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
[ 47, 53, 61, 99 ]
61
[ "47+53=100", "100-99=1", "61*1=61" ]
Current State: 61:[47, 53, 61, 99], Operations: [] Exploring Operation: 47+53=100, Resulting Numbers: [61, 99, 100] Generated Node #2: [61, 99, 100] from Operation: 47+53=100 Current State: 61:[61, 99, 100], Operations: ['47+53=100'] Exploring Operation: 100-99=1, Resulting Numbers: [61, 1] Generated Node #3: [61, 1] from Operation: 100-99=1 Current State: 61:[61, 1], Operations: ['47+53=100', '100-99=1'] Exploring Operation: 61*1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[47, 53, 61, 99], Operations: [] Exploring Operation: 99-61=38, Resulting Numbers: [47, 53, 38] Generated Node #0,0: 61:[47, 53, 38] Operation: 99-61=38 Exploring Operation: 99-47=52, Resulting Numbers: [53, 61, 52] Generated Node #0,1: 61:[53, 61, 52] Operation: 99-47=52 Exploring Operation: 99-53=46, Resulting Numbers: [47, 61, 46] Generated Node #0,2: 61:[47, 61, 46] Operation: 99-53=46 Moving to Node #0,1 Current State: 61:[53, 61, 52], Operations: ['99-47=52'] Exploring Operation: 53+52=105, Resulting Numbers: [61, 105] Generated Node #0,1,0: 61:[61, 105] Operation: 53+52=105 Exploring Operation: 53-52=1, Resulting Numbers: [61, 1] Generated Node #0,1,1: 61:[61, 1] Operation: 53-52=1 Exploring Operation: 61+52=113, Resulting Numbers: [53, 113] Generated Node #0,1,2: 61:[53, 113] Operation: 61+52=113 Moving to Node #0,2 Current State: 61:[47, 61, 46], Operations: ['99-53=46'] Exploring Operation: 61+46=107, Resulting Numbers: [47, 107] Generated Node #0,2,0: 61:[47, 107] Operation: 61+46=107 Exploring Operation: 47-46=1, Resulting Numbers: [61, 1] Generated Node #0,2,1: 61:[61, 1] Operation: 47-46=1 Exploring Operation: 47+46=93, Resulting Numbers: [61, 93] Generated Node #0,2,2: 61:[61, 93] Operation: 47+46=93 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[61, 93], Operations: ['99-53=46', '47+46=93'] Exploring Operation: 93-61=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 61+93=154, Resulting Numbers: [154] 154,61 unequal: No Solution Exploring Operation: 61*93=5673, Resulting Numbers: [5673] 5673,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[47, 107], Operations: ['99-53=46', '61+46=107'] Exploring Operation: 47*107=5029, Resulting Numbers: [5029] 5029,61 unequal: No Solution Exploring Operation: 107-47=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 47+107=154, Resulting Numbers: [154] 154,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[61, 1], Operations: ['99-53=46', '47-46=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[47, 53, 61, 99], Operations: [] Exploring Operation: 99-53=46, Resulting Numbers: [47, 61, 46] Generated Node #0,2: 61:[47, 61, 46] Operation: 99-53=46 Moving to Node #0,2 Current State: 61:[47, 61, 46], Operations: ['99-53=46'] Exploring Operation: 47-46=1, Resulting Numbers: [61, 1] Generated Node #0,2,1: 61:[61, 1] Operation: 47-46=1 Moving to Node #0,2,1 Current State: 61:[61, 1], Operations: ['99-53=46', '47-46=1'] Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_3
sum_heuristic
[ 27, 14, 10, 33 ]
36
[ "27-14=13", "33-10=23", "13+23=36" ]
Current State: 36:[27, 14, 10, 33], Operations: [] Exploring Operation: 27-14=13, Resulting Numbers: [10, 33, 13] Generated Node #2: [10, 33, 13] from Operation: 27-14=13 Current State: 36:[10, 33, 13], Operations: ['27-14=13'] Exploring Operation: 33-10=23, Resulting Numbers: [13, 23] Generated Node #3: [13, 23] from Operation: 33-10=23 Current State: 36:[13, 23], Operations: ['27-14=13', '33-10=23'] Exploring Operation: 13+23=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[27, 14, 10, 33], Operations: [] Exploring Operation: 33-27=6, Resulting Numbers: [14, 10, 6] Generated Node #0,0: 36:[14, 10, 6] Operation: 33-27=6 Moving to Node #0,0 Current State: 36:[14, 10, 6], Operations: ['33-27=6'] Exploring Operation: 14-10=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 36:[6, 4] Operation: 14-10=4 Moving to Node #0,0,0 Current State: 36:[6, 4], Operations: ['33-27=6', '14-10=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,36 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 38, 22, 50, 32 ]
25
[ "38-22=16", "50*16=800", "800/32=25" ]
Current State: 25:[38, 22, 50, 32], Operations: [] Exploring Operation: 38-22=16, Resulting Numbers: [50, 32, 16] Generated Node #2: [50, 32, 16] from Operation: 38-22=16 Current State: 25:[50, 32, 16], Operations: ['38-22=16'] Exploring Operation: 50*16=800, Resulting Numbers: [32, 800] Generated Node #3: [32, 800] from Operation: 50*16=800 Current State: 25:[32, 800], Operations: ['38-22=16', '50*16=800'] Exploring Operation: 800/32=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[38, 22, 50, 32], Operations: [] Exploring Operation: 50-38=12, Resulting Numbers: [22, 32, 12] Generated Node #0,0: 25:[22, 32, 12] Operation: 50-38=12 Exploring Operation: 50-22=28, Resulting Numbers: [38, 32, 28] Generated Node #0,1: 25:[38, 32, 28] Operation: 50-22=28 Exploring Operation: 50-32=18, Resulting Numbers: [38, 22, 18] Generated Node #0,2: 25:[38, 22, 18] Operation: 50-32=18 Moving to Node #0,0 Current State: 25:[22, 32, 12], Operations: ['50-38=12'] Exploring Operation: 32-12=20, Resulting Numbers: [22, 20] Generated Node #0,0,0: 25:[22, 20] Operation: 32-12=20 Exploring Operation: 32-22=10, Resulting Numbers: [12, 10] Generated Node #0,0,1: 25:[12, 10] Operation: 32-22=10 Exploring Operation: 22-12=10, Resulting Numbers: [32, 10] Generated Node #0,0,2: 25:[32, 10] Operation: 22-12=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[22, 20], Operations: ['50-38=12', '32-12=20'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,25 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,25 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 #0,0,1 Current State: 25:[12, 10], Operations: ['50-38=12', '32-22=10'] Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,25 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 #0,0,2 Current State: 25:[32, 10], Operations: ['50-38=12', '22-12=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,25 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,25 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,25 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: 25:[38, 32, 28], Operations: ['50-22=28'] Exploring Operation: 38-32=6, Resulting Numbers: [28, 6] Generated Node #0,1,0: 25:[28, 6] Operation: 38-32=6 Exploring Operation: 32-28=4, Resulting Numbers: [38, 4] Generated Node #0,1,1: 25:[38, 4] Operation: 32-28=4 Exploring Operation: 38-28=10, Resulting Numbers: [32, 10] Generated Node #0,1,2: 25:[32, 10] Operation: 38-28=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[28, 6], Operations: ['50-22=28', '38-32=6'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,25 unequal: No Solution Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 28*6=168, Resulting Numbers: [168] 168,25 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 #0,1,2 Current State: 25:[32, 10], Operations: ['50-22=28', '38-28=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,25 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,25 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,25 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 #0,1,1 Current State: 25:[38, 4], Operations: ['50-22=28', '32-28=4'] Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,25 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,25 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: 25:[38, 22, 18], Operations: ['50-32=18'] Exploring Operation: 38-18=20, Resulting Numbers: [22, 20] Generated Node #0,2,0: 25:[22, 20] Operation: 38-18=20 Exploring Operation: 38-22=16, Resulting Numbers: [18, 16] Generated Node #0,2,1: 25:[18, 16] Operation: 38-22=16 Exploring Operation: 22-18=4, Resulting Numbers: [38, 4] Generated Node #0,2,2: 25:[38, 4] Operation: 22-18=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[22, 20], Operations: ['50-32=18', '38-18=20'] Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,25 unequal: No Solution Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,25 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,25 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 #0,2,2 Current State: 25:[38, 4], Operations: ['50-32=18', '22-18=4'] Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,25 unequal: No Solution Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,25 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,25 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 #0,2,1 Current State: 25:[18, 16], Operations: ['50-32=18', '38-22=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,25 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 20, 99, 97, 55 ]
70
[ "55-20=35", "99-97=2", "35*2=70" ]
Current State: 70:[20, 99, 97, 55], Operations: [] Exploring Operation: 55-20=35, Resulting Numbers: [99, 97, 35] Generated Node #2: [99, 97, 35] from Operation: 55-20=35 Current State: 70:[99, 97, 35], Operations: ['55-20=35'] Exploring Operation: 99-97=2, Resulting Numbers: [35, 2] Generated Node #3: [35, 2] from Operation: 99-97=2 Current State: 70:[35, 2], Operations: ['55-20=35', '99-97=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[20, 99, 97, 55], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [20, 55, 2] Generated Node #0,0: 70:[20, 55, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 70:[20, 55, 2], Operations: ['99-97=2'] Exploring Operation: 55-20=35, Resulting Numbers: [2, 35] Generated Node #0,0,0: 70:[2, 35] Operation: 55-20=35 Moving to Node #0,0,0 Current State: 70:[2, 35], Operations: ['99-97=2', '55-20=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[20, 99, 97, 55], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [20, 55, 2] Generated Node #0,0: 70:[20, 55, 2] Operation: 99-97=2 Moving to Node #0,0 Current State: 70:[20, 55, 2], Operations: ['99-97=2'] Exploring Operation: 55-20=35, Resulting Numbers: [2, 35] Generated Node #0,0,0: 70:[2, 35] Operation: 55-20=35 Moving to Node #0,0,0 Current State: 70:[2, 35], Operations: ['99-97=2', '55-20=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 81, 83, 69, 48 ]
87
[ "81-69=12", "48/12=4", "83+4=87" ]
Current State: 87:[81, 83, 69, 48], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [83, 48, 12] Generated Node #2: [83, 48, 12] from Operation: 81-69=12 Current State: 87:[83, 48, 12], Operations: ['81-69=12'] Exploring Operation: 48/12=4, Resulting Numbers: [83, 4] Generated Node #3: [83, 4] from Operation: 48/12=4 Current State: 87:[83, 4], Operations: ['81-69=12', '48/12=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[81, 83, 69, 48], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [83, 48, 12] Generated Node #0,0: 87:[83, 48, 12] Operation: 81-69=12 Exploring Operation: 83-48=35, Resulting Numbers: [81, 69, 35] Generated Node #0,1: 87:[81, 69, 35] Operation: 83-48=35 Exploring Operation: 69-48=21, Resulting Numbers: [81, 83, 21] Generated Node #0,2: 87:[81, 83, 21] Operation: 69-48=21 Exploring Operation: 81-48=33, Resulting Numbers: [83, 69, 33] Generated Node #0,3: 87:[83, 69, 33] Operation: 81-48=33 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[81, 83, 21], Operations: ['69-48=21'] Exploring Operation: 83-81=2, Resulting Numbers: [21, 2] Generated Node #0,2,0: 87:[21, 2] Operation: 83-81=2 Exploring Operation: 81+21=102, Resulting Numbers: [83, 102] Generated Node #0,2,1: 87:[83, 102] Operation: 81+21=102 Exploring Operation: 83+21=104, Resulting Numbers: [81, 104] Generated Node #0,2,2: 87:[81, 104] Operation: 83+21=104 Exploring Operation: 81-21=60, Resulting Numbers: [83, 60] Generated Node #0,2,3: 87:[83, 60] Operation: 81-21=60 Moving to Node #0,2,0 Current State: 87:[21, 2], Operations: ['69-48=21', '83-81=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,87 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[83, 102], Operations: ['69-48=21', '81+21=102'] Exploring Operation: 83*102=8466, Resulting Numbers: [8466] 8466,87 unequal: No Solution Exploring Operation: 83+102=185, Resulting Numbers: [185] 185,87 unequal: No Solution Exploring Operation: 102-83=19, Resulting Numbers: [19] 19,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[81, 104], Operations: ['69-48=21', '83+21=104'] Exploring Operation: 81*104=8424, Resulting Numbers: [8424] 8424,87 unequal: No Solution Exploring Operation: 104-81=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 81+104=185, Resulting Numbers: [185] 185,87 unequal: No Solution Moving to Node #0,2,3 Current State: 87:[83, 60], Operations: ['69-48=21', '81-21=60'] Exploring Operation: 83+60=143, Resulting Numbers: [143] 143,87 unequal: No Solution Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 83*60=4980, Resulting Numbers: [4980] 4980,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[83, 69, 33], Operations: ['81-48=33'] Exploring Operation: 69-33=36, Resulting Numbers: [83, 36] Generated Node #0,3,0: 87:[83, 36] Operation: 69-33=36 Exploring Operation: 69+33=102, Resulting Numbers: [83, 102] Generated Node #0,3,1: 87:[83, 102] Operation: 69+33=102 Exploring Operation: 83-33=50, Resulting Numbers: [69, 50] Generated Node #0,3,2: 87:[69, 50] Operation: 83-33=50 Exploring Operation: 83-69=14, Resulting Numbers: [33, 14] Generated Node #0,3,3: 87:[33, 14] Operation: 83-69=14 Moving to Node #0,3,0 Current State: 87:[83, 36], Operations: ['81-48=33', '69-33=36'] Exploring Operation: 83*36=2988, Resulting Numbers: [2988] 2988,87 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,87 unequal: No Solution Exploring Operation: 83+36=119, Resulting Numbers: [119] 119,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[33, 14], Operations: ['81-48=33', '83-69=14'] Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,87 unequal: No Solution Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,87 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[83, 102], Operations: ['81-48=33', '69+33=102'] Exploring Operation: 83*102=8466, Resulting Numbers: [8466] 8466,87 unequal: No Solution Exploring Operation: 83+102=185, Resulting Numbers: [185] 185,87 unequal: No Solution Exploring Operation: 102-83=19, Resulting Numbers: [19] 19,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[69, 50], Operations: ['81-48=33', '83-33=50'] Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,87 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,87 unequal: No Solution Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[81, 69, 35], Operations: ['83-48=35'] Exploring Operation: 69-35=34, Resulting Numbers: [81, 34] Generated Node #0,1,0: 87:[81, 34] Operation: 69-35=34 Exploring Operation: 69+35=104, Resulting Numbers: [81, 104] Generated Node #0,1,1: 87:[81, 104] Operation: 69+35=104 Exploring Operation: 81-35=46, Resulting Numbers: [69, 46] Generated Node #0,1,2: 87:[69, 46] Operation: 81-35=46 Exploring Operation: 81-69=12, Resulting Numbers: [35, 12] Generated Node #0,1,3: 87:[35, 12] Operation: 81-69=12 Moving to Node #0,1,0 Current State: 87:[81, 34], Operations: ['83-48=35', '69-35=34'] Exploring Operation: 81+34=115, Resulting Numbers: [115] 115,87 unequal: No Solution Exploring Operation: 81*34=2754, Resulting Numbers: [2754] 2754,87 unequal: No Solution Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[35, 12], Operations: ['83-48=35', '81-69=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,87 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,87 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[81, 104], Operations: ['83-48=35', '69+35=104'] Exploring Operation: 104-81=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 81+104=185, Resulting Numbers: [185] 185,87 unequal: No Solution Exploring Operation: 81*104=8424, Resulting Numbers: [8424] 8424,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[69, 46], Operations: ['83-48=35', '81-35=46'] Exploring Operation: 69+46=115, Resulting Numbers: [115] 115,87 unequal: No Solution Exploring Operation: 69*46=3174, Resulting Numbers: [3174] 3174,87 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[83, 48, 12], Operations: ['81-69=12'] Exploring Operation: 83-48=35, Resulting Numbers: [12, 35] Generated Node #0,0,0: 87:[12, 35] Operation: 83-48=35 Exploring Operation: 83+12=95, Resulting Numbers: [48, 95] Generated Node #0,0,1: 87:[48, 95] Operation: 83+12=95 Exploring Operation: 48/12=4, Resulting Numbers: [83, 4] Generated Node #0,0,2: 87:[83, 4] Operation: 48/12=4 Exploring Operation: 48-12=36, Resulting Numbers: [83, 36] Generated Node #0,0,3: 87:[83, 36] Operation: 48-12=36 Moving to Node #0,0,2 Current State: 87:[83, 4], Operations: ['81-69=12', '48/12=4'] Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,87 unequal: No Solution Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,87 unequal: No Solution Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[81, 83, 69, 48], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [83, 48, 12] Generated Node #0,0: 87:[83, 48, 12] Operation: 81-69=12 Moving to Node #0,0 Current State: 87:[83, 48, 12], Operations: ['81-69=12'] Exploring Operation: 48/12=4, Resulting Numbers: [83, 4] Generated Node #0,0,2: 87:[83, 4] Operation: 48/12=4 Moving to Node #0,0,2 Current State: 87:[83, 4], Operations: ['81-69=12', '48/12=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_4
sum_heuristic
[ 30, 58, 80, 79 ]
28
[ "58-30=28", "80-79=1", "28*1=28" ]
Current State: 28:[30, 58, 80, 79], Operations: [] Exploring Operation: 58-30=28, Resulting Numbers: [80, 79, 28] Generated Node #2: [80, 79, 28] from Operation: 58-30=28 Current State: 28:[80, 79, 28], Operations: ['58-30=28'] Exploring Operation: 80-79=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 80-79=1 Current State: 28:[28, 1], Operations: ['58-30=28', '80-79=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[30, 58, 80, 79], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [30, 58, 1] Generated Node #0,0: 28:[30, 58, 1] Operation: 80-79=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[30, 58, 1], Operations: ['80-79=1'] Exploring Operation: 58-30=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 58-30=28 Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['80-79=1', '58-30=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[30, 58, 80, 79], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [30, 58, 1] Generated Node #0,0: 28:[30, 58, 1] Operation: 80-79=1 Moving to Node #0,0 Current State: 28:[30, 58, 1], Operations: ['80-79=1'] Exploring Operation: 58-30=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 58-30=28 Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['80-79=1', '58-30=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 25, 13, 5, 50 ]
75
[ "25*13=325", "5*50=250", "325-250=75" ]
Current State: 75:[25, 13, 5, 50], Operations: [] Exploring Operation: 25*13=325, Resulting Numbers: [5, 50, 325] Generated Node #2: [5, 50, 325] from Operation: 25*13=325 Current State: 75:[5, 50, 325], Operations: ['25*13=325'] Exploring Operation: 5*50=250, Resulting Numbers: [325, 250] Generated Node #3: [325, 250] from Operation: 5*50=250 Current State: 75:[325, 250], Operations: ['25*13=325', '5*50=250'] Exploring Operation: 325-250=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[25, 13, 5, 50], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [13, 5, 25] Generated Node #0,0: 75:[13, 5, 25] Operation: 50-25=25 Exploring Operation: 50/25=2, Resulting Numbers: [13, 5, 2] Generated Node #0,1: 75:[13, 5, 2] Operation: 50/25=2 Exploring Operation: 25+50=75, Resulting Numbers: [13, 5, 75] Generated Node #0,2: 75:[13, 5, 75] Operation: 25+50=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[13, 5, 25], Operations: ['50-25=25'] Exploring Operation: 25/5=5, Resulting Numbers: [13, 5] Generated Node #0,0,0: 75:[13, 5] Operation: 25/5=5 Exploring Operation: 13-5=8, Resulting Numbers: [25, 8] Generated Node #0,0,1: 75:[25, 8] Operation: 13-5=8 Exploring Operation: 13+5=18, Resulting Numbers: [25, 18] Generated Node #0,0,2: 75:[25, 18] Operation: 13+5=18 Moving to Node #0,0,0 Current State: 75:[13, 5], Operations: ['50-25=25', '25/5=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,75 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[25, 8], Operations: ['50-25=25', '13-5=8'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,75 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,75 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[25, 18], Operations: ['50-25=25', '13+5=18'] Exploring Operation: 25*18=450, Resulting Numbers: [450] 450,75 unequal: No Solution Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,75 unequal: No Solution Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[13, 5, 75], Operations: ['25+50=75'] Exploring Operation: 13-5=8, Resulting Numbers: [75, 8] Generated Node #0,2,0: 75:[75, 8] Operation: 13-5=8 Exploring Operation: 13+5=18, Resulting Numbers: [75, 18] Generated Node #0,2,1: 75:[75, 18] Operation: 13+5=18 Exploring Operation: 75/5=15, Resulting Numbers: [13, 15] Generated Node #0,2,2: 75:[13, 15] Operation: 75/5=15 Moving to Node #0,2,2 Current State: 75:[13, 15], Operations: ['25+50=75', '75/5=15'] Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 13*15=195, Resulting Numbers: [195] 195,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[75, 8], Operations: ['25+50=75', '13-5=8'] Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,75 unequal: No Solution Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,75 unequal: No Solution Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[75, 18], Operations: ['25+50=75', '13+5=18'] Exploring Operation: 75*18=1350, Resulting Numbers: [1350] 1350,75 unequal: No Solution Exploring Operation: 75+18=93, Resulting Numbers: [93] 93,75 unequal: No Solution Exploring Operation: 75-18=57, Resulting Numbers: [57] 57,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[13, 5, 2], Operations: ['50/25=2'] Exploring Operation: 13*2=26, Resulting Numbers: [5, 26] Generated Node #0,1,0: 75:[5, 26] Operation: 13*2=26 Exploring Operation: 13+2=15, Resulting Numbers: [5, 15] Generated Node #0,1,1: 75:[5, 15] Operation: 13+2=15 Exploring Operation: 5-2=3, Resulting Numbers: [13, 3] Generated Node #0,1,2: 75:[13, 3] Operation: 5-2=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[5, 15], Operations: ['50/25=2', '13+2=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[25, 13, 5, 50], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [13, 5, 2] Generated Node #0,1: 75:[13, 5, 2] Operation: 50/25=2 Moving to Node #0,1 Current State: 75:[13, 5, 2], Operations: ['50/25=2'] Exploring Operation: 13+2=15, Resulting Numbers: [5, 15] Generated Node #0,1,1: 75:[5, 15] Operation: 13+2=15 Moving to Node #0,1,1 Current State: 75:[5, 15], Operations: ['50/25=2', '13+2=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 4, 91, 35, 45 ]
97
[ "91-4=87", "45-35=10", "87+10=97" ]
Current State: 97:[4, 91, 35, 45], Operations: [] Exploring Operation: 91-4=87, Resulting Numbers: [35, 45, 87] Generated Node #2: [35, 45, 87] from Operation: 91-4=87 Current State: 97:[35, 45, 87], Operations: ['91-4=87'] Exploring Operation: 45-35=10, Resulting Numbers: [87, 10] Generated Node #3: [87, 10] from Operation: 45-35=10 Current State: 97:[87, 10], Operations: ['91-4=87', '45-35=10'] Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[4, 91, 35, 45], Operations: [] Exploring Operation: 4+91=95, Resulting Numbers: [35, 45, 95] Generated Node #0,0: 97:[35, 45, 95] Operation: 4+91=95 Exploring Operation: 4+45=49, Resulting Numbers: [91, 35, 49] Generated Node #0,1: 97:[91, 35, 49] Operation: 4+45=49 Exploring Operation: 4*35=140, Resulting Numbers: [91, 45, 140] Generated Node #0,2: 97:[91, 45, 140] Operation: 4*35=140 Exploring Operation: 4+35=39, Resulting Numbers: [91, 45, 39] Generated Node #0,3: 97:[91, 45, 39] Operation: 4+35=39 Moving to Node #0,2 Current State: 97:[91, 45, 140], Operations: ['4*35=140'] Exploring Operation: 91-45=46, Resulting Numbers: [140, 46] Generated Node #0,2,0: 97:[140, 46] Operation: 91-45=46 Exploring Operation: 140-45=95, Resulting Numbers: [91, 95] Generated Node #0,2,1: 97:[91, 95] Operation: 140-45=95 Exploring Operation: 91+45=136, Resulting Numbers: [140, 136] Generated Node #0,2,2: 97:[140, 136] Operation: 91+45=136 Exploring Operation: 45+140=185, Resulting Numbers: [91, 185] Generated Node #0,2,3: 97:[91, 185] Operation: 45+140=185 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[91, 95], Operations: ['4*35=140', '140-45=95'] Exploring Operation: 91+95=186, Resulting Numbers: [186] 186,97 unequal: No Solution Exploring Operation: 91*95=8645, Resulting Numbers: [8645] 8645,97 unequal: No Solution Exploring Operation: 95-91=4, Resulting Numbers: [4] 4,97 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:[140, 136], Operations: ['4*35=140', '91+45=136'] Exploring Operation: 140*136=19040, Resulting Numbers: [19040] 19040,97 unequal: No Solution Exploring Operation: 140-136=4, Resulting Numbers: [4] 4,97 unequal: No Solution Exploring Operation: 140+136=276, Resulting Numbers: [276] 276,97 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:[140, 46], Operations: ['4*35=140', '91-45=46'] Exploring Operation: 140*46=6440, Resulting Numbers: [6440] 6440,97 unequal: No Solution Exploring Operation: 140-46=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 140+46=186, Resulting Numbers: [186] 186,97 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 #0,2,3 Current State: 97:[91, 185], Operations: ['4*35=140', '45+140=185'] Exploring Operation: 185-91=94, Resulting Numbers: [94] 94,97 unequal: No Solution Exploring Operation: 91+185=276, Resulting Numbers: [276] 276,97 unequal: No Solution Exploring Operation: 91*185=16835, Resulting Numbers: [16835] 16835,97 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:[91, 35, 49], Operations: ['4+45=49'] Exploring Operation: 35+49=84, Resulting Numbers: [91, 84] Generated Node #0,1,0: 97:[91, 84] Operation: 35+49=84 Exploring Operation: 91+35=126, Resulting Numbers: [49, 126] Generated Node #0,1,1: 97:[49, 126] Operation: 91+35=126 Exploring Operation: 91-35=56, Resulting Numbers: [49, 56] Generated Node #0,1,2: 97:[49, 56] Operation: 91-35=56 Exploring Operation: 49-35=14, Resulting Numbers: [91, 14] Generated Node #0,1,3: 97:[91, 14] Operation: 49-35=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[91, 84], Operations: ['4+45=49', '35+49=84'] Exploring Operation: 91+84=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 91*84=7644, Resulting Numbers: [7644] 7644,97 unequal: No Solution Exploring Operation: 91-84=7, Resulting Numbers: [7] 7,97 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 #0,1,1 Current State: 97:[49, 126], Operations: ['4+45=49', '91+35=126'] Exploring Operation: 49*126=6174, Resulting Numbers: [6174] 6174,97 unequal: No Solution Exploring Operation: 49+126=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 126-49=77, Resulting Numbers: [77] 77,97 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 #0,1,2 Current State: 97:[49, 56], Operations: ['4+45=49', '91-35=56'] Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,97 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,97 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 #0,1,3 Current State: 97:[91, 14], Operations: ['4+45=49', '49-35=14'] Exploring Operation: 91*14=1274, Resulting Numbers: [1274] 1274,97 unequal: No Solution Exploring Operation: 91-14=77, Resulting Numbers: [77] 77,97 unequal: No Solution Exploring Operation: 91+14=105, Resulting Numbers: [105] 105,97 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: 97:[35, 45, 95], Operations: ['4+91=95'] Exploring Operation: 35+45=80, Resulting Numbers: [95, 80] Generated Node #0,0,0: 97:[95, 80] Operation: 35+45=80 Exploring Operation: 35+95=130, Resulting Numbers: [45, 130] Generated Node #0,0,1: 97:[45, 130] Operation: 35+95=130 Exploring Operation: 95-35=60, Resulting Numbers: [45, 60] Generated Node #0,0,2: 97:[45, 60] Operation: 95-35=60 Exploring Operation: 45-35=10, Resulting Numbers: [95, 10] Generated Node #0,0,3: 97:[95, 10] Operation: 45-35=10 Moving to Node #0,3 Current State: 97:[91, 45, 39], Operations: ['4+35=39'] Exploring Operation: 91+39=130, Resulting Numbers: [45, 130] Generated Node #0,3,0: 97:[45, 130] Operation: 91+39=130 Exploring Operation: 91-39=52, Resulting Numbers: [45, 52] Generated Node #0,3,1: 97:[45, 52] Operation: 91-39=52 Exploring Operation: 45+39=84, Resulting Numbers: [91, 84] Generated Node #0,3,2: 97:[91, 84] Operation: 45+39=84 Exploring Operation: 91+45=136, Resulting Numbers: [39, 136] Generated Node #0,3,3: 97:[39, 136] Operation: 91+45=136 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 97:[91, 84], Operations: ['4+35=39', '45+39=84'] Exploring Operation: 91+84=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 91*84=7644, Resulting Numbers: [7644] 7644,97 unequal: No Solution Exploring Operation: 91-84=7, Resulting Numbers: [7] 7,97 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 #0,3,0 Current State: 97:[45, 130], Operations: ['4+35=39', '91+39=130'] Exploring Operation: 45+130=175, Resulting Numbers: [175] 175,97 unequal: No Solution Exploring Operation: 130-45=85, Resulting Numbers: [85] 85,97 unequal: No Solution Exploring Operation: 45*130=5850, Resulting Numbers: [5850] 5850,97 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 #0,3,1 Current State: 97:[45, 52], Operations: ['4+35=39', '91-39=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[4, 91, 35, 45], Operations: [] Exploring Operation: 4+35=39, Resulting Numbers: [91, 45, 39] Generated Node #0,3: 97:[91, 45, 39] Operation: 4+35=39 Moving to Node #0,3 Current State: 97:[91, 45, 39], Operations: ['4+35=39'] Exploring Operation: 91-39=52, Resulting Numbers: [45, 52] Generated Node #0,3,1: 97:[45, 52] Operation: 91-39=52 Moving to Node #0,3,1 Current State: 97:[45, 52], Operations: ['4+35=39', '91-39=52'] Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_4
sum_heuristic
[ 7, 73, 97, 49 ]
71
[ "73-49=24", "7*24=168", "168-97=71" ]
Current State: 71:[7, 73, 97, 49], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [7, 97, 24] Generated Node #2: [7, 97, 24] from Operation: 73-49=24 Current State: 71:[7, 97, 24], Operations: ['73-49=24'] Exploring Operation: 7*24=168, Resulting Numbers: [97, 168] Generated Node #3: [97, 168] from Operation: 7*24=168 Current State: 71:[97, 168], Operations: ['73-49=24', '7*24=168'] Exploring Operation: 168-97=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[7, 73, 97, 49], Operations: [] Exploring Operation: 97-7=90, Resulting Numbers: [73, 49, 90] Generated Node #0,0: 71:[73, 49, 90] Operation: 97-7=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[73, 49, 90], Operations: ['97-7=90'] Exploring Operation: 90-49=41, Resulting Numbers: [73, 41] Generated Node #0,0,0: 71:[73, 41] Operation: 90-49=41 Moving to Node #0,0,0 Current State: 71:[73, 41], Operations: ['97-7=90', '90-49=41'] Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,71 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
[ 61, 88, 96, 30 ]
93
[ "88-61=27", "96-30=66", "27+66=93" ]
Current State: 93:[61, 88, 96, 30], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [96, 30, 27] Generated Node #2: [96, 30, 27] from Operation: 88-61=27 Current State: 93:[96, 30, 27], Operations: ['88-61=27'] Exploring Operation: 96-30=66, Resulting Numbers: [27, 66] Generated Node #3: [27, 66] from Operation: 96-30=66 Current State: 93:[27, 66], Operations: ['88-61=27', '96-30=66'] Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[61, 88, 96, 30], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [96, 30, 27] Generated Node #0,0: 93:[96, 30, 27] Operation: 88-61=27 Exploring Operation: 96-61=35, Resulting Numbers: [88, 30, 35] Generated Node #0,1: 93:[88, 30, 35] Operation: 96-61=35 Exploring Operation: 61+30=91, Resulting Numbers: [88, 96, 91] Generated Node #0,2: 93:[88, 96, 91] Operation: 61+30=91 Exploring Operation: 61-30=31, Resulting Numbers: [88, 96, 31] Generated Node #0,3: 93:[88, 96, 31] Operation: 61-30=31 Moving to Node #0,0 Current State: 93:[96, 30, 27], Operations: ['88-61=27'] Exploring Operation: 30+27=57, Resulting Numbers: [96, 57] Generated Node #0,0,0: 93:[96, 57] Operation: 30+27=57 Exploring Operation: 96-30=66, Resulting Numbers: [27, 66] Generated Node #0,0,1: 93:[27, 66] Operation: 96-30=66 Exploring Operation: 30-27=3, Resulting Numbers: [96, 3] Generated Node #0,0,2: 93:[96, 3] Operation: 30-27=3 Exploring Operation: 96-27=69, Resulting Numbers: [30, 69] Generated Node #0,0,3: 93:[30, 69] Operation: 96-27=69 Moving to Node #0,3 Current State: 93:[88, 96, 31], Operations: ['61-30=31'] Exploring Operation: 96-31=65, Resulting Numbers: [88, 65] Generated Node #0,3,0: 93:[88, 65] Operation: 96-31=65 Exploring Operation: 88+31=119, Resulting Numbers: [96, 119] Generated Node #0,3,1: 93:[96, 119] Operation: 88+31=119 Exploring Operation: 88-31=57, Resulting Numbers: [96, 57] Generated Node #0,3,2: 93:[96, 57] Operation: 88-31=57 Exploring Operation: 96-88=8, Resulting Numbers: [31, 8] Generated Node #0,3,3: 93:[31, 8] Operation: 96-88=8 Moving to Node #0,2 Current State: 93:[88, 96, 91], Operations: ['61+30=91'] Exploring Operation: 91-88=3, Resulting Numbers: [96, 3] Generated Node #0,2,0: 93:[96, 3] Operation: 91-88=3 Exploring Operation: 96-91=5, Resulting Numbers: [88, 5] Generated Node #0,2,1: 93:[88, 5] Operation: 96-91=5 Exploring Operation: 88+91=179, Resulting Numbers: [96, 179] Generated Node #0,2,2: 93:[96, 179] Operation: 88+91=179 Exploring Operation: 96-88=8, Resulting Numbers: [91, 8] Generated Node #0,2,3: 93:[91, 8] Operation: 96-88=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[96, 3], Operations: ['61+30=91', '91-88=3'] Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,93 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[61, 88, 96, 30], Operations: [] Exploring Operation: 61+30=91, Resulting Numbers: [88, 96, 91] Generated Node #0,2: 93:[88, 96, 91] Operation: 61+30=91 Moving to Node #0,2 Current State: 93:[88, 96, 91], Operations: ['61+30=91'] Exploring Operation: 91-88=3, Resulting Numbers: [96, 3] Generated Node #0,2,0: 93:[96, 3] Operation: 91-88=3 Moving to Node #0,2,0 Current State: 93:[96, 3], Operations: ['61+30=91', '91-88=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 52, 1, 4, 41 ]
71
[ "4-1=3", "41*3=123", "123-52=71" ]
Current State: 71:[52, 1, 4, 41], Operations: [] Exploring Operation: 4-1=3, Resulting Numbers: [52, 41, 3] Generated Node #2: [52, 41, 3] from Operation: 4-1=3 Current State: 71:[52, 41, 3], Operations: ['4-1=3'] Exploring Operation: 41*3=123, Resulting Numbers: [52, 123] Generated Node #3: [52, 123] from Operation: 41*3=123 Current State: 71:[52, 123], Operations: ['4-1=3', '41*3=123'] Exploring Operation: 123-52=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[52, 1, 4, 41], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [52, 41, 5] Generated Node #0,0: 71:[52, 41, 5] Operation: 1+4=5 Exploring Operation: 52+1=53, Resulting Numbers: [4, 41, 53] Generated Node #0,1: 71:[4, 41, 53] Operation: 52+1=53 Exploring Operation: 52+4=56, Resulting Numbers: [1, 41, 56] Generated Node #0,2: 71:[1, 41, 56] Operation: 52+4=56 Moving to Node #0,0 Current State: 71:[52, 41, 5], Operations: ['1+4=5'] Exploring Operation: 52+5=57, Resulting Numbers: [41, 57] Generated Node #0,0,0: 71:[41, 57] Operation: 52+5=57 Exploring Operation: 41+5=46, Resulting Numbers: [52, 46] Generated Node #0,0,1: 71:[52, 46] Operation: 41+5=46 Exploring Operation: 52-5=47, Resulting Numbers: [41, 47] Generated Node #0,0,2: 71:[41, 47] Operation: 52-5=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[41, 57], Operations: ['1+4=5', '52+5=57'] Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,71 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[52, 46], Operations: ['1+4=5', '41+5=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,71 unequal: No Solution Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[41, 47], Operations: ['1+4=5', '52-5=47'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,71 unequal: No Solution Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,71 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[4, 41, 53], Operations: ['52+1=53'] Exploring Operation: 4+53=57, Resulting Numbers: [41, 57] Generated Node #0,1,0: 71:[41, 57] Operation: 4+53=57 Exploring Operation: 4+41=45, Resulting Numbers: [53, 45] Generated Node #0,1,1: 71:[53, 45] Operation: 4+41=45 Exploring Operation: 41-4=37, Resulting Numbers: [53, 37] Generated Node #0,1,2: 71:[53, 37] Operation: 41-4=37 Moving to Node #0,2 Current State: 71:[1, 41, 56], Operations: ['52+4=56'] Exploring Operation: 1+56=57, Resulting Numbers: [41, 57] Generated Node #0,2,0: 71:[41, 57] Operation: 1+56=57 Exploring Operation: 1*41=41, Resulting Numbers: [56, 41] Generated Node #0,2,1: 71:[56, 41] Operation: 1*41=41 Exploring Operation: 1+41=42, Resulting Numbers: [56, 42] Generated Node #0,2,2: 71:[56, 42] Operation: 1+41=42 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 71:[41, 57], Operations: ['52+4=56', '1+56=57'] Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 71:[56, 42], Operations: ['52+4=56', '1+41=42'] Exploring Operation: 56*42=2352, Resulting Numbers: [2352] 2352,71 unequal: No Solution Exploring Operation: 56-42=14, Resulting Numbers: [14] 14,71 unequal: No Solution Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 71:[56, 41], Operations: ['52+4=56', '1*41=41'] Exploring Operation: 56+41=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 56-41=15, Resulting Numbers: [15] 15,71 unequal: No Solution Exploring Operation: 56*41=2296, Resulting Numbers: [2296] 2296,71 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: 71:[41, 57], Operations: ['52+1=53', '4+53=57'] Exploring Operation: 41+57=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 41*57=2337, Resulting Numbers: [2337] 2337,71 unequal: No Solution Exploring Operation: 57-41=16, Resulting Numbers: [16] 16,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[53, 45], Operations: ['52+1=53', '4+41=45'] Exploring Operation: 53+45=98, Resulting Numbers: [98] 98,71 unequal: No Solution Exploring Operation: 53*45=2385, Resulting Numbers: [2385] 2385,71 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[53, 37], Operations: ['52+1=53', '41-4=37'] Exploring Operation: 53+37=90, Resulting Numbers: [90] 90,71 unequal: No Solution Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,71 unequal: No Solution Exploring Operation: 53*37=1961, Resulting Numbers: [1961] 1961,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 57, 6, 14, 5 ]
61
[ "6+14=20", "20/5=4", "57+4=61" ]
Current State: 61:[57, 6, 14, 5], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [57, 5, 20] Generated Node #2: [57, 5, 20] from Operation: 6+14=20 Current State: 61:[57, 5, 20], Operations: ['6+14=20'] Exploring Operation: 20/5=4, Resulting Numbers: [57, 4] Generated Node #3: [57, 4] from Operation: 20/5=4 Current State: 61:[57, 4], Operations: ['6+14=20', '20/5=4'] Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[57, 6, 14, 5], Operations: [] Exploring Operation: 14*5=70, Resulting Numbers: [57, 6, 70] Generated Node #0,0: 61:[57, 6, 70] Operation: 14*5=70 Exploring Operation: 6*14=84, Resulting Numbers: [57, 5, 84] Generated Node #0,1: 61:[57, 5, 84] Operation: 6*14=84 Exploring Operation: 6+14=20, Resulting Numbers: [57, 5, 20] Generated Node #0,2: 61:[57, 5, 20] Operation: 6+14=20 Exploring Operation: 6*5=30, Resulting Numbers: [57, 14, 30] Generated Node #0,3: 61:[57, 14, 30] Operation: 6*5=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[57, 6, 70], Operations: ['14*5=70'] Exploring Operation: 6+70=76, Resulting Numbers: [57, 76] Generated Node #0,0,0: 61:[57, 76] Operation: 6+70=76 Exploring Operation: 70-6=64, Resulting Numbers: [57, 64] Generated Node #0,0,1: 61:[57, 64] Operation: 70-6=64 Exploring Operation: 57+6=63, Resulting Numbers: [70, 63] Generated Node #0,0,2: 61:[70, 63] Operation: 57+6=63 Exploring Operation: 57-6=51, Resulting Numbers: [70, 51] Generated Node #0,0,3: 61:[70, 51] Operation: 57-6=51 Moving to Node #0,0,1 Current State: 61:[57, 64], Operations: ['14*5=70', '70-6=64'] Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 57+64=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 57*64=3648, Resulting Numbers: [3648] 3648,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[70, 63], Operations: ['14*5=70', '57+6=63'] Exploring Operation: 70+63=133, Resulting Numbers: [133] 133,61 unequal: No Solution Exploring Operation: 70-63=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 70*63=4410, Resulting Numbers: [4410] 4410,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[70, 51], Operations: ['14*5=70', '57-6=51'] Exploring Operation: 70+51=121, Resulting Numbers: [121] 121,61 unequal: No Solution Exploring Operation: 70*51=3570, Resulting Numbers: [3570] 3570,61 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[57, 76], Operations: ['14*5=70', '6+70=76'] Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,61 unequal: No Solution Exploring Operation: 57+76=133, Resulting Numbers: [133] 133,61 unequal: No Solution Exploring Operation: 57*76=4332, Resulting Numbers: [4332] 4332,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[57, 14, 30], Operations: ['6*5=30'] Exploring Operation: 30-14=16, Resulting Numbers: [57, 16] Generated Node #0,3,0: 61:[57, 16] Operation: 30-14=16 Exploring Operation: 57-14=43, Resulting Numbers: [30, 43] Generated Node #0,3,1: 61:[30, 43] Operation: 57-14=43 Exploring Operation: 57+14=71, Resulting Numbers: [30, 71] Generated Node #0,3,2: 61:[30, 71] Operation: 57+14=71 Exploring Operation: 14+30=44, Resulting Numbers: [57, 44] Generated Node #0,3,3: 61:[57, 44] Operation: 14+30=44 Moving to Node #0,3,3 Current State: 61:[57, 44], Operations: ['6*5=30', '14+30=44'] Exploring Operation: 57+44=101, Resulting Numbers: [101] 101,61 unequal: No Solution Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 57*44=2508, Resulting Numbers: [2508] 2508,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[30, 71], Operations: ['6*5=30', '57+14=71'] Exploring Operation: 30*71=2130, Resulting Numbers: [2130] 2130,61 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 30+71=101, Resulting Numbers: [101] 101,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[30, 43], Operations: ['6*5=30', '57-14=43'] Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 30*43=1290, Resulting Numbers: [1290] 1290,61 unequal: No Solution Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[57, 16], Operations: ['6*5=30', '30-14=16'] Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 57+16=73, Resulting Numbers: [73] 73,61 unequal: No Solution Exploring Operation: 57*16=912, Resulting Numbers: [912] 912,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[57, 5, 84], Operations: ['6*14=84'] Exploring Operation: 57-5=52, Resulting Numbers: [84, 52] Generated Node #0,1,0: 61:[84, 52] Operation: 57-5=52 Exploring Operation: 84-5=79, Resulting Numbers: [57, 79] Generated Node #0,1,1: 61:[57, 79] Operation: 84-5=79 Exploring Operation: 57+5=62, Resulting Numbers: [84, 62] Generated Node #0,1,2: 61:[84, 62] Operation: 57+5=62 Exploring Operation: 5+84=89, Resulting Numbers: [57, 89] Generated Node #0,1,3: 61:[57, 89] Operation: 5+84=89 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[57, 79], Operations: ['6*14=84', '84-5=79'] Exploring Operation: 57*79=4503, Resulting Numbers: [4503] 4503,61 unequal: No Solution Exploring Operation: 79-57=22, Resulting Numbers: [22] 22,61 unequal: No Solution Exploring Operation: 57+79=136, Resulting Numbers: [136] 136,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[84, 62], Operations: ['6*14=84', '57+5=62'] Exploring Operation: 84+62=146, Resulting Numbers: [146] 146,61 unequal: No Solution Exploring Operation: 84*62=5208, Resulting Numbers: [5208] 5208,61 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,61 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 #0,1,0 Current State: 61:[84, 52], Operations: ['6*14=84', '57-5=52'] Exploring Operation: 84-52=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 84+52=136, Resulting Numbers: [136] 136,61 unequal: No Solution Exploring Operation: 84*52=4368, Resulting Numbers: [4368] 4368,61 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 #0,1,3 Current State: 61:[57, 89], Operations: ['6*14=84', '5+84=89'] Exploring Operation: 57+89=146, Resulting Numbers: [146] 146,61 unequal: No Solution Exploring Operation: 89-57=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 57*89=5073, Resulting Numbers: [5073] 5073,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[57, 5, 20], Operations: ['6+14=20'] Exploring Operation: 5+20=25, Resulting Numbers: [57, 25] Generated Node #0,2,0: 61:[57, 25] Operation: 5+20=25 Exploring Operation: 5*20=100, Resulting Numbers: [57, 100] Generated Node #0,2,1: 61:[57, 100] Operation: 5*20=100 Exploring Operation: 57+5=62, Resulting Numbers: [20, 62] Generated Node #0,2,2: 61:[20, 62] Operation: 57+5=62 Exploring Operation: 57-5=52, Resulting Numbers: [20, 52] Generated Node #0,2,3: 61:[20, 52] Operation: 57-5=52 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[57, 25], Operations: ['6+14=20', '5+20=25'] Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,61 unequal: No Solution Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,61 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 #0,2,2 Current State: 61:[20, 62], Operations: ['6+14=20', '57+5=62'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 20*62=1240, Resulting Numbers: [1240] 1240,61 unequal: No Solution Exploring Operation: 20+62=82, Resulting Numbers: [82] 82,61 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 #0,2,1 Current State: 61:[57, 100], Operations: ['6+14=20', '5*20=100'] Exploring Operation: 57*100=5700, Resulting Numbers: [5700] 5700,61 unequal: No Solution Exploring Operation: 57+100=157, Resulting Numbers: [157] 157,61 unequal: No Solution Exploring Operation: 100-57=43, Resulting Numbers: [43] 43,61 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 #0,2,3 Current State: 61:[20, 52], Operations: ['6+14=20', '57-5=52'] Exploring Operation: 20+52=72, Resulting Numbers: [72] 72,61 unequal: No Solution Exploring Operation: 52-20=32, Resulting Numbers: [32] 32,61 unequal: No Solution Exploring Operation: 20*52=1040, Resulting Numbers: [1040] 1040,61 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 No solution found.
0
hs_4
mult_heuristic
[ 40, 30, 45, 47 ]
72
[ "40+30=70", "47-45=2", "70+2=72" ]
Current State: 72:[40, 30, 45, 47], Operations: [] Exploring Operation: 40+30=70, Resulting Numbers: [45, 47, 70] Generated Node #2: [45, 47, 70] from Operation: 40+30=70 Current State: 72:[45, 47, 70], Operations: ['40+30=70'] Exploring Operation: 47-45=2, Resulting Numbers: [70, 2] Generated Node #3: [70, 2] from Operation: 47-45=2 Current State: 72:[70, 2], Operations: ['40+30=70', '47-45=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[40, 30, 45, 47], Operations: [] Exploring Operation: 45-40=5, Resulting Numbers: [30, 47, 5] Generated Node #0,0: 72:[30, 47, 5] Operation: 45-40=5 Exploring Operation: 47-40=7, Resulting Numbers: [30, 45, 7] Generated Node #0,1: 72:[30, 45, 7] Operation: 47-40=7 Exploring Operation: 30+45=75, Resulting Numbers: [40, 47, 75] Generated Node #0,2: 72:[40, 47, 75] Operation: 30+45=75 Exploring Operation: 47-30=17, Resulting Numbers: [40, 45, 17] Generated Node #0,3: 72:[40, 45, 17] Operation: 47-30=17 Exploring Operation: 47-45=2, Resulting Numbers: [40, 30, 2] Generated Node #0,4: 72:[40, 30, 2] Operation: 47-45=2 Moving to Node #0,4 Current State: 72:[40, 30, 2], Operations: ['47-45=2'] Exploring Operation: 40-2=38, Resulting Numbers: [30, 38] Generated Node #0,4,0: 72:[30, 38] Operation: 40-2=38 Exploring Operation: 40+30=70, Resulting Numbers: [2, 70] Generated Node #0,4,1: 72:[2, 70] Operation: 40+30=70 Exploring Operation: 40/2=20, Resulting Numbers: [30, 20] Generated Node #0,4,2: 72:[30, 20] Operation: 40/2=20 Exploring Operation: 30/2=15, Resulting Numbers: [40, 15] Generated Node #0,4,3: 72:[40, 15] Operation: 30/2=15 Exploring Operation: 40-30=10, Resulting Numbers: [2, 10] Generated Node #0,4,4: 72:[2, 10] Operation: 40-30=10 Moving to Node #0,3 Current State: 72:[40, 45, 17], Operations: ['47-30=17'] Exploring Operation: 45-40=5, Resulting Numbers: [17, 5] Generated Node #0,3,0: 72:[17, 5] Operation: 45-40=5 Exploring Operation: 40-17=23, Resulting Numbers: [45, 23] Generated Node #0,3,1: 72:[45, 23] Operation: 40-17=23 Exploring Operation: 45+17=62, Resulting Numbers: [40, 62] Generated Node #0,3,2: 72:[40, 62] Operation: 45+17=62 Exploring Operation: 45-17=28, Resulting Numbers: [40, 28] Generated Node #0,3,3: 72:[40, 28] Operation: 45-17=28 Exploring Operation: 40+45=85, Resulting Numbers: [17, 85] Generated Node #0,3,4: 72:[17, 85] Operation: 40+45=85 Moving to Node #0,1 Current State: 72:[30, 45, 7], Operations: ['47-40=7'] Exploring Operation: 30+7=37, Resulting Numbers: [45, 37] Generated Node #0,1,0: 72:[45, 37] Operation: 30+7=37 Exploring Operation: 30+45=75, Resulting Numbers: [7, 75] Generated Node #0,1,1: 72:[7, 75] Operation: 30+45=75 Exploring Operation: 45-7=38, Resulting Numbers: [30, 38] Generated Node #0,1,2: 72:[30, 38] Operation: 45-7=38 Exploring Operation: 30-7=23, Resulting Numbers: [45, 23] Generated Node #0,1,3: 72:[45, 23] Operation: 30-7=23 Exploring Operation: 45-30=15, Resulting Numbers: [7, 15] Generated Node #0,1,4: 72:[7, 15] Operation: 45-30=15 Moving to Node #0,0 Current State: 72:[30, 47, 5], Operations: ['45-40=5'] Exploring Operation: 30+47=77, Resulting Numbers: [5, 77] Generated Node #0,0,0: 72:[5, 77] Operation: 30+47=77 Exploring Operation: 30-5=25, Resulting Numbers: [47, 25] Generated Node #0,0,1: 72:[47, 25] Operation: 30-5=25 Exploring Operation: 47-30=17, Resulting Numbers: [5, 17] Generated Node #0,0,2: 72:[5, 17] Operation: 47-30=17 Exploring Operation: 30+5=35, Resulting Numbers: [47, 35] Generated Node #0,0,3: 72:[47, 35] Operation: 30+5=35 Exploring Operation: 30/5=6, Resulting Numbers: [47, 6] Generated Node #0,0,4: 72:[47, 6] Operation: 30/5=6 Moving to Node #0,2 Current State: 72:[40, 47, 75], Operations: ['30+45=75'] Exploring Operation: 75-40=35, Resulting Numbers: [47, 35] Generated Node #0,2,0: 72:[47, 35] Operation: 75-40=35 Exploring Operation: 40+75=115, Resulting Numbers: [47, 115] Generated Node #0,2,1: 72:[47, 115] Operation: 40+75=115 Exploring Operation: 40+47=87, Resulting Numbers: [75, 87] Generated Node #0,2,2: 72:[75, 87] Operation: 40+47=87 Exploring Operation: 75-47=28, Resulting Numbers: [40, 28] Generated Node #0,2,3: 72:[40, 28] Operation: 75-47=28 Exploring Operation: 47-40=7, Resulting Numbers: [75, 7] Generated Node #0,2,4: 72:[75, 7] Operation: 47-40=7 Moving to Node #0,4,4 Current State: 72:[2, 10], Operations: ['47-45=2', '40-30=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[17, 5], Operations: ['47-30=17', '45-40=5'] Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[2, 70], Operations: ['47-45=2', '40+30=70'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[40, 30, 45, 47], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [40, 30, 2] Generated Node #0,4: 72:[40, 30, 2] Operation: 47-45=2 Moving to Node #0,4 Current State: 72:[40, 30, 2], Operations: ['47-45=2'] Exploring Operation: 40+30=70, Resulting Numbers: [2, 70] Generated Node #0,4,1: 72:[2, 70] Operation: 40+30=70 Moving to Node #0,4,1 Current State: 72:[2, 70], Operations: ['47-45=2', '40+30=70'] Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.962674
hs_5
mult_heuristic
[ 20, 61, 8, 67 ]
100
[ "61-20=41", "67-8=59", "41+59=100" ]
Current State: 100:[20, 61, 8, 67], Operations: [] Exploring Operation: 61-20=41, Resulting Numbers: [8, 67, 41] Generated Node #2: [8, 67, 41] from Operation: 61-20=41 Current State: 100:[8, 67, 41], Operations: ['61-20=41'] Exploring Operation: 67-8=59, Resulting Numbers: [41, 59] Generated Node #3: [41, 59] from Operation: 67-8=59 Current State: 100:[41, 59], Operations: ['61-20=41', '67-8=59'] Exploring Operation: 41+59=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[20, 61, 8, 67], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [20, 8, 6] Generated Node #0,0: 100:[20, 8, 6] Operation: 67-61=6 Exploring Operation: 67-20=47, Resulting Numbers: [61, 8, 47] Generated Node #0,1: 100:[61, 8, 47] Operation: 67-20=47 Moving to Node #0,0 Current State: 100:[20, 8, 6], Operations: ['67-61=6'] Exploring Operation: 8-6=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 100:[20, 2] Operation: 8-6=2 Exploring Operation: 8*6=48, Resulting Numbers: [20, 48] Generated Node #0,0,1: 100:[20, 48] Operation: 8*6=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[20, 2], Operations: ['67-61=6', '8-6=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,100 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 #0,0,1 Current State: 100:[20, 48], Operations: ['67-61=6', '8*6=48'] Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,100 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: 100:[61, 8, 47], Operations: ['67-20=47'] Exploring Operation: 61-47=14, Resulting Numbers: [8, 14] Generated Node #0,1,0: 100:[8, 14] Operation: 61-47=14 Exploring Operation: 61-8=53, Resulting Numbers: [47, 53] Generated Node #0,1,1: 100:[47, 53] Operation: 61-8=53 Moving to Node #0,1,0 Current State: 100:[8, 14], Operations: ['67-20=47', '61-47=14'] Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,100 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[47, 53], Operations: ['67-20=47', '61-8=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[20, 61, 8, 67], Operations: [] Exploring Operation: 67-20=47, Resulting Numbers: [61, 8, 47] Generated Node #0,1: 100:[61, 8, 47] Operation: 67-20=47 Moving to Node #0,1 Current State: 100:[61, 8, 47], Operations: ['67-20=47'] Exploring Operation: 61-8=53, Resulting Numbers: [47, 53] Generated Node #0,1,1: 100:[47, 53] Operation: 61-8=53 Moving to Node #0,1,1 Current State: 100:[47, 53], Operations: ['67-20=47', '61-8=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 87, 79, 97, 5 ]
84
[ "87-79=8", "97-5=92", "92-8=84" ]
Current State: 84:[87, 79, 97, 5], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [97, 5, 8] Generated Node #2: [97, 5, 8] from Operation: 87-79=8 Current State: 84:[97, 5, 8], Operations: ['87-79=8'] Exploring Operation: 97-5=92, Resulting Numbers: [8, 92] Generated Node #3: [8, 92] from Operation: 97-5=92 Current State: 84:[8, 92], Operations: ['87-79=8', '97-5=92'] Exploring Operation: 92-8=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[87, 79, 97, 5], Operations: [] Exploring Operation: 97-79=18, Resulting Numbers: [87, 5, 18] Generated Node #0,0: 84:[87, 5, 18] Operation: 97-79=18 Exploring Operation: 87-79=8, Resulting Numbers: [97, 5, 8] Generated Node #0,1: 84:[97, 5, 8] Operation: 87-79=8 Exploring Operation: 97-87=10, Resulting Numbers: [79, 5, 10] Generated Node #0,2: 84:[79, 5, 10] Operation: 97-87=10 Exploring Operation: 79+5=84, Resulting Numbers: [87, 97, 84] Generated Node #0,3: 84:[87, 97, 84] Operation: 79+5=84 Exploring Operation: 97-5=92, Resulting Numbers: [87, 79, 92] Generated Node #0,4: 84:[87, 79, 92] Operation: 97-5=92 Moving to Node #0,0 Current State: 84:[87, 5, 18], Operations: ['97-79=18'] Exploring Operation: 87-5=82, Resulting Numbers: [18, 82] Generated Node #0,0,0: 84:[18, 82] Operation: 87-5=82 Exploring Operation: 5*18=90, Resulting Numbers: [87, 90] Generated Node #0,0,1: 84:[87, 90] Operation: 5*18=90 Exploring Operation: 18-5=13, Resulting Numbers: [87, 13] Generated Node #0,0,2: 84:[87, 13] Operation: 18-5=13 Exploring Operation: 5+18=23, Resulting Numbers: [87, 23] Generated Node #0,0,3: 84:[87, 23] Operation: 5+18=23 Exploring Operation: 87+5=92, Resulting Numbers: [18, 92] Generated Node #0,0,4: 84:[18, 92] Operation: 87+5=92 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[87, 13], Operations: ['97-79=18', '18-5=13'] Exploring Operation: 87+13=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 87*13=1131, Resulting Numbers: [1131] 1131,84 unequal: No Solution Exploring Operation: 87-13=74, Resulting Numbers: [74] 74,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[18, 82], Operations: ['97-79=18', '87-5=82'] Exploring Operation: 18+82=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 18*82=1476, Resulting Numbers: [1476] 1476,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[87, 23], Operations: ['97-79=18', '5+18=23'] Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 87+23=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 87*23=2001, Resulting Numbers: [2001] 2001,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[87, 90], Operations: ['97-79=18', '5*18=90'] Exploring Operation: 87+90=177, Resulting Numbers: [177] 177,84 unequal: No Solution Exploring Operation: 87*90=7830, Resulting Numbers: [7830] 7830,84 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 84:[18, 92], Operations: ['97-79=18', '87+5=92'] Exploring Operation: 18*92=1656, Resulting Numbers: [1656] 1656,84 unequal: No Solution Exploring Operation: 18+92=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,84 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: 84:[79, 5, 10], Operations: ['97-87=10'] Exploring Operation: 10-5=5, Resulting Numbers: [79, 5] Generated Node #0,2,0: 84:[79, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [79, 2] Generated Node #0,2,1: 84:[79, 2] Operation: 10/5=2 Exploring Operation: 5+10=15, Resulting Numbers: [79, 15] Generated Node #0,2,2: 84:[79, 15] Operation: 5+10=15 Exploring Operation: 79+5=84, Resulting Numbers: [10, 84] Generated Node #0,2,3: 84:[10, 84] Operation: 79+5=84 Exploring Operation: 79+10=89, Resulting Numbers: [5, 89] Generated Node #0,2,4: 84:[5, 89] Operation: 79+10=89 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[10, 84], Operations: ['97-87=10', '79+5=84'] Exploring Operation: 10+84=94, Resulting Numbers: [94] 94,84 unequal: No Solution Exploring Operation: 10*84=840, Resulting Numbers: [840] 840,84 unequal: No Solution Exploring Operation: 84-10=74, Resulting Numbers: [74] 74,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[79, 2], Operations: ['97-87=10', '10/5=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,84 unequal: No Solution Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[79, 5], Operations: ['97-87=10', '10-5=5'] Exploring Operation: 79*5=395, Resulting Numbers: [395] 395,84 unequal: No Solution Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[87, 79, 97, 5], Operations: [] Exploring Operation: 97-87=10, Resulting Numbers: [79, 5, 10] Generated Node #0,2: 84:[79, 5, 10] Operation: 97-87=10 Moving to Node #0,2 Current State: 84:[79, 5, 10], Operations: ['97-87=10'] Exploring Operation: 10-5=5, Resulting Numbers: [79, 5] Generated Node #0,2,0: 84:[79, 5] Operation: 10-5=5 Moving to Node #0,2,0 Current State: 84:[79, 5], Operations: ['97-87=10', '10-5=5'] Exploring Operation: 79+5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
mult_heuristic
[ 4, 44, 39, 81 ]
61
[ "44-39=5", "4*5=20", "81-20=61" ]
Current State: 61:[4, 44, 39, 81], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [4, 81, 5] Generated Node #2: [4, 81, 5] from Operation: 44-39=5 Current State: 61:[4, 81, 5], Operations: ['44-39=5'] Exploring Operation: 4*5=20, Resulting Numbers: [81, 20] Generated Node #3: [81, 20] from Operation: 4*5=20 Current State: 61:[81, 20], Operations: ['44-39=5', '4*5=20'] Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[4, 44, 39, 81], Operations: [] Exploring Operation: 4+39=43, Resulting Numbers: [44, 81, 43] Generated Node #0,0: 61:[44, 81, 43] Operation: 4+39=43 Exploring Operation: 4+44=48, Resulting Numbers: [39, 81, 48] Generated Node #0,1: 61:[39, 81, 48] Operation: 4+44=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[44, 81, 43], Operations: ['4+39=43'] Exploring Operation: 81-44=37, Resulting Numbers: [43, 37] Generated Node #0,0,0: 61:[43, 37] Operation: 81-44=37 Exploring Operation: 81-43=38, Resulting Numbers: [44, 38] Generated Node #0,0,1: 61:[44, 38] Operation: 81-43=38 Moving to Node #0,0,1 Current State: 61:[44, 38], Operations: ['4+39=43', '81-43=38'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[43, 37], Operations: ['4+39=43', '81-44=37'] Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,61 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[39, 81, 48], Operations: ['4+44=48'] Exploring Operation: 81-39=42, Resulting Numbers: [48, 42] Generated Node #0,1,0: 61:[48, 42] Operation: 81-39=42 Exploring Operation: 39+48=87, Resulting Numbers: [81, 87] Generated Node #0,1,1: 61:[81, 87] Operation: 39+48=87 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[48, 42], Operations: ['4+44=48', '81-39=42'] Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,61 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,61 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:[81, 87], Operations: ['4+44=48', '39+48=87'] Exploring Operation: 87-81=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 81+87=168, Resulting Numbers: [168] 168,61 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 No solution found.
0
hs_2
sum_heuristic
[ 46, 72, 64, 36 ]
87
[ "46*36=1656", "1656/72=23", "64+23=87" ]
Current State: 87:[46, 72, 64, 36], Operations: [] Exploring Operation: 46*36=1656, Resulting Numbers: [72, 64, 1656] Generated Node #2: [72, 64, 1656] from Operation: 46*36=1656 Current State: 87:[72, 64, 1656], Operations: ['46*36=1656'] Exploring Operation: 1656/72=23, Resulting Numbers: [64, 23] Generated Node #3: [64, 23] from Operation: 1656/72=23 Current State: 87:[64, 23], Operations: ['46*36=1656', '1656/72=23'] Exploring Operation: 64+23=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[46, 72, 64, 36], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [64, 36, 26] Generated Node #0,0: 87:[64, 36, 26] Operation: 72-46=26 Exploring Operation: 64-46=18, Resulting Numbers: [72, 36, 18] Generated Node #0,1: 87:[72, 36, 18] Operation: 64-46=18 Exploring Operation: 64-36=28, Resulting Numbers: [46, 72, 28] Generated Node #0,2: 87:[46, 72, 28] Operation: 64-36=28 Exploring Operation: 72-64=8, Resulting Numbers: [46, 36, 8] Generated Node #0,3: 87:[46, 36, 8] Operation: 72-64=8 Moving to Node #0,3 Current State: 87:[46, 36, 8], Operations: ['72-64=8'] Exploring Operation: 46-36=10, Resulting Numbers: [8, 10] Generated Node #0,3,0: 87:[8, 10] Operation: 46-36=10 Exploring Operation: 46-8=38, Resulting Numbers: [36, 38] Generated Node #0,3,1: 87:[36, 38] Operation: 46-8=38 Exploring Operation: 36-8=28, Resulting Numbers: [46, 28] Generated Node #0,3,2: 87:[46, 28] Operation: 36-8=28 Exploring Operation: 46+36=82, Resulting Numbers: [8, 82] Generated Node #0,3,3: 87:[8, 82] Operation: 46+36=82 Moving to Node #0,1 Current State: 87:[72, 36, 18], Operations: ['64-46=18'] Exploring Operation: 72+18=90, Resulting Numbers: [36, 90] Generated Node #0,1,0: 87:[36, 90] Operation: 72+18=90 Exploring Operation: 72/18=4, Resulting Numbers: [36, 4] Generated Node #0,1,1: 87:[36, 4] Operation: 72/18=4 Exploring Operation: 72/36=2, Resulting Numbers: [18, 2] Generated Node #0,1,2: 87:[18, 2] Operation: 72/36=2 Exploring Operation: 36/18=2, Resulting Numbers: [72, 2] Generated Node #0,1,3: 87:[72, 2] Operation: 36/18=2 Moving to Node #0,0 Current State: 87:[64, 36, 26], Operations: ['72-46=26'] Exploring Operation: 64-26=38, Resulting Numbers: [36, 38] Generated Node #0,0,0: 87:[36, 38] Operation: 64-26=38 Exploring Operation: 64+36=100, Resulting Numbers: [26, 100] Generated Node #0,0,1: 87:[26, 100] Operation: 64+36=100 Exploring Operation: 64+26=90, Resulting Numbers: [36, 90] Generated Node #0,0,2: 87:[36, 90] Operation: 64+26=90 Exploring Operation: 64-36=28, Resulting Numbers: [26, 28] Generated Node #0,0,3: 87:[26, 28] Operation: 64-36=28 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 87:[26, 28], Operations: ['72-46=26', '64-36=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[36, 90], Operations: ['72-46=26', '64+26=90'] Exploring Operation: 36*90=3240, Resulting Numbers: [3240] 3240,87 unequal: No Solution Exploring Operation: 36+90=126, Resulting Numbers: [126] 126,87 unequal: No Solution Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[36, 38], Operations: ['72-46=26', '64-26=38'] Exploring Operation: 36+38=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 36*38=1368, Resulting Numbers: [1368] 1368,87 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[26, 100], Operations: ['72-46=26', '64+36=100'] Exploring Operation: 26*100=2600, Resulting Numbers: [2600] 2600,87 unequal: No Solution Exploring Operation: 100-26=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 26+100=126, Resulting Numbers: [126] 126,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 87:[46, 72, 28], Operations: ['64-36=28'] Exploring Operation: 46+28=74, Resulting Numbers: [72, 74] Generated Node #0,2,0: 87:[72, 74] Operation: 46+28=74 Exploring Operation: 72-46=26, Resulting Numbers: [28, 26] Generated Node #0,2,1: 87:[28, 26] Operation: 72-46=26 Exploring Operation: 72+28=100, Resulting Numbers: [46, 100] Generated Node #0,2,2: 87:[46, 100] Operation: 72+28=100 Exploring Operation: 46-28=18, Resulting Numbers: [72, 18] Generated Node #0,2,3: 87:[72, 18] Operation: 46-28=18 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[28, 26], Operations: ['64-36=28', '72-46=26'] Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[72, 18], Operations: ['64-36=28', '46-28=18'] Exploring Operation: 72+18=90, Resulting Numbers: [90] 90,87 unequal: No Solution Exploring Operation: 72*18=1296, Resulting Numbers: [1296] 1296,87 unequal: No Solution Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[72, 74], Operations: ['64-36=28', '46+28=74'] Exploring Operation: 72+74=146, Resulting Numbers: [146] 146,87 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 72*74=5328, Resulting Numbers: [5328] 5328,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[46, 100], Operations: ['64-36=28', '72+28=100'] Exploring Operation: 46*100=4600, Resulting Numbers: [4600] 4600,87 unequal: No Solution Exploring Operation: 100-46=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 46+100=146, Resulting Numbers: [146] 146,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 87:[36, 4], Operations: ['64-46=18', '72/18=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,87 unequal: No Solution Exploring Operation: 36*4=144, Resulting Numbers: [144] 144,87 unequal: No Solution Exploring Operation: 36+4=40, Resulting Numbers: [40] 40,87 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[36, 90], Operations: ['64-46=18', '72+18=90'] Exploring Operation: 36*90=3240, Resulting Numbers: [3240] 3240,87 unequal: No Solution Exploring Operation: 36+90=126, Resulting Numbers: [126] 126,87 unequal: No Solution Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[8, 82], Operations: ['72-64=8', '46+36=82'] Exploring Operation: 8*82=656, Resulting Numbers: [656] 656,87 unequal: No Solution Exploring Operation: 8+82=90, Resulting Numbers: [90] 90,87 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[18, 2], Operations: ['64-46=18', '72/36=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,87 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,87 unequal: No Solution Moving to Node #0,3,0 Current State: 87:[8, 10], Operations: ['72-64=8', '46-36=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[36, 38], Operations: ['72-64=8', '46-8=38'] Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 36*38=1368, Resulting Numbers: [1368] 1368,87 unequal: No Solution Exploring Operation: 36+38=74, Resulting Numbers: [74] 74,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[72, 2], Operations: ['64-46=18', '36/18=2'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,87 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[46, 28], Operations: ['72-64=8', '36-8=28'] Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,87 unequal: No Solution Exploring Operation: 46*28=1288, Resulting Numbers: [1288] 1288,87 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 37, 15, 11, 7 ]
34
[ "37+15=52", "11+7=18", "52-18=34" ]
Current State: 34:[37, 15, 11, 7], Operations: [] Exploring Operation: 37+15=52, Resulting Numbers: [11, 7, 52] Generated Node #2: [11, 7, 52] from Operation: 37+15=52 Current State: 34:[11, 7, 52], Operations: ['37+15=52'] Exploring Operation: 11+7=18, Resulting Numbers: [52, 18] Generated Node #3: [52, 18] from Operation: 11+7=18 Current State: 34:[52, 18], Operations: ['37+15=52', '11+7=18'] Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[37, 15, 11, 7], Operations: [] Exploring Operation: 15+7=22, Resulting Numbers: [37, 11, 22] Generated Node #0,0: 34:[37, 11, 22] Operation: 15+7=22 Exploring Operation: 11+7=18, Resulting Numbers: [37, 15, 18] Generated Node #0,1: 34:[37, 15, 18] Operation: 11+7=18 Exploring Operation: 11-7=4, Resulting Numbers: [37, 15, 4] Generated Node #0,2: 34:[37, 15, 4] Operation: 11-7=4 Exploring Operation: 15-11=4, Resulting Numbers: [37, 7, 4] Generated Node #0,3: 34:[37, 7, 4] Operation: 15-11=4 Exploring Operation: 37-7=30, Resulting Numbers: [15, 11, 30] Generated Node #0,4: 34:[15, 11, 30] Operation: 37-7=30 Moving to Node #0,1 Current State: 34:[37, 15, 18], Operations: ['11+7=18'] Exploring Operation: 37+15=52, Resulting Numbers: [18, 52] Generated Node #0,1,0: 34:[18, 52] Operation: 37+15=52 Exploring Operation: 37-18=19, Resulting Numbers: [15, 19] Generated Node #0,1,1: 34:[15, 19] Operation: 37-18=19 Exploring Operation: 37-15=22, Resulting Numbers: [18, 22] Generated Node #0,1,2: 34:[18, 22] Operation: 37-15=22 Exploring Operation: 15+18=33, Resulting Numbers: [37, 33] Generated Node #0,1,3: 34:[37, 33] Operation: 15+18=33 Exploring Operation: 18-15=3, Resulting Numbers: [37, 3] Generated Node #0,1,4: 34:[37, 3] Operation: 18-15=3 Moving to Node #0,2 Current State: 34:[37, 15, 4], Operations: ['11-7=4'] Exploring Operation: 37-4=33, Resulting Numbers: [15, 33] Generated Node #0,2,0: 34:[15, 33] Operation: 37-4=33 Exploring Operation: 37-15=22, Resulting Numbers: [4, 22] Generated Node #0,2,1: 34:[4, 22] Operation: 37-15=22 Exploring Operation: 15-4=11, Resulting Numbers: [37, 11] Generated Node #0,2,2: 34:[37, 11] Operation: 15-4=11 Exploring Operation: 15+4=19, Resulting Numbers: [37, 19] Generated Node #0,2,3: 34:[37, 19] Operation: 15+4=19 Exploring Operation: 37+4=41, Resulting Numbers: [15, 41] Generated Node #0,2,4: 34:[15, 41] Operation: 37+4=41 Moving to Node #0,3 Current State: 34:[37, 7, 4], Operations: ['15-11=4'] Exploring Operation: 7-4=3, Resulting Numbers: [37, 3] Generated Node #0,3,0: 34:[37, 3] Operation: 7-4=3 Exploring Operation: 7+4=11, Resulting Numbers: [37, 11] Generated Node #0,3,1: 34:[37, 11] Operation: 7+4=11 Exploring Operation: 37-7=30, Resulting Numbers: [4, 30] Generated Node #0,3,2: 34:[4, 30] Operation: 37-7=30 Exploring Operation: 7*4=28, Resulting Numbers: [37, 28] Generated Node #0,3,3: 34:[37, 28] Operation: 7*4=28 Exploring Operation: 37-4=33, Resulting Numbers: [7, 33] Generated Node #0,3,4: 34:[7, 33] Operation: 37-4=33 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 34:[37, 3], Operations: ['15-11=4', '7-4=3'] Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[37, 15, 11, 7], Operations: [] Exploring Operation: 15-11=4, Resulting Numbers: [37, 7, 4] Generated Node #0,3: 34:[37, 7, 4] Operation: 15-11=4 Moving to Node #0,3 Current State: 34:[37, 7, 4], Operations: ['15-11=4'] Exploring Operation: 7-4=3, Resulting Numbers: [37, 3] Generated Node #0,3,0: 34:[37, 3] Operation: 7-4=3 Moving to Node #0,3,0 Current State: 34:[37, 3], Operations: ['15-11=4', '7-4=3'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 50, 45, 2, 45 ]
70
[ "50+45=95", "45+95=140", "140/2=70" ]
Current State: 70:[50, 45, 2, 45], Operations: [] Exploring Operation: 50+45=95, Resulting Numbers: [2, 95] Generated Node #2: [2, 95] from Operation: 50+45=95 Current State: 70:[2, 95], Operations: ['50+45=95'] Exploring Operation: 45+95=140, Resulting Numbers: [2, 140] Generated Node #3: [2, 140] from Operation: 45+95=140 Current State: 70:[2, 140], Operations: ['50+45=95', '45+95=140'] Exploring Operation: 140/2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[50, 45, 2, 45], Operations: [] Exploring Operation: 50-45=5, Resulting Numbers: [2, 45, 5] Generated Node #0,0: 70:[2, 45, 5] Operation: 50-45=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[2, 45, 5], Operations: ['50-45=5'] Exploring Operation: 45/5=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 70:[2, 9] Operation: 45/5=9 Moving to Node #0,0,0 Current State: 70:[2, 9], Operations: ['50-45=5', '45/5=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,70 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
[ 32, 25, 54, 97 ]
50
[ "32-25=7", "97-54=43", "7+43=50" ]
Current State: 50:[32, 25, 54, 97], Operations: [] Exploring Operation: 32-25=7, Resulting Numbers: [54, 97, 7] Generated Node #2: [54, 97, 7] from Operation: 32-25=7 Current State: 50:[54, 97, 7], Operations: ['32-25=7'] Exploring Operation: 97-54=43, Resulting Numbers: [7, 43] Generated Node #3: [7, 43] from Operation: 97-54=43 Current State: 50:[7, 43], Operations: ['32-25=7', '97-54=43'] Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[32, 25, 54, 97], Operations: [] Exploring Operation: 97-54=43, Resulting Numbers: [32, 25, 43] Generated Node #0,0: 50:[32, 25, 43] Operation: 97-54=43 Exploring Operation: 97-25=72, Resulting Numbers: [32, 54, 72] Generated Node #0,1: 50:[32, 54, 72] Operation: 97-25=72 Exploring Operation: 54-32=22, Resulting Numbers: [25, 97, 22] Generated Node #0,2: 50:[25, 97, 22] Operation: 54-32=22 Exploring Operation: 32-25=7, Resulting Numbers: [54, 97, 7] Generated Node #0,3: 50:[54, 97, 7] Operation: 32-25=7 Exploring Operation: 97-32=65, Resulting Numbers: [25, 54, 65] Generated Node #0,4: 50:[25, 54, 65] Operation: 97-32=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[32, 25, 43], Operations: ['97-54=43'] Exploring Operation: 32+25=57, Resulting Numbers: [43, 57] Generated Node #0,0,0: 50:[43, 57] Operation: 32+25=57 Exploring Operation: 43-32=11, Resulting Numbers: [25, 11] Generated Node #0,0,1: 50:[25, 11] Operation: 43-32=11 Exploring Operation: 32+43=75, Resulting Numbers: [25, 75] Generated Node #0,0,2: 50:[25, 75] Operation: 32+43=75 Exploring Operation: 32-25=7, Resulting Numbers: [43, 7] Generated Node #0,0,3: 50:[43, 7] Operation: 32-25=7 Exploring Operation: 43-25=18, Resulting Numbers: [32, 18] Generated Node #0,0,4: 50:[32, 18] Operation: 43-25=18 Moving to Node #0,0,1 Current State: 50:[25, 11], Operations: ['97-54=43', '43-32=11'] Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,50 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[43, 7], Operations: ['97-54=43', '32-25=7'] Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 43*7=301, Resulting Numbers: [301] 301,50 unequal: No Solution Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[32, 25, 54, 97], Operations: [] Exploring Operation: 97-54=43, Resulting Numbers: [32, 25, 43] Generated Node #0,0: 50:[32, 25, 43] Operation: 97-54=43 Moving to Node #0,0 Current State: 50:[32, 25, 43], Operations: ['97-54=43'] Exploring Operation: 32-25=7, Resulting Numbers: [43, 7] Generated Node #0,0,3: 50:[43, 7] Operation: 32-25=7 Moving to Node #0,0,3 Current State: 50:[43, 7], Operations: ['97-54=43', '32-25=7'] Exploring Operation: 43+7=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 71, 80, 14, 52 ]
85
[ "71+80=151", "14+52=66", "151-66=85" ]
Current State: 85:[71, 80, 14, 52], Operations: [] Exploring Operation: 71+80=151, Resulting Numbers: [14, 52, 151] Generated Node #2: [14, 52, 151] from Operation: 71+80=151 Current State: 85:[14, 52, 151], Operations: ['71+80=151'] Exploring Operation: 14+52=66, Resulting Numbers: [151, 66] Generated Node #3: [151, 66] from Operation: 14+52=66 Current State: 85:[151, 66], Operations: ['71+80=151', '14+52=66'] Exploring Operation: 151-66=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[71, 80, 14, 52], Operations: [] Exploring Operation: 71-52=19, Resulting Numbers: [80, 14, 19] Generated Node #0,0: 85:[80, 14, 19] Operation: 71-52=19 Exploring Operation: 71+14=85, Resulting Numbers: [80, 52, 85] Generated Node #0,1: 85:[80, 52, 85] Operation: 71+14=85 Exploring Operation: 80-52=28, Resulting Numbers: [71, 14, 28] Generated Node #0,2: 85:[71, 14, 28] Operation: 80-52=28 Exploring Operation: 14+52=66, Resulting Numbers: [71, 80, 66] Generated Node #0,3: 85:[71, 80, 66] Operation: 14+52=66 Moving to Node #0,0 Current State: 85:[80, 14, 19], Operations: ['71-52=19'] Exploring Operation: 19-14=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 85:[80, 5] Operation: 19-14=5 Exploring Operation: 80+14=94, Resulting Numbers: [19, 94] Generated Node #0,0,1: 85:[19, 94] Operation: 80+14=94 Exploring Operation: 80+19=99, Resulting Numbers: [14, 99] Generated Node #0,0,2: 85:[14, 99] Operation: 80+19=99 Exploring Operation: 80-14=66, Resulting Numbers: [19, 66] Generated Node #0,0,3: 85:[19, 66] Operation: 80-14=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[80, 5], Operations: ['71-52=19', '19-14=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,85 unequal: No Solution Exploring Operation: 80*5=400, Resulting Numbers: [400] 400,85 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[71, 80, 14, 52], Operations: [] Exploring Operation: 71-52=19, Resulting Numbers: [80, 14, 19] Generated Node #0,0: 85:[80, 14, 19] Operation: 71-52=19 Moving to Node #0,0 Current State: 85:[80, 14, 19], Operations: ['71-52=19'] Exploring Operation: 19-14=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 85:[80, 5] Operation: 19-14=5 Moving to Node #0,0,0 Current State: 85:[80, 5], Operations: ['71-52=19', '19-14=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 32, 10, 75, 66 ]
78
[ "32-10=22", "66/22=3", "75+3=78" ]
Current State: 78:[32, 10, 75, 66], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [75, 66, 22] Generated Node #2: [75, 66, 22] from Operation: 32-10=22 Current State: 78:[75, 66, 22], Operations: ['32-10=22'] Exploring Operation: 66/22=3, Resulting Numbers: [75, 3] Generated Node #3: [75, 3] from Operation: 66/22=3 Current State: 78:[75, 3], Operations: ['32-10=22', '66/22=3'] Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[32, 10, 75, 66], Operations: [] Exploring Operation: 66-32=34, Resulting Numbers: [10, 75, 34] Generated Node #0,0: 78:[10, 75, 34] Operation: 66-32=34 Exploring Operation: 10+66=76, Resulting Numbers: [32, 75, 76] Generated Node #0,1: 78:[32, 75, 76] Operation: 10+66=76 Moving to Node #0,0 Current State: 78:[10, 75, 34], Operations: ['66-32=34'] Exploring Operation: 75-34=41, Resulting Numbers: [10, 41] Generated Node #0,0,0: 78:[10, 41] Operation: 75-34=41 Exploring Operation: 34-10=24, Resulting Numbers: [75, 24] Generated Node #0,0,1: 78:[75, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[10, 41], Operations: ['66-32=34', '75-34=41'] Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[75, 24], Operations: ['66-32=34', '34-10=24'] Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 75+24=99, Resulting Numbers: [99] 99,78 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: 78:[32, 75, 76], Operations: ['10+66=76'] Exploring Operation: 75-32=43, Resulting Numbers: [76, 43] Generated Node #0,1,0: 78:[76, 43] Operation: 75-32=43 Exploring Operation: 76-75=1, Resulting Numbers: [32, 1] Generated Node #0,1,1: 78:[32, 1] Operation: 76-75=1 Moving to Node #0,1,0 Current State: 78:[76, 43], Operations: ['10+66=76', '75-32=43'] Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,78 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[32, 1], Operations: ['10+66=76', '76-75=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,78 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 95, 7, 12, 83 ]
96
[ "95-83=12", "7*12=84", "12+84=96" ]
Current State: 96:[95, 7, 12, 83], Operations: [] Exploring Operation: 95-83=12, Resulting Numbers: [7, 12, 12] Generated Node #2: [7, 12, 12] from Operation: 95-83=12 Current State: 96:[7, 12, 12], Operations: ['95-83=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,96 equal: Goal Reached Exploring Operation: 12+84=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[95, 7, 12, 83], Operations: [] Exploring Operation: 95-83=12, Resulting Numbers: [7, 12, 12] Generated Node #0,0: 96:[7, 12, 12] Operation: 95-83=12 Moving to Node #0,0 Current State: 96:[7, 12, 12], Operations: ['95-83=12'] Exploring Operation: 12-7=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 96:[12, 5] Operation: 12-7=5 Moving to Node #0,0,0 Current State: 96:[12, 5], Operations: ['95-83=12', '12-7=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,96 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 35, 72, 8, 93 ]
49
[ "93-35=58", "72/8=9", "58-9=49" ]
Current State: 49:[35, 72, 8, 93], Operations: [] Exploring Operation: 93-35=58, Resulting Numbers: [72, 8, 58] Generated Node #2: [72, 8, 58] from Operation: 93-35=58 Current State: 49:[72, 8, 58], Operations: ['93-35=58'] Exploring Operation: 72/8=9, Resulting Numbers: [58, 9] Generated Node #3: [58, 9] from Operation: 72/8=9 Current State: 49:[58, 9], Operations: ['93-35=58', '72/8=9'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[35, 72, 8, 93], Operations: [] Exploring Operation: 93-72=21, Resulting Numbers: [35, 8, 21] Generated Node #0,0: 49:[35, 8, 21] Operation: 93-72=21 Moving to Node #0,0 Current State: 49:[35, 8, 21], Operations: ['93-72=21'] Exploring Operation: 35+21=56, Resulting Numbers: [8, 56] Generated Node #0,0,0: 49:[8, 56] Operation: 35+21=56 Moving to Node #0,0,0 Current State: 49:[8, 56], Operations: ['93-72=21', '35+21=56'] Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 81, 78, 31 ]
59
[ "81-31=50", "78+31=109", "109-50=59" ]
Current State: 59:[31, 81, 78, 31], Operations: [] Exploring Operation: 81-31=50, Resulting Numbers: [78, 50] Generated Node #2: [78, 50] from Operation: 81-31=50 Current State: 59:[78, 50], Operations: ['81-31=50'] Exploring Operation: 78+31=109, Resulting Numbers: [50, 109] Generated Node #3: [50, 109] from Operation: 78+31=109 Current State: 59:[50, 109], Operations: ['81-31=50', '78+31=109'] Exploring Operation: 109-50=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[31, 81, 78, 31], Operations: [] Exploring Operation: 78-31=47, Resulting Numbers: [31, 81, 47] Generated Node #0,0: 59:[31, 81, 47] Operation: 78-31=47 Exploring Operation: 78-31=47, Resulting Numbers: [81, 31, 47] Generated Node #0,1: 59:[81, 31, 47] Operation: 78-31=47 Exploring Operation: 81-31=50, Resulting Numbers: [31, 78, 50] Generated Node #0,2: 59:[31, 78, 50] Operation: 81-31=50 Exploring Operation: 81-31=50, Resulting Numbers: [78, 31, 50] Generated Node #0,3: 59:[78, 31, 50] Operation: 81-31=50 Exploring Operation: 31+31=62, Resulting Numbers: [81, 78, 62] Generated Node #0,4: 59:[81, 78, 62] Operation: 31+31=62 Moving to Node #0,4 Current State: 59:[81, 78, 62], Operations: ['31+31=62'] Exploring Operation: 78-62=16, Resulting Numbers: [81, 16] Generated Node #0,4,0: 59:[81, 16] Operation: 78-62=16 Exploring Operation: 81-62=19, Resulting Numbers: [78, 19] Generated Node #0,4,1: 59:[78, 19] Operation: 81-62=19 Exploring Operation: 81-78=3, Resulting Numbers: [62, 3] Generated Node #0,4,2: 59:[62, 3] Operation: 81-78=3 Exploring Operation: 81+62=143, Resulting Numbers: [78, 143] Generated Node #0,4,3: 59:[78, 143] Operation: 81+62=143 Exploring Operation: 81+78=159, Resulting Numbers: [62, 159] Generated Node #0,4,4: 59:[62, 159] Operation: 81+78=159 Moving to Node #0,3 Current State: 59:[78, 31, 50], Operations: ['81-31=50'] Exploring Operation: 31+50=81, Resulting Numbers: [78, 81] Generated Node #0,3,0: 59:[78, 81] Operation: 31+50=81 Exploring Operation: 50-31=19, Resulting Numbers: [78, 19] Generated Node #0,3,1: 59:[78, 19] Operation: 50-31=19 Exploring Operation: 78-50=28, Resulting Numbers: [31, 28] Generated Node #0,3,2: 59:[31, 28] Operation: 78-50=28 Exploring Operation: 78+31=109, Resulting Numbers: [50, 109] Generated Node #0,3,3: 59:[50, 109] Operation: 78+31=109 Exploring Operation: 78-31=47, Resulting Numbers: [50, 47] Generated Node #0,3,4: 59:[50, 47] Operation: 78-31=47 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 59:[50, 47], Operations: ['81-31=50', '78-31=47'] Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,59 unequal: No Solution Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,59 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 #0,3,0 Current State: 59:[78, 81], Operations: ['81-31=50', '31+50=81'] Exploring Operation: 78*81=6318, Resulting Numbers: [6318] 6318,59 unequal: No Solution Exploring Operation: 81-78=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 78+81=159, Resulting Numbers: [159] 159,59 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 #0,3,1 Current State: 59:[78, 19], Operations: ['81-31=50', '50-31=19'] Exploring Operation: 78+19=97, Resulting Numbers: [97] 97,59 unequal: No Solution Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[31, 81, 78, 31], Operations: [] Exploring Operation: 81-31=50, Resulting Numbers: [78, 31, 50] Generated Node #0,3: 59:[78, 31, 50] Operation: 81-31=50 Moving to Node #0,3 Current State: 59:[78, 31, 50], Operations: ['81-31=50'] Exploring Operation: 50-31=19, Resulting Numbers: [78, 19] Generated Node #0,3,1: 59:[78, 19] Operation: 50-31=19 Moving to Node #0,3,1 Current State: 59:[78, 19], Operations: ['81-31=50', '50-31=19'] Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 29, 23, 46, 87 ]
72
[ "87/29=3", "23+46=69", "3+69=72" ]
Current State: 72:[29, 23, 46, 87], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [23, 46, 3] Generated Node #2: [23, 46, 3] from Operation: 87/29=3 Current State: 72:[23, 46, 3], Operations: ['87/29=3'] Exploring Operation: 23+46=69, Resulting Numbers: [3, 69] Generated Node #3: [3, 69] from Operation: 23+46=69 Current State: 72:[3, 69], Operations: ['87/29=3', '23+46=69'] Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[29, 23, 46, 87], Operations: [] Exploring Operation: 29+46=75, Resulting Numbers: [23, 87, 75] Generated Node #0,0: 72:[23, 87, 75] Operation: 29+46=75 Exploring Operation: 46-29=17, Resulting Numbers: [23, 87, 17] Generated Node #0,1: 72:[23, 87, 17] Operation: 46-29=17 Exploring Operation: 87/29=3, Resulting Numbers: [23, 46, 3] Generated Node #0,2: 72:[23, 46, 3] Operation: 87/29=3 Exploring Operation: 87-46=41, Resulting Numbers: [29, 23, 41] Generated Node #0,3: 72:[29, 23, 41] Operation: 87-46=41 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[23, 46, 3], Operations: ['87/29=3'] Exploring Operation: 46/23=2, Resulting Numbers: [3, 2] Generated Node #0,2,0: 72:[3, 2] Operation: 46/23=2 Exploring Operation: 46-23=23, Resulting Numbers: [3, 23] Generated Node #0,2,1: 72:[3, 23] Operation: 46-23=23 Exploring Operation: 46-3=43, Resulting Numbers: [23, 43] Generated Node #0,2,2: 72:[23, 43] Operation: 46-3=43 Exploring Operation: 23+46=69, Resulting Numbers: [3, 69] Generated Node #0,2,3: 72:[3, 69] Operation: 23+46=69 Moving to Node #0,2,0 Current State: 72:[3, 2], Operations: ['87/29=3', '46/23=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[3, 23], Operations: ['87/29=3', '46-23=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,72 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,72 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[3, 69], Operations: ['87/29=3', '23+46=69'] Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,72 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[29, 23, 46, 87], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [23, 46, 3] Generated Node #0,2: 72:[23, 46, 3] Operation: 87/29=3 Moving to Node #0,2 Current State: 72:[23, 46, 3], Operations: ['87/29=3'] Exploring Operation: 23+46=69, Resulting Numbers: [3, 69] Generated Node #0,2,3: 72:[3, 69] Operation: 23+46=69 Moving to Node #0,2,3 Current State: 72:[3, 69], Operations: ['87/29=3', '23+46=69'] Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 72, 80, 35, 89 ]
27
[ "89-80=9", "72/9=8", "35-8=27" ]
Current State: 27:[72, 80, 35, 89], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [72, 35, 9] Generated Node #2: [72, 35, 9] from Operation: 89-80=9 Current State: 27:[72, 35, 9], Operations: ['89-80=9'] Exploring Operation: 72/9=8, Resulting Numbers: [35, 8] Generated Node #3: [35, 8] from Operation: 72/9=8 Current State: 27:[35, 8], Operations: ['89-80=9', '72/9=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[72, 80, 35, 89], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [72, 35, 9] Generated Node #0,0: 27:[72, 35, 9] Operation: 89-80=9 Exploring Operation: 89-72=17, Resulting Numbers: [80, 35, 17] Generated Node #0,1: 27:[80, 35, 17] Operation: 89-72=17 Moving to Node #0,0 Current State: 27:[72, 35, 9], Operations: ['89-80=9'] Exploring Operation: 72/9=8, Resulting Numbers: [35, 8] Generated Node #0,0,0: 27:[35, 8] Operation: 72/9=8 Exploring Operation: 72-35=37, Resulting Numbers: [9, 37] Generated Node #0,0,1: 27:[9, 37] Operation: 72-35=37 Moving to Node #0,1 Current State: 27:[80, 35, 17], Operations: ['89-72=17'] Exploring Operation: 80-17=63, Resulting Numbers: [35, 63] Generated Node #0,1,0: 27:[35, 63] Operation: 80-17=63 Exploring Operation: 80-35=45, Resulting Numbers: [17, 45] Generated Node #0,1,1: 27:[17, 45] Operation: 80-35=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[17, 45], Operations: ['89-72=17', '80-35=45'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 17+45=62, Resulting Numbers: [62] 62,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[35, 63], Operations: ['89-72=17', '80-17=63'] Exploring Operation: 35+63=98, Resulting Numbers: [98] 98,27 unequal: No Solution Exploring Operation: 63-35=28, Resulting Numbers: [28] 28,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 27:[35, 8], Operations: ['89-80=9', '72/9=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[72, 80, 35, 89], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [72, 35, 9] Generated Node #0,0: 27:[72, 35, 9] Operation: 89-80=9 Moving to Node #0,0 Current State: 27:[72, 35, 9], Operations: ['89-80=9'] Exploring Operation: 72/9=8, Resulting Numbers: [35, 8] Generated Node #0,0,0: 27:[35, 8] Operation: 72/9=8 Moving to Node #0,0,0 Current State: 27:[35, 8], Operations: ['89-80=9', '72/9=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 49, 96, 28, 16 ]
41
[ "28-16=12", "96/12=8", "49-8=41" ]
Current State: 41:[49, 96, 28, 16], Operations: [] Exploring Operation: 28-16=12, Resulting Numbers: [49, 96, 12] Generated Node #2: [49, 96, 12] from Operation: 28-16=12 Current State: 41:[49, 96, 12], Operations: ['28-16=12'] Exploring Operation: 96/12=8, Resulting Numbers: [49, 8] Generated Node #3: [49, 8] from Operation: 96/12=8 Current State: 41:[49, 8], Operations: ['28-16=12', '96/12=8'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[49, 96, 28, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [49, 28, 6] Generated Node #0,0: 41:[49, 28, 6] Operation: 96/16=6 Exploring Operation: 96-49=47, Resulting Numbers: [28, 16, 47] Generated Node #0,1: 41:[28, 16, 47] Operation: 96-49=47 Exploring Operation: 96-28=68, Resulting Numbers: [49, 16, 68] Generated Node #0,2: 41:[49, 16, 68] Operation: 96-28=68 Exploring Operation: 28+16=44, Resulting Numbers: [49, 96, 44] Generated Node #0,3: 41:[49, 96, 44] Operation: 28+16=44 Exploring Operation: 96-16=80, Resulting Numbers: [49, 28, 80] Generated Node #0,4: 41:[49, 28, 80] Operation: 96-16=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[28, 16, 47], Operations: ['96-49=47'] Exploring Operation: 47-16=31, Resulting Numbers: [28, 31] Generated Node #0,1,0: 41:[28, 31] Operation: 47-16=31 Exploring Operation: 28-16=12, Resulting Numbers: [47, 12] Generated Node #0,1,1: 41:[47, 12] Operation: 28-16=12 Exploring Operation: 47-28=19, Resulting Numbers: [16, 19] Generated Node #0,1,2: 41:[16, 19] Operation: 47-28=19 Exploring Operation: 28+16=44, Resulting Numbers: [47, 44] Generated Node #0,1,3: 41:[47, 44] Operation: 28+16=44 Exploring Operation: 16+47=63, Resulting Numbers: [28, 63] Generated Node #0,1,4: 41:[28, 63] Operation: 16+47=63 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 41:[47, 44], Operations: ['96-49=47', '28+16=44'] Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[28, 31], Operations: ['96-49=47', '47-16=31'] Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 28+31=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 28*31=868, Resulting Numbers: [868] 868,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[47, 12], Operations: ['96-49=47', '28-16=12'] Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,41 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 41:[28, 63], Operations: ['96-49=47', '16+47=63'] Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 28*63=1764, Resulting Numbers: [1764] 1764,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[16, 19], Operations: ['96-49=47', '47-28=19'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[49, 28, 6], Operations: ['96/16=6'] Exploring Operation: 49-28=21, Resulting Numbers: [6, 21] Generated Node #0,0,0: 41:[6, 21] Operation: 49-28=21 Exploring Operation: 49-6=43, Resulting Numbers: [28, 43] Generated Node #0,0,1: 41:[28, 43] Operation: 49-6=43 Exploring Operation: 28-6=22, Resulting Numbers: [49, 22] Generated Node #0,0,2: 41:[49, 22] Operation: 28-6=22 Exploring Operation: 49+6=55, Resulting Numbers: [28, 55] Generated Node #0,0,3: 41:[28, 55] Operation: 49+6=55 Exploring Operation: 28+6=34, Resulting Numbers: [49, 34] Generated Node #0,0,4: 41:[49, 34] Operation: 28+6=34 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[28, 43], Operations: ['96/16=6', '49-6=43'] Exploring Operation: 28*43=1204, Resulting Numbers: [1204] 1204,41 unequal: No Solution Exploring Operation: 28+43=71, Resulting Numbers: [71] 71,41 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 41:[49, 34], Operations: ['96/16=6', '28+6=34'] Exploring Operation: 49*34=1666, Resulting Numbers: [1666] 1666,41 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[49, 22], Operations: ['96/16=6', '28-6=22'] Exploring Operation: 49*22=1078, Resulting Numbers: [1078] 1078,41 unequal: No Solution Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,41 unequal: No Solution Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[28, 55], Operations: ['96/16=6', '49+6=55'] Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,41 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,41 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[6, 21], Operations: ['96/16=6', '49-28=21'] Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,41 unequal: No Solution Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,41 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[49, 16, 68], Operations: ['96-28=68'] Exploring Operation: 68-16=52, Resulting Numbers: [49, 52] Generated Node #0,2,0: 41:[49, 52] Operation: 68-16=52 Exploring Operation: 49+16=65, Resulting Numbers: [68, 65] Generated Node #0,2,1: 41:[68, 65] Operation: 49+16=65 Exploring Operation: 16+68=84, Resulting Numbers: [49, 84] Generated Node #0,2,2: 41:[49, 84] Operation: 16+68=84 Exploring Operation: 49-16=33, Resulting Numbers: [68, 33] Generated Node #0,2,3: 41:[68, 33] Operation: 49-16=33 Exploring Operation: 68-49=19, Resulting Numbers: [16, 19] Generated Node #0,2,4: 41:[16, 19] Operation: 68-49=19 Moving to Node #0,2,0 Current State: 41:[49, 52], Operations: ['96-28=68', '68-16=52'] Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,41 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[68, 33], Operations: ['96-28=68', '49-16=33'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 68*33=2244, Resulting Numbers: [2244] 2244,41 unequal: No Solution Exploring Operation: 68+33=101, Resulting Numbers: [101] 101,41 unequal: No Solution Moving to Node #0,2,4 Current State: 41:[16, 19], Operations: ['96-28=68', '68-49=19'] Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,41 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[68, 65], Operations: ['96-28=68', '49+16=65'] Exploring Operation: 68+65=133, Resulting Numbers: [133] 133,41 unequal: No Solution Exploring Operation: 68*65=4420, Resulting Numbers: [4420] 4420,41 unequal: No Solution Exploring Operation: 68-65=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[49, 84], Operations: ['96-28=68', '16+68=84'] Exploring Operation: 49*84=4116, Resulting Numbers: [4116] 4116,41 unequal: No Solution Exploring Operation: 49+84=133, Resulting Numbers: [133] 133,41 unequal: No Solution Exploring Operation: 84-49=35, Resulting Numbers: [35] 35,41 unequal: No Solution No 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: 41:[49, 28, 80], Operations: ['96-16=80'] Exploring Operation: 80-28=52, Resulting Numbers: [49, 52] Generated Node #0,4,0: 41:[49, 52] Operation: 80-28=52 Exploring Operation: 28+80=108, Resulting Numbers: [49, 108] Generated Node #0,4,1: 41:[49, 108] Operation: 28+80=108 Exploring Operation: 80-49=31, Resulting Numbers: [28, 31] Generated Node #0,4,2: 41:[28, 31] Operation: 80-49=31 Exploring Operation: 49-28=21, Resulting Numbers: [80, 21] Generated Node #0,4,3: 41:[80, 21] Operation: 49-28=21 Exploring Operation: 49+28=77, Resulting Numbers: [80, 77] Generated Node #0,4,4: 41:[80, 77] Operation: 49+28=77 Moving to Node #0,4,0 Current State: 41:[49, 52], Operations: ['96-16=80', '80-28=52'] Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[28, 31], Operations: ['96-16=80', '80-49=31'] Exploring Operation: 28*31=868, Resulting Numbers: [868] 868,41 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 28+31=59, Resulting Numbers: [59] 59,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[80, 21], Operations: ['96-16=80', '49-28=21'] Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[49, 108], Operations: ['96-16=80', '28+80=108'] Exploring Operation: 49+108=157, Resulting Numbers: [157] 157,41 unequal: No Solution Exploring Operation: 49*108=5292, Resulting Numbers: [5292] 5292,41 unequal: No Solution Exploring Operation: 108-49=59, Resulting Numbers: [59] 59,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[80, 77], Operations: ['96-16=80', '49+28=77'] Exploring Operation: 80*77=6160, Resulting Numbers: [6160] 6160,41 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 80+77=157, Resulting Numbers: [157] 157,41 unequal: No Solution No 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: 41:[49, 96, 44], Operations: ['28+16=44'] Exploring Operation: 49-44=5, Resulting Numbers: [96, 5] Generated Node #0,3,0: 41:[96, 5] Operation: 49-44=5 Exploring Operation: 96-44=52, Resulting Numbers: [49, 52] Generated Node #0,3,1: 41:[49, 52] Operation: 96-44=52 Exploring Operation: 96-49=47, Resulting Numbers: [44, 47] Generated Node #0,3,2: 41:[44, 47] Operation: 96-49=47 Exploring Operation: 49+96=145, Resulting Numbers: [44, 145] Generated Node #0,3,3: 41:[44, 145] Operation: 49+96=145 Exploring Operation: 49+44=93, Resulting Numbers: [96, 93] Generated Node #0,3,4: 41:[96, 93] Operation: 49+44=93 Moving to Node #0,3,2 Current State: 41:[44, 47], Operations: ['28+16=44', '96-49=47'] Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,41 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[49, 52], Operations: ['28+16=44', '96-44=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,41 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[96, 5], Operations: ['28+16=44', '49-44=5'] Exploring Operation: 96*5=480, Resulting Numbers: [480] 480,41 unequal: No Solution Exploring Operation: 96-5=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 96+5=101, Resulting Numbers: [101] 101,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[44, 145], Operations: ['28+16=44', '49+96=145'] Exploring Operation: 44*145=6380, Resulting Numbers: [6380] 6380,41 unequal: No Solution Exploring Operation: 44+145=189, Resulting Numbers: [189] 189,41 unequal: No Solution Exploring Operation: 145-44=101, Resulting Numbers: [101] 101,41 unequal: No Solution Moving to Node #0,3,4 Current State: 41:[96, 93], Operations: ['28+16=44', '49+44=93'] Exploring Operation: 96-93=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 96*93=8928, Resulting Numbers: [8928] 8928,41 unequal: No Solution Exploring Operation: 96+93=189, Resulting Numbers: [189] 189,41 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
[ 9, 36, 36, 28 ]
38
[ "9+28=37", "36/36=1", "37+1=38" ]
Current State: 38:[9, 36, 36, 28], Operations: [] Exploring Operation: 9+28=37, Resulting Numbers: [36, 36, 37] Generated Node #2: [36, 36, 37] from Operation: 9+28=37 Current State: 38:[36, 36, 37], Operations: ['9+28=37'] Exploring Operation: 36/36=1, Resulting Numbers: [37, 1] Generated Node #3: [37, 1] from Operation: 36/36=1 Current State: 38:[37, 1], Operations: ['9+28=37', '36/36=1'] Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[9, 36, 36, 28], Operations: [] Exploring Operation: 28-9=19, Resulting Numbers: [36, 36, 19] Generated Node #0,0: 38:[36, 36, 19] Operation: 28-9=19 Moving to Node #0,0 Current State: 38:[36, 36, 19], Operations: ['28-9=19'] Exploring Operation: 36/36=1, Resulting Numbers: [19, 1] Generated Node #0,0,0: 38:[19, 1] Operation: 36/36=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[19, 1], Operations: ['28-9=19', '36/36=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,38 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
[ 12, 34, 5, 61 ]
35
[ "12*5=60", "34+61=95", "95-60=35" ]
Current State: 35:[12, 34, 5, 61], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [34, 61, 60] Generated Node #2: [34, 61, 60] from Operation: 12*5=60 Current State: 35:[34, 61, 60], Operations: ['12*5=60'] Exploring Operation: 34+61=95, Resulting Numbers: [60, 95] Generated Node #3: [60, 95] from Operation: 34+61=95 Current State: 35:[60, 95], Operations: ['12*5=60', '34+61=95'] Exploring Operation: 95-60=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[12, 34, 5, 61], Operations: [] Exploring Operation: 61-12=49, Resulting Numbers: [34, 5, 49] Generated Node #0,0: 35:[34, 5, 49] Operation: 61-12=49 Exploring Operation: 12-5=7, Resulting Numbers: [34, 61, 7] Generated Node #0,1: 35:[34, 61, 7] Operation: 12-5=7 Exploring Operation: 61-34=27, Resulting Numbers: [12, 5, 27] Generated Node #0,2: 35:[12, 5, 27] Operation: 61-34=27 Moving to Node #0,2 Current State: 35:[12, 5, 27], Operations: ['61-34=27'] Exploring Operation: 27-12=15, Resulting Numbers: [5, 15] Generated Node #0,2,0: 35:[5, 15] Operation: 27-12=15 Exploring Operation: 12-5=7, Resulting Numbers: [27, 7] Generated Node #0,2,1: 35:[27, 7] Operation: 12-5=7 Exploring Operation: 12+27=39, Resulting Numbers: [5, 39] Generated Node #0,2,2: 35:[5, 39] Operation: 12+27=39 Moving to Node #0,0 Current State: 35:[34, 5, 49], Operations: ['61-12=49'] Exploring Operation: 49-34=15, Resulting Numbers: [5, 15] Generated Node #0,0,0: 35:[5, 15] Operation: 49-34=15 Exploring Operation: 34+5=39, Resulting Numbers: [49, 39] Generated Node #0,0,1: 35:[49, 39] Operation: 34+5=39 Exploring Operation: 49-5=44, Resulting Numbers: [34, 44] Generated Node #0,0,2: 35:[34, 44] Operation: 49-5=44 Moving to Node #0,1 Current State: 35:[34, 61, 7], Operations: ['12-5=7'] Exploring Operation: 61-7=54, Resulting Numbers: [34, 54] Generated Node #0,1,0: 35:[34, 54] Operation: 61-7=54 Exploring Operation: 34+7=41, Resulting Numbers: [61, 41] Generated Node #0,1,1: 35:[61, 41] Operation: 34+7=41 Exploring Operation: 61-34=27, Resulting Numbers: [7, 27] Generated Node #0,1,2: 35:[7, 27] Operation: 61-34=27 Moving to Node #0,2,2 Current State: 35:[5, 39], Operations: ['61-34=27', '12+27=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[27, 7], Operations: ['61-34=27', '12-5=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,35 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,35 unequal: No Solution Moving to Node #0,1,2 Current State: 35:[7, 27], Operations: ['12-5=7', '61-34=27'] Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,35 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[5, 15], Operations: ['61-34=27', '27-12=15'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[5, 15], Operations: ['61-12=49', '49-34=15'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[34, 44], Operations: ['61-12=49', '49-5=44'] Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 34+44=78, Resulting Numbers: [78] 78,35 unequal: No Solution Exploring Operation: 34*44=1496, Resulting Numbers: [1496] 1496,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[49, 39], Operations: ['61-12=49', '34+5=39'] Exploring Operation: 49*39=1911, Resulting Numbers: [1911] 1911,35 unequal: No Solution Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[34, 54], Operations: ['12-5=7', '61-7=54'] Exploring Operation: 34*54=1836, Resulting Numbers: [1836] 1836,35 unequal: No Solution Exploring Operation: 34+54=88, Resulting Numbers: [88] 88,35 unequal: No Solution Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[61, 41], Operations: ['12-5=7', '34+7=41'] Exploring Operation: 61*41=2501, Resulting Numbers: [2501] 2501,35 unequal: No Solution Exploring Operation: 61+41=102, Resulting Numbers: [102] 102,35 unequal: No Solution Exploring Operation: 61-41=20, Resulting Numbers: [20] 20,35 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 79, 66, 17, 63 ]
15
[ "66*17=1122", "63+1122=1185", "1185/79=15" ]
Current State: 15:[79, 66, 17, 63], Operations: [] Exploring Operation: 66*17=1122, Resulting Numbers: [79, 63, 1122] Generated Node #2: [79, 63, 1122] from Operation: 66*17=1122 Current State: 15:[79, 63, 1122], Operations: ['66*17=1122'] Exploring Operation: 63+1122=1185, Resulting Numbers: [79, 1185] Generated Node #3: [79, 1185] from Operation: 63+1122=1185 Current State: 15:[79, 1185], Operations: ['66*17=1122', '63+1122=1185'] Exploring Operation: 1185/79=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[79, 66, 17, 63], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [79, 17, 3] Generated Node #0,0: 15:[79, 17, 3] Operation: 66-63=3 Exploring Operation: 79-17=62, Resulting Numbers: [66, 63, 62] Generated Node #0,1: 15:[66, 63, 62] Operation: 79-17=62 Exploring Operation: 66-17=49, Resulting Numbers: [79, 63, 49] Generated Node #0,2: 15:[79, 63, 49] Operation: 66-17=49 Exploring Operation: 79-66=13, Resulting Numbers: [17, 63, 13] Generated Node #0,3: 15:[17, 63, 13] Operation: 79-66=13 Exploring Operation: 79-63=16, Resulting Numbers: [66, 17, 16] Generated Node #0,4: 15:[66, 17, 16] Operation: 79-63=16 Moving to Node #0,3 Current State: 15:[17, 63, 13], Operations: ['79-66=13'] Exploring Operation: 17+13=30, Resulting Numbers: [63, 30] Generated Node #0,3,0: 15:[63, 30] Operation: 17+13=30 Exploring Operation: 63+13=76, Resulting Numbers: [17, 76] Generated Node #0,3,1: 15:[17, 76] Operation: 63+13=76 Exploring Operation: 17-13=4, Resulting Numbers: [63, 4] Generated Node #0,3,2: 15:[63, 4] Operation: 17-13=4 Exploring Operation: 63-17=46, Resulting Numbers: [13, 46] Generated Node #0,3,3: 15:[13, 46] Operation: 63-17=46 Exploring Operation: 63-13=50, Resulting Numbers: [17, 50] Generated Node #0,3,4: 15:[17, 50] Operation: 63-13=50 Moving to Node #0,4 Current State: 15:[66, 17, 16], Operations: ['79-63=16'] Exploring Operation: 66-16=50, Resulting Numbers: [17, 50] Generated Node #0,4,0: 15:[17, 50] Operation: 66-16=50 Exploring Operation: 66-17=49, Resulting Numbers: [16, 49] Generated Node #0,4,1: 15:[16, 49] Operation: 66-17=49 Exploring Operation: 66+16=82, Resulting Numbers: [17, 82] Generated Node #0,4,2: 15:[17, 82] Operation: 66+16=82 Exploring Operation: 66+17=83, Resulting Numbers: [16, 83] Generated Node #0,4,3: 15:[16, 83] Operation: 66+17=83 Exploring Operation: 17-16=1, Resulting Numbers: [66, 1] Generated Node #0,4,4: 15:[66, 1] Operation: 17-16=1 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 15:[16, 49], Operations: ['79-63=16', '66-17=49'] Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,15 unequal: No Solution Exploring Operation: 16+49=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 16*49=784, Resulting Numbers: [784] 784,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 15:[17, 50], Operations: ['79-63=16', '66-16=50'] Exploring Operation: 17*50=850, Resulting Numbers: [850] 850,15 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,15 unequal: No Solution Exploring Operation: 17+50=67, Resulting Numbers: [67] 67,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[66, 1], Operations: ['79-63=16', '17-16=1'] Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 15:[17, 82], Operations: ['79-63=16', '66+16=82'] Exploring Operation: 17+82=99, Resulting Numbers: [99] 99,15 unequal: No Solution Exploring Operation: 17*82=1394, Resulting Numbers: [1394] 1394,15 unequal: No Solution Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 15:[16, 83], Operations: ['79-63=16', '66+17=83'] Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,15 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,15 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,15 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: 15:[79, 17, 3], Operations: ['66-63=3'] Exploring Operation: 17-3=14, Resulting Numbers: [79, 14] Generated Node #0,0,0: 15:[79, 14] Operation: 17-3=14 Exploring Operation: 79-17=62, Resulting Numbers: [3, 62] Generated Node #0,0,1: 15:[3, 62] Operation: 79-17=62 Exploring Operation: 17+3=20, Resulting Numbers: [79, 20] Generated Node #0,0,2: 15:[79, 20] Operation: 17+3=20 Exploring Operation: 79-3=76, Resulting Numbers: [17, 76] Generated Node #0,0,3: 15:[17, 76] Operation: 79-3=76 Exploring Operation: 79+3=82, Resulting Numbers: [17, 82] Generated Node #0,0,4: 15:[17, 82] Operation: 79+3=82 Moving to Node #0,1 Current State: 15:[66, 63, 62], Operations: ['79-17=62'] Exploring Operation: 66+63=129, Resulting Numbers: [62, 129] Generated Node #0,1,0: 15:[62, 129] Operation: 66+63=129 Exploring Operation: 66-63=3, Resulting Numbers: [62, 3] Generated Node #0,1,1: 15:[62, 3] Operation: 66-63=3 Exploring Operation: 66+62=128, Resulting Numbers: [63, 128] Generated Node #0,1,2: 15:[63, 128] Operation: 66+62=128 Exploring Operation: 66-62=4, Resulting Numbers: [63, 4] Generated Node #0,1,3: 15:[63, 4] Operation: 66-62=4 Exploring Operation: 63-62=1, Resulting Numbers: [66, 1] Generated Node #0,1,4: 15:[66, 1] Operation: 63-62=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[62, 3], Operations: ['79-17=62', '66-63=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,15 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 15:[63, 4], Operations: ['79-17=62', '66-62=4'] Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,15 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 15:[66, 1], Operations: ['79-17=62', '63-62=1'] Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 66*1=66, Resulting Numbers: [66] 66,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[62, 129], Operations: ['79-17=62', '66+63=129'] Exploring Operation: 129-62=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 62*129=7998, Resulting Numbers: [7998] 7998,15 unequal: No Solution Exploring Operation: 62+129=191, Resulting Numbers: [191] 191,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[63, 128], Operations: ['79-17=62', '66+62=128'] Exploring Operation: 128-63=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 63*128=8064, Resulting Numbers: [8064] 8064,15 unequal: No Solution Exploring Operation: 63+128=191, Resulting Numbers: [191] 191,15 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: 15:[79, 63, 49], Operations: ['66-17=49'] Exploring Operation: 79-63=16, Resulting Numbers: [49, 16] Generated Node #0,2,0: 15:[49, 16] Operation: 79-63=16 Exploring Operation: 63-49=14, Resulting Numbers: [79, 14] Generated Node #0,2,1: 15:[79, 14] Operation: 63-49=14 Exploring Operation: 79+63=142, Resulting Numbers: [49, 142] Generated Node #0,2,2: 15:[49, 142] Operation: 79+63=142 Exploring Operation: 79+49=128, Resulting Numbers: [63, 128] Generated Node #0,2,3: 15:[63, 128] Operation: 79+49=128 Exploring Operation: 79-49=30, Resulting Numbers: [63, 30] Generated Node #0,2,4: 15:[63, 30] Operation: 79-49=30 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[49, 16], Operations: ['66-17=49', '79-63=16'] Exploring Operation: 49+16=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 49*16=784, Resulting Numbers: [784] 784,15 unequal: No Solution Exploring Operation: 49-16=33, Resulting Numbers: [33] 33,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 15:[63, 30], Operations: ['66-17=49', '79-49=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,15 unequal: No Solution Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[79, 14], Operations: ['66-17=49', '63-49=14'] Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 79*14=1106, Resulting Numbers: [1106] 1106,15 unequal: No Solution Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[49, 142], Operations: ['66-17=49', '79+63=142'] Exploring Operation: 49*142=6958, Resulting Numbers: [6958] 6958,15 unequal: No Solution Exploring Operation: 142-49=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 49+142=191, Resulting Numbers: [191] 191,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[63, 128], Operations: ['66-17=49', '79+49=128'] Exploring Operation: 63+128=191, Resulting Numbers: [191] 191,15 unequal: No Solution Exploring Operation: 63*128=8064, Resulting Numbers: [8064] 8064,15 unequal: No Solution Exploring Operation: 128-63=65, Resulting Numbers: [65] 65,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 15:[13, 46], Operations: ['79-66=13', '63-17=46'] Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,15 unequal: No Solution Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[17, 50], Operations: ['79-66=13', '63-13=50'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,15 unequal: No Solution Exploring Operation: 17*50=850, Resulting Numbers: [850] 850,15 unequal: No Solution Exploring Operation: 17+50=67, Resulting Numbers: [67] 67,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[3, 62], Operations: ['66-63=3', '79-17=62'] Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,15 unequal: No Solution Moving to Node #0,3,2 Current State: 15:[63, 4], Operations: ['79-66=13', '17-13=4'] Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,15 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[17, 76], Operations: ['66-63=3', '79-3=76'] Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 17+76=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 17*76=1292, Resulting Numbers: [1292] 1292,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[17, 76], Operations: ['79-66=13', '63+13=76'] Exploring Operation: 17*76=1292, Resulting Numbers: [1292] 1292,15 unequal: No Solution Exploring Operation: 17+76=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[63, 30], Operations: ['79-66=13', '17+13=30'] Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,15 unequal: No Solution Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[79, 14], Operations: ['66-63=3', '17-3=14'] Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,15 unequal: No Solution Exploring Operation: 79*14=1106, Resulting Numbers: [1106] 1106,15 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[79, 20], Operations: ['66-63=3', '17+3=20'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 79*20=1580, Resulting Numbers: [1580] 1580,15 unequal: No Solution Exploring Operation: 79+20=99, Resulting Numbers: [99] 99,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[17, 82], Operations: ['66-63=3', '79+3=82'] Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,15 unequal: No Solution Exploring Operation: 17*82=1394, Resulting Numbers: [1394] 1394,15 unequal: No Solution Exploring Operation: 17+82=99, Resulting Numbers: [99] 99,15 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 7, 58, 14, 47 ]
22
[ "14/7=2", "58-47=11", "2*11=22" ]
Current State: 22:[7, 58, 14, 47], Operations: [] Exploring Operation: 14/7=2, Resulting Numbers: [58, 47, 2] Generated Node #2: [58, 47, 2] from Operation: 14/7=2 Current State: 22:[58, 47, 2], Operations: ['14/7=2'] Exploring Operation: 58-47=11, Resulting Numbers: [2, 11] Generated Node #3: [2, 11] from Operation: 58-47=11 Current State: 22:[2, 11], Operations: ['14/7=2', '58-47=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[7, 58, 14, 47], Operations: [] Exploring Operation: 58-14=44, Resulting Numbers: [7, 47, 44] Generated Node #0,0: 22:[7, 47, 44] Operation: 58-14=44 Exploring Operation: 58-47=11, Resulting Numbers: [7, 14, 11] Generated Node #0,1: 22:[7, 14, 11] Operation: 58-47=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[7, 14, 11], Operations: ['58-47=11'] Exploring Operation: 14/7=2, Resulting Numbers: [11, 2] Generated Node #0,1,0: 22:[11, 2] Operation: 14/7=2 Exploring Operation: 7+14=21, Resulting Numbers: [11, 21] Generated Node #0,1,1: 22:[11, 21] Operation: 7+14=21 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[11, 2], Operations: ['58-47=11', '14/7=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[7, 58, 14, 47], Operations: [] Exploring Operation: 58-47=11, Resulting Numbers: [7, 14, 11] Generated Node #0,1: 22:[7, 14, 11] Operation: 58-47=11 Moving to Node #0,1 Current State: 22:[7, 14, 11], Operations: ['58-47=11'] Exploring Operation: 14/7=2, Resulting Numbers: [11, 2] Generated Node #0,1,0: 22:[11, 2] Operation: 14/7=2 Moving to Node #0,1,0 Current State: 22:[11, 2], Operations: ['58-47=11', '14/7=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 44, 2, 74, 46 ]
74
[ "44+2=46", "74+46=120", "120-46=74" ]
Current State: 74:[44, 2, 74, 46], Operations: [] Exploring Operation: 44+2=46, Resulting Numbers: [74, 46, 46] Generated Node #2: [74, 46, 46] from Operation: 44+2=46 Current State: 74:[74, 46, 46], Operations: ['44+2=46'] Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,74 equal: Goal Reached Exploring Operation: 120-46=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[44, 2, 74, 46], Operations: [] Exploring Operation: 44-2=42, Resulting Numbers: [74, 46, 42] Generated Node #0,0: 74:[74, 46, 42] Operation: 44-2=42 Exploring Operation: 46-2=44, Resulting Numbers: [44, 74, 44] Generated Node #0,1: 74:[44, 74, 44] Operation: 46-2=44 Exploring Operation: 46-44=2, Resulting Numbers: [2, 74, 2] Generated Node #0,2: 74:[2, 74, 2] Operation: 46-44=2 Exploring Operation: 74-44=30, Resulting Numbers: [2, 46, 30] Generated Node #0,3: 74:[2, 46, 30] Operation: 74-44=30 Moving to Node #0,2 Current State: 74:[2, 74, 2], Operations: ['46-44=2'] Exploring Operation: 74/2=37, Resulting Numbers: [2, 37] Generated Node #0,2,0: 74:[2, 37] Operation: 74/2=37 Exploring Operation: 74/2=37, Resulting Numbers: [2, 37] Generated Node #0,2,1: 74:[2, 37] Operation: 74/2=37 Exploring Operation: 2/2=1, Resulting Numbers: [74, 1] Generated Node #0,2,2: 74:[74, 1] Operation: 2/2=1 Exploring Operation: 2+74=76, Resulting Numbers: [2, 76] Generated Node #0,2,3: 74:[2, 76] Operation: 2+74=76 Moving to Node #0,1 Current State: 74:[44, 74, 44], Operations: ['46-2=44'] Exploring Operation: 74-44=30, Resulting Numbers: [44, 30] Generated Node #0,1,0: 74:[44, 30] Operation: 74-44=30 Exploring Operation: 44/44=1, Resulting Numbers: [74, 1] Generated Node #0,1,1: 74:[74, 1] Operation: 44/44=1 Exploring Operation: 44-44=0, Resulting Numbers: [74, 0] Generated Node #0,1,2: 74:[74, 0] Operation: 44-44=0 Exploring Operation: 44+44=88, Resulting Numbers: [74, 88] Generated Node #0,1,3: 74:[74, 88] Operation: 44+44=88 Moving to Node #0,0 Current State: 74:[74, 46, 42], Operations: ['44-2=42'] Exploring Operation: 74-42=32, Resulting Numbers: [46, 32] Generated Node #0,0,0: 74:[46, 32] Operation: 74-42=32 Exploring Operation: 46+42=88, Resulting Numbers: [74, 88] Generated Node #0,0,1: 74:[74, 88] Operation: 46+42=88 Exploring Operation: 74-46=28, Resulting Numbers: [42, 28] Generated Node #0,0,2: 74:[42, 28] Operation: 74-46=28 Exploring Operation: 46-42=4, Resulting Numbers: [74, 4] Generated Node #0,0,3: 74:[74, 4] Operation: 46-42=4 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[74, 4], Operations: ['44-2=42', '46-42=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,74 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 74*4=296, Resulting Numbers: [296] 296,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[46, 32], Operations: ['44-2=42', '74-42=32'] Exploring Operation: 46*32=1472, Resulting Numbers: [1472] 1472,74 unequal: No Solution Exploring Operation: 46+32=78, Resulting Numbers: [78] 78,74 unequal: No Solution Exploring Operation: 46-32=14, Resulting Numbers: [14] 14,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[74, 88], Operations: ['44-2=42', '46+42=88'] Exploring Operation: 74*88=6512, Resulting Numbers: [6512] 6512,74 unequal: No Solution Exploring Operation: 88-74=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 74+88=162, Resulting Numbers: [162] 162,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[42, 28], Operations: ['44-2=42', '74-46=28'] Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,74 unequal: No Solution Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,74 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: 74:[2, 46, 30], Operations: ['74-44=30'] Exploring Operation: 2+30=32, Resulting Numbers: [46, 32] Generated Node #0,3,0: 74:[46, 32] Operation: 2+30=32 Exploring Operation: 46-30=16, Resulting Numbers: [2, 16] Generated Node #0,3,1: 74:[2, 16] Operation: 46-30=16 Exploring Operation: 46-2=44, Resulting Numbers: [30, 44] Generated Node #0,3,2: 74:[30, 44] Operation: 46-2=44 Exploring Operation: 46+30=76, Resulting Numbers: [2, 76] Generated Node #0,3,3: 74:[2, 76] Operation: 46+30=76 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[2, 76], Operations: ['74-44=30', '46+30=76'] Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,74 unequal: No Solution Exploring Operation: 2*76=152, Resulting Numbers: [152] 152,74 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[44, 2, 74, 46], Operations: [] Exploring Operation: 74-44=30, Resulting Numbers: [2, 46, 30] Generated Node #0,3: 74:[2, 46, 30] Operation: 74-44=30 Moving to Node #0,3 Current State: 74:[2, 46, 30], Operations: ['74-44=30'] Exploring Operation: 46+30=76, Resulting Numbers: [2, 76] Generated Node #0,3,3: 74:[2, 76] Operation: 46+30=76 Moving to Node #0,3,3 Current State: 74:[2, 76], Operations: ['74-44=30', '46+30=76'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
mult_heuristic
[ 22, 24, 77, 1 ]
83
[ "24*77=1848", "1848/22=84", "84-1=83" ]
Current State: 83:[22, 24, 77, 1], Operations: [] Exploring Operation: 24*77=1848, Resulting Numbers: [22, 1, 1848] Generated Node #2: [22, 1, 1848] from Operation: 24*77=1848 Current State: 83:[22, 1, 1848], Operations: ['24*77=1848'] Exploring Operation: 1848/22=84, Resulting Numbers: [1, 84] Generated Node #3: [1, 84] from Operation: 1848/22=84 Current State: 83:[1, 84], Operations: ['24*77=1848', '1848/22=84'] Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[22, 24, 77, 1], Operations: [] Exploring Operation: 22+1=23, Resulting Numbers: [24, 77, 23] Generated Node #0,0: 83:[24, 77, 23] Operation: 22+1=23 Exploring Operation: 22+24=46, Resulting Numbers: [77, 1, 46] Generated Node #0,1: 83:[77, 1, 46] Operation: 22+24=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[24, 77, 23], Operations: ['22+1=23'] Exploring Operation: 24+23=47, Resulting Numbers: [77, 47] Generated Node #0,0,0: 83:[77, 47] Operation: 24+23=47 Exploring Operation: 77+23=100, Resulting Numbers: [24, 100] Generated Node #0,0,1: 83:[24, 100] Operation: 77+23=100 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[77, 47], Operations: ['22+1=23', '24+23=47'] Exploring Operation: 77+47=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[24, 100], Operations: ['22+1=23', '77+23=100'] Exploring Operation: 100-24=76, Resulting Numbers: [76] 76,83 unequal: No Solution Exploring Operation: 24+100=124, Resulting Numbers: [124] 124,83 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 #0,1 Current State: 83:[77, 1, 46], Operations: ['22+24=46'] Exploring Operation: 1+46=47, Resulting Numbers: [77, 47] Generated Node #0,1,0: 83:[77, 47] Operation: 1+46=47 Exploring Operation: 77+1=78, Resulting Numbers: [46, 78] Generated Node #0,1,1: 83:[46, 78] Operation: 77+1=78 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[77, 47], Operations: ['22+24=46', '1+46=47'] Exploring Operation: 77+47=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,83 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 #0,1,1 Current State: 83:[46, 78], Operations: ['22+24=46', '77+1=78'] Exploring Operation: 46+78=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 78-46=32, Resulting Numbers: [32] 32,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 76, 74, 57, 98 ]
82
[ "76-74=2", "98-57=41", "2*41=82" ]
Current State: 82:[76, 74, 57, 98], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [57, 98, 2] Generated Node #2: [57, 98, 2] from Operation: 76-74=2 Current State: 82:[57, 98, 2], Operations: ['76-74=2'] Exploring Operation: 98-57=41, Resulting Numbers: [2, 41] Generated Node #3: [2, 41] from Operation: 98-57=41 Current State: 82:[2, 41], Operations: ['76-74=2', '98-57=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[76, 74, 57, 98], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [57, 98, 2] Generated Node #0,0: 82:[57, 98, 2] Operation: 76-74=2 Exploring Operation: 98-57=41, Resulting Numbers: [76, 74, 41] Generated Node #0,1: 82:[76, 74, 41] Operation: 98-57=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[76, 74, 41], Operations: ['98-57=41'] Exploring Operation: 76-74=2, Resulting Numbers: [41, 2] Generated Node #0,1,0: 82:[41, 2] Operation: 76-74=2 Exploring Operation: 76-41=35, Resulting Numbers: [74, 35] Generated Node #0,1,1: 82:[74, 35] Operation: 76-41=35 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[41, 2], Operations: ['98-57=41', '76-74=2'] Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[76, 74, 57, 98], Operations: [] Exploring Operation: 98-57=41, Resulting Numbers: [76, 74, 41] Generated Node #0,1: 82:[76, 74, 41] Operation: 98-57=41 Moving to Node #0,1 Current State: 82:[76, 74, 41], Operations: ['98-57=41'] Exploring Operation: 76-74=2, Resulting Numbers: [41, 2] Generated Node #0,1,0: 82:[41, 2] Operation: 76-74=2 Moving to Node #0,1,0 Current State: 82:[41, 2], Operations: ['98-57=41', '76-74=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 72, 13, 74, 70 ]
59
[ "72+13=85", "74+70=144", "144-85=59" ]
Current State: 59:[72, 13, 74, 70], Operations: [] Exploring Operation: 72+13=85, Resulting Numbers: [74, 70, 85] Generated Node #2: [74, 70, 85] from Operation: 72+13=85 Current State: 59:[74, 70, 85], Operations: ['72+13=85'] Exploring Operation: 74+70=144, Resulting Numbers: [85, 144] Generated Node #3: [85, 144] from Operation: 74+70=144 Current State: 59:[85, 144], Operations: ['72+13=85', '74+70=144'] Exploring Operation: 144-85=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[72, 13, 74, 70], Operations: [] Exploring Operation: 72-13=59, Resulting Numbers: [74, 70, 59] Generated Node #0,0: 59:[74, 70, 59] Operation: 72-13=59 Exploring Operation: 70-13=57, Resulting Numbers: [72, 74, 57] Generated Node #0,1: 59:[72, 74, 57] Operation: 70-13=57 Exploring Operation: 74-13=61, Resulting Numbers: [72, 70, 61] Generated Node #0,2: 59:[72, 70, 61] Operation: 74-13=61 Exploring Operation: 72+13=85, Resulting Numbers: [74, 70, 85] Generated Node #0,3: 59:[74, 70, 85] Operation: 72+13=85 Moving to Node #0,0 Current State: 59:[74, 70, 59], Operations: ['72-13=59'] Exploring Operation: 74-70=4, Resulting Numbers: [59, 4] Generated Node #0,0,0: 59:[59, 4] Operation: 74-70=4 Exploring Operation: 70-59=11, Resulting Numbers: [74, 11] Generated Node #0,0,1: 59:[74, 11] Operation: 70-59=11 Exploring Operation: 74-59=15, Resulting Numbers: [70, 15] Generated Node #0,0,2: 59:[70, 15] Operation: 74-59=15 Exploring Operation: 74+70=144, Resulting Numbers: [59, 144] Generated Node #0,0,3: 59:[59, 144] Operation: 74+70=144 Moving to Node #0,2 Current State: 59:[72, 70, 61], Operations: ['74-13=61'] Exploring Operation: 72+70=142, Resulting Numbers: [61, 142] Generated Node #0,2,0: 59:[61, 142] Operation: 72+70=142 Exploring Operation: 72-70=2, Resulting Numbers: [61, 2] Generated Node #0,2,1: 59:[61, 2] Operation: 72-70=2 Exploring Operation: 72-61=11, Resulting Numbers: [70, 11] Generated Node #0,2,2: 59:[70, 11] Operation: 72-61=11 Exploring Operation: 70-61=9, Resulting Numbers: [72, 9] Generated Node #0,2,3: 59:[72, 9] Operation: 70-61=9 Moving to Node #0,1 Current State: 59:[72, 74, 57], Operations: ['70-13=57'] Exploring Operation: 72+57=129, Resulting Numbers: [74, 129] Generated Node #0,1,0: 59:[74, 129] Operation: 72+57=129 Exploring Operation: 74-57=17, Resulting Numbers: [72, 17] Generated Node #0,1,1: 59:[72, 17] Operation: 74-57=17 Exploring Operation: 74-72=2, Resulting Numbers: [57, 2] Generated Node #0,1,2: 59:[57, 2] Operation: 74-72=2 Exploring Operation: 72-57=15, Resulting Numbers: [74, 15] Generated Node #0,1,3: 59:[74, 15] Operation: 72-57=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[72, 17], Operations: ['70-13=57', '74-57=17'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,59 unequal: No Solution Exploring Operation: 72*17=1224, Resulting Numbers: [1224] 1224,59 unequal: No Solution Exploring Operation: 72+17=89, Resulting Numbers: [89] 89,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[57, 2], Operations: ['70-13=57', '74-72=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[72, 13, 74, 70], Operations: [] Exploring Operation: 70-13=57, Resulting Numbers: [72, 74, 57] Generated Node #0,1: 59:[72, 74, 57] Operation: 70-13=57 Moving to Node #0,1 Current State: 59:[72, 74, 57], Operations: ['70-13=57'] Exploring Operation: 74-72=2, Resulting Numbers: [57, 2] Generated Node #0,1,2: 59:[57, 2] Operation: 74-72=2 Moving to Node #0,1,2 Current State: 59:[57, 2], Operations: ['70-13=57', '74-72=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 49, 92, 41, 84 ]
64
[ "49-41=8", "92-84=8", "8*8=64" ]
Current State: 64:[49, 92, 41, 84], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [92, 84, 8] Generated Node #2: [92, 84, 8] from Operation: 49-41=8 Current State: 64:[92, 84, 8], Operations: ['49-41=8'] Exploring Operation: 92-84=8, Resulting Numbers: [8, 8] Generated Node #3: [8, 8] from Operation: 92-84=8 Current State: 64:[8, 8], Operations: ['49-41=8', '92-84=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[49, 92, 41, 84], Operations: [] Exploring Operation: 92-49=43, Resulting Numbers: [41, 84, 43] Generated Node #0,0: 64:[41, 84, 43] Operation: 92-49=43 Exploring Operation: 49-41=8, Resulting Numbers: [92, 84, 8] Generated Node #0,1: 64:[92, 84, 8] Operation: 49-41=8 Exploring Operation: 92-84=8, Resulting Numbers: [49, 41, 8] Generated Node #0,2: 64:[49, 41, 8] Operation: 92-84=8 Exploring Operation: 84-49=35, Resulting Numbers: [92, 41, 35] Generated Node #0,3: 64:[92, 41, 35] Operation: 84-49=35 Exploring Operation: 92-41=51, Resulting Numbers: [49, 84, 51] Generated Node #0,4: 64:[49, 84, 51] Operation: 92-41=51 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[49, 41, 8], Operations: ['92-84=8'] Exploring Operation: 41-8=33, Resulting Numbers: [49, 33] Generated Node #0,2,0: 64:[49, 33] Operation: 41-8=33 Exploring Operation: 49+41=90, Resulting Numbers: [8, 90] Generated Node #0,2,1: 64:[8, 90] Operation: 49+41=90 Exploring Operation: 49-8=41, Resulting Numbers: [41, 41] Generated Node #0,2,2: 64:[41, 41] Operation: 49-8=41 Exploring Operation: 49-41=8, Resulting Numbers: [8, 8] Generated Node #0,2,3: 64:[8, 8] Operation: 49-41=8 Exploring Operation: 49+8=57, Resulting Numbers: [41, 57] Generated Node #0,2,4: 64:[41, 57] Operation: 49+8=57 Moving to Node #0,2,3 Current State: 64:[8, 8], Operations: ['92-84=8', '49-41=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,64 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[49, 92, 41, 84], Operations: [] Exploring Operation: 92-84=8, Resulting Numbers: [49, 41, 8] Generated Node #0,2: 64:[49, 41, 8] Operation: 92-84=8 Moving to Node #0,2 Current State: 64:[49, 41, 8], Operations: ['92-84=8'] Exploring Operation: 49-41=8, Resulting Numbers: [8, 8] Generated Node #0,2,3: 64:[8, 8] Operation: 49-41=8 Moving to Node #0,2,3 Current State: 64:[8, 8], Operations: ['92-84=8', '49-41=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 45, 71, 16, 23 ]
19
[ "71-45=26", "23-16=7", "26-7=19" ]
Current State: 19:[45, 71, 16, 23], Operations: [] Exploring Operation: 71-45=26, Resulting Numbers: [16, 23, 26] Generated Node #2: [16, 23, 26] from Operation: 71-45=26 Current State: 19:[16, 23, 26], Operations: ['71-45=26'] Exploring Operation: 23-16=7, Resulting Numbers: [26, 7] Generated Node #3: [26, 7] from Operation: 23-16=7 Current State: 19:[26, 7], Operations: ['71-45=26', '23-16=7'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[45, 71, 16, 23], Operations: [] Exploring Operation: 45-16=29, Resulting Numbers: [71, 23, 29] Generated Node #0,0: 19:[71, 23, 29] Operation: 45-16=29 Exploring Operation: 45-23=22, Resulting Numbers: [71, 16, 22] Generated Node #0,1: 19:[71, 16, 22] Operation: 45-23=22 Exploring Operation: 71-45=26, Resulting Numbers: [16, 23, 26] Generated Node #0,2: 19:[16, 23, 26] Operation: 71-45=26 Exploring Operation: 71-16=55, Resulting Numbers: [45, 23, 55] Generated Node #0,3: 19:[45, 23, 55] Operation: 71-16=55 Exploring Operation: 71-23=48, Resulting Numbers: [45, 16, 48] Generated Node #0,4: 19:[45, 16, 48] Operation: 71-23=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[16, 23, 26], Operations: ['71-45=26'] Exploring Operation: 16+23=39, Resulting Numbers: [26, 39] Generated Node #0,2,0: 19:[26, 39] Operation: 16+23=39 Exploring Operation: 26-23=3, Resulting Numbers: [16, 3] Generated Node #0,2,1: 19:[16, 3] Operation: 26-23=3 Exploring Operation: 26-16=10, Resulting Numbers: [23, 10] Generated Node #0,2,2: 19:[23, 10] Operation: 26-16=10 Exploring Operation: 23-16=7, Resulting Numbers: [26, 7] Generated Node #0,2,3: 19:[26, 7] Operation: 23-16=7 Exploring Operation: 16+26=42, Resulting Numbers: [23, 42] Generated Node #0,2,4: 19:[23, 42] Operation: 16+26=42 Moving to Node #0,2,2 Current State: 19:[23, 10], Operations: ['71-45=26', '26-16=10'] Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,19 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,19 unequal: No Solution Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,19 unequal: No Solution Moving to Node #0,2,3 Current State: 19:[26, 7], Operations: ['71-45=26', '23-16=7'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[45, 71, 16, 23], Operations: [] Exploring Operation: 71-45=26, Resulting Numbers: [16, 23, 26] Generated Node #0,2: 19:[16, 23, 26] Operation: 71-45=26 Moving to Node #0,2 Current State: 19:[16, 23, 26], Operations: ['71-45=26'] Exploring Operation: 23-16=7, Resulting Numbers: [26, 7] Generated Node #0,2,3: 19:[26, 7] Operation: 23-16=7 Moving to Node #0,2,3 Current State: 19:[26, 7], Operations: ['71-45=26', '23-16=7'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 26, 22, 87, 20 ]
97
[ "22*87=1914", "26+1914=1940", "1940/20=97" ]
Current State: 97:[26, 22, 87, 20], Operations: [] Exploring Operation: 22*87=1914, Resulting Numbers: [26, 20, 1914] Generated Node #2: [26, 20, 1914] from Operation: 22*87=1914 Current State: 97:[26, 20, 1914], Operations: ['22*87=1914'] Exploring Operation: 26+1914=1940, Resulting Numbers: [20, 1940] Generated Node #3: [20, 1940] from Operation: 26+1914=1940 Current State: 97:[20, 1940], Operations: ['22*87=1914', '26+1914=1940'] Exploring Operation: 1940/20=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[26, 22, 87, 20], Operations: [] Exploring Operation: 26+20=46, Resulting Numbers: [22, 87, 46] Generated Node #0,0: 97:[22, 87, 46] Operation: 26+20=46 Exploring Operation: 26+22=48, Resulting Numbers: [87, 20, 48] Generated Node #0,1: 97:[87, 20, 48] Operation: 26+22=48 Moving to Node #0,0 Current State: 97:[22, 87, 46], Operations: ['26+20=46'] Exploring Operation: 22+46=68, Resulting Numbers: [87, 68] Generated Node #0,0,0: 97:[87, 68] Operation: 22+46=68 Exploring Operation: 22+87=109, Resulting Numbers: [46, 109] Generated Node #0,0,1: 97:[46, 109] Operation: 22+87=109 Moving to Node #0,1 Current State: 97:[87, 20, 48], Operations: ['26+22=48'] Exploring Operation: 87+20=107, Resulting Numbers: [48, 107] Generated Node #0,1,0: 97:[48, 107] Operation: 87+20=107 Exploring Operation: 20+48=68, Resulting Numbers: [87, 68] Generated Node #0,1,1: 97:[87, 68] Operation: 20+48=68 Moving to Node #0,0,0 Current State: 97:[87, 68], Operations: ['26+20=46', '22+46=68'] Exploring Operation: 87+68=155, Resulting Numbers: [155] 155,97 unequal: No Solution Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[87, 68], Operations: ['26+22=48', '20+48=68'] Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,97 unequal: No Solution Exploring Operation: 87+68=155, Resulting Numbers: [155] 155,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[48, 107], Operations: ['26+22=48', '87+20=107'] Exploring Operation: 107-48=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 48+107=155, Resulting Numbers: [155] 155,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[46, 109], Operations: ['26+20=46', '22+87=109'] Exploring Operation: 109-46=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 46+109=155, Resulting Numbers: [155] 155,97 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 41, 90, 11, 45 ]
83
[ "90-41=49", "45-11=34", "49+34=83" ]
Current State: 83:[41, 90, 11, 45], Operations: [] Exploring Operation: 90-41=49, Resulting Numbers: [11, 45, 49] Generated Node #2: [11, 45, 49] from Operation: 90-41=49 Current State: 83:[11, 45, 49], Operations: ['90-41=49'] Exploring Operation: 45-11=34, Resulting Numbers: [49, 34] Generated Node #3: [49, 34] from Operation: 45-11=34 Current State: 83:[49, 34], Operations: ['90-41=49', '45-11=34'] Exploring Operation: 49+34=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[41, 90, 11, 45], Operations: [] Exploring Operation: 41-11=30, Resulting Numbers: [90, 45, 30] Generated Node #0,0: 83:[90, 45, 30] Operation: 41-11=30 Exploring Operation: 90-11=79, Resulting Numbers: [41, 45, 79] Generated Node #0,1: 83:[41, 45, 79] Operation: 90-11=79 Exploring Operation: 41+11=52, Resulting Numbers: [90, 45, 52] Generated Node #0,2: 83:[90, 45, 52] Operation: 41+11=52 Exploring Operation: 41+45=86, Resulting Numbers: [90, 11, 86] Generated Node #0,3: 83:[90, 11, 86] Operation: 41+45=86 Exploring Operation: 11+45=56, Resulting Numbers: [41, 90, 56] Generated Node #0,4: 83:[41, 90, 56] Operation: 11+45=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[90, 45, 52], Operations: ['41+11=52'] Exploring Operation: 90+45=135, Resulting Numbers: [52, 135] Generated Node #0,2,0: 83:[52, 135] Operation: 90+45=135 Exploring Operation: 45+52=97, Resulting Numbers: [90, 97] Generated Node #0,2,1: 83:[90, 97] Operation: 45+52=97 Exploring Operation: 90-52=38, Resulting Numbers: [45, 38] Generated Node #0,2,2: 83:[45, 38] Operation: 90-52=38 Exploring Operation: 90-45=45, Resulting Numbers: [52, 45] Generated Node #0,2,3: 83:[52, 45] Operation: 90-45=45 Exploring Operation: 52-45=7, Resulting Numbers: [90, 7] Generated Node #0,2,4: 83:[90, 7] Operation: 52-45=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[90, 97], Operations: ['41+11=52', '45+52=97'] Exploring Operation: 90+97=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 90*97=8730, Resulting Numbers: [8730] 8730,83 unequal: No Solution Exploring Operation: 97-90=7, Resulting Numbers: [7] 7,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[52, 45], Operations: ['41+11=52', '90-45=45'] Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,83 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[52, 135], Operations: ['41+11=52', '90+45=135'] Exploring Operation: 52+135=187, Resulting Numbers: [187] 187,83 unequal: No Solution Exploring Operation: 135-52=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[41, 90, 11, 45], Operations: [] Exploring Operation: 41+11=52, Resulting Numbers: [90, 45, 52] Generated Node #0,2: 83:[90, 45, 52] Operation: 41+11=52 Moving to Node #0,2 Current State: 83:[90, 45, 52], Operations: ['41+11=52'] Exploring Operation: 90+45=135, Resulting Numbers: [52, 135] Generated Node #0,2,0: 83:[52, 135] Operation: 90+45=135 Moving to Node #0,2,0 Current State: 83:[52, 135], Operations: ['41+11=52', '90+45=135'] Exploring Operation: 135-52=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 50, 73, 27, 64 ]
47
[ "73-64=9", "27/9=3", "50-3=47" ]
Current State: 47:[50, 73, 27, 64], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [50, 27, 9] Generated Node #2: [50, 27, 9] from Operation: 73-64=9 Current State: 47:[50, 27, 9], Operations: ['73-64=9'] Exploring Operation: 27/9=3, Resulting Numbers: [50, 3] Generated Node #3: [50, 3] from Operation: 27/9=3 Current State: 47:[50, 3], Operations: ['73-64=9', '27/9=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[50, 73, 27, 64], Operations: [] Exploring Operation: 73-27=46, Resulting Numbers: [50, 64, 46] Generated Node #0,0: 47:[50, 64, 46] Operation: 73-27=46 Exploring Operation: 73-50=23, Resulting Numbers: [27, 64, 23] Generated Node #0,1: 47:[27, 64, 23] Operation: 73-50=23 Exploring Operation: 64-27=37, Resulting Numbers: [50, 73, 37] Generated Node #0,2: 47:[50, 73, 37] Operation: 64-27=37 Exploring Operation: 73-64=9, Resulting Numbers: [50, 27, 9] Generated Node #0,3: 47:[50, 27, 9] Operation: 73-64=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[50, 64, 46], Operations: ['73-27=46'] Exploring Operation: 64-46=18, Resulting Numbers: [50, 18] Generated Node #0,0,0: 47:[50, 18] Operation: 64-46=18 Exploring Operation: 50-46=4, Resulting Numbers: [64, 4] Generated Node #0,0,1: 47:[64, 4] Operation: 50-46=4 Exploring Operation: 64-50=14, Resulting Numbers: [46, 14] Generated Node #0,0,2: 47:[46, 14] Operation: 64-50=14 Exploring Operation: 50+46=96, Resulting Numbers: [64, 96] Generated Node #0,0,3: 47:[64, 96] Operation: 50+46=96 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[50, 18], Operations: ['73-27=46', '64-46=18'] Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 50+18=68, Resulting Numbers: [68] 68,47 unequal: No Solution Exploring Operation: 50*18=900, Resulting Numbers: [900] 900,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 47:[46, 14], Operations: ['73-27=46', '64-50=14'] Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 46+14=60, Resulting Numbers: [60] 60,47 unequal: No Solution Exploring Operation: 46*14=644, Resulting Numbers: [644] 644,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[64, 4], Operations: ['73-27=46', '50-46=4'] Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,47 unequal: No Solution Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,47 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 47:[64, 96], Operations: ['73-27=46', '50+46=96'] Exploring Operation: 96-64=32, Resulting Numbers: [32] 32,47 unequal: No Solution Exploring Operation: 64+96=160, Resulting Numbers: [160] 160,47 unequal: No Solution Exploring Operation: 64*96=6144, Resulting Numbers: [6144] 6144,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[50, 73, 37], Operations: ['64-27=37'] Exploring Operation: 73-37=36, Resulting Numbers: [50, 36] Generated Node #0,2,0: 47:[50, 36] Operation: 73-37=36 Exploring Operation: 50-37=13, Resulting Numbers: [73, 13] Generated Node #0,2,1: 47:[73, 13] Operation: 50-37=13 Exploring Operation: 73-50=23, Resulting Numbers: [37, 23] Generated Node #0,2,2: 47:[37, 23] Operation: 73-50=23 Exploring Operation: 50+37=87, Resulting Numbers: [73, 87] Generated Node #0,2,3: 47:[73, 87] Operation: 50+37=87 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 47:[50, 36], Operations: ['64-27=37', '73-37=36'] Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 50*36=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 47:[37, 23], Operations: ['64-27=37', '73-50=23'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,47 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 47:[73, 13], Operations: ['64-27=37', '50-37=13'] Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,47 unequal: No Solution Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 73*13=949, Resulting Numbers: [949] 949,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 47:[73, 87], Operations: ['64-27=37', '50+37=87'] Exploring Operation: 87-73=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 73*87=6351, Resulting Numbers: [6351] 6351,47 unequal: No Solution Exploring Operation: 73+87=160, Resulting Numbers: [160] 160,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[27, 64, 23], Operations: ['73-50=23'] Exploring Operation: 64-23=41, Resulting Numbers: [27, 41] Generated Node #0,1,0: 47:[27, 41] Operation: 64-23=41 Exploring Operation: 27+23=50, Resulting Numbers: [64, 50] Generated Node #0,1,1: 47:[64, 50] Operation: 27+23=50 Exploring Operation: 64-27=37, Resulting Numbers: [23, 37] Generated Node #0,1,2: 47:[23, 37] Operation: 64-27=37 Exploring Operation: 27-23=4, Resulting Numbers: [64, 4] Generated Node #0,1,3: 47:[64, 4] Operation: 27-23=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[64, 50], Operations: ['73-50=23', '27+23=50'] Exploring Operation: 64*50=3200, Resulting Numbers: [3200] 3200,47 unequal: No Solution Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 64+50=114, Resulting Numbers: [114] 114,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[27, 41], Operations: ['73-50=23', '64-23=41'] Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,47 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 47:[23, 37], Operations: ['73-50=23', '64-27=37'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,47 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 47:[64, 4], Operations: ['73-50=23', '27-23=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,47 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,47 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[50, 27, 9], Operations: ['73-64=9'] Exploring Operation: 50+9=59, Resulting Numbers: [27, 59] Generated Node #0,3,0: 47:[27, 59] Operation: 50+9=59 Exploring Operation: 27+9=36, Resulting Numbers: [50, 36] Generated Node #0,3,1: 47:[50, 36] Operation: 27+9=36 Exploring Operation: 50-9=41, Resulting Numbers: [27, 41] Generated Node #0,3,2: 47:[27, 41] Operation: 50-9=41 Exploring Operation: 27-9=18, Resulting Numbers: [50, 18] Generated Node #0,3,3: 47:[50, 18] Operation: 27-9=18 Moving to Node #0,3,1 Current State: 47:[50, 36], Operations: ['73-64=9', '27+9=36'] Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,47 unequal: No Solution Exploring Operation: 50*36=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[27, 41], Operations: ['73-64=9', '50-9=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,47 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,47 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[50, 18], Operations: ['73-64=9', '27-9=18'] Exploring Operation: 50+18=68, Resulting Numbers: [68] 68,47 unequal: No Solution Exploring Operation: 50*18=900, Resulting Numbers: [900] 900,47 unequal: No Solution Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[27, 59], Operations: ['73-64=9', '50+9=59'] Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,47 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,47 unequal: No Solution Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 36, 3, 47, 66 ]
74
[ "36+3=39", "47+66=113", "113-39=74" ]
Current State: 74:[36, 3, 47, 66], Operations: [] Exploring Operation: 36+3=39, Resulting Numbers: [47, 66, 39] Generated Node #2: [47, 66, 39] from Operation: 36+3=39 Current State: 74:[47, 66, 39], Operations: ['36+3=39'] Exploring Operation: 47+66=113, Resulting Numbers: [39, 113] Generated Node #3: [39, 113] from Operation: 47+66=113 Current State: 74:[39, 113], Operations: ['36+3=39', '47+66=113'] Exploring Operation: 113-39=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[36, 3, 47, 66], Operations: [] Exploring Operation: 47-3=44, Resulting Numbers: [36, 66, 44] Generated Node #0,0: 74:[36, 66, 44] Operation: 47-3=44 Exploring Operation: 47-36=11, Resulting Numbers: [3, 66, 11] Generated Node #0,1: 74:[3, 66, 11] Operation: 47-36=11 Exploring Operation: 66-36=30, Resulting Numbers: [3, 47, 30] Generated Node #0,2: 74:[3, 47, 30] Operation: 66-36=30 Exploring Operation: 3+66=69, Resulting Numbers: [36, 47, 69] Generated Node #0,3: 74:[36, 47, 69] Operation: 3+66=69 Exploring Operation: 36+47=83, Resulting Numbers: [3, 66, 83] Generated Node #0,4: 74:[3, 66, 83] Operation: 36+47=83 Moving to Node #0,0 Current State: 74:[36, 66, 44], Operations: ['47-3=44'] Exploring Operation: 66-44=22, Resulting Numbers: [36, 22] Generated Node #0,0,0: 74:[36, 22] Operation: 66-44=22 Exploring Operation: 44-36=8, Resulting Numbers: [66, 8] Generated Node #0,0,1: 74:[66, 8] Operation: 44-36=8 Exploring Operation: 36+44=80, Resulting Numbers: [66, 80] Generated Node #0,0,2: 74:[66, 80] Operation: 36+44=80 Exploring Operation: 36+66=102, Resulting Numbers: [44, 102] Generated Node #0,0,3: 74:[44, 102] Operation: 36+66=102 Exploring Operation: 66-36=30, Resulting Numbers: [44, 30] Generated Node #0,0,4: 74:[44, 30] Operation: 66-36=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[66, 8], Operations: ['47-3=44', '44-36=8'] Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[36, 3, 47, 66], Operations: [] Exploring Operation: 47-3=44, Resulting Numbers: [36, 66, 44] Generated Node #0,0: 74:[36, 66, 44] Operation: 47-3=44 Moving to Node #0,0 Current State: 74:[36, 66, 44], Operations: ['47-3=44'] Exploring Operation: 44-36=8, Resulting Numbers: [66, 8] Generated Node #0,0,1: 74:[66, 8] Operation: 44-36=8 Moving to Node #0,0,1 Current State: 74:[66, 8], Operations: ['47-3=44', '44-36=8'] Exploring Operation: 66+8=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 23, 95, 63, 36 ]
61
[ "95-23=72", "72/36=2", "63-2=61" ]
Current State: 61:[23, 95, 63, 36], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [63, 36, 72] Generated Node #2: [63, 36, 72] from Operation: 95-23=72 Current State: 61:[63, 36, 72], Operations: ['95-23=72'] Exploring Operation: 72/36=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 72/36=2 Current State: 61:[63, 2], Operations: ['95-23=72', '72/36=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[23, 95, 63, 36], Operations: [] Exploring Operation: 23+95=118, Resulting Numbers: [63, 36, 118] Generated Node #0,0: 61:[63, 36, 118] Operation: 23+95=118 Exploring Operation: 23+36=59, Resulting Numbers: [95, 63, 59] Generated Node #0,1: 61:[95, 63, 59] Operation: 23+36=59 Exploring Operation: 63-23=40, Resulting Numbers: [95, 36, 40] Generated Node #0,2: 61:[95, 36, 40] Operation: 63-23=40 Exploring Operation: 95-23=72, Resulting Numbers: [63, 36, 72] Generated Node #0,3: 61:[63, 36, 72] Operation: 95-23=72 Exploring Operation: 95-36=59, Resulting Numbers: [23, 63, 59] Generated Node #0,4: 61:[23, 63, 59] Operation: 95-36=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[95, 63, 59], Operations: ['23+36=59'] Exploring Operation: 63-59=4, Resulting Numbers: [95, 4] Generated Node #0,1,0: 61:[95, 4] Operation: 63-59=4 Exploring Operation: 95+59=154, Resulting Numbers: [63, 154] Generated Node #0,1,1: 61:[63, 154] Operation: 95+59=154 Exploring Operation: 95-59=36, Resulting Numbers: [63, 36] Generated Node #0,1,2: 61:[63, 36] Operation: 95-59=36 Exploring Operation: 95-63=32, Resulting Numbers: [59, 32] Generated Node #0,1,3: 61:[59, 32] Operation: 95-63=32 Exploring Operation: 63+59=122, Resulting Numbers: [95, 122] Generated Node #0,1,4: 61:[95, 122] Operation: 63+59=122 Moving to Node #0,1,2 Current State: 61:[63, 36], Operations: ['23+36=59', '95-59=36'] Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,61 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 63*36=2268, Resulting Numbers: [2268] 2268,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[59, 32], Operations: ['23+36=59', '95-63=32'] Exploring Operation: 59*32=1888, Resulting Numbers: [1888] 1888,61 unequal: No Solution Exploring Operation: 59+32=91, Resulting Numbers: [91] 91,61 unequal: No Solution Exploring Operation: 59-32=27, Resulting Numbers: [27] 27,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[95, 4], Operations: ['23+36=59', '63-59=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,61 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,61 unequal: No Solution Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[63, 154], Operations: ['23+36=59', '95+59=154'] Exploring Operation: 63+154=217, Resulting Numbers: [217] 217,61 unequal: No Solution Exploring Operation: 154-63=91, Resulting Numbers: [91] 91,61 unequal: No Solution Exploring Operation: 63*154=9702, Resulting Numbers: [9702] 9702,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[95, 122], Operations: ['23+36=59', '63+59=122'] Exploring Operation: 122-95=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 95+122=217, Resulting Numbers: [217] 217,61 unequal: No Solution Exploring Operation: 95*122=11590, Resulting Numbers: [11590] 11590,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[63, 36, 72], Operations: ['95-23=72'] Exploring Operation: 63+36=99, Resulting Numbers: [72, 99] Generated Node #0,3,0: 61:[72, 99] Operation: 63+36=99 Exploring Operation: 63-36=27, Resulting Numbers: [72, 27] Generated Node #0,3,1: 61:[72, 27] Operation: 63-36=27 Exploring Operation: 36+72=108, Resulting Numbers: [63, 108] Generated Node #0,3,2: 61:[63, 108] Operation: 36+72=108 Exploring Operation: 72-36=36, Resulting Numbers: [63, 36] Generated Node #0,3,3: 61:[63, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [63, 2] Generated Node #0,3,4: 61:[63, 2] Operation: 72/36=2 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 61:[63, 36], Operations: ['95-23=72', '72-36=36'] Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 63*36=2268, Resulting Numbers: [2268] 2268,61 unequal: No Solution Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,61 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 #0,3,1 Current State: 61:[72, 27], Operations: ['95-23=72', '63-36=27'] Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 72+27=99, Resulting Numbers: [99] 99,61 unequal: No Solution Exploring Operation: 72*27=1944, Resulting Numbers: [1944] 1944,61 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 #0,3,0 Current State: 61:[72, 99], Operations: ['95-23=72', '63+36=99'] Exploring Operation: 72*99=7128, Resulting Numbers: [7128] 7128,61 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,61 unequal: No Solution Exploring Operation: 72+99=171, Resulting Numbers: [171] 171,61 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 #0,3,2 Current State: 61:[63, 108], Operations: ['95-23=72', '36+72=108'] Exploring Operation: 63+108=171, Resulting Numbers: [171] 171,61 unequal: No Solution Exploring Operation: 108-63=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 63*108=6804, Resulting Numbers: [6804] 6804,61 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 #0,3,4 Current State: 61:[63, 2], Operations: ['95-23=72', '72/36=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[23, 95, 63, 36], Operations: [] Exploring Operation: 95-23=72, Resulting Numbers: [63, 36, 72] Generated Node #0,3: 61:[63, 36, 72] Operation: 95-23=72 Moving to Node #0,3 Current State: 61:[63, 36, 72], Operations: ['95-23=72'] Exploring Operation: 72/36=2, Resulting Numbers: [63, 2] Generated Node #0,3,4: 61:[63, 2] Operation: 72/36=2 Moving to Node #0,3,4 Current State: 61:[63, 2], Operations: ['95-23=72', '72/36=2'] Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.959201
hs_5
mult_heuristic
[ 45, 47, 2, 3 ]
79
[ "45/3=15", "47*2=94", "94-15=79" ]
Current State: 79:[45, 47, 2, 3], Operations: [] Exploring Operation: 45/3=15, Resulting Numbers: [47, 2, 15] Generated Node #2: [47, 2, 15] from Operation: 45/3=15 Current State: 79:[47, 2, 15], Operations: ['45/3=15'] Exploring Operation: 47*2=94, Resulting Numbers: [15, 94] Generated Node #3: [15, 94] from Operation: 47*2=94 Current State: 79:[15, 94], Operations: ['45/3=15', '47*2=94'] Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[45, 47, 2, 3], Operations: [] Exploring Operation: 45*2=90, Resulting Numbers: [47, 3, 90] Generated Node #0,0: 79:[47, 3, 90] Operation: 45*2=90 Exploring Operation: 47*2=94, Resulting Numbers: [45, 3, 94] Generated Node #0,1: 79:[45, 3, 94] Operation: 47*2=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[47, 3, 90], Operations: ['45*2=90'] Exploring Operation: 47+3=50, Resulting Numbers: [90, 50] Generated Node #0,0,0: 79:[90, 50] Operation: 47+3=50 Exploring Operation: 90-3=87, Resulting Numbers: [47, 87] Generated Node #0,0,1: 79:[47, 87] Operation: 90-3=87 Moving to Node #0,0,0 Current State: 79:[90, 50], Operations: ['45*2=90', '47+3=50'] Exploring Operation: 90+50=140, Resulting Numbers: [140] 140,79 unequal: No Solution Exploring Operation: 90-50=40, Resulting Numbers: [40] 40,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[47, 87], Operations: ['45*2=90', '90-3=87'] Exploring Operation: 87-47=40, Resulting Numbers: [40] 40,79 unequal: No Solution Exploring Operation: 47+87=134, Resulting Numbers: [134] 134,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[45, 3, 94], Operations: ['47*2=94'] Exploring Operation: 94-3=91, Resulting Numbers: [45, 91] Generated Node #0,1,0: 79:[45, 91] Operation: 94-3=91 Exploring Operation: 45+3=48, Resulting Numbers: [94, 48] Generated Node #0,1,1: 79:[94, 48] Operation: 45+3=48 Moving to Node #0,1,0 Current State: 79:[45, 91], Operations: ['47*2=94', '94-3=91'] Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 45+91=136, Resulting Numbers: [136] 136,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[94, 48], Operations: ['47*2=94', '45+3=48'] Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,79 unequal: No Solution Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,79 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
[ 58, 26, 82, 96 ]
48
[ "58+26=84", "84-82=2", "96/2=48" ]
Current State: 48:[58, 26, 82, 96], Operations: [] Exploring Operation: 58+26=84, Resulting Numbers: [82, 96, 84] Generated Node #2: [82, 96, 84] from Operation: 58+26=84 Current State: 48:[82, 96, 84], Operations: ['58+26=84'] Exploring Operation: 84-82=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 84-82=2 Current State: 48:[96, 2], Operations: ['58+26=84', '84-82=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[58, 26, 82, 96], Operations: [] Exploring Operation: 96-26=70, Resulting Numbers: [58, 82, 70] Generated Node #0,0: 48:[58, 82, 70] Operation: 96-26=70 Exploring Operation: 96-58=38, Resulting Numbers: [26, 82, 38] Generated Node #0,1: 48:[26, 82, 38] Operation: 96-58=38 Exploring Operation: 82-26=56, Resulting Numbers: [58, 96, 56] Generated Node #0,2: 48:[58, 96, 56] Operation: 82-26=56 Exploring Operation: 96-82=14, Resulting Numbers: [58, 26, 14] Generated Node #0,3: 48:[58, 26, 14] Operation: 96-82=14 Exploring Operation: 82-58=24, Resulting Numbers: [26, 96, 24] Generated Node #0,4: 48:[26, 96, 24] Operation: 82-58=24 Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[58, 26, 14], Operations: ['96-82=14'] Exploring Operation: 58-14=44, Resulting Numbers: [26, 44] Generated Node #0,3,0: 48:[26, 44] Operation: 58-14=44 Exploring Operation: 26-14=12, Resulting Numbers: [58, 12] Generated Node #0,3,1: 48:[58, 12] Operation: 26-14=12 Exploring Operation: 58+14=72, Resulting Numbers: [26, 72] Generated Node #0,3,2: 48:[26, 72] Operation: 58+14=72 Exploring Operation: 58-26=32, Resulting Numbers: [14, 32] Generated Node #0,3,3: 48:[14, 32] Operation: 58-26=32 Exploring Operation: 26+14=40, Resulting Numbers: [58, 40] Generated Node #0,3,4: 48:[58, 40] Operation: 26+14=40 Moving to Node #0,3,0 Current State: 48:[26, 44], Operations: ['96-82=14', '58-14=44'] Exploring Operation: 26+44=70, Resulting Numbers: [70] 70,48 unequal: No Solution Exploring Operation: 26*44=1144, Resulting Numbers: [1144] 1144,48 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,48 unequal: No Solution Moving to Node #0,3,3 Current State: 48:[14, 32], Operations: ['96-82=14', '58-26=32'] Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 14*32=448, Resulting Numbers: [448] 448,48 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[58, 12], Operations: ['96-82=14', '26-14=12'] Exploring Operation: 58-12=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 58+12=70, Resulting Numbers: [70] 70,48 unequal: No Solution Exploring Operation: 58*12=696, Resulting Numbers: [696] 696,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[58, 40], Operations: ['96-82=14', '26+14=40'] Exploring Operation: 58*40=2320, Resulting Numbers: [2320] 2320,48 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 58+40=98, Resulting Numbers: [98] 98,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[26, 72], Operations: ['96-82=14', '58+14=72'] Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 26*72=1872, Resulting Numbers: [1872] 1872,48 unequal: No Solution Exploring Operation: 26+72=98, Resulting Numbers: [98] 98,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[26, 82, 38], Operations: ['96-58=38'] Exploring Operation: 82-26=56, Resulting Numbers: [38, 56] Generated Node #0,1,0: 48:[38, 56] Operation: 82-26=56 Exploring Operation: 38-26=12, Resulting Numbers: [82, 12] Generated Node #0,1,1: 48:[82, 12] Operation: 38-26=12 Exploring Operation: 26+38=64, Resulting Numbers: [82, 64] Generated Node #0,1,2: 48:[82, 64] Operation: 26+38=64 Exploring Operation: 82-38=44, Resulting Numbers: [26, 44] Generated Node #0,1,3: 48:[26, 44] Operation: 82-38=44 Exploring Operation: 26+82=108, Resulting Numbers: [38, 108] Generated Node #0,1,4: 48:[38, 108] Operation: 26+82=108 Moving to Node #0,1,3 Current State: 48:[26, 44], Operations: ['96-58=38', '82-38=44'] Exploring Operation: 26*44=1144, Resulting Numbers: [1144] 1144,48 unequal: No Solution Exploring Operation: 26+44=70, Resulting Numbers: [70] 70,48 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[38, 56], Operations: ['96-58=38', '82-26=56'] Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,48 unequal: No Solution Exploring Operation: 38+56=94, Resulting Numbers: [94] 94,48 unequal: No Solution Exploring Operation: 38*56=2128, Resulting Numbers: [2128] 2128,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[82, 12], Operations: ['96-58=38', '38-26=12'] Exploring Operation: 82+12=94, Resulting Numbers: [94] 94,48 unequal: No Solution Exploring Operation: 82-12=70, Resulting Numbers: [70] 70,48 unequal: No Solution Exploring Operation: 82*12=984, Resulting Numbers: [984] 984,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[82, 64], Operations: ['96-58=38', '26+38=64'] Exploring Operation: 82*64=5248, Resulting Numbers: [5248] 5248,48 unequal: No Solution Exploring Operation: 82+64=146, Resulting Numbers: [146] 146,48 unequal: No Solution Exploring Operation: 82-64=18, Resulting Numbers: [18] 18,48 unequal: No Solution Moving to Node #0,1,4 Current State: 48:[38, 108], Operations: ['96-58=38', '26+82=108'] Exploring Operation: 38*108=4104, Resulting Numbers: [4104] 4104,48 unequal: No Solution Exploring Operation: 108-38=70, Resulting Numbers: [70] 70,48 unequal: No Solution Exploring Operation: 38+108=146, Resulting Numbers: [146] 146,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 48:[26, 96, 24], Operations: ['82-58=24'] Exploring Operation: 96-24=72, Resulting Numbers: [26, 72] Generated Node #0,4,0: 48:[26, 72] Operation: 96-24=72 Exploring Operation: 26-24=2, Resulting Numbers: [96, 2] Generated Node #0,4,1: 48:[96, 2] Operation: 26-24=2 Exploring Operation: 26+24=50, Resulting Numbers: [96, 50] Generated Node #0,4,2: 48:[96, 50] Operation: 26+24=50 Exploring Operation: 96/24=4, Resulting Numbers: [26, 4] Generated Node #0,4,3: 48:[26, 4] Operation: 96/24=4 Exploring Operation: 96-26=70, Resulting Numbers: [24, 70] Generated Node #0,4,4: 48:[24, 70] Operation: 96-26=70 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 48:[26, 4], Operations: ['82-58=24', '96/24=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,48 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 48:[24, 70], Operations: ['82-58=24', '96-26=70'] Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 24*70=1680, Resulting Numbers: [1680] 1680,48 unequal: No Solution Exploring Operation: 24+70=94, Resulting Numbers: [94] 94,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 48:[26, 72], Operations: ['82-58=24', '96-24=72'] Exploring Operation: 26+72=98, Resulting Numbers: [98] 98,48 unequal: No Solution Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 26*72=1872, Resulting Numbers: [1872] 1872,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 48:[96, 2], Operations: ['82-58=24', '26-24=2'] Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,48 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,48 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,48 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[58, 26, 82, 96], Operations: [] Exploring Operation: 82-58=24, Resulting Numbers: [26, 96, 24] Generated Node #0,4: 48:[26, 96, 24] Operation: 82-58=24 Moving to Node #0,4 Current State: 48:[26, 96, 24], Operations: ['82-58=24'] Exploring Operation: 26-24=2, Resulting Numbers: [96, 2] Generated Node #0,4,1: 48:[96, 2] Operation: 26-24=2 Moving to Node #0,4,1 Current State: 48:[96, 2], Operations: ['82-58=24', '26-24=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.94184
hs_5
sum_heuristic
[ 14, 75, 40, 22 ]
71
[ "14+75=89", "40-22=18", "89-18=71" ]
Current State: 71:[14, 75, 40, 22], Operations: [] Exploring Operation: 14+75=89, Resulting Numbers: [40, 22, 89] Generated Node #2: [40, 22, 89] from Operation: 14+75=89 Current State: 71:[40, 22, 89], Operations: ['14+75=89'] Exploring Operation: 40-22=18, Resulting Numbers: [89, 18] Generated Node #3: [89, 18] from Operation: 40-22=18 Current State: 71:[89, 18], Operations: ['14+75=89', '40-22=18'] Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[14, 75, 40, 22], Operations: [] Exploring Operation: 14+75=89, Resulting Numbers: [40, 22, 89] Generated Node #0,0: 71:[40, 22, 89] Operation: 14+75=89 Exploring Operation: 14+22=36, Resulting Numbers: [75, 40, 36] Generated Node #0,1: 71:[75, 40, 36] Operation: 14+22=36 Exploring Operation: 14+40=54, Resulting Numbers: [75, 22, 54] Generated Node #0,2: 71:[75, 22, 54] Operation: 14+40=54 Exploring Operation: 40+22=62, Resulting Numbers: [14, 75, 62] Generated Node #0,3: 71:[14, 75, 62] Operation: 40+22=62 Exploring Operation: 75-14=61, Resulting Numbers: [40, 22, 61] Generated Node #0,4: 71:[40, 22, 61] Operation: 75-14=61 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[75, 40, 36], Operations: ['14+22=36'] Exploring Operation: 75+36=111, Resulting Numbers: [40, 111] Generated Node #0,1,0: 71:[40, 111] Operation: 75+36=111 Exploring Operation: 75-36=39, Resulting Numbers: [40, 39] Generated Node #0,1,1: 71:[40, 39] Operation: 75-36=39 Exploring Operation: 40-36=4, Resulting Numbers: [75, 4] Generated Node #0,1,2: 71:[75, 4] Operation: 40-36=4 Exploring Operation: 75-40=35, Resulting Numbers: [36, 35] Generated Node #0,1,3: 71:[36, 35] Operation: 75-40=35 Exploring Operation: 40+36=76, Resulting Numbers: [75, 76] Generated Node #0,1,4: 71:[75, 76] Operation: 40+36=76 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 71:[75, 76], Operations: ['14+22=36', '40+36=76'] Exploring Operation: 76-75=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 75+76=151, Resulting Numbers: [151] 151,71 unequal: No Solution Exploring Operation: 75*76=5700, Resulting Numbers: [5700] 5700,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 71:[40, 39], Operations: ['14+22=36', '75-36=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,71 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,71 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[40, 111], Operations: ['14+22=36', '75+36=111'] Exploring Operation: 40*111=4440, Resulting Numbers: [4440] 4440,71 unequal: No Solution Exploring Operation: 40+111=151, Resulting Numbers: [151] 151,71 unequal: No Solution Exploring Operation: 111-40=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[14, 75, 40, 22], Operations: [] Exploring Operation: 14+22=36, Resulting Numbers: [75, 40, 36] Generated Node #0,1: 71:[75, 40, 36] Operation: 14+22=36 Moving to Node #0,1 Current State: 71:[75, 40, 36], Operations: ['14+22=36'] Exploring Operation: 75+36=111, Resulting Numbers: [40, 111] Generated Node #0,1,0: 71:[40, 111] Operation: 75+36=111 Moving to Node #0,1,0 Current State: 71:[40, 111], Operations: ['14+22=36', '75+36=111'] Exploring Operation: 111-40=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 63, 46, 66, 64 ]
54
[ "66-63=3", "64-46=18", "3*18=54" ]
Current State: 54:[63, 46, 66, 64], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [46, 64, 3] Generated Node #2: [46, 64, 3] from Operation: 66-63=3 Current State: 54:[46, 64, 3], Operations: ['66-63=3'] Exploring Operation: 64-46=18, Resulting Numbers: [3, 18] Generated Node #3: [3, 18] from Operation: 64-46=18 Current State: 54:[3, 18], Operations: ['66-63=3', '64-46=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[63, 46, 66, 64], Operations: [] Exploring Operation: 64-63=1, Resulting Numbers: [46, 66, 1] Generated Node #0,0: 54:[46, 66, 1] Operation: 64-63=1 Exploring Operation: 66-63=3, Resulting Numbers: [46, 64, 3] Generated Node #0,1: 54:[46, 64, 3] Operation: 66-63=3 Exploring Operation: 66-64=2, Resulting Numbers: [63, 46, 2] Generated Node #0,2: 54:[63, 46, 2] Operation: 66-64=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[63, 46, 2], Operations: ['66-64=2'] Exploring Operation: 63-2=61, Resulting Numbers: [46, 61] Generated Node #0,2,0: 54:[46, 61] Operation: 63-2=61 Exploring Operation: 46/2=23, Resulting Numbers: [63, 23] Generated Node #0,2,1: 54:[63, 23] Operation: 46/2=23 Exploring Operation: 63-46=17, Resulting Numbers: [2, 17] Generated Node #0,2,2: 54:[2, 17] Operation: 63-46=17 Moving to Node #0,2,2 Current State: 54:[2, 17], Operations: ['66-64=2', '63-46=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[63, 23], Operations: ['66-64=2', '46/2=23'] Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,54 unequal: No Solution Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,54 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[46, 61], Operations: ['66-64=2', '63-2=61'] Exploring Operation: 46+61=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 61-46=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 46*61=2806, Resulting Numbers: [2806] 2806,54 unequal: No Solution No 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: 54:[46, 64, 3], Operations: ['66-63=3'] Exploring Operation: 64-3=61, Resulting Numbers: [46, 61] Generated Node #0,1,0: 54:[46, 61] Operation: 64-3=61 Exploring Operation: 64-46=18, Resulting Numbers: [3, 18] Generated Node #0,1,1: 54:[3, 18] Operation: 64-46=18 Exploring Operation: 46+3=49, Resulting Numbers: [64, 49] Generated Node #0,1,2: 54:[64, 49] Operation: 46+3=49 Moving to Node #0,1,1 Current State: 54:[3, 18], Operations: ['66-63=3', '64-46=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[63, 46, 66, 64], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [46, 64, 3] Generated Node #0,1: 54:[46, 64, 3] Operation: 66-63=3 Moving to Node #0,1 Current State: 54:[46, 64, 3], Operations: ['66-63=3'] Exploring Operation: 64-46=18, Resulting Numbers: [3, 18] Generated Node #0,1,1: 54:[3, 18] Operation: 64-46=18 Moving to Node #0,1,1 Current State: 54:[3, 18], Operations: ['66-63=3', '64-46=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 22, 85, 24, 6 ]
37
[ "22+85=107", "24*6=144", "144-107=37" ]
Current State: 37:[22, 85, 24, 6], Operations: [] Exploring Operation: 22+85=107, Resulting Numbers: [24, 6, 107] Generated Node #2: [24, 6, 107] from Operation: 22+85=107 Current State: 37:[24, 6, 107], Operations: ['22+85=107'] Exploring Operation: 24*6=144, Resulting Numbers: [107, 144] Generated Node #3: [107, 144] from Operation: 24*6=144 Current State: 37:[107, 144], Operations: ['22+85=107', '24*6=144'] Exploring Operation: 144-107=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[22, 85, 24, 6], Operations: [] Exploring Operation: 85-22=63, Resulting Numbers: [24, 6, 63] Generated Node #0,0: 37:[24, 6, 63] Operation: 85-22=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[24, 6, 63], Operations: ['85-22=63'] Exploring Operation: 24+6=30, Resulting Numbers: [63, 30] Generated Node #0,0,0: 37:[63, 30] Operation: 24+6=30 Moving to Node #0,0,0 Current State: 37:[63, 30], Operations: ['85-22=63', '24+6=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,37 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
[ 72, 72, 78, 4 ]
81
[ "72/72=1", "78+4=82", "82-1=81" ]
Current State: 81:[72, 72, 78, 4], Operations: [] Exploring Operation: 72/72=1, Resulting Numbers: [78, 4, 1] Generated Node #2: [78, 4, 1] from Operation: 72/72=1 Current State: 81:[78, 4, 1], Operations: ['72/72=1'] Exploring Operation: 78+4=82, Resulting Numbers: [1, 82] Generated Node #3: [1, 82] from Operation: 78+4=82 Current State: 81:[1, 82], Operations: ['72/72=1', '78+4=82'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[72, 72, 78, 4], Operations: [] Exploring Operation: 72-72=0, Resulting Numbers: [78, 4, 0] Generated Node #0,0: 81:[78, 4, 0] Operation: 72-72=0 Exploring Operation: 78-72=6, Resulting Numbers: [72, 4, 6] Generated Node #0,1: 81:[72, 4, 6] Operation: 78-72=6 Exploring Operation: 72/72=1, Resulting Numbers: [78, 4, 1] Generated Node #0,2: 81:[78, 4, 1] Operation: 72/72=1 Exploring Operation: 78-72=6, Resulting Numbers: [72, 4, 6] Generated Node #0,3: 81:[72, 4, 6] Operation: 78-72=6 Moving to Node #0,2 Current State: 81:[78, 4, 1], Operations: ['72/72=1'] Exploring Operation: 78+1=79, Resulting Numbers: [4, 79] Generated Node #0,2,0: 81:[4, 79] Operation: 78+1=79 Exploring Operation: 4-1=3, Resulting Numbers: [78, 3] Generated Node #0,2,1: 81:[78, 3] Operation: 4-1=3 Exploring Operation: 78+4=82, Resulting Numbers: [1, 82] Generated Node #0,2,2: 81:[1, 82] Operation: 78+4=82 Exploring Operation: 78*1=78, Resulting Numbers: [4, 78] Generated Node #0,2,3: 81:[4, 78] Operation: 78*1=78 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[4, 79], Operations: ['72/72=1', '78+1=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,81 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,81 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 #0,2,1 Current State: 81:[78, 3], Operations: ['72/72=1', '4-1=3'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[72, 72, 78, 4], Operations: [] Exploring Operation: 72/72=1, Resulting Numbers: [78, 4, 1] Generated Node #0,2: 81:[78, 4, 1] Operation: 72/72=1 Moving to Node #0,2 Current State: 81:[78, 4, 1], Operations: ['72/72=1'] Exploring Operation: 4-1=3, Resulting Numbers: [78, 3] Generated Node #0,2,1: 81:[78, 3] Operation: 4-1=3 Moving to Node #0,2,1 Current State: 81:[78, 3], Operations: ['72/72=1', '4-1=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 83, 88, 36, 98 ]
82
[ "88-83=5", "36*5=180", "180-98=82" ]
Current State: 82:[83, 88, 36, 98], Operations: [] Exploring Operation: 88-83=5, Resulting Numbers: [36, 98, 5] Generated Node #2: [36, 98, 5] from Operation: 88-83=5 Current State: 82:[36, 98, 5], Operations: ['88-83=5'] Exploring Operation: 36*5=180, Resulting Numbers: [98, 180] Generated Node #3: [98, 180] from Operation: 36*5=180 Current State: 82:[98, 180], Operations: ['88-83=5', '36*5=180'] Exploring Operation: 180-98=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[83, 88, 36, 98], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [83, 36, 10] Generated Node #0,0: 82:[83, 36, 10] Operation: 98-88=10 Exploring Operation: 98-36=62, Resulting Numbers: [83, 88, 62] Generated Node #0,1: 82:[83, 88, 62] Operation: 98-36=62 Exploring Operation: 88-83=5, Resulting Numbers: [36, 98, 5] Generated Node #0,2: 82:[36, 98, 5] Operation: 88-83=5 Exploring Operation: 83-36=47, Resulting Numbers: [88, 98, 47] Generated Node #0,3: 82:[88, 98, 47] Operation: 83-36=47 Exploring Operation: 98-83=15, Resulting Numbers: [88, 36, 15] Generated Node #0,4: 82:[88, 36, 15] Operation: 98-83=15 Moving to Node #0,0 Current State: 82:[83, 36, 10], Operations: ['98-88=10'] Exploring Operation: 36-10=26, Resulting Numbers: [83, 26] Generated Node #0,0,0: 82:[83, 26] Operation: 36-10=26 Exploring Operation: 83+10=93, Resulting Numbers: [36, 93] Generated Node #0,0,1: 82:[36, 93] Operation: 83+10=93 Exploring Operation: 83-10=73, Resulting Numbers: [36, 73] Generated Node #0,0,2: 82:[36, 73] Operation: 83-10=73 Exploring Operation: 83-36=47, Resulting Numbers: [10, 47] Generated Node #0,0,3: 82:[10, 47] Operation: 83-36=47 Exploring Operation: 36+10=46, Resulting Numbers: [83, 46] Generated Node #0,0,4: 82:[83, 46] Operation: 36+10=46 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 82:[83, 46], Operations: ['98-88=10', '36+10=46'] Exploring Operation: 83+46=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 83-46=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 83*46=3818, Resulting Numbers: [3818] 3818,82 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:[36, 73], Operations: ['98-88=10', '83-10=73'] Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,82 unequal: No Solution Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,82 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 #0,0,3 Current State: 82:[10, 47], Operations: ['98-88=10', '83-36=47'] Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,82 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:[83, 26], Operations: ['98-88=10', '36-10=26'] Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 83+26=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 83*26=2158, Resulting Numbers: [2158] 2158,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[36, 93], Operations: ['98-88=10', '83+10=93'] Exploring Operation: 36+93=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 93-36=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 36*93=3348, Resulting Numbers: [3348] 3348,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 82:[88, 36, 15], Operations: ['98-83=15'] Exploring Operation: 88-15=73, Resulting Numbers: [36, 73] Generated Node #0,4,0: 82:[36, 73] Operation: 88-15=73 Exploring Operation: 88+15=103, Resulting Numbers: [36, 103] Generated Node #0,4,1: 82:[36, 103] Operation: 88+15=103 Exploring Operation: 36-15=21, Resulting Numbers: [88, 21] Generated Node #0,4,2: 82:[88, 21] Operation: 36-15=21 Exploring Operation: 88-36=52, Resulting Numbers: [15, 52] Generated Node #0,4,3: 82:[15, 52] Operation: 88-36=52 Exploring Operation: 36+15=51, Resulting Numbers: [88, 51] Generated Node #0,4,4: 82:[88, 51] Operation: 36+15=51 Moving to Node #0,2 Current State: 82:[36, 98, 5], Operations: ['88-83=5'] Exploring Operation: 36-5=31, Resulting Numbers: [98, 31] Generated Node #0,2,0: 82:[98, 31] Operation: 36-5=31 Exploring Operation: 98-5=93, Resulting Numbers: [36, 93] Generated Node #0,2,1: 82:[36, 93] Operation: 98-5=93 Exploring Operation: 36+5=41, Resulting Numbers: [98, 41] Generated Node #0,2,2: 82:[98, 41] Operation: 36+5=41 Exploring Operation: 98+5=103, Resulting Numbers: [36, 103] Generated Node #0,2,3: 82:[36, 103] Operation: 98+5=103 Exploring Operation: 98-36=62, Resulting Numbers: [5, 62] Generated Node #0,2,4: 82:[5, 62] Operation: 98-36=62 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 82:[36, 93], Operations: ['88-83=5', '98-5=93'] Exploring Operation: 36+93=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 93-36=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 36*93=3348, Resulting Numbers: [3348] 3348,82 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 #0,2,2 Current State: 82:[98, 41], Operations: ['88-83=5', '36+5=41'] Exploring Operation: 98+41=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 98-41=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 98*41=4018, Resulting Numbers: [4018] 4018,82 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 #0,2,4 Current State: 82:[5, 62], Operations: ['88-83=5', '98-36=62'] Exploring Operation: 5+62=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 5*62=310, Resulting Numbers: [310] 310,82 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,82 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:[98, 31], Operations: ['88-83=5', '36-5=31'] Exploring Operation: 98-31=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 98*31=3038, Resulting Numbers: [3038] 3038,82 unequal: No Solution Exploring Operation: 98+31=129, Resulting Numbers: [129] 129,82 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 #0,2,3 Current State: 82:[36, 103], Operations: ['88-83=5', '98+5=103'] Exploring Operation: 103-36=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 36+103=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 36*103=3708, Resulting Numbers: [3708] 3708,82 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: 82:[83, 88, 62], Operations: ['98-36=62'] Exploring Operation: 88+62=150, Resulting Numbers: [83, 150] Generated Node #0,1,0: 82:[83, 150] Operation: 88+62=150 Exploring Operation: 88-62=26, Resulting Numbers: [83, 26] Generated Node #0,1,1: 82:[83, 26] Operation: 88-62=26 Exploring Operation: 83+62=145, Resulting Numbers: [88, 145] Generated Node #0,1,2: 82:[88, 145] Operation: 83+62=145 Exploring Operation: 88-83=5, Resulting Numbers: [62, 5] Generated Node #0,1,3: 82:[62, 5] Operation: 88-83=5 Exploring Operation: 83-62=21, Resulting Numbers: [88, 21] Generated Node #0,1,4: 82:[88, 21] Operation: 83-62=21 Moving to Node #0,3 Current State: 82:[88, 98, 47], Operations: ['83-36=47'] Exploring Operation: 88+47=135, Resulting Numbers: [98, 135] Generated Node #0,3,0: 82:[98, 135] Operation: 88+47=135 Exploring Operation: 98-47=51, Resulting Numbers: [88, 51] Generated Node #0,3,1: 82:[88, 51] Operation: 98-47=51 Exploring Operation: 98+47=145, Resulting Numbers: [88, 145] Generated Node #0,3,2: 82:[88, 145] Operation: 98+47=145 Exploring Operation: 98-88=10, Resulting Numbers: [47, 10] Generated Node #0,3,3: 82:[47, 10] Operation: 98-88=10 Exploring Operation: 88-47=41, Resulting Numbers: [98, 41] Generated Node #0,3,4: 82:[98, 41] Operation: 88-47=41 Moving to Node #0,4,0 Current State: 82:[36, 73], Operations: ['98-83=15', '88-15=73'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,82 unequal: No Solution Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[47, 10], Operations: ['83-36=47', '98-88=10'] Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,82 unequal: No Solution Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[83, 26], Operations: ['98-36=62', '88-62=26'] Exploring Operation: 83+26=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 83*26=2158, Resulting Numbers: [2158] 2158,82 unequal: No Solution Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[88, 51], Operations: ['83-36=47', '98-47=51'] Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,82 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,82 unequal: No Solution Moving to Node #0,3,4 Current State: 82:[98, 41], Operations: ['83-36=47', '88-47=41'] Exploring Operation: 98+41=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 98-41=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 98*41=4018, Resulting Numbers: [4018] 4018,82 unequal: No Solution Moving to Node #0,4,4 Current State: 82:[88, 51], Operations: ['98-83=15', '36+15=51'] Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,82 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[62, 5], Operations: ['98-36=62', '88-83=5'] Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,82 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,82 unequal: No Solution Moving to Node #0,4,3 Current State: 82:[15, 52], Operations: ['98-83=15', '88-36=52'] Exploring Operation: 15+52=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 15*52=780, Resulting Numbers: [780] 780,82 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,82 unequal: No Solution Moving to Node #0,4,2 Current State: 82:[88, 21], Operations: ['98-83=15', '36-15=21'] Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 88+21=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 88*21=1848, Resulting Numbers: [1848] 1848,82 unequal: No Solution Moving to Node #0,1,4 Current State: 82:[88, 21], Operations: ['98-36=62', '83-62=21'] Exploring Operation: 88*21=1848, Resulting Numbers: [1848] 1848,82 unequal: No Solution Exploring Operation: 88+21=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,82 unequal: No Solution Moving to Node #0,4,1 Current State: 82:[36, 103], Operations: ['98-83=15', '88+15=103'] Exploring Operation: 36+103=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 103-36=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 36*103=3708, Resulting Numbers: [3708] 3708,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[98, 135], Operations: ['83-36=47', '88+47=135'] Exploring Operation: 98+135=233, Resulting Numbers: [233] 233,82 unequal: No Solution Exploring Operation: 135-98=37, Resulting Numbers: [37] 37,82 unequal: No Solution Exploring Operation: 98*135=13230, Resulting Numbers: [13230] 13230,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[88, 145], Operations: ['98-36=62', '83+62=145'] Exploring Operation: 88+145=233, Resulting Numbers: [233] 233,82 unequal: No Solution Exploring Operation: 145-88=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 88*145=12760, Resulting Numbers: [12760] 12760,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[83, 150], Operations: ['98-36=62', '88+62=150'] Exploring Operation: 83+150=233, Resulting Numbers: [233] 233,82 unequal: No Solution Exploring Operation: 150-83=67, Resulting Numbers: [67] 67,82 unequal: No Solution Exploring Operation: 83*150=12450, Resulting Numbers: [12450] 12450,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[88, 145], Operations: ['83-36=47', '98+47=145'] Exploring Operation: 88+145=233, Resulting Numbers: [233] 233,82 unequal: No Solution Exploring Operation: 145-88=57, Resulting Numbers: [57] 57,82 unequal: No Solution Exploring Operation: 88*145=12760, Resulting Numbers: [12760] 12760,82 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 82, 62, 51, 12 ]
59
[ "82-62=20", "51-12=39", "20+39=59" ]
Current State: 59:[82, 62, 51, 12], Operations: [] Exploring Operation: 82-62=20, Resulting Numbers: [51, 12, 20] Generated Node #2: [51, 12, 20] from Operation: 82-62=20 Current State: 59:[51, 12, 20], Operations: ['82-62=20'] Exploring Operation: 51-12=39, Resulting Numbers: [20, 39] Generated Node #3: [20, 39] from Operation: 51-12=39 Current State: 59:[20, 39], Operations: ['82-62=20', '51-12=39'] Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[82, 62, 51, 12], Operations: [] Exploring Operation: 82-12=70, Resulting Numbers: [62, 51, 70] Generated Node #0,0: 59:[62, 51, 70] Operation: 82-12=70 Exploring Operation: 62-12=50, Resulting Numbers: [82, 51, 50] Generated Node #0,1: 59:[82, 51, 50] Operation: 62-12=50 Exploring Operation: 51+12=63, Resulting Numbers: [82, 62, 63] Generated Node #0,2: 59:[82, 62, 63] Operation: 51+12=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[62, 51, 70], Operations: ['82-12=70'] Exploring Operation: 70-51=19, Resulting Numbers: [62, 19] Generated Node #0,0,0: 59:[62, 19] Operation: 70-51=19 Exploring Operation: 70-62=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 59:[51, 8] Operation: 70-62=8 Exploring Operation: 62-51=11, Resulting Numbers: [70, 11] Generated Node #0,0,2: 59:[70, 11] Operation: 62-51=11 Moving to Node #0,0,0 Current State: 59:[62, 19], Operations: ['82-12=70', '70-51=19'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 62*19=1178, Resulting Numbers: [1178] 1178,59 unequal: No Solution Exploring Operation: 62+19=81, Resulting Numbers: [81] 81,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[51, 8], Operations: ['82-12=70', '70-62=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[82, 62, 51, 12], Operations: [] Exploring Operation: 82-12=70, Resulting Numbers: [62, 51, 70] Generated Node #0,0: 59:[62, 51, 70] Operation: 82-12=70 Moving to Node #0,0 Current State: 59:[62, 51, 70], Operations: ['82-12=70'] Exploring Operation: 70-62=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 59:[51, 8] Operation: 70-62=8 Moving to Node #0,0,1 Current State: 59:[51, 8], Operations: ['82-12=70', '70-62=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 36, 40, 12, 27 ]
64
[ "36/12=3", "40+27=67", "67-3=64" ]
Current State: 64:[36, 40, 12, 27], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [40, 27, 3] Generated Node #2: [40, 27, 3] from Operation: 36/12=3 Current State: 64:[40, 27, 3], Operations: ['36/12=3'] Exploring Operation: 40+27=67, Resulting Numbers: [3, 67] Generated Node #3: [3, 67] from Operation: 40+27=67 Current State: 64:[3, 67], Operations: ['36/12=3', '40+27=67'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[36, 40, 12, 27], Operations: [] Exploring Operation: 40+27=67, Resulting Numbers: [36, 12, 67] Generated Node #0,0: 64:[36, 12, 67] Operation: 40+27=67 Exploring Operation: 40-36=4, Resulting Numbers: [12, 27, 4] Generated Node #0,1: 64:[12, 27, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[12, 27, 4], Operations: ['40-36=4'] Exploring Operation: 27-12=15, Resulting Numbers: [4, 15] Generated Node #0,1,0: 64:[4, 15] Operation: 27-12=15 Exploring Operation: 12+4=16, Resulting Numbers: [27, 16] Generated Node #0,1,1: 64:[27, 16] Operation: 12+4=16 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[4, 15], Operations: ['40-36=4', '27-12=15'] Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,64 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,64 unequal: No Solution No 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: 64:[27, 16], Operations: ['40-36=4', '12+4=16'] Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,64 unequal: No Solution Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,64 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: 64:[36, 12, 67], Operations: ['40+27=67'] Exploring Operation: 36/12=3, Resulting Numbers: [67, 3] Generated Node #0,0,0: 64:[67, 3] Operation: 36/12=3 Exploring Operation: 67-36=31, Resulting Numbers: [12, 31] Generated Node #0,0,1: 64:[12, 31] Operation: 67-36=31 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[67, 3], Operations: ['40+27=67', '36/12=3'] Exploring Operation: 67+3=70, Resulting Numbers: [70] 70,64 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[36, 40, 12, 27], Operations: [] Exploring Operation: 40+27=67, Resulting Numbers: [36, 12, 67] Generated Node #0,0: 64:[36, 12, 67] Operation: 40+27=67 Moving to Node #0,0 Current State: 64:[36, 12, 67], Operations: ['40+27=67'] Exploring Operation: 36/12=3, Resulting Numbers: [67, 3] Generated Node #0,0,0: 64:[67, 3] Operation: 36/12=3 Moving to Node #0,0,0 Current State: 64:[67, 3], Operations: ['40+27=67', '36/12=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 44, 21, 48, 56 ]
57
[ "44+21=65", "56-48=8", "65-8=57" ]
Current State: 57:[44, 21, 48, 56], Operations: [] Exploring Operation: 44+21=65, Resulting Numbers: [48, 56, 65] Generated Node #2: [48, 56, 65] from Operation: 44+21=65 Current State: 57:[48, 56, 65], Operations: ['44+21=65'] Exploring Operation: 56-48=8, Resulting Numbers: [65, 8] Generated Node #3: [65, 8] from Operation: 56-48=8 Current State: 57:[65, 8], Operations: ['44+21=65', '56-48=8'] Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[44, 21, 48, 56], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [21, 56, 4] Generated Node #0,0: 57:[21, 56, 4] Operation: 48-44=4 Exploring Operation: 44-21=23, Resulting Numbers: [48, 56, 23] Generated Node #0,1: 57:[48, 56, 23] Operation: 44-21=23 Moving to Node #0,0 Current State: 57:[21, 56, 4], Operations: ['48-44=4'] Exploring Operation: 21-4=17, Resulting Numbers: [56, 17] Generated Node #0,0,0: 57:[56, 17] Operation: 21-4=17 Exploring Operation: 56+4=60, Resulting Numbers: [21, 60] Generated Node #0,0,1: 57:[21, 60] Operation: 56+4=60 Moving to Node #0,1 Current State: 57:[48, 56, 23], Operations: ['44-21=23'] Exploring Operation: 48-23=25, Resulting Numbers: [56, 25] Generated Node #0,1,0: 57:[56, 25] Operation: 48-23=25 Exploring Operation: 56-48=8, Resulting Numbers: [23, 8] Generated Node #0,1,1: 57:[23, 8] Operation: 56-48=8 Moving to Node #0,0,0 Current State: 57:[56, 17], Operations: ['48-44=4', '21-4=17'] Exploring Operation: 56+17=73, Resulting Numbers: [73] 73,57 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[21, 60], Operations: ['48-44=4', '56+4=60'] Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[56, 25], Operations: ['44-21=23', '48-23=25'] Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[23, 8], Operations: ['44-21=23', '56-48=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,57 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 14, 90, 18, 27 ]
56
[ "90+18=108", "14*108=1512", "1512/27=56" ]
Current State: 56:[14, 90, 18, 27], Operations: [] Exploring Operation: 90+18=108, Resulting Numbers: [14, 27, 108] Generated Node #2: [14, 27, 108] from Operation: 90+18=108 Current State: 56:[14, 27, 108], Operations: ['90+18=108'] Exploring Operation: 14*108=1512, Resulting Numbers: [27, 1512] Generated Node #3: [27, 1512] from Operation: 14*108=1512 Current State: 56:[27, 1512], Operations: ['90+18=108', '14*108=1512'] Exploring Operation: 1512/27=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[14, 90, 18, 27], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [14, 27, 5] Generated Node #0,0: 56:[14, 27, 5] Operation: 90/18=5 Exploring Operation: 90-27=63, Resulting Numbers: [14, 18, 63] Generated Node #0,1: 56:[14, 18, 63] Operation: 90-27=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[14, 27, 5], Operations: ['90/18=5'] Exploring Operation: 27-14=13, Resulting Numbers: [5, 13] Generated Node #0,0,0: 56:[5, 13] Operation: 27-14=13 Exploring Operation: 14-5=9, Resulting Numbers: [27, 9] Generated Node #0,0,1: 56:[27, 9] Operation: 14-5=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[5, 13], Operations: ['90/18=5', '27-14=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,56 unequal: No Solution No 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: 56:[27, 9], Operations: ['90/18=5', '14-5=9'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,56 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: 56:[14, 18, 63], Operations: ['90-27=63'] Exploring Operation: 14+18=32, Resulting Numbers: [63, 32] Generated Node #0,1,0: 56:[63, 32] Operation: 14+18=32 Exploring Operation: 18-14=4, Resulting Numbers: [63, 4] Generated Node #0,1,1: 56:[63, 4] Operation: 18-14=4 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 56:[63, 4], Operations: ['90-27=63', '18-14=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,56 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,56 unequal: No Solution No 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: 56:[63, 32], Operations: ['90-27=63', '14+18=32'] Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,56 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 50, 62, 15, 64 ]
85
[ "64-62=2", "50*2=100", "100-15=85" ]
Current State: 85:[50, 62, 15, 64], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [50, 15, 2] Generated Node #2: [50, 15, 2] from Operation: 64-62=2 Current State: 85:[50, 15, 2], Operations: ['64-62=2'] Exploring Operation: 50*2=100, Resulting Numbers: [15, 100] Generated Node #3: [15, 100] from Operation: 50*2=100 Current State: 85:[15, 100], Operations: ['64-62=2', '50*2=100'] Exploring Operation: 100-15=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[50, 62, 15, 64], Operations: [] Exploring Operation: 64-50=14, Resulting Numbers: [62, 15, 14] Generated Node #0,0: 85:[62, 15, 14] Operation: 64-50=14 Exploring Operation: 62-50=12, Resulting Numbers: [15, 64, 12] Generated Node #0,1: 85:[15, 64, 12] Operation: 62-50=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[62, 15, 14], Operations: ['64-50=14'] Exploring Operation: 62+14=76, Resulting Numbers: [15, 76] Generated Node #0,0,0: 85:[15, 76] Operation: 62+14=76 Exploring Operation: 62+15=77, Resulting Numbers: [14, 77] Generated Node #0,0,1: 85:[14, 77] Operation: 62+15=77 Moving to Node #0,0,0 Current State: 85:[15, 76], Operations: ['64-50=14', '62+14=76'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 15+76=91, Resulting Numbers: [91] 91,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[14, 77], Operations: ['64-50=14', '62+15=77'] Exploring Operation: 14+77=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[15, 64, 12], Operations: ['62-50=12'] Exploring Operation: 64+12=76, Resulting Numbers: [15, 76] Generated Node #0,1,0: 85:[15, 76] Operation: 64+12=76 Exploring Operation: 15+64=79, Resulting Numbers: [12, 79] Generated Node #0,1,1: 85:[12, 79] Operation: 15+64=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[15, 76], Operations: ['62-50=12', '64+12=76'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 15+76=91, Resulting Numbers: [91] 91,85 unequal: No Solution No 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: 85:[12, 79], Operations: ['62-50=12', '15+64=79'] Exploring Operation: 12+79=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 34, 31, 5, 16 ]
41
[ "34+16=50", "50/5=10", "31+10=41" ]
Current State: 41:[34, 31, 5, 16], Operations: [] Exploring Operation: 34+16=50, Resulting Numbers: [31, 5, 50] Generated Node #2: [31, 5, 50] from Operation: 34+16=50 Current State: 41:[31, 5, 50], Operations: ['34+16=50'] Exploring Operation: 50/5=10, Resulting Numbers: [31, 10] Generated Node #3: [31, 10] from Operation: 50/5=10 Current State: 41:[31, 10], Operations: ['34+16=50', '50/5=10'] Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[34, 31, 5, 16], Operations: [] Exploring Operation: 34+5=39, Resulting Numbers: [31, 16, 39] Generated Node #0,0: 41:[31, 16, 39] Operation: 34+5=39 Exploring Operation: 31+5=36, Resulting Numbers: [34, 16, 36] Generated Node #0,1: 41:[34, 16, 36] Operation: 31+5=36 Exploring Operation: 5+16=21, Resulting Numbers: [34, 31, 21] Generated Node #0,2: 41:[34, 31, 21] Operation: 5+16=21 Moving to Node #0,0 Current State: 41:[31, 16, 39], Operations: ['34+5=39'] Exploring Operation: 31-16=15, Resulting Numbers: [39, 15] Generated Node #0,0,0: 41:[39, 15] Operation: 31-16=15 Exploring Operation: 16+39=55, Resulting Numbers: [31, 55] Generated Node #0,0,1: 41:[31, 55] Operation: 16+39=55 Exploring Operation: 31+16=47, Resulting Numbers: [39, 47] Generated Node #0,0,2: 41:[39, 47] Operation: 31+16=47 Moving to Node #0,1 Current State: 41:[34, 16, 36], Operations: ['31+5=36'] Exploring Operation: 34-16=18, Resulting Numbers: [36, 18] Generated Node #0,1,0: 41:[36, 18] Operation: 34-16=18 Exploring Operation: 34+16=50, Resulting Numbers: [36, 50] Generated Node #0,1,1: 41:[36, 50] Operation: 34+16=50 Exploring Operation: 16+36=52, Resulting Numbers: [34, 52] Generated Node #0,1,2: 41:[34, 52] Operation: 16+36=52 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[36, 50], Operations: ['31+5=36', '34+16=50'] Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,41 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,41 unequal: No Solution Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,41 unequal: No Solution No 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: 41:[34, 52], Operations: ['31+5=36', '16+36=52'] Exploring Operation: 34*52=1768, Resulting Numbers: [1768] 1768,41 unequal: No Solution Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,41 unequal: No Solution No 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: 41:[36, 18], Operations: ['31+5=36', '34-16=18'] Exploring Operation: 36/18=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 36+18=54, Resulting Numbers: [54] 54,41 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: 41:[34, 31, 21], Operations: ['5+16=21'] Exploring Operation: 31+21=52, Resulting Numbers: [34, 52] Generated Node #0,2,0: 41:[34, 52] Operation: 31+21=52 Exploring Operation: 34-21=13, Resulting Numbers: [31, 13] Generated Node #0,2,1: 41:[31, 13] Operation: 34-21=13 Exploring Operation: 34+21=55, Resulting Numbers: [31, 55] Generated Node #0,2,2: 41:[31, 55] Operation: 34+21=55 Moving to Node #0,0,2 Current State: 41:[39, 47], Operations: ['34+5=39', '31+16=47'] Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,41 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 39*47=1833, Resulting Numbers: [1833] 1833,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[34, 52], Operations: ['5+16=21', '31+21=52'] Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,41 unequal: No Solution Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 34*52=1768, Resulting Numbers: [1768] 1768,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[31, 55], Operations: ['5+16=21', '34+21=55'] Exploring Operation: 31+55=86, Resulting Numbers: [86] 86,41 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,41 unequal: No Solution Exploring Operation: 31*55=1705, Resulting Numbers: [1705] 1705,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[31, 55], Operations: ['34+5=39', '16+39=55'] Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,41 unequal: No Solution Exploring Operation: 31*55=1705, Resulting Numbers: [1705] 1705,41 unequal: No Solution Exploring Operation: 31+55=86, Resulting Numbers: [86] 86,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[39, 15], Operations: ['34+5=39', '31-16=15'] Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,41 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[31, 13], Operations: ['5+16=21', '34-21=13'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,41 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,41 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,41 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 76, 12, 75, 70 ]
81
[ "76-12=64", "75+70=145", "145-64=81" ]
Current State: 81:[76, 12, 75, 70], Operations: [] Exploring Operation: 76-12=64, Resulting Numbers: [75, 70, 64] Generated Node #2: [75, 70, 64] from Operation: 76-12=64 Current State: 81:[75, 70, 64], Operations: ['76-12=64'] Exploring Operation: 75+70=145, Resulting Numbers: [64, 145] Generated Node #3: [64, 145] from Operation: 75+70=145 Current State: 81:[64, 145], Operations: ['76-12=64', '75+70=145'] Exploring Operation: 145-64=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[76, 12, 75, 70], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [76, 12, 5] Generated Node #0,0: 81:[76, 12, 5] Operation: 75-70=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[76, 12, 5], Operations: ['75-70=5'] Exploring Operation: 76+5=81, Resulting Numbers: [12, 81] Generated Node #0,0,0: 81:[12, 81] Operation: 76+5=81 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[12, 81], Operations: ['75-70=5', '76+5=81'] Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,81 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, 71, 63, 32 ]
32
[ "71-7=64", "64-63=1", "32*1=32" ]
Current State: 32:[7, 71, 63, 32], Operations: [] Exploring Operation: 71-7=64, Resulting Numbers: [63, 32, 64] Generated Node #2: [63, 32, 64] from Operation: 71-7=64 Current State: 32:[63, 32, 64], Operations: ['71-7=64'] Exploring Operation: 64-63=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 64-63=1 Current State: 32:[32, 1], Operations: ['71-7=64', '64-63=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[7, 71, 63, 32], Operations: [] Exploring Operation: 71-63=8, Resulting Numbers: [7, 32, 8] Generated Node #0,0: 32:[7, 32, 8] Operation: 71-63=8 Exploring Operation: 63-32=31, Resulting Numbers: [7, 71, 31] Generated Node #0,1: 32:[7, 71, 31] Operation: 63-32=31 Exploring Operation: 63/7=9, Resulting Numbers: [71, 32, 9] Generated Node #0,2: 32:[71, 32, 9] Operation: 63/7=9 Exploring Operation: 71-32=39, Resulting Numbers: [7, 63, 39] Generated Node #0,3: 32:[7, 63, 39] Operation: 71-32=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[7, 32, 8], Operations: ['71-63=8'] Exploring Operation: 32/8=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 32:[7, 4] Operation: 32/8=4 Exploring Operation: 7+8=15, Resulting Numbers: [32, 15] Generated Node #0,0,1: 32:[32, 15] Operation: 7+8=15 Exploring Operation: 7+32=39, Resulting Numbers: [8, 39] Generated Node #0,0,2: 32:[8, 39] Operation: 7+32=39 Exploring Operation: 8-7=1, Resulting Numbers: [32, 1] Generated Node #0,0,3: 32:[32, 1] Operation: 8-7=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[7, 4], Operations: ['71-63=8', '32/8=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,32 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[32, 15], Operations: ['71-63=8', '7+8=15'] Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,32 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 32:[32, 1], Operations: ['71-63=8', '8-7=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[7, 71, 63, 32], Operations: [] Exploring Operation: 71-63=8, Resulting Numbers: [7, 32, 8] Generated Node #0,0: 32:[7, 32, 8] Operation: 71-63=8 Moving to Node #0,0 Current State: 32:[7, 32, 8], Operations: ['71-63=8'] Exploring Operation: 8-7=1, Resulting Numbers: [32, 1] Generated Node #0,0,3: 32:[32, 1] Operation: 8-7=1 Moving to Node #0,0,3 Current State: 32:[32, 1], Operations: ['71-63=8', '8-7=1'] Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 19, 81, 25, 79 ]
88
[ "19+25=44", "81-79=2", "44*2=88" ]
Current State: 88:[19, 81, 25, 79], Operations: [] Exploring Operation: 19+25=44, Resulting Numbers: [81, 79, 44] Generated Node #2: [81, 79, 44] from Operation: 19+25=44 Current State: 88:[81, 79, 44], Operations: ['19+25=44'] Exploring Operation: 81-79=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 81-79=2 Current State: 88:[44, 2], Operations: ['19+25=44', '81-79=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[19, 81, 25, 79], Operations: [] Exploring Operation: 19+25=44, Resulting Numbers: [81, 79, 44] Generated Node #0,0: 88:[81, 79, 44] Operation: 19+25=44 Exploring Operation: 81-79=2, Resulting Numbers: [19, 25, 2] Generated Node #0,1: 88:[19, 25, 2] Operation: 81-79=2 Exploring Operation: 79-25=54, Resulting Numbers: [19, 81, 54] Generated Node #0,2: 88:[19, 81, 54] Operation: 79-25=54 Exploring Operation: 19+79=98, Resulting Numbers: [81, 25, 98] Generated Node #0,3: 88:[81, 25, 98] Operation: 19+79=98 Exploring Operation: 25-19=6, Resulting Numbers: [81, 79, 6] Generated Node #0,4: 88:[81, 79, 6] Operation: 25-19=6 Moving to Node #0,1 Current State: 88:[19, 25, 2], Operations: ['81-79=2'] Exploring Operation: 25-19=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 88:[2, 6] Operation: 25-19=6 Exploring Operation: 25-2=23, Resulting Numbers: [19, 23] Generated Node #0,1,1: 88:[19, 23] Operation: 25-2=23 Exploring Operation: 19+2=21, Resulting Numbers: [25, 21] Generated Node #0,1,2: 88:[25, 21] Operation: 19+2=21 Exploring Operation: 19-2=17, Resulting Numbers: [25, 17] Generated Node #0,1,3: 88:[25, 17] Operation: 19-2=17 Exploring Operation: 19+25=44, Resulting Numbers: [2, 44] Generated Node #0,1,4: 88:[2, 44] Operation: 19+25=44 Moving to Node #0,0 Current State: 88:[81, 79, 44], Operations: ['19+25=44'] Exploring Operation: 81-79=2, Resulting Numbers: [44, 2] Generated Node #0,0,0: 88:[44, 2] Operation: 81-79=2 Exploring Operation: 79-44=35, Resulting Numbers: [81, 35] Generated Node #0,0,1: 88:[81, 35] Operation: 79-44=35 Exploring Operation: 79+44=123, Resulting Numbers: [81, 123] Generated Node #0,0,2: 88:[81, 123] Operation: 79+44=123 Exploring Operation: 81+44=125, Resulting Numbers: [79, 125] Generated Node #0,0,3: 88:[79, 125] Operation: 81+44=125 Exploring Operation: 81-44=37, Resulting Numbers: [79, 37] Generated Node #0,0,4: 88:[79, 37] Operation: 81-44=37 Moving to Node #0,4 Current State: 88:[81, 79, 6], Operations: ['25-19=6'] Exploring Operation: 79-6=73, Resulting Numbers: [81, 73] Generated Node #0,4,0: 88:[81, 73] Operation: 79-6=73 Exploring Operation: 81-79=2, Resulting Numbers: [6, 2] Generated Node #0,4,1: 88:[6, 2] Operation: 81-79=2 Exploring Operation: 81+6=87, Resulting Numbers: [79, 87] Generated Node #0,4,2: 88:[79, 87] Operation: 81+6=87 Exploring Operation: 79+6=85, Resulting Numbers: [81, 85] Generated Node #0,4,3: 88:[81, 85] Operation: 79+6=85 Exploring Operation: 81-6=75, Resulting Numbers: [79, 75] Generated Node #0,4,4: 88:[79, 75] Operation: 81-6=75 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 88:[6, 2], Operations: ['25-19=6', '81-79=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,88 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 #0,4,2 Current State: 88:[79, 87], Operations: ['25-19=6', '81+6=87'] Exploring Operation: 87-79=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 79*87=6873, Resulting Numbers: [6873] 6873,88 unequal: No Solution Exploring Operation: 79+87=166, Resulting Numbers: [166] 166,88 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 #0,4,3 Current State: 88:[81, 85], Operations: ['25-19=6', '79+6=85'] Exploring Operation: 81+85=166, Resulting Numbers: [166] 166,88 unequal: No Solution Exploring Operation: 81*85=6885, Resulting Numbers: [6885] 6885,88 unequal: No Solution Exploring Operation: 85-81=4, Resulting Numbers: [4] 4,88 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 #0,4,0 Current State: 88:[81, 73], Operations: ['25-19=6', '79-6=73'] Exploring Operation: 81+73=154, Resulting Numbers: [154] 154,88 unequal: No Solution Exploring Operation: 81*73=5913, Resulting Numbers: [5913] 5913,88 unequal: No Solution Exploring Operation: 81-73=8, Resulting Numbers: [8] 8,88 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 #0,4,4 Current State: 88:[79, 75], Operations: ['25-19=6', '81-6=75'] Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,88 unequal: No Solution Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,88 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: 88:[19, 81, 54], Operations: ['79-25=54'] Exploring Operation: 19+81=100, Resulting Numbers: [54, 100] Generated Node #0,2,0: 88:[54, 100] Operation: 19+81=100 Exploring Operation: 81-54=27, Resulting Numbers: [19, 27] Generated Node #0,2,1: 88:[19, 27] Operation: 81-54=27 Exploring Operation: 19+54=73, Resulting Numbers: [81, 73] Generated Node #0,2,2: 88:[81, 73] Operation: 19+54=73 Exploring Operation: 81-19=62, Resulting Numbers: [54, 62] Generated Node #0,2,3: 88:[54, 62] Operation: 81-19=62 Exploring Operation: 54-19=35, Resulting Numbers: [81, 35] Generated Node #0,2,4: 88:[81, 35] Operation: 54-19=35 Moving to Node #0,3 Current State: 88:[81, 25, 98], Operations: ['19+79=98'] Exploring Operation: 25+98=123, Resulting Numbers: [81, 123] Generated Node #0,3,0: 88:[81, 123] Operation: 25+98=123 Exploring Operation: 98-25=73, Resulting Numbers: [81, 73] Generated Node #0,3,1: 88:[81, 73] Operation: 98-25=73 Exploring Operation: 81-25=56, Resulting Numbers: [98, 56] Generated Node #0,3,2: 88:[98, 56] Operation: 81-25=56 Exploring Operation: 81+25=106, Resulting Numbers: [98, 106] Generated Node #0,3,3: 88:[98, 106] Operation: 81+25=106 Exploring Operation: 98-81=17, Resulting Numbers: [25, 17] Generated Node #0,3,4: 88:[25, 17] Operation: 98-81=17 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 88:[25, 17], Operations: ['19+79=98', '98-81=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,88 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,88 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 #0,3,1 Current State: 88:[81, 73], Operations: ['19+79=98', '98-25=73'] Exploring Operation: 81*73=5913, Resulting Numbers: [5913] 5913,88 unequal: No Solution Exploring Operation: 81-73=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 81+73=154, Resulting Numbers: [154] 154,88 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 #0,3,2 Current State: 88:[98, 56], Operations: ['19+79=98', '81-25=56'] Exploring Operation: 98*56=5488, Resulting Numbers: [5488] 5488,88 unequal: No Solution Exploring Operation: 98+56=154, Resulting Numbers: [154] 154,88 unequal: No Solution Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,88 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 #0,3,3 Current State: 88:[98, 106], Operations: ['19+79=98', '81+25=106'] Exploring Operation: 98*106=10388, Resulting Numbers: [10388] 10388,88 unequal: No Solution Exploring Operation: 98+106=204, Resulting Numbers: [204] 204,88 unequal: No Solution Exploring Operation: 106-98=8, Resulting Numbers: [8] 8,88 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 #0,3,0 Current State: 88:[81, 123], Operations: ['19+79=98', '25+98=123'] Exploring Operation: 123-81=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 81*123=9963, Resulting Numbers: [9963] 9963,88 unequal: No Solution Exploring Operation: 81+123=204, Resulting Numbers: [204] 204,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 88:[2, 44], Operations: ['81-79=2', '19+25=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[19, 81, 25, 79], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [19, 25, 2] Generated Node #0,1: 88:[19, 25, 2] Operation: 81-79=2 Moving to Node #0,1 Current State: 88:[19, 25, 2], Operations: ['81-79=2'] Exploring Operation: 19+25=44, Resulting Numbers: [2, 44] Generated Node #0,1,4: 88:[2, 44] Operation: 19+25=44 Moving to Node #0,1,4 Current State: 88:[2, 44], Operations: ['81-79=2', '19+25=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.942708
hs_5
sum_heuristic
[ 64, 19, 32, 26 ]
77
[ "64+19=83", "32-26=6", "83-6=77" ]
Current State: 77:[64, 19, 32, 26], Operations: [] Exploring Operation: 64+19=83, Resulting Numbers: [32, 26, 83] Generated Node #2: [32, 26, 83] from Operation: 64+19=83 Current State: 77:[32, 26, 83], Operations: ['64+19=83'] Exploring Operation: 32-26=6, Resulting Numbers: [83, 6] Generated Node #3: [83, 6] from Operation: 32-26=6 Current State: 77:[83, 6], Operations: ['64+19=83', '32-26=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[64, 19, 32, 26], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [64, 26, 13] Generated Node #0,0: 77:[64, 26, 13] Operation: 32-19=13 Exploring Operation: 64/32=2, Resulting Numbers: [19, 26, 2] Generated Node #0,1: 77:[19, 26, 2] Operation: 64/32=2 Exploring Operation: 32-26=6, Resulting Numbers: [64, 19, 6] Generated Node #0,2: 77:[64, 19, 6] Operation: 32-26=6 Moving to Node #0,2 Current State: 77:[64, 19, 6], Operations: ['32-26=6'] Exploring Operation: 19-6=13, Resulting Numbers: [64, 13] Generated Node #0,2,0: 77:[64, 13] Operation: 19-6=13 Exploring Operation: 64+19=83, Resulting Numbers: [6, 83] Generated Node #0,2,1: 77:[6, 83] Operation: 64+19=83 Exploring Operation: 64+6=70, Resulting Numbers: [19, 70] Generated Node #0,2,2: 77:[19, 70] Operation: 64+6=70 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 77:[6, 83], Operations: ['32-26=6', '64+19=83'] Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,77 unequal: No Solution Exploring Operation: 6*83=498, Resulting Numbers: [498] 498,77 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[64, 19, 32, 26], Operations: [] Exploring Operation: 32-26=6, Resulting Numbers: [64, 19, 6] Generated Node #0,2: 77:[64, 19, 6] Operation: 32-26=6 Moving to Node #0,2 Current State: 77:[64, 19, 6], Operations: ['32-26=6'] Exploring Operation: 64+19=83, Resulting Numbers: [6, 83] Generated Node #0,2,1: 77:[6, 83] Operation: 64+19=83 Moving to Node #0,2,1 Current State: 77:[6, 83], Operations: ['32-26=6', '64+19=83'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 72, 54, 59, 24 ]
77
[ "72/24=3", "54/3=18", "59+18=77" ]
Current State: 77:[72, 54, 59, 24], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [54, 59, 3] Generated Node #2: [54, 59, 3] from Operation: 72/24=3 Current State: 77:[54, 59, 3], Operations: ['72/24=3'] Exploring Operation: 54/3=18, Resulting Numbers: [59, 18] Generated Node #3: [59, 18] from Operation: 54/3=18 Current State: 77:[59, 18], Operations: ['72/24=3', '54/3=18'] Exploring Operation: 59+18=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[72, 54, 59, 24], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [72, 24, 5] Generated Node #0,0: 77:[72, 24, 5] Operation: 59-54=5 Exploring Operation: 54+24=78, Resulting Numbers: [72, 59, 78] Generated Node #0,1: 77:[72, 59, 78] Operation: 54+24=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[72, 24, 5], Operations: ['59-54=5'] Exploring Operation: 72/24=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 77:[5, 3] Operation: 72/24=3 Exploring Operation: 72+5=77, Resulting Numbers: [24, 77] Generated Node #0,0,1: 77:[24, 77] Operation: 72+5=77 Moving to Node #0,0,0 Current State: 77:[5, 3], Operations: ['59-54=5', '72/24=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[24, 77], Operations: ['59-54=5', '72+5=77'] Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,77 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[72, 59, 78], Operations: ['54+24=78'] Exploring Operation: 78-59=19, Resulting Numbers: [72, 19] Generated Node #0,1,0: 77:[72, 19] Operation: 78-59=19 Exploring Operation: 72-59=13, Resulting Numbers: [78, 13] Generated Node #0,1,1: 77:[78, 13] Operation: 72-59=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[78, 13], Operations: ['54+24=78', '72-59=13'] Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,77 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[72, 19], Operations: ['54+24=78', '78-59=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,77 unequal: No Solution Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 22, 4, 25, 55 ]
14
[ "22*25=550", "550/55=10", "4+10=14" ]
Current State: 14:[22, 4, 25, 55], Operations: [] Exploring Operation: 22*25=550, Resulting Numbers: [4, 55, 550] Generated Node #2: [4, 55, 550] from Operation: 22*25=550 Current State: 14:[4, 55, 550], Operations: ['22*25=550'] Exploring Operation: 550/55=10, Resulting Numbers: [4, 10] Generated Node #3: [4, 10] from Operation: 550/55=10 Current State: 14:[4, 10], Operations: ['22*25=550', '550/55=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[22, 4, 25, 55], Operations: [] Exploring Operation: 55-25=30, Resulting Numbers: [22, 4, 30] Generated Node #0,0: 14:[22, 4, 30] Operation: 55-25=30 Exploring Operation: 55-22=33, Resulting Numbers: [4, 25, 33] Generated Node #0,1: 14:[4, 25, 33] Operation: 55-22=33 Moving to Node #0,0 Current State: 14:[22, 4, 30], Operations: ['55-25=30'] Exploring Operation: 22-4=18, Resulting Numbers: [30, 18] Generated Node #0,0,0: 14:[30, 18] Operation: 22-4=18 Exploring Operation: 30-22=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 14:[4, 8] Operation: 30-22=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[4, 8], Operations: ['55-25=30', '30-22=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,14 unequal: No Solution No 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: 14:[30, 18], Operations: ['55-25=30', '22-4=18'] Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,14 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,14 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: 14:[4, 25, 33], Operations: ['55-22=33'] Exploring Operation: 33-25=8, Resulting Numbers: [4, 8] Generated Node #0,1,0: 14:[4, 8] Operation: 33-25=8 Exploring Operation: 25-4=21, Resulting Numbers: [33, 21] Generated Node #0,1,1: 14:[33, 21] Operation: 25-4=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[4, 8], Operations: ['55-22=33', '33-25=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,14 unequal: No Solution No 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: 14:[33, 21], Operations: ['55-22=33', '25-4=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,14 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
[ 18, 2, 24, 35 ]
25
[ "18*2=36", "35-24=11", "36-11=25" ]
Current State: 25:[18, 2, 24, 35], Operations: [] Exploring Operation: 18*2=36, Resulting Numbers: [24, 35, 36] Generated Node #2: [24, 35, 36] from Operation: 18*2=36 Current State: 25:[24, 35, 36], Operations: ['18*2=36'] Exploring Operation: 35-24=11, Resulting Numbers: [36, 11] Generated Node #3: [36, 11] from Operation: 35-24=11 Current State: 25:[36, 11], Operations: ['18*2=36', '35-24=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[18, 2, 24, 35], Operations: [] Exploring Operation: 35-18=17, Resulting Numbers: [2, 24, 17] Generated Node #0,0: 25:[2, 24, 17] Operation: 35-18=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[2, 24, 17], Operations: ['35-18=17'] Exploring Operation: 24-17=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 25:[2, 7] Operation: 24-17=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[2, 7], Operations: ['35-18=17', '24-17=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,25 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_1
sum_heuristic
[ 5, 82, 18, 56 ]
49
[ "5+82=87", "56-18=38", "87-38=49" ]
Current State: 49:[5, 82, 18, 56], Operations: [] Exploring Operation: 5+82=87, Resulting Numbers: [18, 56, 87] Generated Node #2: [18, 56, 87] from Operation: 5+82=87 Current State: 49:[18, 56, 87], Operations: ['5+82=87'] Exploring Operation: 56-18=38, Resulting Numbers: [87, 38] Generated Node #3: [87, 38] from Operation: 56-18=38 Current State: 49:[87, 38], Operations: ['5+82=87', '56-18=38'] Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[5, 82, 18, 56], Operations: [] Exploring Operation: 82-18=64, Resulting Numbers: [5, 56, 64] Generated Node #0,0: 49:[5, 56, 64] Operation: 82-18=64 Exploring Operation: 82-5=77, Resulting Numbers: [18, 56, 77] Generated Node #0,1: 49:[18, 56, 77] Operation: 82-5=77 Exploring Operation: 82-56=26, Resulting Numbers: [5, 18, 26] Generated Node #0,2: 49:[5, 18, 26] Operation: 82-56=26 Moving to Node #0,0 Current State: 49:[5, 56, 64], Operations: ['82-18=64'] Exploring Operation: 56-5=51, Resulting Numbers: [64, 51] Generated Node #0,0,0: 49:[64, 51] Operation: 56-5=51 Exploring Operation: 64-56=8, Resulting Numbers: [5, 8] Generated Node #0,0,1: 49:[5, 8] Operation: 64-56=8 Exploring Operation: 64-5=59, Resulting Numbers: [56, 59] Generated Node #0,0,2: 49:[56, 59] Operation: 64-5=59 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[5, 8], Operations: ['82-18=64', '64-56=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,49 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 #0,0,0 Current State: 49:[64, 51], Operations: ['82-18=64', '56-5=51'] Exploring Operation: 64-51=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 64*51=3264, Resulting Numbers: [3264] 3264,49 unequal: No Solution Exploring Operation: 64+51=115, Resulting Numbers: [115] 115,49 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 #0,0,2 Current State: 49:[56, 59], Operations: ['82-18=64', '64-5=59'] Exploring Operation: 56+59=115, Resulting Numbers: [115] 115,49 unequal: No Solution Exploring Operation: 59-56=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 56*59=3304, Resulting Numbers: [3304] 3304,49 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: 49:[5, 18, 26], Operations: ['82-56=26'] Exploring Operation: 18-5=13, Resulting Numbers: [26, 13] Generated Node #0,2,0: 49:[26, 13] Operation: 18-5=13 Exploring Operation: 26-18=8, Resulting Numbers: [5, 8] Generated Node #0,2,1: 49:[5, 8] Operation: 26-18=8 Exploring Operation: 18+26=44, Resulting Numbers: [5, 44] Generated Node #0,2,2: 49:[5, 44] Operation: 18+26=44 Moving to Node #0,1 Current State: 49:[18, 56, 77], Operations: ['82-5=77'] Exploring Operation: 77-56=21, Resulting Numbers: [18, 21] Generated Node #0,1,0: 49:[18, 21] Operation: 77-56=21 Exploring Operation: 56-18=38, Resulting Numbers: [77, 38] Generated Node #0,1,1: 49:[77, 38] Operation: 56-18=38 Exploring Operation: 77-18=59, Resulting Numbers: [56, 59] Generated Node #0,1,2: 49:[56, 59] Operation: 77-18=59 Moving to Node #0,2,1 Current State: 49:[5, 8], Operations: ['82-56=26', '26-18=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,49 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,49 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[5, 44], Operations: ['82-56=26', '18+26=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[5, 82, 18, 56], Operations: [] Exploring Operation: 82-56=26, Resulting Numbers: [5, 18, 26] Generated Node #0,2: 49:[5, 18, 26] Operation: 82-56=26 Moving to Node #0,2 Current State: 49:[5, 18, 26], Operations: ['82-56=26'] Exploring Operation: 18+26=44, Resulting Numbers: [5, 44] Generated Node #0,2,2: 49:[5, 44] Operation: 18+26=44 Moving to Node #0,2,2 Current State: 49:[5, 44], Operations: ['82-56=26', '18+26=44'] Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.974826
hs_3
sum_heuristic
[ 96, 62, 28, 66 ]
31
[ "96+28=124", "66-62=4", "124/4=31" ]
Current State: 31:[96, 62, 28, 66], Operations: [] Exploring Operation: 96+28=124, Resulting Numbers: [62, 66, 124] Generated Node #2: [62, 66, 124] from Operation: 96+28=124 Current State: 31:[62, 66, 124], Operations: ['96+28=124'] Exploring Operation: 66-62=4, Resulting Numbers: [124, 4] Generated Node #3: [124, 4] from Operation: 66-62=4 Current State: 31:[124, 4], Operations: ['96+28=124', '66-62=4'] Exploring Operation: 124/4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[96, 62, 28, 66], Operations: [] Exploring Operation: 96-66=30, Resulting Numbers: [62, 28, 30] Generated Node #0,0: 31:[62, 28, 30] Operation: 96-66=30 Moving to Node #0,0 Current State: 31:[62, 28, 30], Operations: ['96-66=30'] Exploring Operation: 62-28=34, Resulting Numbers: [30, 34] Generated Node #0,0,0: 31:[30, 34] Operation: 62-28=34 Moving to Node #0,0,0 Current State: 31:[30, 34], Operations: ['96-66=30', '62-28=34'] Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,31 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 1, 57, 81, 58 ]
81
[ "1+57=58", "81+58=139", "139-58=81" ]
Current State: 81:[1, 57, 81, 58], Operations: [] Exploring Operation: 1+57=58, Resulting Numbers: [81, 58, 58] Generated Node #2: [81, 58, 58] from Operation: 1+57=58 Current State: 81:[81, 58, 58], Operations: ['1+57=58'] Exploring Operation: 81+58=139, Resulting Numbers: [139] 139,81 equal: Goal Reached Exploring Operation: 139-58=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[1, 57, 81, 58], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [1, 58, 24] Generated Node #0,0: 81:[1, 58, 24] Operation: 81-57=24 Exploring Operation: 58-57=1, Resulting Numbers: [1, 81, 1] Generated Node #0,1: 81:[1, 81, 1] Operation: 58-57=1 Exploring Operation: 81-58=23, Resulting Numbers: [1, 57, 23] Generated Node #0,2: 81:[1, 57, 23] Operation: 81-58=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[1, 81, 1], Operations: ['58-57=1'] Exploring Operation: 81/1=81, Resulting Numbers: [1, 81] Generated Node #0,1,0: 81:[1, 81] Operation: 81/1=81 Exploring Operation: 1*81=81, Resulting Numbers: [1, 81] Generated Node #0,1,1: 81:[1, 81] Operation: 1*81=81 Exploring Operation: 1+1=2, Resulting Numbers: [81, 2] Generated Node #0,1,2: 81:[81, 2] Operation: 1+1=2 Moving to Node #0,1,2 Current State: 81:[81, 2], Operations: ['58-57=1', '1+1=2'] Exploring Operation: 81*2=162, Resulting Numbers: [162] 162,81 unequal: No Solution Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[1, 81], Operations: ['58-57=1', '81/1=81'] Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[1, 57, 81, 58], Operations: [] Exploring Operation: 58-57=1, Resulting Numbers: [1, 81, 1] Generated Node #0,1: 81:[1, 81, 1] Operation: 58-57=1 Moving to Node #0,1 Current State: 81:[1, 81, 1], Operations: ['58-57=1'] Exploring Operation: 81/1=81, Resulting Numbers: [1, 81] Generated Node #0,1,0: 81:[1, 81] Operation: 81/1=81 Moving to Node #0,1,0 Current State: 81:[1, 81], Operations: ['58-57=1', '81/1=81'] Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 2, 90, 47, 38 ]
61
[ "2*38=76", "90+47=137", "137-76=61" ]
Current State: 61:[2, 90, 47, 38], Operations: [] Exploring Operation: 2*38=76, Resulting Numbers: [90, 47, 76] Generated Node #2: [90, 47, 76] from Operation: 2*38=76 Current State: 61:[90, 47, 76], Operations: ['2*38=76'] Exploring Operation: 90+47=137, Resulting Numbers: [76, 137] Generated Node #3: [76, 137] from Operation: 90+47=137 Current State: 61:[76, 137], Operations: ['2*38=76', '90+47=137'] Exploring Operation: 137-76=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[2, 90, 47, 38], Operations: [] Exploring Operation: 2+38=40, Resulting Numbers: [90, 47, 40] Generated Node #0,0: 61:[90, 47, 40] Operation: 2+38=40 Exploring Operation: 2*38=76, Resulting Numbers: [90, 47, 76] Generated Node #0,1: 61:[90, 47, 76] Operation: 2*38=76 Exploring Operation: 2+47=49, Resulting Numbers: [90, 38, 49] Generated Node #0,2: 61:[90, 38, 49] Operation: 2+47=49 Exploring Operation: 90-2=88, Resulting Numbers: [47, 38, 88] Generated Node #0,3: 61:[47, 38, 88] Operation: 90-2=88 Exploring Operation: 90/2=45, Resulting Numbers: [47, 38, 45] Generated Node #0,4: 61:[47, 38, 45] Operation: 90/2=45 Moving to Node #0,4 Current State: 61:[47, 38, 45], Operations: ['90/2=45'] Exploring Operation: 45-38=7, Resulting Numbers: [47, 7] Generated Node #0,4,0: 61:[47, 7] Operation: 45-38=7 Exploring Operation: 38+45=83, Resulting Numbers: [47, 83] Generated Node #0,4,1: 61:[47, 83] Operation: 38+45=83 Exploring Operation: 47-38=9, Resulting Numbers: [45, 9] Generated Node #0,4,2: 61:[45, 9] Operation: 47-38=9 Exploring Operation: 47+38=85, Resulting Numbers: [45, 85] Generated Node #0,4,3: 61:[45, 85] Operation: 47+38=85 Exploring Operation: 47+45=92, Resulting Numbers: [38, 92] Generated Node #0,4,4: 61:[38, 92] Operation: 47+45=92 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 61:[47, 83], Operations: ['90/2=45', '38+45=83'] Exploring Operation: 83-47=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 47*83=3901, Resulting Numbers: [3901] 3901,61 unequal: No Solution Exploring Operation: 47+83=130, Resulting Numbers: [130] 130,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 61:[45, 85], Operations: ['90/2=45', '47+38=85'] Exploring Operation: 45+85=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 45*85=3825, Resulting Numbers: [3825] 3825,61 unequal: No Solution Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 61:[38, 92], Operations: ['90/2=45', '47+45=92'] Exploring Operation: 38+92=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 38*92=3496, Resulting Numbers: [3496] 3496,61 unequal: No Solution Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 61:[47, 7], Operations: ['90/2=45', '45-38=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,61 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,61 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 61:[45, 9], Operations: ['90/2=45', '47-38=9'] Exploring Operation: 45*9=405, Resulting Numbers: [405] 405,61 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 45+9=54, Resulting Numbers: [54] 54,61 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,61 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: 61:[90, 47, 76], Operations: ['2*38=76'] Exploring Operation: 47+76=123, Resulting Numbers: [90, 123] Generated Node #0,1,0: 61:[90, 123] Operation: 47+76=123 Exploring Operation: 76-47=29, Resulting Numbers: [90, 29] Generated Node #0,1,1: 61:[90, 29] Operation: 76-47=29 Exploring Operation: 90+47=137, Resulting Numbers: [76, 137] Generated Node #0,1,2: 61:[76, 137] Operation: 90+47=137 Exploring Operation: 90-76=14, Resulting Numbers: [47, 14] Generated Node #0,1,3: 61:[47, 14] Operation: 90-76=14 Exploring Operation: 90-47=43, Resulting Numbers: [76, 43] Generated Node #0,1,4: 61:[76, 43] Operation: 90-47=43 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 61:[76, 43], Operations: ['2*38=76', '90-47=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,61 unequal: No Solution Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[90, 29], Operations: ['2*38=76', '76-47=29'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[2, 90, 47, 38], Operations: [] Exploring Operation: 2*38=76, Resulting Numbers: [90, 47, 76] Generated Node #0,1: 61:[90, 47, 76] Operation: 2*38=76 Moving to Node #0,1 Current State: 61:[90, 47, 76], Operations: ['2*38=76'] Exploring Operation: 76-47=29, Resulting Numbers: [90, 29] Generated Node #0,1,1: 61:[90, 29] Operation: 76-47=29 Moving to Node #0,1,1 Current State: 61:[90, 29], Operations: ['2*38=76', '76-47=29'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 80, 77, 7, 7 ]
14
[ "80-77=3", "7*3=21", "21-7=14" ]
Current State: 14:[80, 77, 7, 7], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [7, 7, 3] Generated Node #2: [7, 7, 3] from Operation: 80-77=3 Current State: 14:[7, 7, 3], Operations: ['80-77=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,14 equal: Goal Reached Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[80, 77, 7, 7], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [7, 7, 3] Generated Node #0,0: 14:[7, 7, 3] Operation: 80-77=3 Exploring Operation: 80-7=73, Resulting Numbers: [77, 7, 73] Generated Node #0,1: 14:[77, 7, 73] Operation: 80-7=73 Exploring Operation: 77/7=11, Resulting Numbers: [80, 7, 11] Generated Node #0,2: 14:[80, 7, 11] Operation: 77/7=11 Exploring Operation: 80-7=73, Resulting Numbers: [77, 7, 73] Generated Node #0,3: 14:[77, 7, 73] Operation: 80-7=73 Exploring Operation: 77/7=11, Resulting Numbers: [80, 7, 11] Generated Node #0,4: 14:[80, 7, 11] Operation: 77/7=11 Moving to Node #0,0 Current State: 14:[7, 7, 3], Operations: ['80-77=3'] Exploring Operation: 7-3=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 14:[7, 4] Operation: 7-3=4 Exploring Operation: 7+7=14, Resulting Numbers: [3, 14] Generated Node #0,0,1: 14:[3, 14] Operation: 7+7=14 Exploring Operation: 7-3=4, Resulting Numbers: [7, 4] Generated Node #0,0,2: 14:[7, 4] Operation: 7-3=4 Exploring Operation: 7-7=0, Resulting Numbers: [3, 0] Generated Node #0,0,3: 14:[3, 0] Operation: 7-7=0 Exploring Operation: 7/7=1, Resulting Numbers: [3, 1] Generated Node #0,0,4: 14:[3, 1] Operation: 7/7=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[3, 14], Operations: ['80-77=3', '7+7=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,14 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,14 unequal: No Solution No 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: 14:[7, 4], Operations: ['80-77=3', '7-3=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,14 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,14 unequal: No Solution No 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: 14:[7, 4], Operations: ['80-77=3', '7-3=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,14 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,14 unequal: No Solution No 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: 14:[3, 1], Operations: ['80-77=3', '7/7=1'] Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,14 unequal: No Solution No 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: 14:[3, 0], Operations: ['80-77=3', '7-7=0'] Exploring Operation: 3-0=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 3*0=0, Resulting Numbers: [0] 0,14 unequal: No Solution Exploring Operation: 3+0=3, Resulting Numbers: [3] 3,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 14:[80, 7, 11], Operations: ['77/7=11'] Exploring Operation: 80+7=87, Resulting Numbers: [11, 87] Generated Node #0,4,0: 14:[11, 87] Operation: 80+7=87 Exploring Operation: 80-7=73, Resulting Numbers: [11, 73] Generated Node #0,4,1: 14:[11, 73] Operation: 80-7=73 Exploring Operation: 80-11=69, Resulting Numbers: [7, 69] Generated Node #0,4,2: 14:[7, 69] Operation: 80-11=69 Exploring Operation: 7+11=18, Resulting Numbers: [80, 18] Generated Node #0,4,3: 14:[80, 18] Operation: 7+11=18 Exploring Operation: 11-7=4, Resulting Numbers: [80, 4] Generated Node #0,4,4: 14:[80, 4] Operation: 11-7=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 14:[7, 69], Operations: ['77/7=11', '80-11=69'] Exploring Operation: 7*69=483, Resulting Numbers: [483] 483,14 unequal: No Solution Exploring Operation: 7+69=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,14 unequal: No Solution No 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: 14:[11, 73], Operations: ['77/7=11', '80-7=73'] Exploring Operation: 11*73=803, Resulting Numbers: [803] 803,14 unequal: No Solution Exploring Operation: 11+73=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 14:[80, 4], Operations: ['77/7=11', '11-7=4'] Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,14 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,14 unequal: No Solution No 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: 14:[80, 18], Operations: ['77/7=11', '7+11=18'] Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,14 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,14 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,14 unequal: No Solution No 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: 14:[11, 87], Operations: ['77/7=11', '80+7=87'] Exploring Operation: 11*87=957, Resulting Numbers: [957] 957,14 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 11+87=98, Resulting Numbers: [98] 98,14 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: 14:[80, 7, 11], Operations: ['77/7=11'] Exploring Operation: 80-11=69, Resulting Numbers: [7, 69] Generated Node #0,2,0: 14:[7, 69] Operation: 80-11=69 Exploring Operation: 7+11=18, Resulting Numbers: [80, 18] Generated Node #0,2,1: 14:[80, 18] Operation: 7+11=18 Exploring Operation: 80+7=87, Resulting Numbers: [11, 87] Generated Node #0,2,2: 14:[11, 87] Operation: 80+7=87 Exploring Operation: 11-7=4, Resulting Numbers: [80, 4] Generated Node #0,2,3: 14:[80, 4] Operation: 11-7=4 Exploring Operation: 80-7=73, Resulting Numbers: [11, 73] Generated Node #0,2,4: 14:[11, 73] Operation: 80-7=73 Moving to Node #0,1 Current State: 14:[77, 7, 73], Operations: ['80-7=73'] Exploring Operation: 77-7=70, Resulting Numbers: [73, 70] Generated Node #0,1,0: 14:[73, 70] Operation: 77-7=70 Exploring Operation: 77-73=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 14:[7, 4] Operation: 77-73=4 Exploring Operation: 77/7=11, Resulting Numbers: [73, 11] Generated Node #0,1,2: 14:[73, 11] Operation: 77/7=11 Exploring Operation: 77+7=84, Resulting Numbers: [73, 84] Generated Node #0,1,3: 14:[73, 84] Operation: 77+7=84 Exploring Operation: 73-7=66, Resulting Numbers: [77, 66] Generated Node #0,1,4: 14:[77, 66] Operation: 73-7=66 Moving to Node #0,3 Current State: 14:[77, 7, 73], Operations: ['80-7=73'] Exploring Operation: 77-73=4, Resulting Numbers: [7, 4] Generated Node #0,3,0: 14:[7, 4] Operation: 77-73=4 Exploring Operation: 77+7=84, Resulting Numbers: [73, 84] Generated Node #0,3,1: 14:[73, 84] Operation: 77+7=84 Exploring Operation: 77/7=11, Resulting Numbers: [73, 11] Generated Node #0,3,2: 14:[73, 11] Operation: 77/7=11 Exploring Operation: 77-7=70, Resulting Numbers: [73, 70] Generated Node #0,3,3: 14:[73, 70] Operation: 77-7=70 Exploring Operation: 73-7=66, Resulting Numbers: [77, 66] Generated Node #0,3,4: 14:[77, 66] Operation: 73-7=66 Moving to Node #0,1,1 Current State: 14:[7, 4], Operations: ['80-7=73', '77-73=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,14 unequal: No Solution Moving to Node #0,3,0 Current State: 14:[7, 4], Operations: ['80-7=73', '77-73=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,14 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[7, 69], Operations: ['77/7=11', '80-11=69'] Exploring Operation: 7+69=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 7*69=483, Resulting Numbers: [483] 483,14 unequal: No Solution Exploring Operation: 69-7=62, Resulting Numbers: [62] 62,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[73, 11], Operations: ['80-7=73', '77/7=11'] Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,14 unequal: No Solution Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,14 unequal: No Solution Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,14 unequal: No Solution Moving to Node #0,3,2 Current State: 14:[73, 11], Operations: ['80-7=73', '77/7=11'] Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,14 unequal: No Solution Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,14 unequal: No Solution Moving to Node #0,2,4 Current State: 14:[11, 73], Operations: ['77/7=11', '80-7=73'] Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,14 unequal: No Solution Exploring Operation: 11+73=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 11*73=803, Resulting Numbers: [803] 803,14 unequal: No Solution Moving to Node #0,2,3 Current State: 14:[80, 4], Operations: ['77/7=11', '11-7=4'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,14 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[80, 18], Operations: ['77/7=11', '7+11=18'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,14 unequal: No Solution Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,14 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,14 unequal: No Solution Moving to Node #0,2,2 Current State: 14:[11, 87], Operations: ['77/7=11', '80+7=87'] Exploring Operation: 11*87=957, Resulting Numbers: [957] 957,14 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 11+87=98, Resulting Numbers: [98] 98,14 unequal: No Solution Moving to Node #0,3,4 Current State: 14:[77, 66], Operations: ['80-7=73', '73-7=66'] Exploring Operation: 77*66=5082, Resulting Numbers: [5082] 5082,14 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 77+66=143, Resulting Numbers: [143] 143,14 unequal: No Solution Moving to Node #0,3,3 Current State: 14:[73, 70], Operations: ['80-7=73', '77-7=70'] Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,14 unequal: No Solution Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,14 unequal: No Solution Moving to Node #0,1,4 Current State: 14:[77, 66], Operations: ['80-7=73', '73-7=66'] Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 77+66=143, Resulting Numbers: [143] 143,14 unequal: No Solution Exploring Operation: 77*66=5082, Resulting Numbers: [5082] 5082,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[73, 70], Operations: ['80-7=73', '77-7=70'] Exploring Operation: 73*70=5110, Resulting Numbers: [5110] 5110,14 unequal: No Solution Exploring Operation: 73-70=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 73+70=143, Resulting Numbers: [143] 143,14 unequal: No Solution Moving to Node #0,3,1 Current State: 14:[73, 84], Operations: ['80-7=73', '77+7=84'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 73*84=6132, Resulting Numbers: [6132] 6132,14 unequal: No Solution Exploring Operation: 73+84=157, Resulting Numbers: [157] 157,14 unequal: No Solution Moving to Node #0,1,3 Current State: 14:[73, 84], Operations: ['80-7=73', '77+7=84'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 73+84=157, Resulting Numbers: [157] 157,14 unequal: No Solution Exploring Operation: 73*84=6132, Resulting Numbers: [6132] 6132,14 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 35, 7, 11, 23 ]
48
[ "35-23=12", "11-7=4", "12*4=48" ]
Current State: 48:[35, 7, 11, 23], Operations: [] Exploring Operation: 35-23=12, Resulting Numbers: [7, 11, 12] Generated Node #2: [7, 11, 12] from Operation: 35-23=12 Current State: 48:[7, 11, 12], Operations: ['35-23=12'] Exploring Operation: 11-7=4, Resulting Numbers: [12, 4] Generated Node #3: [12, 4] from Operation: 11-7=4 Current State: 48:[12, 4], Operations: ['35-23=12', '11-7=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[35, 7, 11, 23], Operations: [] Exploring Operation: 35-23=12, Resulting Numbers: [7, 11, 12] Generated Node #0,0: 48:[7, 11, 12] Operation: 35-23=12 Exploring Operation: 35-11=24, Resulting Numbers: [7, 23, 24] Generated Node #0,1: 48:[7, 23, 24] Operation: 35-11=24 Moving to Node #0,0 Current State: 48:[7, 11, 12], Operations: ['35-23=12'] Exploring Operation: 11-7=4, Resulting Numbers: [12, 4] Generated Node #0,0,0: 48:[12, 4] Operation: 11-7=4 Exploring Operation: 7+11=18, Resulting Numbers: [12, 18] Generated Node #0,0,1: 48:[12, 18] Operation: 7+11=18 Moving to Node #0,1 Current State: 48:[7, 23, 24], Operations: ['35-11=24'] Exploring Operation: 23-7=16, Resulting Numbers: [24, 16] Generated Node #0,1,0: 48:[24, 16] Operation: 23-7=16 Exploring Operation: 24-7=17, Resulting Numbers: [23, 17] Generated Node #0,1,1: 48:[23, 17] Operation: 24-7=17 Moving to Node #0,0,0 Current State: 48:[12, 4], Operations: ['35-23=12', '11-7=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[35, 7, 11, 23], Operations: [] Exploring Operation: 35-23=12, Resulting Numbers: [7, 11, 12] Generated Node #0,0: 48:[7, 11, 12] Operation: 35-23=12 Moving to Node #0,0 Current State: 48:[7, 11, 12], Operations: ['35-23=12'] Exploring Operation: 11-7=4, Resulting Numbers: [12, 4] Generated Node #0,0,0: 48:[12, 4] Operation: 11-7=4 Moving to Node #0,0,0 Current State: 48:[12, 4], Operations: ['35-23=12', '11-7=4'] Exploring Operation: 12*4=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 13, 5, 72, 63 ]
52
[ "72-5=67", "67-63=4", "13*4=52" ]
Current State: 52:[13, 5, 72, 63], Operations: [] Exploring Operation: 72-5=67, Resulting Numbers: [13, 63, 67] Generated Node #2: [13, 63, 67] from Operation: 72-5=67 Current State: 52:[13, 63, 67], Operations: ['72-5=67'] Exploring Operation: 67-63=4, Resulting Numbers: [13, 4] Generated Node #3: [13, 4] from Operation: 67-63=4 Current State: 52:[13, 4], Operations: ['72-5=67', '67-63=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 5, 72, 63], Operations: [] Exploring Operation: 72-13=59, Resulting Numbers: [5, 63, 59] Generated Node #0,0: 52:[5, 63, 59] Operation: 72-13=59 Exploring Operation: 72-63=9, Resulting Numbers: [13, 5, 9] Generated Node #0,1: 52:[13, 5, 9] Operation: 72-63=9 Moving to Node #0,1 Current State: 52:[13, 5, 9], Operations: ['72-63=9'] Exploring Operation: 13-9=4, Resulting Numbers: [5, 4] Generated Node #0,1,0: 52:[5, 4] Operation: 13-9=4 Exploring Operation: 9-5=4, Resulting Numbers: [13, 4] Generated Node #0,1,1: 52:[13, 4] Operation: 9-5=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[13, 4], Operations: ['72-63=9', '9-5=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[13, 5, 72, 63], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [13, 5, 9] Generated Node #0,1: 52:[13, 5, 9] Operation: 72-63=9 Moving to Node #0,1 Current State: 52:[13, 5, 9], Operations: ['72-63=9'] Exploring Operation: 9-5=4, Resulting Numbers: [13, 4] Generated Node #0,1,1: 52:[13, 4] Operation: 9-5=4 Moving to Node #0,1,1 Current State: 52:[13, 4], Operations: ['72-63=9', '9-5=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 16, 36, 5, 7 ]
51
[ "16*5=80", "36-7=29", "80-29=51" ]
Current State: 51:[16, 36, 5, 7], Operations: [] Exploring Operation: 16*5=80, Resulting Numbers: [36, 7, 80] Generated Node #2: [36, 7, 80] from Operation: 16*5=80 Current State: 51:[36, 7, 80], Operations: ['16*5=80'] Exploring Operation: 36-7=29, Resulting Numbers: [80, 29] Generated Node #3: [80, 29] from Operation: 36-7=29 Current State: 51:[80, 29], Operations: ['16*5=80', '36-7=29'] Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[16, 36, 5, 7], Operations: [] Exploring Operation: 36-16=20, Resulting Numbers: [5, 7, 20] Generated Node #0,0: 51:[5, 7, 20] Operation: 36-16=20 Exploring Operation: 36+7=43, Resulting Numbers: [16, 5, 43] Generated Node #0,1: 51:[16, 5, 43] Operation: 36+7=43 Exploring Operation: 16+36=52, Resulting Numbers: [5, 7, 52] Generated Node #0,2: 51:[5, 7, 52] Operation: 16+36=52 Moving to Node #0,2 Current State: 51:[5, 7, 52], Operations: ['16+36=52'] Exploring Operation: 7-5=2, Resulting Numbers: [52, 2] Generated Node #0,2,0: 51:[52, 2] Operation: 7-5=2 Exploring Operation: 5+7=12, Resulting Numbers: [52, 12] Generated Node #0,2,1: 51:[52, 12] Operation: 5+7=12 Exploring Operation: 52-5=47, Resulting Numbers: [7, 47] Generated Node #0,2,2: 51:[7, 47] Operation: 52-5=47 Moving to Node #0,0 Current State: 51:[5, 7, 20], Operations: ['36-16=20'] Exploring Operation: 7-5=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 51:[20, 2] Operation: 7-5=2 Exploring Operation: 20/5=4, Resulting Numbers: [7, 4] Generated Node #0,0,1: 51:[7, 4] Operation: 20/5=4 Exploring Operation: 20-5=15, Resulting Numbers: [7, 15] Generated Node #0,0,2: 51:[7, 15] Operation: 20-5=15 Moving to Node #0,1 Current State: 51:[16, 5, 43], Operations: ['36+7=43'] Exploring Operation: 5+43=48, Resulting Numbers: [16, 48] Generated Node #0,1,0: 51:[16, 48] Operation: 5+43=48 Exploring Operation: 16+5=21, Resulting Numbers: [43, 21] Generated Node #0,1,1: 51:[43, 21] Operation: 16+5=21 Exploring Operation: 16+43=59, Resulting Numbers: [5, 59] Generated Node #0,1,2: 51:[5, 59] Operation: 16+43=59 Moving to Node #0,2,0 Current State: 51:[52, 2], Operations: ['16+36=52', '7-5=2'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,51 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,51 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,51 unequal: No Solution Moving to Node #0,1,0 Current State: 51:[16, 48], Operations: ['36+7=43', '5+43=48'] Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[20, 2], Operations: ['36-16=20', '7-5=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[7, 4], Operations: ['36-16=20', '20/5=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[7, 15], Operations: ['36-16=20', '20-5=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,51 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[52, 12], Operations: ['16+36=52', '5+7=12'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,51 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[7, 47], Operations: ['16+36=52', '52-5=47'] Exploring Operation: 7*47=329, Resulting Numbers: [329] 329,51 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,51 unequal: No Solution Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[5, 59], Operations: ['36+7=43', '16+43=59'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 5*59=295, Resulting Numbers: [295] 295,51 unequal: No Solution Exploring Operation: 5+59=64, Resulting Numbers: [64] 64,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[43, 21], Operations: ['36+7=43', '16+5=21'] Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,51 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,51 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 97, 72, 40, 18 ]
87
[ "72/18=4", "40/4=10", "97-10=87" ]
Current State: 87:[97, 72, 40, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [97, 40, 4] Generated Node #2: [97, 40, 4] from Operation: 72/18=4 Current State: 87:[97, 40, 4], Operations: ['72/18=4'] Exploring Operation: 40/4=10, Resulting Numbers: [97, 10] Generated Node #3: [97, 10] from Operation: 40/4=10 Current State: 87:[97, 10], Operations: ['72/18=4', '40/4=10'] Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[97, 72, 40, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [97, 40, 4] Generated Node #0,0: 87:[97, 40, 4] Operation: 72/18=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[97, 40, 4], Operations: ['72/18=4'] Exploring Operation: 97-4=93, Resulting Numbers: [40, 93] Generated Node #0,0,0: 87:[40, 93] Operation: 97-4=93 Moving to Node #0,0,0 Current State: 87:[40, 93], Operations: ['72/18=4', '97-4=93'] Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,87 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
[ 20, 23, 99, 5 ]
91
[ "23-20=3", "99-5=94", "94-3=91" ]
Current State: 91:[20, 23, 99, 5], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [99, 5, 3] Generated Node #2: [99, 5, 3] from Operation: 23-20=3 Current State: 91:[99, 5, 3], Operations: ['23-20=3'] Exploring Operation: 99-5=94, Resulting Numbers: [3, 94] Generated Node #3: [3, 94] from Operation: 99-5=94 Current State: 91:[3, 94], Operations: ['23-20=3', '99-5=94'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[20, 23, 99, 5], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [99, 5, 3] Generated Node #0,0: 91:[99, 5, 3] Operation: 23-20=3 Exploring Operation: 99-5=94, Resulting Numbers: [20, 23, 94] Generated Node #0,1: 91:[20, 23, 94] Operation: 99-5=94 Exploring Operation: 20/5=4, Resulting Numbers: [23, 99, 4] Generated Node #0,2: 91:[23, 99, 4] Operation: 20/5=4 Exploring Operation: 20-5=15, Resulting Numbers: [23, 99, 15] Generated Node #0,3: 91:[23, 99, 15] Operation: 20-5=15 Exploring Operation: 23-5=18, Resulting Numbers: [20, 99, 18] Generated Node #0,4: 91:[20, 99, 18] Operation: 23-5=18 Moving to Node #0,0 Current State: 91:[99, 5, 3], Operations: ['23-20=3'] Exploring Operation: 5+3=8, Resulting Numbers: [99, 8] Generated Node #0,0,0: 91:[99, 8] Operation: 5+3=8 Exploring Operation: 99-5=94, Resulting Numbers: [3, 94] Generated Node #0,0,1: 91:[3, 94] Operation: 99-5=94 Exploring Operation: 99-3=96, Resulting Numbers: [5, 96] Generated Node #0,0,2: 91:[5, 96] Operation: 99-3=96 Exploring Operation: 5*3=15, Resulting Numbers: [99, 15] Generated Node #0,0,3: 91:[99, 15] Operation: 5*3=15 Exploring Operation: 99+3=102, Resulting Numbers: [5, 102] Generated Node #0,0,4: 91:[5, 102] Operation: 99+3=102 Moving to Node #0,3 Current State: 91:[23, 99, 15], Operations: ['20-5=15'] Exploring Operation: 99-23=76, Resulting Numbers: [15, 76] Generated Node #0,3,0: 91:[15, 76] Operation: 99-23=76 Exploring Operation: 23+99=122, Resulting Numbers: [15, 122] Generated Node #0,3,1: 91:[15, 122] Operation: 23+99=122 Exploring Operation: 99-15=84, Resulting Numbers: [23, 84] Generated Node #0,3,2: 91:[23, 84] Operation: 99-15=84 Exploring Operation: 23-15=8, Resulting Numbers: [99, 8] Generated Node #0,3,3: 91:[99, 8] Operation: 23-15=8 Exploring Operation: 23+15=38, Resulting Numbers: [99, 38] Generated Node #0,3,4: 91:[99, 38] Operation: 23+15=38 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 91:[99, 8], Operations: ['20-5=15', '23-15=8'] Exploring Operation: 99*8=792, Resulting Numbers: [792] 792,91 unequal: No Solution Exploring Operation: 99+8=107, Resulting Numbers: [107] 107,91 unequal: No Solution Exploring Operation: 99-8=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[20, 23, 99, 5], Operations: [] Exploring Operation: 20-5=15, Resulting Numbers: [23, 99, 15] Generated Node #0,3: 91:[23, 99, 15] Operation: 20-5=15 Moving to Node #0,3 Current State: 91:[23, 99, 15], Operations: ['20-5=15'] Exploring Operation: 23-15=8, Resulting Numbers: [99, 8] Generated Node #0,3,3: 91:[99, 8] Operation: 23-15=8 Moving to Node #0,3,3 Current State: 91:[99, 8], Operations: ['20-5=15', '23-15=8'] Exploring Operation: 99-8=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 87, 26, 68, 14 ]
90
[ "68-26=42", "42/14=3", "87+3=90" ]
Current State: 90:[87, 26, 68, 14], Operations: [] Exploring Operation: 68-26=42, Resulting Numbers: [87, 14, 42] Generated Node #2: [87, 14, 42] from Operation: 68-26=42 Current State: 90:[87, 14, 42], Operations: ['68-26=42'] Exploring Operation: 42/14=3, Resulting Numbers: [87, 3] Generated Node #3: [87, 3] from Operation: 42/14=3 Current State: 90:[87, 3], Operations: ['68-26=42', '42/14=3'] Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[87, 26, 68, 14], Operations: [] Exploring Operation: 26+68=94, Resulting Numbers: [87, 14, 94] Generated Node #0,0: 90:[87, 14, 94] Operation: 26+68=94 Exploring Operation: 68-26=42, Resulting Numbers: [87, 14, 42] Generated Node #0,1: 90:[87, 14, 42] Operation: 68-26=42 Exploring Operation: 87-68=19, Resulting Numbers: [26, 14, 19] Generated Node #0,2: 90:[26, 14, 19] Operation: 87-68=19 Moving to Node #0,2 Current State: 90:[26, 14, 19], Operations: ['87-68=19'] Exploring Operation: 26-14=12, Resulting Numbers: [19, 12] Generated Node #0,2,0: 90:[19, 12] Operation: 26-14=12 Exploring Operation: 26+19=45, Resulting Numbers: [14, 45] Generated Node #0,2,1: 90:[14, 45] Operation: 26+19=45 Exploring Operation: 26-19=7, Resulting Numbers: [14, 7] Generated Node #0,2,2: 90:[14, 7] Operation: 26-19=7 Moving to Node #0,1 Current State: 90:[87, 14, 42], Operations: ['68-26=42'] Exploring Operation: 42-14=28, Resulting Numbers: [87, 28] Generated Node #0,1,0: 90:[87, 28] Operation: 42-14=28 Exploring Operation: 87-42=45, Resulting Numbers: [14, 45] Generated Node #0,1,1: 90:[14, 45] Operation: 87-42=45 Exploring Operation: 42/14=3, Resulting Numbers: [87, 3] Generated Node #0,1,2: 90:[87, 3] Operation: 42/14=3 Moving to Node #0,0 Current State: 90:[87, 14, 94], Operations: ['26+68=94'] Exploring Operation: 87+14=101, Resulting Numbers: [94, 101] Generated Node #0,0,0: 90:[94, 101] Operation: 87+14=101 Exploring Operation: 94-14=80, Resulting Numbers: [87, 80] Generated Node #0,0,1: 90:[87, 80] Operation: 94-14=80 Exploring Operation: 94-87=7, Resulting Numbers: [14, 7] Generated Node #0,0,2: 90:[14, 7] Operation: 94-87=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[14, 7], Operations: ['26+68=94', '94-87=7'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,90 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[87, 80], Operations: ['26+68=94', '94-14=80'] Exploring Operation: 87*80=6960, Resulting Numbers: [6960] 6960,90 unequal: No Solution Exploring Operation: 87-80=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 87+80=167, Resulting Numbers: [167] 167,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[94, 101], Operations: ['26+68=94', '87+14=101'] Exploring Operation: 101-94=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 94*101=9494, Resulting Numbers: [9494] 9494,90 unequal: No Solution Exploring Operation: 94+101=195, Resulting Numbers: [195] 195,90 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: 90:[14, 45], Operations: ['87-68=19', '26+19=45'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,90 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[14, 45], Operations: ['68-26=42', '87-42=45'] Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,90 unequal: No Solution Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,90 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[14, 7], Operations: ['87-68=19', '26-19=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[19, 12], Operations: ['87-68=19', '26-14=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[87, 3], Operations: ['68-26=42', '42/14=3'] Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,90 unequal: No Solution Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[87, 26, 68, 14], Operations: [] Exploring Operation: 68-26=42, Resulting Numbers: [87, 14, 42] Generated Node #0,1: 90:[87, 14, 42] Operation: 68-26=42 Moving to Node #0,1 Current State: 90:[87, 14, 42], Operations: ['68-26=42'] Exploring Operation: 42/14=3, Resulting Numbers: [87, 3] Generated Node #0,1,2: 90:[87, 3] Operation: 42/14=3 Moving to Node #0,1,2 Current State: 90:[87, 3], Operations: ['68-26=42', '42/14=3'] Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 74, 7, 46, 87 ]
93
[ "46+87=133", "133/7=19", "74+19=93" ]
Current State: 93:[74, 7, 46, 87], Operations: [] Exploring Operation: 46+87=133, Resulting Numbers: [74, 7, 133] Generated Node #2: [74, 7, 133] from Operation: 46+87=133 Current State: 93:[74, 7, 133], Operations: ['46+87=133'] Exploring Operation: 133/7=19, Resulting Numbers: [74, 19] Generated Node #3: [74, 19] from Operation: 133/7=19 Current State: 93:[74, 19], Operations: ['46+87=133', '133/7=19'] Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[74, 7, 46, 87], Operations: [] Exploring Operation: 74+7=81, Resulting Numbers: [46, 87, 81] Generated Node #0,0: 93:[46, 87, 81] Operation: 74+7=81 Exploring Operation: 46-7=39, Resulting Numbers: [74, 87, 39] Generated Node #0,1: 93:[74, 87, 39] Operation: 46-7=39 Exploring Operation: 74-46=28, Resulting Numbers: [7, 87, 28] Generated Node #0,2: 93:[7, 87, 28] Operation: 74-46=28 Exploring Operation: 87-74=13, Resulting Numbers: [7, 46, 13] Generated Node #0,3: 93:[7, 46, 13] Operation: 87-74=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[7, 87, 28], Operations: ['74-46=28'] Exploring Operation: 7+28=35, Resulting Numbers: [87, 35] Generated Node #0,2,0: 93:[87, 35] Operation: 7+28=35 Exploring Operation: 87-7=80, Resulting Numbers: [28, 80] Generated Node #0,2,1: 93:[28, 80] Operation: 87-7=80 Exploring Operation: 7+87=94, Resulting Numbers: [28, 94] Generated Node #0,2,2: 93:[28, 94] Operation: 7+87=94 Exploring Operation: 28/7=4, Resulting Numbers: [87, 4] Generated Node #0,2,3: 93:[87, 4] Operation: 28/7=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 93:[28, 94], Operations: ['74-46=28', '7+87=94'] Exploring Operation: 28+94=122, Resulting Numbers: [122] 122,93 unequal: No Solution Exploring Operation: 28*94=2632, Resulting Numbers: [2632] 2632,93 unequal: No Solution Exploring Operation: 94-28=66, Resulting Numbers: [66] 66,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 93:[87, 4], Operations: ['74-46=28', '28/7=4'] Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,93 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 93:[87, 35], Operations: ['74-46=28', '7+28=35'] Exploring Operation: 87+35=122, Resulting Numbers: [122] 122,93 unequal: No Solution Exploring Operation: 87*35=3045, Resulting Numbers: [3045] 3045,93 unequal: No Solution Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[28, 80], Operations: ['74-46=28', '87-7=80'] Exploring Operation: 28+80=108, Resulting Numbers: [108] 108,93 unequal: No Solution Exploring Operation: 28*80=2240, Resulting Numbers: [2240] 2240,93 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 93:[7, 46, 13], Operations: ['87-74=13'] Exploring Operation: 7*13=91, Resulting Numbers: [46, 91] Generated Node #0,3,0: 93:[46, 91] Operation: 7*13=91 Exploring Operation: 13-7=6, Resulting Numbers: [46, 6] Generated Node #0,3,1: 93:[46, 6] Operation: 13-7=6 Exploring Operation: 46-13=33, Resulting Numbers: [7, 33] Generated Node #0,3,2: 93:[7, 33] Operation: 46-13=33 Exploring Operation: 46-7=39, Resulting Numbers: [13, 39] Generated Node #0,3,3: 93:[13, 39] Operation: 46-7=39 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 93:[7, 33], Operations: ['87-74=13', '46-13=33'] Exploring Operation: 7*33=231, Resulting Numbers: [231] 231,93 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 7+33=40, Resulting Numbers: [40] 40,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 93:[46, 91], Operations: ['87-74=13', '7*13=91'] Exploring Operation: 46+91=137, Resulting Numbers: [137] 137,93 unequal: No Solution Exploring Operation: 46*91=4186, Resulting Numbers: [4186] 4186,93 unequal: No Solution Exploring Operation: 91-46=45, Resulting Numbers: [45] 45,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 93:[46, 6], Operations: ['87-74=13', '13-7=6'] Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,93 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,93 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 93:[13, 39], Operations: ['87-74=13', '46-7=39'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 13*39=507, Resulting Numbers: [507] 507,93 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 13+39=52, Resulting Numbers: [52] 52,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[46, 87, 81], Operations: ['74+7=81'] Exploring Operation: 46+81=127, Resulting Numbers: [87, 127] Generated Node #0,0,0: 93:[87, 127] Operation: 46+81=127 Exploring Operation: 81-46=35, Resulting Numbers: [87, 35] Generated Node #0,0,1: 93:[87, 35] Operation: 81-46=35 Exploring Operation: 87-81=6, Resulting Numbers: [46, 6] Generated Node #0,0,2: 93:[46, 6] Operation: 87-81=6 Exploring Operation: 87-46=41, Resulting Numbers: [81, 41] Generated Node #0,0,3: 93:[81, 41] Operation: 87-46=41 Moving to Node #0,0,1 Current State: 93:[87, 35], Operations: ['74+7=81', '81-46=35'] Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,93 unequal: No Solution Exploring Operation: 87*35=3045, Resulting Numbers: [3045] 3045,93 unequal: No Solution Exploring Operation: 87+35=122, Resulting Numbers: [122] 122,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[46, 6], Operations: ['74+7=81', '87-81=6'] Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,93 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,93 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[81, 41], Operations: ['74+7=81', '87-46=41'] Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,93 unequal: No Solution Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,93 unequal: No Solution Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[87, 127], Operations: ['74+7=81', '46+81=127'] Exploring Operation: 127-87=40, Resulting Numbers: [40] 40,93 unequal: No Solution Exploring Operation: 87*127=11049, Resulting Numbers: [11049] 11049,93 unequal: No Solution Exploring Operation: 87+127=214, Resulting Numbers: [214] 214,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[74, 87, 39], Operations: ['46-7=39'] Exploring Operation: 74+39=113, Resulting Numbers: [87, 113] Generated Node #0,1,0: 93:[87, 113] Operation: 74+39=113 Exploring Operation: 87-74=13, Resulting Numbers: [39, 13] Generated Node #0,1,1: 93:[39, 13] Operation: 87-74=13 Exploring Operation: 74-39=35, Resulting Numbers: [87, 35] Generated Node #0,1,2: 93:[87, 35] Operation: 74-39=35 Exploring Operation: 87-39=48, Resulting Numbers: [74, 48] Generated Node #0,1,3: 93:[74, 48] Operation: 87-39=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[87, 35], Operations: ['46-7=39', '74-39=35'] Exploring Operation: 87*35=3045, Resulting Numbers: [3045] 3045,93 unequal: No Solution Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,93 unequal: No Solution Exploring Operation: 87+35=122, Resulting Numbers: [122] 122,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 93:[39, 13], Operations: ['46-7=39', '87-74=13'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,93 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[87, 113], Operations: ['46-7=39', '74+39=113'] Exploring Operation: 87*113=9831, Resulting Numbers: [9831] 9831,93 unequal: No Solution Exploring Operation: 113-87=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 87+113=200, Resulting Numbers: [200] 200,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 93:[74, 48], Operations: ['46-7=39', '87-39=48'] Exploring Operation: 74+48=122, Resulting Numbers: [122] 122,93 unequal: No Solution Exploring Operation: 74*48=3552, Resulting Numbers: [3552] 3552,93 unequal: No Solution Exploring Operation: 74-48=26, Resulting Numbers: [26] 26,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 19, 85, 97, 2 ]
71
[ "97-19=78", "2*78=156", "156-85=71" ]
Current State: 71:[19, 85, 97, 2], Operations: [] Exploring Operation: 97-19=78, Resulting Numbers: [85, 2, 78] Generated Node #2: [85, 2, 78] from Operation: 97-19=78 Current State: 71:[85, 2, 78], Operations: ['97-19=78'] Exploring Operation: 2*78=156, Resulting Numbers: [85, 156] Generated Node #3: [85, 156] from Operation: 2*78=156 Current State: 71:[85, 156], Operations: ['97-19=78', '2*78=156'] Exploring Operation: 156-85=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[19, 85, 97, 2], Operations: [] Exploring Operation: 85-2=83, Resulting Numbers: [19, 97, 83] Generated Node #0,0: 71:[19, 97, 83] Operation: 85-2=83 Exploring Operation: 19*2=38, Resulting Numbers: [85, 97, 38] Generated Node #0,1: 71:[85, 97, 38] Operation: 19*2=38 Exploring Operation: 97-19=78, Resulting Numbers: [85, 2, 78] Generated Node #0,2: 71:[85, 2, 78] Operation: 97-19=78 Exploring Operation: 19+2=21, Resulting Numbers: [85, 97, 21] Generated Node #0,3: 71:[85, 97, 21] Operation: 19+2=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[85, 97, 38], Operations: ['19*2=38'] Exploring Operation: 85+38=123, Resulting Numbers: [97, 123] Generated Node #0,1,0: 71:[97, 123] Operation: 85+38=123 Exploring Operation: 85-38=47, Resulting Numbers: [97, 47] Generated Node #0,1,1: 71:[97, 47] Operation: 85-38=47 Exploring Operation: 97+38=135, Resulting Numbers: [85, 135] Generated Node #0,1,2: 71:[85, 135] Operation: 97+38=135 Exploring Operation: 97-38=59, Resulting Numbers: [85, 59] Generated Node #0,1,3: 71:[85, 59] Operation: 97-38=59 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 71:[85, 59], Operations: ['19*2=38', '97-38=59'] Exploring Operation: 85*59=5015, Resulting Numbers: [5015] 5015,71 unequal: No Solution Exploring Operation: 85-59=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 85+59=144, Resulting Numbers: [144] 144,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 71:[97, 47], Operations: ['19*2=38', '85-38=47'] Exploring Operation: 97+47=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 97*47=4559, Resulting Numbers: [4559] 4559,71 unequal: No Solution Exploring Operation: 97-47=50, Resulting Numbers: [50] 50,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[97, 123], Operations: ['19*2=38', '85+38=123'] Exploring Operation: 97+123=220, Resulting Numbers: [220] 220,71 unequal: No Solution Exploring Operation: 97*123=11931, Resulting Numbers: [11931] 11931,71 unequal: No Solution Exploring Operation: 123-97=26, Resulting Numbers: [26] 26,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 71:[85, 135], Operations: ['19*2=38', '97+38=135'] Exploring Operation: 85*135=11475, Resulting Numbers: [11475] 11475,71 unequal: No Solution Exploring Operation: 135-85=50, Resulting Numbers: [50] 50,71 unequal: No Solution Exploring Operation: 85+135=220, Resulting Numbers: [220] 220,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[19, 97, 83], Operations: ['85-2=83'] Exploring Operation: 97-19=78, Resulting Numbers: [83, 78] Generated Node #0,0,0: 71:[83, 78] Operation: 97-19=78 Exploring Operation: 19+83=102, Resulting Numbers: [97, 102] Generated Node #0,0,1: 71:[97, 102] Operation: 19+83=102 Exploring Operation: 19+97=116, Resulting Numbers: [83, 116] Generated Node #0,0,2: 71:[83, 116] Operation: 19+97=116 Exploring Operation: 83-19=64, Resulting Numbers: [97, 64] Generated Node #0,0,3: 71:[97, 64] Operation: 83-19=64 Moving to Node #0,0,0 Current State: 71:[83, 78], Operations: ['85-2=83', '97-19=78'] Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,71 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[97, 64], Operations: ['85-2=83', '83-19=64'] Exploring Operation: 97+64=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 97*64=6208, Resulting Numbers: [6208] 6208,71 unequal: No Solution Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[83, 116], Operations: ['85-2=83', '19+97=116'] Exploring Operation: 83+116=199, Resulting Numbers: [199] 199,71 unequal: No Solution Exploring Operation: 83*116=9628, Resulting Numbers: [9628] 9628,71 unequal: No Solution Exploring Operation: 116-83=33, Resulting Numbers: [33] 33,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[97, 102], Operations: ['85-2=83', '19+83=102'] Exploring Operation: 102-97=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 97*102=9894, Resulting Numbers: [9894] 9894,71 unequal: No Solution Exploring Operation: 97+102=199, Resulting Numbers: [199] 199,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[85, 2, 78], Operations: ['97-19=78'] Exploring Operation: 78-2=76, Resulting Numbers: [85, 76] Generated Node #0,2,0: 71:[85, 76] Operation: 78-2=76 Exploring Operation: 85+2=87, Resulting Numbers: [78, 87] Generated Node #0,2,1: 71:[78, 87] Operation: 85+2=87 Exploring Operation: 2+78=80, Resulting Numbers: [85, 80] Generated Node #0,2,2: 71:[85, 80] Operation: 2+78=80 Exploring Operation: 85-2=83, Resulting Numbers: [78, 83] Generated Node #0,2,3: 71:[78, 83] Operation: 85-2=83 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 71:[85, 76], Operations: ['97-19=78', '78-2=76'] Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 85+76=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 85*76=6460, Resulting Numbers: [6460] 6460,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 71:[78, 83], Operations: ['97-19=78', '85-2=83'] Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[78, 87], Operations: ['97-19=78', '85+2=87'] Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 78*87=6786, Resulting Numbers: [6786] 6786,71 unequal: No Solution Exploring Operation: 78+87=165, Resulting Numbers: [165] 165,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 71:[85, 80], Operations: ['97-19=78', '2+78=80'] Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 85*80=6800, Resulting Numbers: [6800] 6800,71 unequal: No Solution Exploring Operation: 85+80=165, Resulting Numbers: [165] 165,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 71:[85, 97, 21], Operations: ['19+2=21'] Exploring Operation: 97+21=118, Resulting Numbers: [85, 118] Generated Node #0,3,0: 71:[85, 118] Operation: 97+21=118 Exploring Operation: 85-21=64, Resulting Numbers: [97, 64] Generated Node #0,3,1: 71:[97, 64] Operation: 85-21=64 Exploring Operation: 85+21=106, Resulting Numbers: [97, 106] Generated Node #0,3,2: 71:[97, 106] Operation: 85+21=106 Exploring Operation: 97-21=76, Resulting Numbers: [85, 76] Generated Node #0,3,3: 71:[85, 76] Operation: 97-21=76 Moving to Node #0,3,3 Current State: 71:[85, 76], Operations: ['19+2=21', '97-21=76'] Exploring Operation: 85+76=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 85*76=6460, Resulting Numbers: [6460] 6460,71 unequal: No Solution Exploring Operation: 85-76=9, Resulting Numbers: [9] 9,71 unequal: No Solution Moving to Node #0,3,1 Current State: 71:[97, 64], Operations: ['19+2=21', '85-21=64'] Exploring Operation: 97+64=161, Resulting Numbers: [161] 161,71 unequal: No Solution Exploring Operation: 97*64=6208, Resulting Numbers: [6208] 6208,71 unequal: No Solution Exploring Operation: 97-64=33, Resulting Numbers: [33] 33,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[97, 106], Operations: ['19+2=21', '85+21=106'] Exploring Operation: 97+106=203, Resulting Numbers: [203] 203,71 unequal: No Solution Exploring Operation: 106-97=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 97*106=10282, Resulting Numbers: [10282] 10282,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[85, 118], Operations: ['19+2=21', '97+21=118'] Exploring Operation: 85+118=203, Resulting Numbers: [203] 203,71 unequal: No Solution Exploring Operation: 118-85=33, Resulting Numbers: [33] 33,71 unequal: No Solution Exploring Operation: 85*118=10030, Resulting Numbers: [10030] 10030,71 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
[ 53, 76, 1, 55 ]
77
[ "76-53=23", "55-1=54", "23+54=77" ]
Current State: 77:[53, 76, 1, 55], Operations: [] Exploring Operation: 76-53=23, Resulting Numbers: [1, 55, 23] Generated Node #2: [1, 55, 23] from Operation: 76-53=23 Current State: 77:[1, 55, 23], Operations: ['76-53=23'] Exploring Operation: 55-1=54, Resulting Numbers: [23, 54] Generated Node #3: [23, 54] from Operation: 55-1=54 Current State: 77:[23, 54], Operations: ['76-53=23', '55-1=54'] Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[53, 76, 1, 55], Operations: [] Exploring Operation: 76-53=23, Resulting Numbers: [1, 55, 23] Generated Node #0,0: 77:[1, 55, 23] Operation: 76-53=23 Exploring Operation: 53+55=108, Resulting Numbers: [76, 1, 108] Generated Node #0,1: 77:[76, 1, 108] Operation: 53+55=108 Exploring Operation: 55-53=2, Resulting Numbers: [76, 1, 2] Generated Node #0,2: 77:[76, 1, 2] Operation: 55-53=2 Moving to Node #0,2 Current State: 77:[76, 1, 2], Operations: ['55-53=2'] Exploring Operation: 1+2=3, Resulting Numbers: [76, 3] Generated Node #0,2,0: 77:[76, 3] Operation: 1+2=3 Exploring Operation: 76*1=76, Resulting Numbers: [2, 76] Generated Node #0,2,1: 77:[2, 76] Operation: 76*1=76 Exploring Operation: 76+1=77, Resulting Numbers: [2, 77] Generated Node #0,2,2: 77:[2, 77] Operation: 76+1=77 Moving to Node #0,1 Current State: 77:[76, 1, 108], Operations: ['53+55=108'] Exploring Operation: 76+1=77, Resulting Numbers: [108, 77] Generated Node #0,1,0: 77:[108, 77] Operation: 76+1=77 Exploring Operation: 108-76=32, Resulting Numbers: [1, 32] Generated Node #0,1,1: 77:[1, 32] Operation: 108-76=32 Exploring Operation: 108-1=107, Resulting Numbers: [76, 107] Generated Node #0,1,2: 77:[76, 107] Operation: 108-1=107 Moving to Node #0,0 Current State: 77:[1, 55, 23], Operations: ['76-53=23'] Exploring Operation: 55+23=78, Resulting Numbers: [1, 78] Generated Node #0,0,0: 77:[1, 78] Operation: 55+23=78 Exploring Operation: 1+55=56, Resulting Numbers: [23, 56] Generated Node #0,0,1: 77:[23, 56] Operation: 1+55=56 Exploring Operation: 55-23=32, Resulting Numbers: [1, 32] Generated Node #0,0,2: 77:[1, 32] Operation: 55-23=32 Moving to Node #0,2,0 Current State: 77:[76, 3], Operations: ['55-53=2', '1+2=3'] Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,77 unequal: No Solution Exploring Operation: 76*3=228, Resulting Numbers: [228] 228,77 unequal: No Solution Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[2, 77], Operations: ['55-53=2', '76+1=77'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,77 unequal: No Solution Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,77 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[2, 76], Operations: ['55-53=2', '76*1=76'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,77 unequal: No Solution Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[1, 78], Operations: ['76-53=23', '55+23=78'] Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[53, 76, 1, 55], Operations: [] Exploring Operation: 76-53=23, Resulting Numbers: [1, 55, 23] Generated Node #0,0: 77:[1, 55, 23] Operation: 76-53=23 Moving to Node #0,0 Current State: 77:[1, 55, 23], Operations: ['76-53=23'] Exploring Operation: 55+23=78, Resulting Numbers: [1, 78] Generated Node #0,0,0: 77:[1, 78] Operation: 55+23=78 Moving to Node #0,0,0 Current State: 77:[1, 78], Operations: ['76-53=23', '55+23=78'] Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.977431
hs_3
mult_heuristic
[ 65, 69, 64, 32 ]
36
[ "69-65=4", "64-32=32", "4+32=36" ]
Current State: 36:[65, 69, 64, 32], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [64, 32, 4] Generated Node #2: [64, 32, 4] from Operation: 69-65=4 Current State: 36:[64, 32, 4], Operations: ['69-65=4'] Exploring Operation: 64-32=32, Resulting Numbers: [4, 32] Generated Node #3: [4, 32] from Operation: 64-32=32 Current State: 36:[4, 32], Operations: ['69-65=4', '64-32=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[65, 69, 64, 32], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [64, 32, 4] Generated Node #0,0: 36:[64, 32, 4] Operation: 69-65=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[64, 32, 4], Operations: ['69-65=4'] Exploring Operation: 64/32=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 36:[4, 2] Operation: 64/32=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[4, 2], Operations: ['69-65=4', '64/32=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,36 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
sum_heuristic
[ 35, 10, 12, 40 ]
14
[ "35*12=420", "40-10=30", "420/30=14" ]
Current State: 14:[35, 10, 12, 40], Operations: [] Exploring Operation: 35*12=420, Resulting Numbers: [10, 40, 420] Generated Node #2: [10, 40, 420] from Operation: 35*12=420 Current State: 14:[10, 40, 420], Operations: ['35*12=420'] Exploring Operation: 40-10=30, Resulting Numbers: [420, 30] Generated Node #3: [420, 30] from Operation: 40-10=30 Current State: 14:[420, 30], Operations: ['35*12=420', '40-10=30'] Exploring Operation: 420/30=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[35, 10, 12, 40], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [35, 12, 4] Generated Node #0,0: 14:[35, 12, 4] Operation: 40/10=4 Exploring Operation: 35-12=23, Resulting Numbers: [10, 40, 23] Generated Node #0,1: 14:[10, 40, 23] Operation: 35-12=23 Exploring Operation: 40-12=28, Resulting Numbers: [35, 10, 28] Generated Node #0,2: 14:[35, 10, 28] Operation: 40-12=28 Exploring Operation: 40-35=5, Resulting Numbers: [10, 12, 5] Generated Node #0,3: 14:[10, 12, 5] Operation: 40-35=5 Exploring Operation: 35-10=25, Resulting Numbers: [12, 40, 25] Generated Node #0,4: 14:[12, 40, 25] Operation: 35-10=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[10, 12, 5], Operations: ['40-35=5'] Exploring Operation: 12-5=7, Resulting Numbers: [10, 7] Generated Node #0,3,0: 14:[10, 7] Operation: 12-5=7 Exploring Operation: 12-10=2, Resulting Numbers: [5, 2] Generated Node #0,3,1: 14:[5, 2] Operation: 12-10=2 Exploring Operation: 10+5=15, Resulting Numbers: [12, 15] Generated Node #0,3,2: 14:[12, 15] Operation: 10+5=15 Exploring Operation: 10-5=5, Resulting Numbers: [12, 5] Generated Node #0,3,3: 14:[12, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [12, 2] Generated Node #0,3,4: 14:[12, 2] Operation: 10/5=2 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 14:[5, 2], Operations: ['40-35=5', '12-10=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,14 unequal: No Solution No 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: 14:[12, 2], Operations: ['40-35=5', '10/5=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[35, 10, 12, 40], Operations: [] Exploring Operation: 40-35=5, Resulting Numbers: [10, 12, 5] Generated Node #0,3: 14:[10, 12, 5] Operation: 40-35=5 Moving to Node #0,3 Current State: 14:[10, 12, 5], Operations: ['40-35=5'] Exploring Operation: 10/5=2, Resulting Numbers: [12, 2] Generated Node #0,3,4: 14:[12, 2] Operation: 10/5=2 Moving to Node #0,3,4 Current State: 14:[12, 2], Operations: ['40-35=5', '10/5=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 78, 22, 29, 99 ]
14
[ "78-22=56", "99-29=70", "70-56=14" ]
Current State: 14:[78, 22, 29, 99], Operations: [] Exploring Operation: 78-22=56, Resulting Numbers: [29, 99, 56] Generated Node #2: [29, 99, 56] from Operation: 78-22=56 Current State: 14:[29, 99, 56], Operations: ['78-22=56'] Exploring Operation: 99-29=70, Resulting Numbers: [56, 70] Generated Node #3: [56, 70] from Operation: 99-29=70 Current State: 14:[56, 70], Operations: ['78-22=56', '99-29=70'] Exploring Operation: 70-56=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 22, 29, 99], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [22, 29, 21] Generated Node #0,0: 14:[22, 29, 21] Operation: 99-78=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[22, 29, 21], Operations: ['99-78=21'] Exploring Operation: 29-22=7, Resulting Numbers: [21, 7] Generated Node #0,0,0: 14:[21, 7] Operation: 29-22=7 Moving to Node #0,0,0 Current State: 14:[21, 7], Operations: ['99-78=21', '29-22=7'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[78, 22, 29, 99], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [22, 29, 21] Generated Node #0,0: 14:[22, 29, 21] Operation: 99-78=21 Moving to Node #0,0 Current State: 14:[22, 29, 21], Operations: ['99-78=21'] Exploring Operation: 29-22=7, Resulting Numbers: [21, 7] Generated Node #0,0,0: 14:[21, 7] Operation: 29-22=7 Moving to Node #0,0,0 Current State: 14:[21, 7], Operations: ['99-78=21', '29-22=7'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 10, 43, 2, 74 ]
32
[ "10+43=53", "2*53=106", "106-74=32" ]
Current State: 32:[10, 43, 2, 74], Operations: [] Exploring Operation: 10+43=53, Resulting Numbers: [2, 74, 53] Generated Node #2: [2, 74, 53] from Operation: 10+43=53 Current State: 32:[2, 74, 53], Operations: ['10+43=53'] Exploring Operation: 2*53=106, Resulting Numbers: [74, 106] Generated Node #3: [74, 106] from Operation: 2*53=106 Current State: 32:[74, 106], Operations: ['10+43=53', '2*53=106'] Exploring Operation: 106-74=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[10, 43, 2, 74], Operations: [] Exploring Operation: 74-43=31, Resulting Numbers: [10, 2, 31] Generated Node #0,0: 32:[10, 2, 31] Operation: 74-43=31 Exploring Operation: 74/2=37, Resulting Numbers: [10, 43, 37] Generated Node #0,1: 32:[10, 43, 37] Operation: 74/2=37 Exploring Operation: 43-10=33, Resulting Numbers: [2, 74, 33] Generated Node #0,2: 32:[2, 74, 33] Operation: 43-10=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[10, 2, 31], Operations: ['74-43=31'] Exploring Operation: 10/2=5, Resulting Numbers: [31, 5] Generated Node #0,0,0: 32:[31, 5] Operation: 10/2=5 Exploring Operation: 10-2=8, Resulting Numbers: [31, 8] Generated Node #0,0,1: 32:[31, 8] Operation: 10-2=8 Exploring Operation: 2+31=33, Resulting Numbers: [10, 33] Generated Node #0,0,2: 32:[10, 33] Operation: 2+31=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[31, 8], Operations: ['74-43=31', '10-2=8'] Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,32 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[31, 5], Operations: ['74-43=31', '10/2=5'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[10, 33], Operations: ['74-43=31', '2+31=33'] Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,32 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,32 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[10, 43, 37], Operations: ['74/2=37'] Exploring Operation: 43-10=33, Resulting Numbers: [37, 33] Generated Node #0,1,0: 32:[37, 33] Operation: 43-10=33 Exploring Operation: 37-10=27, Resulting Numbers: [43, 27] Generated Node #0,1,1: 32:[43, 27] Operation: 37-10=27 Exploring Operation: 43-37=6, Resulting Numbers: [10, 6] Generated Node #0,1,2: 32:[10, 6] Operation: 43-37=6 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 32:[10, 6], Operations: ['74/2=37', '43-37=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,32 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 32:[37, 33], Operations: ['74/2=37', '43-10=33'] Exploring Operation: 37*33=1221, Resulting Numbers: [1221] 1221,32 unequal: No Solution Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[43, 27], Operations: ['74/2=37', '37-10=27'] Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,32 unequal: No Solution Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[2, 74, 33], Operations: ['43-10=33'] Exploring Operation: 74-33=41, Resulting Numbers: [2, 41] Generated Node #0,2,0: 32:[2, 41] Operation: 74-33=41 Exploring Operation: 74-2=72, Resulting Numbers: [33, 72] Generated Node #0,2,1: 32:[33, 72] Operation: 74-2=72 Exploring Operation: 74/2=37, Resulting Numbers: [33, 37] Generated Node #0,2,2: 32:[33, 37] Operation: 74/2=37 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 32:[33, 37], Operations: ['43-10=33', '74/2=37'] Exploring Operation: 37-33=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 33+37=70, Resulting Numbers: [70] 70,32 unequal: No Solution Exploring Operation: 33*37=1221, Resulting Numbers: [1221] 1221,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[2, 41], Operations: ['43-10=33', '74-33=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,32 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 32:[33, 72], Operations: ['43-10=33', '74-2=72'] Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,32 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 58, 71, 11, 78 ]
62
[ "58+71=129", "78-11=67", "129-67=62" ]
Current State: 62:[58, 71, 11, 78], Operations: [] Exploring Operation: 58+71=129, Resulting Numbers: [11, 78, 129] Generated Node #2: [11, 78, 129] from Operation: 58+71=129 Current State: 62:[11, 78, 129], Operations: ['58+71=129'] Exploring Operation: 78-11=67, Resulting Numbers: [129, 67] Generated Node #3: [129, 67] from Operation: 78-11=67 Current State: 62:[129, 67], Operations: ['58+71=129', '78-11=67'] Exploring Operation: 129-67=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[58, 71, 11, 78], Operations: [] Exploring Operation: 58+11=69, Resulting Numbers: [71, 78, 69] Generated Node #0,0: 62:[71, 78, 69] Operation: 58+11=69 Exploring Operation: 78-11=67, Resulting Numbers: [58, 71, 67] Generated Node #0,1: 62:[58, 71, 67] Operation: 78-11=67 Exploring Operation: 71-11=60, Resulting Numbers: [58, 78, 60] Generated Node #0,2: 62:[58, 78, 60] Operation: 71-11=60 Exploring Operation: 78-71=7, Resulting Numbers: [58, 11, 7] Generated Node #0,3: 62:[58, 11, 7] Operation: 78-71=7 Exploring Operation: 78-58=20, Resulting Numbers: [71, 11, 20] Generated Node #0,4: 62:[71, 11, 20] Operation: 78-58=20 Moving to Node #0,1 Current State: 62:[58, 71, 67], Operations: ['78-11=67'] Exploring Operation: 71-58=13, Resulting Numbers: [67, 13] Generated Node #0,1,0: 62:[67, 13] Operation: 71-58=13 Exploring Operation: 58+67=125, Resulting Numbers: [71, 125] Generated Node #0,1,1: 62:[71, 125] Operation: 58+67=125 Exploring Operation: 67-58=9, Resulting Numbers: [71, 9] Generated Node #0,1,2: 62:[71, 9] Operation: 67-58=9 Exploring Operation: 71-67=4, Resulting Numbers: [58, 4] Generated Node #0,1,3: 62:[58, 4] Operation: 71-67=4 Exploring Operation: 58+71=129, Resulting Numbers: [67, 129] Generated Node #0,1,4: 62:[67, 129] Operation: 58+71=129 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[58, 4], Operations: ['78-11=67', '71-67=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[58, 71, 11, 78], Operations: [] Exploring Operation: 78-11=67, Resulting Numbers: [58, 71, 67] Generated Node #0,1: 62:[58, 71, 67] Operation: 78-11=67 Moving to Node #0,1 Current State: 62:[58, 71, 67], Operations: ['78-11=67'] Exploring Operation: 71-67=4, Resulting Numbers: [58, 4] Generated Node #0,1,3: 62:[58, 4] Operation: 71-67=4 Moving to Node #0,1,3 Current State: 62:[58, 4], Operations: ['78-11=67', '71-67=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 61, 64, 5, 34 ]
55
[ "64-34=30", "30/5=6", "61-6=55" ]
Current State: 55:[61, 64, 5, 34], Operations: [] Exploring Operation: 64-34=30, Resulting Numbers: [61, 5, 30] Generated Node #2: [61, 5, 30] from Operation: 64-34=30 Current State: 55:[61, 5, 30], Operations: ['64-34=30'] Exploring Operation: 30/5=6, Resulting Numbers: [61, 6] Generated Node #3: [61, 6] from Operation: 30/5=6 Current State: 55:[61, 6], Operations: ['64-34=30', '30/5=6'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[61, 64, 5, 34], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [5, 34, 3] Generated Node #0,0: 55:[5, 34, 3] Operation: 64-61=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[5, 34, 3], Operations: ['64-61=3'] Exploring Operation: 5+34=39, Resulting Numbers: [3, 39] Generated Node #0,0,0: 55:[3, 39] Operation: 5+34=39 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[3, 39], Operations: ['64-61=3', '5+34=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 57, 93, 77, 34 ]
75
[ "93-57=36", "77+34=111", "111-36=75" ]
Current State: 75:[57, 93, 77, 34], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [77, 34, 36] Generated Node #2: [77, 34, 36] from Operation: 93-57=36 Current State: 75:[77, 34, 36], Operations: ['93-57=36'] Exploring Operation: 77+34=111, Resulting Numbers: [36, 111] Generated Node #3: [36, 111] from Operation: 77+34=111 Current State: 75:[36, 111], Operations: ['93-57=36', '77+34=111'] Exploring Operation: 111-36=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[57, 93, 77, 34], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [77, 34, 36] Generated Node #0,0: 75:[77, 34, 36] Operation: 93-57=36 Exploring Operation: 57-34=23, Resulting Numbers: [93, 77, 23] Generated Node #0,1: 75:[93, 77, 23] Operation: 57-34=23 Moving to Node #0,0 Current State: 75:[77, 34, 36], Operations: ['93-57=36'] Exploring Operation: 36-34=2, Resulting Numbers: [77, 2] Generated Node #0,0,0: 75:[77, 2] Operation: 36-34=2 Exploring Operation: 34+36=70, Resulting Numbers: [77, 70] Generated Node #0,0,1: 75:[77, 70] Operation: 34+36=70 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[77, 2], Operations: ['93-57=36', '36-34=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[57, 93, 77, 34], Operations: [] Exploring Operation: 93-57=36, Resulting Numbers: [77, 34, 36] Generated Node #0,0: 75:[77, 34, 36] Operation: 93-57=36 Moving to Node #0,0 Current State: 75:[77, 34, 36], Operations: ['93-57=36'] Exploring Operation: 36-34=2, Resulting Numbers: [77, 2] Generated Node #0,0,0: 75:[77, 2] Operation: 36-34=2 Moving to Node #0,0,0 Current State: 75:[77, 2], Operations: ['93-57=36', '36-34=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 93, 9, 73, 13 ]
17
[ "93+73=166", "166-13=153", "153/9=17" ]
Current State: 17:[93, 9, 73, 13], Operations: [] Exploring Operation: 93+73=166, Resulting Numbers: [9, 13, 166] Generated Node #2: [9, 13, 166] from Operation: 93+73=166 Current State: 17:[9, 13, 166], Operations: ['93+73=166'] Exploring Operation: 166-13=153, Resulting Numbers: [9, 153] Generated Node #3: [9, 153] from Operation: 166-13=153 Current State: 17:[9, 153], Operations: ['93+73=166', '166-13=153'] Exploring Operation: 153/9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[93, 9, 73, 13], Operations: [] Exploring Operation: 93-9=84, Resulting Numbers: [73, 13, 84] Generated Node #0,0: 17:[73, 13, 84] Operation: 93-9=84 Exploring Operation: 93-13=80, Resulting Numbers: [9, 73, 80] Generated Node #0,1: 17:[9, 73, 80] Operation: 93-13=80 Exploring Operation: 93-73=20, Resulting Numbers: [9, 13, 20] Generated Node #0,2: 17:[9, 13, 20] Operation: 93-73=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[9, 13, 20], Operations: ['93-73=20'] Exploring Operation: 9+13=22, Resulting Numbers: [20, 22] Generated Node #0,2,0: 17:[20, 22] Operation: 9+13=22 Exploring Operation: 20-9=11, Resulting Numbers: [13, 11] Generated Node #0,2,1: 17:[13, 11] Operation: 20-9=11 Exploring Operation: 13-9=4, Resulting Numbers: [20, 4] Generated Node #0,2,2: 17:[20, 4] Operation: 13-9=4 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[20, 22], Operations: ['93-73=20', '9+13=22'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,17 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 17:[13, 11], Operations: ['93-73=20', '20-9=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,17 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[20, 4], Operations: ['93-73=20', '13-9=4'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,17 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[73, 13, 84], Operations: ['93-9=84'] Exploring Operation: 84-73=11, Resulting Numbers: [13, 11] Generated Node #0,0,0: 17:[13, 11] Operation: 84-73=11 Exploring Operation: 73-13=60, Resulting Numbers: [84, 60] Generated Node #0,0,1: 17:[84, 60] Operation: 73-13=60 Exploring Operation: 84-13=71, Resulting Numbers: [73, 71] Generated Node #0,0,2: 17:[73, 71] Operation: 84-13=71 Moving to Node #0,0,0 Current State: 17:[13, 11], Operations: ['93-9=84', '84-73=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,17 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[84, 60], Operations: ['93-9=84', '73-13=60'] Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[73, 71], Operations: ['93-9=84', '84-13=71'] Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[9, 73, 80], Operations: ['93-13=80'] Exploring Operation: 80-9=71, Resulting Numbers: [73, 71] Generated Node #0,1,0: 17:[73, 71] Operation: 80-9=71 Exploring Operation: 73-9=64, Resulting Numbers: [80, 64] Generated Node #0,1,1: 17:[80, 64] Operation: 73-9=64 Exploring Operation: 80-73=7, Resulting Numbers: [9, 7] Generated Node #0,1,2: 17:[9, 7] Operation: 80-73=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 17:[9, 7], Operations: ['93-13=80', '80-73=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,17 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 17:[73, 71], Operations: ['93-13=80', '80-9=71'] Exploring Operation: 73+71=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 73*71=5183, Resulting Numbers: [5183] 5183,17 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[80, 64], Operations: ['93-13=80', '73-9=64'] Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 80+64=144, Resulting Numbers: [144] 144,17 unequal: No Solution Exploring Operation: 80*64=5120, Resulting Numbers: [5120] 5120,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 26, 66, 3, 17 ]
54
[ "66-26=40", "17-3=14", "40+14=54" ]
Current State: 54:[26, 66, 3, 17], Operations: [] Exploring Operation: 66-26=40, Resulting Numbers: [3, 17, 40] Generated Node #2: [3, 17, 40] from Operation: 66-26=40 Current State: 54:[3, 17, 40], Operations: ['66-26=40'] Exploring Operation: 17-3=14, Resulting Numbers: [40, 14] Generated Node #3: [40, 14] from Operation: 17-3=14 Current State: 54:[40, 14], Operations: ['66-26=40', '17-3=14'] Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[26, 66, 3, 17], Operations: [] Exploring Operation: 66/3=22, Resulting Numbers: [26, 17, 22] Generated Node #0,0: 54:[26, 17, 22] Operation: 66/3=22 Exploring Operation: 66-17=49, Resulting Numbers: [26, 3, 49] Generated Node #0,1: 54:[26, 3, 49] Operation: 66-17=49 Exploring Operation: 26-17=9, Resulting Numbers: [66, 3, 9] Generated Node #0,2: 54:[66, 3, 9] Operation: 26-17=9 Exploring Operation: 66-3=63, Resulting Numbers: [26, 17, 63] Generated Node #0,3: 54:[26, 17, 63] Operation: 66-3=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[26, 17, 22], Operations: ['66/3=22'] Exploring Operation: 22-17=5, Resulting Numbers: [26, 5] Generated Node #0,0,0: 54:[26, 5] Operation: 22-17=5 Exploring Operation: 26-17=9, Resulting Numbers: [22, 9] Generated Node #0,0,1: 54:[22, 9] Operation: 26-17=9 Exploring Operation: 26+22=48, Resulting Numbers: [17, 48] Generated Node #0,0,2: 54:[17, 48] Operation: 26+22=48 Exploring Operation: 26-22=4, Resulting Numbers: [17, 4] Generated Node #0,0,3: 54:[17, 4] Operation: 26-22=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[26, 5], Operations: ['66/3=22', '22-17=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,54 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,54 unequal: No Solution No 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: 54:[17, 4], Operations: ['66/3=22', '26-22=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,54 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,54 unequal: No Solution No 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: 54:[22, 9], Operations: ['66/3=22', '26-17=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,54 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,54 unequal: No Solution No 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: 54:[17, 48], Operations: ['66/3=22', '26+22=48'] Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,54 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,54 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: 54:[26, 3, 49], Operations: ['66-17=49'] Exploring Operation: 26-3=23, Resulting Numbers: [49, 23] Generated Node #0,1,0: 54:[49, 23] Operation: 26-3=23 Exploring Operation: 3+49=52, Resulting Numbers: [26, 52] Generated Node #0,1,1: 54:[26, 52] Operation: 3+49=52 Exploring Operation: 26+3=29, Resulting Numbers: [49, 29] Generated Node #0,1,2: 54:[49, 29] Operation: 26+3=29 Exploring Operation: 49-26=23, Resulting Numbers: [3, 23] Generated Node #0,1,3: 54:[3, 23] Operation: 49-26=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[26, 52], Operations: ['66-17=49', '3+49=52'] Exploring Operation: 26+52=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,54 unequal: No Solution Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 26*52=1352, Resulting Numbers: [1352] 1352,54 unequal: No Solution No 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: 54:[3, 23], Operations: ['66-17=49', '49-26=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,54 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,54 unequal: No Solution No 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: 54:[49, 29], Operations: ['66-17=49', '26+3=29'] Exploring Operation: 49+29=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 49*29=1421, Resulting Numbers: [1421] 1421,54 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,54 unequal: No Solution No 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: 54:[49, 23], Operations: ['66-17=49', '26-3=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,54 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,54 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: 54:[26, 17, 63], Operations: ['66-3=63'] Exploring Operation: 26+17=43, Resulting Numbers: [63, 43] Generated Node #0,3,0: 54:[63, 43] Operation: 26+17=43 Exploring Operation: 63-26=37, Resulting Numbers: [17, 37] Generated Node #0,3,1: 54:[17, 37] Operation: 63-26=37 Exploring Operation: 26-17=9, Resulting Numbers: [63, 9] Generated Node #0,3,2: 54:[63, 9] Operation: 26-17=9 Exploring Operation: 63-17=46, Resulting Numbers: [26, 46] Generated Node #0,3,3: 54:[26, 46] Operation: 63-17=46 Moving to Node #0,3,2 Current State: 54:[63, 9], Operations: ['66-3=63', '26-17=9'] Exploring Operation: 63*9=567, Resulting Numbers: [567] 567,54 unequal: No Solution Exploring Operation: 63/9=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 63-9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[26, 66, 3, 17], Operations: [] Exploring Operation: 66-3=63, Resulting Numbers: [26, 17, 63] Generated Node #0,3: 54:[26, 17, 63] Operation: 66-3=63 Moving to Node #0,3 Current State: 54:[26, 17, 63], Operations: ['66-3=63'] Exploring Operation: 26-17=9, Resulting Numbers: [63, 9] Generated Node #0,3,2: 54:[63, 9] Operation: 26-17=9 Moving to Node #0,3,2 Current State: 54:[63, 9], Operations: ['66-3=63', '26-17=9'] Exploring Operation: 63-9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.958333
hs_4
sum_heuristic
[ 41, 64, 52, 97 ]
68
[ "64-41=23", "97-52=45", "23+45=68" ]
Current State: 68:[41, 64, 52, 97], Operations: [] Exploring Operation: 64-41=23, Resulting Numbers: [52, 97, 23] Generated Node #2: [52, 97, 23] from Operation: 64-41=23 Current State: 68:[52, 97, 23], Operations: ['64-41=23'] Exploring Operation: 97-52=45, Resulting Numbers: [23, 45] Generated Node #3: [23, 45] from Operation: 97-52=45 Current State: 68:[23, 45], Operations: ['64-41=23', '97-52=45'] Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[41, 64, 52, 97], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [41, 52, 33] Generated Node #0,0: 68:[41, 52, 33] Operation: 97-64=33 Exploring Operation: 97-52=45, Resulting Numbers: [41, 64, 45] Generated Node #0,1: 68:[41, 64, 45] Operation: 97-52=45 Moving to Node #0,1 Current State: 68:[41, 64, 45], Operations: ['97-52=45'] Exploring Operation: 45-41=4, Resulting Numbers: [64, 4] Generated Node #0,1,0: 68:[64, 4] Operation: 45-41=4 Exploring Operation: 64-45=19, Resulting Numbers: [41, 19] Generated Node #0,1,1: 68:[41, 19] Operation: 64-45=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 68:[64, 4], Operations: ['97-52=45', '45-41=4'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,68 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[41, 64, 52, 97], Operations: [] Exploring Operation: 97-52=45, Resulting Numbers: [41, 64, 45] Generated Node #0,1: 68:[41, 64, 45] Operation: 97-52=45 Moving to Node #0,1 Current State: 68:[41, 64, 45], Operations: ['97-52=45'] Exploring Operation: 45-41=4, Resulting Numbers: [64, 4] Generated Node #0,1,0: 68:[64, 4] Operation: 45-41=4 Moving to Node #0,1,0 Current State: 68:[64, 4], Operations: ['97-52=45', '45-41=4'] Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 59, 96, 2, 41 ]
92
[ "59+41=100", "96*2=192", "192-100=92" ]
Current State: 92:[59, 96, 2, 41], Operations: [] Exploring Operation: 59+41=100, Resulting Numbers: [96, 2, 100] Generated Node #2: [96, 2, 100] from Operation: 59+41=100 Current State: 92:[96, 2, 100], Operations: ['59+41=100'] Exploring Operation: 96*2=192, Resulting Numbers: [100, 192] Generated Node #3: [100, 192] from Operation: 96*2=192 Current State: 92:[100, 192], Operations: ['59+41=100', '96*2=192'] Exploring Operation: 192-100=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[59, 96, 2, 41], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [96, 2, 18] Generated Node #0,0: 92:[96, 2, 18] Operation: 59-41=18 Exploring Operation: 59+41=100, Resulting Numbers: [96, 2, 100] Generated Node #0,1: 92:[96, 2, 100] Operation: 59+41=100 Moving to Node #0,0 Current State: 92:[96, 2, 18], Operations: ['59-41=18'] Exploring Operation: 96-2=94, Resulting Numbers: [18, 94] Generated Node #0,0,0: 92:[18, 94] Operation: 96-2=94 Exploring Operation: 96/2=48, Resulting Numbers: [18, 48] Generated Node #0,0,1: 92:[18, 48] Operation: 96/2=48 Moving to Node #0,1 Current State: 92:[96, 2, 100], Operations: ['59+41=100'] Exploring Operation: 100-96=4, Resulting Numbers: [2, 4] Generated Node #0,1,0: 92:[2, 4] Operation: 100-96=4 Exploring Operation: 100/2=50, Resulting Numbers: [96, 50] Generated Node #0,1,1: 92:[96, 50] Operation: 100/2=50 Moving to Node #0,1,0 Current State: 92:[2, 4], Operations: ['59+41=100', '100-96=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[18, 94], Operations: ['59-41=18', '96-2=94'] Exploring Operation: 18+94=112, Resulting Numbers: [112] 112,92 unequal: No Solution Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[18, 48], Operations: ['59-41=18', '96/2=48'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,92 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[96, 50], Operations: ['59+41=100', '100/2=50'] Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 96+50=146, Resulting Numbers: [146] 146,92 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 27, 32, 3, 78 ]
96
[ "27*3=81", "81-78=3", "32*3=96" ]
Current State: 96:[27, 32, 3, 78], Operations: [] Exploring Operation: 27*3=81, Resulting Numbers: [32, 78, 81] Generated Node #2: [32, 78, 81] from Operation: 27*3=81 Current State: 96:[32, 78, 81], Operations: ['27*3=81'] Exploring Operation: 81-78=3, Resulting Numbers: [32, 3] Generated Node #3: [32, 3] from Operation: 81-78=3 Current State: 96:[32, 3], Operations: ['27*3=81', '81-78=3'] Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[27, 32, 3, 78], Operations: [] Exploring Operation: 78-27=51, Resulting Numbers: [32, 3, 51] Generated Node #0,0: 96:[32, 3, 51] Operation: 78-27=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[32, 3, 51], Operations: ['78-27=51'] Exploring Operation: 51-3=48, Resulting Numbers: [32, 48] Generated Node #0,0,0: 96:[32, 48] Operation: 51-3=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[32, 48], Operations: ['78-27=51', '51-3=48'] Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 3, 84, 74, 78 ]
12
[ "74-3=71", "78-71=7", "84/7=12" ]
Current State: 12:[3, 84, 74, 78], Operations: [] Exploring Operation: 74-3=71, Resulting Numbers: [84, 78, 71] Generated Node #2: [84, 78, 71] from Operation: 74-3=71 Current State: 12:[84, 78, 71], Operations: ['74-3=71'] Exploring Operation: 78-71=7, Resulting Numbers: [84, 7] Generated Node #3: [84, 7] from Operation: 78-71=7 Current State: 12:[84, 7], Operations: ['74-3=71', '78-71=7'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[3, 84, 74, 78], Operations: [] Exploring Operation: 84-74=10, Resulting Numbers: [3, 78, 10] Generated Node #0,0: 12:[3, 78, 10] Operation: 84-74=10 Exploring Operation: 84-78=6, Resulting Numbers: [3, 74, 6] Generated Node #0,1: 12:[3, 74, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[3, 74, 6], Operations: ['84-78=6'] Exploring Operation: 74-6=68, Resulting Numbers: [3, 68] Generated Node #0,1,0: 12:[3, 68] Operation: 74-6=68 Exploring Operation: 74-3=71, Resulting Numbers: [6, 71] Generated Node #0,1,1: 12:[6, 71] Operation: 74-3=71 Moving to Node #0,1,0 Current State: 12:[3, 68], Operations: ['84-78=6', '74-6=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,12 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[6, 71], Operations: ['84-78=6', '74-3=71'] Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[3, 78, 10], Operations: ['84-74=10'] Exploring Operation: 78/3=26, Resulting Numbers: [10, 26] Generated Node #0,0,0: 12:[10, 26] Operation: 78/3=26 Exploring Operation: 78-10=68, Resulting Numbers: [3, 68] Generated Node #0,0,1: 12:[3, 68] Operation: 78-10=68 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[10, 26], Operations: ['84-74=10', '78/3=26'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 10+26=36, Resulting Numbers: [36] 36,12 unequal: No Solution No 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: 12:[3, 68], Operations: ['84-74=10', '78-10=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,12 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 53, 99, 4, 77 ]
97
[ "99+77=176", "176/4=44", "53+44=97" ]
Current State: 97:[53, 99, 4, 77], Operations: [] Exploring Operation: 99+77=176, Resulting Numbers: [53, 4, 176] Generated Node #2: [53, 4, 176] from Operation: 99+77=176 Current State: 97:[53, 4, 176], Operations: ['99+77=176'] Exploring Operation: 176/4=44, Resulting Numbers: [53, 44] Generated Node #3: [53, 44] from Operation: 176/4=44 Current State: 97:[53, 44], Operations: ['99+77=176', '176/4=44'] Exploring Operation: 53+44=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[53, 99, 4, 77], Operations: [] Exploring Operation: 53-4=49, Resulting Numbers: [99, 77, 49] Generated Node #0,0: 97:[99, 77, 49] Operation: 53-4=49 Exploring Operation: 53+4=57, Resulting Numbers: [99, 77, 57] Generated Node #0,1: 97:[99, 77, 57] Operation: 53+4=57 Exploring Operation: 4+77=81, Resulting Numbers: [53, 99, 81] Generated Node #0,2: 97:[53, 99, 81] Operation: 4+77=81 Exploring Operation: 99-4=95, Resulting Numbers: [53, 77, 95] Generated Node #0,3: 97:[53, 77, 95] Operation: 99-4=95 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[99, 77, 57], Operations: ['53+4=57'] Exploring Operation: 77-57=20, Resulting Numbers: [99, 20] Generated Node #0,1,0: 97:[99, 20] Operation: 77-57=20 Exploring Operation: 99-57=42, Resulting Numbers: [77, 42] Generated Node #0,1,1: 97:[77, 42] Operation: 99-57=42 Exploring Operation: 99+57=156, Resulting Numbers: [77, 156] Generated Node #0,1,2: 97:[77, 156] Operation: 99+57=156 Exploring Operation: 77+57=134, Resulting Numbers: [99, 134] Generated Node #0,1,3: 97:[99, 134] Operation: 77+57=134 Moving to Node #0,1,3 Current State: 97:[99, 134], Operations: ['53+4=57', '77+57=134'] Exploring Operation: 99+134=233, Resulting Numbers: [233] 233,97 unequal: No Solution Exploring Operation: 134-99=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 99*134=13266, Resulting Numbers: [13266] 13266,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[77, 42], Operations: ['53+4=57', '99-57=42'] Exploring Operation: 77+42=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 77*42=3234, Resulting Numbers: [3234] 3234,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[77, 156], Operations: ['53+4=57', '99+57=156'] Exploring Operation: 77+156=233, Resulting Numbers: [233] 233,97 unequal: No Solution Exploring Operation: 156-77=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 77*156=12012, Resulting Numbers: [12012] 12012,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[99, 20], Operations: ['53+4=57', '77-57=20'] Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 99+20=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 99*20=1980, Resulting Numbers: [1980] 1980,97 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 Current State: 97:[53, 99, 81], Operations: ['4+77=81'] Exploring Operation: 99-53=46, Resulting Numbers: [81, 46] Generated Node #0,2,0: 97:[81, 46] Operation: 99-53=46 Exploring Operation: 53+81=134, Resulting Numbers: [99, 134] Generated Node #0,2,1: 97:[99, 134] Operation: 53+81=134 Exploring Operation: 81-53=28, Resulting Numbers: [99, 28] Generated Node #0,2,2: 97:[99, 28] Operation: 81-53=28 Exploring Operation: 53+99=152, Resulting Numbers: [81, 152] Generated Node #0,2,3: 97:[81, 152] Operation: 53+99=152 Moving to Node #0,2,1 Current State: 97:[99, 134], Operations: ['4+77=81', '53+81=134'] Exploring Operation: 99*134=13266, Resulting Numbers: [13266] 13266,97 unequal: No Solution Exploring Operation: 134-99=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 99+134=233, Resulting Numbers: [233] 233,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[81, 46], Operations: ['4+77=81', '99-53=46'] Exploring Operation: 81*46=3726, Resulting Numbers: [3726] 3726,97 unequal: No Solution Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 81+46=127, Resulting Numbers: [127] 127,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[81, 152], Operations: ['4+77=81', '53+99=152'] Exploring Operation: 152-81=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 81*152=12312, Resulting Numbers: [12312] 12312,97 unequal: No Solution Exploring Operation: 81+152=233, Resulting Numbers: [233] 233,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[99, 28], Operations: ['4+77=81', '81-53=28'] Exploring Operation: 99*28=2772, Resulting Numbers: [2772] 2772,97 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 99+28=127, Resulting Numbers: [127] 127,97 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 #0,3 Current State: 97:[53, 77, 95], Operations: ['99-4=95'] Exploring Operation: 53+95=148, Resulting Numbers: [77, 148] Generated Node #0,3,0: 97:[77, 148] Operation: 53+95=148 Exploring Operation: 53+77=130, Resulting Numbers: [95, 130] Generated Node #0,3,1: 97:[95, 130] Operation: 53+77=130 Exploring Operation: 77-53=24, Resulting Numbers: [95, 24] Generated Node #0,3,2: 97:[95, 24] Operation: 77-53=24 Exploring Operation: 95-53=42, Resulting Numbers: [77, 42] Generated Node #0,3,3: 97:[77, 42] Operation: 95-53=42 Moving to Node #0,3,1 Current State: 97:[95, 130], Operations: ['99-4=95', '53+77=130'] Exploring Operation: 130-95=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 95+130=225, Resulting Numbers: [225] 225,97 unequal: No Solution Exploring Operation: 95*130=12350, Resulting Numbers: [12350] 12350,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[77, 148], Operations: ['99-4=95', '53+95=148'] Exploring Operation: 148-77=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 77*148=11396, Resulting Numbers: [11396] 11396,97 unequal: No Solution Exploring Operation: 77+148=225, Resulting Numbers: [225] 225,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[77, 42], Operations: ['99-4=95', '95-53=42'] Exploring Operation: 77+42=119, Resulting Numbers: [119] 119,97 unequal: No Solution Exploring Operation: 77*42=3234, Resulting Numbers: [3234] 3234,97 unequal: No Solution Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[95, 24], Operations: ['99-4=95', '77-53=24'] Exploring Operation: 95-24=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 95*24=2280, Resulting Numbers: [2280] 2280,97 unequal: No Solution Exploring Operation: 95+24=119, Resulting Numbers: [119] 119,97 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 Current State: 97:[99, 77, 49], Operations: ['53-4=49'] Exploring Operation: 99-49=50, Resulting Numbers: [77, 50] Generated Node #0,0,0: 97:[77, 50] Operation: 99-49=50 Exploring Operation: 77+49=126, Resulting Numbers: [99, 126] Generated Node #0,0,1: 97:[99, 126] Operation: 77+49=126 Exploring Operation: 77-49=28, Resulting Numbers: [99, 28] Generated Node #0,0,2: 97:[99, 28] Operation: 77-49=28 Exploring Operation: 99+49=148, Resulting Numbers: [77, 148] Generated Node #0,0,3: 97:[77, 148] Operation: 99+49=148 Moving to Node #0,0,1 Current State: 97:[99, 126], Operations: ['53-4=49', '77+49=126'] Exploring Operation: 99+126=225, Resulting Numbers: [225] 225,97 unequal: No Solution Exploring Operation: 99*126=12474, Resulting Numbers: [12474] 12474,97 unequal: No Solution Exploring Operation: 126-99=27, Resulting Numbers: [27] 27,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[77, 50], Operations: ['53-4=49', '99-49=50'] Exploring Operation: 77-50=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 77*50=3850, Resulting Numbers: [3850] 3850,97 unequal: No Solution Exploring Operation: 77+50=127, Resulting Numbers: [127] 127,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[77, 148], Operations: ['53-4=49', '99+49=148'] Exploring Operation: 148-77=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 77*148=11396, Resulting Numbers: [11396] 11396,97 unequal: No Solution Exploring Operation: 77+148=225, Resulting Numbers: [225] 225,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[99, 28], Operations: ['53-4=49', '77-49=28'] Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,97 unequal: No Solution Exploring Operation: 99+28=127, Resulting Numbers: [127] 127,97 unequal: No Solution Exploring Operation: 99*28=2772, Resulting Numbers: [2772] 2772,97 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
[ 31, 33, 60, 43 ]
47
[ "31+33=64", "60-43=17", "64-17=47" ]
Current State: 47:[31, 33, 60, 43], Operations: [] Exploring Operation: 31+33=64, Resulting Numbers: [60, 43, 64] Generated Node #2: [60, 43, 64] from Operation: 31+33=64 Current State: 47:[60, 43, 64], Operations: ['31+33=64'] Exploring Operation: 60-43=17, Resulting Numbers: [64, 17] Generated Node #3: [64, 17] from Operation: 60-43=17 Current State: 47:[64, 17], Operations: ['31+33=64', '60-43=17'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[31, 33, 60, 43], Operations: [] Exploring Operation: 60-31=29, Resulting Numbers: [33, 43, 29] Generated Node #0,0: 47:[33, 43, 29] Operation: 60-31=29 Exploring Operation: 31+33=64, Resulting Numbers: [60, 43, 64] Generated Node #0,1: 47:[60, 43, 64] Operation: 31+33=64 Exploring Operation: 60-33=27, Resulting Numbers: [31, 43, 27] Generated Node #0,2: 47:[31, 43, 27] Operation: 60-33=27 Exploring Operation: 33+43=76, Resulting Numbers: [31, 60, 76] Generated Node #0,3: 47:[31, 60, 76] Operation: 33+43=76 Exploring Operation: 31+43=74, Resulting Numbers: [33, 60, 74] Generated Node #0,4: 47:[33, 60, 74] Operation: 31+43=74 Moving to Node #0,1 Current State: 47:[60, 43, 64], Operations: ['31+33=64'] Exploring Operation: 60+43=103, Resulting Numbers: [64, 103] Generated Node #0,1,0: 47:[64, 103] Operation: 60+43=103 Exploring Operation: 43+64=107, Resulting Numbers: [60, 107] Generated Node #0,1,1: 47:[60, 107] Operation: 43+64=107 Exploring Operation: 64-60=4, Resulting Numbers: [43, 4] Generated Node #0,1,2: 47:[43, 4] Operation: 64-60=4 Exploring Operation: 60-43=17, Resulting Numbers: [64, 17] Generated Node #0,1,3: 47:[64, 17] Operation: 60-43=17 Exploring Operation: 64-43=21, Resulting Numbers: [60, 21] Generated Node #0,1,4: 47:[60, 21] Operation: 64-43=21 Moving to Node #0,0 Current State: 47:[33, 43, 29], Operations: ['60-31=29'] Exploring Operation: 43+29=72, Resulting Numbers: [33, 72] Generated Node #0,0,0: 47:[33, 72] Operation: 43+29=72 Exploring Operation: 33+29=62, Resulting Numbers: [43, 62] Generated Node #0,0,1: 47:[43, 62] Operation: 33+29=62 Exploring Operation: 33-29=4, Resulting Numbers: [43, 4] Generated Node #0,0,2: 47:[43, 4] Operation: 33-29=4 Exploring Operation: 43-29=14, Resulting Numbers: [33, 14] Generated Node #0,0,3: 47:[33, 14] Operation: 43-29=14 Exploring Operation: 33+43=76, Resulting Numbers: [29, 76] Generated Node #0,0,4: 47:[29, 76] Operation: 33+43=76 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[43, 62], Operations: ['60-31=29', '33+29=62'] Exploring Operation: 43+62=105, Resulting Numbers: [105] 105,47 unequal: No Solution Exploring Operation: 43*62=2666, Resulting Numbers: [2666] 2666,47 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[33, 72], Operations: ['60-31=29', '43+29=72'] Exploring Operation: 33*72=2376, Resulting Numbers: [2376] 2376,47 unequal: No Solution Exploring Operation: 33+72=105, Resulting Numbers: [105] 105,47 unequal: No Solution Exploring Operation: 72-33=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[43, 4], Operations: ['60-31=29', '33-29=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[31, 33, 60, 43], Operations: [] Exploring Operation: 60-31=29, Resulting Numbers: [33, 43, 29] Generated Node #0,0: 47:[33, 43, 29] Operation: 60-31=29 Moving to Node #0,0 Current State: 47:[33, 43, 29], Operations: ['60-31=29'] Exploring Operation: 33-29=4, Resulting Numbers: [43, 4] Generated Node #0,0,2: 47:[43, 4] Operation: 33-29=4 Moving to Node #0,0,2 Current State: 47:[43, 4], Operations: ['60-31=29', '33-29=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 46, 36, 34, 9 ]
74
[ "46-9=37", "36-34=2", "37*2=74" ]
Current State: 74:[46, 36, 34, 9], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [36, 34, 37] Generated Node #2: [36, 34, 37] from Operation: 46-9=37 Current State: 74:[36, 34, 37], Operations: ['46-9=37'] Exploring Operation: 36-34=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 36-34=2 Current State: 74:[37, 2], Operations: ['46-9=37', '36-34=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[46, 36, 34, 9], Operations: [] Exploring Operation: 46+34=80, Resulting Numbers: [36, 9, 80] Generated Node #0,0: 74:[36, 9, 80] Operation: 46+34=80 Exploring Operation: 46-9=37, Resulting Numbers: [36, 34, 37] Generated Node #0,1: 74:[36, 34, 37] Operation: 46-9=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[36, 34, 37], Operations: ['46-9=37'] Exploring Operation: 37-34=3, Resulting Numbers: [36, 3] Generated Node #0,1,0: 74:[36, 3] Operation: 37-34=3 Exploring Operation: 36-34=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 74:[37, 2] Operation: 36-34=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[37, 2], Operations: ['46-9=37', '36-34=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[46, 36, 34, 9], Operations: [] Exploring Operation: 46-9=37, Resulting Numbers: [36, 34, 37] Generated Node #0,1: 74:[36, 34, 37] Operation: 46-9=37 Moving to Node #0,1 Current State: 74:[36, 34, 37], Operations: ['46-9=37'] Exploring Operation: 36-34=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 74:[37, 2] Operation: 36-34=2 Moving to Node #0,1,1 Current State: 74:[37, 2], Operations: ['46-9=37', '36-34=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 97, 1, 64, 58 ]
26
[ "97-1=96", "64+58=122", "122-96=26" ]
Current State: 26:[97, 1, 64, 58], Operations: [] Exploring Operation: 97-1=96, Resulting Numbers: [64, 58, 96] Generated Node #2: [64, 58, 96] from Operation: 97-1=96 Current State: 26:[64, 58, 96], Operations: ['97-1=96'] Exploring Operation: 64+58=122, Resulting Numbers: [96, 122] Generated Node #3: [96, 122] from Operation: 64+58=122 Current State: 26:[96, 122], Operations: ['97-1=96', '64+58=122'] Exploring Operation: 122-96=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[97, 1, 64, 58], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [1, 58, 33] Generated Node #0,0: 26:[1, 58, 33] Operation: 97-64=33 Exploring Operation: 97-58=39, Resulting Numbers: [1, 64, 39] Generated Node #0,1: 26:[1, 64, 39] Operation: 97-58=39 Exploring Operation: 64-58=6, Resulting Numbers: [97, 1, 6] Generated Node #0,2: 26:[97, 1, 6] Operation: 64-58=6 Exploring Operation: 64-1=63, Resulting Numbers: [97, 58, 63] Generated Node #0,3: 26:[97, 58, 63] Operation: 64-1=63 Exploring Operation: 97-1=96, Resulting Numbers: [64, 58, 96] Generated Node #0,4: 26:[64, 58, 96] Operation: 97-1=96 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[1, 58, 33], Operations: ['97-64=33'] Exploring Operation: 1*58=58, Resulting Numbers: [33, 58] Generated Node #0,0,0: 26:[33, 58] Operation: 1*58=58 Exploring Operation: 58/1=58, Resulting Numbers: [33, 58] Generated Node #0,0,1: 26:[33, 58] Operation: 58/1=58 Exploring Operation: 58-1=57, Resulting Numbers: [33, 57] Generated Node #0,0,2: 26:[33, 57] Operation: 58-1=57 Exploring Operation: 58-33=25, Resulting Numbers: [1, 25] Generated Node #0,0,3: 26:[1, 25] Operation: 58-33=25 Exploring Operation: 33-1=32, Resulting Numbers: [58, 32] Generated Node #0,0,4: 26:[58, 32] Operation: 33-1=32 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 26:[1, 25], Operations: ['97-64=33', '58-33=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[97, 1, 64, 58], Operations: [] Exploring Operation: 97-64=33, Resulting Numbers: [1, 58, 33] Generated Node #0,0: 26:[1, 58, 33] Operation: 97-64=33 Moving to Node #0,0 Current State: 26:[1, 58, 33], Operations: ['97-64=33'] Exploring Operation: 58-33=25, Resulting Numbers: [1, 25] Generated Node #0,0,3: 26:[1, 25] Operation: 58-33=25 Moving to Node #0,0,3 Current State: 26:[1, 25], Operations: ['97-64=33', '58-33=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 54, 54, 91, 71 ]
18
[ "54*54=2916", "91+71=162", "2916/162=18" ]
Current State: 18:[54, 54, 91, 71], Operations: [] Exploring Operation: 54*54=2916, Resulting Numbers: [91, 71, 2916] Generated Node #2: [91, 71, 2916] from Operation: 54*54=2916 Current State: 18:[91, 71, 2916], Operations: ['54*54=2916'] Exploring Operation: 91+71=162, Resulting Numbers: [2916, 162] Generated Node #3: [2916, 162] from Operation: 91+71=162 Current State: 18:[2916, 162], Operations: ['54*54=2916', '91+71=162'] Exploring Operation: 2916/162=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[54, 54, 91, 71], Operations: [] Exploring Operation: 91-54=37, Resulting Numbers: [54, 71, 37] Generated Node #0,0: 18:[54, 71, 37] Operation: 91-54=37 Exploring Operation: 91-71=20, Resulting Numbers: [54, 54, 20] Generated Node #0,1: 18:[54, 54, 20] Operation: 91-71=20 Exploring Operation: 91-54=37, Resulting Numbers: [54, 71, 37] Generated Node #0,2: 18:[54, 71, 37] Operation: 91-54=37 Moving to Node #0,1 Current State: 18:[54, 54, 20], Operations: ['91-71=20'] Exploring Operation: 54/54=1, Resulting Numbers: [20, 1] Generated Node #0,1,0: 18:[20, 1] Operation: 54/54=1 Exploring Operation: 54-20=34, Resulting Numbers: [54, 34] Generated Node #0,1,1: 18:[54, 34] Operation: 54-20=34 Exploring Operation: 54-54=0, Resulting Numbers: [20, 0] Generated Node #0,1,2: 18:[20, 0] Operation: 54-54=0 Moving to Node #0,0 Current State: 18:[54, 71, 37], Operations: ['91-54=37'] Exploring Operation: 71-54=17, Resulting Numbers: [37, 17] Generated Node #0,0,0: 18:[37, 17] Operation: 71-54=17 Exploring Operation: 54-37=17, Resulting Numbers: [71, 17] Generated Node #0,0,1: 18:[71, 17] Operation: 54-37=17 Exploring Operation: 71-37=34, Resulting Numbers: [54, 34] Generated Node #0,0,2: 18:[54, 34] Operation: 71-37=34 Moving to Node #0,2 Current State: 18:[54, 71, 37], Operations: ['91-54=37'] Exploring Operation: 71-37=34, Resulting Numbers: [54, 34] Generated Node #0,2,0: 18:[54, 34] Operation: 71-37=34 Exploring Operation: 54-37=17, Resulting Numbers: [71, 17] Generated Node #0,2,1: 18:[71, 17] Operation: 54-37=17 Exploring Operation: 71-54=17, Resulting Numbers: [37, 17] Generated Node #0,2,2: 18:[37, 17] Operation: 71-54=17 Moving to Node #0,1,0 Current State: 18:[20, 1], Operations: ['91-71=20', '54/54=1'] Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[20, 0], Operations: ['91-71=20', '54-54=0'] Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[37, 17], Operations: ['91-54=37', '71-54=17'] Exploring Operation: 37*17=629, Resulting Numbers: [629] 629,18 unequal: No Solution Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 37+17=54, Resulting Numbers: [54] 54,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[37, 17], Operations: ['91-54=37', '71-54=17'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 37+17=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 37*17=629, Resulting Numbers: [629] 629,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[54, 34], Operations: ['91-71=20', '54-20=34'] Exploring Operation: 54*34=1836, Resulting Numbers: [1836] 1836,18 unequal: No Solution Exploring Operation: 54+34=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[54, 34], Operations: ['91-54=37', '71-37=34'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 54*34=1836, Resulting Numbers: [1836] 1836,18 unequal: No Solution Exploring Operation: 54+34=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[54, 34], Operations: ['91-54=37', '71-37=34'] Exploring Operation: 54*34=1836, Resulting Numbers: [1836] 1836,18 unequal: No Solution Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 54+34=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[71, 17], Operations: ['91-54=37', '54-37=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 71+17=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 71*17=1207, Resulting Numbers: [1207] 1207,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[71, 17], Operations: ['91-54=37', '54-37=17'] Exploring Operation: 71-17=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 71*17=1207, Resulting Numbers: [1207] 1207,18 unequal: No Solution Exploring Operation: 71+17=88, Resulting Numbers: [88] 88,18 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 4, 36, 71, 56 ]
93
[ "56/4=14", "36+71=107", "107-14=93" ]
Current State: 93:[4, 36, 71, 56], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [36, 71, 14] Generated Node #2: [36, 71, 14] from Operation: 56/4=14 Current State: 93:[36, 71, 14], Operations: ['56/4=14'] Exploring Operation: 36+71=107, Resulting Numbers: [14, 107] Generated Node #3: [14, 107] from Operation: 36+71=107 Current State: 93:[14, 107], Operations: ['56/4=14', '36+71=107'] Exploring Operation: 107-14=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[4, 36, 71, 56], Operations: [] Exploring Operation: 36+56=92, Resulting Numbers: [4, 71, 92] Generated Node #0,0: 93:[4, 71, 92] Operation: 36+56=92 Exploring Operation: 71-36=35, Resulting Numbers: [4, 56, 35] Generated Node #0,1: 93:[4, 56, 35] Operation: 71-36=35 Exploring Operation: 71-56=15, Resulting Numbers: [4, 36, 15] Generated Node #0,2: 93:[4, 36, 15] Operation: 71-56=15 Exploring Operation: 56-36=20, Resulting Numbers: [4, 71, 20] Generated Node #0,3: 93:[4, 71, 20] Operation: 56-36=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[4, 36, 15], Operations: ['71-56=15'] Exploring Operation: 15-4=11, Resulting Numbers: [36, 11] Generated Node #0,2,0: 93:[36, 11] Operation: 15-4=11 Exploring Operation: 36-15=21, Resulting Numbers: [4, 21] Generated Node #0,2,1: 93:[4, 21] Operation: 36-15=21 Exploring Operation: 4+15=19, Resulting Numbers: [36, 19] Generated Node #0,2,2: 93:[36, 19] Operation: 4+15=19 Exploring Operation: 36-4=32, Resulting Numbers: [15, 32] Generated Node #0,2,3: 93:[15, 32] Operation: 36-4=32 Moving to Node #0,2,1 Current State: 93:[4, 21], Operations: ['71-56=15', '36-15=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,93 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,93 unequal: No Solution Moving to Node #0,2,3 Current State: 93:[15, 32], Operations: ['71-56=15', '36-4=32'] Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,93 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,93 unequal: No Solution Moving to Node #0,2,0 Current State: 93:[36, 11], Operations: ['71-56=15', '15-4=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,93 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,93 unequal: No Solution Moving to Node #0,2,2 Current State: 93:[36, 19], Operations: ['71-56=15', '4+15=19'] Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,93 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,93 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[4, 71, 92], Operations: ['36+56=92'] Exploring Operation: 4+71=75, Resulting Numbers: [92, 75] Generated Node #0,0,0: 93:[92, 75] Operation: 4+71=75 Exploring Operation: 71-4=67, Resulting Numbers: [92, 67] Generated Node #0,0,1: 93:[92, 67] Operation: 71-4=67 Exploring Operation: 4+92=96, Resulting Numbers: [71, 96] Generated Node #0,0,2: 93:[71, 96] Operation: 4+92=96 Exploring Operation: 92-71=21, Resulting Numbers: [4, 21] Generated Node #0,0,3: 93:[4, 21] Operation: 92-71=21 Moving to Node #0,0,3 Current State: 93:[4, 21], Operations: ['36+56=92', '92-71=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,93 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[92, 75], Operations: ['36+56=92', '4+71=75'] Exploring Operation: 92*75=6900, Resulting Numbers: [6900] 6900,93 unequal: No Solution Exploring Operation: 92+75=167, Resulting Numbers: [167] 167,93 unequal: No Solution Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[71, 96], Operations: ['36+56=92', '4+92=96'] Exploring Operation: 71+96=167, Resulting Numbers: [167] 167,93 unequal: No Solution Exploring Operation: 96-71=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 71*96=6816, Resulting Numbers: [6816] 6816,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[92, 67], Operations: ['36+56=92', '71-4=67'] Exploring Operation: 92*67=6164, Resulting Numbers: [6164] 6164,93 unequal: No Solution Exploring Operation: 92+67=159, Resulting Numbers: [159] 159,93 unequal: No Solution Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[4, 56, 35], Operations: ['71-36=35'] Exploring Operation: 56+35=91, Resulting Numbers: [4, 91] Generated Node #0,1,0: 93:[4, 91] Operation: 56+35=91 Exploring Operation: 56/4=14, Resulting Numbers: [35, 14] Generated Node #0,1,1: 93:[35, 14] Operation: 56/4=14 Exploring Operation: 56-4=52, Resulting Numbers: [35, 52] Generated Node #0,1,2: 93:[35, 52] Operation: 56-4=52 Exploring Operation: 56-35=21, Resulting Numbers: [4, 21] Generated Node #0,1,3: 93:[4, 21] Operation: 56-35=21 Moving to Node #0,1,0 Current State: 93:[4, 91], Operations: ['71-36=35', '56+35=91'] Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 4*91=364, Resulting Numbers: [364] 364,93 unequal: No Solution Exploring Operation: 4+91=95, Resulting Numbers: [95] 95,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[4, 21], Operations: ['71-36=35', '56-35=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,93 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,93 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[35, 14], Operations: ['71-36=35', '56/4=14'] Exploring Operation: 35*14=490, Resulting Numbers: [490] 490,93 unequal: No Solution Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,93 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[35, 52], Operations: ['71-36=35', '56-4=52'] Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,93 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 93:[4, 71, 20], Operations: ['56-36=20'] Exploring Operation: 71+20=91, Resulting Numbers: [4, 91] Generated Node #0,3,0: 93:[4, 91] Operation: 71+20=91 Exploring Operation: 71-20=51, Resulting Numbers: [4, 51] Generated Node #0,3,1: 93:[4, 51] Operation: 71-20=51 Exploring Operation: 4+71=75, Resulting Numbers: [20, 75] Generated Node #0,3,2: 93:[20, 75] Operation: 4+71=75 Exploring Operation: 20/4=5, Resulting Numbers: [71, 5] Generated Node #0,3,3: 93:[71, 5] Operation: 20/4=5 Moving to Node #0,3,0 Current State: 93:[4, 91], Operations: ['56-36=20', '71+20=91'] Exploring Operation: 4*91=364, Resulting Numbers: [364] 364,93 unequal: No Solution Exploring Operation: 4+91=95, Resulting Numbers: [95] 95,93 unequal: No Solution Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[4, 51], Operations: ['56-36=20', '71-20=51'] Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,93 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,93 unequal: No Solution Moving to Node #0,3,3 Current State: 93:[71, 5], Operations: ['56-36=20', '20/4=5'] Exploring Operation: 71*5=355, Resulting Numbers: [355] 355,93 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,93 unequal: No Solution Exploring Operation: 71+5=76, Resulting Numbers: [76] 76,93 unequal: No Solution Moving to Node #0,3,2 Current State: 93:[20, 75], Operations: ['56-36=20', '4+71=75'] Exploring Operation: 20*75=1500, Resulting Numbers: [1500] 1500,93 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 20+75=95, Resulting Numbers: [95] 95,93 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
[ 12, 17, 56, 16 ]
67
[ "17-12=5", "56+16=72", "72-5=67" ]
Current State: 67:[12, 17, 56, 16], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [56, 16, 5] Generated Node #2: [56, 16, 5] from Operation: 17-12=5 Current State: 67:[56, 16, 5], Operations: ['17-12=5'] Exploring Operation: 56+16=72, Resulting Numbers: [5, 72] Generated Node #3: [5, 72] from Operation: 56+16=72 Current State: 67:[5, 72], Operations: ['17-12=5', '56+16=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[12, 17, 56, 16], Operations: [] Exploring Operation: 12+16=28, Resulting Numbers: [17, 56, 28] Generated Node #0,0: 67:[17, 56, 28] Operation: 12+16=28 Exploring Operation: 12+17=29, Resulting Numbers: [56, 16, 29] Generated Node #0,1: 67:[56, 16, 29] Operation: 12+17=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[17, 56, 28], Operations: ['12+16=28'] Exploring Operation: 17+28=45, Resulting Numbers: [56, 45] Generated Node #0,0,0: 67:[56, 45] Operation: 17+28=45 Exploring Operation: 17+56=73, Resulting Numbers: [28, 73] Generated Node #0,0,1: 67:[28, 73] Operation: 17+56=73 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[56, 45], Operations: ['12+16=28', '17+28=45'] Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,67 unequal: No Solution Exploring Operation: 56+45=101, Resulting Numbers: [101] 101,67 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, 73], Operations: ['12+16=28', '17+56=73'] Exploring Operation: 28+73=101, Resulting Numbers: [101] 101,67 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,67 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 #0,1 Current State: 67:[56, 16, 29], Operations: ['12+17=29'] Exploring Operation: 56+16=72, Resulting Numbers: [29, 72] Generated Node #0,1,0: 67:[29, 72] Operation: 56+16=72 Exploring Operation: 16+29=45, Resulting Numbers: [56, 45] Generated Node #0,1,1: 67:[56, 45] Operation: 16+29=45 Moving to Node #0,1,1 Current State: 67:[56, 45], Operations: ['12+17=29', '16+29=45'] Exploring Operation: 56+45=101, Resulting Numbers: [101] 101,67 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[29, 72], Operations: ['12+17=29', '56+16=72'] Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,67 unequal: No Solution Exploring Operation: 29+72=101, Resulting Numbers: [101] 101,67 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
[ 9, 20, 87, 83 ]
35
[ "9*87=783", "783-83=700", "700/20=35" ]
Current State: 35:[9, 20, 87, 83], Operations: [] Exploring Operation: 9*87=783, Resulting Numbers: [20, 83, 783] Generated Node #2: [20, 83, 783] from Operation: 9*87=783 Current State: 35:[20, 83, 783], Operations: ['9*87=783'] Exploring Operation: 783-83=700, Resulting Numbers: [20, 700] Generated Node #3: [20, 700] from Operation: 783-83=700 Current State: 35:[20, 700], Operations: ['9*87=783', '783-83=700'] Exploring Operation: 700/20=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[9, 20, 87, 83], Operations: [] Exploring Operation: 87-83=4, Resulting Numbers: [9, 20, 4] Generated Node #0,0: 35:[9, 20, 4] Operation: 87-83=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[9, 20, 4], Operations: ['87-83=4'] Exploring Operation: 20/4=5, Resulting Numbers: [9, 5] Generated Node #0,0,0: 35:[9, 5] Operation: 20/4=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[9, 5], Operations: ['87-83=4', '20/4=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 60, 80, 48, 18 ]
88
[ "48+18=66", "80*66=5280", "5280/60=88" ]
Current State: 88:[60, 80, 48, 18], Operations: [] Exploring Operation: 48+18=66, Resulting Numbers: [60, 80, 66] Generated Node #2: [60, 80, 66] from Operation: 48+18=66 Current State: 88:[60, 80, 66], Operations: ['48+18=66'] Exploring Operation: 80*66=5280, Resulting Numbers: [60, 5280] Generated Node #3: [60, 5280] from Operation: 80*66=5280 Current State: 88:[60, 5280], Operations: ['48+18=66', '80*66=5280'] Exploring Operation: 5280/60=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[60, 80, 48, 18], Operations: [] Exploring Operation: 80-60=20, Resulting Numbers: [48, 18, 20] Generated Node #0,0: 88:[48, 18, 20] Operation: 80-60=20 Exploring Operation: 60+18=78, Resulting Numbers: [80, 48, 78] Generated Node #0,1: 88:[80, 48, 78] Operation: 60+18=78 Exploring Operation: 60-18=42, Resulting Numbers: [80, 48, 42] Generated Node #0,2: 88:[80, 48, 42] Operation: 60-18=42 Exploring Operation: 60-48=12, Resulting Numbers: [80, 18, 12] Generated Node #0,3: 88:[80, 18, 12] Operation: 60-48=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[48, 18, 20], Operations: ['80-60=20'] Exploring Operation: 20-18=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 88:[48, 2] Operation: 20-18=2 Exploring Operation: 48-20=28, Resulting Numbers: [18, 28] Generated Node #0,0,1: 88:[18, 28] Operation: 48-20=28 Exploring Operation: 18+20=38, Resulting Numbers: [48, 38] Generated Node #0,0,2: 88:[48, 38] Operation: 18+20=38 Exploring Operation: 48-18=30, Resulting Numbers: [20, 30] Generated Node #0,0,3: 88:[20, 30] Operation: 48-18=30 Moving to Node #0,0,0 Current State: 88:[48, 2], Operations: ['80-60=20', '20-18=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[48, 38], Operations: ['80-60=20', '18+20=38'] Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[18, 28], Operations: ['80-60=20', '48-20=28'] Exploring Operation: 18*28=504, Resulting Numbers: [504] 504,88 unequal: No Solution Exploring Operation: 18+28=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[20, 30], Operations: ['80-60=20', '48-18=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,88 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 #0,3 Current State: 88:[80, 18, 12], Operations: ['60-48=12'] Exploring Operation: 18+12=30, Resulting Numbers: [80, 30] Generated Node #0,3,0: 88:[80, 30] Operation: 18+12=30 Exploring Operation: 80+18=98, Resulting Numbers: [12, 98] Generated Node #0,3,1: 88:[12, 98] Operation: 80+18=98 Exploring Operation: 18-12=6, Resulting Numbers: [80, 6] Generated Node #0,3,2: 88:[80, 6] Operation: 18-12=6 Exploring Operation: 80+12=92, Resulting Numbers: [18, 92] Generated Node #0,3,3: 88:[18, 92] Operation: 80+12=92 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[18, 92], Operations: ['60-48=12', '80+12=92'] Exploring Operation: 18+92=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 18*92=1656, Resulting Numbers: [1656] 1656,88 unequal: No Solution Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,88 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:[80, 6], Operations: ['60-48=12', '18-12=6'] Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,88 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 #0,3,1 Current State: 88:[12, 98], Operations: ['60-48=12', '80+18=98'] Exploring Operation: 12+98=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 98-12=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 12*98=1176, Resulting Numbers: [1176] 1176,88 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:[80, 30], Operations: ['60-48=12', '18+12=30'] Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,88 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,88 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 #0,2 Current State: 88:[80, 48, 42], Operations: ['60-18=42'] Exploring Operation: 80-48=32, Resulting Numbers: [42, 32] Generated Node #0,2,0: 88:[42, 32] Operation: 80-48=32 Exploring Operation: 48+42=90, Resulting Numbers: [80, 90] Generated Node #0,2,1: 88:[80, 90] Operation: 48+42=90 Exploring Operation: 80-42=38, Resulting Numbers: [48, 38] Generated Node #0,2,2: 88:[48, 38] Operation: 80-42=38 Exploring Operation: 48-42=6, Resulting Numbers: [80, 6] Generated Node #0,2,3: 88:[80, 6] Operation: 48-42=6 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[80, 90], Operations: ['60-18=42', '48+42=90'] Exploring Operation: 80+90=170, Resulting Numbers: [170] 170,88 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 80*90=7200, Resulting Numbers: [7200] 7200,88 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:[48, 38], Operations: ['60-18=42', '80-42=38'] Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,88 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,88 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:[80, 6], Operations: ['60-18=42', '48-42=6'] Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,88 unequal: No Solution Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,88 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:[42, 32], Operations: ['60-18=42', '80-48=32'] Exploring Operation: 42-32=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 42*32=1344, Resulting Numbers: [1344] 1344,88 unequal: No Solution Exploring Operation: 42+32=74, Resulting Numbers: [74] 74,88 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:[80, 48, 78], Operations: ['60+18=78'] Exploring Operation: 80-78=2, Resulting Numbers: [48, 2] Generated Node #0,1,0: 88:[48, 2] Operation: 80-78=2 Exploring Operation: 48+78=126, Resulting Numbers: [80, 126] Generated Node #0,1,1: 88:[80, 126] Operation: 48+78=126 Exploring Operation: 80-48=32, Resulting Numbers: [78, 32] Generated Node #0,1,2: 88:[78, 32] Operation: 80-48=32 Exploring Operation: 78-48=30, Resulting Numbers: [80, 30] Generated Node #0,1,3: 88:[80, 30] Operation: 78-48=30 Moving to Node #0,1,0 Current State: 88:[48, 2], Operations: ['60+18=78', '80-78=2'] Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[80, 30], Operations: ['60+18=78', '78-48=30'] Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[78, 32], Operations: ['60+18=78', '80-48=32'] Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,88 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[80, 126], Operations: ['60+18=78', '48+78=126'] Exploring Operation: 80*126=10080, Resulting Numbers: [10080] 10080,88 unequal: No Solution Exploring Operation: 80+126=206, Resulting Numbers: [206] 206,88 unequal: No Solution Exploring Operation: 126-80=46, Resulting Numbers: [46] 46,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 74, 25, 91, 23 ]
31
[ "74+25=99", "91-23=68", "99-68=31" ]
Current State: 31:[74, 25, 91, 23], Operations: [] Exploring Operation: 74+25=99, Resulting Numbers: [91, 23, 99] Generated Node #2: [91, 23, 99] from Operation: 74+25=99 Current State: 31:[91, 23, 99], Operations: ['74+25=99'] Exploring Operation: 91-23=68, Resulting Numbers: [99, 68] Generated Node #3: [99, 68] from Operation: 91-23=68 Current State: 31:[99, 68], Operations: ['74+25=99', '91-23=68'] Exploring Operation: 99-68=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[74, 25, 91, 23], Operations: [] Exploring Operation: 91-74=17, Resulting Numbers: [25, 23, 17] Generated Node #0,0: 31:[25, 23, 17] Operation: 91-74=17 Exploring Operation: 74-25=49, Resulting Numbers: [91, 23, 49] Generated Node #0,1: 31:[91, 23, 49] Operation: 74-25=49 Exploring Operation: 74-23=51, Resulting Numbers: [25, 91, 51] Generated Node #0,2: 31:[25, 91, 51] Operation: 74-23=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[25, 23, 17], Operations: ['91-74=17'] Exploring Operation: 25+23=48, Resulting Numbers: [17, 48] Generated Node #0,0,0: 31:[17, 48] Operation: 25+23=48 Exploring Operation: 23+17=40, Resulting Numbers: [25, 40] Generated Node #0,0,1: 31:[25, 40] Operation: 23+17=40 Exploring Operation: 25+17=42, Resulting Numbers: [23, 42] Generated Node #0,0,2: 31:[23, 42] Operation: 25+17=42 Moving to Node #0,0,1 Current State: 31:[25, 40], Operations: ['91-74=17', '23+17=40'] Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,31 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[23, 42], Operations: ['91-74=17', '25+17=42'] Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[17, 48], Operations: ['91-74=17', '25+23=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[74, 25, 91, 23], Operations: [] Exploring Operation: 91-74=17, Resulting Numbers: [25, 23, 17] Generated Node #0,0: 31:[25, 23, 17] Operation: 91-74=17 Moving to Node #0,0 Current State: 31:[25, 23, 17], Operations: ['91-74=17'] Exploring Operation: 25+23=48, Resulting Numbers: [17, 48] Generated Node #0,0,0: 31:[17, 48] Operation: 25+23=48 Moving to Node #0,0,0 Current State: 31:[17, 48], Operations: ['91-74=17', '25+23=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic