Resulting Numbers: [89] 89,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 22:[53, 86, 56], Operations: ['90-34=56'] Exploring Operation: 53+86=139, Resulting Numbers: [56, 139] Generated Node #0,4,0: 22:[56, 139] Operation: 53+86=139 Exploring Operation: 56-53=3, Resulting Numbers: [86, 3] Generated Node #0,4,1: 22:[86, 3] Operation: 56-53=3 Exploring Operation: 86-56=30, Resulting Numbers: [53, 30] Generated Node #0,4,2: 22:[53, 30] Operation: 86-56=30 Exploring Operation: 53+56=109, Resulting Numbers: [86, 109] Generated Node #0,4,3: 22:[86, 109] Operation: 53+56=109 Exploring Operation: 86-53=33, Resulting Numbers: [56, 33] Generated Node #0,4,4: 22:[56, 33] Operation: 86-53=33 Moving to Node #0,4,2 Current State: 22:[53, 30], Operations: ['90-34=56', '86-56=30'] Exploring Operation: 53*30=1590, Resulting Numbers: [1590] 1590,22 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,4,4 Current State: 22:[56, 33], Operations: ['90-34=56', '86-53=33'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 56+33=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 56*33=1848, Resulting Numbers: [1848] 1848,22 unequal: No Solution Moving to Node #0,4,1 Current State: 22:[86, 3], Operations: ['90-34=56', '56-53=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,22 unequal: No Solution Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,22 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,22 unequal: No Solution Moving to Node #0,4,0 Current State: 22:[56, 139], Operations: ['90-34=56', '53+86=139'] Exploring Operation: 56+139=195, Resulting Numbers: [195] 195,22 unequal: No Solution Exploring Operation: 56*139=7784, Resulting Numbers: [7784] 7784,22 unequal: No Solution Exploring Operation: 139-56=83, Resulting Numbers: [83] 83,22 unequal: No Solution Moving to Node #0,4,3 Current State: 22:[86, 109], Operations: ['90-34=56', '53+56=109'] Exploring Operation: 86+109=195, Resulting Numbers: [195] 195,22 unequal: No Solution Exploring Operation: 86*109=9374, Resulting Numbers: [9374] 9374,22 unequal: No Solution Exploring Operation: 109-86=23, Resulting Numbers: [23] 23,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 72, 54, 1, 21 ]
40
[ "72-54=18", "1+21=22", "18+22=40" ]
Current State: 40:[72, 54, 1, 21], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [1, 21, 18] Generated Node #2: [1, 21, 18] from Operation: 72-54=18 Current State: 40:[1, 21, 18], Operations: ['72-54=18'] Exploring Operation: 1+21=22, Resulting Numbers: [18, 22] Generated Node #3: [18, 22] from Operation: 1+21=22 Current State: 40:[18, 22], Operations: ['72-54=18', '1+21=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[72, 54, 1, 21], Operations: [] Exploring Operation: 54-1=53, Resulting Numbers: [72, 21, 53] Generated Node #0,0: 40:[72, 21, 53] Operation: 54-1=53 Exploring Operation: 72-1=71, Resulting Numbers: [54, 21, 71] Generated Node #0,1: 40:[54, 21, 71] Operation: 72-1=71 Exploring Operation: 72-21=51, Resulting Numbers: [54, 1, 51] Generated Node #0,2: 40:[54, 1, 51] Operation: 72-21=51 Exploring Operation: 54-21=33, Resulting Numbers: [72, 1, 33] Generated Node #0,3: 40:[72, 1, 33] Operation: 54-21=33 Exploring Operation: 72-54=18, Resulting Numbers: [1, 21, 18] Generated Node #0,4: 40:[1, 21, 18] Operation: 72-54=18 Start Sub Search at level 1: Moving to Node #0,4 Current State: 40:[1, 21, 18], Operations: ['72-54=18'] Exploring Operation: 21-1=20, Resulting Numbers: [18, 20] Generated Node #0,4,0: 40:[18, 20] Operation: 21-1=20 Exploring Operation: 21-18=3, Resulting Numbers: [1, 3] Generated Node #0,4,1: 40:[1, 3] Operation: 21-18=3 Exploring Operation: 21+18=39, Resulting Numbers: [1, 39] Generated Node #0,4,2: 40:[1, 39] Operation: 21+18=39 Exploring Operation: 1+18=19, Resulting Numbers: [21, 19] Generated Node #0,4,3: 40:[21, 19] Operation: 1+18=19 Exploring Operation: 1*21=21, Resulting Numbers: [18, 21] Generated Node #0,4,4: 40:[18, 21] Operation: 1*21=21 Moving to Node #0,4,0 Current State: 40:[18, 20], Operations: ['72-54=18', '21-1=20'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,40 unequal: No Solution Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,4,2 Current State: 40:[1, 39], Operations: ['72-54=18', '21+18=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,40 unequal: No Solution Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[72, 54, 1, 21], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [1, 21, 18] Generated Node #0,4: 40:[1, 21, 18] Operation: 72-54=18 Moving to Node #0,4 Current State: 40:[1, 21, 18], Operations: ['72-54=18'] Exploring Operation: 21+18=39, Resulting Numbers: [1, 39] Generated Node #0,4,2: 40:[1, 39] Operation: 21+18=39 Moving to Node #0,4,2 Current State: 40:[1, 39], Operations: ['72-54=18', '21+18=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 79, 91, 85, 62 ]
60
[ "79+91=170", "170/85=2", "62-2=60" ]
Current State: 60:[79, 91, 85, 62], Operations: [] Exploring Operation: 79+91=170, Resulting Numbers: [85, 62, 170] Generated Node #2: [85, 62, 170] from Operation: 79+91=170 Current State: 60:[85, 62, 170], Operations: ['79+91=170'] Exploring Operation: 170/85=2, Resulting Numbers: [62, 2] Generated Node #3: [62, 2] from Operation: 170/85=2 Current State: 60:[62, 2], Operations: ['79+91=170', '170/85=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[79, 91, 85, 62], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [79, 91, 23] Generated Node #0,0: 60:[79, 91, 23] Operation: 85-62=23 Exploring Operation: 85-79=6, Resulting Numbers: [91, 62, 6] Generated Node #0,1: 60:[91, 62, 6] Operation: 85-79=6 Exploring Operation: 91-62=29, Resulting Numbers: [79, 85, 29] Generated Node #0,2: 60:[79, 85, 29] Operation: 91-62=29 Exploring Operation: 91-79=12, Resulting Numbers: [85, 62, 12] Generated Node #0,3: 60:[85, 62, 12] Operation: 91-79=12 Exploring Operation: 91-85=6, Resulting Numbers: [79, 62, 6] Generated Node #0,4: 60:[79, 62, 6] Operation: 91-85=6 Moving to Node #0,4 Current State: 60:[79, 62, 6], Operations: ['91-85=6'] Exploring Operation: 62+6=68, Resulting Numbers: [79, 68] Generated Node #0,4,0: 60:[79, 68] Operation: 62+6=68 Exploring Operation: 79-6=73, Resulting Numbers: [62, 73] Generated Node #0,4,1: 60:[62, 73] Operation: 79-6=73 Exploring Operation: 79+6=85, Resulting Numbers: [62, 85] Generated Node #0,4,2: 60:[62, 85] Operation: 79+6=85 Exploring Operation: 62-6=56, Resulting Numbers: [79, 56] Generated Node #0,4,3: 60:[79, 56] Operation: 62-6=56 Exploring Operation: 79-62=17, Resulting Numbers: [6, 17] Generated Node #0,4,4: 60:[6, 17] Operation: 79-62=17 Moving to Node #0,3 Current State: 60:[85, 62, 12], Operations: ['91-79=12'] Exploring Operation: 85-62=23, Resulting Numbers: [12, 23] Generated Node #0,3,0: 60:[12, 23] Operation: 85-62=23 Exploring Operation: 85-12=73, Resulting Numbers: [62, 73] Generated Node #0,3,1: 60:[62, 73] Operation: 85-12=73 Exploring Operation: 62+12=74, Resulting Numbers: [85, 74] Generated Node #0,3,2: 60:[85, 74] Operation: 62+12=74 Exploring Operation: 85+12=97, Resulting Numbers: [62, 97] Generated Node #0,3,3: 60:[62, 97] Operation: 85+12=97 Exploring Operation: 62-12=50, Resulting Numbers: [85, 50] Generated Node #0,3,4: 60:[85, 50] Operation: 62-12=50 Moving to Node #0,1 Current State: 60:[91, 62, 6], Operations: ['85-79=6'] Exploring Operation: 91+6=97, Resulting Numbers: [62, 97] Generated Node #0,1,0: 60:[62, 97] Operation: 91+6=97 Exploring Operation: 62-6=56, Resulting Numbers: [91, 56] Generated Node #0,1,1: 60:[91, 56] Operation: 62-6=56 Exploring Operation: 62+6=68, Resulting Numbers: [91, 68] Generated Node #0,1,2: 60:[91, 68] Operation: 62+6=68 Exploring Operation: 91-62=29, Resulting Numbers: [6, 29] Generated Node #0,1,3: 60:[6, 29] Operation: 91-62=29 Exploring Operation: 91-6=85, Resulting Numbers: [62, 85] Generated Node #0,1,4: 60:[62, 85] Operation: 91-6=85 Moving to Node #0,2 Current State: 60:[79, 85, 29], Operations: ['91-62=29'] Exploring Operation: 85-29=56, Resulting Numbers: [79, 56] Generated Node #0,2,0: 60:[79, 56] Operation: 85-29=56 Exploring Operation: 79+29=108, Resulting Numbers: [85, 108] Generated Node #0,2,1: 60:[85, 108] Operation: 79+29=108 Exploring Operation: 85+29=114, Resulting Numbers: [79, 114] Generated Node #0,2,2: 60:[79, 114] Operation: 85+29=114 Exploring Operation: 85-79=6, Resulting Numbers: [29, 6] Generated Node #0,2,3: 60:[29, 6] Operation: 85-79=6 Exploring Operation: 79-29=50, Resulting Numbers: [85, 50] Generated Node #0,2,4: 60:[85, 50] Operation: 79-29=50 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 60:[29, 6], Operations: ['91-62=29', '85-79=6'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,60 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[79, 56], Operations: ['91-62=29', '85-29=56'] Exploring Operation: 79-56=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 79+56=135, Resulting Numbers: [135] 135,60 unequal: No Solution Exploring Operation: 79*56=4424, Resulting Numbers: [4424] 4424,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 60:[85, 50], Operations: ['91-62=29', '79-29=50'] Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,60 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[85, 108], Operations: ['91-62=29', '79+29=108'] Exploring Operation: 85*108=9180, Resulting Numbers: [9180] 9180,60 unequal: No Solution Exploring Operation: 108-85=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 85+108=193, Resulting Numbers: [193] 193,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[79, 114], Operations: ['91-62=29', '85+29=114'] Exploring Operation: 79*114=9006, Resulting Numbers: [9006] 9006,60 unequal: No Solution Exploring Operation: 79+114=193, Resulting Numbers: [193] 193,60 unequal: No Solution Exploring Operation: 114-79=35, Resulting Numbers: [35] 35,60 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: 60:[79, 91, 23], Operations: ['85-62=23'] Exploring Operation: 79-23=56, Resulting Numbers: [91, 56] Generated Node #0,0,0: 60:[91, 56] Operation: 79-23=56 Exploring Operation: 91+23=114, Resulting Numbers: [79, 114] Generated Node #0,0,1: 60:[79, 114] Operation: 91+23=114 Exploring Operation: 91-79=12, Resulting Numbers: [23, 12] Generated Node #0,0,2: 60:[23, 12] Operation: 91-79=12 Exploring Operation: 91-23=68, Resulting Numbers: [79, 68] Generated Node #0,0,3: 60:[79, 68] Operation: 91-23=68 Exploring Operation: 79+23=102, Resulting Numbers: [91, 102] Generated Node #0,0,4: 60:[91, 102] Operation: 79+23=102 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[23, 12], Operations: ['85-62=23', '91-79=12'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 23*12=276, Resulting Numbers: [276] 276,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 60:[79, 68], Operations: ['85-62=23', '91-23=68'] Exploring Operation: 79*68=5372, Resulting Numbers: [5372] 5372,60 unequal: No Solution Exploring Operation: 79+68=147, Resulting Numbers: [147] 147,60 unequal: No Solution Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[91, 56], Operations: ['85-62=23', '79-23=56'] Exploring Operation: 91-56=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 91*56=5096, Resulting Numbers: [5096] 5096,60 unequal: No Solution Exploring Operation: 91+56=147, Resulting Numbers: [147] 147,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[79, 114], Operations: ['85-62=23', '91+23=114'] Exploring Operation: 79+114=193, Resulting Numbers: [193] 193,60 unequal: No Solution Exploring Operation: 114-79=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 79*114=9006, Resulting Numbers: [9006] 9006,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 60:[91, 102], Operations: ['85-62=23', '79+23=102'] Exploring Operation: 91+102=193, Resulting Numbers: [193] 193,60 unequal: No Solution Exploring Operation: 102-91=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 91*102=9282, Resulting Numbers: [9282] 9282,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 60:[6, 29], Operations: ['85-79=6', '91-62=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,60 unequal: No Solution Moving to Node #0,4,4 Current State: 60:[6, 17], Operations: ['91-85=6', '79-62=17'] Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,60 unequal: No Solution Moving to Node #0,3,0 Current State: 60:[12, 23], Operations: ['91-79=12', '85-62=23'] Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,60 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[62, 73], Operations: ['91-79=12', '85-12=73'] Exploring Operation: 62+73=135, Resulting Numbers: [135] 135,60 unequal: No Solution Exploring Operation: 62*73=4526, Resulting Numbers: [4526] 4526,60 unequal: No Solution Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,60 unequal: No Solution Moving to Node #0,4,1 Current State: 60:[62, 73], Operations: ['91-85=6', '79-6=73'] Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 62*73=4526, Resulting Numbers: [4526] 4526,60 unequal: No Solution Exploring Operation: 62+73=135, Resulting Numbers: [135] 135,60 unequal: No Solution Moving to Node #0,4,3 Current State: 60:[79, 56], Operations: ['91-85=6', '62-6=56'] Exploring Operation: 79*56=4424, Resulting Numbers: [4424] 4424,60 unequal: No Solution Exploring Operation: 79+56=135, Resulting Numbers: [135] 135,60 unequal: No Solution Exploring Operation: 79-56=23, Resulting Numbers: [23] 23,60 unequal: No Solution Moving to Node #0,1,4 Current State: 60:[62, 85], Operations: ['85-79=6', '91-6=85'] Exploring Operation: 62*85=5270, Resulting Numbers: [5270] 5270,60 unequal: No Solution Exploring Operation: 85-62=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 62+85=147, Resulting Numbers: [147] 147,60 unequal: No Solution Moving to Node #0,4,2 Current State: 60:[62, 85], Operations: ['91-85=6', '79+6=85'] Exploring Operation: 62+85=147, Resulting Numbers: [147] 147,60 unequal: No Solution Exploring Operation: 85-62=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 62*85=5270, Resulting Numbers: [5270] 5270,60 unequal: No Solution Moving to Node #0,4,0 Current State: 60:[79, 68], Operations: ['91-85=6', '62+6=68'] Exploring Operation: 79*68=5372, Resulting Numbers: [5372] 5372,60 unequal: No Solution Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 79+68=147, Resulting Numbers: [147] 147,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[91, 56], Operations: ['85-79=6', '62-6=56'] Exploring Operation: 91*56=5096, Resulting Numbers: [5096] 5096,60 unequal: No Solution Exploring Operation: 91-56=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 91+56=147, Resulting Numbers: [147] 147,60 unequal: No Solution Moving to Node #0,3,4 Current State: 60:[85, 50], Operations: ['91-79=12', '62-12=50'] Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 85+50=135, Resulting Numbers: [135] 135,60 unequal: No Solution Exploring Operation: 85*50=4250, Resulting Numbers: [4250] 4250,60 unequal: No Solution Moving to Node #0,1,0 Current State: 60:[62, 97], Operations: ['85-79=6', '91+6=97'] Exploring Operation: 62*97=6014, Resulting Numbers: [6014] 6014,60 unequal: No Solution Exploring Operation: 62+97=159, Resulting Numbers: [159] 159,60 unequal: No Solution Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,60 unequal: No Solution Moving to Node #0,1,2 Current State: 60:[91, 68], Operations: ['85-79=6', '62+6=68'] Exploring Operation: 91*68=6188, Resulting Numbers: [6188] 6188,60 unequal: No Solution Exploring Operation: 91+68=159, Resulting Numbers: [159] 159,60 unequal: No Solution Exploring Operation: 91-68=23, Resulting Numbers: [23] 23,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[85, 74], Operations: ['91-79=12', '62+12=74'] Exploring Operation: 85-74=11, Resulting Numbers: [11] 11,60 unequal: No Solution Exploring Operation: 85+74=159, Resulting Numbers: [159] 159,60 unequal: No Solution Exploring Operation: 85*74=6290, Resulting Numbers: [6290] 6290,60 unequal: No Solution Moving to Node #0,3,3 Current State: 60:[62, 97], Operations: ['91-79=12', '85+12=97'] Exploring Operation: 62*97=6014, Resulting Numbers: [6014] 6014,60 unequal: No Solution Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 62+97=159, Resulting Numbers: [159] 159,60 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 23, 66, 36, 6 ]
36
[ "23*6=138", "66+36=102", "138-102=36" ]
Current State: 36:[23, 66, 36, 6], Operations: [] Exploring Operation: 23*6=138, Resulting Numbers: [66, 36, 138] Generated Node #2: [66, 36, 138] from Operation: 23*6=138 Current State: 36:[66, 36, 138], Operations: ['23*6=138'] Exploring Operation: 66+36=102, Resulting Numbers: [138, 102] Generated Node #3: [138, 102] from Operation: 66+36=102 Current State: 36:[138, 102], Operations: ['23*6=138', '66+36=102'] Exploring Operation: 138-102=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[23, 66, 36, 6], Operations: [] Exploring Operation: 66/6=11, Resulting Numbers: [23, 36, 11] Generated Node #0,0: 36:[23, 36, 11] Operation: 66/6=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[23, 36, 11], Operations: ['66/6=11'] Exploring Operation: 23-11=12, Resulting Numbers: [36, 12] Generated Node #0,0,0: 36:[36, 12] Operation: 23-11=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[36, 12], Operations: ['66/6=11', '23-11=12'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 23, 5, 24, 63 ]
32
[ "63-23=40", "40/5=8", "24+8=32" ]
Current State: 32:[23, 5, 24, 63], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [5, 24, 40] Generated Node #2: [5, 24, 40] from Operation: 63-23=40 Current State: 32:[5, 24, 40], Operations: ['63-23=40'] Exploring Operation: 40/5=8, Resulting Numbers: [24, 8] Generated Node #3: [24, 8] from Operation: 40/5=8 Current State: 32:[24, 8], Operations: ['63-23=40', '40/5=8'] Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[23, 5, 24, 63], Operations: [] Exploring Operation: 63-24=39, Resulting Numbers: [23, 5, 39] Generated Node #0,0: 32:[23, 5, 39] Operation: 63-24=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[23, 5, 39], Operations: ['63-24=39'] Exploring Operation: 39-23=16, Resulting Numbers: [5, 16] Generated Node #0,0,0: 32:[5, 16] Operation: 39-23=16 Moving to Node #0,0,0 Current State: 32:[5, 16], Operations: ['63-24=39', '39-23=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,32 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
[ 2, 78, 2, 68 ]
90
[ "2*78=156", "68-2=66", "156-66=90" ]
Current State: 90:[2, 78, 2, 68], Operations: [] Exploring Operation: 2*78=156, Resulting Numbers: [68, 156] Generated Node #2: [68, 156] from Operation: 2*78=156 Current State: 90:[68, 156], Operations: ['2*78=156'] Exploring Operation: 68-2=66, Resulting Numbers: [156, 66] Generated Node #3: [156, 66] from Operation: 68-2=66 Current State: 90:[156, 66], Operations: ['2*78=156', '68-2=66'] Exploring Operation: 156-66=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[2, 78, 2, 68], Operations: [] Exploring Operation: 78/2=39, Resulting Numbers: [2, 68, 39] Generated Node #0,0: 90:[2, 68, 39] Operation: 78/2=39 Exploring Operation: 68/2=34, Resulting Numbers: [78, 2, 34] Generated Node #0,1: 90:[78, 2, 34] Operation: 68/2=34 Exploring Operation: 78-68=10, Resulting Numbers: [2, 2, 10] Generated Node #0,2: 90:[2, 2, 10] Operation: 78-68=10 Exploring Operation: 68/2=34, Resulting Numbers: [2, 78, 34] Generated Node #0,3: 90:[2, 78, 34] Operation: 68/2=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[2, 2, 10], Operations: ['78-68=10'] Exploring Operation: 10/2=5, Resulting Numbers: [2, 5] Generated Node #0,2,0: 90:[2, 5] Operation: 10/2=5 Exploring Operation: 2+2=4, Resulting Numbers: [10, 4] Generated Node #0,2,1: 90:[10, 4] Operation: 2+2=4 Exploring Operation: 10/2=5, Resulting Numbers: [2, 5] Generated Node #0,2,2: 90:[2, 5] Operation: 10/2=5 Exploring Operation: 2*2=4, Resulting Numbers: [10, 4] Generated Node #0,2,3: 90:[10, 4] Operation: 2*2=4 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[2, 5], Operations: ['78-68=10', '10/2=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,90 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,90 unequal: No Solution No 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: 90:[2, 5], Operations: ['78-68=10', '10/2=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,90 unequal: No Solution No 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: 90:[10, 4], Operations: ['78-68=10', '2+2=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,90 unequal: No Solution No 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: 90:[10, 4], Operations: ['78-68=10', '2*2=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,90 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,90 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: 90:[78, 2, 34], Operations: ['68/2=34'] Exploring Operation: 34/2=17, Resulting Numbers: [78, 17] Generated Node #0,1,0: 90:[78, 17] Operation: 34/2=17 Exploring Operation: 78/2=39, Resulting Numbers: [34, 39] Generated Node #0,1,1: 90:[34, 39] Operation: 78/2=39 Exploring Operation: 78-34=44, Resulting Numbers: [2, 44] Generated Node #0,1,2: 90:[2, 44] Operation: 78-34=44 Exploring Operation: 78+2=80, Resulting Numbers: [34, 80] Generated Node #0,1,3: 90:[34, 80] Operation: 78+2=80 Moving to Node #0,1,2 Current State: 90:[2, 44], Operations: ['68/2=34', '78-34=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,90 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[34, 39], Operations: ['68/2=34', '78/2=39'] Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,90 unequal: No Solution Exploring Operation: 34*39=1326, Resulting Numbers: [1326] 1326,90 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[78, 17], Operations: ['68/2=34', '34/2=17'] Exploring Operation: 78*17=1326, Resulting Numbers: [1326] 1326,90 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,90 unequal: No Solution Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,90 unequal: No Solution Moving to Node #0,1,3 Current State: 90:[34, 80], Operations: ['68/2=34', '78+2=80'] Exploring Operation: 34*80=2720, Resulting Numbers: [2720] 2720,90 unequal: No Solution Exploring Operation: 80-34=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 34+80=114, Resulting Numbers: [114] 114,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[2, 78, 34], Operations: ['68/2=34'] Exploring Operation: 78-34=44, Resulting Numbers: [2, 44] Generated Node #0,3,0: 90:[2, 44] Operation: 78-34=44 Exploring Operation: 34/2=17, Resulting Numbers: [78, 17] Generated Node #0,3,1: 90:[78, 17] Operation: 34/2=17 Exploring Operation: 78/2=39, Resulting Numbers: [34, 39] Generated Node #0,3,2: 90:[34, 39] Operation: 78/2=39 Exploring Operation: 2+78=80, Resulting Numbers: [34, 80] Generated Node #0,3,3: 90:[34, 80] Operation: 2+78=80 Moving to Node #0,3,0 Current State: 90:[2, 44], Operations: ['68/2=34', '78-34=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,90 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,90 unequal: No Solution Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[34, 39], Operations: ['68/2=34', '78/2=39'] Exploring Operation: 34*39=1326, Resulting Numbers: [1326] 1326,90 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[78, 17], Operations: ['68/2=34', '34/2=17'] Exploring Operation: 78*17=1326, Resulting Numbers: [1326] 1326,90 unequal: No Solution Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,90 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[34, 80], Operations: ['68/2=34', '2+78=80'] Exploring Operation: 34+80=114, Resulting Numbers: [114] 114,90 unequal: No Solution Exploring Operation: 80-34=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 34*80=2720, Resulting Numbers: [2720] 2720,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[2, 68, 39], Operations: ['78/2=39'] Exploring Operation: 68+39=107, Resulting Numbers: [2, 107] Generated Node #0,0,0: 90:[2, 107] Operation: 68+39=107 Exploring Operation: 68/2=34, Resulting Numbers: [39, 34] Generated Node #0,0,1: 90:[39, 34] Operation: 68/2=34 Exploring Operation: 68-39=29, Resulting Numbers: [2, 29] Generated Node #0,0,2: 90:[2, 29] Operation: 68-39=29 Exploring Operation: 2+68=70, Resulting Numbers: [39, 70] Generated Node #0,0,3: 90:[39, 70] Operation: 2+68=70 Moving to Node #0,0,2 Current State: 90:[2, 29], Operations: ['78/2=39', '68-39=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[39, 34], Operations: ['78/2=39', '68/2=34'] Exploring Operation: 39*34=1326, Resulting Numbers: [1326] 1326,90 unequal: No Solution Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 39+34=73, Resulting Numbers: [73] 73,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[2, 107], Operations: ['78/2=39', '68+39=107'] Exploring Operation: 2+107=109, Resulting Numbers: [109] 109,90 unequal: No Solution Exploring Operation: 2*107=214, Resulting Numbers: [214] 214,90 unequal: No Solution Exploring Operation: 107-2=105, Resulting Numbers: [105] 105,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[39, 70], Operations: ['78/2=39', '2+68=70'] Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,90 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,90 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